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no TFPT parent","id":"python_verification:verification/v1031_quantum_tensor_curvature.py","line_count":335,"path":"verification/v1031_quantum_tensor_curvature.py","sha256":"8a6a7d3768fbd893fb0567f6d11a47d86bc4af1f63d9e7bbfe471a1486f3cedd","type":"python_verification"},{"bytes":10482,"checked_by_registry":false,"claim_ids":["GRAV.FREE.CURVATURE.COVARIANT.01"],"cluster":"frontier","description_excerpt":"Positive covariant local free curvature field with helicities plus/minus two; nonlinear gravity open","id":"python_verification:verification/v1032_covariant_curvature.py","line_count":265,"path":"verification/v1032_covariant_curvature.py","sha256":"2ba2ff1636eb1f712705d1b50b9e1be703597271d40209e6fb7ecf1ad099aefb","type":"python_verification"},{"bytes":22190,"checked_by_registry":false,"claim_ids":["SEAM.MMST.DISORDER.REGISTER.01"],"cluster":"frontier","description_excerpt":"Auxiliary Z4 flux corners and twist weight/parity obstruction; MMST open; full repository required","id":"python_verification:verification/v1033_charged_disorder.py","line_count":607,"path":"verification/v1033_charged_disorder.py","sha256":"5053d08ad5448f33f2c6d141f92ed1e06f5dfb9762f92af2bab9816c0ad161b8","type":"python_verification"},{"bytes":23301,"checked_by_registry":false,"claim_ids":["CHIRAL4D.MIRROR.FACTORIZED.BOUND.01"],"cluster":"frontier","description_excerpt":"Factorized mirror gap and bare-hopping relative-bound obstruction; no interacting gap theorem; full repository required","id":"python_verification:verification/v1034_parent_mirror.py","line_count":568,"path":"verification/v1034_parent_mirror.py","sha256":"a4f7d7712f1d0525ab496e4430a28bda7a51eb3c5ae909c949c4374b9c3107e2","type":"python_verification"},{"bytes":22124,"checked_by_registry":false,"claim_ids":["GRAV.LINEAR.SOURCE.WARD.01"],"cluster":"frontier","description_excerpt":"Physical Fourier Ward propagation for prescribed sources and dynamical-source obstructions; universal quantum coupling open","id":"python_verification:verification/v1035_matter_coupling.py","line_count":509,"path":"verification/v1035_matter_coupling.py","sha256":"ca574ba9d25952b3f004381d67091423c22234a256772902d900e46bceb20e56","type":"python_verification"},{"bytes":8153,"checked_by_registry":false,"claim_ids":["HOR.TRISECT.01"],"cluster":"registry","description_excerpt":"Trisection normal form (the canonical coordinate exists): the SdS horizon cubic is uniformized by ANGLE TRISECTION — r = 2cos θ gives r³−3r = 2cos 3θ exactly, so cubic ⇔ cos 3θ = −3m (ℤ₃ trisection deck = the triality of coker Q = ℤ/N_fam); centered angle ψ: m = cos(ψ)/N_fam and S_tot/S_dS = 4/3 − (2/3)cos(2ψ/3) — ONE cosine whose mean (|μ₄|/N_fam), amplitude and frequency (|ℤ₂|/N_fam) are glue atoms; canonical curva","id":"python_verification:verification/v103_trisection_normal_form.py","line_count":158,"path":"verification/v103_trisection_normal_form.py","sha256":"6244a54be62972f3a417b281a88e303c0ea5af05633b619a8d43b4eebabb6028","type":"python_verification"},{"bytes":6707,"checked_by_registry":false,"claim_ids":["HOR.CLOCK.01"],"cluster":"registry","description_excerpt":"The CLASSICAL Nariai clock is the anchor (third appearance) + the honest (2/3)-test: static pin — φ(ρ) = ρ solves the dS₂ static-patch equation with m² = −2Λ = −|ℤ₂|Λ exactly (the exact SdS family itself pins the modulus mass; Laplace-type linearization = standard GR, Ginsparg–Perry 1983 / Bousso–Hawking 1997, typed external); Ginsparg–Perry tower (l(l+1)−2)Λ with exactly ONE negative mode; THE CLOCK in Hubble units:","id":"python_verification:verification/v104_nariai_clock.py","line_count":130,"path":"verification/v104_nariai_clock.py","sha256":"9835a6b3d50ce00b32dcf650b6a7f0ad02049e4a8c8cd33aead7a694efab32fb","type":"python_verification"},{"bytes":8623,"checked_by_registry":false,"claim_ids":["SYNTH.INVENTORY.01"],"cluster":"registry","description_excerpt":"THE RESIDUAL INVENTORY — one constant, one anchor, one clock to find, and the COMPLETE machine-pinned gap list: (A) 2/3 = |ℤ₂|/N_fam appears EXACTLY in seven independent places across both sectors (Koide branch point, gap base (2/3)⁶, basin attractor; Nariai bound, branch separation, canonical amplitude+frequency, curvature base (2/3)^N_fam) + the anchor triptych (configuration / Nariai roots / clock spectrum); (B) R","id":"python_verification:verification/v105_residual_inventory.py","line_count":162,"path":"verification/v105_residual_inventory.py","sha256":"fc8632b93c576415dd81d8ef98b07df70add35e47e6b14134239cafa26d1a2e9","type":"python_verification"},{"bytes":8007,"checked_by_registry":false,"claim_ids":["ARCH.QUAD.01"],"cluster":"registry","description_excerpt":"External-review validation (v79-style identities + disciplined typing): SEED NORMAL FORM — φ₀ = (|μ₄|/N_fam)·c₃ + Ω_adm·c₃^|μ₄| exactly (linear seam term + topological 4th-order correction; 4/3 = |μ₄|/N_fam, 48 = Ω_adm, exponent = |μ₄|); hypercharge second moment computed from the explicit charge table: Tr X = 0, Tr X² = 120 = 5! (X = 6Y, 16 states); FACTORIAL SPINE: 5! = 120 = |R⁺(E₈)| = Σ E₈ exponents = Tr X², 240 ","id":"python_verification:verification/v106_review_validation.py","line_count":156,"path":"verification/v106_review_validation.py","sha256":"d412eca2d5b8a25e733ae9337094a6a5bd37c2965d0d372622f8e3aa7c001377","type":"python_verification"},{"bytes":6272,"checked_by_registry":false,"claim_ids":["HOR.CLOCK.02"],"cluster":"registry","description_excerpt":"Quantum-clock target made quantitative (the R1 programme, first computation): the classical Ginsparg–Perry clock has per-l equations λ²+λ+(l(l+1)−2) = 0 — l=0 anchor pair {1,−2}, l=1 zero modes {0,−1}, l≥2 complex with Re = −1/2 = −δ (audit); NEW EXACT CROSS-LINK: the classical decay set {0,−1,−2} = −Spec(V) = −N_fam × cusp weights — the classical seam clock decays on the transfer operator's OWN grading (v69/v95); EX","id":"python_verification:verification/v107_quantum_clock_target.py","line_count":123,"path":"verification/v107_quantum_clock_target.py","sha256":"f03cf9fc41058332994c6793d8a127057201380ed881726cea247c34ee3e8a08","type":"python_verification"},{"bytes":5976,"checked_by_registry":false,"claim_ids":["CAR.LADDER.01"],"cluster":"registry","description_excerpt":"PASCAL LADDER THEOREM (red-team Target B sharpened to zero slack): 2^{g−1} = Σ_{k≤K} C(g,k) ⟺ g = 2K+1 for every K (odd-g midpoint identity by binomial symmetry; even-g excluded by the strict straddle around 2^{g−1}); EXACT EQUIVALENCE: carrier selection g=5 ⟺ truncation degree K=2 — the Pascal-selection residual IS the one named hypothesis Quadratic Boundary Locality (v106); neighbour worlds: K=1 → one-family world ","id":"python_verification:verification/v108_pascal_ladder.py","line_count":122,"path":"verification/v108_pascal_ladder.py","sha256":"f3ed20229bb35dd4cd45aac612f69e8e4817babb75d41b9a01d41fa40df7f392","type":"python_verification"},{"bytes":6411,"checked_by_registry":false,"claim_ids":["CAR.PAIR.01"],"cluster":"registry","description_excerpt":"SHEET-PAIRING LEMMA (the first exact rep-theoretic anchor of QBL; ties Target B to the sheet ℤ₂): character-exact weight multisets from the D₅ spinor weights (±½)⁵ alone — NO SCALAR WITHIN A SHEET (zero-weight multiplicity of S⁺⊗S⁺ = 0: the odd slot count g=5 flips the sign parity of −w, a parity theorem of the five-slot code); THE SCALAR LIVES ACROSS THE SHEETS: S⁺⊗S⁻ = Λ⁰⊕Λ²⊕Λ⁴ exactly (256 = 1+45+210) with zero-mo","id":"python_verification:verification/v109_sheet_pairing.py","line_count":150,"path":"verification/v109_sheet_pairing.py","sha256":"0db2e76a9221a40f2fbefef954e453ce833c2160e2e411525541266c5286ca7d","type":"python_verification"},{"bytes":4744,"checked_by_registry":false,"claim_ids":["FLAV.KQ.01"],"cluster":"flavor","description_excerpt":"K=R+QΣ, L=R+Q(I+Σ); det ladder ∏ = 1920 = |W(D₅)|","id":"python_verification:verification/v10_projection_involution.py","line_count":107,"path":"verification/v10_projection_involution.py","sha256":"e56277f6656d884cd0603fb51f21c725266d652624d02540d1b68ac288c703be","type":"python_verification"},{"bytes":6239,"checked_by_registry":false,"claim_ids":["CAR.PAIR.02"],"cluster":"registry","description_excerpt":"CALDERÓN-SHEET SELECTION THEOREM (the v109 follow-up): the certified bilinear data of a Calderón involution ε (ε²=1) on H = S⁺⊕S⁻ are ⟨f, εg⟩; with the v109 singlet counts per sheet block (0,0,1,1) the exact statement is 'a scalar two-point datum exists ⟺ ε is sheet-odd' — sheet-odd certifies exactly 1+1 = 2 = |ℤ₂| invariant kernels (one per orientation), sheet-even certifies NONE; THE TWO KERNELS = THE GLUE AMBIGUIT","id":"python_verification:verification/v110_calderon_sheet.py","line_count":131,"path":"verification/v110_calderon_sheet.py","sha256":"b457047610e44c49767be2cd1bcf2303cb483dc1a69fe37ceadc5fdb10274f8b","type":"python_verification"},{"bytes":8636,"checked_by_registry":false,"claim_ids":["CAR.QTRANS.01"],"cluster":"registry","description_excerpt":"QUADRATIC-TRANSPORT THEOREM (the transport half of the QBL analytic core becomes a theorem): grade seam transport by Clifford degree in the 10 field operators on the 5-slot Fock space (integer Jordan–Wigner model; spanning claims via mod-p full-rank certificates, valid over ℚ) — PARITY: all 10 linear words are sheet-odd, all 45 quadratic words sheet-even (code-preserving transport has even Clifford degree, the same ℤ","id":"python_verification:verification/v111_quadratic_transport.py","line_count":201,"path":"verification/v111_quadratic_transport.py","sha256":"c01b4b9a4d178eb5b72d5001540e289150e60c7ae989134b02864f54acd14b3b","type":"python_verification"},{"bytes":7350,"checked_by_registry":false,"claim_ids":["CAR.COUNT.01"],"cluster":"registry","description_excerpt":"SELF-COUNTING CHANNEL (the Pascal closure is an IDENTITY of the certified channel, not an extra requirement): CANONICAL BIJECTION — for odd g negation w ↦ −w maps S⁺ bijectively into the opposite sheet, so the Cartan-neutral kernels of the certified channel are exactly the pairs (w,−w), ONE PER CODE STATE: #neutral kernels = dim S⁺ = 2^{g−1} exactly (4, 16, 64 for g = 3,5,7) — the channel counts the code; PASCAL PART","id":"python_verification:verification/v112_selfcounting_channel.py","line_count":152,"path":"verification/v112_selfcounting_channel.py","sha256":"c9517d903e2b89868311da1dd8880a5a9d705ff015f4d6cba8ac199c5166860f","type":"python_verification"},{"bytes":7795,"checked_by_registry":false,"claim_ids":["CAR.QFREE.01"],"cluster":"registry","description_excerpt":"ONE KERNEL IS THE WHOLE NET (the QBL input merges with the R2/holomorphy premise): MAJORANA BOOKKEEPING — c(D₅)₁ = 45/9 = 5 = g_car, c(A₃)₁ = 15/5 = 3 = N_fam; the carrier net (D₅)₁×(A₃)₁ = SO(10)₁×SO(6)₁ = 10+6 = 16 FREE MAJORANA FERMIONS, c = 16/2 = 8 — the whole extension tower carrier(μ=16) → SO(16)₁(μ=4) → E8₁(μ=1) carries the SAME 16 fermions, only the certified glue grows (index 2×2 = 4 = |μ₄|); WICK/PFAFFIAN ","id":"python_verification:verification/v113_quasifree_kernel.py","line_count":176,"path":"verification/v113_quasifree_kernel.py","sha256":"a033fe9c292d22b5bbc343aa0d8e352df14a0918e4124fd7596bf7f81e01ff51","type":"python_verification"},{"bytes":9173,"checked_by_registry":false,"claim_ids":["GATE.UWALL.06"],"cluster":"registry","description_excerpt":"TORSION NORMAL FORM + THE δ = 1/2 THEOREM (executes the v41 'genericity future work'; δ = 1/2 stops being an observation): FLATNESS = μ₄ TORSION [I, symbolic generic M] — ∏ₖ Uᵏ M U⁻ᵏ = (MU)⁴ exactly, so the ℤ₄-family flatness of the (U_wall) bundle IS the torsion statement 'T = MU is a fourth root of unity' (the μ₄ atom = the ORDER of the twisted cusp generator); δ THEOREM [I, both directions]: on the involutive bran","id":"python_verification:verification/v114_torsion_delta.py","line_count":191,"path":"verification/v114_torsion_delta.py","sha256":"8e1938e0a1a05bd90d877efc4d098d7d6b955f70e5a6df5002d69e209228db3c","type":"python_verification"},{"bytes":10962,"checked_by_registry":false,"claim_ids":["GATE.UWALL.07"],"cluster":"registry","description_excerpt":"THE ANCHOR PINS THE RESIDUE (exact normal form for the U_wall flat-bundle residue; answers the v114 branch question): μ₄-AVERAGE LEMMA [I] — Σₖ Uᵏ X U⁻ᵏ = 4 diag(X): μ₄ conjugation-averaging IS the diagonal projection ⇒ exponents at infinity = 4 diag(A₀) ⇒ anchor splitting 𝒪(−2)⊕𝒪(−1)² ⟺ diag A₀ = (2,1,1)/4 = ANCHOR/|μ₄| (v33's diagonal was forced, not chosen); THE (8,0,5)/144 LEMMA [I]: anchor diagonal + cusp spectr","id":"python_verification:verification/v115_anchor_residue.py","line_count":258,"path":"verification/v115_anchor_residue.py","sha256":"26d84469128747ef11be7513316e6c61f03517632d3a82a197413fe93af814a6","type":"python_verification"},{"bytes":8060,"checked_by_registry":false,"claim_ids":["GATE.UWALL.08"],"cluster":"registry","description_excerpt":"RESONANCE THEOREM (the v115 [N] findings promoted to [I] by a LINEAR computation — the anticipated Gröbner step was unnecessary): TWISTED-AVERAGE LEMMA [I] — at infinity the equivariant system reads dY/dw = −(1/w)(B₀ + B₁w + …)Y with B_m = Σₖ i^{km} Uᵏ A₀ U⁻ᵏ; the twisted μ₄ averages collapse to B₀ = 4 diag(A₀) and B₁ = 4a₁₂E₁₂ + 4ā₁₃E₃₁ (only the eigenvalue-ratio −i cells survive); RESONANCE THEOREM [I]: the anchor ","id":"python_verification:verification/v116_resonance_uniqueness.py","line_count":170,"path":"verification/v116_resonance_uniqueness.py","sha256":"e9cbeb665cf8c1a2bed3f34281be06aee4c661d784e7f13a5bd8e9be37f577ca","type":"python_verification"},{"bytes":8778,"checked_by_registry":false,"claim_ids":["GATE.UWALL.09"],"cluster":"registry","description_excerpt":"THE MONODROMY IS THE WEYL GROUP OF A₃ (the U_wall holonomy is an EXACT 24-element representation; the harmonic diagonal becomes a theorem): THE EXACT MONODROMY [I] — M̃₀ = [[0, −(1+i)/2, (1−i)/2], [−(1+i)/2, −i/2, −1/2], [(1−i)/2, −1/2, i/2]] (entries in ½ℤ[i]) is unitary, det 1, tr 0, char poly λ³−1 (cusp class EXACT), M̃₀³ = 1, diag M̃₀ = (0, −i/2, +i/2) ⇒ d₁ = 0 AND δ = ½ are exact matrix entries — the v20 hand va","id":"python_verification:verification/v117_monodromy_weyl_a3.py","line_count":206,"path":"verification/v117_monodromy_weyl_a3.py","sha256":"55eca6a64144f6e49789f3f1bbe84e256764e7ce92b207044be693f8684d5df5","type":"python_verification"},{"bytes":6633,"checked_by_registry":false,"claim_ids":["FLAV.H2.02"],"cluster":"registry","description_excerpt":"THE HEXAGON IS THE SIGN-TWISTED FAMILY SPECTRUM (first exact piece of the H2 dictionary; the v20 lepton coefficients are resolvent determinants of the exact W(A₃) monodromy): SIGN-TWIST LEMMA [I] — −M̃₀ has order 6 ((−M̃₀)³ = −1) and spec(M̃₀) ∪ spec(−M̃₀) = μ₆: the 6-site hypercharge hexagon spectrum IS the family monodromy spectrum plus its sheet twist (ℤ₆ = ℤ₂×ℤ₃ = (−1)×⟨M̃₀⟩); the v20 denominators 5/4 − cos(rπ/3)","id":"python_verification:verification/v118_hexagon_family_dictionary.py","line_count":142,"path":"verification/v118_hexagon_family_dictionary.py","sha256":"48b7a05bcd877afe13f0a92cce4087e86c23172823e605cda21c6a8ceafa6e37","type":"python_verification"},{"bytes":7219,"checked_by_registry":false,"claim_ids":["ARCH.TRIAD.01"],"cluster":"registry","description_excerpt":"SECOND EXTERNAL-REVIEW VALIDATION (triad + 121 audit + micro-identities, all exact): ANCHOR RATIO TRIAD [I] — the three elementary symmetric values of the anchor normalised by the family count, (e₃,e₁,e₂)/p₀ = (2/3, 4/3, 5/3) = (Koide branch/sheet ratio, seed gain |μ₄|/N_fam, carrier branch); the canonical flow's critical points are EXACTLY (2,5) = (e₃,e₂) with inflection 7/2 = (e₃+e₂)/2 — the recurring fractions are","id":"python_verification:verification/v119_review_validation_2.py","line_count":150,"path":"verification/v119_review_validation_2.py","sha256":"e91c80ccc4a0e85df9b837ccbb733c87cda3f72bb51f7135acf897ce5a45603f","type":"python_verification"},{"bytes":2353,"checked_by_registry":false,"claim_ids":["FLAV.KQ.01"],"cluster":"flavor","description_excerpt":"K, Q are the unique nonneg-integer matrices (enumeration)","id":"python_verification:verification/v11_unique_KQ.py","line_count":60,"path":"verification/v11_unique_KQ.py","sha256":"c67fd8e598f758277ba17fdc600560cf8de76a335f0ed773ac154c83d90c8741","type":"python_verification"},{"bytes":5664,"checked_by_registry":false,"claim_ids":["FLAV.H2.03"],"cluster":"registry","description_excerpt":"THE ADDRESS TABLE (the open H2 item structured; exact arithmetic on FROZEN v18/v20 integers — the red-team firewall): THE LEPTON WORDS ARE THE COMPILER ATOMS [I] — (L_e, L_μ, L_τ) = (8, 5, 3) = (rank E8, g_car, N_fam) = (p₀+e₂, e₂, p₀), in mass order (longest word = lightest lepton); ADDRESSES = EUCLIDEAN DIVISION BY THE HEXAGON [I]: (r,w) = L divmod p₂ with p₂ = 6 = |R⁺(A₃)| itself an atom: e → (2,1), μ → (5,0), τ →","id":"python_verification:verification/v120_address_table.py","line_count":117,"path":"verification/v120_address_table.py","sha256":"223760338b44e90c1a277011725730c9d3d6b970d277490615512d4da455da0e","type":"python_verification"},{"bytes":5947,"checked_by_registry":false,"claim_ids":["FLAV.H2.04"],"cluster":"registry","description_excerpt":"THE ADDRESS TABLE IS PINNED (the per-fermion assignment closes at the information level; exact census theorem): THE WORD TABLE IS THE RESIDUE OPERATOR [I] — the established identity L = R + 2U (v95) says the word-length table IS L[sector][generation] with rows (up; down; lepton) = ((7,3,0); (7,5,2); (8,5,3)) = the v18/v20 words verbatim; addresses = R's entries + one hexagon turn for generation 1, and R's first colum","id":"python_verification:verification/v121_address_pinning.py","line_count":124,"path":"verification/v121_address_pinning.py","sha256":"81daa2644115b24ae7c43878e358f617e39dae5726c20eae49a296d96550c0a8","type":"python_verification"},{"bytes":5431,"checked_by_registry":false,"claim_ids":["FLAV.H2.05"],"cluster":"registry","description_excerpt":"THE MARGINS ARE THEOREMS (the established frozen selectors pin R uniquely — the v121 atom margins lose their input status): three selectors, all frozen BEFORE the address question was posed — (S1) the D₄ annihilator n = (5,−9,6) with nᵀR = (8,0,0) (v94: kills the (c₂,c₃) plane, n·a = 8), (S2) det R = 8 = rank E8 (v71 quartet (3,4,8,20)), (S3) det K = 4 = |μ₄| with K = R + QΣ (the diamond), plus the definitional hexag","id":"python_verification:verification/v122_margin_theorem.py","line_count":119,"path":"verification/v122_margin_theorem.py","sha256":"d35cbd2ed636412594800fb3d1bcba6320f78df11dc856cc1bc3dc076c008bdb","type":"python_verification"},{"bytes":6964,"checked_by_registry":false,"claim_ids":["SYNTH.INVENTORY.02"],"cluster":"registry","description_excerpt":"RESIDUAL INVENTORY UPDATED (post v110–v122; the v105 gap list re-pinned with sharper contents, same cardinality): thirteen new ledger rows machine-checked (CAR.PAIR.02, CAR.QTRANS.01, CAR.COUNT.01, CAR.QFREE.01, GATE.UWALL.06–09, FLAV.H2.02–05, ARCH.TRIAD.01); R2 CARRIES THREE LOADS — the single index-4 boundary-net statement closes, when proven, the metric gate (GATE.METRIC.06), the carrier choice (CAR.QFREE.01 upgr","id":"python_verification:verification/v123_inventory_update.py","line_count":139,"path":"verification/v123_inventory_update.py","sha256":"91d91b1ed21f04fdc8d2ec20bd2090ae7ac86f7435018aeb30dd2f7d6ed170a1","type":"python_verification"},{"bytes":5489,"checked_by_registry":false,"claim_ids":["HOR.CLOCK.03"],"cluster":"registry","description_excerpt":"THE RESUMMED CLOCK (R1's bend acquires a closed form — the transfer spectrum IS the geometric resummation of a weight-linear clock): SPECTRUM READING [I] — the frozen transfer eigenvalues {1, (2/3)⁶, (1/3)⁶} are EXACTLY λₙ = (1 − n/N_fam)^{p₂} for n = 0,1,2 (p₂ = 6 = the hexagon size); CLOSED-FORM CLOCK [I]: rate(n) = −6 ln(1 − n/3) reproduces {0, Δ, 6 ln 3} and the v107 bend log₃∕₂3 becomes a one-line consequence; T","id":"python_verification:verification/v124_resummed_clock.py","line_count":116,"path":"verification/v124_resummed_clock.py","sha256":"6ad0c465cbdebe8ca4032e18c988966f52ac60b0ea85b52dbcac52083d36ce58","type":"python_verification"},{"bytes":5487,"checked_by_registry":false,"claim_ids":["GATE.METRIC.08"],"cluster":"registry","description_excerpt":"THE GLUE Q-SYSTEM (the index-4 μ₄ extension exists as an explicit Longo Q-system; R2 sharpens from 'find' to 'match'): Q-SYSTEM AXIOMS [I] on A = ℂ[ℤ₄] (glue group algebra): associativity, unit law, FROBENIUS (m⊗1)(1⊗m*) = m*m = (1⊗m)(m*⊗1), SPECIALNESS mm* = |ℤ₄|·id — all exact ⇒ a special C* Frobenius algebra = Longo Q-system with dim θ = 4: JONES INDEX [B:A] = 4 = |μ₄| (the v89 Carrier Index Lemma value); KLM μ_ca","id":"python_verification:verification/v125_glue_qsystem.py","line_count":121,"path":"verification/v125_glue_qsystem.py","sha256":"7231c07cecd3e39c402806bca101c4e5483126bc4ae48974ea72b1b96ad033d7","type":"python_verification"},{"bytes":5170,"checked_by_registry":false,"claim_ids":["HOR.CLOCK.04"],"cluster":"registry","description_excerpt":"THE CLOCK AND THE WALL SHARE A SPECTRUM (the v124 resummed-clock weights ARE the Mehta–Seshadri parabolic weights; R1's first checkpoint passes classically): THE WEIGHTS ARE THE PARABOLIC WEIGHTS [I] — the arguments n/N_fam = {0, 1/3, 2/3} of the resummed logarithm are EXACTLY spec A₀* (the exact U_wall residue, v115); spectral bridge λₙ = (1 − αₙ)^{p₂} over α ∈ spec A₀* reproduces the frozen transfer spectrum {1, (2","id":"python_verification:verification/v126_clock_wall_bridge.py","line_count":107,"path":"verification/v126_clock_wall_bridge.py","sha256":"ca81230ce9ba5d72404c5198345bc328c5c6c6e18b68f94b03a2571d8f81beb2","type":"python_verification"},{"bytes":5624,"checked_by_registry":false,"claim_ids":["HOR.CLOCK.05"],"cluster":"registry","description_excerpt":"THE CLOCK IS A LOG-DETERMINANT (the geometric tail is the standard ring/RPA resummation; the 'O(1) resummation' demanded by v107 is now TYPED): LOG-DET IDENTITY [I] — for a rank-1 insertion P (tr Pᵏ = 1): −ln det(1 − αP) = −ln(1 − α) = Σₖ αᵏ/k, so the resummed clock is EXACTLY rate = −p₂ Tr ln(1 − αP): p₂ = 6 identical one-loop ring towers, ONE PER HEXAGON SITE (= positive root of A₃), coupling α = the Mehta–Seshadri","id":"python_verification:verification/v127_ring_resummation.py","line_count":116,"path":"verification/v127_ring_resummation.py","sha256":"5de0295475ccf05e27817ac7ec3fd93bfec01acdea0327794ab45f75d78b0f60","type":"python_verification"},{"bytes":6479,"checked_by_registry":false,"claim_ids":["E8.GRADE.01"],"cluster":"registry","description_excerpt":"THE GRADED HULL + THE ZERO-MODE MULTIPLICITY (both named computations R1/R2 gain their structural anchors): R2 HALF — EXPLICIT COSET CONSTRUCTION [I]: the 240 E8 roots built as explicit norm-2 vectors in D₅⊕A₃+glue coordinates decompose over the glue ℤ₄ as 240 = 52 + 64 + 60 + 64 (C₀ = carrier 40+12, C₁ = (16,4̄), C₂ = (10,6), C₃ = (16̄,4)) — the v89 branching as vectors; THE GRADING IS EXACT [I]: for ALL 6720 root p","id":"python_verification:verification/v128_graded_hull.py","line_count":160,"path":"verification/v128_graded_hull.py","sha256":"27de4db51eaecb32799f034d6f2dc0bdd4e9a9e59139cad42846200095a302dc","type":"python_verification"},{"bytes":5213,"checked_by_registry":false,"claim_ids":["HOR.CLOCK.06"],"cluster":"registry","description_excerpt":"THE CLOCK IS AN ENTROPY POWER LAW (what the resummation argument 1 − n/N_fam IS physically): THE THREE ENTROPY LEVELS [I] — the established Nariai bookkeeping (v101) has S/S_dS ∈ {1, 2/3, 1/3} (pure dS; two-horizon total; single horizon — deficit S_dS/3 per step): EXACTLY the complementary cusp weights; THE CLOCK IS AN ENTROPY POWER LAW [I]: λₙ = (Sₙ/S_dS)^{p₂} = the frozen transfer spectrum, rate(n) = p₂ ln(S_dS/Sₙ)","id":"python_verification:verification/v129_entropy_power_law.py","line_count":107,"path":"verification/v129_entropy_power_law.py","sha256":"9f41ea31db064c8a63879bced40e588161f2961a8beb2b8690914130d67b6507","type":"python_verification"},{"bytes":2792,"checked_by_registry":false,"claim_ids":["FLAV.KQ.01"],"cluster":"flavor","description_excerpt":"sector / generation polynomials of K; anchor det ladder","id":"python_verification:verification/v12_mass_generation_polynomials.py","line_count":64,"path":"verification/v12_mass_generation_polynomials.py","sha256":"3921e75e5e6e30cded7cb603354748265f2e873fed9d74260e1bd7283673179c","type":"python_verification"},{"bytes":4885,"checked_by_registry":false,"claim_ids":["HOR.CLOCK.07"],"cluster":"registry","description_excerpt":"THE BORN SQUARE (the amplitude weight is h = N_fam = half the zero-mode count; the clock exponent p₂ = 2h is its Born square — the v128 multiplicity and the v129 weight are ONE object): EXPONENT BOOKKEEPING [I] — each zero mode trades a Gaussian integral for a moduli factor ∝ S^{1/2} (standard collective coordinates); with n_zero = 6 the transition AMPLITUDE scales as A ∼ (S/S_dS)^{n_zero/2} = (S/S_dS)³ and the PROBA","id":"python_verification:verification/v130_born_square.py","line_count":103,"path":"verification/v130_born_square.py","sha256":"3efb6b755e57a0e338dd03ddfceafea81a0663668ce7e3d3f7c236c9a4822d79","type":"python_verification"},{"bytes":4779,"checked_by_registry":false,"claim_ids":["HOR.CLOCK.08"],"cluster":"registry","description_excerpt":"THE MEASURE IS THE AREA (the per-mode S^{1/2} of the Born square is the zero-mode NORM, computed exactly; the R1 residue narrows to one determinant-ratio cancellation): ZERO-MODE NORM = AREA [I] — on S²(r) the L² norm² of each of the three normalised l=1 harmonics is EXACTLY r² = A/(4π) (all three integrated exactly): the norm of every zero mode IS the horizon area, hence the entropy; JACOBIAN BOOKKEEPING [I]: the co","id":"python_verification:verification/v131_measure_is_area.py","line_count":99,"path":"verification/v131_measure_is_area.py","sha256":"6cc5cad3be8af18a7c49f76da4d89dbf44da4be50b727dfffa3cdcce2d1f6e33","type":"python_verification"},{"bytes":5579,"checked_by_registry":false,"claim_ids":["HOR.CLOCK.09"],"cluster":"registry","description_excerpt":"THE DET-RATIO ANOMALY IS THE KOIDE CONSTANT (the v131 'last step' acquires its first exact invariant): SPECTRAL SETUP — the Ginsparg–Perry sphere operator on unit S² is L = −Δ − 2 (the −2 = −|ℤ₂| = the v104 modulus mass), eigenvalues (l+2)(l−1), kernel = 3 zero modes (l=1); THE HEAT COEFFICIENT IS MADE OF ATOMS [I]: a₁ = R/6 − E = 1/3 + 2 = 1/N_fam + |ℤ₂| = 7/3; THE ANOMALY IS THE KOIDE CONSTANT [I]: ζ(0)|det′ = a₁ −","id":"python_verification:verification/v132_detratio_anomaly.py","line_count":125,"path":"verification/v132_detratio_anomaly.py","sha256":"959ffe6dadf34e8d59a51d59eba60d10f6771d730cf6ca2d84486bfa663058e0","type":"python_verification"},{"bytes":6090,"checked_by_registry":false,"claim_ids":["HOR.CLOCK.10"],"cluster":"registry","description_excerpt":"THE ZETA BUDGET, BOTH ROUTES COMPUTED EXACTLY (the reduced seam route carries pure anchor-ratio anomalies; the naive 4d route does not — the budget computation structurally selects the reduced seam reading): Euclidean Nariai = S²×S², so the temporal dS₂ sector continues to the SAME unit sphere; THE REDUCED ROUTE [I]: each 2d sector carries the v132 operator with ζ(0)|det′ = −2/3; two sectors give budget = −4/3 = −e₁/","id":"python_verification:verification/v133_zeta_budget.py","line_count":131,"path":"verification/v133_zeta_budget.py","sha256":"ae7c481fa74df7510e91858a3c1288ca21fc62cade93c353205778a8795a6645","type":"python_verification"},{"bytes":5446,"checked_by_registry":false,"claim_ids":["FLAV.DUAL.01"],"cluster":"registry","description_excerpt":"THE DUAL ANCHOR LEMMA (the inverse flavor response of the anchor IS the Nariai root — the third purely algebraic leg of the flavor↔horizon bridge): d := aᵀR⁻¹ = aᵀL⁻¹ = (−1/2, −1/2, 1) with d·1 = 0, d·a = 1 and d = (3/2)(a − (4/3)1) — the normalised TRACELESS anchor — and (1,1,−2) = −2d: the inverse flavor response stores exactly the Nariai double-root structure (v101) up to sign and scale, so the horizon is not glue","id":"python_verification:verification/v134_dual_anchor.py","line_count":116,"path":"verification/v134_dual_anchor.py","sha256":"702b4a2a4394c89bc3af3a021eb599ba7b50322aa93b4522d1193cda59959e99","type":"python_verification"},{"bytes":6027,"checked_by_registry":false,"claim_ids":["FLAV.SURF.01"],"cluster":"registry","description_excerpt":"THE DETERMINANT SURFACE (the sheet diamond is a 2d surface with iso-volume WALLS at the discrete atoms): det M(s,t) = 3s(t+1)(t+2) + t² + 5t + 8 on the established diamond M(s,t) = R + Q·diag(s,t,t) (v94/v95) — two iso-volume walls INDEPENDENT of s: t = −2 ⇒ det = 2 = |Z₂| (the Z₂ wall) and t = −1 ⇒ det = 4 = |μ₄| (the μ₄ wall; K = M(1,−1) lies on it, so det K = 4 is a LAYER, not an isolated hit); the winding line t ","id":"python_verification:verification/v135_det_surface.py","line_count":128,"path":"verification/v135_det_surface.py","sha256":"1e513c8f35422948b174a337871c146d734af42d64081e2f0908afe729ced486","type":"python_verification"},{"bytes":8510,"checked_by_registry":false,"claim_ids":["GATE.UWALL.10"],"cluster":"registry","description_excerpt":"THE DUAL-NORMAL SELECTOR ((d,n) pins R COLUMNWISE; the R4′ residue is bounded): COLUMN NORMAL FORM [I]: d·c_j = a_j and n·c_j = 8δ₁ⱼ for the columns of R; the common kernel of (d,n) is the primitive vector (6,8,7) (audit: p₂, rank E₈, scalaron-7), so within the address box {0..5}³ each line contains at most one lattice point — brute-force census (216 per column): c₁ = (1,1,2) = a, c₂ = (3,5,5), c₃ = (0,2,3) are each ","id":"python_verification:verification/v136_dual_normal_selector.py","line_count":187,"path":"verification/v136_dual_normal_selector.py","sha256":"cbd564df37a3002b8eafda9ce99aa62af054b58817c8f2e8760904890fc66862","type":"python_verification"},{"bytes":5498,"checked_by_registry":false,"claim_ids":["FLAV.QGEO.04"],"cluster":"registry","description_excerpt":"THE Q₊ GRADING IS COHOMOLOGY (the R5/GATE.QGEO dictionary at the spectrum level): BASIS + CHARACTERS [I]: b₁(ℙ¹∖μ₄) = 3 = N_fam with holomorphic basis ω_k = z^(k−1)dz/(z⁴−1), k = 1,2,3 (regular at infinity; the trivial character is absent); the μ₄ character of ω_k is i^k, so H¹ = χ₁⊕χ₂⊕χ₃ with each nontrivial character exactly once, and the residue vector over the punctures is the character vector ζ^k/4 exactly; THE ","id":"python_verification:verification/v137_qplus_cohomology.py","line_count":116,"path":"verification/v137_qplus_cohomology.py","sha256":"f5c697e9cba9cb14d788a3cbe3844d4539928413be30f9326513c72844f8a80a","type":"python_verification"},{"bytes":5602,"checked_by_registry":false,"claim_ids":["HOR.CLOCK.11"],"cluster":"registry","description_excerpt":"THE VOLKOV–WIPF FIREWALL (R1 typed closure; external values verified against arXiv:2506.02142 Table 4.1, which agrees with Volkov–Wipf hep-th/0003081): EXTERNAL DATUM [I, typed external]: α_bulk = 22/45, α_edge = −8/3, α_PI = −98/45 for d = 3 (S²×S², 4d); THE EDGE MATCH [I] — the structural finding: α_edge = −8/3 = 2 × (−4/3), the external edge factor consists of TWO IDENTICAL COPIES (one per horizon) and the per-cop","id":"python_verification:verification/v138_vw_firewall.py","line_count":113,"path":"verification/v138_vw_firewall.py","sha256":"fecb8ef949ce6cf6490d9cd863acf801e52a2b818a6c23f119eb8c8ac4562e5d","type":"python_verification"},{"bytes":5107,"checked_by_registry":false,"claim_ids":["GATE.UWALL.11"],"cluster":"registry","description_excerpt":"THE SELECTOR TRIANGLE (anchor + A₀* zero mode + three atoms ⇒ R; the R4′ residue shrinks to three pairings): d IS ANCHOR DATA [I]: d = (3/2)a − 2·1 exactly — the dual anchor (v134) has a closed form that never mentions R, so the first selector of the pair (d,n) is DERIVED, not residual; THE FRAME [I]: (1, a, σ) is a basis of ℤ³ with det(1|a|σ) = 11 = ‖Pl(K)‖₁ — the quark constant as the frame volume (σ = the A₀* zero","id":"python_verification:verification/v139_selector_triangle.py","line_count":117,"path":"verification/v139_selector_triangle.py","sha256":"858853ca4424f20262c2272d9f71fa1c3fb05837897701500bbdce26e2ba27f9","type":"python_verification"},{"bytes":2751,"checked_by_registry":false,"claim_ids":["EM.BUDGET.01","FLAV.QGEO.01","GATE.QGEO.01"],"cluster":"frontier","description_excerpt":"gate closures: M = 41 = 10 b₁; Q₊ = A₃ exponents","id":"python_verification:verification/v13_open_gates.py","line_count":59,"path":"verification/v13_open_gates.py","sha256":"892b757498342f24d41683c33a65eba3e1e133d41143b72b66ddb518737bd131","type":"python_verification"},{"bytes":5498,"checked_by_registry":false,"claim_ids":["FLAV.QGEO.05"],"cluster":"registry","description_excerpt":"THE CANONICAL MAP EXISTS AND IS RIGID (the GATE.QGEO naturality residue collapses to ONE ℤ₃ choice): THREE μ₄ ACTIONS, ONE MATCH [I]: the plain deck U = diag(1,i,−i) has characters (0,1,3) — an invariant line, missing 2 — and CANNOT match H¹; the sheet-twisted deck −U (characters (2,3,1)) and the cusp exponential i^{Q₊} (characters (1,2,3)) both carry the character SET {1,2,3} = the H¹ set (v137) — only the SIGN-TWIS","id":"python_verification:verification/v140_canonical_map.py","line_count":113,"path":"verification/v140_canonical_map.py","sha256":"514549015070d48fa329a5b3e37958b6ee69e18b874b04e4a880561f4e60f7cd","type":"python_verification"},{"bytes":7885,"checked_by_registry":false,"claim_ids":["FLAV.QGEO.06"],"cluster":"registry","description_excerpt":"deck selection: the v140 ℤ₃ choice DERIVED — the integer deck G=T_A·Σ (v97/v98) pairs the Q₊=1 line with the self-conjugate character 2, excluding i^{Q₊} and selecting the sheet-twisted −U assignment (2,3,1); only the established sheet ℤ₂ remains; Euler grading = Q₊∘ρ","id":"python_verification:verification/v141_deck_selection.py","line_count":153,"path":"verification/v141_deck_selection.py","sha256":"8c29d8bdc2b0e8c6953343ab41b9d3311cb35145318cda013df7b0cacf0721a0","type":"python_verification"},{"bytes":7305,"checked_by_registry":false,"claim_ids":["GATE.UWALL.12"],"cluster":"registry","description_excerpt":"frame integrality (R4′): integer covectors in the (1,a,σ) dual frame = index-11 sublattice (x−3y+z ≡ 0 mod 11); with (2,8) established the σ-pairing is forced ≡ 0 mod 11; primitivity forces even line parameter — three pairings reduce to two (since v145: the values are atom identities — residue = one lift map)","id":"python_verification:verification/v142_frame_integrality.py","line_count":155,"path":"verification/v142_frame_integrality.py","sha256":"2e837d439484778fdf4ec32493e2b7b838a3d721861375ed679408f279444ea8","type":"python_verification"},{"bytes":7043,"checked_by_registry":false,"claim_ids":["GATE.METRIC.09"],"cluster":"registry","description_excerpt":"graded Frobenius (R2): the ℤ₄-graded hull carries exact coset duality (−C₁=C₃), the glue average is the carrier projector (index 4), each sector is one Weyl orbit (simple current) — the ℂ[ℤ₄] Q-system realised at the finite Lie level; residual = the conformal-net step","id":"python_verification:verification/v143_graded_frobenius.py","line_count":139,"path":"verification/v143_graded_frobenius.py","sha256":"5fa32b7534810c8008f334309d490d646b17c8683a94b8dc4b9b58c9123ffa05","type":"python_verification"},{"bytes":6391,"checked_by_registry":false,"claim_ids":["HOR.CLOCK.12"],"cluster":"registry","description_excerpt":"det-ratio cancellation (R1): r_b·r_c = 1−Δ²/3 exact (e₂-rigidity) ⇒ det′-ratio = (1−Δ²/3)^{4/3}: no first-order term in the horizon split; deficit coefficient 32/27 = |μ₄|(2/3)³; the finite-weight absorption stays [P] with its obstruction stated sharply (the bend since shown det′-clean, v147)","id":"python_verification:verification/v144_detratio_family.py","line_count":130,"path":"verification/v144_detratio_family.py","sha256":"9ef10ed07f1305fe87da50e221954f7ba9645cd0a259b3c2f020cb51feb02052","type":"python_verification"},{"bytes":4979,"checked_by_registry":false,"claim_ids":["GATE.UWALL.13"],"cluster":"registry","description_excerpt":"R4′ values = ATOM IDENTITIES: given the lift n = w₀(σ)+|μ₄|e₃ (w₀ = A₃ exponent duality), n·1 = |μ₄|−|ℤ₂| = 2, n·a = |μ₄|·a₃ = 8 via the new closure |μ₄|+g_car = N_fam² (4+5=9, σ⊥w₀(a)), n·σ = ‖σ‖²−N²+|μ₄|g = 121 — residue = derive the ONE map","id":"python_verification:verification/v145_pairing_atoms.py","line_count":108,"path":"verification/v145_pairing_atoms.py","sha256":"9ebf6510ab0289bf2fe78162cbf27ca5789ba3d8f48edb0d8e7158ee50980364","type":"python_verification"},{"bytes":5649,"checked_by_registry":false,"claim_ids":["FLAV.QGEO.07"],"cluster":"registry","description_excerpt":"Möbius-D4 realisation (R5 floor): ⟨z↦iz, z↦1/z⟩ = D4 acts on H¹(P¹∖μ₄) EXACTLY as the integer model ⟨G,T_A,Σ⟩ — ι swaps χ₁↔χ₃ with +1 on χ₂ (det −1) = T_A; δι = Σ; parities and reflection classes match — the premise reduces to the module identification itself","id":"python_verification:verification/v146_moebius_d4.py","line_count":121,"path":"verification/v146_moebius_d4.py","sha256":"a8f22458c32d9912d2d89fd823bcdee181607f8f4349e144f24dc095b3622f1a","type":"python_verification"},{"bytes":6017,"checked_by_registry":false,"claim_ids":["HOR.CLOCK.13"],"cluster":"registry","description_excerpt":"clock = Gaussian zero-mode integral (R1): variance ratio (1−α) (norm=area, v131) ⇒ Born² Γ-ratio (1−α)^{p₂}, rate = −p₂ln(1−α) = the v127 ring sum term by term; the BEND log_{3/2}3 lives between the two Nariai levels of ONE geometry ⇒ det′-clean; obstruction localised to the α=0 reference","id":"python_verification:verification/v147_clock_gaussian.py","line_count":122,"path":"verification/v147_clock_gaussian.py","sha256":"b0626988e151de097182f5f1938d13c16d3831d303d2a497246719e297ada4f3","type":"python_verification"},{"bytes":5283,"checked_by_registry":false,"claim_ids":["GATE.METRIC.10"],"cluster":"registry","description_excerpt":"NS/R census (R2 scoped, corrected): the untwisted (NS) module carries only even classes {0,2}×{0,2} — the odd glue sectors are RAMOND modules; the R zero-mode module (256) splits 128+128 into the odd sectors of the two Lagrangian glues: choosing the glue = choosing the R-projection; 248 = 120(NS)+128(R)","id":"python_verification:verification/v148_fock_census.py","line_count":108,"path":"verification/v148_fock_census.py","sha256":"206b54a93311e89e55f39f1478c58ef0bf4d277b3d6ba249afb93382586b57a4","type":"python_verification"},{"bytes":4711,"checked_by_registry":false,"claim_ids":["GATE.UWALL.14"],"cluster":"registry","description_excerpt":"both dual normals are ANCHOR DATA (R4′): in the cusp frame n pairs to (6,3,5) = (p₂,p₀,e₂)(a) — one anchor invariant per Q₊ line (d = (3/2)a−2·1 in the generation frame); equivalent to (2,8,121) and the w₀-lift; residue = ONE assignment (which invariant on which line)","id":"python_verification:verification/v149_cusp_normal.py","line_count":103,"path":"verification/v149_cusp_normal.py","sha256":"8d9b60844576b7477e44ec4e87639c4bfc45d387551f186d2e63e0fedbd8b7ab","type":"python_verification"},{"bytes":2890,"checked_by_registry":false,"claim_ids":["CAR.UNIQ.01"],"cluster":"core","description_excerpt":"g_car=5 unique; split (3,2); Tr Y = Tr Y³ = 0","id":"python_verification:verification/v14_carrier_uniqueness.py","line_count":65,"path":"verification/v14_carrier_uniqueness.py","sha256":"68bcdb41dc122a548cb1d3e304c25b2cf4e3a82ae3c9eb47e3d99d772ef1b1e4","type":"python_verification"},{"bytes":6393,"checked_by_registry":false,"claim_ids":["SEAM.EHMODEL.01"],"cluster":"registry","description_excerpt":"EH form from replica (R3, model level): conical deficit exact + t-independent (Cheeger image sum (N²−1)/(12N)); gap ⇒ Δlogdet′ = 2C(γ)ln m FINITE, cutoff-independent; linearisation = (ln m/12π)·∫√gR — the EH form; target equation k = c₃/2 ⟺ ln m = 3/4 = q(A₃); Calderón transfer + normalisation stay open (Calderón transfer since answered: the DtN kernel is conically clean, v151)","id":"python_verification:verification/v150_replica_eh_model.py","line_count":132,"path":"verification/v150_replica_eh_model.py","sha256":"a6d2fce7db74460f7e1d661600058a6cbd4fb608598b32bd768325aa56dddcb1","type":"python_verification"},{"bytes":6035,"checked_by_registry":false,"claim_ids":["SEAM.EHMODEL.02"],"cluster":"registry","description_excerpt":"BFK split (R3): Kac corner constant is boundary-condition independent (C_N = C_D, via doubling) ⇒ the conical deficit of the Calderón/DtN jump determinant VANISHES identically — the seam-reduced action inherits the v150 EH form via BFK; the EH content sits in the local half determinants; residue = q(A₃) normalisation + kernel premise","id":"python_verification:verification/v151_bfk_split.py","line_count":126,"path":"verification/v151_bfk_split.py","sha256":"126950875abcf38e3e99daf9b68e30c75f3db404bbb76a1eae57e7f51f8e7be8","type":"python_verification"},{"bytes":5554,"checked_by_registry":false,"claim_ids":["SEAM.EHMODEL.03"],"cluster":"registry","description_excerpt":"R3 normalisation IS the dimensionful anchor: k = ln(m/μ)/(12π) — ln m is scale-ambiguous, only m/μ is physical; k = c₃/2 ⟺ m/μ = e^{3/4} is the induced-gravity anchor 1/G (v68), not a separate gap; the irreducibles stay {one scale, π}; audit: the log-ratio = 3/4 = q(A₃) is the target value, NOT a derivation","id":"python_verification:verification/v152_norm_is_anchor.py","line_count":112,"path":"verification/v152_norm_is_anchor.py","sha256":"e0691a147c02521b105a2ceb21768bbd61f34410359f2f5dd3940a47df888e36","type":"python_verification"},{"bytes":6142,"checked_by_registry":false,"claim_ids":["ANCHOR.VGEO.02"],"cluster":"registry","description_excerpt":"No-Unit Theorem (v_geo re-typed): dimensionless data are scale-invariant under L→λL, a mass/1/G is not, so a dimensionless compiler cannot select an absolute scale; the three residuals collapse — U_point ~ v_geo, 1/G ~ v_geo², m/μ = e^{3/4} (a ratio); v_geo is an irreducible metrology primitive, not an open gap; irreducibles stay {one unit, π}","id":"python_verification:verification/v153_no_unit_theorem.py","line_count":121,"path":"verification/v153_no_unit_theorem.py","sha256":"bddd83c9d328e023a27242a72af6468b5da5c0b05582cb34bac34a810dfbeb6a","type":"python_verification"},{"bytes":5399,"checked_by_registry":false,"claim_ids":["GATE.METRIC.11"],"cluster":"registry","description_excerpt":"Simple-Current Extension Theorem (the central G_net theorem): A = (D5)1(x)(A3)1 extended by the isotropic glue L=<(1,1)> has index |L|=4, c=5+3=8, μ(B)=μ(A)/|L|²=16/16=1 ⇒ holomorphic ⇒ B=(E8)1 (unique even-unimodular rank-8); SO(16)1 excluded; finite realisation in hand (v125/v128/v143/v148); residue = the seam-side identification 'seam net = A'","id":"python_verification:verification/v154_simple_current_theorem.py","line_count":107,"path":"verification/v154_simple_current_theorem.py","sha256":"928aff32e0e5d9d440d326cb6f8a12dbb119d7cf86ccf6c2ea95a469f185e4c5","type":"python_verification"},{"bytes":7346,"checked_by_registry":false,"claim_ids":["GATE.METRIC.12"],"cluster":"registry","description_excerpt":"quasi-free in ⇒ quasi-free out (Python-only): the boundary marginal of a Gaussian bulk is the compression PΓP — a contraction, hence a valid covariance — so the G_net analytic premise (v110(b)/v113 'one kernel') FOLLOWS from 'the seam bulk is a RP free field', the same premise as v59 (area law) and v150/v151 (EH); the seam-side identification reduces to ONE shared physical premise","id":"python_verification:verification/v155_quasifree_boundary.py","line_count":138,"path":"verification/v155_quasifree_boundary.py","sha256":"83b2fb94b4fc1c577b8a10497c02d2acece8774d75351095265274a9db0da24d","type":"python_verification"},{"bytes":7106,"checked_by_registry":false,"claim_ids":["GATE.METRIC.13"],"cluster":"registry","description_excerpt":"constructive route (Route 3), exact endpoint: DtN of the 2d Laplacian = |k| (free chiral dispersion); 16 free Majoranas c=8=5+3; E8 currents 248 = 120 (NS bilinears) + 128 (R spinor); the (E8)1 character E4/eta^8 = q^{-1/3}(1+248q+4124q²+...) = j^{1/3} verified to order 4 ⇒ B=(E8)1 CHECKED not asserted; residual = free-bulk premise (v155) + net existence","id":"python_verification:verification/v156_seam_net_construction.py","line_count":134,"path":"verification/v156_seam_net_construction.py","sha256":"2d8d86bbc393eda3d4779017111f2d67a4c94644bab9a37e6b6685e58570a4aa","type":"python_verification"},{"bytes":6577,"checked_by_registry":false,"claim_ids":["GATE.METRIC.14"],"cluster":"registry","description_excerpt":"freeness as a rigid fixed point (simplicity-first reframing of premise A): (i) the DtN/Calderón symbol is universally |k| (Lee-Uhlmann, bulk-detail-independent — the free dispersion is not a premise); (ii) a holomorphic c=8 theory has NO marginal (1,1) field (all fields h̄=0) ⇒ rigid, isolated, no room for an interaction; (iii) the same |Z2| that halves 8π in c3 IS the Ramond projection giving μ=1 (holomorphic); (iv)","id":"python_verification:verification/v157_rigid_fixed_point.py","line_count":123,"path":"verification/v157_rigid_fixed_point.py","sha256":"d958f06ada104b85e5ee5f6594c28715a31a08f2cb41328cf92cbb578aa27711","type":"python_verification"},{"bytes":5956,"checked_by_registry":false,"claim_ids":["GATE.METRIC.15"],"cluster":"registry","description_excerpt":"the free chiral c=8 fixed point is STABLE (exact dimension count, finite core of A): chiral Majorana h=1/2, bilinear current h=1, quartic h=2; the relevant window (0,1) for bosonic ops is EMPTY, the h=1 currents are chiral (not (1,1)-marginal, v157), the lowest interaction (quartic) is h=2 > 1 irrelevant ⇒ isolated stable fixed point; (A) reduces to a basin-of-attraction statement","id":"python_verification:verification/v158_fixed_point_stable.py","line_count":118,"path":"verification/v158_fixed_point_stable.py","sha256":"9b3ca511c1b71259167204f50e492cf95468920ff6e1b24c7e34d402dc6aed25","type":"python_verification"},{"bytes":6292,"checked_by_registry":false,"claim_ids":["EM.BUDGET.02"],"cluster":"registry","description_excerpt":"PyR@TE cross-check of the F_transfer gauge inputs: the carrier/SM content gives (b1,b2,b3)=(41/10,−19/6,−7) by the textbook one-loop formula; 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(2) Wick functoriality ⇒ a kernel-preserving transport fixes the whole quasi-free state; (3) the Perron-Frobenius dichotomy (a fixed κ_{2n} = a SECOND fixed ray, kills uniquene","id":"python_verification:verification/v160_seam_gaussianity_from_pf.py","line_count":272,"path":"verification/v160_seam_gaussianity_from_pf.py","sha256":"b1df030b7f9645e7915490180c20b70c14fa7dfe1c12006edd1018f0e7a19e00","type":"python_verification"},{"bytes":10888,"checked_by_registry":false,"claim_ids":["GATE.METRIC.17"],"cluster":"registry","description_excerpt":"the cone reduces to one particle (discharges v160's scope premise via Bogoliubov second quantisation): a quasi-free transport is T = Γ(t), the second quantisation of a one-particle contraction t; Γ(t) acts on the degree-m correlator sector as the exterior power Λ^m(t), so (1) spec(Γ(t)|deg m) = products of m one-particle eigenvalues [E]; (2) THE CONE GAP EQUALS THE ONE-PARTICLE GAP — sub-leading eigenvalue over the w","id":"python_verification:verification/v161_one_particle_reduction.py","line_count":185,"path":"verification/v161_one_particle_reduction.py","sha256":"5f68aecdddf9be30df446de0a452b6b7c154615b81a9c604f18c43fa00ee1896","type":"python_verification"},{"bytes":9682,"checked_by_registry":false,"claim_ids":["GATE.METRIC.18"],"cluster":"registry","description_excerpt":"the final identification, forced as far as it goes — the v161 one-particle statement carries NO new open content: (1) the gap (2/3)^6 is FORCED — cusp weights = spec(A0*) = {0,1/3,2/3} (parabolic residue, v115), transfer eigenvalue (1-α)^{p2}, p2 = 6 = |R+(A3)|, all carrier data [E]; (2) μ4-equivariance forces the generator diagonal in the cusp basis — Σ_k U^k X U^{-k} = |μ4| diag(X), commutant of U = diagonal algebr","id":"python_verification:verification/v162_seam_transport_identification.py","line_count":161,"path":"verification/v162_seam_transport_identification.py","sha256":"1d3a80006bcff439f88b83d7f3b64d03a7b8d9cea15308ca7c68fde86beb5225","type":"python_verification"},{"bytes":5761,"checked_by_registry":false,"claim_ids":["FLAV.RGSTAB.01"],"cluster":"registry","description_excerpt":"F_transfer scale-tagging: the lepton-mixing seeds (sin²θ₁₂=1/3−φ₀/2=0.3067, sin²θ₁₃=φ₀·e^(−5/6)=0.0231) are RG-STABLE — PMNS running is y_τ²-suppressed (~1.8e-5 ≪ precision), so seam value = measured value; the quark mass-ratio readouts (m_t/m_b~41) run through y_t² ~ O(10–15%) and carry a scale tag. 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The residual collapses from v123's FIVE classes to: Tier 0 — the irreducible core {π, v_geo}, a THEOREM (No-Unit, v153, ANCHOR.VGEO.01/02), nothing to close; Tier 1 — ONE hinge (seam = flavour = horizon): A2 net existence (a","id":"python_verification:verification/v167_inventory_post_closure.py","line_count":143,"path":"verification/v167_inventory_post_closure.py","sha256":"b53e28c16db22f958cca682a6f7ca2cca3ebaa20053b999ce11bf06dc18e038c","type":"python_verification"},{"bytes":6248,"checked_by_registry":false,"claim_ids":["QGEO.RIGID.01","QGEO.REALIZE.01"],"cluster":"registry","description_excerpt":"the QGEO Rigidity Theorem — the FINITE half of the Tier-1 hinge GATE.QGEO, hardened. EXACT: μ4={1,i,−1,−i} has cross-ratio 2 and Möbius stabiliser ⟨z→iz, z→1/z⟩ of order 8=|D4| (faithful: 4-cycle + reflection) ⇒ four marks with faithful D4 are the μ4 square up to Möbius; H¹(ℙ¹∖μ4) rank 4−1=3=N_fam; the forms ω_k=z^{k−1}dz/(z⁴−1) (k=1,2,3) are μ4-eigenforms with z→iz eigenvalue i^k = the three nontrivial characters χ1","id":"python_verification:verification/v168_qgeo_rigidity.py","line_count":130,"path":"verification/v168_qgeo_rigidity.py","sha256":"e521cf3ea8006ff2a7da0b0abcc1dc393ee637183ae013fec2c8195c3c1cf5c0","type":"python_verification"},{"bytes":6406,"checked_by_registry":false,"claim_ids":["FR.ETAB.02"],"cluster":"registry","description_excerpt":"the η_B leptogenesis transfer operationalised (Tier-3 F_transfer, NOT a new class): type-I thermal leptogenesis η_B ~ 0.96e-2·ε₁·κ_f (sphaleron 28/79) fed by TFPT's NO neutrino spectrum + the predicted δ_CP=240°. Davidson-Ibarra ε₁=(3/16π)M1·m3/v² ~ 8.5e-7 for M1=1e10 GeV; efficiency κ_f(m̃₁) ~ 0.03–0.19. 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The K4 edge products (12,18,30,24,40,60) are all carrier blocks; ΣdetM=81=N_fam⁴; all seven 248-slices (D8,D5×A3,E6×A2,E7×A1,F4×G2,A4×A4,A8) follow from P,D,Δ=13,(e1,e2,dimS+); one affine map row(C+sU+tV)=(7,11,13)+s(3,3,3)+t(1,2,3) g","id":"python_verification:verification/v170_diamond_slice_compression.py","line_count":135,"path":"verification/v170_diamond_slice_compression.py","sha256":"8d4a49363e582ee1b58f234df2ba416232af75287ac38000902780ed4e42aea4","type":"python_verification"},{"bytes":5577,"checked_by_registry":false,"claim_ids":["QFT.OSMOMENT.01"],"cluster":"registry","description_excerpt":"Atomic OS Moment Lemma + Sugawara Gap Safety: spec(T)={1,64/729,1/729} makes C(n)=A+Br^n+Cs^n a positive moment sequence, so every OS Hankel matrix factorises as a Vandermonde Gram ⇒ reflection positivity (a clean proof, not a numeric Gram test); cluster constant 729/665, correlation length ξ=0.41105, Källén-Lehmann masses 6log(3/2),6log3; gap safety Δ_eff=6log(3/2)−31/(4π²)>0 with 31=1+h^∨(E8) and c((E8)1)=248/31=8 ","id":"python_verification:verification/v171_os_moment_cluster.py","line_count":114,"path":"verification/v171_os_moment_cluster.py","sha256":"f74b0058b3e3f13dc5135796e220e07ad5c6032bcaa2db35f3a4aaa455041097","type":"python_verification"},{"bytes":5009,"checked_by_registry":false,"claim_ids":["SEED.ANOMALY.01"],"cluster":"registry","description_excerpt":"trace-anomaly origin of the seed prefactor 4/3: over the seam S² (χ=2) the (E8)1 (c=8) Weyl anomaly is c·χ/6=8/3, halved by the one-sided |Z2| to 4/3 = dimS+/dim g_SM = 16/12 = the seed base (4/3)c3=1/(6π). Plus QCD b3=11−⅔N_f=7 = scalaron exponent Ω_adm−10b1=48−41 (confinement↔inflation share one integer), and the Volkov-Wipf factorisation −98/45=−2·7²/dim(D5) (audit). Gives the seed prefactor and the QCD/scalaron i","id":"python_verification:verification/v172_trace_anomaly_seed.py","line_count":90,"path":"verification/v172_trace_anomaly_seed.py","sha256":"7995cda376f028270d677497044a561255dbc394b574c13385bcb11a39ef0637","type":"python_verification"},{"bytes":5683,"checked_by_registry":false,"claim_ids":["FLAV.STRONGCP.02"],"cluster":"registry","description_excerpt":"Strong CP as Pfaffian reality: a self-dual CAR (16-Majorana) model demonstration of θ_eff=0 — the sheet-odd Calderón involution {D,Σ}=0 pairs the spectrum (±λ), γ5-Hermiticity (D†=γ5Dγ5) makes the fermion-measure Pfaffian real (arg∈{0,π}), and reflection positivity (Z>0) selects the positive branch ⇒ θ_eff=0. The CAR/Pfaffian form of the tfpt_2 polar+γ5+sheet+RP derivation.","id":"python_verification:verification/v173_pfaffian_cp_car.py","line_count":105,"path":"verification/v173_pfaffian_cp_car.py","sha256":"4564783e2df7707fbe132bf0c5559fb6678b38a32b5828638e6ae6f7117a136d","type":"python_verification"},{"bytes":4681,"checked_by_registry":false,"claim_ids":["QFT.FOCK.01"],"cluster":"registry","description_excerpt":"seam Fock-space readings: (1) CAR cone compression — dim Λ^even(ℝ¹⁶)=2¹⁵=32768 reduces to a 16-dim one-particle problem under quasi-free Bogoliubov (2¹⁵/16=2¹¹), the explicit count behind v161 (''the QFT cone is large but not independent''); (2) Witten index = the Plücker norm 11 = Σ_{k≤2}C(4,k), with 11=dim S⁺ − g_car (full 4-corner Fock 2⁴=16) and c_u/c_d=55/117 reading the QBL-protected boundary state space; (3) A","id":"python_verification:verification/v174_seam_fock_readings.py","line_count":88,"path":"verification/v174_seam_fock_readings.py","sha256":"0890cda9da4a02287de37fbd809dce0f388877ae79854d5a0f12fc48b511b063","type":"python_verification"},{"bytes":9050,"checked_by_registry":false,"claim_ids":["QFT.NETRP.01"],"cluster":"registry","description_excerpt":"the heavy artillery — net existence (A2) and full-cone reflection positivity discharged to [E], isolating QGEO.REALIZE.01 as the single open premise (nothing fabricated): (1) FULL-CONE RP FOR ALL m — the CAR second-quantisation functor Γ(t)=⊕_m Λ^m(t) of the one-particle seam contraction t acts on the complete Fock space Λ^•(ℝ¹⁶) (dim 2¹⁶=65536); the exterior-power spectrum theorem makes every eigenvalue a subset pro","id":"python_verification:verification/v175_net_existence_full_cone.py","line_count":164,"path":"verification/v175_net_existence_full_cone.py","sha256":"969ccd9c2a6ba5a4edb46219ff3aeeaa5c3e7c67ff01bed49ccc981dc7960426","type":"python_verification"},{"bytes":8019,"checked_by_registry":false,"claim_ids":["QGEO.REALIZE.02"],"cluster":"registry","description_excerpt":"the Seam Collar Realisation Theorem assembled as ONE central statement + reduction certificate (the single structural proof obligation of the theory, formulated cleanly — NOT a fabricated proof): the theorem 'the seam collar's conformal boundary is ℙ¹∖μ₄ with H¹ grading (1,2,3), Calderón contraction = rank-8 K_Σ, index-4 extension = (E8)₁' decomposes into six steps, FIVE already [E] — geometry/uniformisation (v168: c","id":"python_verification:verification/v176_seam_collar_realisation.py","line_count":143,"path":"verification/v176_seam_collar_realisation.py","sha256":"f7f4c9de2010f9b947db1861608469c1b2a67e401640a82d5c3b1b5c6d336061","type":"python_verification"},{"bytes":8236,"checked_by_registry":false,"claim_ids":["QGEO.TREE.01","QGEO.MARKS.01","QGEO.KERNEL.01"],"cluster":"registry","description_excerpt":"the QGEO proof tree — the v176 'one realisation premise' split into its honest constituents: REALIZE = MARKS · UNIFORM · COHOM · MODULE · KERNEL · NET, with FOUR nodes closed CONSTRUCTIVELY as [E] and the open residual sharpened into exactly TWO named obligations. [E] UNIFORM (Lemma 2, constructive): an order-4 Möbius map conjugates to z↦iz, a non-fixed orbit scales to μ₄, the reflection z↦1/z gives στρτ=ρ⁻¹ (D4 orde","id":"python_verification:verification/v177_seam_marking_kernel.py","line_count":142,"path":"verification/v177_seam_marking_kernel.py","sha256":"bf6ad1e0d4dd21ca3b66790b004c2d202a67ea1e94a249c4f09437cc4b6a1c09","type":"python_verification"},{"bytes":9349,"checked_by_registry":false,"claim_ids":["QGEO.REDUCE.01"],"cluster":"registry","description_excerpt":"an honest ATTEMPT at the two open obligations QGEO.MARKS.01 + QGEO.KERNEL.01 — NOT a closure (they are genuine constructive-geometry/AQFT statements, not finite computations), but a deeper reduction: each finite/algebraic CORE is closed [E] and each obligation reduced to ONE sharper irreducible [O] premise. MARKS finite core [E]: a genus-0 double with an order-4 clock ρ (~z↦iz, fixed points {0,∞}) and sheet reflectio","id":"python_verification:verification/v178_marks_kernel_attempt.py","line_count":152,"path":"verification/v178_marks_kernel_attempt.py","sha256":"3d98e1d8ab0a9cbd5f1d9e914818baffa506ca1269cd09ddff0a4d01822c8036","type":"python_verification"},{"bytes":8632,"checked_by_registry":false,"claim_ids":["QGEO.CONF.01"],"cluster":"registry","description_excerpt":"the two residual premises (MARKS-residual + KERNEL-residual) collapse to ONE geometric premise QGEO.CONF.01 (honest unification, the conformal realisation stays OPEN). MARKS's residual is NOT three independent assumptions: (1) genus-0 IS P1 — c3=1/(|Z2|·2π·χ(S²))=1/(8π) with χ(S²)=2 ⇒ g=0, the same χ=2 that gives the '8' (v58/v73); (2) the order-4 clock IS the carrier — Coxeter element of W(A3)=S4, order h(A3)=4=|μ4|","id":"python_verification:verification/v179_conformal_realisation.py","line_count":143,"path":"verification/v179_conformal_realisation.py","sha256":"2e5a1a2c044ffb06a92839d91afc806a9acf385fa78c87f12019a6859b83e8fa","type":"python_verification"},{"bytes":2476,"checked_by_registry":false,"claim_ids":["FLAV.RESOLV.01"],"cluster":"frontier","description_excerpt":"finite hexagonal resolvent (the quark c backbone)","id":"python_verification:verification/v17_hexagonal_resolvent.py","line_count":58,"path":"verification/v17_hexagonal_resolvent.py","sha256":"b41a5cbab3ec83793ea903db1377dea15f89fbd2cd6022cb79ec66f0fe463b1e","type":"python_verification"},{"bytes":7662,"checked_by_registry":false,"claim_ids":["QGEO.ISO.01"],"cluster":"registry","description_excerpt":"cracking QGEO.CONF.01 one level further — the conformal-realisation premise is REPLACED, via three classical theorems, by a strictly MILDER, non-circular premise QGEO.ISO.01: 'the carrier clock is an order-4 orientation-preserving ISOMETRY of the RP seam metric'. (1) Uniformisation (Poincaré-Koebe): a genus-0 Riemann surface is conformally ℙ¹, so the genus-0 seam double (P1, v179) IS ℙ¹ — the target is produced, not ","id":"python_verification:verification/v180_clock_is_mobius.py","line_count":138,"path":"verification/v180_clock_is_mobius.py","sha256":"f5a6fb459906b0df6bbc640f63766cea5ebf9df6cffb4c339e5c18d9bd12100b","type":"python_verification"},{"bytes":6382,"checked_by_registry":false,"claim_ids":["QGEO.SYM.01"],"cluster":"registry","description_excerpt":"the FINAL honest reduction + the explicit identification of BEDROCK. The isometry premise QGEO.ISO.01 (v180) is weakened one more genuine step — to a CONFORMAL-symmetry premise QGEO.SYM.01 — via equivariant uniformisation (Nielsen realisation, finite cyclic on genus-0): a CONFORMAL automorphism (strictly weaker than an isometry — every isometry is conformal, conformal allows any positive scale) already suffices to pu","id":"python_verification:verification/v181_clock_is_conformal_symmetry.py","line_count":107,"path":"verification/v181_clock_is_conformal_symmetry.py","sha256":"5b383a435ab8284370dda6a72406b9441a0e4facaeb1ac84cb0e14d19dd00298","type":"python_verification"},{"bytes":7321,"checked_by_registry":false,"claim_ids":["REVIEW.MAP.01"],"cluster":"registry","description_excerpt":"the four external-review concerns reduce to the two already-named residuals + one data-only item: A (mapping 2D→4D, ''why read the masses as Plücker 11?''), B (UV-gravity abstractness), C (grammar-tuning/meta-look-elsewhere), D (Koide Möbius flow). A [I]/[C]: 11=Σ_{k≤2}C(4,k)=dim S⁺−g_car=16−5 (QBL count, v174), the 2D→4D step is the holographic reduction ⇒ A = QGEO.SYM.01 + F_transfer. B [I]: 'gravity = geometric bo","id":"python_verification:verification/v182_reviewer_residual_map.py","line_count":118,"path":"verification/v182_reviewer_residual_map.py","sha256":"7edc68e802cd17c73abafb5d98eb05bc1fbf24c430e9b8ee2254b3944bb9b87c","type":"python_verification"},{"bytes":5633,"checked_by_registry":false,"claim_ids":["FR.KOIDE.07"],"cluster":"registry","description_excerpt":"the Koide source→pole factor 53/54 has an OPERATOR origin (external-review proposal, validated): u_pole/u_source = aᵀ(R+Q)𝟙 / (2·𝟙ᵀRa) = 53/(2·27) = 53/54. (1) 𝟙ᵀRa=27 is the E6×A2 cubic family block (248 = dim E6 78 + det R 8 + 2·27·N_fam); (2) F=R+Q is the MISSING Sheet-Diamond corner M(1,1) with det B_F=52=dim F4 (v80) and anchor response aᵀ(R+Q)𝟙=53=52+1; (3) 53/54 = 1−1/(2N_fam³) exactly (54=2·27); (4) negative ","id":"python_verification:verification/v183_koide_f_corner_transfer.py","line_count":112,"path":"verification/v183_koide_f_corner_transfer.py","sha256":"d739384d36081dc2272680d0683433c4047f7a824437a1c275b594dd6d2d7c89","type":"python_verification"},{"bytes":6100,"checked_by_registry":false,"claim_ids":["FR.ETAB.03"],"cluster":"registry","description_excerpt":"HONEST test of the external-review η_B proposal (M_1=M_R·φ0⁴, m̃1=m_3/A_Lambda) — firewall verdict: SHARPER SCENARIO, not a closure. The washout anchors plausibly (m̃1=m_3/A_Lambda=m_3/10≈5e-3 eV, A_Lambda=10=|E(K5)| atom, in the strong-washout window) [C]; but M_1 does NOT anchor — M_R is the seesaw scale ~v²/m_3≈6e14 GeV, and the nearest clean TFPT powers of Mbar both MISS it (c3-power off ~75%, φ0-power off ~40%),","id":"python_verification:verification/v184_etaB_anchored_boltzmann.py","line_count":110,"path":"verification/v184_etaB_anchored_boltzmann.py","sha256":"bc5ddc18ee89b55ea628b687a7b444c8a35eb64ba3d2a700a6ae97895c1f785f","type":"python_verification"},{"bytes":6253,"checked_by_registry":false,"claim_ids":["FR.DM.03"],"cluster":"registry","description_excerpt":"axion relic, honest misalignment estimate: the determinant-line axion f_a=M_scal/128≈2.39e11 GeV (m_a≈23.8 µeV) CAN provide all dark matter, but ONLY near the θ_i≈170° hilltop where the relic is exponentially sensitive — so the axion DM branch stays a [C] SCENARIO. The harmonic misalignment UNDER-produces at this f_a (prefactor ~0.026/θ², θ~O(1) gives ~21% of Ω_DM, need θ_eff²~4.7), so the 170° hilltop anharmonic enh","id":"python_verification:verification/v185_axion_relic_solver.py","line_count":107,"path":"verification/v185_axion_relic_solver.py","sha256":"34483faac9fa93b3efb570f3c6546f5f22d5606ceb46dcce38e59123f20279c7","type":"python_verification"},{"bytes":5323,"checked_by_registry":false,"claim_ids":["FR.TRANSFER.01"],"cluster":"registry","description_excerpt":"the F_transfer discipline guard (CI-style firewall, the machine-readable form of the Frontier rule): the four continuous-transfer frontier observables — Koide (FR.KOIDE.*), η_B (FR.ETAB.*), axion (FR.DM.*), m_p/m_e+Λ_QCD (FR.MPME.*/QCD.LAMBDA.*) — must NEVER be typed as primitive [E]/[N] compiler predictions; each must carry a [C]/[A]/[O] marker. Reads the ledger and enforces it (all active frontier rows pass; exact ","id":"python_verification:verification/v187_ftransfer_laws.py","line_count":102,"path":"verification/v187_ftransfer_laws.py","sha256":"6e514f99af6f926acb5180c13b26db97d47ff0bd8b130f22186a370a73248720","type":"python_verification"},{"bytes":5415,"checked_by_registry":false,"claim_ids":["AUDIT.WORDING.01"],"cluster":"registry","description_excerpt":"the frontier-wording guard (a prose sentinel, no new physics): v187 protects the ledger typing, this guard protects the prose. It forbids stale sentences whose semantics an earlier round superseded — 'leptogenesis interface (mE)' (v184 retyped Route B to [C]), 'closed branch also fixes the leptogenesis inputs' (M_R is the seesaw scale, not a compiler power), 'relic scale f_a,m_a open' (v185: the scales define the bra","id":"python_verification:verification/v188_frontier_wording_guard.py","line_count":111,"path":"verification/v188_frontier_wording_guard.py","sha256":"89c8e3a589f551241915927d0f535c2039cf4827b9f87c6786fbb8b3edc033e2","type":"python_verification"},{"bytes":4438,"checked_by_registry":false,"claim_ids":["ARCH.RRCAR.01"],"cluster":"registry","description_excerpt":"the Riemann-Roch carrier reading: (g_car, N_fam)=(5,3) are the two canonical invariants of ONE object, the four-point seam divisor D=µ₄ on P¹. [E] math: h⁰(P¹,O(µ₄))=deg+1=5 (function side) and rank H₁(P¹∖µ₄)=deg−1=3 (cycle side, already QGEO.COHOM.01/v177); g_car=5=rank(D₅) (carrier=so(10) half-spinor, rank D₅+rank A₃=5+3=8, v1), N_fam=3=(dim S⁺−1)/g_car. [C]: 'carrier = the meromorphic seam-mode space H⁰(P¹,O(µ₄))'","id":"python_verification:verification/v189_riemann_roch_carrier.py","line_count":86,"path":"verification/v189_riemann_roch_carrier.py","sha256":"4d84ef7b00722363f833c1e43b289b31e9d62056b78b8a70e8176db08c94602a","type":"python_verification"},{"bytes":4478,"checked_by_registry":false,"claim_ids":["FLAV.QUARK.01"],"cluster":"masses","description_excerpt":"quark source ratios; lepton c=(16/7,4/3,7/6); full hierarchy","id":"python_verification:verification/v18_quark_yukawa.py","line_count":86,"path":"verification/v18_quark_yukawa.py","sha256":"194a0e83e6121015a102934ad30169698ab94be505d6b1ff97f8e35cd8e6765b","type":"python_verification"},{"bytes":2601,"checked_by_registry":false,"claim_ids":["HOR.NARIAI.02"],"cluster":"registry","description_excerpt":"the one-line Nariai entropy bound: the SdS entropy ratio S_tot/S_dS=(x²+1)/Φ₃(x) (x=r_b/r_c; Φ₃=x²+x+1 the N_fam=3 cyclotomic; already in tfpt_horizon_readouts) satisfies S_tot ≥ (2/3)S_dS with equality exactly at the Nariai merge x=1, via the perfect square 3(x²+1)−2Φ₃(x)=(x−1)²≥0 — a variation-free proof of the entropy floor (global minimum on x>0 is 2/3=|Z₂|/N_fam).","id":"python_verification:verification/v190_nariai_entropy_bound.py","line_count":55,"path":"verification/v190_nariai_entropy_bound.py","sha256":"05d99f3a2d6cce65a1346d34a69b880e292a8ad669bd021a2159aa64226ff550","type":"python_verification"},{"bytes":4829,"checked_by_registry":false,"claim_ids":["HOR.BRANCHLINE.01"],"cluster":"registry","description_excerpt":"the universal branch line, HONESTLY typed [C] — an exact affine RELABELING, not a theorem. The map q=7/2+(N_fam²/2)m carries the SdS branch points m=±1/N_fam onto the flavor branch points {2,5}={|Z₂|,g_car} (m=0→7/2). [E] arithmetic, but the map exists for ANY two pairs of points (two intervals are always affinely equivalent), so the slope N_fam²/2 and midpoint 7/2 are DETERMINED by the data, not forced independent p","id":"python_verification:verification/v191_universal_branch_line.py","line_count":87,"path":"verification/v191_universal_branch_line.py","sha256":"c635c3ab72db71ed06291aa855885d3e41967f3143486715c182689d81ceba47","type":"python_verification"},{"bytes":4687,"checked_by_registry":false,"claim_ids":["QGEO.ENERGY.01"],"cluster":"registry","description_excerpt":"the energy-conserving-clock reformulation, HONESTLY typed: QGEO.ENERGY.01 (ρ*Λ_Σρ=Λ_Σ — the carrier clock preserves the Calderón/DtN energy form) RELOCATES the bedrock QGEO.SYM.01 to a more checkable operator identity, but does NOT eliminate it. The downstream chain (conformality→Möbius→z↦iz→µ₄→QGEO.SYM.01) already exists (v180/v181); the new upstream link (energy invariance ⇒ conformality in 2D) is checkable on the ","id":"python_verification:verification/v192_qgeo_energy_clock.py","line_count":90,"path":"verification/v192_qgeo_energy_clock.py","sha256":"d9eb0a1fa4811dc540b9ab2513d7a9c9ae4f1d1276c615cf28771230e78e34b0","type":"python_verification"},{"bytes":5149,"checked_by_registry":false,"claim_ids":["QGEO.ENERGY.02"],"cluster":"registry","description_excerpt":"QGEO.ENERGY.02: the energy-COMMUTATOR contract (non-circular sharpening of QGEO.ENERGY.01): [ρ,Λ_Σ]=0 on the rank-8 Calderón polarisation, ρ the carrier clock, Λ_Σ the DtN energy form of the RAW RP seam. Three sub-claims: (1) [E] ρ is carrier-defined (Coxeter of W(A3)=S4, order 4=|µ4|, v117), not imported from the seam; (2) [O] the non-circularity hinge — Λ_Σ must be the RAW RP-seam DtN, not the µ4 normal form (circu","id":"python_verification:verification/v193_qgeo_energy_commutator.py","line_count":94,"path":"verification/v193_qgeo_energy_commutator.py","sha256":"b75f0ad657e511a14fd3f8da02fe51710240ac4fcab83a6994c2ff0c00d27aba","type":"python_verification"},{"bytes":5846,"checked_by_registry":false,"claim_ids":["QGEO.DTN.01"],"cluster":"registry","description_excerpt":"QGEO.DTN.01 — subclaim 2 of QGEO.ENERGY.02 ('the raw RP-seam DtN is RP-definable') tackled: a REDUCTION, not a closure. (1) [E] finite core: ρ:z↦iz on H¹=⟨w1,w2,w3⟩, wk=z^{k-1}dz/(z⁴−1), acts as ρ*wk=i^k wk (characters i,−1,−i distinct), so [ρ,Λ_Σ]=0 on H¹ (v177). (2) [I] hinge met: the DtN/transfer operator is RP-canonical (Osterwalder–Schrader, v54) on a quasi-free seam state (v155), so Λ_Σ is RP-definable without ","id":"python_verification:verification/v194_raw_seam_dtn_rp.py","line_count":107,"path":"verification/v194_raw_seam_dtn_rp.py","sha256":"a71e9a42aa40a4b6b0f0e671834b55280461a40535cf8ddcb79a743d37f9221b","type":"python_verification"},{"bytes":5060,"checked_by_registry":false,"claim_ids":["QGEO.MARKS.02"],"cluster":"registry","description_excerpt":"QGEO.MARKS.02 — a Lefschetz/character derivation of the four seam marks (review path 2): instead of positing D4 marks, they are FORCED to be a free µ4 orbit. [E]: ρ:z↦iz (order 4) fixes only {0,∞}; H¹=χ1+χ2+χ3 (A3 exponents (1,2,3), v177) has no trivial character ⇒ no puncture at a fixed point; rank H_1=n−1=3 ⇒ n=4 ⇒ exactly one free orbit ⇒ marks = µ4 (cross-ratio 2); Tr(ρ|H¹)=i+i²+i³=−1, L(ρ)=1+1=2=#fixed. [O] resi","id":"python_verification:verification/v195_marks_lefschetz_character.py","line_count":90,"path":"verification/v195_marks_lefschetz_character.py","sha256":"a19022c0872dd2130bd77cb21e93345851a6a8b17ba0a5dd2bbea48138b474be","type":"python_verification"},{"bytes":5208,"checked_by_registry":false,"claim_ids":["QGEO.VARI.01"],"cluster":"registry","description_excerpt":"QGEO.VARI.01 — the E_fail variational functional (review path 1), a numerically-testable sharpening of the v194/ENERGY.02 target: E_fail = ‖[ρ,Λ_Σ]‖²_HS + ‖ρ⁴−1‖² + ‖ΘρΘ−ρ⁻¹‖², with E_fail=0 ⇔ the QGEO.SYM.01 conditions. [E] on the finite H¹ block (ρ=diag(i,−1,−i), Λ diagonal, Θ=conj) all three vanish ⇒ E_fail=0; [N] a µ4-breaking Λ or non-order-4 ρ gives E_fail>0 (µ4 is a true minimiser); [I] the zero locus = the se","id":"python_verification:verification/v196_seam_energy_functional.py","line_count":97,"path":"verification/v196_seam_energy_functional.py","sha256":"fa447e51ca493cc0eb2f011299c1943042dc8fa8f59112276549e0a3f96a0166","type":"python_verification"},{"bytes":3908,"checked_by_registry":false,"claim_ids":["ARCH.RRCAR.02"],"cluster":"registry","description_excerpt":"ARCH.RRCAR.02 — hardening the Riemann–Roch carrier from g_car to D5 itself (review point 7): the 5-dim carrier mode space C_car:=H⁰(P¹,O(µ4)) generates the so(10)=D5 half-spinor by its even Clifford algebra. [I] dim Λ^even(C⁵)=C(5,0)+C(5,2)+C(5,4)=1+10+5=16=2^{g_car−1}=dim S⁺; so(10)=D5 half-spinor 2⁴=16=S⁺=Λ^even(C_car); closes the chain µ4→g_car→D5 from one four-point divisor (cycle side rank H_1=3=N_fam(A3); funct","id":"python_verification:verification/v197_rr_carrier_clifford_d5.py","line_count":72,"path":"verification/v197_rr_carrier_clifford_d5.py","sha256":"84b093de7dd97a91f9ab4f4a18fdca20ebefb4a7e0fa8324ef45983beafcb8c9","type":"python_verification"},{"bytes":6107,"checked_by_registry":false,"claim_ids":["QGEO.MODULAR.01"],"cluster":"registry","description_excerpt":"QGEO.MODULAR.01 — cracking the bedrock to a state-invariance. The v194 residual ([ρ,Λ_Σ]=0 on full L², framed as Bisognano–Wichmann with a circularity worry) is (a) made EXACT at the principal-symbol level and (b) reduced via Tomita–Takesaki to a clean state-invariance. [E] the DtN principal symbol |k|=√(−d²) is diag(|n|) and the clock ρ:z↦iz is diag(i^n) in the Fourier basis — both diagonal ⇒ [ρ,|k|]=0 exactly on AL","id":"python_verification:verification/v198_modular_commutator_reduction.py","line_count":100,"path":"verification/v198_modular_commutator_reduction.py","sha256":"9a5cac328a021e192a3c68af52e8103484d3c1e066570ad33cd5d26c1e8dc113","type":"python_verification"},{"bytes":5645,"checked_by_registry":false,"claim_ids":["QGEO.STATE.01"],"cluster":"registry","description_excerpt":"QGEO.STATE.01 (work package A) — attacking ω∘ρ=ω directly on the raw seam: a further localising reduction, not a closure. [E] setup non-circular (ρ = Coxeter of W(A3)=S4, ρ⁴=1, an automorphism of the raw CAR algebra; both carrier-side, no seam geometry); [E] ground-state reduction ω∘ρ=ω ⟺ [ρ,H₁]=0 (C_Σ=½(1+sgn H₁)); [E] character criterion: [ρ,H₁]=0 ⟺ H₁ block-diagonal in the four μ4-character classes {n=r mod 4} (bl","id":"python_verification:verification/v199_seam_state_invariance.py","line_count":100,"path":"verification/v199_seam_state_invariance.py","sha256":"566ea460d3d4198e6437c528f96f921d0b857abb167ad37216e9fee9c38dab0e","type":"python_verification"},{"bytes":5670,"checked_by_registry":false,"claim_ids":["FLAV.UFSTAR.01","GATE.QGEO.01","GATE.RU.01"],"cluster":"frontier","description_excerpt":"exact monodromy pole; D₄ SU(3) monodromy moduli","id":"python_verification:verification/v19_monodromy_moduli.py","line_count":137,"path":"verification/v19_monodromy_moduli.py","sha256":"83a51608571328b2f15d8da10574a2525ed9cd1cbf21d723b071ec24d9d97d32","type":"python_verification"},{"bytes":5584,"checked_by_registry":false,"claim_ids":["E8.GLU.01","E8.NUM.01"],"cluster":"core","description_excerpt":"E₈ glue: disc ℤ₄, q(D₅)+q(A₃)=2, 240=16·5·3, 248","id":"python_verification:verification/v1_e8_glue.py","line_count":145,"path":"verification/v1_e8_glue.py","sha256":"1978d66a85974e5fa189cf4dec507f9be4c4dcc113e90eb1b33a9aae9259a0d7","type":"python_verification"},{"bytes":4387,"checked_by_registry":false,"claim_ids":["QGEO.VARI.02"],"cluster":"registry","description_excerpt":"QGEO.VARI.02 (work package B) — the discretised variational test: v196 had E_fail=0 at the μ4 config on the fixed block; here the clock angle is free and E_fail is minimised over it. [N] scanning E_fail(θ)=‖ρ(θ)⁴−1‖²+faithfulness over θ∈(0,π) gives the unique minimum at θ=π/2 (E_fail=0: order-4 AND three distinct characters i,−1,−i = the (1,2,3) grading); decoys (0, π, π/3, 2π/3) all lose. So argmin E_fail = the μ4 n","id":"python_verification:verification/v200_seam_variational_scan.py","line_count":81,"path":"verification/v200_seam_variational_scan.py","sha256":"231896f53ae03ef7052af133aad701dab2457f316a8545ee56b05279eb1dc6b4","type":"python_verification"},{"bytes":8255,"checked_by_registry":false,"claim_ids":["QGEO.SUBPRIN.01"],"cluster":"registry","description_excerpt":"QGEO.SUBPRIN.01 — the v199 bedrock residual reduced one genuine step further: block-diagonality of the sub-principal symbol is NOT an independent postulate. [E] the seam DtN is Λ=|k|+M_f, M_f = multiplication by a curvature function f(θ) (standard Steklov sub-principal), so ⟨n|M_f|n'⟩=f_{n-n'}. [E] M_f is μ4-character-block-diagonal ⟺ f has Fourier support only on modes ≡0 (mod 4) ⟺ f is Z4-invariant (|k| already com","id":"python_verification:verification/v201_seam_subprincipal_marks.py","line_count":143,"path":"verification/v201_seam_subprincipal_marks.py","sha256":"d80dc3f61f38b0499e167b38b9c08a6c09573c2cfcfd6da3341bb1ddeb0dd8db","type":"python_verification"},{"bytes":7943,"checked_by_registry":false,"claim_ids":["FR.RAREKAON.01"],"cluster":"flavor","description_excerpt":"the rare kaon sector K → π ν ν̄ from the TFPT CKM point ([C] downstream flavor readout, NOT a compiler power). The kernel fixes the full CKM matrix (s₁₂=λ_C, s₂₃=φ₀/(1+λ_C)=|V_cb|, s₁₃=λ_C³/3, δ=π/3+3λ_C²=1.19823 rad; v18/v88) with no flavor fit; feeding the exact point into the standard Brod–Gorbahn–Stamou short-distance formulas gives BR(K⁺→π⁺νν̄)=9.45×10⁻¹¹ and BR(K_L→π⁰νν̄)=3.33×10⁻¹¹. [I] CKM point + exact apex ","id":"python_verification:verification/v202_rare_kaon.py","line_count":142,"path":"verification/v202_rare_kaon.py","sha256":"04e9e19416c79411fd4af7a7425994f4efb958faa19567039e90ef2a144d126a","type":"python_verification"},{"bytes":6777,"checked_by_registry":false,"claim_ids":["HOR.EHT.01"],"cluster":"horizon","description_excerpt":"the EHT achromatic polarization-rotation intercept β_BH around a horizon-scale black hole — the surviving core of the old UFE/BH notes (NOT the RN-type metric, superseded by Nariai/seam=horizon v101–v104/v190; only the polarization signature). [E] the coupling is a compiler number: β_BH(r)=Q_e^eff Q_m^eff/(256π⁴r²)=16c₃⁴(Q_eQ_m/r²), 16c₃⁴=1/(256π⁴) exactly. [E] α-kernel cross-link: 16c₃⁴=δ_top/3, δ_top=48c₃⁴=3/(256π⁴","id":"python_verification:verification/v203_eht_achromatic.py","line_count":112,"path":"verification/v203_eht_achromatic.py","sha256":"f9881fb5a14cf89a9416a3c90937b4175a95bdb55d58642190026d16b955f0a4","type":"python_verification"},{"bytes":5462,"checked_by_registry":false,"claim_ids":["FR.MUONG2.01"],"cluster":"frontier","description_excerpt":"the muon anomalous magnetic moment a_μ=(g_μ−2)/2 as a seam vertex readout ([C] downstream, NOT a compiler power; archive integration of the old muon-g2 note). The carrier fixes the second-order topological defect δ₂=B·γ·δ_top²=(5/4)δ_top² (δ_top=Ω_adm c₃⁴=48c₃⁴=3/256π⁴, v2/v23; B·γ=(3/2)(5/6)=5/4 the carrier compression quotient, v51); the seam-loop projection a_μ^seam=δ₂/(2π)=45/(524288π⁹)≈2.879×10⁻⁹. [E] the VALUE ","id":"python_verification:verification/v204_muon_seam_g2.py","line_count":106,"path":"verification/v204_muon_seam_g2.py","sha256":"3102fef025e71ba421a22c64d14a13bbc934826cc6b8d4ba386bfcd90777e5b4","type":"python_verification"},{"bytes":4251,"checked_by_registry":false,"claim_ids":["GRAV.XI.01"],"cluster":"gravity","description_excerpt":"ξ=c₃/φ_tree=3/4: an INDEPENDENT route to the gravitational 3/4 (archive integration of the old Eliminating-K note). The torsion-compression ansatz κ²=ξφ₀/c₃² with the Einstein limit κ²=8πG fixes ξ=8πc₃²/φ₀=c₃/φ₀ (since 8πc₃²=c₃), and at tree level φ_tree=1/(6π) this is EXACTLY 3/4. [E] tree identity ξ=c₃/φ_tree=(1/8π)/(1/6π)=3/4; [E] Einstein-limit reduction 8πc₃²=c₃ ⇒ G is an output, not an input; [E] OVER-DETERMINA","id":"python_verification:verification/v205_xi_threequarter.py","line_count":90,"path":"verification/v205_xi_threequarter.py","sha256":"2a6898b2cfe36d8030a7eb4add0e7ff5be902d536c8850b1adbf8f18b7896d80","type":"python_verification"},{"bytes":4707,"checked_by_registry":false,"claim_ids":["GRAV.H0.01"],"cluster":"gravity","description_excerpt":"the cosmological-constant Letter branch: the seam number δ_Σ=m₁e^{−2πα⁻¹/3} with the lowest-block m₁=Ω_adm=48, the Planck-convention split, and the quantitative H₀=66.5..67.1 (archive integration of the tfpt-31 CC note; sharpens the qualitative H₀-vs-Λ row). [N] δ_Σ^lead=48 e^{−2π·137.036/3}≈1.085×10⁻¹²³; [E] convention split M_Pl⁴/M̄_Pl⁴=(8π)²=631.65 (unreduced vs reduced Planck density — must be displayed); [N] ρ_Λ","id":"python_verification:verification/v206_h0_lambda_branch.py","line_count":91,"path":"verification/v206_h0_lambda_branch.py","sha256":"1efc9a0cab5f4c658651c8819610f77b2332acbc61320cd2269672b10e613e6d","type":"python_verification"},{"bytes":4037,"checked_by_registry":false,"claim_ids":["GRAV.ASYMP.01"],"cluster":"frontier","description_excerpt":"Asymptotic Safety as a SECOND, independent, [P] route to the metric sector (archive integration of the old Five-Problems note). The current theory closes QG via the discrete seam-net/AQFT programme (v175; open premise QGEO.REALIZE.01); this records a COMPLEMENTARY continuum-FRG argument that a non-Gaussian UV fixed point exists from the same axioms — a plausibility cross-check, NOT load-bearing, does NOT close G_metr","id":"python_verification:verification/v207_asymptotic_safety.py","line_count":79,"path":"verification/v207_asymptotic_safety.py","sha256":"1319afaf79f62e395d26b8c55721a077e6fc3af2a34cd0d902d945614d2a8046","type":"python_verification"},{"bytes":4568,"checked_by_registry":false,"claim_ids":["HOR.BHTHERMO.01"],"cluster":"horizon","description_excerpt":"black-hole thermodynamics from the seam: the modular Hawking temperature and the scalaron-corrected Wald entropy (archive integration of the dropped tfpt-42 stationary-horizons/compact-objects section, re-typed through the current Tomita–Takesaki seam work v198/v199). [E] MODULAR T_H: Δ^{it}=e^{−2πtK_H} (Bisognano–Wichmann) ⇒ KMS at β=2π and T_H=κ/(2π); the 2π IS the seam unit 1/(4c₃) (1/2π=4c₃, v58), reproducing T_H","id":"python_verification:verification/v208_bh_thermodynamics.py","line_count":87,"path":"verification/v208_bh_thermodynamics.py","sha256":"ed633bb912f464b0a82cd60e348019fb4539a69aa6d8f348857c771da19b7afc","type":"python_verification"},{"bytes":4430,"checked_by_registry":false,"claim_ids":["HOR.BHCORE.01"],"cluster":"horizon","description_excerpt":"the black hole as a seam fixed point (topological defect), NOT a singularity: the honest [P] synthesis of the old Five-Problems BH picture, with the SUPERSEDED torsion/RN-vortex metric DROPPED (RN-type metric superseded by Nariai/seam=horizon v101–v104/v190; cf. v203). Built entirely from established suite atoms. [E] NO SINGULARITY = SEAM FIXED POINT: the gapped attractor multiplier λ₂=(2/3)⁶=64/729 with gap Δ=6log(3","id":"python_verification:verification/v209_bh_regular_core.py","line_count":87,"path":"verification/v209_bh_regular_core.py","sha256":"da96da5f8e627e60fdc1563c9c4ef096232ad82f76491d9255b5ed80b8162104","type":"python_verification"},{"bytes":4238,"checked_by_registry":false,"claim_ids":["FLAV.LEPTONC.01"],"cluster":"masses","description_excerpt":"lepton c's derived (δ=½ resolvent; product 32/9)","id":"python_verification:verification/v20_lepton_c_derivation.py","line_count":89,"path":"verification/v20_lepton_c_derivation.py","sha256":"7b0663a0e35aa9fc480e38b9691c7f6fad7af3bb93e19571ee90d04197e4d7b1","type":"python_verification"},{"bytes":9484,"checked_by_registry":false,"claim_ids":["QGEO.MARKLOCAL.01"],"cluster":"registry","description_excerpt":"a numerical SHARPENING of v201/QGEO.SUBPRIN.01 on REALISTIC Steklov curvature profiles, carried to the quasi-free STATE level (the actual ω∘ρ=ω, not just [ρ,Λ]=0); NOT a closure of QGEO.SYM.01. A real von-Mises curvature bump g(θ) localised at a puncture, summed over the four μ4 marks f(θ)=Σ_{j=0}^3 g(θ−jπ/2), builds the Steklov DtN Λ=|D_θ|+M_f. [E] every off-(mod 4) Fourier coefficient of the REAL f vanishes to <1e-","id":"python_verification:verification/v210_mark_local_dtn.py","line_count":191,"path":"verification/v210_mark_local_dtn.py","sha256":"5a464a7bb8bb23e81d6a91aa7205b3d9000262a0150203fdbc13d0f4696995a3","type":"python_verification"},{"bytes":5636,"checked_by_registry":false,"claim_ids":["DM.AXION.SPINE.01"],"cluster":"frontier","description_excerpt":"axion DM, the spine-angle branch θ_i = π N_fam/g_car = 3π/5 (108°): an ALTERNATIVE, more robust misalignment angle than the determinant-line hilltop θ_i≈170° (v185, which over-produces Ω_a h²≈0.66). [I] rational motive θ_i=π N_fam/g_car=3π/5=108° exactly (spine quotient 3/5, no fit); [N] the v185 finite-T solver (θ=1→0.03) reaches Ω_DM at θ≈106°, so 108° is essentially on target (harmonic 0.03θ²=0.107); [C] ROBUST: 1","id":"python_verification:verification/v211_axion_spine_angle.py","line_count":103,"path":"verification/v211_axion_spine_angle.py","sha256":"eb14ea64a938bf6f2c901275d35226988951eed075d62663dfe9cb6763d0ce9b","type":"python_verification"},{"bytes":5988,"checked_by_registry":false,"claim_ids":["FR.ETAB.04"],"cluster":"frontier","description_excerpt":"leptogenesis, the scalaron-decuple branch: both Boltzmann inputs share the decuple A_Λ=10=|E(K₅)| — M₁=M_scal φ₀²/A_Λ≈8.65×10⁹ GeV and m̃₁=m₃/A_Λ≈5 meV. A cleaner [C] route than v184's M₁=M_R φ₀⁴ (which only relocated the free input to the un-pinned seesaw M_R). [I] shared decuple A_Λ=10; [N] M₁=M_scal φ₀²/A_Λ=8.65×10⁹ GeV (M_scal=c₃^{7/2} M̄≈3.06×10¹³, φ₀≈0.053172) inside the thermal window [3×10⁹,3×10¹⁰] (v169); [N","id":"python_verification:verification/v212_leptogenesis_decuple.py","line_count":113,"path":"verification/v212_leptogenesis_decuple.py","sha256":"d9e03b2839a38b6cdf436ac66ed81dbe30f13573ec88952e156ab100b13e1d5e","type":"python_verification"},{"bytes":7307,"checked_by_registry":false,"claim_ids":["CONTRACT.F.01"],"cluster":"frontier","description_excerpt":"the F_transfer FUNCTOR CONTRACT (CONTRACT.F.01): the four frontier transfers are ONE typed functor F_transfer = F_observable∘F_threshold∘F_RG with four structural axioms, each instance a discrete compiler kernel [E/I] composed with an external continuous solver [C/O]; consolidates v183 (F_pole), v212 (F_Boltzmann), v211 (F_relic), v164/FR.MPME (F_QCD), the structural complement of the v187 typing guard. [I] axiom 1 μ","id":"python_verification:verification/v213_ftransfer_functor.py","line_count":129,"path":"verification/v213_ftransfer_functor.py","sha256":"278d24d76f72d0c28495556b2db4cfcfe4d35bbf73a7216af88b57b35325fa02","type":"python_verification"},{"bytes":8591,"checked_by_registry":false,"claim_ids":["QGEO.PILLOW.01"],"cluster":"registry","description_excerpt":"the PILLOWCASE reduction of QGEO.SYM.01 (QGEO.PILLOW.01): the two separately-tracked open QGEO residuals — v180/QGEO.ISO.01 (the carrier clock is an order-4 isometry of the seam metric) and v201/QGEO.SUBPRIN.01 (the DtN sub-principal symbol is mark-local, the seam flat away from the μ4 marks) — are ONE statement, 'the seam carries the uniformising flat orbifold (pillowcase) metric', and the order-4 clock is DERIVED f","id":"python_verification:verification/v214_seam_pillowcase.py","line_count":150,"path":"verification/v214_seam_pillowcase.py","sha256":"71169a6c9b78ca1c3f240f0ac92c669e2905db9237658f6e54369ca023f4fd15","type":"python_verification"},{"bytes":10261,"checked_by_registry":false,"claim_ids":["QGEO.KILL.01"],"cluster":"registry","description_excerpt":"the bedrock QGEO.SYM.01 (ω∘ρ=ω) recast as a FALSIFIABLE kill-test (QGEO.KILL.01), not a proof-promise — a foundational symmetry cannot be derived from nothing (v181/v153), and Bisognano–Wichmann would presuppose the covariance it should produce. Non-circular reduction (v198/v199/v201): ω∘ρ=ω ⟺ [ρ,C]=0; the principal symbol |k| commutes exactly, so the residual is the sub-principal M_f with [ρ,M_f]=0 ⟺ f Z4-invariant;","id":"python_verification:verification/v215_seam_deck_killtest.py","line_count":184,"path":"verification/v215_seam_deck_killtest.py","sha256":"f4c6c0d0dc29067102b23b5b9fdfb128eab37e7946222f8efab9a36dcae75808","type":"python_verification"},{"bytes":7241,"checked_by_registry":false,"claim_ids":["QGEO.MARKS.03"],"cluster":"registry","description_excerpt":"the FOUR seam marks EMERGE from Gauss-Bonnet (QGEO.MARKS.03), executing the K1 lever of the v215 kill-test. [E] mark count = 2χ: Z2 branch points (deficit π) on a flat sphere (χ=2) give n·π = 2π·χ = 4π ⟹ n = 2χ = 4 = |μ4| = e1(a) = N_fam+1 (the same χ=2 as the 8 in c3=1/(8π)). [E] the Euclidean sphere 2-orbifolds (χ_orb=0) are exactly (2,3,6),(2,4,4),(3,3,3),(2,2,2,2). [E] all-order-2 (the |Z2| sheet branch) ⟹ unique","id":"python_verification:verification/v216_marks_gauss_bonnet.py","line_count":131,"path":"verification/v216_marks_gauss_bonnet.py","sha256":"a1b618c30d42a71d5636787c9744251018103f3f2cdecd310a072987f77fab3f","type":"python_verification"},{"bytes":8095,"checked_by_registry":false,"claim_ids":["QGEO.EMERGE.01"],"cluster":"registry","description_excerpt":"the NUMERICAL emergence scan (QGEO.EMERGE.01, sibling of v216 as v210 is to v201): with the number of marks n AND their positions FREE, the 4-equally-spaced (square) config is the joint minimiser of {clock-invariance + 3-family cohomology + transfer gap (2/3)⁶} on the actual seam DtN/state. [N] n=4 equally-spaced ⟹ ‖ρ4 C ρ4†−C‖~1e-14 (clock-invariant state); [N] family count selects n=4 (scan n∈{2..8}, only n−1=3=N_f","id":"python_verification:verification/v217_marks_emergence_scan.py","line_count":163,"path":"verification/v217_marks_emergence_scan.py","sha256":"3a92a84d660c5c15ebf66464e2528503b84255923602551ea4a591ad19962de5","type":"python_verification"},{"bytes":11342,"checked_by_registry":false,"claim_ids":["DIAMOND.AXIS.01","DIAMOND.PLUCKER.01","DIAMOND.SPECTRAL.01"],"cluster":"registry","description_excerpt":"Diamond axis geometry: the Sheet Diamond (v94) is a discrete geometry with two axes around the centered cross (v95: C center, U winding, V sheet), and the missing corner F is the transfer completion. Three exact [E] lemmas + honest audit/heuristic typing, no new numbers. [E] AXIS CURVATURE: det(C+xU)=14+6x linear (winding flat, slope 6=|R⁺(A₃)|), det(C+yV)=14+14y+4y² quadratic with 2nd difference 8=rank E₈; det B(C+x","id":"python_verification:verification/v218_diamond_axis_geometry.py","line_count":216,"path":"verification/v218_diamond_axis_geometry.py","sha256":"573a712170900ef327b7ff5188a229201678d76d90e884b02f9792017fd9b0cd","type":"python_verification"},{"bytes":11631,"checked_by_registry":false,"claim_ids":["MCKAY.E8.01"],"cluster":"core","description_excerpt":"McKay bedrock: WHY the atoms are 2,3,5. E₈ is the exceptional TOP of the McKay tower of finite SU(2) subgroups (2T→Ê₆, 2O→Ê₇, 2I→Ê₈). The McKay graph is BUILT from the group: the 120 icosians close to 2I (orders {1,2,3,4,5,6,10}, containing the 2,3,5 axes), 9 conjugacy classes, Dixon irrep degrees {1,2,2,3,3,4,4,5,6} (sum 30=h(E₈), sum² 120=|R⁺(E₈)|); the natural-rep McKay adjacency IS the affine E₈ graph with marks ","id":"python_verification:verification/v219_icosahedral_mckay.py","line_count":285,"path":"verification/v219_icosahedral_mckay.py","sha256":"1281629938617cf116c578e085686bb9f35591f77f5eb240573922914023f0a1","type":"python_verification"},{"bytes":3748,"checked_by_registry":false,"claim_ids":["FLAV.SOLAR.02"],"cluster":"neutrinos","description_excerpt":"solar coeff = q(A₃) = 3/4; sin²θ₁₂ = 1/3 − φ₀/2","id":"python_verification:verification/v21_solar_product_quark.py","line_count":74,"path":"verification/v21_solar_product_quark.py","sha256":"de503a11f70d3750b09132a71a0e1c8a6a55025e4d0aac3fd93222c601b9082f","type":"python_verification"},{"bytes":4373,"checked_by_registry":false,"claim_ids":["CP.MOD.01"],"cluster":"flavor","description_excerpt":"CP lives in the HEXAGONAL phase fiber, not the square seam deck (a geometric sharpening of red-team Target D). The seam deck is the SQUARE modulus j(i)=1728, Aut Z/4 (the μ₄ clock); its exceptional partner is the HEX modulus j(ρ)=0, ρ=e^{iπ/3}, Aut Z/6, CM by ℤ[ω], arg(ρ)=π/3. The frozen leading CKM reading δ=π/3+3λ_C²=68.654° (v88) has leading term π/3=arg(ρ); the |Z₂| alternative π/3+2λ_C² is the frozen look-elsewh","id":"python_verification:verification/v220_cp_hexagonal_modulus.py","line_count":85,"path":"verification/v220_cp_hexagonal_modulus.py","sha256":"b3b07f2cdfcb6632febbab9a88e4b6b1fc9200984f9da88afcdcde81f4fbeb74","type":"python_verification"},{"bytes":5632,"checked_by_registry":false,"claim_ids":["QEC.SEAM.01"],"cluster":"horizon","description_excerpt":"The seam as a FINITE recoverability code (recovery rate (2/3)⁶=64/729). Code dimension dim S⁺=16=2^(g_car−1); the gapped transport T on the cusp-weight 3-space (deviations (1,−1,0) and the Nariai anchor (1,1,−2)) is symmetric, doubly stochastic (CPTP), spectrum {1,(2/3)⁶,(1/3)⁶}; on the trace-zero subspace ||T δ||≤(2/3)⁶||δ|| so ||Tⁿ δ||≤(2/3)^{6n}||δ|| (Knill-Laflamme-type bound); a free ratio breaks it. Holographic","id":"python_verification:verification/v221_seam_qecc.py","line_count":112,"path":"verification/v221_seam_qecc.py","sha256":"4bb7156fd414a388f64979d0df66ab139aca04291a33bf9de0cc6ed663d30fac","type":"python_verification"},{"bytes":4681,"checked_by_registry":false,"claim_ids":["CMNORM.DUAL.01"],"cluster":"core","description_excerpt":"CM-norm duality: the two exceptional moduli give 41 and 7. SQUARE (Gaussian ℤ[i], j=1728): N(g_car+i|μ₄|)=5²+4²=41=10b₁ (the EM index IS the Gaussian norm of the carrier-glue vector); N(3+2i)=13=Δ_Q. HEX (Eisenstein ℤ[ω], j=0): N(3+2ω)=3²−3·2+2²=7=scalaron. The (3,2)=(colour,weak) split generates (5,6,7,13) by sum/product/Eisenstein/Gauss norm; rings rigid (Eisenstein of (5,4)=21≠41).","id":"python_verification:verification/v222_cm_norm_duality.py","line_count":96,"path":"verification/v222_cm_norm_duality.py","sha256":"2b4bb2c93f06a91203863bca753f6f5f7b128917c933f0050a7470e0f3c5f105","type":"python_verification"},{"bytes":4667,"checked_by_registry":false,"claim_ids":["COX.CLOCK.01"],"cluster":"horizon","description_excerpt":"The μ₄ clock is the order-4 character of the E₈ Coxeter cycle. (ℤ/30)ˣ={1,7,11,13,17,19,23,29}=the E₈ exponents=live Coxeter phases; φ(30)=8=rank E₈, 30=2·3·5. (ℤ/30)ˣ≅ℤ/4×ℤ/2 with order-4 generator 7 (7²=19,7⁴=1 mod 30): a literal μ₄ clock ⟨7⟩={1,7,13,19} on the exponents; conjugate pairs m+(30−m)=30 give |μ₄|=4 invariant planes the clock permutes. Only E₈ has φ(h)=rank AND h=2·3·5.","id":"python_verification:verification/v223_coxeter_totative_clock.py","line_count":96,"path":"verification/v223_coxeter_totative_clock.py","sha256":"16d842f84eb65ef8b98cc4ab256436eca92eb1a8985a891bc869bf3e6c7c6571","type":"python_verification"},{"bytes":4814,"checked_by_registry":false,"claim_ids":["FTR.PATH.01"],"cluster":"masses","description_excerpt":"F_transfer as ONE path on the Sheet Diamond, not four external interfaces. Family M(s,t)=R+Q diag(s,t,t): the transfer corners K=M(1,−1),C=M(1,0),F=M(1,1) lie on the SHEET axis (s=1). The sheet axis is curved det M(1,t)=4t²+14t+14 (2nd diff 8=rank E₈), the winding axis det M(s,0)=6s+8 flat (slope 6=|R⁺(A₃)|); Plücker ladder Pl(C)−Pl(K)=(1,8,10), Pl(F)−Pl(C)=(1,8,16). F_transfer = the K→C→F sheet geodesic, Koide sourc","id":"python_verification:verification/v224_diamond_ftransfer_path.py","line_count":110,"path":"verification/v224_diamond_ftransfer_path.py","sha256":"1c3ac6a33dab79b97867224405001cb4167dfa2210ceb372d8117222b918a1ae","type":"python_verification"},{"bytes":4241,"checked_by_registry":false,"claim_ids":["DUAL.FRAME.01"],"cluster":"flavor","description_excerpt":"The dual normal frame (d,n): one boundary compass for flavor+horizon, with CP as orientation. d=aᵀR⁻¹=aᵀL⁻¹=(−1/2,−1/2,1)=−½(1,1,−2) (the Nariai/horizon normal; d·1=0, d·a=1); n=(5,−9,6) with nᵀR=(det R,0,0)=(8,0,0), nᵀL=(20,0,0) (first-generation/torsion selector). Oriented volume det(1,d,n)=21=N_fam·scalaron. CP as orientation: Im det(1,d,ρn)=21 sin(π/3) for ρ=e^{iπ/3} — CP sits where the magnitude bijection (Targe","id":"python_verification:verification/v225_dual_normal_frame.py","line_count":87,"path":"verification/v225_dual_normal_frame.py","sha256":"bd525c278639fe0b204d04137e0e7aa0f720c302760c5526b4b50bfb17672f3a","type":"python_verification"},{"bytes":3385,"checked_by_registry":false,"claim_ids":["E8.CHAN.01"],"cluster":"core","description_excerpt":"248=120+128 as a magnitude/phase channel typing (replaces the over-strong S⁻-dark-matter reading). E₈ exponents {1,7,11,13,17,19,23,29} sum 120=|R⁺(E₈)| (MAGNITUDE channel); E₈ degrees {2,8,12,14,18,20,24,30} sum 128=2^(rank−1)=rank·dim S⁺ (PHASE/GLUE channel); 248=120+128=adj(D₈)+spinor(D₈); deg−exp sum=rank=8. Ratios+products (Target D) live in 120, the un-covered CP phases in 128; the dark-sector reading of 128 st","id":"python_verification:verification/v227_degree_exponent_channel_split.py","line_count":66,"path":"verification/v227_degree_exponent_channel_split.py","sha256":"c750c5787b27b5627cc35dde3c333fd56be5f2c0bfd39b760a0dcbdc1acff600","type":"python_verification"},{"bytes":3834,"checked_by_registry":false,"claim_ids":["QGEO.RR.01"],"cluster":"core","description_excerpt":"P2 as the mode space of a degree-4 seam divisor (a Riemann-Roch INDEX GATE; bedrock language for P2, not a proof from nothing). deg D=4=|μ₄| on P¹ ⇒ h⁰(O(D))=5=g_car (Riemann-Roch, genus 0); rank H₁(P¹ minus 4 marks)=3=N_fam; h⁰+rankH₁=8=rank E₈, h⁰−rankH₁=2=|Z₂|; Λᵉᵛᵉⁿ(C⁵)=1+10+5=16=dim S⁺. Conditional on the raw seam producing the degree-4 divisor (=QGEO.SYM.01).","id":"python_verification:verification/v228_rr_index_gate.py","line_count":80,"path":"verification/v228_rr_index_gate.py","sha256":"eabd3597d3bd5418a88b860523eb1bda7bf6b0432e1e874772a8d1aeb864934c","type":"python_verification"},{"bytes":4528,"checked_by_registry":false,"claim_ids":["LEP.FROB.01"],"cluster":"masses","description_excerpt":"The charged leptons as an étale Frobenius algebra over the μ₆ resolvent. Exact coefficients (c_e,c_μ,c_τ)=(16/7,4/3,7/6), ring closure c_e c_τ=8/3=|Z₂|c_μ, product 32/9=2^g_car/N_fam². A=ℚ[t]/(m), m=∏(t−c): the trace-form Gram is nondegenerate (det=disc(m)≠0, A étale) — a commutative Frobenius algebra. The C₆ shift has charpoly t⁶−1 (spectrum μ₆=μ₃ family ×μ₂ sheet). PMNS extension via Aut(A)+the hex CM point is [C].","id":"python_verification:verification/v229_lepton_frobenius_algebra.py","line_count":91,"path":"verification/v229_lepton_frobenius_algebra.py","sha256":"f6fd90fe244764528a3a4144769a6d780bd3fdd6c88dfd284712e37e92d41b7e","type":"python_verification"},{"bytes":4016,"checked_by_registry":false,"claim_ids":["GATE.QGEO.01","GATE.RU.01","GATE.NSTAR.01","GATE.METRIC.01"],"cluster":"frontier","description_excerpt":"residual-gates audit: forced part vs named residual","id":"python_verification:verification/v22_open_gates_audit.py","line_count":76,"path":"verification/v22_open_gates_audit.py","sha256":"bdf736fccbe5083cfe34a33d99d44208a8de889f617dc94151790f1006a8fd82","type":"python_verification"},{"bytes":3122,"checked_by_registry":false,"claim_ids":["CENTER.NORM.01"],"cluster":"flavor","description_excerpt":"The Sheet-Diamond center budget (7,11,13) is the three LOCAL NORMS of the theory. C=R+Q diag(1,0,0), row sums (7,11,13): 7=N_ℤ[ω](3+2ω) (Eisenstein/hex = scalaron), 13=N_ℤ[i](3+2i) (Gauss/square = Δ_Q), 11=C(4,0)+C(4,1)+C(4,2)=1+4+6 (QBL boundary Fock count on 4 μ₄ corners=dim S⁺−g_car=16−5). The two CM rings (v222) and the seam boundary count meet in one operator center; the ring assignment is rigid.","id":"python_verification:verification/v230_center_budget_norms.py","line_count":78,"path":"verification/v230_center_budget_norms.py","sha256":"bb8f9799f91891c2604351fee44f0fd8da1fb22c793b5f280ee076c8e826e61a","type":"python_verification"},{"bytes":5338,"checked_by_registry":false,"claim_ids":["CP.MU6.01"],"cluster":"flavor","description_excerpt":"Both CP phases are mu6 powers of ONE hexagonal CM unit, split by the sheet -- a structural reduction of red-team Target D. With rho=e^{i pi/3} (the j=0 Eisenstein CM unit): delta_CKM leading = arg(rho^1)=pi/3 (quark), delta_PMNS = arg(rho^4)=4pi/3 (lepton, the phase lattice); rho^4=-rho so delta_PMNS = delta_CKM,lead + pi = (CM unit)x(Z2 sheet, rho^3=-1) -- the two CP phases are ONE hexagonal unit on the two sheets, ","id":"python_verification:verification/v231_cp_mu6_phases.py","line_count":107,"path":"verification/v231_cp_mu6_phases.py","sha256":"9e3567f184de3b5ec14f21df3c969d89bf3953d69edc288c29a3b564ccad3b26","type":"python_verification"},{"bytes":5858,"checked_by_registry":false,"claim_ids":["TOPO.E8.01"],"cluster":"horizon","description_excerpt":"The seam as the E8 Kleinian singularity -- a canonical algebraic-geometric MODEL for the open seam-realisation premise QGEO.REALIZE.01 (the du Val side of the McKay correspondence, v219). The McKay graph of 2I is affine E8; dropping the unique trivial-rep node (single Kac mark=1) leaves the finite E8 Dynkin on 8 nodes = the dual intersection graph of the 8 exceptional P^1's of the minimal resolution of C^2/2I (trival","id":"python_verification:verification/v232_e8_kleinian_seam.py","line_count":110,"path":"verification/v232_e8_kleinian_seam.py","sha256":"c561d42e5b6d446d84726549ecf57dd6a878151b771b40fd70c24761c47a0c06","type":"python_verification"},{"bytes":6196,"checked_by_registry":false,"claim_ids":["CP.TRIALITY.01"],"cluster":"flavor","description_excerpt":"The CP phase is the UNIVERSAL family/triality phase, only sheet-split -- one step past v231 in mu6 = mu3 (family/triality) x mu2 (sheet). mu6=mu3 x mu2 (gcd(3,2)=1): the Z3 triality centre {1,omega,omega^2} = cusp weights {0,1/3,2/3}x2pi, sheet mu2={1,-1}; rho = omega^2*(-1). SAME FAMILY CLASS: rho^4 = rho^1*rho^3 with rho^3 in mu2, so quark (rho^1) and lepton (rho^4) CP phases have the SAME image in mu6/mu2~mu3 and ","id":"python_verification:verification/v233_cp_triality_phase.py","line_count":103,"path":"verification/v233_cp_triality_phase.py","sha256":"43b34998aa882f2207fc1ebaa74b67cf157a5c8de977a62afa363d8f0284b94c","type":"python_verification"},{"bytes":6443,"checked_by_registry":false,"claim_ids":["GATE.HOLO.01"],"cluster":"frontier","description_excerpt":"The Seam-Holomorphy selection certificate: the entire structural residual is ONE condition with THREE equivalent faces, all forcing E8. THE CONDITION: 'the seam carries no nontrivial abelian sector.' (i) AQFT: the boundary net is holomorphic (mu-index 1); (ii) geometry: the seam link is a homology 3-sphere <=> the binary group is perfect <=> 2I; (iii) rep theory: exactly one 1-dim irrep. #(mark-1 affine-Dynkin nodes)","id":"python_verification:verification/v234_seam_holomorphy_selection.py","line_count":117,"path":"verification/v234_seam_holomorphy_selection.py","sha256":"58b8eb3621fcb2705f5a2d8345c31340fd1d279fd5a8d0848e354624f3713396","type":"python_verification"},{"bytes":7140,"checked_by_registry":false,"claim_ids":["GATE.HOLO.02"],"cluster":"frontier","description_excerpt":"The closing step in abelian Chern-Simons language: holomorphic <=> det K = 1 -- a genuine reduction (not a closure) of GATE.HOLO.01 into standard anyon-condensation physics. A free gapped bosonic 2+1d bulk = an even integer K-matrix with #anyons = |det K|, edge c = signature(K), holomorphic <=> |det K| = 1. The TFPT extension tower (v92) IS the condensation tower read by det: carrier D5(+)A3 (det 16, 16 anyons) -> SO","id":"python_verification:verification/v235_seam_chern_simons.py","line_count":144,"path":"verification/v235_seam_chern_simons.py","sha256":"47c41d25a809275988e6118db9d2870ed535084da6d05cbca1abd52d03f2d8e3","type":"python_verification"},{"bytes":6099,"checked_by_registry":false,"claim_ids":["TOPO.BRIESKORN.01"],"cluster":"horizon","description_excerpt":"The (2,3,5) Brieskorn singularity x^2+y^3+z^5 is the ONE generator of the discrete skeleton -- the capstone of the icosahedral round (v55/v219/v223/v232/v233). Its exponents ARE the atoms (|Z2|,N_fam,g_car)=(2,3,5). Milnor number mu=(2-1)(3-1)(5-1)=1*2*4=8=rank E8 = the '8' in c3=1/(8 pi) (a fifth independent origin). The Milnor monodromy eigenvalues are the eight primitive 30th roots e^{2pi i m/30}, m the E8 exponen","id":"python_verification:verification/v236_brieskorn_capstone.py","line_count":108,"path":"verification/v236_brieskorn_capstone.py","sha256":"7ddf6def219c8ff696c59a76c9ac94ee4338bbc32ad992fc2a0cb0cfb2bed1b3","type":"python_verification"},{"bytes":6836,"checked_by_registry":false,"claim_ids":["GATE.HOLO.03"],"cluster":"frontier","description_excerpt":"The closing step as a PHYSICAL condition: no topological ground-state degeneracy <=> det K=1 <=> the seam bulk is short-range-entangled (SRE/invertible). Sharpens GATE.HOLO.02's residual from definitional to physical/falsifiable. The K-matrix ground-state degeneracy on a genus-g surface is |det K|^g (carrier D5(+)A3->16, D8->4, E8->1 on the torus), so 'no degeneracy on any closed surface' <=> det K=1. Among rank-8 ev","id":"python_verification:verification/v237_seam_sre_closure.py","line_count":131,"path":"verification/v237_seam_sre_closure.py","sha256":"6c3345697ad31f738a1930f79312aac2d9a586bcbf5a274ea624b801e61f8dd6","type":"python_verification"},{"bytes":10455,"checked_by_registry":false,"claim_ids":["DYN.SEMIGROUP.01"],"cluster":"registry","description_excerpt":"DYN.SEMIGROUP.01 — the STATIC→DYNAMIC flip: the seam's modular flow (reversible) and its recovery channel read as a Markov/Lindblad generator (irreversible), with the dissipative gap = the OS mass gap. Companion to v196/v198 (modular) and v221/v64 (recovery), which state the structure statically; this reads the SAME objects dynamically. [E] the modular flow σ_t=e^{i t Λ_Σ} is a unitary one-parameter group (Tomita–Tak","id":"python_verification:verification/v238_modular_lindblad_dynamics.py","line_count":181,"path":"verification/v238_modular_lindblad_dynamics.py","sha256":"7938425550d9ad7f199e875f22c52609f4eeeb25b9f51df9a49af508a3576645","type":"python_verification"},{"bytes":6138,"checked_by_registry":false,"claim_ids":["DYN.KMS.01"],"cluster":"registry","description_excerpt":"DYN.KMS.01 — KMS / thermal time: the modular flow of v238 makes the seam state a KMS (thermal) state at β=1, and the geometric normalisation fixes the seam temperature via 2π = 1/(4c3). [E] KMS at β=1: ω(A σ_i(B)) = ω(BA) (ω(X)=Tr(ρX), ρ=e^{−Λ_Σ}/Z), so modular time (v238) is a thermal time (Connes–Rovelli); NEG β≠1 fails (Tomita–Takesaki pins β=1). [E] the seam unit β_phys = 2π = 1/(4c3) (v58) makes the KMS temperat","id":"python_verification:verification/v239_kms_thermal_time.py","line_count":120,"path":"verification/v239_kms_thermal_time.py","sha256":"cac2d121c789de726085f83049cac1d45b251949571a27da9ea8029cba1735c5","type":"python_verification"},{"bytes":2595,"checked_by_registry":false,"claim_ids":["ANCHOR.GEN.01"],"cluster":"core","description_excerpt":"anchor a=(1,1,2): e_k=(4,5,2); power sums → 240, 248","id":"python_verification:verification/v23_anchor_generator.py","line_count":66,"path":"verification/v23_anchor_generator.py","sha256":"e782df61e9190f7087d3c93e2524388a037784f7d21d2a251399f195357982dd","type":"python_verification"},{"bytes":7421,"checked_by_registry":false,"claim_ids":["DYN.GNS.01"],"cluster":"registry","description_excerpt":"DYN.GNS.01 — GNS / OS reconstruction (finite toy): the Hilbert space and a POSITIVE Hamiltonian are OUTPUTS of the seam data (M, ω), not inputs. [E] GNS: ⟨A,B⟩=Tr(ρ A†B) Hermitian positive-definite (ρ>0), dim n², identity cyclic+separating. [E] modular flow σ_t(x)=ρ^{it} x ρ^{−it} is a state-preserving *-automorphism, generator i[log ρ,·]=Λ_Σ (v238). [E] OS Hamiltonian H_OS=−log T (the v221 transfer) is POSITIVE — ei","id":"python_verification:verification/v240_gns_os_reconstruction.py","line_count":143,"path":"verification/v240_gns_os_reconstruction.py","sha256":"9c2f5a46007479b3e2557d9406392a5067f28228c97e04f979925ce9cd854480","type":"python_verification"},{"bytes":6605,"checked_by_registry":false,"claim_ids":["DHR.SECTORS.01"],"cluster":"registry","description_excerpt":"DHR.SECTORS.01 — particles = DHR superselection sectors: the carrier discriminant/anyon content and the v235/v237 condensation tower as an abelian MTC. Carrier form (Lean-verified, FORM.GLUE.01): on Z4×Z4, q(x,y)=(5x²+3y²)/8 mod 1, θ(a)=e^{2πi q(a)}. [E] 16 sectors = Z4×Z4 (= det K_carrier = dim S⁺), fusion = abelian group law. [E] bosonic/condensable ⟺ θ=1 ⟺ isotropic ⟺ 5x²+3y²≡0 mod 8 — the six elements {(0,0),(1,1","id":"python_verification:verification/v241_dhr_sectors.py","line_count":137,"path":"verification/v241_dhr_sectors.py","sha256":"b6d5dac63b9118d2bf4362c9d751e944950bc19542fad4e6d1a4bc05328c2a85","type":"python_verification"},{"bytes":5563,"checked_by_registry":false,"claim_ids":["DHR.MODULAR.01"],"cluster":"registry","description_excerpt":"DHR.MODULAR.01 — spin-statistics and the modular (S,T) data of the carrier MTC: statistics + the fusion ring recovered from modular data + the anyon central charge c=8. Same MTC as v241 (Z4×Z4, q=(5x²+3y²)/8, θ=e^{2πi q}). [E] spin-statistics: T=diag(θ_a) → 6 bosons (θ=1), 2 fermions (θ=−1) = {(0,2),(2,0)}, 8 anyons. [E] modular S_ab=(1/√16)e^{−2πi B(a,b)} unitary, symmetric, S²=C (charge conjugation), S⁴=I. [E] Verl","id":"python_verification:verification/v242_spin_statistics_modular.py","line_count":121,"path":"verification/v242_spin_statistics_modular.py","sha256":"8855974b235303c015f8faed6da7058924dcd23d636f1d66480f83f445862278","type":"python_verification"},{"bytes":6721,"checked_by_registry":false,"claim_ids":["DHR.SMATRIX.01"],"cluster":"registry","description_excerpt":"DHR.SMATRIX.01 — scattering: the Haag–Ruelle skeleton + the braiding S-matrix. The seam net has a mass gap (v64/v238) so Haag–Ruelle constructs asymptotic states; for the abelian anyon MTC (v241/v242) the 2-particle S-matrix is the monodromy M(a,b)=θ(a+b)/(θ(a)θ(b))=e^{2πi B(a,b)}. [E] mass gap Δ=6 log(3/2)>0 → HR in/out states (gapped-net theorem). [E] 2-particle S = monodromy: |M|=1, diagonal in conserved anyon lab","id":"python_verification:verification/v243_haag_ruelle_braiding.py","line_count":137,"path":"verification/v243_haag_ruelle_braiding.py","sha256":"9eeb537e64ce255087f560799fa2e42eb93c5036ba9b36e4d41439e752103708","type":"python_verification"},{"bytes":6346,"checked_by_registry":false,"claim_ids":["CONTRACT.QFT4D.01"],"cluster":"registry","description_excerpt":"CONTRACT.QFT4D.01 — the 4d Lagrangian via Connes' spectral action: the honest contract for the Phase-3 gap (2d seam net → 4d physics). A single Dirac operator whose Tr f(D/Λ) yields gravity AND matter. [E] carrier spinor = one generation: SO(10) half-spinor = dim S⁺ = 2^(g_car−1) = 16 (15 + ν_R), N_fam=3. [E] SM gauge group inside the carrier: SU(3)×SU(2)×U(1) (dim 12) ⊂ SU(5) (24) ⊂ SO(10)=D5 (45); color SU(3) ⊂ A3=","id":"python_verification:verification/v244_spectral_action_contract.py","line_count":104,"path":"verification/v244_spectral_action_contract.py","sha256":"8cab7ef1ffcac6026ac3eda238d75cac0d95d296a32ccfd2500d6a32c5bc3a3c","type":"python_verification"},{"bytes":6434,"checked_by_registry":false,"claim_ids":["QFT4D.MATTER.01"],"cluster":"registry","description_excerpt":"QFT4D.MATTER.01 — the computable core of CONTRACT.QFT4D.01 (v244): the spectral-action / NCG matter content, discharging the rep-theory + tree-relation core to [E]. The carrier half-spinor is the SO(10) 16. [E] 16 = one generation: SO(10) 16 = SU(5)(10+5bar+1); SM dims 6+3+1+2+3+1 = 16 = dim S⁺, N_fam=3 (15 Weyl fermions + ν_R). 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[X] tension: pairwise crossings spread ~4 decades (a1=a2 ~1e13, a1=a3 ~2.4e14, a2=a3 ~1e17 G","id":"python_verification:verification/v246_unification_data_crosscheck.py","line_count":139,"path":"verification/v246_unification_data_crosscheck.py","sha256":"11670c7b129fbae1bd62e8fd210134d8e874fcf2afccce8265dff2c1c78b9fe7","type":"python_verification"},{"bytes":4859,"checked_by_registry":false,"claim_ids":["PS.E8BRANCH.01"],"cluster":"registry","description_excerpt":"PS.E8BRANCH.01 — the E8 audit hull forbids the 126 and supplies exactly {1,10,16,45} for SO(10). Carrier D5⊕A3 = SO(10)×SU(4) ⊂ E8 (via SO(16)); 248 = (45,1)+(1,15)+(10,6)+(16,4)+(16bar,4bar) = 248. [E] ranks 5+3=8; [E] dims=248 (SO(16): 120 adj + 128 spinor); [E] SO(10) content {1,10,16,45}, the 126 ABSENT → 126_H algebraically forbidden, 10+16+45 E8-supplied not fitted; [E] CAVEAT only one 45/one 15 → proton-margin","id":"python_verification:verification/v247_e8_branching_no126.py","line_count":96,"path":"verification/v247_e8_branching_no126.py","sha256":"16a43f14e53db9a4815e6c854b22e164e779ca97b89ca6c0371a8dc5c6f9a090","type":"python_verification"},{"bytes":5978,"checked_by_registry":false,"claim_ids":["PS.ALGEBRA.01"],"cluster":"registry","description_excerpt":"PS.ALGEBRA.01 — the Pati-Salam NCG algebra A_F = ℍ_L⊕ℍ_R⊕M₄(ℂ) and its exact SM matching. [E] unimodular group SU(2)_L×SU(2)_R×SU(4)_c (ranks 5, dims 21); [E] 16=(4,2,1)+(4̄,1,2)=8+8; [E] Y=T₃R+(B−L)/2 gives the exact SM hypercharges and Q=T₃L+Y the exact charges (B−L = SU(4)_c gen, lepton = 4th colour); [E] matching α1⁻¹=(3/5)α2R⁻¹+(2/5)α4⁻¹, sin²θ_W=3/8. 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Majora","id":"python_verification:verification/v252_full_finite_triple.py","line_count":375,"path":"verification/v252_full_finite_triple.py","sha256":"820254440e178430422e50605067775656236602996307f67c9e69124ba5d163","type":"python_verification"},{"bytes":6987,"checked_by_registry":false,"claim_ids":["PS.KAPPA.01"],"cluster":"registry","description_excerpt":"PS.KAPPA.01 — pinning κ in M_PS = κ·M_s, discharging residual 6(b) of v249. M_s = c₃^{7/2}·Mbar ≈ 3.06e13 GeV (exact). [E] scalaron scale exact; [E] κ pinned by RG (scan PDG errors × the two E8-allowed contents) to a tight O(1) interval ~1.3 (1-loop [1.0,1.7], 2-loop [1.0,1.2]) — pinned, not free. [C] heat-kernel origin: κ = √((f₂/f₀)·c_PS/c_grav), a ratio of heat-kernel traces over the 96-dim H_F (v252) — Λ cancels,","id":"python_verification:verification/v253_kappa_scalaron_ps.py","line_count":131,"path":"verification/v253_kappa_scalaron_ps.py","sha256":"7f36d33225a6a04788fbe88f82ae768813dbf1ac9c3ff6d783628faee2fb876c","type":"python_verification"},{"bytes":8050,"checked_by_registry":false,"claim_ids":["PS.NCG.FLUCT.01"],"cluster":"registry","description_excerpt":"PS.NCG.FLUCT.01 — the inner fluctuations Ω¹_D(A_F) of the finite Dirac operator computed explicitly (reuses the v252 triple); closes v250 #5 (Higgs content, not 126) + the no-junk obligation + the σ quantum numbers. [E] Ω¹_{D_F} purely chirality-odd → finite fluctuations are scalars; [E] no junk / no 126: SM-algebra 1-forms sit exactly in the Higgs-doublet pattern (the single (1,2)_{1/2}); [E] σ (ν_R Majorana) direct","id":"python_verification:verification/v254_inner_fluctuations.py","line_count":170,"path":"verification/v254_inner_fluctuations.py","sha256":"7a1e93470b65dc8aa56106aa420392a986e8448816f5aa624b44600a696b642c","type":"python_verification"},{"bytes":6549,"checked_by_registry":false,"claim_ids":["PS.SPECACT.01"],"cluster":"registry","description_excerpt":"PS.SPECACT.01 — the spectral-action heat-kernel (Seeley-DeWitt) expansion S = 2f₄Λ⁴a₀ + 2f₂Λ²a₂ + f₀a₄ over the finite triple; closes v252 #11 (spectral-action expansion) and makes κ(f₂/f₀) explicit. [E] expansion structure (a₀ cosmological, a₂ Einstein-Hilbert+Higgs-mass, a₄ Yang-Mills+Weyl²+R²+Higgs-quartic, N=96); [E] trace inputs b/a²=1/3 (top-dominated, Chamseddine-Connes); [E] sin²θ_W=3/8 (cross-check v245); [C","id":"python_verification:verification/v255_spectral_action_expansion.py","line_count":120,"path":"verification/v255_spectral_action_expansion.py","sha256":"7fa2b814d4da3e944c8e3de8261a708dda9c05b4ac89bff44a773a70020a7427","type":"python_verification"},{"bytes":6205,"checked_by_registry":false,"claim_ids":["PS.NCG.ORIENT.01"],"cluster":"registry","description_excerpt":"PS.NCG.ORIENT.01 — orientability and Poincaré duality treated honestly (no faked proof). KO-dim 6 forces the intersection form cap(p,q)=Tr(γ π(p) J π(q) J⁻¹) to be antisymmetric. 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[E] strict orientability fails (γ not in span{λ(a)ρ(b)});","id":"python_verification:verification/v257_quasiorient_modpd.py","line_count":127,"path":"verification/v257_quasiorient_modpd.py","sha256":"67e548d61614fb083f56a72e62f5037959ac26106e892c7c00eef7bbd3de4d8e","type":"python_verification"},{"bytes":8838,"checked_by_registry":false,"claim_ids":["PS.DIRAC.03"],"cluster":"registry","description_excerpt":"PS.DIRAC.03 — D_F is the modular/covariance INDUCTION of the boundary seam state, not an independent posit; closes the 'posited Yukawa vs derived operator' gap of v250/v252 (Q2: Dirac as Kasparov product + covariance formula). 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[E] KMS cutoff moments f_0=f(0","id":"python_verification:verification/v259_modular_cutoff_kappa.py","line_count":118,"path":"verification/v259_modular_cutoff_kappa.py","sha256":"cc4ed41b68b91dba52e8e30552a41e671bba1d84a1c03837455c96c5121c18b8","type":"python_verification"},{"bytes":2300,"checked_by_registry":false,"claim_ids":["FR.KOIDE.02","FR.DM.02"],"cluster":"frontier","description_excerpt":"conjectures: Koide φ₀/24; axion f_a = M_scal/128","id":"python_verification:verification/v25_frontier_conjectures.py","line_count":51,"path":"verification/v25_frontier_conjectures.py","sha256":"427162816e5e036fff89aa3c3f71a082498262409d1c244c219c4bbeacb595c4","type":"python_verification"},{"bytes":8894,"checked_by_registry":false,"claim_ids":["ARCH.K3.01"],"cluster":"registry","description_excerpt":"ARCH.K3.01 — one Kummer/K3 surface carries the SEAM, the CARRIER-16 and the E8 lattice as facets of one smooth object, the geometric unification of the v1 'glue D5(+)A3 + mu4 => E8' step (the K3/Kummer proposal). The seam square torus tau=i (j=1728, v214) under the elliptic involution z->-z squares to the Kummer K3. [E] E8 Cartan even, det 1, positive-definite (the unique even unimodular pos-def rank-8 lattice); [E] ","id":"python_verification:verification/v260_k3_kummer_unification.py","line_count":171,"path":"verification/v260_k3_kummer_unification.py","sha256":"c9c485642e8fec784ba6bb84df03805660cd2bf2f03d7d00f8815e9ead8a40c4","type":"python_verification"},{"bytes":10108,"checked_by_registry":false,"claim_ids":["QFT.MSC.01"],"cluster":"registry","description_excerpt":"QFT.MSC.01 — the MODULAR SPECTRAL CLOSURE: the assembly/reduction certificate turning the whole QFT layer (v238-v260) into ONE relative object TFPT_QFT=(A_Sigma,omega_Sigma,Delta_Sigma,rho,A_F,H_F,D_F,J,gamma,S_rel) reduced to ONE open premise (like v176/v234, an assembly cert, not new physics). [E] one index=marks=fixed points=glue order: Jones [B:A]=4 (v89) = |mu4|=4 (v92) = seam marks 2chi=4 (v216) = pillowcase/Ku","id":"python_verification:verification/v261_modular_spectral_closure.py","line_count":179,"path":"verification/v261_modular_spectral_closure.py","sha256":"48b45cf116968f3f225fc1691d08ac11e466d7faca0948c6a413bc10897b03d0","type":"python_verification"},{"bytes":6330,"checked_by_registry":false,"claim_ids":["FR.MPME.02"],"cluster":"registry","description_excerpt":"FR.MPME.02 — the F_QCD transfer pipeline for m_p/m_e, implemented as a real solver (the one F_transfer pipeline that was contract-only, experiments/ftransfer/qcd_matching_mp_me). NOT a compiler power -- a [C] standard-physics transfer reproduction. 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[E] M_nu=-m_D M_R^{-1} m_D^T symmetric + seesaw-suppressed (light masses an output of D_F, not a fit matrix); [E] mu-tau-symmetric (m_D,M_R) give mu-tau-symmetric M_nu (the v9 texture is in the seesaw image); [C] diagonalising gives theta23","id":"python_verification:verification/v263_mnu_from_df.py","line_count":130,"path":"verification/v263_mnu_from_df.py","sha256":"f478d883111fee3aa35045798eb9f5b293bf9bd4b02995f4086ae60d11b1d02c","type":"python_verification"},{"bytes":7010,"checked_by_registry":false,"claim_ids":["QGEO.ENERGY.03"],"cluster":"registry","description_excerpt":"QGEO.ENERGY.03 — the raw-seam => mark-locality REDUCTION (NOT a closure of QGEO.SYM.01). 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[E] c=8 (Sugawara, 248/31=g_car+N_fam), but c=8 alone does not pin the net; [E] the discriminator is holomorphy — det Cartan(E8)=1 (1 primary, holomorphic) vs the c=8 counterexample det Cartan(D8=SO(16))=4 (4 primar","id":"python_verification:verification/v277_seam_calderon_e8_match.py","line_count":122,"path":"verification/v277_seam_calderon_e8_match.py","sha256":"fb151c3f0d8e523d1c96710d79057964c0800aa3cd45913e9c090d33145921da","type":"python_verification"},{"bytes":6200,"checked_by_registry":false,"claim_ids":["QFT4D.SPERT.04"],"cluster":"registry","description_excerpt":"QFT4D.SPERT.04 — the S_pert → S_phys LSZ bridge + one-loop unitarity: connects the EG perturbative S-matrix (v269/v271/v273) to the physical asymptotic S-matrix (S_phys = LSZ on the OS Wightman functions, v240). 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[E] character orthogonality: a mark-sourced curvature f=Σ_{j<4} g(θ−jπ/2) has Fourier support only on m≡0 mod 4 (nonzero modes {0,±4,±8,±12}; the 4th-root mark sum Σ_{j<4}((−i)^m)^j=4[4|m]); [E] ","id":"python_verification:verification/v288_full_l2_subprincipal_z4.py","line_count":133,"path":"verification/v288_full_l2_subprincipal_z4.py","sha256":"e9d63abaf30c619b8a757dd9d2f78a41a911c4f81a1258a157d006a638cf87e7","type":"python_verification"},{"bytes":7640,"checked_by_registry":false,"claim_ids":["MARKLOCAL.RAW.01"],"cluster":"frontier","description_excerpt":"MARKLOCAL.RAW.01 — decompose the ONE remaining Route-B residual ('why is the raw seam sub-principal term mark-local?') into a 5-lemma chain and isolate the single open analytic lemma. [C] L1 conic parametrix: conic Steklov DtN = |D_θ| + M_f + cone sources (b-calculus/Melrose, imported); [O] L2 FLAT-AWAY — the one open analytic lemma: RP+gap+4 marks ⇒ curvature vanishes away from the marks (the flat-pillowcase realisa","id":"python_verification:verification/v289_marklocal_raw.py","line_count":135,"path":"verification/v289_marklocal_raw.py","sha256":"a6ecfd3f4e254e3bf8730d861e64e40389c366a37db64136b51f1392f5e9379b","type":"python_verification"},{"bytes":2779,"checked_by_registry":false,"claim_ids":["CONTRACT.G.01","GRAV.FR.01"],"cluster":"gravity","description_excerpt":"R + R² closed: f(R), scalaron c₃^(7/2)M̄; n_s, r, A_s","id":"python_verification:verification/v28_gravity_fR.py","line_count":64,"path":"verification/v28_gravity_fR.py","sha256":"d9d92706e7362d7cf0f621d7ea1d0a58127d45a85d9c40903ecda1a30117142f","type":"python_verification"},{"bytes":6504,"checked_by_registry":false,"claim_ids":["SEAM.ADVERSARY.01"],"cluster":"frontier","description_excerpt":"SEAM.ADVERSARY.01 — the Route-B red-team that Z4 block-diagonality is NOT mark-locality. 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[E] SPECTRAL-RIGIDITY route: scanning f=ε·cos(4θ), the spectrum deviation from the flat ladder is 0 only at ε=0 and grows with |ε| — flat is th","id":"python_verification:verification/v291_flataway_contract.py","line_count":112,"path":"verification/v291_flataway_contract.py","sha256":"80bb241fd50aed6f25f4f1713ea4b72837a415a41b31f30b66b6827a288de046","type":"python_verification"},{"bytes":5576,"checked_by_registry":false,"claim_ids":["FLATAWAY.HEAT.01"],"cluster":"frontier","description_excerpt":"FLATAWAY.HEAT.01 — the Heat-Kernel route made precise: reduces Flat-Away to ONE named spectral invariant. [E] the heat-trace deviation ΔTr(e^{−tΛ}) = c(t)ε²+O(ε⁴) is a positive-definite quadratic form in the off-mark curvature (c_k(t)>0 for every Z4 mode 4k: 0.066/0.047/0.033; positive on all combinations, no cancellation), so ΔTr=0 ⟺ f=0; leading invariant ‖f‖_L² (Parseval). [O] reduction: Flat-Away ⟸ 'the seam fixe","id":"python_verification:verification/v292_flataway_heat_reduction.py","line_count":114,"path":"verification/v292_flataway_heat_reduction.py","sha256":"863e71c71f7fafcc1f497f1efcf9e20627defe17fd47950a7d7015f0a98d3663","type":"python_verification"},{"bytes":6259,"checked_by_registry":false,"claim_ids":["FLATAWAY.SPEC.01"],"cluster":"frontier","description_excerpt":"FLATAWAY.SPEC.01 — the Spectral-Rigidity route upgraded from one direction (v291) to the FULL smooth-Z4 space. [E] splitting mechanism: the degenerate flat Steklov level |n| is split by mode 4k at |n|=2k by ±ε/2 (modes 4,8,12 split levels 2,4,6); [E] S=Σ(Δλ)² ~ 0.50ε² (quadratic); [E] the Hessian over modes {4,8,12} has eigenvalues ~{0.497,0.500,0.503}>0, so the flat seam is a STRICT isolated minimum over the whole Z","id":"python_verification:verification/v293_flataway_spectral_hessian.py","line_count":136,"path":"verification/v293_flataway_spectral_hessian.py","sha256":"088902cf254816e795d5d2d39beb25be1c2435f6397aca62c9127e7bfcbc6529","type":"python_verification"},{"bytes":6452,"checked_by_registry":false,"claim_ids":["FLATAWAY.ENERGY.01"],"cluster":"frontier","description_excerpt":"FLATAWAY.ENERGY.01 — the RP-energy / Troyanov route: the flat pillowcase is the unique constant-curvature minimiser at the fixed mark divisor. [E] prescribed divisor + Gauss-Bonnet: S² with 4 cone angles π, Σ(2π−θ)=4π=2πχ; [C] Troyanov/Euclidean-cone uniqueness: the prescribed cone divisor carries a UNIQUE constant-curvature (flat) metric (Troyanov 1991), excluding smooth off-mark curvature; [E] strictly convex curva","id":"python_verification:verification/v294_flataway_rp_energy.py","line_count":112,"path":"verification/v294_flataway_rp_energy.py","sha256":"1adc345d5f4b29ca3346579fa43b981eef6bbc959a288f21e0f8ff01242f2262","type":"python_verification"},{"bytes":8092,"checked_by_registry":false,"claim_ids":["FLATAWAY.A2.01","FORM.FLATAWAY.01"],"cluster":"frontier","description_excerpt":"FLATAWAY.A2.01 — the EXACT analytic a₂ coefficient, upgrading the v292 positive-definiteness from numerical to a proof. [E] first variation vanishes: d/dε Tr e^{−tΛ(ε)}|₀ = −t f̂(0) Σe^{−t|n|} = 0 (smooth off-mark curvature has zero mean, Gauss-Bonnet); [E] convexity ⇒ global minimum: φ(x)=e^{−tx} strictly convex ⇒ Λ↦Tr e^{−tΛ} convex (Klein/Peierls), so ε=0 is the GLOBAL minimum and ΔTr≥0 for ALL ε (verified even in","id":"python_verification:verification/v295_flataway_a2_exact.py","line_count":150,"path":"verification/v295_flataway_a2_exact.py","sha256":"4970641d0c43e0c1a06a62e84037fa04b67da753d2ca0f28aa39cd600c2919dd","type":"python_verification"},{"bytes":6512,"checked_by_registry":false,"claim_ids":["FLATAWAY.A2.CLOSED.01"],"cluster":"frontier","description_excerpt":"FLATAWAY.A2.CLOSED.01 — the exact a₂ coefficient in CLOSED FORM (replacing v295's validated-numeric sum). [E] the operator tails telescope to a geometric series (Φ(n,n+4k)=e^{−nt}C_k/(16k²), C_k+D_k e^{−4kt}=4kt(1−e^{−4kt})), giving W_k^tail=t(1−e^{−4kt})/(8k(1−e^{−t})); [E] the middle is finite (4k−1 terms incl. the degenerate diagonal Φ(2k,2k)=(t²/2)e^{−2kt}); [E] closed form W_k(t)=t(1−e^{−4kt})/(8k(1−e^{−t}))+½Σ_","id":"python_verification:verification/v296_flataway_a2_closed.py","line_count":125,"path":"verification/v296_flataway_a2_closed.py","sha256":"31d745feef3d1827ff3953d4ac310f391b296a8bb03131e88419474645e530b0","type":"python_verification"},{"bytes":6487,"checked_by_registry":false,"claim_ids":["SEAM.EQUIV.A.LIT.01"],"cluster":"frontier","description_excerpt":"SEAM.EQUIV.A.LIT.01 — Route A's 'one standard import' written out as a precise CITABLE theorem stack. [E] LIT-A invertible/SRE bulk ⇒ trivial bulk topological order (Kitaev, Ann.Phys.321 2006; Freed-Hopkins, Geom.Topol.25 2021); [E] LIT-B bulk MTC = Drinfeld center, trivial center ⇒ holomorphic boundary net (Müger, JPAA 180 2003; Kawahigashi-Longo-Müger, CMP 219 2001); [E] LIT-C holomorphic c=8 net ⇒ (E8)₁ (Conway-Sl","id":"python_verification:verification/v297_route_a_literature_stack.py","line_count":108,"path":"verification/v297_route_a_literature_stack.py","sha256":"d2357d89823d46ab2d4f5d1fe19c84ede0b844e7e981f483a9865fc93184ad02","type":"python_verification"},{"bytes":6792,"checked_by_registry":false,"claim_ids":["E8.NETWORK.01"],"cluster":"frontier","description_excerpt":"E8 as a network attractor — a computational-substrate (Wolfram-program) reading of the (2,3,5)/McKay hull, on the v219 bedrock; an HONEST audit of the 'TFPT as hypergraph' idea, not a derivation. [E] the E8 Kac marks (1,2,3,4,5,6,4,2,3) are the UNIQUE attractor of the minimal lazy graph update m←(A+2I)/4·m on the affine-E8/(2,3,5) McKay graph (converges from any positive start; A·m=2m, top eigenvalue 2). [E] the sphe","id":"python_verification:verification/v298_e8_network_attractor.py","line_count":119,"path":"verification/v298_e8_network_attractor.py","sha256":"21ec8a17606df03ef6692a5b2e5fb94eb8c9c4647730cf570ee15d87031066bc","type":"python_verification"},{"bytes":13273,"checked_by_registry":false,"claim_ids":["HYP.0D.01"],"cluster":"frontier","description_excerpt":"The hypergraph/Wolfram bridge, hardened: **the 3-arm (2,3,·) branch type** is the irreducible seed on which a LOCAL witness-based spectral growth REACHES E8 as the last finite point (E6→E7→E8, then stops at the affine boundary Ê8; E8 = maximal FINITE point) — NOT 'P2 derived'. [E] HYP.ICO.01 icosahedron = 3-uniform hypergraph (12 V, 20 hyperedges, 30 edges=h(E8)), |Aut(graph)|=120=|I_h|=A5×ℤ₂ (the McKay group is the ","id":"python_verification:verification/v299_hypergraph_0d_autonomous.py","line_count":269,"path":"verification/v299_hypergraph_0d_autonomous.py","sha256":"0c4ecc2112669c92c0c07652ac1cf3a0df4c034dab574add63539ed82ba64b24","type":"python_verification"},{"bytes":3859,"checked_by_registry":false,"claim_ids":["GATE.UWALL.01","CONTRACT.U.01","CONTRACT.G.01"],"cluster":"frontier","description_excerpt":"contract certs: wall enumeration; G5 gap-dominance","id":"python_verification:verification/v29_research_contract_certs.py","line_count":89,"path":"verification/v29_research_contract_certs.py","sha256":"984bb2d73dfbb40a66020cdedda90ec79e801433cb096d4489765b295a3d2cc5","type":"python_verification"},{"bytes":2063,"checked_by_registry":false,"claim_ids":["CAR.PAS.01","CAR.SM.01"],"cluster":"core","description_excerpt":"g_car=5 Pascal closure; 16=1+5+10, Ω_adm=48, b₁=41/10","id":"python_verification:verification/v2_carrier_pascal.py","line_count":50,"path":"verification/v2_carrier_pascal.py","sha256":"ede9ffd57db5aba27eeb6f163a76abafe2ece51a99ab28b1d5aa2fda74db4ef1","type":"python_verification"},{"bytes":10245,"checked_by_registry":false,"claim_ids":["FLATAWAY.RIGID.01"],"cluster":"frontier","description_excerpt":"FLATAWAY.RIGID.01 — the attack on Flat-Away: (I) HARDEN the obstruction from a soft minimum (v291/v293) to a DISCRETE one, (II) DERIVE the external pin from the (E8)₁ data. [E] FLAT FINGERPRINT: spec(|D_θ|) is the integer ladder, every level n≥1 of multiplicity exactly 2 — a discrete fingerprint, not a norm. [E] EXACT DEGENERATE SPLIT: the resonant mode 4k splits level 2k by gap = g_k (sympy 2×2 [[2k,g/2],[g/2,2k]] ⇒","id":"python_verification:verification/v300_flataway_rigid.py","line_count":179,"path":"verification/v300_flataway_rigid.py","sha256":"06518c6142216d69ce228c53a0f5a47bd6982e75983d202fe7dc8369828da479","type":"python_verification"},{"bytes":7340,"checked_by_registry":false,"claim_ids":["SEAM.EQUIV.A.INV.01"],"cluster":"frontier","description_excerpt":"SEAM.EQUIV.A.INV.01 — discharge Route A's single open hypothesis (v297 LIT-A: 'the raw quasi-free seam bulk is invertible/SRE') via the free-fermion classification. Since v300 collapsed Route B into Route A, this is the LAST unconditional gap of SEAM.EQUIV.01. [E] carrier = 16 Majoranas, c=8: g_car+N_fam=5+3=8=16/2 (v148). [E] SO(16)₁ ⊃ (E8)₁: dim so(16)=120 currents + 128 spinor = 248 = dim E8 (v154). [C] free-fermi","id":"python_verification:verification/v301_route_a_invertible.py","line_count":122,"path":"verification/v301_route_a_invertible.py","sha256":"3c2edba648219f084674ccba4c1199c4be5ddea012cf43d4df7c2463e326060a","type":"python_verification"},{"bytes":7021,"checked_by_registry":false,"claim_ids":["SEAM.EQUIV.GAP.01"],"cluster":"frontier","description_excerpt":"SEAM.EQUIV.GAP.01 — the LAST lever: after v300/v301 the whole open content of SEAM.EQUIV.01 was 'the quasi-free seam bulk is gapped'; this shows that gap is NOT a free input but the established RECOVERY GAP of the seam transfer operator. [E] TRANSFER SPECTRUM spec(T)={1,(2/3)^6,(1/3)^6}={1,64/729,1/729} (v160/v162), simple leading Perron eigenvalue 1, rest <1. [E] THE GAP IS DERIVED: Δ=−ln((2/3)^6)=6 ln(3/2)=2 N_fam ","id":"python_verification:verification/v302_seam_gap.py","line_count":113,"path":"verification/v302_seam_gap.py","sha256":"4a97a40d30829715e6f13777b20cd47ee05d211b4a31a18768ca98367b704cf0","type":"python_verification"},{"bytes":9459,"checked_by_registry":false,"claim_ids":["FR.DYNAMICS.01"],"cluster":"frontier","description_excerpt":"FR.DYNAMICS.01 — the discrete->dynamic lens on F_transfer: is the main-branch mechanism (a gapped, positivity-preserving relaxation to a UNIQUE attractor; local-averaging update -> E8 marks, gap 6 log(3/2)) also the shape of the four F_transfer instances? [E] F_pole (Koide) IS the seam dynamics: the source->pole/branch relaxation is the Moebius map with fixed-point multiplier F'=(2/3)^6 = lambda_2 = the seam clock su","id":"python_verification:verification/v303_ftransfer_dynamics.py","line_count":157,"path":"verification/v303_ftransfer_dynamics.py","sha256":"871ccecb97e8f0ab1aa150c6442efbc4c173e3966e5e9958ea6adfeebe300449","type":"python_verification"},{"bytes":8807,"checked_by_registry":false,"claim_ids":["QGAMB.IDG.01"],"cluster":"frontier","description_excerpt":"QGAMB.IDG.01 — the KMS spectral-action cutoff suggests a NONLOCAL (infinite-derivative) graviton form factor; under entire analyticity the Stelle ghost is a TRUNCATION ARTEFACT — a CONDITIONAL narrowing of the red-team rt_F perturbative-gravity attack, NOT a closure of QG.AMB.01 (no new parameter: the cutoff is the v259 seam KMS weight). [E] STELLE GHOST = TRUNCATION ARTEFACT: the local four-derivative propagator 1/(","id":"python_verification:verification/v304_idg_nonlocal_ghost.py","line_count":138,"path":"verification/v304_idg_nonlocal_ghost.py","sha256":"f09784a8628e268d97ce9083206df743596f7445935a57e6cddda998c8ccf0b6","type":"python_verification"},{"bytes":12070,"checked_by_registry":false,"claim_ids":["WITNESS.ECON.01"],"cluster":"registry","description_excerpt":"Witness-independence / generator-economy audit (structural anti-numerology firewall, companion to v100): every headline integer (4,5,2,3,16,8,240,248,120,30,1920,48,6) is a documented image of the single anchor a=(1,1,2) with pi the only transcendental primitive -> 13 atoms / 2 free primitives = 6.5x compression made explicit (the recurring 2/3=|Z2|/N_fam and (2/3)^6 are ONE ratio); E8/g_car/anchor are overdetermined","id":"python_verification:verification/v305_witness_independence.py","line_count":213,"path":"verification/v305_witness_independence.py","sha256":"afe701f420a8ae99fa7b017f2e94d54ada7687da5a2dd5d2229e46dd070ca7a8","type":"python_verification"},{"bytes":8182,"checked_by_registry":false,"claim_ids":["SEED.CROSSVAL.01"],"cluster":"registry","description_excerpt":"Leave-one-out cross-validation of the shared seed phi0: back-solving phi0 independently from the 5 seed-grammar observables (sin^2 theta12, sin^2 theta13, beta, Omega_b, lambda_C; NuFIT 6.0 / ACT DR6 / Planck / PDG centrals) and error-weighted-averaging reproduces the axiom seed phi0=1/(6pi)+48 c3^4=0.0531720 to 0.04% (one real seed, not a per-observable fit); leave-one-out predicts every held-out observable within 3","id":"python_verification:verification/v306_seed_crossval.py","line_count":167,"path":"verification/v306_seed_crossval.py","sha256":"f2ed164cfe7c7ce66ed9e3787e3839b83e8ac21869309213000f3e5d9319d9b5","type":"python_verification"},{"bytes":12244,"checked_by_registry":false,"claim_ids":["DATA.WATCHDOG.01"],"cluster":"frontier","description_excerpt":"Data watchdog: the operational decision pipeline over the frozen registry (v84). Classifies all 20 entries (16 predictions + 2 assigned textures + 2 bands) PASS/WATCH/TENSION/KILL by live n_sigma vs repo-documented current bests (CODATA 2022, NuFIT 6.0, ACT DR6, Planck 2018, PDG 2024, BK18); no decidable prediction in KILL (theory alive); watch items alpha^-1 (1.9 sigma), s23 (1.8 sigma) and the most-tensioned core s","id":"python_verification:verification/v307_data_watchdog.py","line_count":241,"path":"verification/v307_data_watchdog.py","sha256":"a6b00cc25bc2b31a55cef01f0cd14f27c9c62f181ac114490bcb1ea26eced690","type":"python_verification"},{"bytes":6308,"checked_by_registry":false,"claim_ids":["SEAM.EQUIV.CHAIN.01","FORM.SEAMEQUIV.01"],"cluster":"frontier","description_excerpt":"TOE attack 1 -- the SEAM.EQUIV.01 keystone as a composition certificate: the v297 stack as ONE well-typed chain gap>0 -> invertible (Kitaev) -> holomorphic c=8 (Mueger/KLM) -> (E8)_1 (Conway-Sloane), with exact discriminators |det Cartan(E8)|=1 vs |det Cartan(D8)|=4, carrier tower 4*4=16->4->1, c=g_car+N_fam=8; the input gap = the derived recovery gap 6 ln(3/2)>0. The only undischarged premise is the cited OS step --","id":"python_verification:verification/v308_seam_equiv_chain.py","line_count":119,"path":"verification/v308_seam_equiv_chain.py","sha256":"dd7aa3f6d423a22270ae81899f9f996c42f60679ec58d3056a85641ddddb0e9b","type":"python_verification"},{"bytes":5982,"checked_by_registry":false,"claim_ids":["QGEO.MODHAM.01"],"cluster":"frontier","description_excerpt":"TOE attack 2 -- the bedrock omega o rho = omega via an explicit modular Hamiltonian, non-circular: marks=4 from Gauss-Bonnet (v216) + the order-4 clock from cross-ratio 2 (v214) => mu4 derived not assumed; the quasi-free modular Hamiltonian K=log((1-C)/C) round-trips to the seam operator and [rho,K]=0 <=> omega o rho = omega (a Z2 profile breaks it). Residual = Bisognano-Wichmann intrinsicality of the raw collar; NOT","id":"python_verification:verification/v309_modular_bedrock.py","line_count":128,"path":"verification/v309_modular_bedrock.py","sha256":"8d6462e1e1bb81a0305e3d1dc24ab2244d88072e8b9a6f67a2062156b895969c","type":"python_verification"},{"bytes":3960,"checked_by_registry":false,"claim_ids":["CONTRACT.U.01"],"cluster":"uwall","description_excerpt":"D₄-fixed SU(3) character variety is positive-dimensional","id":"python_verification:verification/v30_d4_character_variety.py","line_count":93,"path":"verification/v30_d4_character_variety.py","sha256":"fcf2a760f2a69b632ee796cbe5d321c30410a3d5d524f3cd37c18aa06a5c090e","type":"python_verification"},{"bytes":5582,"checked_by_registry":false,"claim_ids":["CAR.SM.ANOM.01"],"cluster":"registry","description_excerpt":"TOE attack 3 -- the carrier half-spinor IS one anomaly-free SM generation with the SM RG: 16=Lambda^even(C^5)=1+10+5 -> SU(5)<SO(10) as 10+5bar+1 = one generation; gauge-anomaly-free (sum Y=0, sum Y^3=0, [SU2]^2U1=[SU3]^2U1=0, exact) and reproduces (b1,b2,b3)=(41/10,-19/6,-7); a 4th family shifts b1, so N_fam=3 pins the RG. Closes the spectrum+anomaly+beta sub-question; the full EG S-matrix + Yukawa stay open","id":"python_verification:verification/v310_carrier_sm_anomaly.py","line_count":104,"ownership":{"claim_scope":"Only local ledger rows apply; the dependency copy does not transfer physical or arithmetic claims.","owner":"TFPT","relation":"TFPT mathematical source copied as a dependency in Prime Front","sibling":"Prime Front"},"path":"verification/v310_carrier_sm_anomaly.py","sha256":"c4898aef237d50f8247a2ee36be0a0fd6933e3fa547f08ead84ed34f7ec26c25","type":"python_verification"},{"bytes":5521,"checked_by_registry":false,"claim_ids":["QGAMB.CLUSTER.01"],"cluster":"frontier","description_excerpt":"TOE attack 4 -- the physical QG measure as a gap-decoupled, exponentially-clustering object: the transfer spectrum {1,(2/3)^6,(1/3)^6} gives geometric clustering at rate (2/3)^6, correlation length 1/(6 ln(3/2)), finite susceptibility 729/665; the v76 margin 6 ln(3/2)-31/(4pi^2)~1.648>0 decouples the physical sector from the un-built ambient. Spectral-action a2=EH/a4=R^2/72 (v36) + KMS beta=1 (v259); QG.AMB.01 stays ","id":"python_verification:verification/v311_gap_decoupled_measure.py","line_count":110,"path":"verification/v311_gap_decoupled_measure.py","sha256":"a2495feefd0f01e0d28a896508c9358fd8d9540cc7115a70b2138aff0221d606","type":"python_verification"},{"bytes":5611,"checked_by_registry":false,"claim_ids":["HYP.INJECT.01"],"cluster":"frontier","description_excerpt":"TOE attack 5 -- the hypergraph substrate sharpened: the affine-E8 Kac marks are the Perron eigenvector (A.marks=2 marks) and the subleading eigenvalue is exactly 2cos(pi/5)=golden ratio (the 5-fold/icosahedral signature), but the recovery rate (2/3)^6 is NOT any eigenvalue and phi0 is not a rational edge fraction; so a full-structure rewrite must inject exactly two non-graph-spectral data: the cusp weight 2/3=|Z2|/N_","id":"python_verification:verification/v312_hypergraph_substrate.py","line_count":108,"path":"verification/v312_hypergraph_substrate.py","sha256":"8f4f6abd645506a44a599366e424a1795ae6d41eb29469645351529d7873f1e6","type":"python_verification"},{"bytes":6562,"checked_by_registry":false,"claim_ids":["GOLD.ATOMS.01"],"cluster":"frontier","description_excerpt":"The golden ratio is the g_car=5 signature -- the (2,3,5) atoms ARE the affine-E8 network spectral angles (v312 follow-up, exact). The charpoly factors x(x^2-4)(x^2-1)(x^2-x-1)(x^2+x-1), the golden minimal polynomial x^2-x-1 divides it (phi=2cos(pi/5) exact eigenvalue); the non-trivial eigenvalues are 2cos(pi/k) for k in {2,3,5}={|Z2|,N_fam,g_car} (0,1,phi,1/phi) so the golden ratio is the g_car=5 (5-fold) signature -","id":"python_verification:verification/v313_golden_atoms_spectral.py","line_count":124,"path":"verification/v313_golden_atoms_spectral.py","sha256":"fb6ecd33815a1c16a8c19153b2a641b1ce301dae954e9a501a77cce96d742582","type":"python_verification"},{"bytes":6682,"checked_by_registry":false,"claim_ids":["RATE.TRANSLATE.01"],"cluster":"frontier","description_excerpt":"Do the discrete-kernel and dynamic rates translate? An exact number-field split. The affine-E8 adjacency spectrum splits into the rational part {0,+-1,+-2} in Q and the golden part {+-phi,+-1/phi} in Q(sqrt5); the dynamic transfer spectrum {1,(2/3)^6,(1/3)^6} is entirely rational. So the family rates DO translate (the rational discrete angles 2cos(pi/2)=0=|Z2|, 2cos(pi/3)=1=N_fam build the recovery rate (2/3)^6=(|Z2|","id":"python_verification:verification/v314_rate_translation.py","line_count":123,"path":"verification/v314_rate_translation.py","sha256":"1e7200d76d20ed799c57caa234485fad3701e577da888f3ef4808bb2965aa541","type":"python_verification"},{"bytes":6396,"checked_by_registry":false,"claim_ids":["COX.COUPLE.01"],"cluster":"frontier","description_excerpt":"Couple or factorize? The order-30 Coxeter sectors couple as a cyclotomic field (v314 follow-up). GROUP FACTORIZES: gcd(5,6)=1 => Z/30 = Z/5 x Z/6 (direct product, group-decoupled). EXPONENTS FACTOR: E8 exponents=totatives(30)=totatives(5)x totatives(6), phi(30)=4*2=8=rank E8. FIELD COUPLES: [Q(zeta30):Q]=8=rank E8, Q(zeta30) is the compositum of the carrier Q(zeta5) (contains sqrt5) and the family Q(zeta3). GALOIS = ","id":"python_verification:verification/v315_coxeter_coupling.py","line_count":120,"path":"verification/v315_coxeter_coupling.py","sha256":"490969af0827cf8829f236e3999710bb526396dc9eb2ee0672d8bdd5c6af7b0c","type":"python_verification"},{"bytes":6151,"checked_by_registry":false,"claim_ids":["GALOIS.READOUT.01"],"cluster":"frontier","description_excerpt":"Does the Galois mu4 x Z2 (v315) organize the physical readouts? Yes -- the CP phases. The hexagonal CP unit rho=zeta_6=zeta_30^5 is the order-6=2 N_fam FAMILY factor c^5 of v315 (the carrier is zeta_5=zeta_30^6); delta_CKM,lead=pi/3=arg(zeta_6), delta_PMNS=4pi/3=arg(zeta_6^4) (power 4=|mu4|), zeta_6^4=-zeta_6 the sheet flip (mu6=mu3 x mu2). The Galois Z2=Gal(Q(zeta6)/Q)={zeta_6->zeta_6^5=conj} IS CP conjugation (delt","id":"python_verification:verification/v316_galois_readout.py","line_count":106,"path":"verification/v316_galois_readout.py","sha256":"e402ec3e9a6beaf4c75f47f6393cfdd6efcdceec7801a394dd18db1d0f7e0573","type":"python_verification"},{"bytes":5799,"checked_by_registry":false,"claim_ids":["GALOIS.FAMILY.01"],"cluster":"frontier","description_excerpt":"Are the 3 generations a mu3/Galois orbit? Yes (mu3), refined 1+2 by Galois (v316 follow-up). The 3 cusp weights {0,1/3,2/3} (Spec(Q+)={1,2,3}=A3 exponents) map under w->e^{2pi i w} to the 3rd roots of unity {1,zeta_3,zeta_3^2}; the cyclic family symmetry w->w+1/3 is a transitive mu3 orbit (the family IS the cube-root orbit). The transfer eigenvalues (1-w)^6={1,(2/3)^6,(1/3)^6} attach to the weights (attractor=eigenva","id":"python_verification:verification/v317_galois_family.py","line_count":103,"path":"verification/v317_galois_family.py","sha256":"1b2e982246d4d8f19d6ba542e3fa9267709a6bf34dd19d2180bd11eec860c096","type":"python_verification"},{"bytes":5805,"checked_by_registry":false,"claim_ids":["ARITH.CAPSTONE.01"],"cluster":"core","description_excerpt":"The capstone: the SM structural sector is Q(zeta30) + Galois mu4 x Z2, and the complete input is {a, pi, v_geo} (synthesis of the v313-v317 arc). The structural sector (3 generations, 2 CP phases, orbit/hierarchy) lives in Q(zeta30): [Q(zeta30):Q]=phi(30)=8=rank E8, 30=|Z2|*N_fam*g_car=h(E8), Galois (Z/30)^x=mu4 x Z2. Rigidity: forced by the anchor atoms {2,3,5}=e(a). Magnitude reduction: phi0=(4/3)c3+48 c3^4 is a pu","id":"python_verification:verification/v318_arithmetic_capstone.py","line_count":107,"path":"verification/v318_arithmetic_capstone.py","sha256":"cdeda2f4b1e14bec5e2fa3f511fde225fc077d163b868fdbd807d83315e6946b","type":"python_verification"},{"bytes":8658,"checked_by_registry":false,"claim_ids":["TRANSLATE.CLOCK.01"],"cluster":"horizon","description_excerpt":"The translation clock: the discrete<->dynamic bridge IS the order-30 Coxeter element, a clock with two coprime hands 5 x 6, read law-inclusive (0..5) or live-only (1..5). The only object holding both the static carrier (Q(sqrt5)) and the dynamic family (rational) data is the order-30 Coxeter element (v314); 30 = h(E8) = g_car*(2 N_fam) = 5*6, gcd(5,6)=1 => Z/30 = Z/5 x Z/6 (v315). DYNAMIC HAND (Z/6 = 2 N_fam, ticks 0","id":"python_verification:verification/v319_translation_clock.py","line_count":147,"path":"verification/v319_translation_clock.py","sha256":"470630b658826a6c4eda8673ae19f08c45bce66267371b8cced7b73d956e97c1","type":"python_verification"},{"bytes":4194,"checked_by_registry":false,"claim_ids":["CONTRACT.U.01"],"cluster":"uwall","description_excerpt":"R(ρ): integer R but continuous ρ-invariants","id":"python_verification:verification/v31_R_dictionary.py","line_count":101,"path":"verification/v31_R_dictionary.py","sha256":"168cfd99a75f54231cc178f56dcd234647040ae0616dfbdfe0ae48f6b599a3d1","type":"python_verification"},{"bytes":5167,"checked_by_registry":false,"claim_ids":["GALOIS.CP.PREDICT.01"],"cluster":"frontier","description_excerpt":"A NEW falsifiable prediction from the Galois structure: the two CP phases are locked, delta_PMNS = delta_CKM,lead + pi. Both phases are powers of one hexagonal unit rho=zeta_6 (v316): delta_CKM,lead=arg(rho)=pi/3=60deg, delta_PMNS=arg(rho^4)=4pi/3=240deg, rho^4=-rho, so delta_PMNS-delta_CKM,lead=pi exactly (the Z2 sheet flip) -- the quark and lepton leading CP phases are NOT independent. Prediction of record: delta_P","id":"python_verification:verification/v320_galois_cp_relation.py","line_count":95,"path":"verification/v320_galois_cp_relation.py","sha256":"523ece28d6b6eb1d04e1b4deeadaa4d98baa4969e6d864c798a9de267e2b1889","type":"python_verification"},{"bytes":5539,"checked_by_registry":false,"claim_ids":["KILL.BOARD.01"],"cluster":"frontier","description_excerpt":"The forward kill-test board: the decisive upcoming measurements, ranked (forward companion to v307). Each entry is locked to a freeze_file.csv kill row: #1 JUNO sin^2 theta12=0.306747 (fastest), #2 CMB-S4/LiteBIRD r (kill r>0.01), #3 DESI/Euclid w=-1, #4 DUNE/Hyper-K delta_PMNS=240deg (the new v320 Galois-CP relation), #5 DUNE/LEGEND/nEXO ordering+m_betabeta, #6 PSI n2EDM nEDM, #7 JUNO sin^2 theta13 (~2 sigma now), #","id":"python_verification:verification/v321_killtest_board.py","line_count":99,"path":"verification/v321_killtest_board.py","sha256":"debba6d7a00df62cbb70dac97b6b707eb4e37c4398d2f13371c571cddc08d610","type":"python_verification"},{"bytes":7228,"checked_by_registry":false,"claim_ids":["GALOIS.CP.SHARPEN.01"],"cluster":"frontier","description_excerpt":"The v320 CP-lock prediction sharpened into a quantitative kill test. The leading CP phase sits on the six hexagonal nodes arg(rho^k)=k*60deg; delta_CKM,lead=60deg (node 1), delta_PMNS,lead=240deg (node 4). The node selector IS the deck order: delta_PMNS,lead=|mu4|*delta_CKM,lead=4*(pi/3)=4pi/3=delta_CKM,lead+pi (rho^4=-rho). Sub-leading budget: delta_CKM,full=pi/3+3 lambda^2 (~68.7deg); the lepton sub-leading is a se","id":"python_verification:verification/v322_cp_lock_sharpened.py","line_count":124,"path":"verification/v322_cp_lock_sharpened.py","sha256":"b3261e7af6d7261306c2f32f681b6b3d29bf4fbf9fc3b352182f05a710d80c71","type":"python_verification"},{"bytes":7879,"checked_by_registry":false,"claim_ids":["QGEO.BW.01","FORM.QGEO.BW.01"],"cluster":"frontier","description_excerpt":"The keystone pushed one step: Bisognano-Wichmann makes the seam modular flow GEOMETRIC, so the mu4 deck invariance is not an independent axiom. The clock rho=diag(i^n)=exp(i(pi/2)L) is a geometric rotation (L=diag(n) the rotation generator, rho^4=I, mu4 in U(1)_rot). For a rotation-covariant covariance C=f(L) the modular Hamiltonian K=log((1-C)/C)=g(L), so [K,L]=0 (the modular flow commutes with all rotations) and [r","id":"python_verification:verification/v323_bw_geometric_modular.py","line_count":156,"path":"verification/v323_bw_geometric_modular.py","sha256":"cfef049d611a93ab594892fb78c9a0dfb2faa7f51286e3961331e7e3d1088230","type":"python_verification"},{"bytes":8016,"checked_by_registry":false,"claim_ids":["HYP.FIBER.01"],"cluster":"frontier","description_excerpt":"The minimal hypergraph substrate that works: a (2,3,5)-network FIBERED by a 3-fold cusp channel reproduces both the E8 skeleton and the recovery gap (the constructive v312 follow-up). Network factor (carrier/5-fold): T_net=(A+2I)/4 fixes the Kac marks (eigenvalue 1=E8 skeleton), subleading (phi+2)/4 (golden); (2/3)^6 NOT in its spectrum (v312 negative). Cusp fiber (family/3-fold): T_cusp=diag((1-w)^{2N_fam}), w in {0","id":"python_verification:verification/v324_hypergraph_fiber.py","line_count":143,"path":"verification/v324_hypergraph_fiber.py","sha256":"81b2211d35635972d9b92559f15d62660df7c9e5014693ab674eff982f2d3149","type":"python_verification"},{"bytes":7015,"checked_by_registry":false,"claim_ids":["QGEO.KEYSTONE.01","FORM.CARTAN.DET.01"],"cluster":"frontier","description_excerpt":"The seam keystone as ONE citable theorem: the raw seam state is the flat tau=i pillowcase state, with EXACTLY ONE open lemma. IF (raw RP-collar seam state = flat tau=i pillowcase / rotation-invariant state) THEN 4 square marks + mu4 deck + omega o rho=omega + holomorphic c=8 => (E8)_1, with the carrier recovery gap as input. Pieces (all exact): n=2chi(S^2)=4 (v216); cross-ratio 2 => j=1728 (v214/v267); flat orbifold ","id":"python_verification:verification/v325_pillowcase_keystone.py","line_count":131,"path":"verification/v325_pillowcase_keystone.py","sha256":"5d8c9e2d89fc10a2a3f173e697ea87c4e39fa36d48276c020da16f586b97ecec","type":"python_verification"},{"bytes":8606,"checked_by_registry":false,"claim_ids":["FR.SUITE.01"],"cluster":"frontier","description_excerpt":"The F_transfer solver suite: the four transfer readouts as ONE runnable harness, each a gapped relaxation to a unique attractor, with values + uncertainties + honest typing (productises v303). F_pole (Koide): Moebius contraction to Q*=2/3 with multiplier (2/3)^6 = the seam-clock subleading eigenvalue, unique attractor at the SEAM rate. F_Boltzmann (eta_B): washout contraction to the balance 6.1e-11, monotone (H-theor","id":"python_verification:verification/v326_ftransfer_suite.py","line_count":157,"path":"verification/v326_ftransfer_suite.py","sha256":"06de6ee1ed756d2c187f50e9cb2de4ce3b23796db5266bb4e1f406178e55441f","type":"python_verification"},{"bytes":6876,"checked_by_registry":false,"claim_ids":["HYP.REWRITE.01"],"cluster":"frontier","description_excerpt":"Deriving the cusp weight 2/3 from a minimal rewrite (sharpening v324/v312). A minimal local rule -- a family channel with N_fam=3 slots, one absorbing attractor (w=0) and |Z2|=2 surviving -- supplies the cusp fiber. M=[[1,0,0],[0,1/3,1/3],[0,1/3,1/3]] has spectrum {1,2/3,0}; 2/3=(N_fam-1)/N_fam=|Z2|/N_fam EMERGES from the rule arity, not injected. Over the order-6=2 N_fam hand the rate is (2/3)^6=64/729 = the recover","id":"python_verification:verification/v327_hypergraph_rewrite.py","line_count":124,"path":"verification/v327_hypergraph_rewrite.py","sha256":"5c55ee1d7e13a18f71e984a713b13ab7db0ae5618dc11b590c7e889c0acf1cb7","type":"python_verification"},{"bytes":5864,"checked_by_registry":false,"claim_ids":["FLAV.TH13.PRESSURE.01"],"cluster":"neutrinos","description_excerpt":"The theta13 pressure point: the honest weak spot, quantified and pre-registered. sin^2 theta13 = phi0 e^{-5/6} = 0.023108 vs NuFIT 6.0 NO (0.02195 +- 0.00058) is +2.0 sigma -- the most-tensioned CORE prediction (v62/v307). theta13 is the carrier hypercharge trace (exponent gamma=tr_E Y^2=5/6 EXACT, v268), NOT the seesaw mu-tau breaking that sets theta12 -- distinct channels (a theta13 pull does not move theta12). No ","id":"python_verification:verification/v328_theta13_pressure.py","line_count":98,"path":"verification/v328_theta13_pressure.py","sha256":"a38930faff62d47871c9ea7986ae0940c7faf80d48c9332b999b3cdea1855276","type":"python_verification"},{"bytes":7542,"checked_by_registry":false,"claim_ids":["QGEO.OSGAP.01"],"cluster":"frontier","description_excerpt":"Closing the OS step: the bulk gap IS the transfer gap (second quantization), and assembling the single sufficient premise of the whole bedrock. [E] OS GAP = TRANSFER GAP: the OS/Euclidean many-body Hamiltonian dGamma(-log T) has spectrum = sums of single-mode energies, so the many-body (bulk) gap = the smallest positive single-mode energy = 6 ln(3/2), INDEPENDENT of system size -- exactly 'OS bulk gap = transfer gap'","id":"python_verification:verification/v329_os_gap_reduction.py","line_count":132,"path":"verification/v329_os_gap_reduction.py","sha256":"12aea00b54a7c6bb79daf32b8c3f7471f9b8ec82561f25e71cc97135da3e7166","type":"python_verification"},{"bytes":5034,"checked_by_registry":false,"claim_ids":["CONTRACT.U.01","RH.SPLIT.01"],"cluster":"uwall","description_excerpt":"RH route: splitting 𝒪(−2)⊕𝒪(−1)² ⇔ diag(A₀)=(½,¼,¼)","id":"python_verification:verification/v32_rh_splitting.py","line_count":100,"path":"verification/v32_rh_splitting.py","sha256":"7aff73fc0695f201269dc87fc147fec7137946db3901e8d6278463ddacbe53a2","type":"python_verification"},{"bytes":7916,"checked_by_registry":false,"claim_ids":["QGAMB.MEASURE.01"],"cluster":"frontier","description_excerpt":"Constructing the ambient measure on the gap-decoupled admissible sector as a bona fide Osterwalder-Schrader object (with the honest fence). [E] REFLECTION POSITIVITY: the seam transfer T (v221/v311; spectrum {1,(2/3)^6,(1/3)^6}) is symmetric PSD => the finite-volume measures are RP. [E] EXPONENTIAL CLUSTERING: C(n)/C(n-1) -> lambda_2=(2/3)^6 (xi=1/Delta, Delta=6 ln(3/2)). [E] TIGHTNESS => PROJECTIVE LIMIT: chi=sum_n ","id":"python_verification:verification/v330_qgamb_admissible_measure.py","line_count":136,"path":"verification/v330_qgamb_admissible_measure.py","sha256":"21cbeb2b96d9ee581da3a9c45be400d77d232730ba37bbb19cb4cec07fb5e5be","type":"python_verification"},{"bytes":7049,"checked_by_registry":false,"claim_ids":["QGEO.NECESS.01","FORM.MU4COMM.01"],"cluster":"frontier","description_excerpt":"The NECESSITY of H reduced: rotation-invariance of the seam DtN is EQUIVALENT to the four marks at the square (tau=i), so the one open lemma is exactly the order-4 CM selection (the necessity companion to v329's sufficiency). [E] SQUARE => [rho,Lambda]=0: marks at {0,pi/2,pi,3pi/2} make the curvature Z4-symmetric (Fourier support 0 mod 4), M_f couples only modes differing by 4Z (the v201/v210 sufficiency as a DtN |k|","id":"python_verification:verification/v331_necessity_of_H.py","line_count":127,"path":"verification/v331_necessity_of_H.py","sha256":"5dee9560ad3ca3a6b19984e251bcdbba65b8b645d188f1f0296bfe7a182e041b","type":"python_verification"},{"bytes":7258,"checked_by_registry":false,"claim_ids":["QGAMB.METRIC.01"],"cluster":"frontier","description_excerpt":"The metric sector of QG.AMB.01 characterized: the obstruction is exactly the conformal-mode (Gibbons-Hawking-Perry) problem, the physical sector is gap-insulated, and the only route is the conditional IDG taming (makes v330's metric-sector fence precise). [E] CONFORMAL-MODE WRONG SIGN: c_conf(D)=-(D-1)(D-2)/4 is NEGATIVE for D>=3 (c_conf(4)=-3/2) while the TT coefficient is positive -- the conformal-factor problem. [","id":"python_verification:verification/v332_qgamb_metric_sector.py","line_count":114,"path":"verification/v332_qgamb_metric_sector.py","sha256":"f27418f3602bf809b2249593d1c306f8f3441719e9b081bb7233d930e0f5d2fd","type":"python_verification"},{"bytes":6756,"checked_by_registry":false,"claim_ids":["QGEO.CMSELECT.01"],"cluster":"frontier","description_excerpt":"The CM-selection mechanism: tau=i (the square) is the UNIQUE order-4 modulus and the attractor of mark-equilibration, so the last keystone residual is 'the deck acts geometrically', not 'why the square' (the v331 follow-up). [E] ORDER-4 MODULAR ELEMENT: S=[[0,-1],[1,0]] in SL(2,Z) has S^2=-I, S^4=I and fixes tau=i; the unique order-4 elliptic point of PSL(2,Z) (the other, rho, is order 3). [E] DECK ORDER -> CM POINT:","id":"python_verification:verification/v333_cm_selection.py","line_count":126,"path":"verification/v333_cm_selection.py","sha256":"b260ecc9c2971311fd00d7d429f58f99e0abac47ecf9969f70e2b109cc12671d","type":"python_verification"},{"bytes":6783,"checked_by_registry":false,"claim_ids":["QGAMB.CONFORMAL.01"],"cluster":"frontier","description_excerpt":"The conformal-mode resolution: the Gibbons-Hawking-Perry contour rotation (IR sign) + the infinite-derivative (IDG) dressing (UV pole) give a CONDITIONALLY convergent metric-sector measure; the residual is the nonperturbative validity of the contour (the v332 follow-up). [E] THE OBSTRUCTION: c_conf(4)=-3/2<0, the unrotated conformal Gaussian diverges. [E] GHP CONTOUR ROTATION: phi->i phi flips the sign, int(exp(-|c|p","id":"python_verification:verification/v334_conformal_resolution.py","line_count":121,"path":"verification/v334_conformal_resolution.py","sha256":"1426cf457992731d332706f2303552d3bd59770c101ea0ecd3d88b4d525eefd3","type":"python_verification"},{"bytes":6964,"checked_by_registry":false,"claim_ids":["SEAM.EQUIV.UNIFY.01"],"cluster":"core","description_excerpt":"The keystone unification: there is ONE open theorem (SEAM.EQUIV.01), QGEO.SYM.01 is its COROLLARY (a conformal-net axiom), and QG.AMB.01 is a decoupled general QG problem, NOT a TFPT gate. [E] QGEO.SYM.01 = COROLLARY: a chiral conformal net has a Moebius-covariant vacuum (the unique invariant positive-energy vector, a NET AXIOM); rotations U(1) < Moebius => rotation-invariant vacuum; the mu4 clock = rotation by pi/2 ","id":"python_verification:verification/v335_seam_equiv_unify.py","line_count":111,"path":"verification/v335_seam_equiv_unify.py","sha256":"04854b5445a8c31f8c38e2d376dc2b4b0fae623cec9fc5b734a76c205732517c","type":"python_verification"},{"bytes":8359,"checked_by_registry":false,"claim_ids":["SEAM.EQUIV.CONTINUUM.01"],"cluster":"core","description_excerpt":"The ONE open lemma of SEAM.EQUIV.01, stated precisely and mapped to the recent rigorous literature: the continuum-limit and OS-reconstruction legs are now CITABLE, the genuinely-open residual narrows. [C] CONTINUUM LEG: Osborne-Stottmeister (CFT from Lattice Fermions, CMP 398 (2023) 219; legacy internal token MMST, on the MMST/Morinelli-Morsella-Stottmeister-Tanimoto OAR framework, arXiv:2010.11121) give the chiral-C","id":"python_verification:verification/v336_continuum_limit.py","line_count":120,"path":"verification/v336_continuum_limit.py","sha256":"6fdcde19f3931065e0f1d0cad230a45209eed987cb50ff6b50c4e5d273455046","type":"python_verification"},{"bytes":6118,"checked_by_registry":false,"claim_ids":["DECOUPLING.THEOREM.01"],"cluster":"frontier","description_excerpt":"THE DECOUPLING THEOREM (consolidated, citable): every TFPT dimensionless readout factors through the gapped admissible sector and is INDEPENDENT of the ambient QG measure -- the theorem that makes the QG.AMB.01 reclassification (v335) honest. [E] GAP MARGIN: Delta - 2*dim(E8)*c3^2 = 6 ln(3/2) - 31/(4 pi^2) ~ 1.648 > 0. [E] FACTORIZATION: every readout (mass ratios, mixings, alpha^-1, R+R^2) is a function of the admis","id":"python_verification:verification/v337_decoupling_theorem.py","line_count":97,"path":"verification/v337_decoupling_theorem.py","sha256":"47643ad26ee60f44ed74dc121b7635c491ff32b26dd1300a1bf111844f5f0216","type":"python_verification"},{"bytes":5892,"checked_by_registry":false,"claim_ids":["THETA13.BUDGET.01"],"cluster":"neutrinos","description_excerpt":"THETA13.BUDGET.01: the theta13 sub-leading budget vs the current global fit -- the +2 sigma pressure point (v328) quantified against BOTH NuFIT 6.0 NO variants and JUNO; neither defuses nor excludes, fences correctly. [N] SK-DEPENDENT TENSION: sin^2 theta13 = phi0 e^{-5/6} = 0.023108 is +2.0 sigma vs the no-SK central (0.02195) and +1.7 sigma vs the with-SK NO best fit (0.02215) -- NOT a clean 2 sigma. [E] WITHIN 3 S","id":"python_verification:verification/v338_theta13_budget.py","line_count":98,"path":"verification/v338_theta13_budget.py","sha256":"1e39e1a6970dbdedf7b0191b74964ee1a8dd93fb01e525b84f6c2a4c3c737deb","type":"python_verification"},{"bytes":7815,"checked_by_registry":false,"claim_ids":["FIRSTPRINCIPLES.BOUNDARY.01"],"cluster":"frontier","description_excerpt":"The honest first-principles boundary, mapped precisely -- answers (a) can M_Planck/v_geo be computed? and (b) can F_transfer be made first-principles? Both NO, with the exact reason per residual, classified into FOUR kinds. [E] v_geo/M_Planck FORBIDDEN BY THEOREM (No-Unit, v153): a mass is dimension 1 while every TFPT datum is dimension 0, so no dimensionless map outputs a scale; over-determined (gravity = dark energ","id":"python_verification:verification/v339_firstprinciples_boundary.py","line_count":126,"path":"verification/v339_firstprinciples_boundary.py","sha256":"f6f1bbe5cdc094c7fe32aac5bd92be22833121f41b611aab374836d11685573b","type":"python_verification"},{"bytes":3863,"checked_by_registry":false,"claim_ids":["RH.BUNDLE.01"],"cluster":"uwall","description_excerpt":"explicit valid (U_wall) flat bundle (RH solve)","id":"python_verification:verification/v33_explicit_flat_bundle.py","line_count":84,"path":"verification/v33_explicit_flat_bundle.py","sha256":"1babfc23211903730b3abebdead117d34a97ddd23d6c6d22119e7cff7b6f1a25","type":"python_verification"},{"bytes":6653,"checked_by_registry":false,"claim_ids":["AS.RECONCILE.01"],"cluster":"frontier","description_excerpt":"A_s is predicted (not missing), is DIMENSIONLESS (so it does NOT define an absolute mass), and the apparent -11 sigma tension is a reheating-channel question -- reconciled with the archived old derivation (TFPT v4.5/v4.6). [E] A_s = N_star^2 (M_scal/Mbar)^2/(24 pi^2) = N_star^2 c3^7/(24 pi^2) (v86); M_scal/Mbar = c3^{7/2} = 1.2565e-5 is a PURE RATIO, so A_s carries NO absolute scale -- it pins N_star, NOT M_bar => A_","id":"python_verification:verification/v340_As_reconcile.py","line_count":107,"path":"verification/v340_As_reconcile.py","sha256":"e42af560ef291569e5427c8f8f908f4af16daa12dc8cc8ac1cf4826834b05792","type":"python_verification"},{"bytes":8439,"checked_by_registry":false,"claim_ids":["ALPHA.QUILLEN.01"],"cluster":"em","description_excerpt":"The alpha fixed point reformulated as the STATIONARITY of a U(1) determinant line, every ingredient identified as an index / heat-kernel coefficient / discriminant form -- NOT a free knob (the 'derive the FORM' step). F_{U(1)} = a^3 - 2 c3^3 a^2 - (4/5) c3^6 M ln(1/phi_seam) = 0 in Quillen form: [a^3 - 2 c3^3 a^2] (det-line variation) = [8 b1 c3^6] (anomaly counterterm) * [ln(1/phi_seam)] (seam response). [E] M=41 a ","id":"python_verification:verification/v341_alpha_quillen.py","line_count":143,"path":"verification/v341_alpha_quillen.py","sha256":"aae72373f6055a058381825606cd7b75d31a2f75ee6dc0c22c3481e5602f0b62","type":"python_verification"},{"bytes":7196,"checked_by_registry":false,"claim_ids":["EM.WARD.02"],"cluster":"em","description_excerpt":"The heat-kernel sharpening of EM.WARD.01: DERIVES the ORIGIN and STRUCTURE of the F_{U(1)} determinant-line terms from textbook Seeley-DeWitt/Gilkey coefficients, advancing the EM-Ward origin from [P] to [E] for the STRUCTURE; NO new gate. [E] c3=1/(8pi) the boundary GAUSS-BONNET coefficient (seam = flat pillowcase chi=2, oint K = 4pi, v216). [E] the alpha^2 term is the GILKEY gauge-curvature coeff: a4 has 30 Omega^2","id":"python_verification:verification/v342_em_ward_heatkernel.py","line_count":112,"path":"verification/v342_em_ward_heatkernel.py","sha256":"34ec90333066565a2d858bd871db1a54e83c878d40990616d925035a19738f00","type":"python_verification"},{"bytes":9024,"checked_by_registry":false,"claim_ids":["FOUR.ROUTES.01"],"cluster":"frontier","description_excerpt":"The honest investigation of the four black-hole-birth solution routes (A finite causal diamond, B Carlip-Cardy near-horizon CFT, C modular/thermal flow, D self-reproduction attractor) -- direct answer to 'which closes ALL problems and is 100% provable': NONE individually, but they CONVERGE on the same two irreducible residuals as v335 (SEAM.EQUIV.01 + the decoupled QG contour). [E] ROUTE A reframes QG.AMB to a FINITE","id":"python_verification:verification/v343_four_routes_analysis.py","line_count":128,"path":"verification/v343_four_routes_analysis.py","sha256":"f4b5224512b028082669eda9fdc2962d111c97d67320ce6ab506d58e1c7f03ee","type":"python_verification"},{"bytes":8711,"checked_by_registry":false,"claim_ids":["SEAM.DETK.01"],"cluster":"core","description_excerpt":"The bird's-eye synthesis of the ONE open keystone bit, det K=1 -- a full-spectrum map of SEAM.EQUIV.01's only open residual. [E] det K=1 is ONE statement with SIX equivalent faces (holomorphy / homology-sphere link H_1=0 / one 1-dim irrep / det Cartan=1 / full mu4 condensation / tau=i CM), unified by |det Cartan| = |H_1(link)| = #1-dim irreps across ADE (A_n->n+1, D_n->4, E6->3, E7->2, E8->1) -- ONLY E8 gives 1. [E] ","id":"python_verification:verification/v344_detk_synthesis.py","line_count":135,"path":"verification/v344_detk_synthesis.py","sha256":"3e88c3c03727a08683a4ebb8d026672905a4eb55035635faf73f9e9bf162b92a","type":"python_verification"},{"bytes":8263,"checked_by_registry":false,"claim_ids":["SEAM.DETK.02"],"cluster":"core","description_excerpt":"EXECUTE the combinatorial core of route R3 (the hypergraph-homotopy route to det K=1, v344): computes explicitly that the (2,3,5)-rewrite attractor graph's plumbing link is the POINCARE homology sphere (H_1=0), only E8 among ADE; R3's combinatorial half is now [E]-complete, the geometric bridge (= SEAM.EQUIV.01) stays [O]. Plumbing topology (Brieskorn): link H_1 = coker(Cartan). [E] SNF(E8 Cartan) = identity => coker","id":"python_verification:verification/v345_hypergraph_homotopy.py","line_count":165,"path":"verification/v345_hypergraph_homotopy.py","sha256":"150a9c968ec2177535792eba369eb4249301513677a8548f77d20155d828c43f","type":"python_verification"},{"bytes":6553,"checked_by_registry":false,"claim_ids":["SEAM.EQUIV.GEOM.01"],"cluster":"core","description_excerpt":"The geometric bridge as an explicit six-link chain raw-seam => det K=1, with the ONE open arrow pinned -- the honest capstone of the SEAM.EQUIV.01 investigation. L1 [E/C] raw seam -> mu4 + four marks (v216); L2 [O] mu4 + (2,3,5) atoms -> 2I orbifold C^2/Gamma (THE OPEN ARROW = SEAM.EQUIV.01); L3 [E] 2I -> affine E8 McKay (v219); L4 [E] 2I -> E8 du Val (v232); L5 [E] C^2/2I -> Poincare link H_1=0 (v345); L6 [E] H_1=0 ","id":"python_verification:verification/v346_seam_geometric_bridge.py","line_count":98,"path":"verification/v346_seam_geometric_bridge.py","sha256":"1139d15244ec9ee17c87e6bd903e3c7a61d6e893015beb51c65e874bbf273a7e","type":"python_verification"},{"bytes":8086,"checked_by_registry":false,"claim_ids":["SEAM.EQUIV.CLOSURE.01"],"cluster":"core","description_excerpt":"The closure-mode classification of the one open arrow L2 (the seam-orbifold realisation, v346) -- a direct honest answer to 'is there ANY other way to FULLY solve it?'. [E] THE PRECISE LOCUS: the seam gives the pillowcase base S^2(2,2,2,2), chi_orb=0 (EUCLIDEAN, v216), but the 2I/E8 structure is the Seifert base S^2(2,3,5), chi_orb=1/30 (SPHERICAL); L2 must bridge a FLAT 4-marked base to a SPHERICAL 3-marked base -- ","id":"python_verification:verification/v347_seam_closure_modes.py","line_count":115,"path":"verification/v347_seam_closure_modes.py","sha256":"60582193ef429b5d0434c9492b4402fa3efd93697a63e741f9b1be0c6ddefe9b","type":"python_verification"},{"bytes":7470,"checked_by_registry":false,"claim_ids":["SEAM.EQUIV.RIGID.01"],"cluster":"core","description_excerpt":"Route B (the rigidity route) for the one open arrow L2, carried out -- it lands on a strikingly SIMPLE statement: the whole keystone reduces to ONE question, does the raw seam carry the golden ratio? [E] rigidity closes the crystallographic part: the order-4 clock has a UNIQUE normal form z->iz (Nielsen/Kerckhoff, v180), Troyanov gives the unique flat pillowcase metric (v284). [E] downstream is a LATTICE identity: E8","id":"python_verification:verification/v348_seam_rigidity_route.py","line_count":104,"path":"verification/v348_seam_rigidity_route.py","sha256":"c407a5ad4145072f11998c51f082c6e9b9ccb6a05d32fef42fca98a86778bc7f","type":"python_verification"},{"bytes":7453,"checked_by_registry":false,"claim_ids":["SEAM.EQUIV.GOLDEN.01"],"cluster":"core","description_excerpt":"The honest test of the v348 question 'does the RAW seam carry the golden ratio (before assuming E8)?'. Answer, computed: NO -- the bare carrier (D5, A3) and the dynamical seam data are NOT golden; the golden ratio genuinely enters WITH the icosahedral/E8 identification. A NEGATIVE result that prevents a false closure. [E] RAW CARRIER NOT GOLDEN: golden needs 5|h; D5 has h=8 (2cos(2pi/8)=sqrt2), A3 has h=4 -- no 5-fol","id":"python_verification:verification/v349_raw_seam_golden_test.py","line_count":114,"path":"verification/v349_raw_seam_golden_test.py","sha256":"92fc1e971dac05996a43b077ca8c22e053a6437a419bce1986675e93bda127fa","type":"python_verification"},{"bytes":4309,"checked_by_registry":false,"claim_ids":["H2.BRIDGE.01"],"cluster":"uwall","description_excerpt":"H2 bridge attempt: honest negative on lepton amplitudes","id":"python_verification:verification/v34_h2_bridge_attempt.py","line_count":99,"path":"verification/v34_h2_bridge_attempt.py","sha256":"01acf20c04d4702b9284a110cce03e2e945cc129e530f00962a773e5dd2beeff","type":"python_verification"},{"bytes":7705,"checked_by_registry":false,"claim_ids":["SEAM.EQUIV.BOOTSTRAP.01"],"cluster":"core","description_excerpt":"The honest CORRECTION of v349's framing (prompted by the right objection: the inputs are not axioms, they are back-determined by the theory). [E] THE INPUTS ARE BOOTSTRAP-FORCED, NOT FREE AXIOMS (v6): g_car=5 over-determined three ways (rank-fill, Coxeter-match g_car=max prime of h(E8)=30, Pascal). [E] g_car=5 IS THE ICOSAHEDRAL 5-FOLD, not the D5 rank: g_car = max prime of h(E8)=30=2*3*5; the atoms (2,3,5) ARE the p","id":"python_verification:verification/v350_bootstrap_inputs_correction.py","line_count":108,"path":"verification/v350_bootstrap_inputs_correction.py","sha256":"ac79766fae9a95a5b5eedd4afc95beb4c3539c2263bd2017b306aebbd791a471","type":"python_verification"},{"bytes":6633,"checked_by_registry":false,"claim_ids":["SEAM.EQUIV.CONTINUUM.02"],"cluster":"core","description_excerpt":"The continuum realisation sharpened -- the 'c=8 ambiguity' flagged open in v277/v344 (E8 vs SO(16) both have c=8) is RESOLVED, non-circularly, by the seam's ORDER-4 mu4 clock. [E] E8 (det 1, holomorphic) vs D8=SO(16) (det 4). [E] the order-4 clock (the four Gauss-Bonnet marks, |mu4|=4=h(A3), v216): index-4 extension D5(+)A3 = E8 (v154), index-2 = SO(16); so order-4 selects E8 (16->4->1) not SO(16) (16->4) -- the orde","id":"python_verification:verification/v351_continuum_realisation_sharpened.py","line_count":97,"path":"verification/v351_continuum_realisation_sharpened.py","sha256":"9c6b24807be4fcf3a87985ffe8feed91229f5a96f42512af68cf52f66a73b76e","type":"python_verification"},{"bytes":6354,"checked_by_registry":false,"claim_ids":["TFPT.IRREDUCIBLE.01"],"cluster":"core","description_excerpt":"The framework reduction -- the deepest answer to 'the inputs are not axioms, they are back-determined'. [E] P2 (g_car=5) FORCED three ways (v6): rank-fill, Coxeter-match (g_car=max prime of h(E8)=30), Pascal. [E] P1 (c3=1/(8pi)) FORCED: c3 is the boundary Gauss-Bonnet coefficient (v216/v342), the 8 over-determined four ways (8=rank E8=h(D5)=phi(30)=det R, v54/v6); only pi is non-forced (the boundary transcendental). ","id":"python_verification:verification/v352_framework_irreducible.py","line_count":92,"path":"verification/v352_framework_irreducible.py","sha256":"563355a4a35e3c8a810f47ca65e70ced7efccaa4ab3151f6036eca4e46618f4c","type":"python_verification"},{"bytes":7186,"checked_by_registry":false,"claim_ids":["TFPT.SELFLOOP.01"],"cluster":"core","description_excerpt":"The bird's-eye rethink (refining v352): TFPT is not a LINEAR theory (axioms -> theorems) but a CLOSED SELF-CONSISTENT LOOP whose outputs fix its own inputs, with ZERO free adjustable dimensionless parameters. [E] IT IS A LOOP: outputs fix inputs (g_car=5 = max prime of h(E8)=30; the 8 in c3 = rank E8) and inputs fix outputs; the arrows close into a circle (v6) with a unique fixed point (v56). [E] ZERO FREE DIALS: eve","id":"python_verification:verification/v353_selfloop_capstone.py","line_count":104,"path":"verification/v353_selfloop_capstone.py","sha256":"e11b548ade152eaad1dbc974492f577612c5eef5187bfdd16b43e04eefead730","type":"python_verification"},{"bytes":8139,"checked_by_registry":false,"claim_ids":["E8.REVERSE.AUDIT.01"],"cluster":"registry","description_excerpt":"The REVERSE numerology audit + what the golden ratio means. The forward rule (v305) is one-directional (every readout must map onto E8); the reverse question: how much E8 structure maps onto NOTHING? [E] E8 has 8 Casimir invariant degrees {2,8,12,14,18,20,24,30}; THREE feed a readout (2 metric, 8 rank->c3, 30 Coxeter->g_car) and FIVE are UNMAPPED {12,14,18,20,24} -- 3/8 load-bearing, 5/8 not. [E] ECONOMY, NOT PROMISC","id":"python_verification:verification/v354_e8_reverse_audit.py","line_count":110,"path":"verification/v354_e8_reverse_audit.py","sha256":"aeacc858d379d929440e50030e77ab775a5b52949b04873c326c24ad981f114a","type":"python_verification"},{"bytes":8190,"checked_by_registry":false,"claim_ids":["E8.UNMAPPED.BANDWIDTH.01"],"cluster":"registry","description_excerpt":"A disciplined bandwidth search of the unmapped E8 region (next step after v354), run with a STRICT discriminator: a candidate counts only if it is a FORCED identity (a theorem about E8), never a numerical coincidence -- because mining a rich object for matches is the numerology temptation. [E] FORCED SET-LEVEL (the real collective content): sum(degrees)=128=dim S+ the spinor half of 248=120+128; sum(exponents)=120=#p","id":"python_verification:verification/v355_e8_unmapped_bandwidth.py","line_count":121,"path":"verification/v355_e8_unmapped_bandwidth.py","sha256":"11d7a248be3d51240d264e91bd22746af2169f425c07a9622ec6f53567c34d2e","type":"python_verification"},{"bytes":7950,"checked_by_registry":false,"claim_ids":["SEAM.EQUIV.CONTINUUM.03"],"cluster":"core","description_excerpt":"Direction A: the continuum chain of SEAM.EQUIV.01 assembled theorem-by-theorem, residual reduced to ONE lattice-realization input tied to the seam's one-sidedness. Chain: gapped (v302) quasi-free 16-Majorana collar (v155/v160) -> invertible (Kitaev, v301) -> the NONTRIVIAL invertible phase (c_-=8) -> a non-gappable anomalous chiral edge (anomaly inflow: edge EXISTENCE follows, reducing the v336/v351 'does the edge ex","id":"python_verification:verification/v356_continuum_mmst_applicability.py","line_count":120,"path":"verification/v356_continuum_mmst_applicability.py","sha256":"4d076d55ef31ac0a7336e06af2e47b2f73428c080d634c496446d572dcbb6450","type":"python_verification"},{"bytes":8557,"checked_by_registry":false,"claim_ids":["GRAV.ENTROPY.EQUILIBRIUM.01"],"cluster":"core","description_excerpt":"The entanglement-equilibrium derivation (Jacobson 2015 / Faulkner et al., delta S = delta<K>) with TFPT's atoms -> the LINEARISED Einstein equation falls out PARAMETER-FREE, and the two formerly-open pieces are closed. [E] parameter-free Einstein coeff G_ab=(1/c3)T_ab, 1/c3=8pi fixed (Unruh 1/(2pi)=4c3, EH 1/(16pi)=c3/2, Einstein 8pi=1/c3, Bekenstein 1/4=1/|mu4|). [E] THERMO=GEO coincidence (new): the first law's 2pi","id":"python_verification:verification/v358_grav_entropy_equilibrium.py","line_count":121,"path":"verification/v358_grav_entropy_equilibrium.py","sha256":"f5f0beb9178b8fffcde3b5b9458d75c025b3c1f7f2affffd24b8d7c938ca4ce2","type":"python_verification"},{"bytes":8173,"checked_by_registry":false,"claim_ids":["GRAV.NONLINEAR.01"],"cluster":"core","description_excerpt":"The FULL covariant Einstein equation, parameter-free (Direction 1, extends v358). The Jacobson-2015 fixed-VOLUME entanglement equilibrium brings in the EINSTEIN TENSOR G_ab (not just R_ab) -- the unique divergence-free metric tensor (Lovelock) -- so equilibrium yields the full covariant G_ab + Lambda g_ab = (1/c3) T_ab with conservation built in. [C/E] fixed-volume -> Einstein tensor (trace=-R in d=4). [E] Lovelock =","id":"python_verification:verification/v359_grav_nonlinear_einstein.py","line_count":119,"path":"verification/v359_grav_nonlinear_einstein.py","sha256":"607d1ed5742664fd809c40ec53e1b473c230663b2e5949c8bee5aa7ae4ceb98a","type":"python_verification"},{"bytes":3900,"checked_by_registry":false,"claim_ids":["BOUNDARY.01"],"cluster":"frontier","description_excerpt":"the discrete ↔ continuous boundary; cross-ratio cleanness","id":"python_verification:verification/v35_quark_qcd_boundary.py","line_count":88,"path":"verification/v35_quark_qcd_boundary.py","sha256":"0f244778714be5b39ac0c8b6c76bfc1bc9bffff34218d00c435ddc7c806a83d4","type":"python_verification"},{"bytes":6774,"checked_by_registry":false,"claim_ids":["GRAV.GAPCORR.01"],"cluster":"core","description_excerpt":"Direction 2: the gap-induced higher-curvature correction to GR -- the disciplined result. Does the seam transfer gap give a NEW forced near-term GR-deviation beyond the known R^2 scalaron? With the v354/v355 discriminator: NO. [E] the leading higher-curvature term IS the R^2 scalaron (a4=R^2/72 v36; M_scal^2/Mbar^2=c3^7, exp 7=g+N-1) -- already in TFPT, already falsifiable via n_s=1-2/N*, r=12/N*^2 (CMB-S4). [C] it i","id":"python_verification:verification/v360_grav_gap_corrections.py","line_count":103,"path":"verification/v360_grav_gap_corrections.py","sha256":"2d2ba9d18b8856e5b7b1dd34aceffd08fb17badd9f64cdfb7be5039e3119fa69","type":"python_verification"},{"bytes":7061,"checked_by_registry":false,"claim_ids":["GRAV.BACKREACT.01"],"cluster":"core","description_excerpt":"Direction 5: the matter-gravity backreaction with the explicit J3 flux -- two forced facts + an honest decline. [E] the carrier's gravitational anomaly is FORCED: c_-=8 (16 Majoranas=dim S+=2^(g_car-1); chiral central charge 16/2=8=g_car+N_fam, the same c_- as v358). [E] the backreaction is FINITE -> Lambda from alpha: the matter vacuum energy through G_ab=(1/c3)T_ab is gap-suppressed (Decoupling Thm v337) to rho_Lam","id":"python_verification:verification/v361_grav_backreaction.py","line_count":105,"path":"verification/v361_grav_backreaction.py","sha256":"c412314a87a2018a1fe9aadb098ad4d25fd1e5cadd1cbce513b9d31660648dd4","type":"python_verification"},{"bytes":7213,"checked_by_registry":false,"claim_ids":["VGEO.SHARPEN.01"],"cluster":"core","description_excerpt":"Direction 6: v_geo is the SINGLE dimensionful input of the WHOLE theory -- confirmed across matter AND gravity -- and irreducibly primitive. The No-Unit Theorem (v153) showed the dimensionless compiler cannot output a scale (v_geo a forced unit). SHARPENING after the parameter-free gravity (v358/v359/v361): the gravity sector adds NO new scale either -- 1/c3=8pi and the Lambda prefactor (8pi)^2*48c3^4=3/(4pi^2) are d","id":"python_verification:verification/v364_vgeo_sharpen.py","line_count":104,"path":"verification/v364_vgeo_sharpen.py","sha256":"0017c8bbdd4dc319c406c7254a6c8f7dd646254f07e5346e36402c1c51fda33a","type":"python_verification"},{"bytes":8522,"checked_by_registry":false,"claim_ids":["QGAMB.SADDLE.01"],"cluster":"core","description_excerpt":"Direction 3: the QG measure (gate C7/QG.AMB.01) as one-loop GAUSSIAN fluctuations around the PARAMETER-FREE saddle (v358/v359). [E] the fluctuation stiffness is 1/c3=8pi (no free dial), so the one-loop problem is well-posed (it was NOT before v358). [E] the fluctuation operator is gapped M>=Delta_eff=6 ln(3/2)-31/(4pi^2)~1.648>0 (v76/v337) => mode-by-mode Gaussian convergence, no zero/negative modes besides the saddl","id":"python_verification:verification/v365_qg_oneloop_saddle.py","line_count":132,"path":"verification/v365_qg_oneloop_saddle.py","sha256":"85810db7380a9f9a9d2242b0763c2418edce824d67dce16c992989817f278bce","type":"python_verification"},{"bytes":7203,"checked_by_registry":false,"claim_ids":["SEAM.MMST.INCLASS.01","SEAM.EQUIV.MMST.01"],"cluster":"core","description_excerpt":"Direction 7: the seam collar is IN MMST's free-lattice-fermion scaling-limit class, so the chiral scaling limit is a chiral CFT of central charge 8 pinned to (E8)_1 -- reducing SEAM.EQUIV.01 to the single S3 lattice-realisation input. Osborne-Stottmeister (arXiv:2107.13834, CMP 398 (2023) 219; legacy internal token MMST, on the MMST/Morinelli-Morsella-Stottmeister-Tanimoto OAR framework): free lattice fermions (CAR q","id":"python_verification:verification/v366_mmst_seam_collar.py","line_count":114,"path":"verification/v366_mmst_seam_collar.py","sha256":"c349773dc520ef36a2084b7cb6ea3e66dd4c787dfab3fa5de435e052f6873837","type":"python_verification"},{"bytes":7911,"checked_by_registry":false,"claim_ids":["SEAM.S3.LATTICE.01"],"cluster":"core","description_excerpt":"Track 1: the EXPLICIT lattice realisation of the S3 input -- a concrete gapped chiral-Majorana (p+ip) lattice model whose edge is the 16-Majorana SO(16)_1 carrier, mu4-condensed to (E8)_1; turns the abstract S3 residual (v356/v366) into a RUNNABLE model with a numerically computed topological invariant. [E] bulk gapped (band gap 2>0 at M=1). [E] non-trivial Chern number (Fukui-Hatsugai-Suzuki: |C|=1 at M=1, C=0 at M=","id":"python_verification:verification/v367_seam_s3_lattice.py","line_count":151,"path":"verification/v367_seam_s3_lattice.py","sha256":"d43a91462b2f54cf9677b4e0352630ff4ba6030dee50b14a1e2418875f457129","type":"python_verification"},{"bytes":7069,"checked_by_registry":false,"claim_ids":["SEAM.S3.INFLOW.01"],"cluster":"core","description_excerpt":"Track 1: the bulk-edge / anomaly-inflow leg (S4 of the v356 chain) made CONCRETE on the v367 lattice model -- a finite STRIP of the gapped p+ip model has a realised, non-gappable chiral edge, so edge EXISTENCE follows from the invertible bulk (anomaly inflow), NOT a separate assumption. [E] topo in-gap edge states (M=1 strip min_kx|E|~0) vs trivial clean gap (M=3, neg control); [E] the near-zero state is edge-localis","id":"python_verification:verification/v368_seam_s3_inflow.py","line_count":124,"path":"verification/v368_seam_s3_inflow.py","sha256":"f7f3b78ab82cdf37d1d851c46de6960f6444ca88e4bf86c24ca1e1539baaf31d","type":"python_verification"},{"bytes":9839,"checked_by_registry":false,"claim_ids":["QGAMB.REDUNDANCY.01"],"cluster":"frontier","description_excerpt":"Track 2 (next-plan v2): the AMBIENT REDUNDANCY statement -- the holographic route to Gravity-complete that SIDESTEPS building the general Euclidean QG measure (C7/QG.AMB.01). Instead of constructing the non-perturbative ambient measure (the conformal-factor swamp, v332/v334), assemble the established discriminators that prove the ambient sector carries NO physical d.o.f. relative to the holomorphic boundary algebra, ","id":"python_verification:verification/v369_qgamb_redundancy.py","line_count":154,"path":"verification/v369_qgamb_redundancy.py","sha256":"89e640abf05b9c86212b5e30c896e7f6458e7ad43660a507f62068452fc6b195","type":"python_verification"},{"bytes":3721,"checked_by_registry":false,"claim_ids":["QG.G2.01","QG.GAPDEC.01"],"cluster":"gravity","description_excerpt":"G2 spectral action → R + R²; gap-decoupling Δ_eff = 1.648","id":"python_verification:verification/v36_spectral_action_g2.py","line_count":76,"path":"verification/v36_spectral_action_g2.py","sha256":"b05a1d491b75df6a0427f203517fcc8547c6fbd7c6083c90c39eef210bc09e3a","type":"python_verification"},{"bytes":9393,"checked_by_registry":false,"claim_ids":["GRAV.SPIN2.UNITARITY.01"],"cluster":"frontier","description_excerpt":"Track 2: the Barnes-Rivers spin decomposition of the graviton propagator -- perturbative graviton unitarity SECTOR-BY-SECTOR (extends v304's scalar pole algebra to the tensor spin structure + combines with v334's spin-0 conformal mode). [E] projector completeness: tr P2=(d-2)(d+1)/2, tr P1=d-1, tr P0s=tr P0w=1 sum to d(d+1)/2; the d=4 split is 5+3+1+1=10. [E] EH structure: spin-2 coefficient +1, spin-0 scalar -1/(d-2","id":"python_verification:verification/v370_grav_spin2_unitarity.py","line_count":142,"path":"verification/v370_grav_spin2_unitarity.py","sha256":"c4f24dc36967c2c3e81180c19bda43763503a46cfc84405dfdce3bb9f19fb00a","type":"python_verification"},{"bytes":5276,"checked_by_registry":false,"claim_ids":["FR.POLE.SOLVE.01"],"cluster":"frontier","description_excerpt":"Track 3 (F_transfer): the Koide source->pole transfer as a typed solver -- promotes the experiments/ftransfer solve into the ledger with a kill test (does NOT re-prove 53/54 v183 or Q*=2/3 v82/v101). [E] Q_pole=Koide(PDG poles)=2/3 to 3e-6, Q_src(phi0-ladder)=0.66446 (0.33% below). 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[E] axion spine angle 3pi/5=pi*N_fam/g_ca","id":"python_verification:verification/v397_external_clock_probe.py","line_count":102,"path":"verification/v397_external_clock_probe.py","sha256":"0dcca10be5fc28ca9f628e99c70520b68f7fcbcac696f3005847d9e123d93ea5","type":"python_verification"},{"bytes":8663,"checked_by_registry":false,"claim_ids":["SEAM.RIGIDITY.01"],"cluster":"registry","description_excerpt":"Seam State Rigidity Theorem (Paper A / G_net): RP-definability hinge (OS transfer + quasi-free) + band-limited mu4-character core swept N=4..64 + holomorphy=>(E8)_1; [O] full-L^2 / intrinsic BW","id":"python_verification:verification/v398_seam_state_rigidity.py","line_count":154,"path":"verification/v398_seam_state_rigidity.py","sha256":"a59143b7545a1244bd75c55c046e8f6ab17f381f736ad0b0ff5062fb07682c91","type":"python_verification"},{"bytes":6591,"checked_by_registry":false,"claim_ids":["GRAVITY.COMPLETE.01"],"cluster":"frontier","description_excerpt":"Gravity-complete = Boundary-complete + Ambient-redundancy (Paper B): local equation parameter-free (v358/v359) + redundancy discriminators (v369) + O_phys subset A_Sigma over 5 readout classes","id":"python_verification:verification/v399_gravity_complete.py","line_count":113,"path":"verification/v399_gravity_complete.py","sha256":"87bf93ed80ae0dde2a12b16a033a16a03766f1868ca546495728222f5f61616a","type":"python_verification"},{"bytes":5151,"checked_by_registry":false,"claim_ids":["GATE.UWALL.03"],"cluster":"uwall","description_excerpt":"selectors: splitting type = a, det R = 8, Spec(Q₊)","id":"python_verification:verification/v39_uwall_selectors.py","line_count":96,"path":"verification/v39_uwall_selectors.py","sha256":"c84171976085ce38d3cfa8bfafc7b81f222ee756f3ae4f5257484b8f4b8787e6","type":"python_verification"},{"bytes":5912,"checked_by_registry":false,"claim_ids":["EM.FP.01"],"cluster":"em","description_excerpt":"α⁻¹ = 137.0359992168 unique root of F_U(1)=0; ablation","id":"python_verification:verification/v3_em_alpha.py","line_count":140,"path":"verification/v3_em_alpha.py","sha256":"22f769d9f89e74e2279c06b11c75d6da4d7455ef185fb2f79869a30932ebc3e8","type":"python_verification"},{"bytes":6597,"checked_by_registry":false,"claim_ids":["GRAV.NONLOCAL.01"],"cluster":"frontier","description_excerpt":"Nonlocal spectral-gravity action; local R+R^2 is its IR projection (Paper C): entire form factor one pole + truncation-zero monotone + IR matching to R+R^2 with scale c3^7","id":"python_verification:verification/v400_grav_nonlocal_action.py","line_count":111,"path":"verification/v400_grav_nonlocal_action.py","sha256":"fa26d47a90d10cb6b6ad41e8a9d331ea67710dedbd883366abd1b355a73af176","type":"python_verification"},{"bytes":6837,"checked_by_registry":false,"claim_ids":["METROLOGY.CLOSURE.01"],"cluster":"frontier","description_excerpt":"Metrology closure {a, pi, v_geo} (Paper D): 0 dimensionless dials + 1 unit; dimensional bookkeeping (No-Unit) + gravity adds no unit + G-vs-Lambda 0.11%; v_geo theorem-forbidden","id":"python_verification:verification/v401_metrology_closure.py","line_count":117,"path":"verification/v401_metrology_closure.py","sha256":"9ff5680b380bcc8c0a46d5591fde0c10b3abac6cde4f261ae38e29031835c566","type":"python_verification"},{"bytes":7271,"checked_by_registry":false,"claim_ids":["FTRANSFER.SUITE.01"],"cluster":"frontier","description_excerpt":"F_transfer functor suite (Paper E): the four frontier sectors as one F_observable o F_threshold o F_RG with exact atom sources + kill-test coverage + the firewall","id":"python_verification:verification/v402_ftransfer_suite.py","line_count":117,"path":"verification/v402_ftransfer_suite.py","sha256":"fb6fc268259f703b033b70a6bf0b24d4c52e4a132e285083a29ed1b0b4b50cb0","type":"python_verification"},{"bytes":8017,"checked_by_registry":false,"claim_ids":["ARITH.HULL.01"],"cluster":"frontier","description_excerpt":"ARITH.HULL.01: the three number-field facets (v390) COMPOSE to K=Q(i,sqrt-3,sqrt5), a degree-8=rank(E8) abelian field -- the arithmetic hull dual to the E8 lattice hull. [E] -1,-3,5 independent in Q*/(Q*)^2 so [K:Q]=2^3=8=rank E8=g_car+N_fam, Galois (Z/2)^3 order 8; 2^omega(h(E8))=2^3=8=rank E8 is E8-special (E7: h=18, omega=2, 2^2=4!=7). [E] exactly 7 quadratic subfields {-1,-3,5,3,-5,-15,15} = 4 imaginary (|mu4|, C","id":"python_verification:verification/v403_facet_compositum.py","line_count":153,"path":"verification/v403_facet_compositum.py","sha256":"34602d99aeb74755040244174695ef486850bff5bf46633f9eb23a15885e03f5","type":"python_verification"},{"bytes":7035,"checked_by_registry":false,"claim_ids":["E8.CMDUAL.01"],"cluster":"frontier","description_excerpt":"E8.CMDUAL.01: the (E8)_1 vacuum character chi_E8=E4/eta^8=j^{1/3} at the two CM points -- 12 at the seam (tau=i), 0 at the family (tau=omega), extending v282. [E] chi_E8^3=j (q-series). [E] SEAM tau=i (Q(i), order 4): cross-ratio 2 => j=1728 => chi_E8(i)=12 (E8 present, v214/v282). [E] FAMILY tau=omega (Q(sqrt-3), order 6): equianharmonic lambda (lambda^2-lambda+1=0) => j=0 => chi_E8(omega)=0 (E4 vanishes, v220/v267)","id":"python_verification:verification/v404_e8_char_cm_duality.py","line_count":121,"path":"verification/v404_e8_char_cm_duality.py","sha256":"525a457c96ff275433d08a57398caa76e997940a0e586dfc1e14f61c34517d2d","type":"python_verification"},{"bytes":7999,"checked_by_registry":false,"claim_ids":["SEAM.EQUIV.02"],"cluster":"frontier","description_excerpt":"SEAM.EQUIV.02: the dual keystone at tau=omega -- the family/flavor sector as the order-3 Eisenstein/A2 face of E8, dual to the seam = (E8)_1 at tau=i (v404). A named contract, NOT a closure. [E] chi_E8(omega)=0 (E8 degenerates at the family CM point) vs chi_E8(i)=12. [E] A2 = the tau=omega Eisenstein lattice (Cartan det 3=N_fam, h=3=N_fam, mu6=mu3 x mu2). [E] R lives in E6 x A2: 248=78+8+2*27*3, ||R||_F^2=78=dim E6, ","id":"python_verification:verification/v405_seam_equiv_omega.py","line_count":134,"path":"verification/v405_seam_equiv_omega.py","sha256":"10ba46ab87e6a1b634e83be76c7966ad8fe3fe6db1d5ce96ad8eee8cb9cd8635","type":"python_verification"},{"bytes":6357,"checked_by_registry":false,"claim_ids":["FLAV.PMNS.CLOSE.01"],"cluster":"neutrinos","description_excerpt":"FLAV.PMNS.CLOSE.01: the PMNS dynamics closed modulo the tau=omega keystone (v405) -- the CP-phase ORIGIN is the family CM point and the absolute scale is one v_geo-class unit, so PMNS has zero free flavor dials beyond v_geo. [E] the three angles (sin^2 th12=1/3-phi0/2, th23=1/2, sin^2 th13=phi0 e^{-5/6}; v9/v268) assemble to a unitary U_PMNS (v270). [C] CP-phase origin: delta_PMNS=4pi/3 is the tau=omega CM phase (v40","id":"python_verification:verification/v406_pmns_phase_origin.py","line_count":108,"path":"verification/v406_pmns_phase_origin.py","sha256":"b00e2152e510897b02c121999443bf186c757dcf7b395263d2c6f80712bd9350","type":"python_verification"},{"bytes":6731,"checked_by_registry":false,"claim_ids":["FLAV.SELECTOR.CLOSE.01"],"cluster":"uwall","description_excerpt":"FLAV.SELECTOR.CLOSE.01: the R4' residue folds into the tau=omega keystone (v405) -- the three (d,n) selector pairings ARE the tau=omega family-slice atoms. [E] the frame (1,a,sigma) is a Z^3 basis det=11=||Pl(K)||_1, n=(5,-9,6) the unique covector with n.1=2, n.a=8, n.sigma=121=11^2 -> (d,n)=>R columnwise (v136/v139). [E] n.a=8=rank E8=dim A2=det R = the A2 (tau=omega) block dimension reading R in E6 x A2. [E] the pa","id":"python_verification:verification/v407_dn_pairings_omega.py","line_count":116,"path":"verification/v407_dn_pairings_omega.py","sha256":"64696c1c123906cb34f1aebe276dd00f6cb91dd20dd2e0becb99296bddf07eb0","type":"python_verification"},{"bytes":8500,"checked_by_registry":false,"claim_ids":["HYP.PHI0.PUNCTURE.01"],"cluster":"frontier","description_excerpt":"HYP.PHI0.PUNCTURE.01: name the phi0 puncture term dtop = 48 c3^4 as the order-4 local boundary heat-kernel (Seeley-DeWitt) contact term of the mu4 puncture divisor -- the analytic complement of the icosahedral tree term (v396, HYP.PHI0.01). [E] THE SPLIT IS EXACT: phi0 = phibase + dtop = 1/(6 pi) + 48 c3^4 (v396/ARCH.QUAD.01), a tree term plus a fourth-order boundary correction. [E] PUNCTURE COUNT = Omega_adm = N_fam","id":"python_verification:verification/v408_phi0_puncture_heatkernel.py","line_count":129,"path":"verification/v408_phi0_puncture_heatkernel.py","sha256":"db1e58d685fa8b53d6e0ca777b77e8982f87c3514a2ba66e16158ad56945e933","type":"python_verification"},{"bytes":8375,"checked_by_registry":false,"claim_ids":["RES.COXETER.SYMMETRY.01","FORM.COXETER.PRIME2.01"],"cluster":"frontier","description_excerpt":"RES.COXETER.SYMMETRY.01 closed as a STRUCTURAL LEMMA: prime-2 is NECESSARY but NOT autonomous -- no prime-2-only attractor exists (resolves the v394/COXETER.ATOMS.01 open question's falsifiable corollary). [E] SHEET INVOLUTION: sigma=diag(1,-1,-1), sigma^2=I, spectrum {+1,-1} (parity). [E] SHEET PROJECTOR P=(I+sigma)/2=diag(1,0,0), P^2=P, spectrum {0,1} (projection). [E] NO CONTRACTION RATE: none of {-1,0,1} lies in ","id":"python_verification:verification/v409_coxeter_prime2_lemma.py","line_count":129,"path":"verification/v409_coxeter_prime2_lemma.py","sha256":"e0779b170d5e9085ff26ed0dd55a3b549d96c59b5ccc237753b46293d4639d5b","type":"python_verification"},{"bytes":6229,"checked_by_registry":false,"claim_ids":["GATE.UWALL.04"],"cluster":"uwall","description_excerpt":"harmonic metric = finite linear algebra (polystable ⇒ unitary)","id":"python_verification:verification/v40_harmonic_metric.py","line_count":137,"path":"verification/v40_harmonic_metric.py","sha256":"52c76c5f5992f5e317b6277e5313c8f3f92650304bc967930466940c3039e39a","type":"python_verification"},{"bytes":7070,"checked_by_registry":false,"claim_ids":["SHEET.GEN.BINARY.01"],"cluster":"registry","description_excerpt":"The sheet generator V = Q diag(0,1,1) (the rank-2 sheet axis of the centered cross, v95/v218) is a binary internal compiler: V^n = ((0,2^(n-1),0),(0,2^n,0),(0,2^(n+1)-2,1)) (induction F(n)V=F(n+1)), so V^n.1 = (2^(n-1),2^n,2^(n+1)-1) = (1,2,3),(2,4,7),(4,8,15),(8,16,31); 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the operator on the Z2 wall, J=M(1,-2)=C-2V=((4,1,0),(4,1,2),(5,1,1)), was unnamed and completes the sheet axis J,K,C,F=M(1,-2..1). chi_J=lambda^3-6lambda^2+3lambda-2 gives (tr,e2,det)=(6,3,2)=(|R^+(A3)|,N_fam,|Z2|); a.J.a=30=h(E8), det(I+J)=12=dim g_SM=chi_E8(i), det(2","id":"python_verification:verification/v412_sheet_source_corner_J.py","line_count":82,"path":"verification/v412_sheet_source_corner_J.py","sha256":"6dc64fada7aeae2c3ad4b555f43dd41d9bb3758e5df08daaea3370e8658a434e","type":"python_verification"},{"bytes":4509,"checked_by_registry":false,"claim_ids":["DIAMOND.SHEET.CALCULUS.01"],"cluster":"registry","description_excerpt":"The sheet axis is a discrete characteristic-difference calculator: on M_t=C+tV (v95/v218) the elementary-symmetric coefficients encode atoms as DIFFERENCE ORDERS -- e1(t)=3t+12, e2(t)=2t^2+15t+25, e3(t)=det M_t=4t^2+14t+14 give Delta e1=3=N_fam, Delta^2 e2=4=|mu4|, Delta^2 e3=8=rank E8 (the e3 curvature cross-cited to v218/v224; the full (e1,e2,e3) ladder is new); the anchor energy a.M_t.a=52+11t (step 11=a.V.a, v410","id":"python_verification:verification/v413_sheet_characteristic_calculus.py","line_count":99,"path":"verification/v413_sheet_characteristic_calculus.py","sha256":"01d451781ba19dcd0064dc85aefc2eda30fdf441d85985d2a9731902a7dc8555","type":"python_verification"},{"bytes":2319,"checked_by_registry":false,"claim_ids":["DIAMOND.CENTER.RESOLVENT.01"],"cluster":"registry","description_excerpt":"The center C is a resolvent portal G2 -> F4 -> E8: the center C=M(1,0) (v95) is the t=0 evaluation of V; tr C=12=dim g_SM=chi_E8(i), det C=14=dim G2, sum C=31=2^g_car-1=248/8; the shifted determinants climb the exceptional ladder det(C)=14=dim G2, det(I+C)=52=dim F4, det(2I+C)=120=|R^+(E8)| -- the shell ladder G2->F4->E8^+ as det(C+kI), k=0,1,2 (the resolvent ladder is the new content; reading audit-typed).","id":"python_verification:verification/v414_center_resolvent_portal.py","line_count":59,"path":"verification/v414_center_resolvent_portal.py","sha256":"5b2779034bd729184a2e40ab5304c1c473dd9c429300d2a36f584753453a6c70","type":"python_verification"},{"bytes":6880,"checked_by_registry":false,"claim_ids":["DIAMOND.GAUSS.01"],"cluster":"flavor","description_excerpt":"The square CM-norm dictionary is operator-realised and the mu4 deck is intrinsic: the Gaussian arithmetic of v222/v230 lifted from numbers to OPERATORS via J=[U,V]/3, the complex structure born from the commutator of the binary V and ternary U compilers (v410/v95). J=((-1,1,0),(-2,1,0),(-3,1,0)) is integer, Spec(J)={i,-i,0}, J^2=-I on the rank-2 image, J^3+J=0 (a mu4 quarter-turn); 3I+2J has spectrum {3+2i,3-2i,3} an","id":"python_verification:verification/v415_gaussian_operator.py","line_count":132,"path":"verification/v415_gaussian_operator.py","sha256":"fd097db8e95c6a56dbc9f5173991c134220b58880b8aec29ae808ee45a6d83a0","type":"python_verification"},{"bytes":5123,"checked_by_registry":false,"claim_ids":["ARITH.TRICHOTOMY.01"],"cluster":"core","description_excerpt":"The atom trichotomy: {2,3,5} are ramified/inert/split in the two exceptional CM rings, and each atom is the unique ramified prime of one quadratic facet of K=Q(i,sqrt-3,sqrt5) (v403). Z[i] (square/seam, tau=i): 2=|Z2| ramifies (2=-i(1+i)^2), 3=N_fam inert (norm 9=N_fam^2), 5=g_car splits ((2+i)(2-i)) -- the carrier rank factors on the seam; Z[omega] (hex/flavor, tau=omega): 3=N_fam ramifies (N(1-omega)=3), 2 inert (n","id":"python_verification:verification/v416_atom_trichotomy.py","line_count":113,"path":"verification/v416_atom_trichotomy.py","sha256":"d46e4f092c6e5953ea10f023a718d54ebf1c11ba19830f8ad10e9bb325fa81b3","type":"python_verification"},{"bytes":7802,"checked_by_registry":false,"claim_ids":["DIAMOND.EISEN.01"],"cluster":"flavor","description_excerpt":"The Eisenstein/CP operator (hex dual of v415): the family rotation P=(1 2 3) and the CP clock W=-P^2 put the tau=omega flavor side on operators, unified with the seam into ONE order-30 clock. P^3=I, P^2+P+I=ONES (Eisenstein omega^2+omega+1=0 on the plane perp to (1,1,1)); (3I+2P)(3I+2P^2)=7I+6 ONES with Spec {7,7,25} -- 7=N_omega(3+2omega)=scalaron on the omega-plane, 25=g_car^2 on (1,1,1) -- the dual of v415's {13,1","id":"python_verification:verification/v417_eisenstein_cp_operator.py","line_count":147,"path":"verification/v417_eisenstein_cp_operator.py","sha256":"c5f1fe26b9e6fd30bf2ad45354de6819a184c4a86b491f19ab21cb53b21c2b7e","type":"python_verification"},{"bytes":8291,"checked_by_registry":false,"claim_ids":["ARITH.NORMTRIPLE.01"],"cluster":"core","description_excerpt":"The cyclotomic norm triple: the carrier split (3,2) read in the three atom-rings gives (7,13,55)=(scalaron, Delta_Q, quark numerator), and the missing carrier-5 clock of v417 is found as the 4x4 Phi5-companion C5. C5 has chi=x^4+x^3+x^2+x+1, C5^5=I, tr=-1, and the golden ratio is its real-part data (2cos(72)=1/phi, 2cos(144)=-phi; output-side, v313/v349; dim 4, not 3 -- refines v417's gap); N_Z[zeta5](3+2 zeta5)=det(","id":"python_verification:verification/v418_cyclotomic_norm_triple.py","line_count":150,"path":"verification/v418_cyclotomic_norm_triple.py","sha256":"88b95b445bfce64f7d20a6bf9c84ed1c8de56f0367ced908cc163e01d62b0ba2","type":"python_verification"},{"bytes":5810,"checked_by_registry":false,"claim_ids":["SEAM.GALOIS.01"],"cluster":"core","description_excerpt":"The seam mu4 IS the carrier's Galois group: a positive resolution of the v409/RES.COXETER.SYMMETRY.01 cyclic/Galois asymmetry. 30=2*3*5 is squarefree so Z/30 has no order-4 element -- the seam mu4 (order 4) cannot be a cyclic hand and is forced onto the Galois side; (Z/30)^x = (Z/2)^x x (Z/3)^x x (Z/5)^x = mu4 x Z2 (order phi(30)=8=rank E8), where the mu4 (Z/4) factor IS (Z/5)^x (carrier 5) and the Z2 IS (Z/3)^x (fam","id":"python_verification:verification/v419_seam_galois_carrier.py","line_count":110,"path":"verification/v419_seam_galois_carrier.py","sha256":"cc6152ad7ea68c67725020e386e49eec32810ab25bb483c76bae99964399c2fd","type":"python_verification"},{"bytes":6704,"checked_by_registry":false,"claim_ids":["GATE.UWALL.05"],"cluster":"uwall","description_excerpt":"final leg test: amplitudes = δ=½ resolvent; honest negative","id":"python_verification:verification/v41_leg_assignment.py","line_count":142,"path":"verification/v41_leg_assignment.py","sha256":"e9ba522426bdc67ad027fbaa7867e6dabdb1a962c169aa1ae8b10ea76eb2c64f","type":"python_verification"},{"bytes":5732,"checked_by_registry":false,"claim_ids":["FR.POLE.QED.01"],"cluster":"frontier","description_excerpt":"F_pole external: the Koide source->pole transfer is a ONE-LOOP ELECTROMAGNETIC effect, not an algebraic step -- the honest 'do the external physics' follow-up to v93 and the clock No-Go. 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[E] E8 IS FIXED BY ITS DEGREE MULTISET: from deg(E8)={2,8,12,14,18,20,24,30} alone -- rank=#deg=8 (=2nd deg), h=max=30, #pos roots=Σexp=120, #roots=240, dim=248, |W|=∏deg=696729600, Σdeg=128=2^7=dim S^+. [E] THE JOINT","id":"python_verification:verification/v437_e8_degree_joint.py","line_count":100,"path":"verification/v437_e8_degree_joint.py","sha256":"a502dc852fb03fcdc8951870058af1339721c1eda8139e3f06f95ead8be2bbef","type":"python_verification"},{"bytes":7828,"checked_by_registry":false,"claim_ids":["SEAM.EQUIV.BW.HSMI.01"],"cluster":"frontier","description_excerpt":"SEAM.EQUIV.BW.HSMI.01: the half-sided modular inclusion (Borchers/Wiesbrock) as an INTRINSIC Bisognano-Wichmann route for face (ii) of SEAM.EQUIV.01 -- geometric modular flow WITHOUT presupposing covariance. [E] STANDARD-PAIR ALGEBRA (ladder, exact): K=diag(n), P=raising shift give [K,P]=P and the Borchers scaling Δ^{it}PΔ^{-it}=e^{-t}P. 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[E] EXPONENTIAL CLUSTERING: |⟨c_i†c_j⟩|~e^{-r/ξ}, ξ finite and STABLE across N (gapped ⇒ Hastings-Koma deca","id":"python_verification:verification/v439_seam_lieb_robinson.py","line_count":146,"path":"verification/v439_seam_lieb_robinson.py","sha256":"322d5f457532d168080afd7828c4405cf3c36a6ffc6c5d0e82568ecc8fec30c3","type":"python_verification"},{"bytes":5614,"checked_by_registry":false,"claim_ids":["GATE.UWALL.16"],"cluster":"masses","description_excerpt":"Λ²F bridge: exterior leg = 𝟑̄; discrete H2 invariant","id":"python_verification:verification/v43_exterior_bridge.py","line_count":138,"path":"verification/v43_exterior_bridge.py","sha256":"0907a66b21c96c67f815dc4c4db8c35a8319bf30d3b2c39c197da84911d0318b","type":"python_verification"},{"bytes":7177,"checked_by_registry":false,"claim_ids":["SEAM.EQUIV.LTORP.BETA.01"],"cluster":"frontier","description_excerpt":"SEAM.EQUIV.LTORP.BETA.01: the β-interpolation connecting the NPW26-PROVEN trace case (β=0) to the seam's β=1 KMS case along an obstruction-free homotopy -- upgrading the single-point v426 witness for v424 sub-step (ii) to a PATH argument. 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[E] MMST HYPOTHESES: D=16 Majoranas (=2^{g_car-1}), c=8 (=g_car+N_fam), rank E8=8, range rank≤c≤D (8≤8≤16), gapped, quasi-free CAR -- all internal computed","id":"python_verification:verification/v441_seam_applicability_ledger.py","line_count":120,"path":"verification/v441_seam_applicability_ledger.py","sha256":"1b9abfcaf6c843da94260c6ce4dd6bceb2884054146b7564f2bf80fae8a80626","type":"python_verification"},{"bytes":7139,"checked_by_registry":false,"claim_ids":["SEAM.RIGIDITY.UNIFORM.01"],"cluster":"frontier","description_excerpt":"SEAM.RIGIDITY.UNIFORM.01: the uniform-in-N hardening of the Seam State Rigidity Theorem (v398) -- the band-limited rigidity is NOT a small-N artifact. [E] EXACT UNIFORM 4-SECTOR COMMUTATION: ρ=diag(i^n) has EXACTLY 4 distinct eigenvalues for all N, and a genuinely character-block-diagonal K (random Hermitian within each n mod 4 class, not merely diagonal) has [ρ,K]=0 EXACTLY for N=4..256 (extends v398's N≤64). 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assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/AnchorLadder.lean:TFPT.Carrier.AnchorLadder.rank_step","line_end":55,"line_start":53,"module_context_as_written":[],"name":"rank_step","path":"experiments/lean4-carrier-rigidity/TfptCarrier/AnchorLadder.lean","qualified_name":"TFPT.Carrier.AnchorLadder.rank_step","statement_as_written":"theorem rank_step : p 4 - p 3 = 8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/AnchorLadder.lean:TFPT.Carrier.AnchorLadder.dim_e8","line_end":58,"line_start":56,"module_context_as_written":[],"name":"dim_e8","path":"experiments/lean4-carrier-rigidity/TfptCarrier/AnchorLadder.lean","qualified_name":"TFPT.Carrier.AnchorLadder.dim_e8","statement_as_written":"theorem dim_e8 : p 1 * p 2 * p 3 + (p 4 - p 3) = 248","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/AnchorLadder.lean:TFPT.Carrier.AnchorLadder.binary_ladder","line_end":63,"line_start":59,"module_context_as_written":[],"name":"binary_ladder","path":"experiments/lean4-carrier-rigidity/TfptCarrier/AnchorLadder.lean","qualified_name":"TFPT.Carrier.AnchorLadder.binary_ladder","statement_as_written":"theorem binary_ladder (n : ℕ) : p (n + 1) - p n = 2 ^ n","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/AnchorLadder.lean:TFPT.Carrier.AnchorLadder.elementary_symmetric","line_end":70,"line_start":64,"module_context_as_written":[],"name":"elementary_symmetric","path":"experiments/lean4-carrier-rigidity/TfptCarrier/AnchorLadder.lean","qualified_name":"TFPT.Carrier.AnchorLadder.elementary_symmetric","statement_as_written":"theorem elementary_symmetric :\n    (1 + 1 + 2 = 4) ∧ (1 * 1 + 1 * 2 + 1 * 2 = 5) ∧ (1 * 1 * 2 = 2)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/AnchorLadder.lean:TFPT.Carrier.AnchorLadder.cube_step_ge_54","line_end":87,"line_start":71,"module_context_as_written":[],"name":"cube_step_ge_54","path":"experiments/lean4-carrier-rigidity/TfptCarrier/AnchorLadder.lean","qualified_name":"TFPT.Carrier.AnchorLadder.cube_step_ge_54","statement_as_written":"theorem cube_step_ge_54 (x : ℕ) (hx : 3 ≤ x) : 54 ≤ x ^ 3 * (x - 1)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/AnchorLadder.lean:TFPT.Carrier.AnchorLadder.overshoot_ge_three","line_end":101,"line_start":88,"module_context_as_written":[],"name":"overshoot_ge_three","path":"experiments/lean4-carrier-rigidity/TfptCarrier/AnchorLadder.lean","qualified_name":"TFPT.Carrier.AnchorLadder.overshoot_ge_three","statement_as_written":"theorem overshoot_ge_three (w : ℕ) (hw : 3 ≤ w) : w ^ 3 + 54 ≤ w ^ 4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/AnchorLadder.lean:TFPT.Carrier.AnchorLadder.rankgap_uniqueness","line_end":135,"line_start":102,"module_context_as_written":[],"name":"rankgap_uniqueness","path":"experiments/lean4-carrier-rigidity/TfptCarrier/AnchorLadder.lean","qualified_name":"TFPT.Carrier.AnchorLadder.rankgap_uniqueness","statement_as_written":"theorem rankgap_uniqueness (x y z : ℕ)\n    (hx : 1 ≤ x) (hy : 1 ≤ y) (hz : 1 ≤ z)\n    (h : x ^ 4 + y ^ 4 + z ^ 4 = x ^ 3 + y ^ 3 + z ^ 3 + 8) :\n    (x = 1 ∧ y = 1 ∧ z = 2) ∨ (x = 1 ∧ y = 2 ∧ z = 1) ∨\n    (x = 2 ∧ y = 1 ∧ z = 1)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/AnchorLadder.lean:TFPT.Carrier.AnchorLadder.rankgap_anchor","line_end":143,"line_start":136,"module_context_as_written":[],"name":"rankgap_anchor","path":"experiments/lean4-carrier-rigidity/TfptCarrier/AnchorLadder.lean","qualified_name":"TFPT.Carrier.AnchorLadder.rankgap_anchor","statement_as_written":"theorem rankgap_anchor :\n    1 ^ 4 + 1 ^ 4 + 2 ^ 4 = 1 ^ 3 + 1 ^ 3 + 2 ^ 3 + 8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"abbrev","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.Label","line_end":110,"line_start":105,"module_context_as_written":[],"name":"Label","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.Label","statement_as_written":"abbrev Label","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.G","line_end":118,"line_start":111,"module_context_as_written":[],"name":"G","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.G","statement_as_written":"def G : Matrix (Fin 4) (Fin 4) (ZMod 2)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.symp","line_end":121,"line_start":119,"module_context_as_written":[],"name":"symp","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.symp","statement_as_written":"def symp (x y : Label) : ZMod 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.sigmaMap","line_end":125,"line_start":122,"module_context_as_written":[],"name":"sigmaMap","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.sigmaMap","statement_as_written":"def sigmaMap (v : Label) : Label","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.sigma_symplectic","line_end":130,"line_start":126,"module_context_as_written":[],"name":"sigma_symplectic","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.sigma_symplectic","statement_as_written":"theorem sigma_symplectic :\n    ∀ x y : Label, symp (sigmaMap x) (sigmaMap y) = symp x y","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.iota","line_end":137,"line_start":131,"module_context_as_written":[],"name":"iota","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.iota","statement_as_written":"def iota (v : Label) : Fin 5 → ZMod 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.iota_even","line_end":140,"line_start":138,"module_context_as_written":[],"name":"iota_even","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.iota_even","statement_as_written":"theorem iota_even : ∀ v : Label, (∑ i, iota v i) = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.iota_injective","line_end":144,"line_start":141,"module_context_as_written":[],"name":"iota_injective","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.iota_injective","statement_as_written":"theorem iota_injective :\n    ∀ v w : Label, iota v = iota w → v = w","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.beta","line_end":147,"line_start":145,"module_context_as_written":[],"name":"beta","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.beta","statement_as_written":"def beta (v w : Label) : ZMod 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.beta_eq_symp","line_end":151,"line_start":148,"module_context_as_written":[],"name":"beta_eq_symp","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.beta_eq_symp","statement_as_written":"theorem beta_eq_symp : ∀ v w : Label, beta v w = symp v w","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.wtIota","line_end":157,"line_start":152,"module_context_as_written":[],"name":"wtIota","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.wtIota","statement_as_written":"def wtIota (v : Label) : ℕ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.qstar","line_end":160,"line_start":158,"module_context_as_written":[],"name":"qstar","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.qstar","statement_as_written":"def qstar (v : Label) : ZMod 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.qstar_refines","line_end":166,"line_start":161,"module_context_as_written":[],"name":"qstar_refines","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.qstar_refines","statement_as_written":"theorem qstar_refines :\n    ∀ v w : Label, qstar (v + w) + qstar v + qstar w = symp v w","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.qstar_sigma_invariant","line_end":170,"line_start":167,"module_context_as_written":[],"name":"qstar_sigma_invariant","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.qstar_sigma_invariant","statement_as_written":"theorem qstar_sigma_invariant :\n    ∀ v : Label, qstar (sigmaMap v) = qstar v","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.qc","line_end":174,"line_start":171,"module_context_as_written":[],"name":"qc","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.qc","statement_as_written":"def qc (c v : Label) : ZMod 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.qc_injective","line_end":179,"line_start":175,"module_context_as_written":[],"name":"qc_injective","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.qc_injective","statement_as_written":"theorem qc_injective :\n    ∀ c c' : Label, (∀ v, qc c v = qc c' v) → c = c'","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.anchorA","line_end":182,"line_start":180,"module_context_as_written":[],"name":"anchorA","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.anchorA","statement_as_written":"def anchorA : Label","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.Fsigma","line_end":185,"line_start":183,"module_context_as_written":[],"name":"Fsigma","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.Fsigma","statement_as_written":"def Fsigma : Label","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.selector_unique","line_end":193,"line_start":186,"module_context_as_written":[],"name":"selector_unique","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.selector_unique","statement_as_written":"theorem selector_unique :\n    ∀ c : Label,\n      ((∀ v, qc c (sigmaMap v) = qc c v) ∧ qc c anchorA = 1 ∧\n        qc c Fsigma = 0) ↔ c = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.zeros","line_end":200,"line_start":194,"module_context_as_written":[],"name":"zeros","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.zeros","statement_as_written":"def zeros (c : Label) : ℕ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.arf_offset_law","line_end":206,"line_start":201,"module_context_as_written":[],"name":"arf_offset_law","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.arf_offset_law","statement_as_written":"theorem arf_offset_law :\n    ∀ c : Label, zeros c = if qstar c = 0 then 6 else 10","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.arf_census","line_end":213,"line_start":207,"module_context_as_written":[],"name":"arf_census","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.arf_census","statement_as_written":"theorem arf_census :\n    (Finset.univ.filter fun c : Label => zeros c = 6).card = 6 ∧\n    (Finset.univ.filter fun c : Label => zeros c = 10).card = 10","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.word_decomposition","line_end":221,"line_start":214,"module_context_as_written":[],"name":"word_decomposition","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.word_decomposition","statement_as_written":"theorem word_decomposition :\n    (Finset.univ.filter fun v : Label => v ≠ 0 ∧ qstar v = 0).card = 5\n    ∧ (Finset.univ.filter fun v : Label => qstar v = 1).card = 10","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.orbit_partition_counts","line_end":230,"line_start":222,"module_context_as_written":[],"name":"orbit_partition_counts","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.orbit_partition_counts","statement_as_written":"theorem orbit_partition_counts :\n    (Finset.univ.filter fun c : Label => c = 0).card = 1 ∧\n    (Finset.univ.filter fun c : Label => c ≠ 0 ∧ qstar c = 0).card = 5\n    ∧ (Finset.univ.filter fun c : Label => qstar c = 1).card = 10","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.X","line_end":236,"line_start":231,"module_context_as_written":[],"name":"X","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.X","statement_as_written":"def X : Fin 5 → ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.X_traceless","line_end":239,"line_start":237,"module_context_as_written":[],"name":"X_traceless","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.X_traceless","statement_as_written":"theorem X_traceless : (∑ i, X i) = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.X_primitive","line_end":244,"line_start":240,"module_context_as_written":[],"name":"X_primitive","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.X_primitive","statement_as_written":"theorem X_primitive :\n    Nat.gcd (Int.natAbs (X 0)) (Nat.gcd (Int.natAbs (X 3))\n      (Int.natAbs (X 4))) = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.Xw","line_end":247,"line_start":245,"module_context_as_written":[],"name":"Xw","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.Xw","statement_as_written":"def Xw (v : Label) : ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.moment_card","line_end":250,"line_start":248,"module_context_as_written":[],"name":"moment_card","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.moment_card","statement_as_written":"theorem moment_card : Fintype.card Label = 16","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.moment_one","line_end":253,"line_start":251,"module_context_as_written":[],"name":"moment_one","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.moment_one","statement_as_written":"theorem moment_one : (∑ v : Label, Xw v) = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.moment_two","line_end":257,"line_start":254,"module_context_as_written":[],"name":"moment_two","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.moment_two","statement_as_written":"theorem moment_two : (∑ v : Label, Xw v ^ 2) = 120","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.moment_three","line_end":261,"line_start":258,"module_context_as_written":[],"name":"moment_three","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.moment_three","statement_as_written":"theorem moment_three : (∑ v : Label, Xw v ^ 3) = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.moment_chain","line_end":267,"line_start":262,"module_context_as_written":[],"name":"moment_chain","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.moment_chain","statement_as_written":"theorem moment_chain :\n    120 / 3 = 40 ∧ 40 + 1 = 41 ∧ 2 * 120 = 240 ∧ 240 + 8 = 248","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.chiNSR_is_anchor_bit","line_end":274,"line_start":268,"module_context_as_written":[],"name":"chiNSR_is_anchor_bit","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.chiNSR_is_anchor_bit","statement_as_written":"theorem chiNSR_is_anchor_bit :\n    ∀ v : Label, symp v Fsigma = v 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.ps_split","line_end":282,"line_start":275,"module_context_as_written":[],"name":"ps_split","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.ps_split","statement_as_written":"theorem ps_split :\n    (Finset.univ.filter fun v : Label => v 0 + v 1 + v 2 = 1).card = 8\n    ∧ (Finset.univ.filter fun v : Label =>\n        v 0 + v 1 + v 2 = 0).card = 8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.sigma_slot_split","line_end":293,"line_start":283,"module_context_as_written":[],"name":"sigma_slot_split","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.sigma_slot_split","statement_as_written":"theorem sigma_slot_split :\n    ∀ v : Label,\n      iota (sigmaMap v)\n        = ![iota v 2, iota v 0, iota v 1, iota v 3, iota v 4]","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.dotForm","line_end":298,"line_start":294,"module_context_as_written":[],"name":"dotForm","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.dotForm","statement_as_written":"def dotForm (v w : Label) : ZMod 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.e0","line_end":301,"line_start":299,"module_context_as_written":[],"name":"e0","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.e0","statement_as_written":"def e0 : Label","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean:TfptCarrier.ArfSpinorCompiler.dot_form_no_refinement","line_end":323,"line_start":302,"module_context_as_written":[],"name":"dot_form_no_refinement","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ArfSpinorCompiler.lean","qualified_name":"TfptCarrier.ArfSpinorCompiler.dot_form_no_refinement","statement_as_written":"theorem dot_form_no_refinement :\n    ¬ ∃ q : Label → ZMod 2,\n      ∀ v w : Label, q (v + w) + q v + q w = dotForm v w","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"axiom","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/BWKeystone.lean:TfptCarrier.BWKeystone.RotationInvariantVacuum","line_end":41,"line_start":36,"module_context_as_written":[{"line":36,"source_text":"axiom RotationInvariantVacuum : Prop"},{"line":42,"source_text":"axiom GeometricModularFlow : Prop"},{"line":45,"source_text":"axiom Mu4ModularSymmetry : Prop"},{"line":48,"source_text":"axiom StateInvariance : Prop"},{"line":50,"source_text":"axiom bw_geometric : SeamIsE8 → RotationInvariantVacuum → GeometricModularFlow"},{"line":56,"source_text":"axiom geometric_clock : GeometricModularFlow → Mu4ModularSymmetry"},{"line":59,"source_text":"axiom clock_state_invariance : Mu4ModularSymmetry → StateInvariance"},{"line":87,"source_text":"axiom conformal_net_vacuum_rotation_invariant : SeamIsE8 → RotationInvariantVacuum"}],"name":"RotationInvariantVacuum","path":"experiments/lean4-carrier-rigidity/TfptCarrier/BWKeystone.lean","qualified_name":"TfptCarrier.BWKeystone.RotationInvariantVacuum","statement_as_written":"axiom RotationInvariantVacuum : Prop","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"axiom","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/BWKeystone.lean:TfptCarrier.BWKeystone.GeometricModularFlow","line_end":44,"line_start":42,"module_context_as_written":[{"line":36,"source_text":"axiom RotationInvariantVacuum : Prop"},{"line":42,"source_text":"axiom GeometricModularFlow : Prop"},{"line":45,"source_text":"axiom Mu4ModularSymmetry : Prop"},{"line":48,"source_text":"axiom StateInvariance : Prop"},{"line":50,"source_text":"axiom bw_geometric : SeamIsE8 → RotationInvariantVacuum → GeometricModularFlow"},{"line":56,"source_text":"axiom geometric_clock : GeometricModularFlow → Mu4ModularSymmetry"},{"line":59,"source_text":"axiom clock_state_invariance : Mu4ModularSymmetry → StateInvariance"},{"line":87,"source_text":"axiom conformal_net_vacuum_rotation_invariant : SeamIsE8 → RotationInvariantVacuum"}],"name":"GeometricModularFlow","path":"experiments/lean4-carrier-rigidity/TfptCarrier/BWKeystone.lean","qualified_name":"TfptCarrier.BWKeystone.GeometricModularFlow","statement_as_written":"axiom GeometricModularFlow : Prop","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify 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RotationInvariantVacuum"}],"name":"Mu4ModularSymmetry","path":"experiments/lean4-carrier-rigidity/TfptCarrier/BWKeystone.lean","qualified_name":"TfptCarrier.BWKeystone.Mu4ModularSymmetry","statement_as_written":"axiom Mu4ModularSymmetry : Prop","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"axiom","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/BWKeystone.lean:TfptCarrier.BWKeystone.StateInvariance","line_end":49,"line_start":48,"module_context_as_written":[{"line":36,"source_text":"axiom RotationInvariantVacuum : Prop"},{"line":42,"source_text":"axiom GeometricModularFlow : Prop"},{"line":45,"source_text":"axiom Mu4ModularSymmetry : Prop"},{"line":48,"source_text":"axiom StateInvariance : Prop"},{"line":50,"source_text":"axiom bw_geometric : SeamIsE8 → RotationInvariantVacuum → GeometricModularFlow"},{"line":56,"source_text":"axiom geometric_clock : GeometricModularFlow → Mu4ModularSymmetry"},{"line":59,"source_text":"axiom clock_state_invariance : Mu4ModularSymmetry → StateInvariance"},{"line":87,"source_text":"axiom conformal_net_vacuum_rotation_invariant : SeamIsE8 → RotationInvariantVacuum"}],"name":"StateInvariance","path":"experiments/lean4-carrier-rigidity/TfptCarrier/BWKeystone.lean","qualified_name":"TfptCarrier.BWKeystone.StateInvariance","statement_as_written":"axiom StateInvariance : Prop","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"axiom","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/BWKeystone.lean:TfptCarrier.BWKeystone.bw_geometric","line_end":55,"line_start":50,"module_context_as_written":[{"line":36,"source_text":"axiom RotationInvariantVacuum : Prop"},{"line":42,"source_text":"axiom GeometricModularFlow : Prop"},{"line":45,"source_text":"axiom Mu4ModularSymmetry : Prop"},{"line":48,"source_text":"axiom StateInvariance : Prop"},{"line":50,"source_text":"axiom bw_geometric : SeamIsE8 → RotationInvariantVacuum → GeometricModularFlow"},{"line":56,"source_text":"axiom geometric_clock : GeometricModularFlow → Mu4ModularSymmetry"},{"line":59,"source_text":"axiom clock_state_invariance : Mu4ModularSymmetry → StateInvariance"},{"line":87,"source_text":"axiom conformal_net_vacuum_rotation_invariant : SeamIsE8 → RotationInvariantVacuum"}],"name":"bw_geometric","path":"experiments/lean4-carrier-rigidity/TfptCarrier/BWKeystone.lean","qualified_name":"TfptCarrier.BWKeystone.bw_geometric","statement_as_written":"axiom bw_geometric : SeamIsE8 → RotationInvariantVacuum → GeometricModularFlow","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"axiom","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/BWKeystone.lean:TfptCarrier.BWKeystone.geometric_clock","line_end":58,"line_start":56,"module_context_as_written":[{"line":36,"source_text":"axiom RotationInvariantVacuum : Prop"},{"line":42,"source_text":"axiom GeometricModularFlow : Prop"},{"line":45,"source_text":"axiom Mu4ModularSymmetry : Prop"},{"line":48,"source_text":"axiom StateInvariance : Prop"},{"line":50,"source_text":"axiom bw_geometric : SeamIsE8 → RotationInvariantVacuum → GeometricModularFlow"},{"line":56,"source_text":"axiom geometric_clock : GeometricModularFlow → Mu4ModularSymmetry"},{"line":59,"source_text":"axiom clock_state_invariance : Mu4ModularSymmetry → StateInvariance"},{"line":87,"source_text":"axiom conformal_net_vacuum_rotation_invariant : SeamIsE8 → RotationInvariantVacuum"}],"name":"geometric_clock","path":"experiments/lean4-carrier-rigidity/TfptCarrier/BWKeystone.lean","qualified_name":"TfptCarrier.BWKeystone.geometric_clock","statement_as_written":"axiom geometric_clock : GeometricModularFlow → Mu4ModularSymmetry","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"axiom","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/BWKeystone.lean:TfptCarrier.BWKeystone.clock_state_invariance","line_end":60,"line_start":59,"module_context_as_written":[{"line":36,"source_text":"axiom RotationInvariantVacuum : Prop"},{"line":42,"source_text":"axiom GeometricModularFlow : Prop"},{"line":45,"source_text":"axiom Mu4ModularSymmetry : Prop"},{"line":48,"source_text":"axiom StateInvariance : Prop"},{"line":50,"source_text":"axiom bw_geometric : SeamIsE8 → RotationInvariantVacuum → GeometricModularFlow"},{"line":56,"source_text":"axiom geometric_clock : GeometricModularFlow → Mu4ModularSymmetry"},{"line":59,"source_text":"axiom clock_state_invariance : Mu4ModularSymmetry → StateInvariance"},{"line":87,"source_text":"axiom conformal_net_vacuum_rotation_invariant : SeamIsE8 → RotationInvariantVacuum"}],"name":"clock_state_invariance","path":"experiments/lean4-carrier-rigidity/TfptCarrier/BWKeystone.lean","qualified_name":"TfptCarrier.BWKeystone.clock_state_invariance","statement_as_written":"axiom clock_state_invariance : Mu4ModularSymmetry → StateInvariance","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/BWKeystone.lean:TfptCarrier.BWKeystone.qgeoFromSeam","line_end":66,"line_start":61,"module_context_as_written":[{"line":36,"source_text":"axiom RotationInvariantVacuum : Prop"},{"line":42,"source_text":"axiom GeometricModularFlow : Prop"},{"line":45,"source_text":"axiom Mu4ModularSymmetry : Prop"},{"line":48,"source_text":"axiom StateInvariance : Prop"},{"line":50,"source_text":"axiom bw_geometric : SeamIsE8 → RotationInvariantVacuum → GeometricModularFlow"},{"line":56,"source_text":"axiom geometric_clock : GeometricModularFlow → Mu4ModularSymmetry"},{"line":59,"source_text":"axiom clock_state_invariance : Mu4ModularSymmetry → StateInvariance"},{"line":87,"source_text":"axiom conformal_net_vacuum_rotation_invariant : SeamIsE8 → RotationInvariantVacuum"}],"name":"qgeoFromSeam","path":"experiments/lean4-carrier-rigidity/TfptCarrier/BWKeystone.lean","qualified_name":"TfptCarrier.BWKeystone.qgeoFromSeam","statement_as_written":"theorem qgeoFromSeam : SeamIsE8 → RotationInvariantVacuum → StateInvariance","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/BWKeystone.lean:TfptCarrier.BWKeystone.bedrockReducesToRotationInvariance","line_end":75,"line_start":67,"module_context_as_written":[{"line":36,"source_text":"axiom RotationInvariantVacuum : Prop"},{"line":42,"source_text":"axiom GeometricModularFlow : Prop"},{"line":45,"source_text":"axiom Mu4ModularSymmetry : Prop"},{"line":48,"source_text":"axiom StateInvariance : Prop"},{"line":50,"source_text":"axiom bw_geometric : SeamIsE8 → RotationInvariantVacuum → GeometricModularFlow"},{"line":56,"source_text":"axiom geometric_clock : GeometricModularFlow → Mu4ModularSymmetry"},{"line":59,"source_text":"axiom clock_state_invariance : Mu4ModularSymmetry → StateInvariance"},{"line":87,"source_text":"axiom conformal_net_vacuum_rotation_invariant : SeamIsE8 → RotationInvariantVacuum"}],"name":"bedrockReducesToRotationInvariance","path":"experiments/lean4-carrier-rigidity/TfptCarrier/BWKeystone.lean","qualified_name":"TfptCarrier.BWKeystone.bedrockReducesToRotationInvariance","statement_as_written":"theorem bedrockReducesToRotationInvariance : RotationInvariantVacuum → StateInvariance","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify 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RotationInvariantVacuum"}],"name":"bw_strictly_stronger","path":"experiments/lean4-carrier-rigidity/TfptCarrier/BWKeystone.lean","qualified_name":"TfptCarrier.BWKeystone.bw_strictly_stronger","statement_as_written":"theorem bw_strictly_stronger : (1 ∣ 4) ∧ ¬ ((4 : Nat) ∣ 1)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"axiom","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/BWKeystone.lean:TfptCarrier.BWKeystone.conformal_net_vacuum_rotation_invariant","line_end":98,"line_start":87,"module_context_as_written":[{"line":36,"source_text":"axiom RotationInvariantVacuum : Prop"},{"line":42,"source_text":"axiom GeometricModularFlow : Prop"},{"line":45,"source_text":"axiom Mu4ModularSymmetry : Prop"},{"line":48,"source_text":"axiom StateInvariance : Prop"},{"line":50,"source_text":"axiom bw_geometric : SeamIsE8 → RotationInvariantVacuum → GeometricModularFlow"},{"line":56,"source_text":"axiom geometric_clock : GeometricModularFlow → Mu4ModularSymmetry"},{"line":59,"source_text":"axiom clock_state_invariance : Mu4ModularSymmetry → StateInvariance"},{"line":87,"source_text":"axiom conformal_net_vacuum_rotation_invariant : SeamIsE8 → RotationInvariantVacuum"}],"name":"conformal_net_vacuum_rotation_invariant","path":"experiments/lean4-carrier-rigidity/TfptCarrier/BWKeystone.lean","qualified_name":"TfptCarrier.BWKeystone.conformal_net_vacuum_rotation_invariant","statement_as_written":"axiom conformal_net_vacuum_rotation_invariant : SeamIsE8 → RotationInvariantVacuum","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/BWKeystone.lean:TfptCarrier.BWKeystone.stateInvarianceFromSeam","line_end":102,"line_start":99,"module_context_as_written":[{"line":36,"source_text":"axiom RotationInvariantVacuum : Prop"},{"line":42,"source_text":"axiom GeometricModularFlow : Prop"},{"line":45,"source_text":"axiom Mu4ModularSymmetry : Prop"},{"line":48,"source_text":"axiom StateInvariance : Prop"},{"line":50,"source_text":"axiom bw_geometric : SeamIsE8 → RotationInvariantVacuum → GeometricModularFlow"},{"line":56,"source_text":"axiom geometric_clock : GeometricModularFlow → Mu4ModularSymmetry"},{"line":59,"source_text":"axiom clock_state_invariance : Mu4ModularSymmetry → StateInvariance"},{"line":87,"source_text":"axiom conformal_net_vacuum_rotation_invariant : SeamIsE8 → RotationInvariantVacuum"}],"name":"stateInvarianceFromSeam","path":"experiments/lean4-carrier-rigidity/TfptCarrier/BWKeystone.lean","qualified_name":"TfptCarrier.BWKeystone.stateInvarianceFromSeam","statement_as_written":"theorem stateInvarianceFromSeam : SeamIsE8 → StateInvariance","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/BWKeystone.lean:TfptCarrier.BWKeystone.qgeoSymIsCorollary","line_end":114,"line_start":103,"module_context_as_written":[{"line":36,"source_text":"axiom RotationInvariantVacuum : Prop"},{"line":42,"source_text":"axiom GeometricModularFlow : Prop"},{"line":45,"source_text":"axiom Mu4ModularSymmetry : Prop"},{"line":48,"source_text":"axiom StateInvariance : Prop"},{"line":50,"source_text":"axiom bw_geometric : SeamIsE8 → RotationInvariantVacuum → GeometricModularFlow"},{"line":56,"source_text":"axiom geometric_clock : GeometricModularFlow → Mu4ModularSymmetry"},{"line":59,"source_text":"axiom clock_state_invariance : Mu4ModularSymmetry → StateInvariance"},{"line":87,"source_text":"axiom conformal_net_vacuum_rotation_invariant : SeamIsE8 → RotationInvariantVacuum"}],"name":"qgeoSymIsCorollary","path":"experiments/lean4-carrier-rigidity/TfptCarrier/BWKeystone.lean","qualified_name":"TfptCarrier.BWKeystone.qgeoSymIsCorollary","statement_as_written":"theorem qgeoSymIsCorollary : StateInvariance","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"instance","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/BoundaryPolarization.lean:TFPT.Carrier.BoundaryPolarization.invertibleTwoEnd","line_end":82,"line_start":63,"module_context_as_written":[{"line":60,"source_text":"variable (R : Type*) [Semiring R] [Invertible (2 : R)]"},{"line":62,"source_text":"variable (M : Type*) [AddCommMonoid M] [Module R M]"},{"line":109,"source_text":"variable {K : Type*} [Field K]"},{"line":111,"source_text":"variable {H : Type*} [AddCommGroup H] [Module K H]"}],"name":"invertibleTwoEnd","path":"experiments/lean4-carrier-rigidity/TfptCarrier/BoundaryPolarization.lean","qualified_name":"TFPT.Carrier.BoundaryPolarization.invertibleTwoEnd","statement_as_written":"noncomputable instance invertibleTwoEnd :\n    Invertible (2 : Module.End R M)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"structure","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/BoundaryPolarization.lean:TFPT.Carrier.BoundaryPolarization.BoundaryPolarization","line_end":111,"line_start":83,"module_context_as_written":[{"line":60,"source_text":"variable (R : Type*) [Semiring R] [Invertible (2 : R)]"},{"line":62,"source_text":"variable (M : Type*) [AddCommMonoid M] [Module R M]"},{"line":109,"source_text":"variable {K : Type*} [Field K]"},{"line":111,"source_text":"variable {H : Type*} [AddCommGroup H] [Module K H]"}],"name":"BoundaryPolarization","path":"experiments/lean4-carrier-rigidity/TfptCarrier/BoundaryPolarization.lean","qualified_name":"TFPT.Carrier.BoundaryPolarization.BoundaryPolarization","statement_as_written":"structure BoundaryPolarization\n    (K : Type*) [Field K]\n    (H : Type*) [AddCommGroup H] [Module K H]","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/BoundaryPolarization.lean:TFPT.Carrier.BoundaryPolarization.BoundaryPolarization.projector","line_end":126,"line_start":112,"module_context_as_written":[{"line":60,"source_text":"variable (R : Type*) [Semiring R] [Invertible (2 : R)]"},{"line":62,"source_text":"variable (M : Type*) [AddCommMonoid M] [Module R M]"},{"line":109,"source_text":"variable {K : Type*} [Field K]"},{"line":111,"source_text":"variable {H : Type*} [AddCommGroup H] [Module K H]"}],"name":"projector","path":"experiments/lean4-carrier-rigidity/TfptCarrier/BoundaryPolarization.lean","qualified_name":"TFPT.Carrier.BoundaryPolarization.BoundaryPolarization.projector","statement_as_written":"noncomputable def projector (P : BoundaryPolarization K H) :\n    Module.End K H","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/BoundaryPolarization.lean:TFPT.Carrier.BoundaryPolarization.BoundaryPolarization.projector_isIdempotent","line_end":136,"line_start":127,"module_context_as_written":[{"line":60,"source_text":"variable (R : Type*) [Semiring R] [Invertible (2 : R)]"},{"line":62,"source_text":"variable (M : Type*) [AddCommMonoid M] [Module R M]"},{"line":109,"source_text":"variable {K : Type*} [Field K]"},{"line":111,"source_text":"variable {H : Type*} [AddCommGroup H] [Module K H]"}],"name":"projector_isIdempotent","path":"experiments/lean4-carrier-rigidity/TfptCarrier/BoundaryPolarization.lean","qualified_name":"TFPT.Carrier.BoundaryPolarization.BoundaryPolarization.projector_isIdempotent","statement_as_written":"theorem projector_isIdempotent (P : BoundaryPolarization K H) :\n    P.projector * P.projector = P.projector","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/BoundaryPolarization.lean:TFPT.Carrier.BoundaryPolarization.BoundaryPolarization.toCalderonProjector","line_end":153,"line_start":137,"module_context_as_written":[{"line":60,"source_text":"variable (R : Type*) [Semiring R] [Invertible (2 : R)]"},{"line":62,"source_text":"variable (M : Type*) [AddCommMonoid M] [Module R M]"},{"line":109,"source_text":"variable {K : Type*} [Field K]"},{"line":111,"source_text":"variable {H : Type*} [AddCommGroup H] [Module K H]"}],"name":"toCalderonProjector","path":"experiments/lean4-carrier-rigidity/TfptCarrier/BoundaryPolarization.lean","qualified_name":"TFPT.Carrier.BoundaryPolarization.BoundaryPolarization.toCalderonProjector","statement_as_written":"noncomputable def toCalderonProjector\n    [Invertible (2 : K)]\n    (P : BoundaryPolarization K H) :\n    TFPT.Carrier.CalderonProjector.CalderonProjector\n      (Module.End K H)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/BoundaryPolarization.lean:TFPT.Carrier.BoundaryPolarization.BoundaryPolarization.toCarrierInvolution","line_end":168,"line_start":154,"module_context_as_written":[{"line":60,"source_text":"variable (R : Type*) [Semiring R] [Invertible (2 : R)]"},{"line":62,"source_text":"variable (M : Type*) [AddCommMonoid M] [Module R M]"},{"line":109,"source_text":"variable {K : Type*} [Field K]"},{"line":111,"source_text":"variable {H : Type*} [AddCommGroup H] [Module K H]"}],"name":"toCarrierInvolution","path":"experiments/lean4-carrier-rigidity/TfptCarrier/BoundaryPolarization.lean","qualified_name":"TFPT.Carrier.BoundaryPolarization.BoundaryPolarization.toCarrierInvolution","statement_as_written":"noncomputable def toCarrierInvolution\n    [Invertible (2 : K)]\n    (P : BoundaryPolarization K H) :\n    TFPT.Carrier.InvolutionProjectors.CarrierInvolution\n      (Module.End K H)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/BoundaryPolarization.lean:TFPT.Carrier.BoundaryPolarization.BoundaryPolarization.toCalderonCertificate","line_end":183,"line_start":169,"module_context_as_written":[{"line":60,"source_text":"variable (R : Type*) [Semiring R] [Invertible (2 : R)]"},{"line":62,"source_text":"variable (M : Type*) [AddCommMonoid M] [Module R M]"},{"line":109,"source_text":"variable {K : Type*} [Field K]"},{"line":111,"source_text":"variable {H : Type*} [AddCommGroup H] [Module K H]"}],"name":"toCalderonCertificate","path":"experiments/lean4-carrier-rigidity/TfptCarrier/BoundaryPolarization.lean","qualified_name":"TFPT.Carrier.BoundaryPolarization.BoundaryPolarization.toCalderonCertificate","statement_as_written":"noncomputable def toCalderonCertificate\n    [Invertible (2 : K)]\n    (P : BoundaryPolarization K H) :\n    TFPT.Carrier.CalderonInterface.CalderonCertificate\n      (Module.End K H)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/BoundaryPolarization.lean:BoundaryPolarization.ofCarrierInvolution","line_end":260,"line_start":184,"module_context_as_written":[{"line":60,"source_text":"variable (R : Type*) [Semiring R] [Invertible (2 : R)]"},{"line":62,"source_text":"variable (M : Type*) [AddCommMonoid M] [Module R M]"},{"line":109,"source_text":"variable {K : Type*} [Field K]"},{"line":111,"source_text":"variable {H : Type*} [AddCommGroup H] [Module K H]"}],"name":"BoundaryPolarization.ofCarrierInvolution","path":"experiments/lean4-carrier-rigidity/TfptCarrier/BoundaryPolarization.lean","qualified_name":"BoundaryPolarization.ofCarrierInvolution","statement_as_written":"noncomputable def BoundaryPolarization.ofCarrierInvolution\n    {K : Type*} [Field K] [Invertible (2 : K)]\n    {H : Type*} [AddCommGroup H] [Module K H]\n    (c : TFPT.Carrier.InvolutionProjectors.CarrierInvolution\n          (Module.End K H)) :\n    BoundaryPolarization K H","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"structure","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/BoundaryYukawaKernelInterface.lean:TFPT.Carrier.BoundaryYukawaKernelInterface.BoundaryYukawaKernel","line_end":98,"line_start":68,"module_context_as_written":[{"line":96,"source_text":"variable {K : Type*} [Field K]"},{"line":98,"source_text":"variable {E : Type*} [AddCommGroup E] [Module K E] [FiniteDimensional K E]"}],"name":"BoundaryYukawaKernel","path":"experiments/lean4-carrier-rigidity/TfptCarrier/BoundaryYukawaKernelInterface.lean","qualified_name":"TFPT.Carrier.BoundaryYukawaKernelInterface.BoundaryYukawaKernel","statement_as_written":"structure BoundaryYukawaKernel\n    (K : Type*) [Field K]\n    (E : Type*) [AddCommGroup E] [Module K E]\n    [FiniteDimensional K E]","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/BoundaryYukawaKernelInterface.lean:TFPT.Carrier.BoundaryYukawaKernelInterface.BoundaryYukawaKernel.finrank_E_eq_three","line_end":106,"line_start":99,"module_context_as_written":[{"line":96,"source_text":"variable {K : Type*} [Field K]"},{"line":98,"source_text":"variable {E : Type*} [AddCommGroup E] [Module K E] [FiniteDimensional K E]"}],"name":"finrank_E_eq_three","path":"experiments/lean4-carrier-rigidity/TfptCarrier/BoundaryYukawaKernelInterface.lean","qualified_name":"TFPT.Carrier.BoundaryYukawaKernelInterface.BoundaryYukawaKernel.finrank_E_eq_three","statement_as_written":"theorem finrank_E_eq_three (b : BoundaryYukawaKernel K E) :\n    Module.finrank K E = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/BoundaryYukawaKernelInterface.lean:TFPT.Carrier.BoundaryYukawaKernelInterface.BoundaryYukawaKernel.ofFinrankEqThree","line_end":126,"line_start":107,"module_context_as_written":[{"line":96,"source_text":"variable {K : Type*} [Field K]"},{"line":98,"source_text":"variable {E : Type*} [AddCommGroup E] [Module K E] [FiniteDimensional K E]"}],"name":"ofFinrankEqThree","path":"experiments/lean4-carrier-rigidity/TfptCarrier/BoundaryYukawaKernelInterface.lean","qualified_name":"TFPT.Carrier.BoundaryYukawaKernelInterface.BoundaryYukawaKernel.ofFinrankEqThree","statement_as_written":"noncomputable def ofFinrankEqThree\n    [Nontrivial E] (h : Module.finrank K E = 3) :\n    BoundaryYukawaKernel K E","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/BoundaryYukawaKernelInterface.lean:TFPT.Carrier.BoundaryYukawaKernelInterface.BoundaryYukawaKernel.nonempty_iff_finrank_eq_three","line_end":134,"line_start":127,"module_context_as_written":[{"line":96,"source_text":"variable {K : Type*} [Field K]"},{"line":98,"source_text":"variable {E : Type*} [AddCommGroup E] [Module K E] [FiniteDimensional K E]"}],"name":"nonempty_iff_finrank_eq_three","path":"experiments/lean4-carrier-rigidity/TfptCarrier/BoundaryYukawaKernelInterface.lean","qualified_name":"TFPT.Carrier.BoundaryYukawaKernelInterface.BoundaryYukawaKernel.nonempty_iff_finrank_eq_three","statement_as_written":"theorem nonempty_iff_finrank_eq_three [Nontrivial E] :\n    Nonempty (BoundaryYukawaKernel K E) ↔ Module.finrank K E = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/BoundaryYukawaKernelInterface.lean:TFPT.Carrier.BoundaryYukawaKernelInterface.BoundaryYukawaKernel.toYukawaRankCertificate","line_end":147,"line_start":135,"module_context_as_written":[{"line":96,"source_text":"variable {K : Type*} [Field K]"},{"line":98,"source_text":"variable {E : Type*} [AddCommGroup E] [Module K E] [FiniteDimensional K E]"}],"name":"toYukawaRankCertificate","path":"experiments/lean4-carrier-rigidity/TfptCarrier/BoundaryYukawaKernelInterface.lean","qualified_name":"TFPT.Carrier.BoundaryYukawaKernelInterface.BoundaryYukawaKernel.toYukawaRankCertificate","statement_as_written":"noncomputable def toYukawaRankCertificate (b : BoundaryYukawaKernel K E) :\n    TFPT.Carrier.YukawaRank.YukawaRankCertificate K E","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"structure","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CalderonInterface.lean:TFPT.Carrier.CalderonInterface.CalderonCertificate","line_end":85,"line_start":57,"module_context_as_written":[{"line":84,"source_text":"variable {A : Type*} [Ring A]"}],"name":"CalderonCertificate","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CalderonInterface.lean","qualified_name":"TFPT.Carrier.CalderonInterface.CalderonCertificate","statement_as_written":"structure CalderonCertificate (A : Type*) [Ring A]","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CalderonInterface.lean:TFPT.Carrier.CalderonInterface.CalderonCertificate.toCarrierInvolution","line_end":94,"line_start":86,"module_context_as_written":[{"line":84,"source_text":"variable {A : Type*} [Ring A]"}],"name":"toCarrierInvolution","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CalderonInterface.lean","qualified_name":"TFPT.Carrier.CalderonInterface.CalderonCertificate.toCarrierInvolution","statement_as_written":"def toCarrierInvolution (c : CalderonCertificate A) :\n    TFPT.Carrier.InvolutionProjectors.CarrierInvolution A","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CalderonInterface.lean:CalderonCertificate.ofCarrierInvolution","line_end":112,"line_start":95,"module_context_as_written":[{"line":84,"source_text":"variable {A : Type*} [Ring A]"}],"name":"CalderonCertificate.ofCarrierInvolution","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CalderonInterface.lean","qualified_name":"CalderonCertificate.ofCarrierInvolution","statement_as_written":"def CalderonCertificate.ofCarrierInvolution\n    {A : Type*} [Ring A]\n    (c : TFPT.Carrier.InvolutionProjectors.CarrierInvolution A) :\n    CalderonCertificate A","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"structure","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CalderonProjector.lean:TFPT.Carrier.CalderonProjector.CalderonProjector","line_end":80,"line_start":52,"module_context_as_written":[{"line":79,"source_text":"variable {A : Type*} [Ring A] [Invertible (2 : A)]"}],"name":"CalderonProjector","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CalderonProjector.lean","qualified_name":"TFPT.Carrier.CalderonProjector.CalderonProjector","statement_as_written":"structure CalderonProjector (A : Type*) [Ring A] [Invertible (2 : A)]","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CalderonProjector.lean:TFPT.Carrier.CalderonProjector.CalderonProjector.eps","line_end":84,"line_start":81,"module_context_as_written":[{"line":79,"source_text":"variable {A : Type*} [Ring A] [Invertible (2 : A)]"}],"name":"eps","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CalderonProjector.lean","qualified_name":"TFPT.Carrier.CalderonProjector.CalderonProjector.eps","statement_as_written":"def eps (c : CalderonProjector A) : A","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CalderonProjector.lean:TFPT.Carrier.CalderonProjector.CalderonProjector.eps_sq","line_end":102,"line_start":85,"module_context_as_written":[{"line":79,"source_text":"variable {A : Type*} [Ring A] [Invertible (2 : A)]"}],"name":"eps_sq","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CalderonProjector.lean","qualified_name":"TFPT.Carrier.CalderonProjector.CalderonProjector.eps_sq","statement_as_written":"theorem eps_sq (c : CalderonProjector A) : c.eps * c.eps = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CalderonProjector.lean:TFPT.Carrier.CalderonProjector.CalderonProjector.toCarrierInvolution","line_end":114,"line_start":103,"module_context_as_written":[{"line":79,"source_text":"variable {A : Type*} [Ring A] [Invertible (2 : A)]"}],"name":"toCarrierInvolution","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CalderonProjector.lean","qualified_name":"TFPT.Carrier.CalderonProjector.CalderonProjector.toCarrierInvolution","statement_as_written":"def toCarrierInvolution (c : CalderonProjector A) :\n    TFPT.Carrier.InvolutionProjectors.CarrierInvolution A","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CalderonProjector.lean:TFPT.Carrier.CalderonProjector.CalderonProjector.toCalderonCertificate","line_end":131,"line_start":115,"module_context_as_written":[{"line":79,"source_text":"variable {A : Type*} [Ring A] [Invertible (2 : A)]"}],"name":"toCalderonCertificate","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CalderonProjector.lean","qualified_name":"TFPT.Carrier.CalderonProjector.CalderonProjector.toCalderonCertificate","statement_as_written":"def toCalderonCertificate (c : CalderonProjector A) :\n    TFPT.Carrier.CalderonInterface.CalderonCertificate A","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"structure","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CarrierData.lean:TFPT.Carrier.CarrierData.CarrierPremises","line_end":78,"line_start":46,"module_context_as_written":[{"line":75,"source_text":"variable {K M : Type*}"},{"line":77,"source_text":"variable [Field K] [CharZero K] [AddCommGroup M] [Module K M] [FiniteDimensional K M]"},{"line":78,"source_text":"variable (cp : CarrierPremises K M)"}],"name":"CarrierPremises","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CarrierData.lean","qualified_name":"TFPT.Carrier.CarrierData.CarrierPremises","statement_as_written":"structure CarrierPremises\n    (K : Type*) [Field K] [CharZero K]\n    (M : Type*) [AddCommGroup M] [Module K M] [FiniteDimensional K M]","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CarrierData.lean:TFPT.Carrier.CarrierData.CarrierPremises.Y","line_end":82,"line_start":79,"module_context_as_written":[{"line":75,"source_text":"variable {K M : Type*}"},{"line":77,"source_text":"variable [Field K] [CharZero K] [AddCommGroup M] [Module K M] [FiniteDimensional K M]"},{"line":78,"source_text":"variable (cp : CarrierPremises K M)"}],"name":"Y","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CarrierData.lean","qualified_name":"TFPT.Carrier.CarrierData.CarrierPremises.Y","statement_as_written":"noncomputable def Y : Module.End K M","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CarrierData.lean:TFPT.Carrier.CarrierData.CarrierPremises.primitive_pair_eq_sm","line_end":108,"line_start":83,"module_context_as_written":[{"line":75,"source_text":"variable {K M : Type*}"},{"line":77,"source_text":"variable [Field K] [CharZero K] [AddCommGroup M] [Module K M] [FiniteDimensional K M]"},{"line":78,"source_text":"variable (cp : CarrierPremises K M)"}],"name":"primitive_pair_eq_sm","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CarrierData.lean","qualified_name":"TFPT.Carrier.CarrierData.CarrierPremises.primitive_pair_eq_sm","statement_as_written":"theorem primitive_pair_eq_sm\n    (qm qp : ℤ)\n    (htrace : 3 * qm + 2 * qp = 0)\n    (hsign_m : qm < 0)\n    (hsign_p : 0 < qp)\n    (hgcd : Int.gcd qm qp = 1) :\n    qm = -2 ∧ qp = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CarrierData.lean:TFPT.Carrier.CarrierData.CarrierPremises.trace_Y_eq_zero","line_end":127,"line_start":109,"module_context_as_written":[{"line":75,"source_text":"variable {K M : Type*}"},{"line":77,"source_text":"variable [Field K] [CharZero K] [AddCommGroup M] [Module K M] [FiniteDimensional K M]"},{"line":78,"source_text":"variable (cp : CarrierPremises K M)"}],"name":"trace_Y_eq_zero","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CarrierData.lean","qualified_name":"TFPT.Carrier.CarrierData.CarrierPremises.trace_Y_eq_zero","statement_as_written":"theorem trace_Y_eq_zero : LinearMap.trace K M cp.Y = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CarrierData.lean:TFPT.Carrier.CarrierData.CarrierPremises.carrier_polynomial_Y","line_end":212,"line_start":128,"module_context_as_written":[{"line":75,"source_text":"variable {K M : Type*}"},{"line":77,"source_text":"variable [Field K] [CharZero K] [AddCommGroup M] [Module K M] [FiniteDimensional K M]"},{"line":78,"source_text":"variable (cp : CarrierPremises K M)"}],"name":"carrier_polynomial_Y","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CarrierData.lean","qualified_name":"TFPT.Carrier.CarrierData.CarrierPremises.carrier_polynomial_Y","statement_as_written":"theorem carrier_polynomial_Y :\n    (6 : ℕ) • (cp.Y * cp.Y) - cp.Y - 1 = (0 : Module.End K M)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CarrierData.lean:TFPT.Carrier.CarrierData.CarrierPremises.hypercharge_carrier_packet","line_end":248,"line_start":213,"module_context_as_written":[{"line":75,"source_text":"variable {K M : Type*}"},{"line":77,"source_text":"variable [Field K] [CharZero K] [AddCommGroup M] [Module K M] [FiniteDimensional K M]"},{"line":78,"source_text":"variable (cp : CarrierPremises K M)"}],"name":"hypercharge_carrier_packet","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CarrierData.lean","qualified_name":"TFPT.Carrier.CarrierData.CarrierPremises.hypercharge_carrier_packet","statement_as_written":"theorem hypercharge_carrier_packet\n    (qm qp : ℤ)\n    (htrace : 3 * qm + 2 * qp = 0)\n    (hsign_m : qm < 0)\n    (hsign_p : 0 < qp)\n    (hgcd : Int.gcd qm qp = 1) :\n    (qm = -2 ∧ qp = 3)\n    ∧ LinearMap.trace K M cp.Y = 0\n    ∧ (6 : ℕ) • (cp.Y * cp.Y) - cp.Y - 1 = (0 : Module.End K M)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CarrierRankUniqueness.lean:TFPT.Carrier.CarrierRankUniqueness.pascal_growth","line_end":53,"line_start":34,"module_context_as_written":[],"name":"pascal_growth","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CarrierRankUniqueness.lean","qualified_name":"TFPT.Carrier.CarrierRankUniqueness.pascal_growth","statement_as_written":"theorem pascal_growth : ∀ g : ℕ, 6 ≤ g → g ^ 2 + g + 2 < 2 ^ g","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CarrierRankUniqueness.lean:TFPT.Carrier.CarrierRankUniqueness.carrier_rank_pascal_unique","line_end":69,"line_start":54,"module_context_as_written":[],"name":"carrier_rank_pascal_unique","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CarrierRankUniqueness.lean","qualified_name":"TFPT.Carrier.CarrierRankUniqueness.carrier_rank_pascal_unique","statement_as_written":"theorem carrier_rank_pascal_unique (g : ℕ) :\n    2 ^ g = g ^ 2 + g + 2 ↔ g = 5","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CarrierRankUniqueness.lean:TFPT.Carrier.CarrierRankUniqueness.g_car_unique","line_end":78,"line_start":70,"module_context_as_written":[],"name":"g_car_unique","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CarrierRankUniqueness.lean","qualified_name":"TFPT.Carrier.CarrierRankUniqueness.g_car_unique","statement_as_written":"theorem g_car_unique : (∃! g : ℕ, 2 ^ g = g ^ 2 + g + 2)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CarrierRankUniqueness.lean:TFPT.Carrier.CarrierRankUniqueness.carrier_closure_integers","line_end":88,"line_start":79,"module_context_as_written":[],"name":"carrier_closure_integers","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CarrierRankUniqueness.lean","qualified_name":"TFPT.Carrier.CarrierRankUniqueness.carrier_closure_integers","statement_as_written":"theorem carrier_closure_integers :\n    (2 ^ (5 - 1) - 1) / 5 = 3 ∧ 5 + 3 = 8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean:TfptCarrier.CartanDeterminants.cartanA3","line_end":33,"line_start":30,"module_context_as_written":[],"name":"cartanA3","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean","qualified_name":"TfptCarrier.CartanDeterminants.cartanA3","statement_as_written":"def cartanA3 : Matrix (Fin 3) (Fin 3) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean:TfptCarrier.CartanDeterminants.cartanA3_det","line_end":37,"line_start":34,"module_context_as_written":[],"name":"cartanA3_det","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean","qualified_name":"TfptCarrier.CartanDeterminants.cartanA3_det","statement_as_written":"theorem cartanA3_det : cartanA3.det = 4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean:TfptCarrier.CartanDeterminants.cartanD5","line_end":47,"line_start":38,"module_context_as_written":[],"name":"cartanD5","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean","qualified_name":"TfptCarrier.CartanDeterminants.cartanD5","statement_as_written":"def cartanD5 : Matrix (Fin 5) (Fin 5) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean:TfptCarrier.CartanDeterminants.cartanD5_det","line_end":50,"line_start":48,"module_context_as_written":[],"name":"cartanD5_det","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean","qualified_name":"TfptCarrier.CartanDeterminants.cartanD5_det","statement_as_written":"theorem cartanD5_det : cartanD5.det = 4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean:TfptCarrier.CartanDeterminants.carrier_index_from_dets","line_end":56,"line_start":51,"module_context_as_written":[],"name":"carrier_index_from_dets","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean","qualified_name":"TfptCarrier.CartanDeterminants.carrier_index_from_dets","statement_as_written":"theorem carrier_index_from_dets :\n    cartanD5.det * cartanA3.det = 16","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean:TfptCarrier.CartanDeterminants.cartanE8","line_end":76,"line_start":57,"module_context_as_written":[],"name":"cartanE8","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean","qualified_name":"TfptCarrier.CartanDeterminants.cartanE8","statement_as_written":"def cartanE8 : Matrix (Fin 8) (Fin 8) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean:TfptCarrier.CartanDeterminants.cartanE8inv","line_end":90,"line_start":77,"module_context_as_written":[],"name":"cartanE8inv","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean","qualified_name":"TfptCarrier.CartanDeterminants.cartanE8inv","statement_as_written":"def cartanE8inv : Matrix (Fin 8) (Fin 8) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean:TfptCarrier.CartanDeterminants.cartanE8_mul_inv","line_end":93,"line_start":91,"module_context_as_written":[],"name":"cartanE8_mul_inv","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean","qualified_name":"TfptCarrier.CartanDeterminants.cartanE8_mul_inv","statement_as_written":"theorem cartanE8_mul_inv : cartanE8 * cartanE8inv = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean:TfptCarrier.CartanDeterminants.cartanE8_det_isUnit","line_end":115,"line_start":94,"module_context_as_written":[],"name":"cartanE8_det_isUnit","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean","qualified_name":"TfptCarrier.CartanDeterminants.cartanE8_det_isUnit","statement_as_written":"theorem cartanE8_det_isUnit : IsUnit cartanE8.det","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean:TfptCarrier.CartanDeterminants.cartanE8_transpose","line_end":117,"line_start":116,"module_context_as_written":[],"name":"cartanE8_transpose","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean","qualified_name":"TfptCarrier.CartanDeterminants.cartanE8_transpose","statement_as_written":"theorem cartanE8_transpose : cartanE8.transpose = cartanE8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean:TfptCarrier.CartanDeterminants.cartanE8_even","line_end":120,"line_start":118,"module_context_as_written":[],"name":"cartanE8_even","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean","qualified_name":"TfptCarrier.CartanDeterminants.cartanE8_even","statement_as_written":"theorem cartanE8_even : ∀ i, cartanE8 i i = 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean:TfptCarrier.CartanDeterminants.cartanE8_even_unimodular","line_end":127,"line_start":121,"module_context_as_written":[],"name":"cartanE8_even_unimodular","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean","qualified_name":"TfptCarrier.CartanDeterminants.cartanE8_even_unimodular","statement_as_written":"theorem cartanE8_even_unimodular :\n    (∀ i, cartanE8 i i = 2) ∧ cartanE8.IsSymm ∧ IsUnit cartanE8.det","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean:TfptCarrier.CartanDeterminants.cartanD5_even","line_end":132,"line_start":128,"module_context_as_written":[],"name":"cartanD5_even","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean","qualified_name":"TfptCarrier.CartanDeterminants.cartanD5_even","statement_as_written":"theorem cartanD5_even : ∀ i, cartanD5 i i = 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean:TfptCarrier.CartanDeterminants.cartanD8","line_end":156,"line_start":133,"module_context_as_written":[],"name":"cartanD8","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean","qualified_name":"TfptCarrier.CartanDeterminants.cartanD8","statement_as_written":"def cartanD8 : Matrix (Fin 8) (Fin 8) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean:TfptCarrier.CartanDeterminants.cartanD8_transpose","line_end":160,"line_start":157,"module_context_as_written":[],"name":"cartanD8_transpose","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean","qualified_name":"TfptCarrier.CartanDeterminants.cartanD8_transpose","statement_as_written":"theorem cartanD8_transpose : cartanD8.transpose = cartanD8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean:TfptCarrier.CartanDeterminants.cartanD8_even","line_end":162,"line_start":161,"module_context_as_written":[],"name":"cartanD8_even","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean","qualified_name":"TfptCarrier.CartanDeterminants.cartanD8_even","statement_as_written":"theorem cartanD8_even : ∀ i, cartanD8 i i = 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean:TfptCarrier.CartanDeterminants.four_not_isUnit","line_end":170,"line_start":163,"module_context_as_written":[],"name":"four_not_isUnit","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean","qualified_name":"TfptCarrier.CartanDeterminants.four_not_isUnit","statement_as_written":"theorem four_not_isUnit : ¬ IsUnit (4 : ℤ)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean:TfptCarrier.CartanDeterminants.holomorphy_discriminator_arith","line_end":177,"line_start":171,"module_context_as_written":[],"name":"holomorphy_discriminator_arith","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean","qualified_name":"TfptCarrier.CartanDeterminants.holomorphy_discriminator_arith","statement_as_written":"theorem holomorphy_discriminator_arith : IsUnit cartanE8.det ∧ ¬ IsUnit (4 : ℤ)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CohomologyGrading.lean:TFPT.Carrier.CohomologyGrading.omega1","line_end":44,"line_start":41,"module_context_as_written":[],"name":"omega1","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CohomologyGrading.lean","qualified_name":"TFPT.Carrier.CohomologyGrading.omega1","statement_as_written":"noncomputable def omega1 (z : ℂ) : ℂ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CohomologyGrading.lean:TFPT.Carrier.CohomologyGrading.omega2","line_end":45,"line_start":45,"module_context_as_written":[],"name":"omega2","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CohomologyGrading.lean","qualified_name":"TFPT.Carrier.CohomologyGrading.omega2","statement_as_written":"noncomputable def omega2 (z : ℂ) : ℂ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CohomologyGrading.lean:TFPT.Carrier.CohomologyGrading.omega3","line_end":46,"line_start":46,"module_context_as_written":[],"name":"omega3","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CohomologyGrading.lean","qualified_name":"TFPT.Carrier.CohomologyGrading.omega3","statement_as_written":"noncomputable def omega3 (z : ℂ) : ℂ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CohomologyGrading.lean:TFPT.Carrier.CohomologyGrading.denom_clock_invariant","line_end":50,"line_start":47,"module_context_as_written":[],"name":"denom_clock_invariant","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CohomologyGrading.lean","qualified_name":"TFPT.Carrier.CohomologyGrading.denom_clock_invariant","statement_as_written":"theorem denom_clock_invariant (z : ℂ) : (Complex.I * z) ^ 4 - 1 = z ^ 4 - 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CohomologyGrading.lean:TFPT.Carrier.CohomologyGrading.omega1_pullback","line_end":58,"line_start":51,"module_context_as_written":[],"name":"omega1_pullback","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CohomologyGrading.lean","qualified_name":"TFPT.Carrier.CohomologyGrading.omega1_pullback","statement_as_written":"theorem omega1_pullback (z : ℂ) :\n    omega1 (Complex.I * z) * Complex.I = Complex.I * omega1 z","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CohomologyGrading.lean:TFPT.Carrier.CohomologyGrading.omega2_pullback","line_end":67,"line_start":59,"module_context_as_written":[],"name":"omega2_pullback","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CohomologyGrading.lean","qualified_name":"TFPT.Carrier.CohomologyGrading.omega2_pullback","statement_as_written":"theorem omega2_pullback (z : ℂ) :\n    omega2 (Complex.I * z) * Complex.I = (-1 : ℂ) * omega2 z","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CohomologyGrading.lean:TFPT.Carrier.CohomologyGrading.omega3_pullback","line_end":78,"line_start":68,"module_context_as_written":[],"name":"omega3_pullback","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CohomologyGrading.lean","qualified_name":"TFPT.Carrier.CohomologyGrading.omega3_pullback","statement_as_written":"theorem omega3_pullback (z : ℂ) :\n    omega3 (Complex.I * z) * Complex.I = (-Complex.I) * omega3 z","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CohomologyGrading.lean:TFPT.Carrier.CohomologyGrading.character_grading","line_end":86,"line_start":79,"module_context_as_written":[],"name":"character_grading","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CohomologyGrading.lean","qualified_name":"TFPT.Carrier.CohomologyGrading.character_grading","statement_as_written":"theorem character_grading :\n    (Complex.I ^ 1, Complex.I ^ 2, Complex.I ^ 3)\n      = (Complex.I, (-1 : ℂ), -Complex.I)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CohomologyGrading.lean:TFPT.Carrier.CohomologyGrading.sigmaPull","line_end":92,"line_start":87,"module_context_as_written":[],"name":"sigmaPull","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CohomologyGrading.lean","qualified_name":"TFPT.Carrier.CohomologyGrading.sigmaPull","statement_as_written":"noncomputable def sigmaPull (g : ℂ → ℂ) (z : ℂ) : ℂ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CohomologyGrading.lean:TFPT.Carrier.CohomologyGrading.omega1_reflection","line_end":107,"line_start":93,"module_context_as_written":[],"name":"omega1_reflection","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CohomologyGrading.lean","qualified_name":"TFPT.Carrier.CohomologyGrading.omega1_reflection","statement_as_written":"theorem omega1_reflection (z : ℂ) (hz : z ≠ 0) (hz4 : z ^ 4 - 1 ≠ 0) :\n    sigmaPull omega1 z = omega3 z","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CohomologyGrading.lean:TFPT.Carrier.CohomologyGrading.omega2_reflection","line_end":122,"line_start":108,"module_context_as_written":[],"name":"omega2_reflection","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CohomologyGrading.lean","qualified_name":"TFPT.Carrier.CohomologyGrading.omega2_reflection","statement_as_written":"theorem omega2_reflection (z : ℂ) (hz : z ≠ 0) (hz4 : z ^ 4 - 1 ≠ 0) :\n    sigmaPull omega2 z = omega2 z","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CohomologyGrading.lean:TFPT.Carrier.CohomologyGrading.omega3_reflection","line_end":139,"line_start":123,"module_context_as_written":[],"name":"omega3_reflection","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CohomologyGrading.lean","qualified_name":"TFPT.Carrier.CohomologyGrading.omega3_reflection","statement_as_written":"theorem omega3_reflection (z : ℂ) (hz : z ≠ 0) (hz4 : z ^ 4 - 1 ≠ 0) :\n    sigmaPull omega3 z = omega1 z","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CohomologyGrading.lean:TFPT.Carrier.CohomologyGrading.cohom_grading","line_end":157,"line_start":140,"module_context_as_written":[],"name":"cohom_grading","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CohomologyGrading.lean","qualified_name":"TFPT.Carrier.CohomologyGrading.cohom_grading","statement_as_written":"theorem cohom_grading :\n    (∀ z : ℂ, omega1 (Complex.I * z) * Complex.I = Complex.I * omega1 z) ∧\n    (∀ z : ℂ, omega2 (Complex.I * z) * Complex.I = (-1 : ℂ) * omega2 z) ∧\n    (∀ z : ℂ, omega3 (Complex.I * z) * Complex.I = (-Complex.I) * omega3 z) ∧\n    (∀ z : ℂ, z ≠ 0 → z ^ 4 - 1 ≠ 0 → sigmaPull omega1 z = omega3 z) ∧\n    (∀ z : ℂ, z ≠ 0 → z ^ 4 - 1 ≠ 0 → sigmaPull omega2 z = omega2 z) ∧\n    (∀ z : ℂ, z ≠ 0 → z ^ 4 - 1 ≠ 0 → sigmaPull omega3 z = omega1 z)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.CU","line_end":39,"line_start":36,"module_context_as_written":[],"name":"CU","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.CU","statement_as_written":"def CU : Matrix (Fin 3) (Fin 3) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.CV","line_end":43,"line_start":40,"module_context_as_written":[],"name":"CV","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.CV","statement_as_written":"def CV : Matrix (Fin 3) (Fin 3) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.CU_quadratic","line_end":47,"line_start":44,"module_context_as_written":[],"name":"CU_quadratic","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.CU_quadratic","statement_as_written":"theorem CU_quadratic : CU * CU = 3 • CU","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.CU_trace","line_end":50,"line_start":48,"module_context_as_written":[],"name":"CU_trace","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.CU_trace","statement_as_written":"theorem CU_trace : Matrix.trace CU = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.CV_cubic","line_end":54,"line_start":51,"module_context_as_written":[],"name":"CV_cubic","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.CV_cubic","statement_as_written":"theorem CV_cubic : CV * CV * CV = 3 • (CV * CV) - 2 • CV","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.CV_trace","line_end":57,"line_start":55,"module_context_as_written":[],"name":"CV_trace","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.CV_trace","statement_as_written":"theorem CV_trace : Matrix.trace CV = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.joint_trace_UV","line_end":60,"line_start":58,"module_context_as_written":[],"name":"joint_trace_UV","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.joint_trace_UV","statement_as_written":"theorem joint_trace_UV : Matrix.trace (CU * CV) = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.joint_trace_UVV","line_end":63,"line_start":61,"module_context_as_written":[],"name":"joint_trace_UVV","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.joint_trace_UVV","statement_as_written":"theorem joint_trace_UVV : Matrix.trace (CU * CV * CV) = 6","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.W","line_end":74,"line_start":64,"module_context_as_written":[],"name":"W","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.W","statement_as_written":"def W : Matrix (Fin 7) (Fin 9) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.S","line_end":84,"line_start":75,"module_context_as_written":[],"name":"S","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.S","statement_as_written":"def S : Matrix (Fin 7) (Fin 9) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.T","line_end":94,"line_start":85,"module_context_as_written":[],"name":"T","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.T","statement_as_written":"def T : Matrix (Fin 7) (Fin 7) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.P","line_end":104,"line_start":95,"module_context_as_written":[],"name":"P","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.P","statement_as_written":"def P : Matrix (Fin 7) (Fin 7) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.Pinv","line_end":114,"line_start":105,"module_context_as_written":[],"name":"Pinv","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.Pinv","statement_as_written":"def Pinv : Matrix (Fin 7) (Fin 7) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.D","line_end":118,"line_start":115,"module_context_as_written":[],"name":"D","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.D","statement_as_written":"def D : Matrix (Fin 7) (Fin 7) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.words_factor","line_end":121,"line_start":119,"module_context_as_written":[],"name":"words_factor","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.words_factor","statement_as_written":"theorem words_factor : W = T * S","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.P_unimodular","line_end":124,"line_start":122,"module_context_as_written":[],"name":"P_unimodular","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.P_unimodular","statement_as_written":"theorem P_unimodular : P * Pinv = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.smith_certificate","line_end":130,"line_start":125,"module_context_as_written":[],"name":"smith_certificate","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.smith_certificate","statement_as_written":"theorem smith_certificate : P * T = D","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.Smin","line_end":140,"line_start":131,"module_context_as_written":[],"name":"Smin","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.Smin","statement_as_written":"def Smin : Matrix (Fin 7) (Fin 7) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.SminInv","line_end":151,"line_start":141,"module_context_as_written":[],"name":"SminInv","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.SminInv","statement_as_written":"def SminInv : Matrix (Fin 7) (Fin 7) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.S_primitive","line_end":153,"line_start":152,"module_context_as_written":[],"name":"S_primitive","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.S_primitive","statement_as_written":"theorem S_primitive : Smin * SminInv = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.index_is_three_pow_four","line_end":158,"line_start":154,"module_context_as_written":[],"name":"index_is_three_pow_four","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.index_is_three_pow_four","statement_as_written":"theorem index_is_three_pow_four : (1 * 1 * 1 * 3 * 3 * 3 * 3 : ℤ) = 3 ^ 4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.Jfix","line_end":168,"line_start":159,"module_context_as_written":[],"name":"Jfix","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.Jfix","statement_as_written":"def Jfix : Matrix (Fin 3) (Fin 3) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.Jfix_symmetric","line_end":170,"line_start":169,"module_context_as_written":[],"name":"Jfix_symmetric","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.Jfix_symmetric","statement_as_written":"theorem Jfix_symmetric : Jfix.transpose = Jfix","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.Jfix_det","line_end":174,"line_start":171,"module_context_as_written":[],"name":"Jfix_det","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.Jfix_det","statement_as_written":"theorem Jfix_det : Jfix.det = 72","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.Jfix_det_factorization","line_end":176,"line_start":175,"module_context_as_written":[],"name":"Jfix_det_factorization","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.Jfix_det_factorization","statement_as_written":"theorem Jfix_det_factorization : (72 : ℤ) = 8 * 3 ^ 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.CVdual","line_end":181,"line_start":177,"module_context_as_written":[],"name":"CVdual","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.CVdual","statement_as_written":"def CVdual : Matrix (Fin 3) (Fin 3) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.CV_dual_certificate","line_end":186,"line_start":182,"module_context_as_written":[],"name":"CV_dual_certificate","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.CV_dual_certificate","statement_as_written":"theorem CV_dual_certificate : CV.transpose * Jfix = Jfix * CVdual","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.CVdual_cubic","line_end":191,"line_start":187,"module_context_as_written":[],"name":"CVdual_cubic","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.CVdual_cubic","statement_as_written":"theorem CVdual_cubic :\n    CVdual * CVdual * CVdual = 3 • (CVdual * CVdual) - 2 • CVdual","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean:TfptCarrier.CoverEmbedding.dual_joint_trace","line_end":196,"line_start":192,"module_context_as_written":[],"name":"dual_joint_trace","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoverEmbedding.lean","qualified_name":"TfptCarrier.CoverEmbedding.dual_joint_trace","statement_as_written":"theorem dual_joint_trace : Matrix.trace (CU * CVdual) = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoxeterPrime2.lean:TFPT.Carrier.CoxeterPrime2.IsContractionRate","line_end":44,"line_start":41,"module_context_as_written":[],"name":"IsContractionRate","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoxeterPrime2.lean","qualified_name":"TFPT.Carrier.CoxeterPrime2.IsContractionRate","statement_as_written":"def IsContractionRate (r : ℝ) : Prop","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoxeterPrime2.lean:TFPT.Carrier.CoxeterPrime2.involution_eigenvalue","line_end":53,"line_start":45,"module_context_as_written":[],"name":"involution_eigenvalue","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoxeterPrime2.lean","qualified_name":"TFPT.Carrier.CoxeterPrime2.involution_eigenvalue","statement_as_written":"theorem involution_eigenvalue {r : ℝ} (hr : r * r = 1) : r = 1 ∨ r = -1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoxeterPrime2.lean:TFPT.Carrier.CoxeterPrime2.idempotent_eigenvalue","line_end":63,"line_start":54,"module_context_as_written":[],"name":"idempotent_eigenvalue","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoxeterPrime2.lean","qualified_name":"TFPT.Carrier.CoxeterPrime2.idempotent_eigenvalue","statement_as_written":"theorem idempotent_eigenvalue {r : ℝ} (hr : r * r = r) : r = 0 ∨ r = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoxeterPrime2.lean:TFPT.Carrier.CoxeterPrime2.involution_not_contraction","line_end":71,"line_start":64,"module_context_as_written":[],"name":"involution_not_contraction","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoxeterPrime2.lean","qualified_name":"TFPT.Carrier.CoxeterPrime2.involution_not_contraction","statement_as_written":"theorem involution_not_contraction {r : ℝ} (hr : r * r = 1) :\n    ¬ IsContractionRate r","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoxeterPrime2.lean:TFPT.Carrier.CoxeterPrime2.idempotent_not_contraction","line_end":79,"line_start":72,"module_context_as_written":[],"name":"idempotent_not_contraction","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoxeterPrime2.lean","qualified_name":"TFPT.Carrier.CoxeterPrime2.idempotent_not_contraction","statement_as_written":"theorem idempotent_not_contraction {r : ℝ} (hr : r * r = r) :\n    ¬ IsContractionRate r","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoxeterPrime2.lean:TFPT.Carrier.CoxeterPrime2.seam_rate_is_contraction","line_end":83,"line_start":80,"module_context_as_written":[],"name":"seam_rate_is_contraction","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoxeterPrime2.lean","qualified_name":"TFPT.Carrier.CoxeterPrime2.seam_rate_is_contraction","statement_as_written":"theorem seam_rate_is_contraction : IsContractionRate ((2 : ℝ) / 3)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoxeterPrime2.lean:TFPT.Carrier.CoxeterPrime2.sheet_eigenvalues_not_contraction","line_end":90,"line_start":84,"module_context_as_written":[],"name":"sheet_eigenvalues_not_contraction","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoxeterPrime2.lean","qualified_name":"TFPT.Carrier.CoxeterPrime2.sheet_eigenvalues_not_contraction","statement_as_written":"theorem sheet_eigenvalues_not_contraction :\n    (¬ IsContractionRate (1 : ℝ)) ∧ (¬ IsContractionRate (-1 : ℝ))","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoxeterPrime2.lean:TFPT.Carrier.CoxeterPrime2.projector_eigenvalues_not_contraction","line_end":97,"line_start":91,"module_context_as_written":[],"name":"projector_eigenvalues_not_contraction","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoxeterPrime2.lean","qualified_name":"TFPT.Carrier.CoxeterPrime2.projector_eigenvalues_not_contraction","statement_as_written":"theorem projector_eigenvalues_not_contraction :\n    (¬ IsContractionRate (0 : ℝ)) ∧ (¬ IsContractionRate (1 : ℝ))","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoxeterPrime2.lean:TFPT.Carrier.CoxeterPrime2.no_prime2_only_attractor","line_end":113,"line_start":98,"module_context_as_written":[],"name":"no_prime2_only_attractor","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoxeterPrime2.lean","qualified_name":"TFPT.Carrier.CoxeterPrime2.no_prime2_only_attractor","statement_as_written":"theorem no_prime2_only_attractor :\n    (∀ r : ℝ, r * r = 1 → ¬ IsContractionRate r) ∧\n    (∀ r : ℝ, r * r = r → ¬ IsContractionRate r) ∧\n    IsContractionRate ((2 : ℝ) / 3)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoxeterPrime2.lean:TFPT.Carrier.CoxeterPrime2.parity_eigenvalue_remembers_start","line_end":120,"line_start":114,"module_context_as_written":[],"name":"parity_eigenvalue_remembers_start","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoxeterPrime2.lean","qualified_name":"TFPT.Carrier.CoxeterPrime2.parity_eigenvalue_remembers_start","statement_as_written":"theorem parity_eigenvalue_remembers_start (xstar x0 : ℝ) (n : ℕ) :\n    iter 1 xstar x0 n - xstar = x0 - xstar","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/CoxeterPrime2.lean:TFPT.Carrier.CoxeterPrime2.seam_rate_has_attractor","line_end":130,"line_start":121,"module_context_as_written":[],"name":"seam_rate_has_attractor","path":"experiments/lean4-carrier-rigidity/TfptCarrier/CoxeterPrime2.lean","qualified_name":"TFPT.Carrier.CoxeterPrime2.seam_rate_has_attractor","statement_as_written":"theorem seam_rate_has_attractor (xstar x0 : ℝ) :\n    Filter.Tendsto (iter (2 / 3) xstar x0) Filter.atTop (nhds xstar)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/DeterminantCharacter.lean:TFPT.Carrier.DeterminantCharacter.torusMatrix","line_end":47,"line_start":40,"module_context_as_written":[{"line":37,"source_text":"variable (K : Type*) [Field K]"},{"line":39,"source_text":"variable (m n : ℕ)"},{"line":46,"source_text":"variable {K m n}"}],"name":"torusMatrix","path":"experiments/lean4-carrier-rigidity/TfptCarrier/DeterminantCharacter.lean","qualified_name":"TFPT.Carrier.DeterminantCharacter.torusMatrix","statement_as_written":"def torusMatrix (lam : K) (qm qp : ℤ) :\n    Matrix (Fin (m + n)) (Fin (m + n)) K","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/DeterminantCharacter.lean:TFPT.Carrier.DeterminantCharacter.det_torusMatrix","line_end":79,"line_start":48,"module_context_as_written":[{"line":37,"source_text":"variable (K : Type*) [Field K]"},{"line":39,"source_text":"variable (m n : ℕ)"},{"line":46,"source_text":"variable {K m n}"}],"name":"det_torusMatrix","path":"experiments/lean4-carrier-rigidity/TfptCarrier/DeterminantCharacter.lean","qualified_name":"TFPT.Carrier.DeterminantCharacter.det_torusMatrix","statement_as_written":"theorem det_torusMatrix\n    (lam : K) (qm qp : ℤ) (hlam : lam ≠ 0) :\n    Matrix.det (torusMatrix K m n lam qm qp) = lam ^ ((m : ℤ) * qm + (n : ℤ) * qp)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/DeterminantCharacter.lean:TFPT.Carrier.DeterminantCharacter.det_torusMatrix_eq_one_iff","line_end":93,"line_start":80,"module_context_as_written":[{"line":37,"source_text":"variable (K : Type*) [Field K]"},{"line":39,"source_text":"variable (m n : ℕ)"},{"line":46,"source_text":"variable {K m n}"}],"name":"det_torusMatrix_eq_one_iff","path":"experiments/lean4-carrier-rigidity/TfptCarrier/DeterminantCharacter.lean","qualified_name":"TFPT.Carrier.DeterminantCharacter.det_torusMatrix_eq_one_iff","statement_as_written":"theorem det_torusMatrix_eq_one_iff\n    (lam : K) (qm qp : ℤ) (hlam : lam ≠ 0) :\n    Matrix.det (torusMatrix K m n lam qm qp) = 1\n      ↔ lam ^ ((m : ℤ) * qm + (n : ℤ) * qp) = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/DeterminantCharacter.lean:TFPT.Carrier.DeterminantCharacter.trace_zero_of_det_one_forall_rat","line_end":117,"line_start":94,"module_context_as_written":[{"line":37,"source_text":"variable (K : Type*) [Field K]"},{"line":39,"source_text":"variable (m n : ℕ)"},{"line":46,"source_text":"variable {K m n}"}],"name":"trace_zero_of_det_one_forall_rat","path":"experiments/lean4-carrier-rigidity/TfptCarrier/DeterminantCharacter.lean","qualified_name":"TFPT.Carrier.DeterminantCharacter.trace_zero_of_det_one_forall_rat","statement_as_written":"theorem trace_zero_of_det_one_forall_rat\n    (qm qp : ℤ)\n    (hdet : ∀ lam : ℚ, 0 < lam → lam ≠ 1\n              → Matrix.det (torusMatrix ℚ m n lam qm qp) = 1) :\n    (m : ℤ) * qm + (n : ℤ) * qp = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/DeterminantCharacter.lean:TFPT.Carrier.DeterminantCharacter.trace_zero_of_det_one_at_two","line_end":138,"line_start":118,"module_context_as_written":[{"line":37,"source_text":"variable (K : Type*) [Field K]"},{"line":39,"source_text":"variable (m n : ℕ)"},{"line":46,"source_text":"variable {K m n}"}],"name":"trace_zero_of_det_one_at_two","path":"experiments/lean4-carrier-rigidity/TfptCarrier/DeterminantCharacter.lean","qualified_name":"TFPT.Carrier.DeterminantCharacter.trace_zero_of_det_one_at_two","statement_as_written":"theorem trace_zero_of_det_one_at_two\n    (qm qp : ℤ)\n    (hdet : Matrix.det (torusMatrix ℚ m n (2 : ℚ) qm qp) = 1) :\n    (m : ℤ) * qm + (n : ℤ) * qp = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean:TfptCarrier.FlavorFeedback.R","line_end":77,"line_start":73,"module_context_as_written":[],"name":"R","path":"experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean","qualified_name":"TfptCarrier.FlavorFeedback.R","statement_as_written":"def R : Matrix (Fin 3) (Fin 3) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean:TfptCarrier.FlavorFeedback.deform","line_end":82,"line_start":78,"module_context_as_written":[],"name":"deform","path":"experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean","qualified_name":"TfptCarrier.FlavorFeedback.deform","statement_as_written":"def deform : Matrix (Fin 3) (Fin 3) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean:TfptCarrier.FlavorFeedback.Rs","line_end":85,"line_start":83,"module_context_as_written":[],"name":"Rs","path":"experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean","qualified_name":"TfptCarrier.FlavorFeedback.Rs","statement_as_written":"def Rs (s : ℤ) : Matrix (Fin 3) (Fin 3) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean:TfptCarrier.FlavorFeedback.P","line_end":88,"line_start":86,"module_context_as_written":[],"name":"P","path":"experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean","qualified_name":"TfptCarrier.FlavorFeedback.P","statement_as_written":"def P : Matrix (Fin 3) (Fin 3) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean:TfptCarrier.FlavorFeedback.b0","line_end":91,"line_start":89,"module_context_as_written":[],"name":"b0","path":"experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean","qualified_name":"TfptCarrier.FlavorFeedback.b0","statement_as_written":"def b0 : Fin 3 → ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean:TfptCarrier.FlavorFeedback.b1","line_end":94,"line_start":92,"module_context_as_written":[],"name":"b1","path":"experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean","qualified_name":"TfptCarrier.FlavorFeedback.b1","statement_as_written":"def b1 : Fin 3 → ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean:TfptCarrier.FlavorFeedback.b2","line_end":97,"line_start":95,"module_context_as_written":[],"name":"b2","path":"experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean","qualified_name":"TfptCarrier.FlavorFeedback.b2","statement_as_written":"def b2 : Fin 3 → ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean:TfptCarrier.FlavorFeedback.F","line_end":101,"line_start":98,"module_context_as_written":[],"name":"F","path":"experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean","qualified_name":"TfptCarrier.FlavorFeedback.F","statement_as_written":"def F (s : ℤ) : Matrix (Fin 3) (Fin 3) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean:TfptCarrier.FlavorFeedback.Rs_eq","line_end":109,"line_start":102,"module_context_as_written":[],"name":"Rs_eq","path":"experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean","qualified_name":"TfptCarrier.FlavorFeedback.Rs_eq","statement_as_written":"theorem Rs_eq (s : ℤ) :\n    Rs s = !![1 + s, 3, 0; 1 + s, 5, 2; 2 + s, 5, 3]","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean:TfptCarrier.FlavorFeedback.action_b0","line_end":121,"line_start":110,"module_context_as_written":[],"name":"action_b0","path":"experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean","qualified_name":"TfptCarrier.FlavorFeedback.action_b0","statement_as_written":"theorem action_b0 (s : ℤ) :\n    Rs s *ᵥ b0 = (s + 4) • b0 + 4 • b2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean:TfptCarrier.FlavorFeedback.action_b1","line_end":129,"line_start":122,"module_context_as_written":[],"name":"action_b1","path":"experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean","qualified_name":"TfptCarrier.FlavorFeedback.action_b1","statement_as_written":"theorem action_b1 (s : ℤ) : Rs s *ᵥ b1 = b2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean:TfptCarrier.FlavorFeedback.action_b2","line_end":137,"line_start":130,"module_context_as_written":[],"name":"action_b2","path":"experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean","qualified_name":"TfptCarrier.FlavorFeedback.action_b2","statement_as_written":"theorem action_b2 (s : ℤ) :\n    Rs s *ᵥ b2 = (3 : ℤ) • b0 - (2 : ℤ) • b1 + (5 : ℤ) • b2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean:TfptCarrier.FlavorFeedback.conjugation","line_end":150,"line_start":138,"module_context_as_written":[],"name":"conjugation","path":"experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean","qualified_name":"TfptCarrier.FlavorFeedback.conjugation","statement_as_written":"theorem conjugation (s : ℤ) : P * F s = Rs s * P","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean:TfptCarrier.FlavorFeedback.charpoly_Rs","line_end":166,"line_start":151,"module_context_as_written":[],"name":"charpoly_Rs","path":"experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean","qualified_name":"TfptCarrier.FlavorFeedback.charpoly_Rs","statement_as_written":"theorem charpoly_Rs (s : ℤ) :\n    (Rs s).charpoly\n      = (X - C (s + 4)) * (X ^ 2 - C 5 * X + C 2) - C 12 * X","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean:TfptCarrier.FlavorFeedback.charpoly_L","line_end":173,"line_start":167,"module_context_as_written":[],"name":"charpoly_L","path":"experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean","qualified_name":"TfptCarrier.FlavorFeedback.charpoly_L","statement_as_written":"theorem charpoly_L :\n    (Rs 6).charpoly = X ^ 3 - 15 * X ^ 2 + 40 * X - 20","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean:TfptCarrier.FlavorFeedback.det_P","line_end":178,"line_start":174,"module_context_as_written":[],"name":"det_P","path":"experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean","qualified_name":"TfptCarrier.FlavorFeedback.det_P","statement_as_written":"theorem det_P : P.det = -4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean:TfptCarrier.FlavorFeedback.natAbs_det_P","line_end":182,"line_start":179,"module_context_as_written":[],"name":"natAbs_det_P","path":"experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean","qualified_name":"TfptCarrier.FlavorFeedback.natAbs_det_P","statement_as_written":"theorem natAbs_det_P : P.det.natAbs = 4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean:TfptCarrier.FlavorFeedback.minor2","line_end":187,"line_start":183,"module_context_as_written":[],"name":"minor2","path":"experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean","qualified_name":"TfptCarrier.FlavorFeedback.minor2","statement_as_written":"def minor2 (A : Matrix (Fin 3) (Fin 3) ℤ) (i j : Fin 3) : ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean:TfptCarrier.FlavorFeedback.snf_gcd_entries","line_end":193,"line_start":188,"module_context_as_written":[],"name":"snf_gcd_entries","path":"experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean","qualified_name":"TfptCarrier.FlavorFeedback.snf_gcd_entries","statement_as_written":"theorem snf_gcd_entries :\n    (Finset.univ.gcd fun p : Fin 3 × Fin 3 => P p.1 p.2) = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean:TfptCarrier.FlavorFeedback.snf_gcd_minors","line_end":208,"line_start":194,"module_context_as_written":[],"name":"snf_gcd_minors","path":"experiments/lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean","qualified_name":"TfptCarrier.FlavorFeedback.snf_gcd_minors","statement_as_written":"theorem snf_gcd_minors :\n    (Finset.univ.gcd fun p : Fin 3 × Fin 3 => minor2 P p.1 p.2)\n      = 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/G31Orders.lean:TfptCarrier.G31Orders.wd5_order","line_end":27,"line_start":25,"module_context_as_written":[],"name":"wd5_order","path":"experiments/lean4-carrier-rigidity/TfptCarrier/G31Orders.lean","qualified_name":"TfptCarrier.G31Orders.wd5_order","statement_as_written":"theorem wd5_order : (1920 : ℕ) = 2 ^ 4 * Nat.factorial 5","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/G31Orders.lean:TfptCarrier.G31Orders.wa3_order","line_end":30,"line_start":28,"module_context_as_written":[],"name":"wa3_order","path":"experiments/lean4-carrier-rigidity/TfptCarrier/G31Orders.lean","qualified_name":"TfptCarrier.G31Orders.wa3_order","statement_as_written":"theorem wa3_order : (24 : ℕ) = Nat.factorial 4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/G31Orders.lean:TfptCarrier.G31Orders.g31_order_factorization","line_end":35,"line_start":31,"module_context_as_written":[],"name":"g31_order_factorization","path":"experiments/lean4-carrier-rigidity/TfptCarrier/G31Orders.lean","qualified_name":"TfptCarrier.G31Orders.g31_order_factorization","statement_as_written":"theorem g31_order_factorization : (46080 : ℕ) = 1920 * 24","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/G31Orders.lean:TfptCarrier.G31Orders.g31_degree_product","line_end":38,"line_start":36,"module_context_as_written":[],"name":"g31_degree_product","path":"experiments/lean4-carrier-rigidity/TfptCarrier/G31Orders.lean","qualified_name":"TfptCarrier.G31Orders.g31_degree_product","statement_as_written":"theorem g31_degree_product : (8 : ℕ) * 12 * 20 * 24 = 46080","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/G31Orders.lean:TfptCarrier.G31Orders.g31_reflection_count","line_end":44,"line_start":39,"module_context_as_written":[],"name":"g31_reflection_count","path":"experiments/lean4-carrier-rigidity/TfptCarrier/G31Orders.lean","qualified_name":"TfptCarrier.G31Orders.g31_reflection_count","statement_as_written":"theorem g31_reflection_count :\n    (8 - 1) + (12 - 1) + (20 - 1) + (24 - 1) = (60 : ℕ)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/G31Orders.lean:TfptCarrier.G31Orders.clock_orbit_count","line_end":50,"line_start":45,"module_context_as_written":[],"name":"clock_orbit_count","path":"experiments/lean4-carrier-rigidity/TfptCarrier/G31Orders.lean","qualified_name":"TfptCarrier.G31Orders.clock_orbit_count","statement_as_written":"theorem clock_orbit_count : (240 : ℕ) = 4 * 60","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean:TfptCarrier.G31WordOrders.gi","line_end":44,"line_start":42,"module_context_as_written":[],"name":"gi","path":"experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean","qualified_name":"TfptCarrier.G31WordOrders.gi","statement_as_written":"def gi : GaussianInt","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean:TfptCarrier.G31WordOrders.gi_sq","line_end":46,"line_start":45,"module_context_as_written":[],"name":"gi_sq","path":"experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean","qualified_name":"TfptCarrier.G31WordOrders.gi_sq","statement_as_written":"theorem gi_sq : gi ^ 2 = -1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean:TfptCarrier.G31WordOrders.C_gi_sq","line_end":50,"line_start":47,"module_context_as_written":[],"name":"C_gi_sq","path":"experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean","qualified_name":"TfptCarrier.G31WordOrders.C_gi_sq","statement_as_written":"theorem C_gi_sq : (C gi : Polynomial GaussianInt) ^ 2 = -1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean:TfptCarrier.G31WordOrders.chiW","line_end":55,"line_start":51,"module_context_as_written":[],"name":"chiW","path":"experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean","qualified_name":"TfptCarrier.G31WordOrders.chiW","statement_as_written":"noncomputable def chiW : Polynomial GaussianInt","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean:TfptCarrier.G31WordOrders.chiU","line_end":60,"line_start":56,"module_context_as_written":[],"name":"chiU","path":"experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean","qualified_name":"TfptCarrier.G31WordOrders.chiU","statement_as_written":"noncomputable def chiU : Polynomial GaussianInt","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean:TfptCarrier.G31WordOrders.chiW_dvd","line_end":70,"line_start":61,"module_context_as_written":[],"name":"chiW_dvd","path":"experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean","qualified_name":"TfptCarrier.G31WordOrders.chiW_dvd","statement_as_written":"theorem chiW_dvd : chiW ∣ (X : Polynomial GaussianInt) ^ 24 - 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean:TfptCarrier.G31WordOrders.chiU_dvd","line_end":79,"line_start":71,"module_context_as_written":[],"name":"chiU_dvd","path":"experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean","qualified_name":"TfptCarrier.G31WordOrders.chiU_dvd","statement_as_written":"theorem chiU_dvd : chiU ∣ (X : Polynomial GaussianInt) ^ 20 - 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean:TfptCarrier.G31WordOrders.W","line_end":88,"line_start":80,"module_context_as_written":[],"name":"W","path":"experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean","qualified_name":"TfptCarrier.G31WordOrders.W","statement_as_written":"def W : Matrix (Fin 4) (Fin 4) GaussianInt","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean:TfptCarrier.G31WordOrders.U","line_end":95,"line_start":89,"module_context_as_written":[],"name":"U","path":"experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean","qualified_name":"TfptCarrier.G31WordOrders.U","statement_as_written":"def U : Matrix (Fin 4) (Fin 4) GaussianInt","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean:TfptCarrier.G31WordOrders.aeval_W_chiW","line_end":102,"line_start":96,"module_context_as_written":[],"name":"aeval_W_chiW","path":"experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean","qualified_name":"TfptCarrier.G31WordOrders.aeval_W_chiW","statement_as_written":"theorem aeval_W_chiW : Polynomial.aeval W chiW = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean:TfptCarrier.G31WordOrders.aeval_U_chiU","line_end":109,"line_start":103,"module_context_as_written":[],"name":"aeval_U_chiU","path":"experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean","qualified_name":"TfptCarrier.G31WordOrders.aeval_U_chiU","statement_as_written":"theorem aeval_U_chiU : Polynomial.aeval U chiU = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean:TfptCarrier.G31WordOrders.dvd_implies_W_pow","line_end":118,"line_start":110,"module_context_as_written":[],"name":"dvd_implies_W_pow","path":"experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean","qualified_name":"TfptCarrier.G31WordOrders.dvd_implies_W_pow","statement_as_written":"theorem dvd_implies_W_pow {d : ℕ}\n    (h : chiW ∣ (X : Polynomial GaussianInt) ^ d - 1) : W ^ d = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean:TfptCarrier.G31WordOrders.dvd_implies_U_pow","line_end":127,"line_start":119,"module_context_as_written":[],"name":"dvd_implies_U_pow","path":"experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean","qualified_name":"TfptCarrier.G31WordOrders.dvd_implies_U_pow","statement_as_written":"theorem dvd_implies_U_pow {d : ℕ}\n    (h : chiU ∣ (X : Polynomial GaussianInt) ^ d - 1) : U ^ d = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean:TfptCarrier.G31WordOrders.W_pow_24","line_end":130,"line_start":128,"module_context_as_written":[],"name":"W_pow_24","path":"experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean","qualified_name":"TfptCarrier.G31WordOrders.W_pow_24","statement_as_written":"theorem W_pow_24 : W ^ 24 = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean:TfptCarrier.G31WordOrders.U_pow_20","line_end":133,"line_start":131,"module_context_as_written":[],"name":"U_pow_20","path":"experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean","qualified_name":"TfptCarrier.G31WordOrders.U_pow_20","statement_as_written":"theorem U_pow_20 : U ^ 20 = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean:TfptCarrier.G31WordOrders.chiW_not_dvd_proper","line_end":143,"line_start":134,"module_context_as_written":[],"name":"chiW_not_dvd_proper","path":"experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean","qualified_name":"TfptCarrier.G31WordOrders.chiW_not_dvd_proper","statement_as_written":"theorem chiW_not_dvd_proper :\n    ∀ d ∈ [1, 2, 3, 4, 6, 8, 12],\n      ¬ chiW ∣ (X : Polynomial GaussianInt) ^ d - 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean:TfptCarrier.G31WordOrders.chiU_not_dvd_proper","line_end":155,"line_start":144,"module_context_as_written":[],"name":"chiU_not_dvd_proper","path":"experiments/lean4-carrier-rigidity/TfptCarrier/G31WordOrders.lean","qualified_name":"TfptCarrier.G31WordOrders.chiU_not_dvd_proper","statement_as_written":"theorem chiU_not_dvd_proper :\n    ∀ d ∈ [1, 2, 4, 5, 10],\n      ¬ chiU ∣ (X : Polynomial GaussianInt) ^ d - 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.par","line_end":88,"line_start":84,"module_context_as_written":[],"name":"par","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.par","statement_as_written":"def par (n : ℤ) : ZMod 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify 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assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.piSig","line_end":100,"line_start":97,"module_context_as_written":[],"name":"piSig","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.piSig","statement_as_written":"def piSig : Fin 8 → Fin 8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.code_piJ_invariant","line_end":106,"line_start":101,"module_context_as_written":[],"name":"code_piJ_invariant","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.code_piJ_invariant","statement_as_written":"theorem code_piJ_invariant :\n    ∀ c ∈ HammingCode.code, (fun k => c (piJ k)) ∈ HammingCode.code","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.code_piSig_invariant","line_end":112,"line_start":107,"module_context_as_written":[],"name":"code_piSig_invariant","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.code_piSig_invariant","statement_as_written":"theorem code_piSig_invariant :\n    ∀ c ∈ HammingCode.code, (fun k => c (piSig k)) ∈ HammingCode.code","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.Jmat","line_end":125,"line_start":113,"module_context_as_written":[],"name":"Jmat","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.Jmat","statement_as_written":"def Jmat : Matrix (Fin 8) (Fin 8) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.Smat","line_end":136,"line_start":126,"module_context_as_written":[],"name":"Smat","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.Smat","statement_as_written":"def Smat : Matrix (Fin 8) (Fin 8) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.J_sq","line_end":139,"line_start":137,"module_context_as_written":[],"name":"J_sq","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.J_sq","statement_as_written":"theorem J_sq : Jmat * Jmat = -1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.J_skew","line_end":142,"line_start":140,"module_context_as_written":[],"name":"J_skew","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.J_skew","statement_as_written":"theorem J_skew : Jmat.transpose = -Jmat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.one_add_J_gram","line_end":148,"line_start":143,"module_context_as_written":[],"name":"one_add_J_gram","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.one_add_J_gram","statement_as_written":"theorem one_add_J_gram :\n    (1 + Jmat).transpose * (1 + Jmat) = (2 : ℤ) • 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.sigma_cubed_ambient","line_end":151,"line_start":149,"module_context_as_written":[],"name":"sigma_cubed_ambient","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.sigma_cubed_ambient","statement_as_written":"theorem sigma_cubed_ambient : Smat * Smat * Smat = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.J_sigma_commute","line_end":154,"line_start":152,"module_context_as_written":[],"name":"J_sigma_commute","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.J_sigma_commute","statement_as_written":"theorem J_sigma_commute : Jmat * Smat = Smat * Jmat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.Bmat","line_end":169,"line_start":155,"module_context_as_written":[],"name":"Bmat","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.Bmat","statement_as_written":"def Bmat : Matrix (Fin 8) (Fin 8) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.basis_rows_in_code","line_end":174,"line_start":170,"module_context_as_written":[],"name":"basis_rows_in_code","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.basis_rows_in_code","statement_as_written":"theorem basis_rows_in_code :\n    ∀ i : Fin 8, mod2 (Bmat i) ∈ HammingCode.code","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.CJ","line_end":185,"line_start":175,"module_context_as_written":[],"name":"CJ","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.CJ","statement_as_written":"def CJ : Matrix (Fin 8) (Fin 8) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.CS","line_end":196,"line_start":186,"module_context_as_written":[],"name":"CS","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.CS","statement_as_written":"def CS : Matrix (Fin 8) (Fin 8) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.Amat","line_end":207,"line_start":197,"module_context_as_written":[],"name":"Amat","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.Amat","statement_as_written":"def Amat : Matrix (Fin 8) (Fin 8) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.lattice_J","line_end":209,"line_start":208,"module_context_as_written":[],"name":"lattice_J","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.lattice_J","statement_as_written":"theorem lattice_J : Bmat * Jmat = CJ * Bmat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.lattice_sigma","line_end":211,"line_start":210,"module_context_as_written":[],"name":"lattice_sigma","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.lattice_sigma","statement_as_written":"theorem lattice_sigma : Bmat * Smat = CS * Bmat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.lattice_one_add_J","line_end":215,"line_start":212,"module_context_as_written":[],"name":"lattice_one_add_J","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.lattice_one_add_J","statement_as_written":"theorem lattice_one_add_J : Bmat * (1 + Jmat) = Amat * Bmat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.snfDiag","line_end":220,"line_start":216,"module_context_as_written":[],"name":"snfDiag","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.snfDiag","statement_as_written":"def snfDiag : Fin 8 → ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.Dsnf","line_end":223,"line_start":221,"module_context_as_written":[],"name":"Dsnf","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.Dsnf","statement_as_written":"def Dsnf : Matrix (Fin 8) (Fin 8) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.Pmat","line_end":234,"line_start":224,"module_context_as_written":[],"name":"Pmat","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.Pmat","statement_as_written":"def Pmat : Matrix (Fin 8) (Fin 8) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.Pinv","line_end":245,"line_start":235,"module_context_as_written":[],"name":"Pinv","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.Pinv","statement_as_written":"def Pinv : Matrix (Fin 8) (Fin 8) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.Qmat","line_end":256,"line_start":246,"module_context_as_written":[],"name":"Qmat","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.Qmat","statement_as_written":"def Qmat : Matrix (Fin 8) (Fin 8) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.Qinv","line_end":267,"line_start":257,"module_context_as_written":[],"name":"Qinv","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.Qinv","statement_as_written":"def Qinv : Matrix (Fin 8) (Fin 8) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.P_unimodular","line_end":270,"line_start":268,"module_context_as_written":[],"name":"P_unimodular","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.P_unimodular","statement_as_written":"theorem P_unimodular : Pmat * Pinv = 1 ∧ Pinv * Pmat = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.Q_unimodular","line_end":273,"line_start":271,"module_context_as_written":[],"name":"Q_unimodular","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.Q_unimodular","statement_as_written":"theorem Q_unimodular : Qmat * Qinv = 1 ∧ Qinv * Qmat = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.smith_certificate","line_end":279,"line_start":274,"module_context_as_written":[],"name":"smith_certificate","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.smith_certificate","statement_as_written":"theorem smith_certificate : Pmat * Amat * Qmat = Dsnf","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.smith_converse_ingredient","line_end":283,"line_start":280,"module_context_as_written":[],"name":"smith_converse_ingredient","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.smith_converse_ingredient","statement_as_written":"theorem smith_converse_ingredient : Dsnf * Qinv = Pmat * Amat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.index_sixteen","line_end":288,"line_start":284,"module_context_as_written":[],"name":"index_sixteen","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.index_sixteen","statement_as_written":"theorem index_sixteen : Dsnf.det = 16","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.index_is_norm_pow_four","line_end":290,"line_start":289,"module_context_as_written":[],"name":"index_is_norm_pow_four","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.index_is_norm_pow_four","statement_as_written":"theorem index_is_norm_pow_four : (16 : ℤ) = 2 ^ 4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.snf_exponent_two","line_end":296,"line_start":291,"module_context_as_written":[],"name":"snf_exponent_two","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.snf_exponent_two","statement_as_written":"theorem snf_exponent_two :\n    (∀ i : Fin 8, snfDiag i = 1 ∨ snfDiag i = 2) ∧ snfDiag 7 = 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.rowMul","line_end":302,"line_start":297,"module_context_as_written":[],"name":"rowMul","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.rowMul","statement_as_written":"def rowMul (c : Fin 8 → ℤ) (M : Matrix (Fin 8) (Fin 8) ℤ) : Fin 8 → ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.labelOf","line_end":307,"line_start":303,"module_context_as_written":[],"name":"labelOf","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.labelOf","statement_as_written":"def labelOf (c : Fin 8 → ℤ) : Fin 4 → ZMod 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.label_kills_one_add_J","line_end":314,"line_start":308,"module_context_as_written":[],"name":"label_kills_one_add_J","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.label_kills_one_add_J","statement_as_written":"theorem label_kills_one_add_J :\n    ∀ i : Fin 8, ∀ j : Fin 4,\n      par ((Amat * Qmat) i (Fin.natAdd 4 j)) = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.rootCoords","line_end":560,"line_start":315,"module_context_as_written":[],"name":"rootCoords","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.rootCoords","statement_as_written":"def rootCoords : List (Fin 8 → ℤ)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.labelData","line_end":803,"line_start":561,"module_context_as_written":[],"name":"labelData","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.labelData","statement_as_written":"def labelData : List (Fin 4 → ZMod 2)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.rootCoords_length","line_end":805,"line_start":804,"module_context_as_written":[],"name":"rootCoords_length","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.rootCoords_length","statement_as_written":"theorem rootCoords_length : rootCoords.length = 240","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.labelData_length","line_end":809,"line_start":806,"module_context_as_written":[],"name":"labelData_length","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.labelData_length","statement_as_written":"theorem labelData_length : labelData.length = 240","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.rootCoords_nodup","line_end":813,"line_start":810,"module_context_as_written":[],"name":"rootCoords_nodup","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.rootCoords_nodup","statement_as_written":"theorem rootCoords_nodup : rootCoords.Nodup","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.roots_norm_four","line_end":818,"line_start":814,"module_context_as_written":[],"name":"roots_norm_four","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.roots_norm_four","statement_as_written":"theorem roots_norm_four :\n    ∀ c ∈ rootCoords, (∑ j, rowMul c Bmat j ^ 2) = 4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.roots_in_code","line_end":824,"line_start":819,"module_context_as_written":[],"name":"roots_in_code","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.roots_in_code","statement_as_written":"theorem roots_in_code :\n    ∀ c ∈ rootCoords, mod2 (rowMul c Bmat) ∈ HammingCode.code","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.labels_eq","line_end":826,"line_start":825,"module_context_as_written":[],"name":"labels_eq","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.labels_eq","statement_as_written":"theorem labels_eq : rootCoords.map labelOf = labelData","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.census_zero_class_empty","line_end":831,"line_start":827,"module_context_as_written":[],"name":"census_zero_class_empty","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.census_zero_class_empty","statement_as_written":"theorem census_zero_class_empty : ∀ l ∈ labelData, l ≠ 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.census_equidistribution","line_end":835,"line_start":832,"module_context_as_written":[],"name":"census_equidistribution","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.census_equidistribution","statement_as_written":"theorem census_equidistribution :\n    ∀ s : Fin 4 → ZMod 2, s ≠ 0 → labelData.count s = 16","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.Rsig","line_end":848,"line_start":836,"module_context_as_written":[],"name":"Rsig","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.Rsig","statement_as_written":"def Rsig : Matrix (Fin 8) (Fin 8) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.RJ","line_end":859,"line_start":849,"module_context_as_written":[],"name":"RJ","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.RJ","statement_as_written":"def RJ : Matrix (Fin 8) (Fin 8) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.Msig","line_end":866,"line_start":860,"module_context_as_written":[],"name":"Msig","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.Msig","statement_as_written":"def Msig : Matrix (Fin 4) (Fin 4) (ZMod 2)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.sigma_transport","line_end":868,"line_start":867,"module_context_as_written":[],"name":"sigma_transport","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.sigma_transport","statement_as_written":"theorem sigma_transport : CS * Qmat = Qmat * Rsig","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.mu4_transport","line_end":870,"line_start":869,"module_context_as_written":[],"name":"mu4_transport","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.mu4_transport","statement_as_written":"theorem mu4_transport : CJ * Qmat = Qmat * RJ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.sigma_label_block","line_end":879,"line_start":871,"module_context_as_written":[],"name":"sigma_label_block","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.sigma_label_block","statement_as_written":"theorem sigma_label_block :\n    (∀ i : Fin 4, ∀ j : Fin 4,\n      par (Rsig (Fin.castAdd 4 i) (Fin.natAdd 4 j)) = 0) ∧\n    (∀ i : Fin 4, ∀ j : Fin 4,\n      Msig i j = par (Rsig (Fin.natAdd 4 i) (Fin.natAdd 4 j)))","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.mu4_acts_trivially_on_labels","line_end":889,"line_start":880,"module_context_as_written":[],"name":"mu4_acts_trivially_on_labels","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.mu4_acts_trivially_on_labels","statement_as_written":"theorem mu4_acts_trivially_on_labels :\n    ∀ i : Fin 8, ∀ j : Fin 4,\n      par (RJ i (Fin.natAdd 4 j)) = if i = Fin.natAdd 4 j then 1 else 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.census_mu4_stable","line_end":893,"line_start":890,"module_context_as_written":[],"name":"census_mu4_stable","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.census_mu4_stable","statement_as_written":"theorem census_mu4_stable :\n    rootCoords.map (fun c => labelOf (rowMul c CJ)) = labelData","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.rowMul4","line_end":900,"line_start":894,"module_context_as_written":[],"name":"rowMul4","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.rowMul4","statement_as_written":"def rowMul4 (l : Fin 4 → ZMod 2) (M : Matrix (Fin 4) (Fin 4) (ZMod 2)) :\n    Fin 4 → ZMod 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.census_sigma_equivariant","line_end":905,"line_start":901,"module_context_as_written":[],"name":"census_sigma_equivariant","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.census_sigma_equivariant","statement_as_written":"theorem census_sigma_equivariant :\n    rootCoords.map (fun c => labelOf (rowMul c CS))\n      = labelData.map (fun l => rowMul4 l Msig)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.sigma_cubed","line_end":910,"line_start":906,"module_context_as_written":[],"name":"sigma_cubed","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.sigma_cubed","statement_as_written":"theorem sigma_cubed : Msig * Msig * Msig = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.sigma_nontrivial","line_end":913,"line_start":911,"module_context_as_written":[],"name":"sigma_nontrivial","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.sigma_nontrivial","statement_as_written":"theorem sigma_nontrivial : Msig ≠ 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.sigma_fixed_space","line_end":919,"line_start":914,"module_context_as_written":[],"name":"sigma_fixed_space","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.sigma_fixed_space","statement_as_written":"theorem sigma_fixed_space :\n    (Finset.univ.filter fun l : Fin 4 → ZMod 2 =>\n      rowMul4 l Msig = l).card = 4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.sigma_fixed_nontrivial","line_end":924,"line_start":920,"module_context_as_written":[],"name":"sigma_fixed_nontrivial","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.sigma_fixed_nontrivial","statement_as_written":"theorem sigma_fixed_nontrivial :\n    (Finset.univ.filter fun l : Fin 4 → ZMod 2 =>\n      l ≠ 0 ∧ rowMul4 l Msig = l).card = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.F1","line_end":927,"line_start":925,"module_context_as_written":[],"name":"F1","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.F1","statement_as_written":"def F1 : Fin 4 → ZMod 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.F2","line_end":930,"line_start":928,"module_context_as_written":[],"name":"F2","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.F2","statement_as_written":"def F2 : Fin 4 → ZMod 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.F3","line_end":933,"line_start":931,"module_context_as_written":[],"name":"F3","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.F3","statement_as_written":"def F3 : Fin 4 → ZMod 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.anchor","line_end":936,"line_start":934,"module_context_as_written":[],"name":"anchor","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.anchor","statement_as_written":"def anchor : Fin 4 → ZMod 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.family_three_cycle","line_end":941,"line_start":937,"module_context_as_written":[],"name":"family_three_cycle","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.family_three_cycle","statement_as_written":"theorem family_three_cycle :\n    rowMul4 F1 Msig = F2 ∧ rowMul4 F2 Msig = F3 ∧ rowMul4 F3 Msig = F1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.anchor_fixed","line_end":944,"line_start":942,"module_context_as_written":[],"name":"anchor_fixed","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.anchor_fixed","statement_as_written":"theorem anchor_fixed : rowMul4 anchor Msig = anchor ∧ anchor ≠ 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.family_anchor_spans","line_end":951,"line_start":945,"module_context_as_written":[],"name":"family_anchor_spans","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.family_anchor_spans","statement_as_written":"theorem family_anchor_spans :\n    ∀ v : Fin 4 → ZMod 2,\n      ∃ a b c d : ZMod 2, v = a • F1 + b • F2 + c • F3 + d • anchor","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.cCoord","line_end":956,"line_start":952,"module_context_as_written":[],"name":"cCoord","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.cCoord","statement_as_written":"def cCoord : Fin 8 → ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.coord_root_ambient","line_end":961,"line_start":957,"module_context_as_written":[],"name":"coord_root_ambient","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.coord_root_ambient","statement_as_written":"theorem coord_root_ambient :\n    rowMul cCoord Bmat = ![2, 0, 0, 0, 0, 0, 0, 0]","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.coord_root_in_roots","line_end":964,"line_start":962,"module_context_as_written":[],"name":"coord_root_in_roots","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.coord_root_in_roots","statement_as_written":"theorem coord_root_in_roots : cCoord ∈ rootCoords","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.coord_class_eq_family_sum","line_end":970,"line_start":965,"module_context_as_written":[],"name":"coord_class_eq_family_sum","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.coord_class_eq_family_sum","statement_as_written":"theorem coord_class_eq_family_sum : labelOf cCoord = F1 + F2 + F3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean:TfptCarrier.GaussianCodeBridge.coord_class_sigma_fixed","line_end":976,"line_start":971,"module_context_as_written":[],"name":"coord_class_sigma_fixed","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean","qualified_name":"TfptCarrier.GaussianCodeBridge.coord_class_sigma_fixed","statement_as_written":"theorem coord_class_sigma_fixed :\n    rowMul4 (labelOf cCoord) Msig = labelOf cCoord","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianShells.lean:TfptCarrier.GaussianShells.sigma3","line_end":72,"line_start":69,"module_context_as_written":[{"line":108,"source_text":"variable (S : ShellSystem)"}],"name":"sigma3","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianShells.lean","qualified_name":"TfptCarrier.GaussianShells.sigma3","statement_as_written":"def sigma3 (n : ℕ) : ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"structure","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianShells.lean:TfptCarrier.GaussianShells.ShellSystem","line_end":109,"line_start":73,"module_context_as_written":[{"line":108,"source_text":"variable (S : ShellSystem)"}],"name":"ShellSystem","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianShells.lean","qualified_name":"TfptCarrier.GaussianShells.ShellSystem","statement_as_written":"structure ShellSystem","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianShells.lean:TfptCarrier.GaussianShells.ShellSystem.dvd_diff","line_end":115,"line_start":110,"module_context_as_written":[{"line":108,"source_text":"variable (S : ShellSystem)"}],"name":"dvd_diff","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianShells.lean","qualified_name":"TfptCarrier.GaussianShells.ShellSystem.dvd_diff","statement_as_written":"theorem dvd_diff (n : ℕ) : (15 : ℤ) ∣ S.ΘL n - S.Θ0 n","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianShells.lean:TfptCarrier.GaussianShells.ShellSystem.decomposition","line_end":121,"line_start":116,"module_context_as_written":[{"line":108,"source_text":"variable (S : ShellSystem)"}],"name":"decomposition","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianShells.lean","qualified_name":"TfptCarrier.GaussianShells.ShellSystem.decomposition","statement_as_written":"theorem decomposition (n : ℕ) : S.ΘL n = S.Θ0 n + 15 * S.Θv n","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianShells.lean:TfptCarrier.GaussianShells.ShellSystem.walshU","line_end":131,"line_start":122,"module_context_as_written":[{"line":108,"source_text":"variable (S : ShellSystem)"}],"name":"walshU","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianShells.lean","qualified_name":"TfptCarrier.GaussianShells.ShellSystem.walshU","statement_as_written":"def walshU (n : ℕ) : ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianShells.lean:TfptCarrier.GaussianShells.ShellSystem.walsh_formula","line_end":139,"line_start":132,"module_context_as_written":[{"line":108,"source_text":"variable (S : ShellSystem)"}],"name":"walsh_formula","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianShells.lean","qualified_name":"TfptCarrier.GaussianShells.ShellSystem.walsh_formula","statement_as_written":"theorem walsh_formula (n : ℕ) :\n    15 * S.walshU n = 16 * S.Θ0 n - S.ΘL n","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianShells.lean:TfptCarrier.GaussianShells.ShellSystem.theta_v_odd","line_end":151,"line_start":140,"module_context_as_written":[{"line":108,"source_text":"variable (S : ShellSystem)"}],"name":"theta_v_odd","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianShells.lean","qualified_name":"TfptCarrier.GaussianShells.ShellSystem.theta_v_odd","statement_as_written":"theorem theta_v_odd (m : ℕ) :\n    S.Θv (2 * m + 1) = 16 * sigma3 (2 * m + 1)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianShells.lean:TfptCarrier.GaussianShells.ShellSystem.walsh_odd","line_end":159,"line_start":152,"module_context_as_written":[{"line":108,"source_text":"variable (S : ShellSystem)"}],"name":"walsh_odd","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianShells.lean","qualified_name":"TfptCarrier.GaussianShells.ShellSystem.walsh_odd","statement_as_written":"theorem walsh_odd (m : ℕ) :\n    S.walshU (2 * m + 1) = -16 * sigma3 (2 * m + 1)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianShells.lean:TfptCarrier.GaussianShells.ShellSystem.walsh_odd_ratio","line_end":167,"line_start":160,"module_context_as_written":[{"line":108,"source_text":"variable (S : ShellSystem)"}],"name":"walsh_odd_ratio","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianShells.lean","qualified_name":"TfptCarrier.GaussianShells.ShellSystem.walsh_odd_ratio","statement_as_written":"theorem walsh_odd_ratio (m : ℕ) :\n    15 * S.walshU (2 * m + 1) = -S.ΘL (2 * m + 1)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GaussianShells.lean:TfptCarrier.GaussianShells.ShellSystem.walsh_even","line_end":184,"line_start":168,"module_context_as_written":[{"line":108,"source_text":"variable (S : ShellSystem)"}],"name":"walsh_even","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GaussianShells.lean","qualified_name":"TfptCarrier.GaussianShells.ShellSystem.walsh_even","statement_as_written":"theorem walsh_even (m : ℕ) (hm : m ≠ 0) :\n    S.walshU (2 * m) = 16 * (16 * sigma3 m - sigma3 (2 * m))","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"abbrev","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean:TFPT.Carrier.GlueUniqueness.El","line_end":40,"line_start":37,"module_context_as_written":[],"name":"El","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean","qualified_name":"TFPT.Carrier.GlueUniqueness.El","statement_as_written":"abbrev El","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean:TFPT.Carrier.GlueUniqueness.add","line_end":43,"line_start":41,"module_context_as_written":[],"name":"add","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean","qualified_name":"TFPT.Carrier.GlueUniqueness.add","statement_as_written":"def add (a b : El) : El","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean:TFPT.Carrier.GlueUniqueness.qZ","line_end":47,"line_start":44,"module_context_as_written":[],"name":"qZ","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean","qualified_name":"TFPT.Carrier.GlueUniqueness.qZ","statement_as_written":"def qZ (a : El) : ℕ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean:TFPT.Carrier.GlueUniqueness.isotropic","line_end":52,"line_start":48,"module_context_as_written":[],"name":"isotropic","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean","qualified_name":"TFPT.Carrier.GlueUniqueness.isotropic","statement_as_written":"def isotropic (a : El) : Prop","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean:TFPT.Carrier.GlueUniqueness.orbit","line_end":56,"line_start":53,"module_context_as_written":[],"name":"orbit","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean","qualified_name":"TFPT.Carrier.GlueUniqueness.orbit","statement_as_written":"def orbit (g : El) : List El","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean:TFPT.Carrier.GlueUniqueness.isotropic_elements_classified","line_end":63,"line_start":57,"module_context_as_written":[],"name":"isotropic_elements_classified","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean","qualified_name":"TFPT.Carrier.GlueUniqueness.isotropic_elements_classified","statement_as_written":"theorem isotropic_elements_classified :\n    ∀ a : El, isotropic a ↔\n      a ∈ ([((0:Fin 4),(0:Fin 4)), (1,1), (1,3), (2,2), (3,1), (3,3)] : List El)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean:TFPT.Carrier.GlueUniqueness.isotropic_order4_classified","line_end":70,"line_start":64,"module_context_as_written":[],"name":"isotropic_order4_classified","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean","qualified_name":"TFPT.Carrier.GlueUniqueness.isotropic_order4_classified","statement_as_written":"theorem isotropic_order4_classified :\n    ∀ a : El, (isotropic a ∧ (a.1.val % 2 = 1 ∨ a.2.val % 2 = 1)) ↔\n      a ∈ ([((1:Fin 4),(1:Fin 4)), (1,3), (3,1), (3,3)] : List El)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean:TFPT.Carrier.GlueUniqueness.H1","line_end":73,"line_start":71,"module_context_as_written":[],"name":"H1","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean","qualified_name":"TFPT.Carrier.GlueUniqueness.H1","statement_as_written":"def H1 : List El","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean:TFPT.Carrier.GlueUniqueness.H2","line_end":76,"line_start":74,"module_context_as_written":[],"name":"H2","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean","qualified_name":"TFPT.Carrier.GlueUniqueness.H2","statement_as_written":"def H2 : List El","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean:TFPT.Carrier.GlueUniqueness.orbit33_eq_H1","line_end":81,"line_start":77,"module_context_as_written":[],"name":"orbit33_eq_H1","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean","qualified_name":"TFPT.Carrier.GlueUniqueness.orbit33_eq_H1","statement_as_written":"theorem orbit33_eq_H1 : ∀ a : El, a ∈ orbit (3, 3) ↔ a ∈ H1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean:TFPT.Carrier.GlueUniqueness.orbit31_eq_H2","line_end":85,"line_start":82,"module_context_as_written":[],"name":"orbit31_eq_H2","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean","qualified_name":"TFPT.Carrier.GlueUniqueness.orbit31_eq_H2","statement_as_written":"theorem orbit31_eq_H2 : ∀ a : El, a ∈ orbit (3, 1) ↔ a ∈ H2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean:TFPT.Carrier.GlueUniqueness.glues_isotropic","line_end":92,"line_start":86,"module_context_as_written":[],"name":"glues_isotropic","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean","qualified_name":"TFPT.Carrier.GlueUniqueness.glues_isotropic","statement_as_written":"theorem glues_isotropic :\n    qZ (0, 0) = 0 ∧ qZ (1, 1) = 0 ∧ qZ (2, 2) = 0 ∧ qZ (3, 3) = 0 ∧\n    qZ (1, 3) = 0 ∧ qZ (3, 1) = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean:TFPT.Carrier.GlueUniqueness.klein_not_isotropic","line_end":100,"line_start":93,"module_context_as_written":[],"name":"klein_not_isotropic","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean","qualified_name":"TFPT.Carrier.GlueUniqueness.klein_not_isotropic","statement_as_written":"theorem klein_not_isotropic : ¬ isotropic ((2 : Fin 4), (0 : Fin 4))","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean:TFPT.Carrier.GlueUniqueness.spinor_swap_exchanges","line_end":108,"line_start":101,"module_context_as_written":[],"name":"spinor_swap_exchanges","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean","qualified_name":"TFPT.Carrier.GlueUniqueness.spinor_swap_exchanges","statement_as_written":"theorem spinor_swap_exchanges :\n    H1.map (fun a => ((a.1, -a.2) : El)) = [(0, 0), (1, 3), (2, 2), (3, 1)] ∧\n    H2.map (fun a => ((a.1, -a.2) : El)) = [(0, 0), (1, 1), (2, 2), (3, 3)]","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean:TFPT.Carrier.GlueUniqueness.unique_halfway_stage","line_end":116,"line_start":109,"module_context_as_written":[],"name":"unique_halfway_stage","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean","qualified_name":"TFPT.Carrier.GlueUniqueness.unique_halfway_stage","statement_as_written":"theorem unique_halfway_stage :\n    ∀ a : El, (isotropic a ∧ a ≠ (0, 0) ∧ add a a = (0, 0)) ↔\n      a = ((2 : Fin 4), (2 : Fin 4))","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean:TFPT.Carrier.GlueUniqueness.carrier_index_lemma","line_end":124,"line_start":117,"module_context_as_written":[],"name":"carrier_index_lemma","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean","qualified_name":"TFPT.Carrier.GlueUniqueness.carrier_index_lemma","statement_as_written":"theorem carrier_index_lemma :\n    4 * 4 = 16 ∧ (4 : ℕ) ^ 2 * 1 = 16 ∧ 16 / 4 ^ 2 = 1 ∧ 4 = 2 ^ 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean:TFPT.Carrier.GlueUniqueness.glue_sectors_are_currents","line_end":134,"line_start":125,"module_context_as_written":[],"name":"glue_sectors_are_currents","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean","qualified_name":"TFPT.Carrier.GlueUniqueness.glue_sectors_are_currents","statement_as_written":"theorem glue_sectors_are_currents :\n    4 + 4 = 8 ∧ 5 + 3 = 8 ∧ 45 + 15 + 16 * 4 + 16 * 4 + 10 * 6 = 248","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GramCompactness.lean:TfptCarrier.GramCompactness.dotProduct_mulVec_expand","line_end":76,"line_start":70,"module_context_as_written":[{"line":68,"source_text":"variable {ι : Type*} [Fintype ι]"},{"line":110,"source_text":"variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E]"}],"name":"dotProduct_mulVec_expand","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GramCompactness.lean","qualified_name":"TfptCarrier.GramCompactness.dotProduct_mulVec_expand","statement_as_written":"theorem dotProduct_mulVec_expand (M : Matrix ι ι ℝ) (x : ι → ℝ) :\n    x ⬝ᵥ (M *ᵥ x) = ∑ i, ∑ j, x i * M i j * x j","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GramCompactness.lean:TfptCarrier.GramCompactness.posSemidef_of_tendsto","line_end":113,"line_start":77,"module_context_as_written":[{"line":68,"source_text":"variable {ι : Type*} [Fintype ι]"},{"line":110,"source_text":"variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E]"}],"name":"posSemidef_of_tendsto","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GramCompactness.lean","qualified_name":"TfptCarrier.GramCompactness.posSemidef_of_tendsto","statement_as_written":"theorem posSemidef_of_tendsto {α : Type*} {l : Filter α} [l.NeBot]\n    (f : α → Matrix ι ι ℝ) (G : Matrix ι ι ℝ)\n    (hf : ∀ a, (f a).PosSemidef)\n    (hlim : ∀ i j, Tendsto (fun a => f a i j) l (𝓝 (G i j))) :\n    G.PosSemidef","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GramCompactness.lean:TfptCarrier.GramCompactness.gram","line_end":120,"line_start":114,"module_context_as_written":[{"line":68,"source_text":"variable {ι : Type*} [Fintype ι]"},{"line":110,"source_text":"variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E]"}],"name":"gram","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GramCompactness.lean","qualified_name":"TfptCarrier.GramCompactness.gram","statement_as_written":"def gram (v : ι → E) : Matrix ι ι ℝ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GramCompactness.lean:TfptCarrier.GramCompactness.gram_apply","line_end":122,"line_start":121,"module_context_as_written":[{"line":68,"source_text":"variable {ι : Type*} [Fintype ι]"},{"line":110,"source_text":"variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E]"}],"name":"gram_apply","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GramCompactness.lean","qualified_name":"TfptCarrier.GramCompactness.gram_apply","statement_as_written":"theorem gram_apply (v : ι → E) (i j : ι) :\n    gram v i j = inner ℝ (v i) (v j)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GramCompactness.lean:TfptCarrier.GramCompactness.gram_dotProduct_eq","line_end":133,"line_start":123,"module_context_as_written":[{"line":68,"source_text":"variable {ι : Type*} [Fintype ι]"},{"line":110,"source_text":"variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E]"}],"name":"gram_dotProduct_eq","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GramCompactness.lean","qualified_name":"TfptCarrier.GramCompactness.gram_dotProduct_eq","statement_as_written":"theorem gram_dotProduct_eq (v : ι → E) (x : ι → ℝ) :\n    x ⬝ᵥ (gram v *ᵥ x)\n      = inner ℝ (∑ i, x i • v i) (∑ j, x j • v j)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GramCompactness.lean:TfptCarrier.GramCompactness.gram_posSemidef","line_end":145,"line_start":134,"module_context_as_written":[{"line":68,"source_text":"variable {ι : Type*} [Fintype ι]"},{"line":110,"source_text":"variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E]"}],"name":"gram_posSemidef","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GramCompactness.lean","qualified_name":"TfptCarrier.GramCompactness.gram_posSemidef","statement_as_written":"theorem gram_posSemidef (v : ι → E) : (gram v).PosSemidef","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GramCompactness.lean:TfptCarrier.GramCompactness.posSemidef_limit_of_gram","line_end":158,"line_start":146,"module_context_as_written":[{"line":68,"source_text":"variable {ι : Type*} [Fintype ι]"},{"line":110,"source_text":"variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E]"}],"name":"posSemidef_limit_of_gram","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GramCompactness.lean","qualified_name":"TfptCarrier.GramCompactness.posSemidef_limit_of_gram","statement_as_written":"theorem posSemidef_limit_of_gram (v : ℕ → ι → E) (G : Matrix ι ι ℝ)\n    (hlim : ∀ i j,\n      Tendsto (fun n => inner ℝ (v n i) (v n j)) atTop (𝓝 (G i j))) :\n    G.PosSemidef","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GramCompactness.lean:TfptCarrier.GramCompactness.exists_subseq_posSemidef_limit","line_end":190,"line_start":159,"module_context_as_written":[{"line":68,"source_text":"variable {ι : Type*} [Fintype ι]"},{"line":110,"source_text":"variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E]"}],"name":"exists_subseq_posSemidef_limit","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GramCompactness.lean","qualified_name":"TfptCarrier.GramCompactness.exists_subseq_posSemidef_limit","statement_as_written":"theorem exists_subseq_posSemidef_limit (A : ℕ → Matrix ι ι ℝ) (C : ℝ)\n    (hPSD : ∀ n, (A n).PosSemidef)\n    (hbound : ∀ n i j, |A n i j| ≤ C) :\n    ∃ (G : Matrix ι ι ℝ) (φ : ℕ → ℕ), StrictMono φ ∧ G.PosSemidef ∧\n      ∀ i j, Tendsto (fun n => A (φ n) i j) atTop (𝓝 (G i j))","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/GramCompactness.lean:TfptCarrier.GramCompactness.exists_subseq_gram_limit","line_end":205,"line_start":191,"module_context_as_written":[{"line":68,"source_text":"variable {ι : Type*} [Fintype ι]"},{"line":110,"source_text":"variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E]"}],"name":"exists_subseq_gram_limit","path":"experiments/lean4-carrier-rigidity/TfptCarrier/GramCompactness.lean","qualified_name":"TfptCarrier.GramCompactness.exists_subseq_gram_limit","statement_as_written":"theorem exists_subseq_gram_limit (v : ℕ → ι → E) (C : ℝ)\n    (hbound : ∀ n i j, |inner ℝ (v n i) (v n j)| ≤ C) :\n    ∃ (G : Matrix ι ι ℝ) (φ : ℕ → ℕ), StrictMono φ ∧ G.PosSemidef ∧\n      ∀ i j, Tendsto (fun n => inner ℝ (v (φ n) i) (v (φ n) j)) atTop\n        (𝓝 (G i j))","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"abbrev","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean:TfptCarrier.HammingCode.V8","line_end":41,"line_start":39,"module_context_as_written":[],"name":"V8","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean","qualified_name":"TfptCarrier.HammingCode.V8","statement_as_written":"abbrev V8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean:TfptCarrier.HammingCode.code","line_end":61,"line_start":42,"module_context_as_written":[],"name":"code","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean","qualified_name":"TfptCarrier.HammingCode.code","statement_as_written":"def code : List V8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean:TfptCarrier.HammingCode.dot","line_end":64,"line_start":62,"module_context_as_written":[],"name":"dot","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean","qualified_name":"TfptCarrier.HammingCode.dot","statement_as_written":"def dot (u v : V8) : ZMod 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean:TfptCarrier.HammingCode.wt","line_end":67,"line_start":65,"module_context_as_written":[],"name":"wt","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean","qualified_name":"TfptCarrier.HammingCode.wt","statement_as_written":"def wt (v : V8) : ℕ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean:TfptCarrier.HammingCode.H","line_end":74,"line_start":68,"module_context_as_written":[],"name":"H","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean","qualified_name":"TfptCarrier.HammingCode.H","statement_as_written":"def H : Fin 4 → V8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean:TfptCarrier.HammingCode.syndrome","line_end":77,"line_start":75,"module_context_as_written":[],"name":"syndrome","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean","qualified_name":"TfptCarrier.HammingCode.syndrome","statement_as_written":"def syndrome (v : V8) : Fin 4 → ZMod 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean:TfptCarrier.HammingCode.code_card","line_end":80,"line_start":78,"module_context_as_written":[],"name":"code_card","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean","qualified_name":"TfptCarrier.HammingCode.code_card","statement_as_written":"theorem code_card : code.length = 16 ∧ code.Nodup","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean:TfptCarrier.HammingCode.code_subgroup","line_end":87,"line_start":81,"module_context_as_written":[],"name":"code_subgroup","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean","qualified_name":"TfptCarrier.HammingCode.code_subgroup","statement_as_written":"theorem code_subgroup :\n    (fun _ => 0 : V8) ∈ code ∧ ∀ u ∈ code, ∀ v ∈ code, u + v ∈ code","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean:TfptCarrier.HammingCode.code_self_dual","line_end":90,"line_start":88,"module_context_as_written":[],"name":"code_self_dual","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean","qualified_name":"TfptCarrier.HammingCode.code_self_dual","statement_as_written":"theorem code_self_dual : ∀ u ∈ code, ∀ v ∈ code, dot u v = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean:TfptCarrier.HammingCode.code_syndrome_zero","line_end":93,"line_start":91,"module_context_as_written":[],"name":"code_syndrome_zero","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean","qualified_name":"TfptCarrier.HammingCode.code_syndrome_zero","statement_as_written":"theorem code_syndrome_zero : ∀ c ∈ code, syndrome c = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean:TfptCarrier.HammingCode.code_weight_distribution","line_end":100,"line_start":94,"module_context_as_written":[],"name":"code_weight_distribution","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean","qualified_name":"TfptCarrier.HammingCode.code_weight_distribution","statement_as_written":"theorem code_weight_distribution :\n    (code.countP fun v => wt v = 0) = 1 ∧\n    (code.countP fun v => wt v = 4) = 14 ∧\n    (code.countP fun v => wt v = 8) = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean:TfptCarrier.HammingCode.leaders","line_end":119,"line_start":101,"module_context_as_written":[],"name":"leaders","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean","qualified_name":"TfptCarrier.HammingCode.leaders","statement_as_written":"def leaders : List V8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean:TfptCarrier.HammingCode.leaders_syndromes_complete","line_end":124,"line_start":120,"module_context_as_written":[],"name":"leaders_syndromes_complete","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean","qualified_name":"TfptCarrier.HammingCode.leaders_syndromes_complete","statement_as_written":"theorem leaders_syndromes_complete :\n    (leaders.map syndrome).Nodup ∧ leaders.length = 16","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean:TfptCarrier.HammingCode.leaders_syndromes_surjective","line_end":128,"line_start":125,"module_context_as_written":[],"name":"leaders_syndromes_surjective","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean","qualified_name":"TfptCarrier.HammingCode.leaders_syndromes_surjective","statement_as_written":"theorem leaders_syndromes_surjective :\n    ∀ s : Fin 4 → ZMod 2, s ∈ leaders.map syndrome","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean:TfptCarrier.HammingCode.leaders_weight_distribution","line_end":134,"line_start":129,"module_context_as_written":[],"name":"leaders_weight_distribution","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean","qualified_name":"TfptCarrier.HammingCode.leaders_weight_distribution","statement_as_written":"theorem leaders_weight_distribution :\n    (leaders.countP fun v => wt v = 0) = 1 ∧\n    (leaders.countP fun v => wt v = 1) = 8 ∧\n    (leaders.countP fun v => wt v = 2) = 7","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean:TfptCarrier.HammingCode.leaders_minimal","line_end":142,"line_start":135,"module_context_as_written":[],"name":"leaders_minimal","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HammingCode.lean","qualified_name":"TfptCarrier.HammingCode.leaders_minimal","statement_as_written":"theorem leaders_minimal :\n    ∀ l ∈ leaders, ∀ c ∈ code, wt l ≤ wt (l + c)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"abbrev","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HiggsIndexShadow.lean:TFPT.Carrier.HiggsIndexShadow.DegreeOneBinaryForms","line_end":54,"line_start":45,"module_context_as_written":[{"line":43,"source_text":"variable (K : Type*) [Field K]"},{"line":90,"source_text":"variable {K}"},{"line":92,"source_text":"variable {Eplus : Type*} [AddCommGroup Eplus] [Module K Eplus]"}],"name":"DegreeOneBinaryForms","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HiggsIndexShadow.lean","qualified_name":"TFPT.Carrier.HiggsIndexShadow.DegreeOneBinaryForms","statement_as_written":"abbrev DegreeOneBinaryForms : Type _","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HiggsIndexShadow.lean:TFPT.Carrier.HiggsIndexShadow.finrank_degreeOneBinaryForms","line_end":71,"line_start":55,"module_context_as_written":[{"line":43,"source_text":"variable (K : Type*) [Field K]"},{"line":90,"source_text":"variable {K}"},{"line":92,"source_text":"variable {Eplus : Type*} [AddCommGroup Eplus] [Module K Eplus]"}],"name":"finrank_degreeOneBinaryForms","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HiggsIndexShadow.lean","qualified_name":"TFPT.Carrier.HiggsIndexShadow.finrank_degreeOneBinaryForms","statement_as_written":"theorem finrank_degreeOneBinaryForms :\n    Module.finrank K (DegreeOneBinaryForms K) = 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"structure","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HiggsIndexShadow.lean:TFPT.Carrier.HiggsIndexShadow.HiggsIndexCertificate","line_end":97,"line_start":72,"module_context_as_written":[{"line":43,"source_text":"variable (K : Type*) [Field K]"},{"line":90,"source_text":"variable {K}"},{"line":92,"source_text":"variable {Eplus : Type*} [AddCommGroup Eplus] [Module K Eplus]"}],"name":"HiggsIndexCertificate","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HiggsIndexShadow.lean","qualified_name":"TFPT.Carrier.HiggsIndexShadow.HiggsIndexCertificate","statement_as_written":"structure HiggsIndexCertificate\n    (K : Type*) [Field K]\n    (Eplus : Type*) [AddCommGroup Eplus] [Module K Eplus]","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HiggsIndexShadow.lean:HiggsIndexCertificate.finrank_Eplus_eq_two","line_end":113,"line_start":98,"module_context_as_written":[{"line":43,"source_text":"variable (K : Type*) [Field K]"},{"line":90,"source_text":"variable {K}"},{"line":92,"source_text":"variable {Eplus : Type*} [AddCommGroup Eplus] [Module K Eplus]"}],"name":"HiggsIndexCertificate.finrank_Eplus_eq_two","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HiggsIndexShadow.lean","qualified_name":"HiggsIndexCertificate.finrank_Eplus_eq_two","statement_as_written":"theorem HiggsIndexCertificate.finrank_Eplus_eq_two\n    (cert : HiggsIndexCertificate K Eplus) :\n    Module.finrank K Eplus = 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"abbrev","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HiggsSchemeCohomologyShadow.lean:TFPT.Carrier.HiggsSchemeCohomologyShadow.O_one","line_end":78,"line_start":70,"module_context_as_written":[{"line":68,"source_text":"variable (K : Type*) [Field K]"},{"line":89,"source_text":"variable {K}"}],"name":"O_one","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HiggsSchemeCohomologyShadow.lean","qualified_name":"TFPT.Carrier.HiggsSchemeCohomologyShadow.O_one","statement_as_written":"noncomputable abbrev O_one : Submodule K (MvPolynomial (Fin 2) K)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HiggsSchemeCohomologyShadow.lean:TFPT.Carrier.HiggsSchemeCohomologyShadow.O_one.X_mem","line_end":82,"line_start":79,"module_context_as_written":[{"line":68,"source_text":"variable (K : Type*) [Field K]"},{"line":89,"source_text":"variable {K}"}],"name":"X_mem","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HiggsSchemeCohomologyShadow.lean","qualified_name":"TFPT.Carrier.HiggsSchemeCohomologyShadow.O_one.X_mem","statement_as_written":"theorem X_mem (i : Fin 2) : (MvPolynomial.X i : MvPolynomial (Fin 2) K) ∈ O_one K","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HiggsSchemeCohomologyShadow.lean:TFPT.Carrier.HiggsSchemeCohomologyShadow.O_one.Xsub","line_end":90,"line_start":83,"module_context_as_written":[{"line":68,"source_text":"variable (K : Type*) [Field K]"},{"line":89,"source_text":"variable {K}"}],"name":"Xsub","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HiggsSchemeCohomologyShadow.lean","qualified_name":"TFPT.Carrier.HiggsSchemeCohomologyShadow.O_one.Xsub","statement_as_written":"noncomputable def Xsub (i : Fin 2) : O_one K","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HiggsSchemeCohomologyShadow.lean:TFPT.Carrier.HiggsSchemeCohomologyShadow.fromBinaryForm","line_end":97,"line_start":91,"module_context_as_written":[{"line":68,"source_text":"variable (K : Type*) [Field K]"},{"line":89,"source_text":"variable {K}"}],"name":"fromBinaryForm","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HiggsSchemeCohomologyShadow.lean","qualified_name":"TFPT.Carrier.HiggsSchemeCohomologyShadow.fromBinaryForm","statement_as_written":"noncomputable def fromBinaryForm\n    (p : TFPT.Carrier.HiggsTopForm.DegreeOneTwoVarForm K) :\n    O_one K","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HiggsSchemeCohomologyShadow.lean:TFPT.Carrier.HiggsSchemeCohomologyShadow.fromBinaryFormLinear","line_end":113,"line_start":98,"module_context_as_written":[{"line":68,"source_text":"variable (K : Type*) [Field K]"},{"line":89,"source_text":"variable {K}"}],"name":"fromBinaryFormLinear","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HiggsSchemeCohomologyShadow.lean","qualified_name":"TFPT.Carrier.HiggsSchemeCohomologyShadow.fromBinaryFormLinear","statement_as_written":"noncomputable def fromBinaryFormLinear :\n    TFPT.Carrier.HiggsTopForm.DegreeOneTwoVarForm K →ₗ[K] O_one K","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HiggsSchemeCohomologyShadow.lean:TFPT.Carrier.HiggsSchemeCohomologyShadow.fromBinaryForm_val","line_end":121,"line_start":114,"module_context_as_written":[{"line":68,"source_text":"variable (K : Type*) [Field K]"},{"line":89,"source_text":"variable {K}"}],"name":"fromBinaryForm_val","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HiggsSchemeCohomologyShadow.lean","qualified_name":"TFPT.Carrier.HiggsSchemeCohomologyShadow.fromBinaryForm_val","statement_as_written":"private theorem fromBinaryForm_val\n    (p : TFPT.Carrier.HiggsTopForm.DegreeOneTwoVarForm K) :\n    (fromBinaryForm p : MvPolynomial (Fin 2) K) =\n      p.coeffX • MvPolynomial.X (0 : Fin 2) +\n      p.coeffY • MvPolynomial.X (1 : Fin 2)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HiggsSchemeCohomologyShadow.lean:TFPT.Carrier.HiggsSchemeCohomologyShadow.fromBinaryFormLinear_injective","line_end":156,"line_start":122,"module_context_as_written":[{"line":68,"source_text":"variable (K : Type*) [Field K]"},{"line":89,"source_text":"variable {K}"}],"name":"fromBinaryFormLinear_injective","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HiggsSchemeCohomologyShadow.lean","qualified_name":"TFPT.Carrier.HiggsSchemeCohomologyShadow.fromBinaryFormLinear_injective","statement_as_written":"private theorem fromBinaryFormLinear_injective :\n    Function.Injective (fromBinaryFormLinear (K","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HiggsSchemeCohomologyShadow.lean:TFPT.Carrier.HiggsSchemeCohomologyShadow.fromBinaryFormLinear_surjective","line_end":175,"line_start":157,"module_context_as_written":[{"line":68,"source_text":"variable (K : Type*) [Field K]"},{"line":89,"source_text":"variable {K}"}],"name":"fromBinaryFormLinear_surjective","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HiggsSchemeCohomologyShadow.lean","qualified_name":"TFPT.Carrier.HiggsSchemeCohomologyShadow.fromBinaryFormLinear_surjective","statement_as_written":"private theorem fromBinaryFormLinear_surjective :\n    Function.Surjective (fromBinaryFormLinear (K","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HiggsSchemeCohomologyShadow.lean:TFPT.Carrier.HiggsSchemeCohomologyShadow.toDegreeOneTwoVarForm","line_end":186,"line_start":176,"module_context_as_written":[{"line":68,"source_text":"variable (K : Type*) [Field K]"},{"line":89,"source_text":"variable {K}"}],"name":"toDegreeOneTwoVarForm","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HiggsSchemeCohomologyShadow.lean","qualified_name":"TFPT.Carrier.HiggsSchemeCohomologyShadow.toDegreeOneTwoVarForm","statement_as_written":"noncomputable def toDegreeOneTwoVarForm :\n    TFPT.Carrier.HiggsTopForm.DegreeOneTwoVarForm K ≃ₗ[K] O_one K","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HiggsSchemeCohomologyShadow.lean:TFPT.Carrier.HiggsSchemeCohomologyShadow.finrank_O_one_eq_two","line_end":197,"line_start":187,"module_context_as_written":[{"line":68,"source_text":"variable (K : Type*) [Field K]"},{"line":89,"source_text":"variable {K}"}],"name":"finrank_O_one_eq_two","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HiggsSchemeCohomologyShadow.lean","qualified_name":"TFPT.Carrier.HiggsSchemeCohomologyShadow.finrank_O_one_eq_two","statement_as_written":"theorem finrank_O_one_eq_two : Module.finrank K (O_one K) = 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HiggsSchemeCohomologyShadow.lean:TFPT.Carrier.HiggsSchemeCohomologyShadow.toHiggsTopForm","line_end":214,"line_start":198,"module_context_as_written":[{"line":68,"source_text":"variable (K : Type*) [Field K]"},{"line":89,"source_text":"variable {K}"}],"name":"toHiggsTopForm","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HiggsSchemeCohomologyShadow.lean","qualified_name":"TFPT.Carrier.HiggsSchemeCohomologyShadow.toHiggsTopForm","statement_as_written":"noncomputable def toHiggsTopForm\n    {Eplus : Type*} [AddCommGroup Eplus] [Module K Eplus]\n    (h : Eplus ≃ₗ[K] O_one K) :\n    TFPT.Carrier.HiggsTopForm.HiggsTopForm K Eplus","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"structure","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HiggsTopForm.lean:TFPT.Carrier.HiggsTopForm.DegreeOneTwoVarForm","line_end":126,"line_start":73,"module_context_as_written":[{"line":56,"source_text":"variable (K : Type*) [Field K]"},{"line":80,"source_text":"variable {K}"},{"line":125,"source_text":"variable (K) in"},{"line":144,"source_text":"variable (K) in"},{"line":180,"source_text":"variable {K}"},{"line":182,"source_text":"variable {Eplus : Type*} [AddCommGroup Eplus] [Module K Eplus]"}],"name":"DegreeOneTwoVarForm","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HiggsTopForm.lean","qualified_name":"TFPT.Carrier.HiggsTopForm.DegreeOneTwoVarForm","statement_as_written":"structure DegreeOneTwoVarForm (K : Type*) [Field K]","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HiggsTopForm.lean:TFPT.Carrier.HiggsTopForm.DegreeOneTwoVarForm.toBinaryForms","line_end":145,"line_start":127,"module_context_as_written":[{"line":56,"source_text":"variable (K : Type*) [Field K]"},{"line":80,"source_text":"variable {K}"},{"line":125,"source_text":"variable (K) in"},{"line":144,"source_text":"variable (K) in"},{"line":180,"source_text":"variable {K}"},{"line":182,"source_text":"variable {Eplus : Type*} [AddCommGroup Eplus] [Module K Eplus]"}],"name":"toBinaryForms","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HiggsTopForm.lean","qualified_name":"TFPT.Carrier.HiggsTopForm.DegreeOneTwoVarForm.toBinaryForms","statement_as_written":"def toBinaryForms :\n    DegreeOneTwoVarForm K ≃ₗ[K] TFPT.Carrier.HiggsIndexShadow.DegreeOneBinaryForms K","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HiggsTopForm.lean:TFPT.Carrier.HiggsTopForm.DegreeOneTwoVarForm.finrank_eq_two","line_end":160,"line_start":146,"module_context_as_written":[{"line":56,"source_text":"variable (K : Type*) [Field K]"},{"line":80,"source_text":"variable {K}"},{"line":125,"source_text":"variable (K) in"},{"line":144,"source_text":"variable (K) in"},{"line":180,"source_text":"variable {K}"},{"line":182,"source_text":"variable {Eplus : Type*} [AddCommGroup Eplus] [Module K Eplus]"}],"name":"finrank_eq_two","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HiggsTopForm.lean","qualified_name":"TFPT.Carrier.HiggsTopForm.DegreeOneTwoVarForm.finrank_eq_two","statement_as_written":"theorem finrank_eq_two :\n    Module.finrank K (DegreeOneTwoVarForm K) = 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"structure","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HiggsTopForm.lean:TFPT.Carrier.HiggsTopForm.HiggsTopForm","line_end":186,"line_start":161,"module_context_as_written":[{"line":56,"source_text":"variable (K : Type*) [Field K]"},{"line":80,"source_text":"variable {K}"},{"line":125,"source_text":"variable (K) in"},{"line":144,"source_text":"variable (K) in"},{"line":180,"source_text":"variable {K}"},{"line":182,"source_text":"variable {Eplus : Type*} [AddCommGroup Eplus] [Module K Eplus]"}],"name":"HiggsTopForm","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HiggsTopForm.lean","qualified_name":"TFPT.Carrier.HiggsTopForm.HiggsTopForm","statement_as_written":"structure HiggsTopForm\n    (K : Type*) [Field K]\n    (Eplus : Type*) [AddCommGroup Eplus] [Module K Eplus]","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HiggsTopForm.lean:TFPT.Carrier.HiggsTopForm.HiggsTopForm.finrank_Eplus_eq_two","line_end":198,"line_start":187,"module_context_as_written":[{"line":56,"source_text":"variable (K : Type*) [Field K]"},{"line":80,"source_text":"variable {K}"},{"line":125,"source_text":"variable (K) in"},{"line":144,"source_text":"variable (K) in"},{"line":180,"source_text":"variable {K}"},{"line":182,"source_text":"variable {Eplus : Type*} [AddCommGroup Eplus] [Module K Eplus]"}],"name":"finrank_Eplus_eq_two","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HiggsTopForm.lean","qualified_name":"TFPT.Carrier.HiggsTopForm.HiggsTopForm.finrank_Eplus_eq_two","statement_as_written":"theorem finrank_Eplus_eq_two (h : HiggsTopForm K Eplus) :\n    Module.finrank K Eplus = 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/HiggsTopForm.lean:TFPT.Carrier.HiggsTopForm.HiggsTopForm.toHiggsIndexCertificate","line_end":212,"line_start":199,"module_context_as_written":[{"line":56,"source_text":"variable (K : Type*) [Field K]"},{"line":80,"source_text":"variable {K}"},{"line":125,"source_text":"variable (K) in"},{"line":144,"source_text":"variable (K) in"},{"line":180,"source_text":"variable {K}"},{"line":182,"source_text":"variable {Eplus : Type*} [AddCommGroup Eplus] [Module K Eplus]"}],"name":"toHiggsIndexCertificate","path":"experiments/lean4-carrier-rigidity/TfptCarrier/HiggsTopForm.lean","qualified_name":"TFPT.Carrier.HiggsTopForm.HiggsTopForm.toHiggsIndexCertificate","statement_as_written":"def toHiggsIndexCertificate (h : HiggsTopForm K Eplus) :\n    TFPT.Carrier.HiggsIndexShadow.HiggsIndexCertificate K Eplus","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"abbrev","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/Hypercharge.lean:TFPT.Carrier.Hypercharge.I","line_end":32,"line_start":30,"module_context_as_written":[],"name":"I","path":"experiments/lean4-carrier-rigidity/TfptCarrier/Hypercharge.lean","qualified_name":"TFPT.Carrier.Hypercharge.I","statement_as_written":"abbrev I","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/Hypercharge.lean:TFPT.Carrier.Hypercharge.Y","line_end":43,"line_start":33,"module_context_as_written":[],"name":"Y","path":"experiments/lean4-carrier-rigidity/TfptCarrier/Hypercharge.lean","qualified_name":"TFPT.Carrier.Hypercharge.Y","statement_as_written":"def Y : Matrix I I ℚ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"lemma","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/Hypercharge.lean:TFPT.Carrier.Hypercharge.Y_diag_entries","line_end":49,"line_start":44,"module_context_as_written":[],"name":"Y_diag_entries","path":"experiments/lean4-carrier-rigidity/TfptCarrier/Hypercharge.lean","qualified_name":"TFPT.Carrier.Hypercharge.Y_diag_entries","statement_as_written":"lemma Y_diag_entries (i : I) : Y i i =\n    (![(-1/3 : ℚ), -1/3, -1/3, 1/2, 1/2]) i","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"lemma","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/Hypercharge.lean:TFPT.Carrier.Hypercharge.Y_off_diag_zero","line_end":54,"line_start":50,"module_context_as_written":[],"name":"Y_off_diag_zero","path":"experiments/lean4-carrier-rigidity/TfptCarrier/Hypercharge.lean","qualified_name":"TFPT.Carrier.Hypercharge.Y_off_diag_zero","statement_as_written":"lemma Y_off_diag_zero (i j : I) (h : i ≠ j) : Y i j = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/Hypercharge.lean:TFPT.Carrier.Hypercharge.trace_Y","line_end":68,"line_start":55,"module_context_as_written":[],"name":"trace_Y","path":"experiments/lean4-carrier-rigidity/TfptCarrier/Hypercharge.lean","qualified_name":"TFPT.Carrier.Hypercharge.trace_Y","statement_as_written":"theorem trace_Y : Y.trace = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/Hypercharge.lean:TFPT.Carrier.Hypercharge.Y_carrier_polynomial","line_end":89,"line_start":69,"module_context_as_written":[],"name":"Y_carrier_polynomial","path":"experiments/lean4-carrier-rigidity/TfptCarrier/Hypercharge.lean","qualified_name":"TFPT.Carrier.Hypercharge.Y_carrier_polynomial","statement_as_written":"theorem Y_carrier_polynomial : (6 : ℚ) • (Y * Y) - Y - 1 = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"structure","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean:TFPT.Carrier.InvolutionProjectors.CarrierInvolution","line_end":48,"line_start":32,"module_context_as_written":[{"line":47,"source_text":"variable {A : Type*} [Ring A] [Invertible (2 : A)]"},{"line":83,"source_text":"variable (c : CarrierInvolution A)"}],"name":"CarrierInvolution","path":"experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean","qualified_name":"TFPT.Carrier.InvolutionProjectors.CarrierInvolution","statement_as_written":"structure CarrierInvolution (A : Type*) [Ring A]","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"lemma","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean:TFPT.Carrier.InvolutionProjectors.CarrierInvolution.two_commute","line_end":53,"line_start":49,"module_context_as_written":[{"line":47,"source_text":"variable {A : Type*} [Ring A] [Invertible (2 : A)]"},{"line":83,"source_text":"variable (c : CarrierInvolution A)"}],"name":"two_commute","path":"experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean","qualified_name":"TFPT.Carrier.InvolutionProjectors.CarrierInvolution.two_commute","statement_as_written":"private lemma two_commute (x : A) : Commute (2 : A) x","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"lemma","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean:TFPT.Carrier.InvolutionProjectors.CarrierInvolution.invOf_two_commute","line_end":57,"line_start":54,"module_context_as_written":[{"line":47,"source_text":"variable {A : Type*} [Ring A] [Invertible (2 : A)]"},{"line":83,"source_text":"variable (c : CarrierInvolution A)"}],"name":"invOf_two_commute","path":"experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean","qualified_name":"TFPT.Carrier.InvolutionProjectors.CarrierInvolution.invOf_two_commute","statement_as_written":"private lemma invOf_two_commute (x : A) : Commute (⅟(2 : A)) x","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"lemma","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean:TFPT.Carrier.InvolutionProjectors.CarrierInvolution.idem_of_self_double","line_end":73,"line_start":58,"module_context_as_written":[{"line":47,"source_text":"variable {A : Type*} [Ring A] [Invertible (2 : A)]"},{"line":83,"source_text":"variable (c : CarrierInvolution A)"}],"name":"idem_of_self_double","path":"experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean","qualified_name":"TFPT.Carrier.InvolutionProjectors.CarrierInvolution.idem_of_self_double","statement_as_written":"private lemma idem_of_self_double {x : A} (hx : x * x = 2 * x) :\n    (x * ⅟(2 : A)) * (x * ⅟(2 : A)) = x * ⅟(2 : A)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"lemma","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean:TFPT.Carrier.InvolutionProjectors.CarrierInvolution.orth_of_annihilate","line_end":84,"line_start":74,"module_context_as_written":[{"line":47,"source_text":"variable {A : Type*} [Ring A] [Invertible (2 : A)]"},{"line":83,"source_text":"variable (c : CarrierInvolution A)"}],"name":"orth_of_annihilate","path":"experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean","qualified_name":"TFPT.Carrier.InvolutionProjectors.CarrierInvolution.orth_of_annihilate","statement_as_written":"private lemma orth_of_annihilate {x y : A} (hxy : x * y = 0) :\n    (x * ⅟(2 : A)) * (y * ⅟(2 : A)) = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean:TFPT.Carrier.InvolutionProjectors.CarrierInvolution.Pminus","line_end":87,"line_start":85,"module_context_as_written":[{"line":47,"source_text":"variable {A : Type*} [Ring A] [Invertible (2 : A)]"},{"line":83,"source_text":"variable (c : CarrierInvolution A)"}],"name":"Pminus","path":"experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean","qualified_name":"TFPT.Carrier.InvolutionProjectors.CarrierInvolution.Pminus","statement_as_written":"noncomputable def Pminus : A","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean:TFPT.Carrier.InvolutionProjectors.CarrierInvolution.Pplus","line_end":90,"line_start":88,"module_context_as_written":[{"line":47,"source_text":"variable {A : Type*} [Ring A] [Invertible (2 : A)]"},{"line":83,"source_text":"variable (c : CarrierInvolution A)"}],"name":"Pplus","path":"experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean","qualified_name":"TFPT.Carrier.InvolutionProjectors.CarrierInvolution.Pplus","statement_as_written":"noncomputable def Pplus : A","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean:TFPT.Carrier.InvolutionProjectors.CarrierInvolution.Pminus_add_Pplus","line_end":100,"line_start":91,"module_context_as_written":[{"line":47,"source_text":"variable {A : Type*} [Ring A] [Invertible (2 : A)]"},{"line":83,"source_text":"variable (c : CarrierInvolution A)"}],"name":"Pminus_add_Pplus","path":"experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean","qualified_name":"TFPT.Carrier.InvolutionProjectors.CarrierInvolution.Pminus_add_Pplus","statement_as_written":"theorem Pminus_add_Pplus : c.Pminus + c.Pplus = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"lemma","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean:TFPT.Carrier.InvolutionProjectors.CarrierInvolution.sq_minus","line_end":112,"line_start":101,"module_context_as_written":[{"line":47,"source_text":"variable {A : Type*} [Ring A] [Invertible (2 : A)]"},{"line":83,"source_text":"variable (c : CarrierInvolution A)"}],"name":"sq_minus","path":"experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean","qualified_name":"TFPT.Carrier.InvolutionProjectors.CarrierInvolution.sq_minus","statement_as_written":"private lemma sq_minus :\n    (1 - c.eps) * (1 - c.eps) = 2 * (1 - c.eps)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"lemma","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean:TFPT.Carrier.InvolutionProjectors.CarrierInvolution.sq_plus","line_end":124,"line_start":113,"module_context_as_written":[{"line":47,"source_text":"variable {A : Type*} [Ring A] [Invertible (2 : A)]"},{"line":83,"source_text":"variable (c : CarrierInvolution A)"}],"name":"sq_plus","path":"experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean","qualified_name":"TFPT.Carrier.InvolutionProjectors.CarrierInvolution.sq_plus","statement_as_written":"private lemma sq_plus :\n    (1 + c.eps) * (1 + c.eps) = 2 * (1 + c.eps)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"lemma","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean:TFPT.Carrier.InvolutionProjectors.CarrierInvolution.mul_pm","line_end":133,"line_start":125,"module_context_as_written":[{"line":47,"source_text":"variable {A : Type*} [Ring A] [Invertible (2 : A)]"},{"line":83,"source_text":"variable (c : CarrierInvolution A)"}],"name":"mul_pm","path":"experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean","qualified_name":"TFPT.Carrier.InvolutionProjectors.CarrierInvolution.mul_pm","statement_as_written":"private lemma mul_pm :\n    (1 - c.eps) * (1 + c.eps) = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"lemma","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean:TFPT.Carrier.InvolutionProjectors.CarrierInvolution.mul_mp","line_end":142,"line_start":134,"module_context_as_written":[{"line":47,"source_text":"variable {A : Type*} [Ring A] [Invertible (2 : A)]"},{"line":83,"source_text":"variable (c : CarrierInvolution A)"}],"name":"mul_mp","path":"experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean","qualified_name":"TFPT.Carrier.InvolutionProjectors.CarrierInvolution.mul_mp","statement_as_written":"private lemma mul_mp :\n    (1 + c.eps) * (1 - c.eps) = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean:TFPT.Carrier.InvolutionProjectors.CarrierInvolution.Pminus_idem","line_end":146,"line_start":143,"module_context_as_written":[{"line":47,"source_text":"variable {A : Type*} [Ring A] [Invertible (2 : A)]"},{"line":83,"source_text":"variable (c : CarrierInvolution A)"}],"name":"Pminus_idem","path":"experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean","qualified_name":"TFPT.Carrier.InvolutionProjectors.CarrierInvolution.Pminus_idem","statement_as_written":"theorem Pminus_idem : c.Pminus * c.Pminus = c.Pminus","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean:TFPT.Carrier.InvolutionProjectors.CarrierInvolution.Pplus_idem","line_end":150,"line_start":147,"module_context_as_written":[{"line":47,"source_text":"variable {A : Type*} [Ring A] [Invertible (2 : A)]"},{"line":83,"source_text":"variable (c : CarrierInvolution A)"}],"name":"Pplus_idem","path":"experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean","qualified_name":"TFPT.Carrier.InvolutionProjectors.CarrierInvolution.Pplus_idem","statement_as_written":"theorem Pplus_idem : c.Pplus * c.Pplus = c.Pplus","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean:TFPT.Carrier.InvolutionProjectors.CarrierInvolution.Pminus_mul_Pplus","line_end":154,"line_start":151,"module_context_as_written":[{"line":47,"source_text":"variable {A : Type*} [Ring A] [Invertible (2 : A)]"},{"line":83,"source_text":"variable (c : CarrierInvolution A)"}],"name":"Pminus_mul_Pplus","path":"experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean","qualified_name":"TFPT.Carrier.InvolutionProjectors.CarrierInvolution.Pminus_mul_Pplus","statement_as_written":"theorem Pminus_mul_Pplus : c.Pminus * c.Pplus = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean:TFPT.Carrier.InvolutionProjectors.CarrierInvolution.Pplus_mul_Pminus","line_end":158,"line_start":155,"module_context_as_written":[{"line":47,"source_text":"variable {A : Type*} [Ring A] [Invertible (2 : A)]"},{"line":83,"source_text":"variable (c : CarrierInvolution A)"}],"name":"Pplus_mul_Pminus","path":"experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean","qualified_name":"TFPT.Carrier.InvolutionProjectors.CarrierInvolution.Pplus_mul_Pminus","statement_as_written":"theorem Pplus_mul_Pminus : c.Pplus * c.Pminus = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean:TFPT.Carrier.InvolutionProjectors.CarrierInvolution.toPolarization","line_end":185,"line_start":159,"module_context_as_written":[{"line":47,"source_text":"variable {A : Type*} [Ring A] [Invertible (2 : A)]"},{"line":83,"source_text":"variable (c : CarrierInvolution A)"}],"name":"toPolarization","path":"experiments/lean4-carrier-rigidity/TfptCarrier/InvolutionProjectors.lean","qualified_name":"TFPT.Carrier.InvolutionProjectors.CarrierInvolution.toPolarization","statement_as_written":"noncomputable def toPolarization : TFPT.Carrier.Polarization A","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/KronheimerMarks.lean:TfptCarrier.KronheimerMarks.adjE8affine","line_end":45,"line_start":33,"module_context_as_written":[],"name":"adjE8affine","path":"experiments/lean4-carrier-rigidity/TfptCarrier/KronheimerMarks.lean","qualified_name":"TfptCarrier.KronheimerMarks.adjE8affine","statement_as_written":"def adjE8affine : Matrix (Fin 9) (Fin 9) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/KronheimerMarks.lean:TfptCarrier.KronheimerMarks.cartanE8affine","line_end":49,"line_start":46,"module_context_as_written":[],"name":"cartanE8affine","path":"experiments/lean4-carrier-rigidity/TfptCarrier/KronheimerMarks.lean","qualified_name":"TfptCarrier.KronheimerMarks.cartanE8affine","statement_as_written":"def cartanE8affine : Matrix (Fin 9) (Fin 9) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/KronheimerMarks.lean:TfptCarrier.KronheimerMarks.marks","line_end":55,"line_start":50,"module_context_as_written":[],"name":"marks","path":"experiments/lean4-carrier-rigidity/TfptCarrier/KronheimerMarks.lean","qualified_name":"TfptCarrier.KronheimerMarks.marks","statement_as_written":"def marks : Fin 9 → ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/KronheimerMarks.lean:TfptCarrier.KronheimerMarks.marks_null","line_end":60,"line_start":56,"module_context_as_written":[],"name":"marks_null","path":"experiments/lean4-carrier-rigidity/TfptCarrier/KronheimerMarks.lean","qualified_name":"TfptCarrier.KronheimerMarks.marks_null","statement_as_written":"theorem marks_null : cartanE8affine.mulVec marks = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/KronheimerMarks.lean:TfptCarrier.KronheimerMarks.marks_perron","line_end":64,"line_start":61,"module_context_as_written":[],"name":"marks_perron","path":"experiments/lean4-carrier-rigidity/TfptCarrier/KronheimerMarks.lean","qualified_name":"TfptCarrier.KronheimerMarks.marks_perron","statement_as_written":"theorem marks_perron : adjE8affine.mulVec marks = fun i => 2 * marks i","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/KronheimerMarks.lean:TfptCarrier.KronheimerMarks.marks_sq_sum","line_end":68,"line_start":65,"module_context_as_written":[],"name":"marks_sq_sum","path":"experiments/lean4-carrier-rigidity/TfptCarrier/KronheimerMarks.lean","qualified_name":"TfptCarrier.KronheimerMarks.marks_sq_sum","statement_as_written":"theorem marks_sq_sum : (∑ i, marks i ^ 2) = 120","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/KronheimerMarks.lean:TfptCarrier.KronheimerMarks.two_I_order","line_end":72,"line_start":69,"module_context_as_written":[],"name":"two_I_order","path":"experiments/lean4-carrier-rigidity/TfptCarrier/KronheimerMarks.lean","qualified_name":"TfptCarrier.KronheimerMarks.two_I_order","statement_as_written":"theorem two_I_order : (120 : ℤ) = 4 * 30 ∧ (30 : ℤ) = 2 * 3 * 5","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/KronheimerMarks.lean:TfptCarrier.KronheimerMarks.marks_adj_quadratic","line_end":76,"line_start":73,"module_context_as_written":[],"name":"marks_adj_quadratic","path":"experiments/lean4-carrier-rigidity/TfptCarrier/KronheimerMarks.lean","qualified_name":"TfptCarrier.KronheimerMarks.marks_adj_quadratic","statement_as_written":"theorem marks_adj_quadratic : (∑ i, marks i * adjE8affine.mulVec marks i) = 240","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/KronheimerMarks.lean:TfptCarrier.KronheimerMarks.kronheimer_dimension_count","line_end":85,"line_start":77,"module_context_as_written":[],"name":"kronheimer_dimension_count","path":"experiments/lean4-carrier-rigidity/TfptCarrier/KronheimerMarks.lean","qualified_name":"TfptCarrier.KronheimerMarks.kronheimer_dimension_count","statement_as_written":"theorem kronheimer_dimension_count :\n    2 * (∑ i, marks i * adjE8affine.mulVec marks i)\n      - 4 * ((∑ i, marks i ^ 2) - 1) = 4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/KronheimerMarks.lean:TfptCarrier.KronheimerMarks.kronheimer_input_data","line_end":99,"line_start":86,"module_context_as_written":[],"name":"kronheimer_input_data","path":"experiments/lean4-carrier-rigidity/TfptCarrier/KronheimerMarks.lean","qualified_name":"TfptCarrier.KronheimerMarks.kronheimer_input_data","statement_as_written":"theorem kronheimer_input_data :\n    cartanE8affine.mulVec marks = 0\n    ∧ adjE8affine.mulVec marks = (fun i => 2 * marks i)\n    ∧ (∑ i, marks i ^ 2) = 120\n    ∧ 2 * (∑ i, marks i * adjE8affine.mulVec marks i)\n        - 4 * ((∑ i, marks i ^ 2) - 1) = 4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/LatticeRigidityGeneral.lean:TFPT.Carrier.LatticeRigidityGeneral.primitive_trace_free_pair_general","line_end":174,"line_start":42,"module_context_as_written":[],"name":"primitive_trace_free_pair_general","path":"experiments/lean4-carrier-rigidity/TfptCarrier/LatticeRigidityGeneral.lean","qualified_name":"TFPT.Carrier.LatticeRigidityGeneral.primitive_trace_free_pair_general","statement_as_written":"theorem primitive_trace_free_pair_general\n    (m n : ℕ)\n    (hm : 0 < m) (hn : 0 < n)\n    (qm qp : ℤ)\n    (htrace : (m : ℤ) * qm + (n : ℤ) * qp = 0)\n    (hneg : qm < 0)\n    (hpos : 0 < qp)\n    (hgcd : Int.gcd qm qp = 1) :\n    qm = -((n / Nat.gcd m n : ℕ) : ℤ) ∧\n    qp = ((m / Nat.gcd m n : ℕ) : ℤ)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/LatticeRigidityGeneral.lean:TFPT.Carrier.LatticeRigidityGeneral.primitive_trace_free_pair_3_2","line_end":197,"line_start":175,"module_context_as_written":[],"name":"primitive_trace_free_pair_3_2","path":"experiments/lean4-carrier-rigidity/TfptCarrier/LatticeRigidityGeneral.lean","qualified_name":"TFPT.Carrier.LatticeRigidityGeneral.primitive_trace_free_pair_3_2","statement_as_written":"theorem primitive_trace_free_pair_3_2\n    (qm qp : ℤ)\n    (htrace : 3 * qm + 2 * qp = 0)\n    (hneg : qm < 0)\n    (hpos : 0 < qp)\n    (hgcd : Int.gcd qm qp = 1) :\n    qm = -2 ∧ qp = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/LorentzCongruence.lean:TfptCarrier.LorentzCongruence.P","line_end":43,"line_start":39,"module_context_as_written":[],"name":"P","path":"experiments/lean4-carrier-rigidity/TfptCarrier/LorentzCongruence.lean","qualified_name":"TfptCarrier.LorentzCongruence.P","statement_as_written":"def P : Matrix (Fin 3) (Fin 3) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/LorentzCongruence.lean:TfptCarrier.LorentzCongruence.Jdet","line_end":48,"line_start":44,"module_context_as_written":[],"name":"Jdet","path":"experiments/lean4-carrier-rigidity/TfptCarrier/LorentzCongruence.lean","qualified_name":"TfptCarrier.LorentzCongruence.Jdet","statement_as_written":"def Jdet : Matrix (Fin 3) (Fin 3) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/LorentzCongruence.lean:TfptCarrier.LorentzCongruence.lorentz_congruence","line_end":55,"line_start":49,"module_context_as_written":[],"name":"lorentz_congruence","path":"experiments/lean4-carrier-rigidity/TfptCarrier/LorentzCongruence.lean","qualified_name":"TfptCarrier.LorentzCongruence.lorentz_congruence","statement_as_written":"theorem lorentz_congruence :\n    P.transpose * Jdet * P = CoverEmbedding.Jfix","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/LorentzCongruence.lean:TfptCarrier.LorentzCongruence.P_det","line_end":58,"line_start":56,"module_context_as_written":[],"name":"P_det","path":"experiments/lean4-carrier-rigidity/TfptCarrier/LorentzCongruence.lean","qualified_name":"TfptCarrier.LorentzCongruence.P_det","statement_as_written":"theorem P_det : P.det = -6","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/LorentzCongruence.lean:TfptCarrier.LorentzCongruence.Jdet_det","line_end":62,"line_start":59,"module_context_as_written":[],"name":"Jdet_det","path":"experiments/lean4-carrier-rigidity/TfptCarrier/LorentzCongruence.lean","qualified_name":"TfptCarrier.LorentzCongruence.Jdet_det","statement_as_written":"theorem Jdet_det : Jdet.det = 2 ∧ CoverEmbedding.Jfix.det = 72","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/LorentzCongruence.lean:TfptCarrier.LorentzCongruence.Jfix_det_index_six","line_end":68,"line_start":63,"module_context_as_written":[],"name":"Jfix_det_index_six","path":"experiments/lean4-carrier-rigidity/TfptCarrier/LorentzCongruence.lean","qualified_name":"TfptCarrier.LorentzCongruence.Jfix_det_index_six","statement_as_written":"theorem Jfix_det_index_six : (72 : ℤ) = 2 * 6 ^ 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/MathlibBridge.lean:Polarization.toCompleteOrthogonalIdempotents","line_end":39,"line_start":33,"module_context_as_written":[{"line":31,"source_text":"variable {A : Type*} [Ring A]"}],"name":"Polarization.toCompleteOrthogonalIdempotents","path":"experiments/lean4-carrier-rigidity/TfptCarrier/MathlibBridge.lean","qualified_name":"Polarization.toCompleteOrthogonalIdempotents","statement_as_written":"theorem Polarization.toCompleteOrthogonalIdempotents (p : Polarization A) :\n    CompleteOrthogonalIdempotents ![p.Pm, p.Pp]","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/MathlibBridge.lean:Polarization.ofCompleteOrthogonalIdempotents","line_end":58,"line_start":40,"module_context_as_written":[{"line":31,"source_text":"variable {A : Type*} [Ring A]"}],"name":"Polarization.ofCompleteOrthogonalIdempotents","path":"experiments/lean4-carrier-rigidity/TfptCarrier/MathlibBridge.lean","qualified_name":"Polarization.ofCompleteOrthogonalIdempotents","statement_as_written":"def Polarization.ofCompleteOrthogonalIdempotents\n    (e : Fin 2 → A)\n    (he : CompleteOrthogonalIdempotents e) :\n    Polarization A","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean:TFPT.Carrier.MobiusUniformisation.rho","line_end":43,"line_start":40,"module_context_as_written":[],"name":"rho","path":"experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean","qualified_name":"TFPT.Carrier.MobiusUniformisation.rho","statement_as_written":"def rho (z : ℂ) : ℂ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean:TFPT.Carrier.MobiusUniformisation.rhoInv","line_end":46,"line_start":44,"module_context_as_written":[],"name":"rhoInv","path":"experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean","qualified_name":"TFPT.Carrier.MobiusUniformisation.rhoInv","statement_as_written":"def rhoInv (z : ℂ) : ℂ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean:TFPT.Carrier.MobiusUniformisation.sigma","line_end":49,"line_start":47,"module_context_as_written":[],"name":"sigma","path":"experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean","qualified_name":"TFPT.Carrier.MobiusUniformisation.sigma","statement_as_written":"noncomputable def sigma (z : ℂ) : ℂ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean:TFPT.Carrier.MobiusUniformisation.mu4","line_end":52,"line_start":50,"module_context_as_written":[],"name":"mu4","path":"experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean","qualified_name":"TFPT.Carrier.MobiusUniformisation.mu4","statement_as_written":"def mu4 : List ℂ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean:TFPT.Carrier.MobiusUniformisation.I_pow_four","line_end":58,"line_start":53,"module_context_as_written":[],"name":"I_pow_four","path":"experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean","qualified_name":"TFPT.Carrier.MobiusUniformisation.I_pow_four","statement_as_written":"theorem I_pow_four : (Complex.I) ^ 4 = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean:TFPT.Carrier.MobiusUniformisation.inv_I'","line_end":64,"line_start":59,"module_context_as_written":[],"name":"inv_I'","path":"experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean","qualified_name":"TFPT.Carrier.MobiusUniformisation.inv_I'","statement_as_written":"theorem inv_I' : (Complex.I)⁻¹ = -Complex.I","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean:TFPT.Carrier.MobiusUniformisation.rho_pow_four","line_end":73,"line_start":65,"module_context_as_written":[],"name":"rho_pow_four","path":"experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean","qualified_name":"TFPT.Carrier.MobiusUniformisation.rho_pow_four","statement_as_written":"theorem rho_pow_four (z : ℂ) : rho (rho (rho (rho z))) = z","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean:TFPT.Carrier.MobiusUniformisation.rho_order_exactly_four","line_end":79,"line_start":74,"module_context_as_written":[],"name":"rho_order_exactly_four","path":"experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean","qualified_name":"TFPT.Carrier.MobiusUniformisation.rho_order_exactly_four","statement_as_written":"theorem rho_order_exactly_four : rho (rho 1) ≠ 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean:TFPT.Carrier.MobiusUniformisation.sigma_invol","line_end":85,"line_start":80,"module_context_as_written":[],"name":"sigma_invol","path":"experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean","qualified_name":"TFPT.Carrier.MobiusUniformisation.sigma_invol","statement_as_written":"theorem sigma_invol (z : ℂ) : sigma (sigma z) = z","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean:TFPT.Carrier.MobiusUniformisation.sigma_rho_sigma","line_end":92,"line_start":86,"module_context_as_written":[],"name":"sigma_rho_sigma","path":"experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean","qualified_name":"TFPT.Carrier.MobiusUniformisation.sigma_rho_sigma","statement_as_written":"theorem sigma_rho_sigma (z : ℂ) : sigma (rho (sigma z)) = rhoInv z","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean:TFPT.Carrier.MobiusUniformisation.orbit_scales_to_mu4","line_end":106,"line_start":93,"module_context_as_written":[],"name":"orbit_scales_to_mu4","path":"experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean","qualified_name":"TFPT.Carrier.MobiusUniformisation.orbit_scales_to_mu4","statement_as_written":"theorem orbit_scales_to_mu4 (a : ℂ) (ha : a ≠ 0) :\n    a / a = 1 ∧\n    (Complex.I * a) / a = Complex.I ∧\n    (-a) / a = -1 ∧\n    (-Complex.I * a) / a = -Complex.I","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean:TFPT.Carrier.MobiusUniformisation.sigma_perm_mu4","line_end":117,"line_start":107,"module_context_as_written":[],"name":"sigma_perm_mu4","path":"experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean","qualified_name":"TFPT.Carrier.MobiusUniformisation.sigma_perm_mu4","statement_as_written":"theorem sigma_perm_mu4 :\n    sigma 1 = 1 ∧ sigma (-1) = -1 ∧\n    sigma Complex.I = -Complex.I ∧ sigma (-Complex.I) = Complex.I","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean:TFPT.Carrier.MobiusUniformisation.mult_order_four_iff","line_end":145,"line_start":118,"module_context_as_written":[],"name":"mult_order_four_iff","path":"experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean","qualified_name":"TFPT.Carrier.MobiusUniformisation.mult_order_four_iff","statement_as_written":"theorem mult_order_four_iff (ζ : ℂ) :\n    (ζ ^ 4 = 1 ∧ ζ ^ 2 ≠ 1) ↔ (ζ = Complex.I ∨ ζ = -Complex.I)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean:TFPT.Carrier.MobiusUniformisation.uniformisation_normal_form","line_end":163,"line_start":146,"module_context_as_written":[],"name":"uniformisation_normal_form","path":"experiments/lean4-carrier-rigidity/TfptCarrier/MobiusUniformisation.lean","qualified_name":"TFPT.Carrier.MobiusUniformisation.uniformisation_normal_form","statement_as_written":"theorem uniformisation_normal_form :\n    (∀ z : ℂ, rho (rho (rho (rho z))) = z) ∧\n    rho (rho 1) ≠ 1 ∧\n    (∀ z : ℂ, sigma (sigma z) = z) ∧\n    (∀ z : ℂ, sigma (rho (sigma z)) = rhoInv z) ∧\n    (∀ ζ : ℂ, (ζ ^ 4 = 1 ∧ ζ ^ 2 ≠ 1) ↔ (ζ = Complex.I ∨ ζ = -Complex.I))","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/Mu4Commutation.lean:TfptCarrier.Mu4Commutation.I","line_end":25,"line_start":23,"module_context_as_written":[],"name":"I","path":"experiments/lean4-carrier-rigidity/TfptCarrier/Mu4Commutation.lean","qualified_name":"TfptCarrier.Mu4Commutation.I","statement_as_written":"def I : GaussianInt","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/Mu4Commutation.lean:TfptCarrier.Mu4Commutation.i_pow_four","line_end":28,"line_start":26,"module_context_as_written":[],"name":"i_pow_four","path":"experiments/lean4-carrier-rigidity/TfptCarrier/Mu4Commutation.lean","qualified_name":"TfptCarrier.Mu4Commutation.i_pow_four","statement_as_written":"theorem i_pow_four : I ^ 4 = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/Mu4Commutation.lean:TfptCarrier.Mu4Commutation.i_pow_two","line_end":31,"line_start":29,"module_context_as_written":[],"name":"i_pow_two","path":"experiments/lean4-carrier-rigidity/TfptCarrier/Mu4Commutation.lean","qualified_name":"TfptCarrier.Mu4Commutation.i_pow_two","statement_as_written":"theorem i_pow_two : I ^ 2 = -1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/Mu4Commutation.lean:TfptCarrier.Mu4Commutation.rho","line_end":35,"line_start":32,"module_context_as_written":[],"name":"rho","path":"experiments/lean4-carrier-rigidity/TfptCarrier/Mu4Commutation.lean","qualified_name":"TfptCarrier.Mu4Commutation.rho","statement_as_written":"def rho : Matrix (Fin 6) (Fin 6) GaussianInt","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/Mu4Commutation.lean:TfptCarrier.Mu4Commutation.M4","line_end":39,"line_start":36,"module_context_as_written":[],"name":"M4","path":"experiments/lean4-carrier-rigidity/TfptCarrier/Mu4Commutation.lean","qualified_name":"TfptCarrier.Mu4Commutation.M4","statement_as_written":"def M4 : Matrix (Fin 6) (Fin 6) GaussianInt","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/Mu4Commutation.lean:TfptCarrier.Mu4Commutation.M2","line_end":45,"line_start":40,"module_context_as_written":[],"name":"M2","path":"experiments/lean4-carrier-rigidity/TfptCarrier/Mu4Commutation.lean","qualified_name":"TfptCarrier.Mu4Commutation.M2","statement_as_written":"def M2 : Matrix (Fin 6) (Fin 6) GaussianInt","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/Mu4Commutation.lean:TfptCarrier.Mu4Commutation.mu4_commutes_offset4","line_end":50,"line_start":46,"module_context_as_written":[],"name":"mu4_commutes_offset4","path":"experiments/lean4-carrier-rigidity/TfptCarrier/Mu4Commutation.lean","qualified_name":"TfptCarrier.Mu4Commutation.mu4_commutes_offset4","statement_as_written":"theorem mu4_commutes_offset4 : rho * M4 = M4 * rho","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/Mu4Commutation.lean:TfptCarrier.Mu4Commutation.mu4_not_commutes_offset2","line_end":55,"line_start":51,"module_context_as_written":[],"name":"mu4_not_commutes_offset2","path":"experiments/lean4-carrier-rigidity/TfptCarrier/Mu4Commutation.lean","qualified_name":"TfptCarrier.Mu4Commutation.mu4_not_commutes_offset2","statement_as_written":"theorem mu4_not_commutes_offset2 : rho * M2 ≠ M2 * rho","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"abbrev","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.Label","line_end":96,"line_start":92,"module_context_as_written":[],"name":"Label","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.Label","statement_as_written":"abbrev Label","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.sigL","line_end":100,"line_start":97,"module_context_as_written":[],"name":"sigL","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.sigL","statement_as_written":"def sigL (l : Label) : Label","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.nonzeroLabels","line_end":103,"line_start":101,"module_context_as_written":[],"name":"nonzeroLabels","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.nonzeroLabels","statement_as_written":"def nonzeroLabels : Finset Label","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.orbitOf","line_end":106,"line_start":104,"module_context_as_written":[],"name":"orbitOf","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.orbitOf","statement_as_written":"def orbitOf (l : Label) : Finset Label","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.fix_id_card","line_end":111,"line_start":107,"module_context_as_written":[],"name":"fix_id_card","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.fix_id_card","statement_as_written":"theorem fix_id_card : nonzeroLabels.card = 15","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.fix_sigma_card","line_end":115,"line_start":112,"module_context_as_written":[],"name":"fix_sigma_card","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.fix_sigma_card","statement_as_written":"theorem fix_sigma_card :\n    (nonzeroLabels.filter fun l => sigL l = l).card = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.fix_sigma_sq_card","line_end":119,"line_start":116,"module_context_as_written":[],"name":"fix_sigma_sq_card","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.fix_sigma_sq_card","statement_as_written":"theorem fix_sigma_sq_card :\n    (nonzeroLabels.filter fun l => sigL (sigL l) = l).card = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.burnside_arithmetic","line_end":122,"line_start":120,"module_context_as_written":[],"name":"burnside_arithmetic","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.burnside_arithmetic","statement_as_written":"theorem burnside_arithmetic : (15 + 3 + 3) / 3 = 7","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.orbit_count","line_end":126,"line_start":123,"module_context_as_written":[],"name":"orbit_count","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.orbit_count","statement_as_written":"theorem orbit_count : (nonzeroLabels.image orbitOf).card = 7","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.fixed_orbit_count","line_end":131,"line_start":127,"module_context_as_written":[],"name":"fixed_orbit_count","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.fixed_orbit_count","statement_as_written":"theorem fixed_orbit_count :\n    ((nonzeroLabels.image orbitOf).filter fun o => o.card = 1).card = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.moved_orbit_count","line_end":136,"line_start":132,"module_context_as_written":[],"name":"moved_orbit_count","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.moved_orbit_count","statement_as_written":"theorem moved_orbit_count :\n    ((nonzeroLabels.image orbitOf).filter fun o => o.card = 3).card = 4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.orbit_sizes_exhaustive","line_end":146,"line_start":137,"module_context_as_written":[],"name":"orbit_sizes_exhaustive","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.orbit_sizes_exhaustive","statement_as_written":"theorem orbit_sizes_exhaustive :\n    ∀ l : Label, l ≠ 0 →\n      (sigL l = l ∨\n        (sigL l ≠ l ∧ sigL (sigL l) ≠ l ∧ sigL (sigL l) ≠ sigL l))","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.Bfix","line_end":152,"line_start":147,"module_context_as_written":[],"name":"Bfix","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.Bfix","statement_as_written":"def Bfix : List Label","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.O1","line_end":155,"line_start":153,"module_context_as_written":[],"name":"O1","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.O1","statement_as_written":"def O1 : List Label","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.O2","line_end":158,"line_start":156,"module_context_as_written":[],"name":"O2","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.O2","statement_as_written":"def O2 : List Label","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.O3","line_end":161,"line_start":159,"module_context_as_written":[],"name":"O3","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.O3","statement_as_written":"def O3 : List Label","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.O4","line_end":164,"line_start":162,"module_context_as_written":[],"name":"O4","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.O4","statement_as_written":"def O4 : List Label","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.blocks_cover","line_end":169,"line_start":165,"module_context_as_written":[],"name":"blocks_cover","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.blocks_cover","statement_as_written":"theorem blocks_cover :\n    ∀ l : Label, l ≠ 0 →\n      (l ∈ Bfix ∨ l ∈ O1 ∨ l ∈ O2 ∨ l ∈ O3 ∨ l ∈ O4)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.blocks_disjoint","line_end":175,"line_start":170,"module_context_as_written":[],"name":"blocks_disjoint","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.blocks_disjoint","statement_as_written":"theorem blocks_disjoint :\n    (Bfix ++ O1 ++ O2 ++ O3 ++ O4).Nodup ∧\n    (Bfix ++ O1 ++ O2 ++ O3 ++ O4).length = 15","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.fix_block_canonical","line_end":180,"line_start":176,"module_context_as_written":[],"name":"fix_block_canonical","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.fix_block_canonical","statement_as_written":"theorem fix_block_canonical :\n    ∀ l : Label, (l ∈ Bfix ↔ (l ≠ 0 ∧ sigL l = l))","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.moved_blocks_canonical","line_end":193,"line_start":181,"module_context_as_written":[],"name":"moved_blocks_canonical","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.moved_blocks_canonical","statement_as_written":"theorem moved_blocks_canonical :\n    (∀ l ∈ O1, orbitOf l = ({![0, 0, 1, 0], ![0, 1, 0, 1], ![0, 1, 1, 0]} :\n        Finset Label)) ∧\n    (∀ l ∈ O2, orbitOf l = ({![0, 1, 0, 0], ![0, 1, 1, 1], ![0, 0, 1, 1]} :\n        Finset Label)) ∧\n    (∀ l ∈ O3, orbitOf l = ({![1, 0, 1, 0], ![1, 1, 0, 1], ![1, 1, 1, 0]} :\n        Finset Label)) ∧\n    (∀ l ∈ O4, orbitOf l = ({![1, 1, 0, 0], ![1, 1, 1, 1], ![1, 0, 1, 1]} :\n        Finset Label))","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.O1_is_family_orbit","line_end":197,"line_start":194,"module_context_as_written":[],"name":"O1_is_family_orbit","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.O1_is_family_orbit","statement_as_written":"theorem O1_is_family_orbit : O1 = [F1, F2, F3]","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.Bfix_contents","line_end":205,"line_start":198,"module_context_as_written":[],"name":"Bfix_contents","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.Bfix_contents","statement_as_written":"theorem Bfix_contents :\n    Bfix = [anchor, F1 + F2 + F3, anchor + (F1 + F2 + F3)]","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.packet_counts","line_end":213,"line_start":206,"module_context_as_written":[],"name":"packet_counts","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.packet_counts","statement_as_written":"theorem packet_counts :\n    labelData.countP (· ∈ Bfix) = 48 ∧\n    labelData.countP (· ∈ O1) = 48 ∧\n    labelData.countP (· ∈ O2) = 48 ∧\n    labelData.countP (· ∈ O3) = 48 ∧\n    labelData.countP (· ∈ O4) = 48","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.packet_partition_240","line_end":217,"line_start":214,"module_context_as_written":[],"name":"packet_partition_240","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.packet_partition_240","statement_as_written":"theorem packet_partition_240 : 5 * 48 = 240","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.gCar_reconstruction","line_end":227,"line_start":218,"module_context_as_written":[],"name":"gCar_reconstruction","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.gCar_reconstruction","statement_as_written":"theorem gCar_reconstruction :\n    1 + ((nonzeroLabels.image orbitOf).filter fun o => o.card = 3).card\n      = 5","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.gCar_packet_reading","line_end":230,"line_start":228,"module_context_as_written":[],"name":"gCar_packet_reading","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.gCar_packet_reading","statement_as_written":"theorem gCar_packet_reading : (1 + 4) * 48 = 240","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.sigV8","line_end":237,"line_start":231,"module_context_as_written":[],"name":"sigV8","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.sigV8","statement_as_written":"def sigV8 (x : V8) : V8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.cosetFixed","line_end":245,"line_start":238,"module_context_as_written":[],"name":"cosetFixed","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.cosetFixed","statement_as_written":"def cosetFixed (x : V8) : Prop","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.cosetFixed_well_defined","line_end":250,"line_start":246,"module_context_as_written":[],"name":"cosetFixed_well_defined","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.cosetFixed_well_defined","statement_as_written":"theorem cosetFixed_well_defined :\n    ∀ l ∈ leaders, ∀ c ∈ code, (cosetFixed (l + c) ↔ cosetFixed l)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.fixed_coset_count","line_end":255,"line_start":251,"module_context_as_written":[],"name":"fixed_coset_count","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.fixed_coset_count","statement_as_written":"theorem fixed_coset_count :\n    (leaders.countP fun l => cosetFixed l) = 4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.anchor_weights","line_end":263,"line_start":256,"module_context_as_written":[],"name":"anchor_weights","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.anchor_weights","statement_as_written":"theorem anchor_weights :\n    ((leaders.filter fun l => cosetFixed l).map wt) = [0, 2, 1, 1]","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.anchor_weights_multiset","line_end":270,"line_start":264,"module_context_as_written":[],"name":"anchor_weights_multiset","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.anchor_weights_multiset","statement_as_written":"theorem anchor_weights_multiset :\n    ((leaders.filter fun l => cosetFixed l).countP fun l => wt l = 0) = 1 ∧\n    ((leaders.filter fun l => cosetFixed l).countP fun l => wt l = 1) = 2 ∧\n    ((leaders.filter fun l => cosetFixed l).countP fun l => wt l = 2) = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.anchor_pair_leaders","line_end":280,"line_start":271,"module_context_as_written":[],"name":"anchor_pair_leaders","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.anchor_pair_leaders","statement_as_written":"theorem anchor_pair_leaders :\n    (![0, 0, 0, 0, 0, 0, 1, 0] : V8) ∈\n      (leaders.filter fun l => cosetFixed l) ∧\n    (![0, 0, 0, 0, 0, 0, 0, 1] : V8) ∈\n      (leaders.filter fun l => cosetFixed l) ∧\n    (![0, 0, 0, 0, 0, 0, 1, 1] : V8) ∈\n      (leaders.filter fun l => cosetFixed l)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.anchor_elementary_symmetric","line_end":288,"line_start":281,"module_context_as_written":[],"name":"anchor_elementary_symmetric","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.anchor_elementary_symmetric","statement_as_written":"theorem anchor_elementary_symmetric :\n    (1 + 1 + 2 = 4) ∧ (1 * 1 + 1 * 2 + 2 * 1 = 5) ∧ (1 * 1 * 2 = 2)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.q_is_quotient_order","line_end":294,"line_start":289,"module_context_as_written":[],"name":"q_is_quotient_order","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.q_is_quotient_order","statement_as_written":"theorem q_is_quotient_order : Fintype.card Label = 16","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.q_normal_roots","line_end":297,"line_start":295,"module_context_as_written":[],"name":"q_normal_roots","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.q_normal_roots","statement_as_written":"theorem q_normal_roots : 16 * 15 = 240","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.q_log_two","line_end":300,"line_start":298,"module_context_as_written":[],"name":"q_log_two","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.q_log_two","statement_as_written":"theorem q_log_two : 2 ^ 4 = 16","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.q_normal_dim","line_end":303,"line_start":301,"module_context_as_written":[],"name":"q_normal_dim","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.q_normal_dim","statement_as_written":"theorem q_normal_dim : 16 * 15 + 2 * 4 = 248","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.c3_coefficient_reconstruction","line_end":312,"line_start":304,"module_context_as_written":[],"name":"c3_coefficient_reconstruction","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.c3_coefficient_reconstruction","statement_as_written":"theorem c3_coefficient_reconstruction : (1 : ℚ) / (2 * 4) = 1 / 8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.c3_dim_ties_to_quotient","line_end":315,"line_start":313,"module_context_as_written":[],"name":"c3_dim_ties_to_quotient","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.c3_dim_ties_to_quotient","statement_as_written":"theorem c3_dim_ties_to_quotient : 2 ^ 4 = Fintype.card Label","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.Mfree","line_end":327,"line_start":316,"module_context_as_written":[],"name":"Mfree","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.Mfree","statement_as_written":"def Mfree : Matrix (Fin 4) (Fin 4) (ZMod 2)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.Mfree_cubed","line_end":330,"line_start":328,"module_context_as_written":[],"name":"Mfree_cubed","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.Mfree_cubed","statement_as_written":"theorem Mfree_cubed : Mfree * Mfree * Mfree = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.Mfree_fixed_point_free","line_end":334,"line_start":331,"module_context_as_written":[],"name":"Mfree_fixed_point_free","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.Mfree_fixed_point_free","statement_as_written":"theorem Mfree_fixed_point_free :\n    ∀ l : Label, rowMul4 l Mfree = l → l = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.Mfree_orbit_count","line_end":344,"line_start":335,"module_context_as_written":[],"name":"Mfree_orbit_count","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.Mfree_orbit_count","statement_as_written":"theorem Mfree_orbit_count :\n    (nonzeroLabels.image fun l =>\n      ({l, rowMul4 l Mfree, rowMul4 (rowMul4 l Mfree) Mfree} :\n        Finset Label)).card = 5","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean:TfptCarrier.OrbitPacket.burnside_free_class","line_end":350,"line_start":345,"module_context_as_written":[],"name":"burnside_free_class","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrbitPacket.lean","qualified_name":"TfptCarrier.OrbitPacket.burnside_free_class","statement_as_written":"theorem burnside_free_class : (15 + 0 + 0) / 3 = 5 ∧ (5 : ℕ) ≠ 7","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"structure","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrientedDeterminantCarrier.lean:TFPT.Carrier.OrientedDeterminantCarrier.PrimitiveOrientedDeterminantCarrier","line_end":70,"line_start":39,"module_context_as_written":[{"line":69,"source_text":"variable {m n : ℕ}"}],"name":"PrimitiveOrientedDeterminantCarrier","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrientedDeterminantCarrier.lean","qualified_name":"TFPT.Carrier.OrientedDeterminantCarrier.PrimitiveOrientedDeterminantCarrier","statement_as_written":"structure PrimitiveOrientedDeterminantCarrier (m n : ℕ)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrientedDeterminantCarrier.lean:TFPT.Carrier.OrientedDeterminantCarrier.PrimitiveOrientedDeterminantCarrier.to_rigidity_pair_eq","line_end":84,"line_start":71,"module_context_as_written":[{"line":69,"source_text":"variable {m n : ℕ}"}],"name":"to_rigidity_pair_eq","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrientedDeterminantCarrier.lean","qualified_name":"TFPT.Carrier.OrientedDeterminantCarrier.PrimitiveOrientedDeterminantCarrier.to_rigidity_pair_eq","statement_as_written":"theorem to_rigidity_pair_eq\n    (hm : 0 < m) (hn : 0 < n)\n    (c : PrimitiveOrientedDeterminantCarrier m n) :\n    c.q_minus = -((n / Nat.gcd m n : ℕ) : ℤ) ∧\n    c.q_plus = ((m / Nat.gcd m n : ℕ) : ℤ)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/OrientedDeterminantCarrier.lean:TFPT.Carrier.OrientedDeterminantCarrier.PrimitiveOrientedDeterminantCarrier.sm_pair_eq","line_end":101,"line_start":85,"module_context_as_written":[{"line":69,"source_text":"variable {m n : ℕ}"}],"name":"sm_pair_eq","path":"experiments/lean4-carrier-rigidity/TfptCarrier/OrientedDeterminantCarrier.lean","qualified_name":"TFPT.Carrier.OrientedDeterminantCarrier.PrimitiveOrientedDeterminantCarrier.sm_pair_eq","statement_as_written":"theorem sm_pair_eq\n    (c : PrimitiveOrientedDeterminantCarrier 3 2) :\n    c.q_minus = -2 ∧ c.q_plus = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ParityWeightLaws.lean:TFPT.Carrier.ParityWeightLaws.S0","line_end":10,"line_start":7,"module_context_as_written":[],"name":"S0","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ParityWeightLaws.lean","qualified_name":"TFPT.Carrier.ParityWeightLaws.S0","statement_as_written":"def S0 : Matrix (Fin 3) (Fin 3) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ParityWeightLaws.lean:TFPT.Carrier.ParityWeightLaws.V","line_end":13,"line_start":11,"module_context_as_written":[],"name":"V","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ParityWeightLaws.lean","qualified_name":"TFPT.Carrier.ParityWeightLaws.V","statement_as_written":"def V : Matrix (Fin 3) (Fin 3) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ParityWeightLaws.lean:TFPT.Carrier.ParityWeightLaws.S0_involution","line_end":18,"line_start":14,"module_context_as_written":[],"name":"S0_involution","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ParityWeightLaws.lean","qualified_name":"TFPT.Carrier.ParityWeightLaws.S0_involution","statement_as_written":"theorem S0_involution : S0 * S0 = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ParityWeightLaws.lean:TFPT.Carrier.ParityWeightLaws.S0_commutes_V","line_end":23,"line_start":19,"module_context_as_written":[],"name":"S0_commutes_V","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ParityWeightLaws.lean","qualified_name":"TFPT.Carrier.ParityWeightLaws.S0_commutes_V","statement_as_written":"theorem S0_commutes_V : S0 * V = V * S0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ParityWeightLaws.lean:TFPT.Carrier.ParityWeightLaws.S0_trace","line_end":26,"line_start":24,"module_context_as_written":[],"name":"S0_trace","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ParityWeightLaws.lean","qualified_name":"TFPT.Carrier.ParityWeightLaws.S0_trace","statement_as_written":"theorem S0_trace : Matrix.trace S0 = -1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ParityWeightLaws.lean:TFPT.Carrier.ParityWeightLaws.A","line_end":39,"line_start":27,"module_context_as_written":[],"name":"A","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ParityWeightLaws.lean","qualified_name":"TFPT.Carrier.ParityWeightLaws.A","statement_as_written":"def A : Matrix (Fin 3) (Fin 3) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ParityWeightLaws.lean:TFPT.Carrier.ParityWeightLaws.B","line_end":42,"line_start":40,"module_context_as_written":[],"name":"B","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ParityWeightLaws.lean","qualified_name":"TFPT.Carrier.ParityWeightLaws.B","statement_as_written":"def B : Matrix (Fin 3) (Fin 3) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ParityWeightLaws.lean:TFPT.Carrier.ParityWeightLaws.A_involution","line_end":47,"line_start":43,"module_context_as_written":[],"name":"A_involution","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ParityWeightLaws.lean","qualified_name":"TFPT.Carrier.ParityWeightLaws.A_involution","statement_as_written":"theorem A_involution : A * A = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ParityWeightLaws.lean:TFPT.Carrier.ParityWeightLaws.B_involution","line_end":52,"line_start":48,"module_context_as_written":[],"name":"B_involution","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ParityWeightLaws.lean","qualified_name":"TFPT.Carrier.ParityWeightLaws.B_involution","statement_as_written":"theorem B_involution : B * B = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ParityWeightLaws.lean:TFPT.Carrier.ParityWeightLaws.A_commutes_V","line_end":57,"line_start":53,"module_context_as_written":[],"name":"A_commutes_V","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ParityWeightLaws.lean","qualified_name":"TFPT.Carrier.ParityWeightLaws.A_commutes_V","statement_as_written":"theorem A_commutes_V : A * V = V * A","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ParityWeightLaws.lean:TFPT.Carrier.ParityWeightLaws.B_commutes_V","line_end":62,"line_start":58,"module_context_as_written":[],"name":"B_commutes_V","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ParityWeightLaws.lean","qualified_name":"TFPT.Carrier.ParityWeightLaws.B_commutes_V","statement_as_written":"theorem B_commutes_V : B * V = V * B","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ParityWeightLaws.lean:TFPT.Carrier.ParityWeightLaws.klein_closure","line_end":71,"line_start":63,"module_context_as_written":[],"name":"klein_closure","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ParityWeightLaws.lean","qualified_name":"TFPT.Carrier.ParityWeightLaws.klein_closure","statement_as_written":"theorem klein_closure : A * B = S0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/PascalLadder.lean:TFPT.Carrier.PascalLadder.pascalSum","line_end":39,"line_start":37,"module_context_as_written":[],"name":"pascalSum","path":"experiments/lean4-carrier-rigidity/TfptCarrier/PascalLadder.lean","qualified_name":"TFPT.Carrier.PascalLadder.pascalSum","statement_as_written":"def pascalSum (g K : ℕ) : ℕ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/PascalLadder.lean:TFPT.Carrier.PascalLadder.ladder_solves","line_end":48,"line_start":40,"module_context_as_written":[],"name":"ladder_solves","path":"experiments/lean4-carrier-rigidity/TfptCarrier/PascalLadder.lean","qualified_name":"TFPT.Carrier.PascalLadder.ladder_solves","statement_as_written":"theorem ladder_solves (K : ℕ) : pascalSum (2 * K + 1) K = 2 ^ (2 * K)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/PascalLadder.lean:TFPT.Carrier.PascalLadder.ladder_unique_K2","line_end":58,"line_start":49,"module_context_as_written":[],"name":"ladder_unique_K2","path":"experiments/lean4-carrier-rigidity/TfptCarrier/PascalLadder.lean","qualified_name":"TFPT.Carrier.PascalLadder.ladder_unique_K2","statement_as_written":"theorem ladder_unique_K2 :\n    ∀ g : ℕ, 1 ≤ g → g ≤ 40 → (2 ^ (g - 1) = pascalSum g 2 ↔ g = 5)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/PascalLadder.lean:TFPT.Carrier.PascalLadder.carrier_world","line_end":64,"line_start":59,"module_context_as_written":[],"name":"carrier_world","path":"experiments/lean4-carrier-rigidity/TfptCarrier/PascalLadder.lean","qualified_name":"TFPT.Carrier.PascalLadder.carrier_world","statement_as_written":"theorem carrier_world :\n    2 * 2 + 1 = 5 ∧ 2 ^ 4 = 16 ∧ (2 ^ 4 - 1) / 5 = 3 ∧ 5 + 3 = 8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/PascalLadder.lean:TFPT.Carrier.PascalLadder.neighbour_worlds","line_end":75,"line_start":65,"module_context_as_written":[],"name":"neighbour_worlds","path":"experiments/lean4-carrier-rigidity/TfptCarrier/PascalLadder.lean","qualified_name":"TFPT.Carrier.PascalLadder.neighbour_worlds","statement_as_written":"theorem neighbour_worlds :\n    ((2 ^ 2 - 1) / 3 = 1 ∧ 3 + 1 ≠ 8) ∧\n    ((2 ^ 6 - 1) / 7 = 9 ∧ 7 + 9 ≠ 8) ∧\n    ¬ (9 ∣ 2 ^ 8 - 1)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"structure","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/Polarization.lean:TFPT.Carrier.Polarization","line_end":59,"line_start":36,"module_context_as_written":[{"line":58,"source_text":"variable {A : Type*} [Ring A] [Algebra ℚ A]"}],"name":"Polarization","path":"experiments/lean4-carrier-rigidity/TfptCarrier/Polarization.lean","qualified_name":"TFPT.Carrier.Polarization","statement_as_written":"structure Polarization (A : Type*) [Ring A]","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/Polarization.lean:TFPT.Carrier.Polarization.sixY","line_end":69,"line_start":60,"module_context_as_written":[{"line":58,"source_text":"variable {A : Type*} [Ring A] [Algebra ℚ A]"}],"name":"sixY","path":"experiments/lean4-carrier-rigidity/TfptCarrier/Polarization.lean","qualified_name":"TFPT.Carrier.Polarization.sixY","statement_as_written":"def sixY (p : Polarization A) : A","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"lemma","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/Polarization.lean:TFPT.Carrier.Polarization.sixY_sq","line_end":93,"line_start":70,"module_context_as_written":[{"line":58,"source_text":"variable {A : Type*} [Ring A] [Algebra ℚ A]"}],"name":"sixY_sq","path":"experiments/lean4-carrier-rigidity/TfptCarrier/Polarization.lean","qualified_name":"TFPT.Carrier.Polarization.sixY_sq","statement_as_written":"lemma sixY_sq (p : Polarization A) :\n    p.sixY * p.sixY = 4 * p.Pm + 9 * p.Pp","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/Polarization.lean:TFPT.Carrier.Polarization.sixY_carrier_polynomial","line_end":126,"line_start":94,"module_context_as_written":[{"line":58,"source_text":"variable {A : Type*} [Ring A] [Algebra ℚ A]"}],"name":"sixY_carrier_polynomial","path":"experiments/lean4-carrier-rigidity/TfptCarrier/Polarization.lean","qualified_name":"TFPT.Carrier.Polarization.sixY_carrier_polynomial","statement_as_written":"theorem sixY_carrier_polynomial (p : Polarization A) :\n    p.sixY * p.sixY - p.sixY - 6 = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/Polarization.lean:TFPT.Carrier.Polarization.Y","line_end":139,"line_start":127,"module_context_as_written":[{"line":58,"source_text":"variable {A : Type*} [Ring A] [Algebra ℚ A]"}],"name":"Y","path":"experiments/lean4-carrier-rigidity/TfptCarrier/Polarization.lean","qualified_name":"TFPT.Carrier.Polarization.Y","statement_as_written":"noncomputable def Y (p : Polarization A) : A","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/PositiveDescentMaster.lean:TfptCarrier.PositiveDescentMaster.exists_limit","line_end":74,"line_start":66,"module_context_as_written":[{"line":64,"source_text":"variable {m : ℕ}"}],"name":"exists_limit","path":"experiments/lean4-carrier-rigidity/TfptCarrier/PositiveDescentMaster.lean","qualified_name":"TfptCarrier.PositiveDescentMaster.exists_limit","statement_as_written":"theorem exists_limit (p : ℕ → (Fin m → ℝ)) (δ : ℕ → ℝ)\n    (hδ : ∀ n, dist (p n) (p (n + 1)) ≤ δ n) (hs : Summable δ) :\n    ∃ q : Fin m → ℝ, Tendsto p atTop (𝓝 q)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/PositiveDescentMaster.lean:TfptCarrier.PositiveDescentMaster.limit_unique","line_end":80,"line_start":75,"module_context_as_written":[{"line":64,"source_text":"variable {m : ℕ}"}],"name":"limit_unique","path":"experiments/lean4-carrier-rigidity/TfptCarrier/PositiveDescentMaster.lean","qualified_name":"TfptCarrier.PositiveDescentMaster.limit_unique","statement_as_written":"theorem limit_unique {p : ℕ → (Fin m → ℝ)} {q q' : Fin m → ℝ}\n    (h : Tendsto p atTop (𝓝 q)) (h' : Tendsto p atTop (𝓝 q')) :\n    q = q'","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/PositiveDescentMaster.lean:TfptCarrier.PositiveDescentMaster.tail_bound","line_end":89,"line_start":81,"module_context_as_written":[{"line":64,"source_text":"variable {m : ℕ}"}],"name":"tail_bound","path":"experiments/lean4-carrier-rigidity/TfptCarrier/PositiveDescentMaster.lean","qualified_name":"TfptCarrier.PositiveDescentMaster.tail_bound","statement_as_written":"theorem tail_bound (p : ℕ → (Fin m → ℝ)) (δ : ℕ → ℝ) {q : Fin m → ℝ}\n    (hδ : ∀ n, dist (p n) (p (n + 1)) ≤ δ n) (hs : Summable δ)\n    (hq : Tendsto p atTop (𝓝 q)) (n : ℕ) :\n    dist (p n) q ≤ ∑' k, δ (n + k)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/PositiveDescentMaster.lean:TfptCarrier.PositiveDescentMaster.limit_nonneg","line_end":100,"line_start":90,"module_context_as_written":[{"line":64,"source_text":"variable {m : ℕ}"}],"name":"limit_nonneg","path":"experiments/lean4-carrier-rigidity/TfptCarrier/PositiveDescentMaster.lean","qualified_name":"TfptCarrier.PositiveDescentMaster.limit_nonneg","statement_as_written":"theorem limit_nonneg {p : ℕ → (Fin m → ℝ)} {q : Fin m → ℝ}\n    (hq : Tendsto p atTop (𝓝 q)) (hp : ∀ n i, 0 ≤ p n i) :\n    ∀ i, 0 ≤ q i","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/PositiveDescentMaster.lean:TfptCarrier.PositiveDescentMaster.sector_tendsto","line_end":109,"line_start":101,"module_context_as_written":[{"line":64,"source_text":"variable {m : ℕ}"}],"name":"sector_tendsto","path":"experiments/lean4-carrier-rigidity/TfptCarrier/PositiveDescentMaster.lean","qualified_name":"TfptCarrier.PositiveDescentMaster.sector_tendsto","statement_as_written":"theorem sector_tendsto (S : Finset (Fin m)) {p : ℕ → (Fin m → ℝ)}\n    {q : Fin m → ℝ} (hq : Tendsto p atTop (𝓝 q)) :\n    Tendsto (fun n => ∑ i ∈ S, p n i) atTop (𝓝 (∑ i ∈ S, q i))","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/PositiveDescentMaster.lean:TfptCarrier.PositiveDescentMaster.master_core","line_end":125,"line_start":110,"module_context_as_written":[{"line":64,"source_text":"variable {m : ℕ}"}],"name":"master_core","path":"experiments/lean4-carrier-rigidity/TfptCarrier/PositiveDescentMaster.lean","qualified_name":"TfptCarrier.PositiveDescentMaster.master_core","statement_as_written":"theorem master_core (p : ℕ → (Fin m → ℝ)) (δ : ℕ → ℝ)\n    (hpos : ∀ n i, 0 ≤ p n i)\n    (hδ : ∀ n, dist (p n) (p (n + 1)) ≤ δ n) (hs : Summable δ) :\n    ∃ q : Fin m → ℝ, Tendsto p atTop (𝓝 q) ∧ (∀ i, 0 ≤ q i) ∧\n      ∀ S : Finset (Fin m),\n        Tendsto (fun n => ∑ i ∈ S, p n i) atTop (𝓝 (∑ i ∈ S, q i)) ∧\n          0 ≤ ∑ i ∈ S, q i","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/PositiveDescentMaster.lean:TfptCarrier.PositiveDescentMaster.mu4_char_sum","line_end":134,"line_start":126,"module_context_as_written":[{"line":64,"source_text":"variable {m : ℕ}"}],"name":"mu4_char_sum","path":"experiments/lean4-carrier-rigidity/TfptCarrier/PositiveDescentMaster.lean","qualified_name":"TfptCarrier.PositiveDescentMaster.mu4_char_sum","statement_as_written":"theorem mu4_char_sum : (∑ j : Fin 4, (Complex.I : ℂ) ^ (j : ℕ)) = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"abbrev","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.Label","line_end":105,"line_start":100,"module_context_as_written":[],"name":"Label","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.Label","statement_as_written":"abbrev Label","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.G","line_end":114,"line_start":106,"module_context_as_written":[],"name":"G","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.G","statement_as_written":"def G : Matrix (Fin 4) (Fin 4) (ZMod 2)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.symp","line_end":117,"line_start":115,"module_context_as_written":[],"name":"symp","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.symp","statement_as_written":"def symp (x y : Label) : ZMod 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.card_label","line_end":120,"line_start":118,"module_context_as_written":[],"name":"card_label","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.card_label","statement_as_written":"theorem card_label : Fintype.card Label = 16","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.points","line_end":123,"line_start":121,"module_context_as_written":[],"name":"points","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.points","statement_as_written":"def points : Finset Label","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.points_card","line_end":125,"line_start":124,"module_context_as_written":[],"name":"points_card","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.points_card","statement_as_written":"theorem points_card : points.card = 15","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.G_symm","line_end":130,"line_start":126,"module_context_as_written":[],"name":"G_symm","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.G_symm","statement_as_written":"theorem G_symm : G.transpose = G","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.symp_alternating","line_end":134,"line_start":131,"module_context_as_written":[],"name":"symp_alternating","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.symp_alternating","statement_as_written":"theorem symp_alternating : ∀ x : Label, symp x x = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.symp_symmetric","line_end":137,"line_start":135,"module_context_as_written":[],"name":"symp_symmetric","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.symp_symmetric","statement_as_written":"theorem symp_symmetric : ∀ x y : Label, symp x y = symp y x","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.symp_add_left","line_end":142,"line_start":138,"module_context_as_written":[],"name":"symp_add_left","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.symp_add_left","statement_as_written":"theorem symp_add_left :\n    ∀ x y z : Label, symp (x + y) z = symp x z + symp y z","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.symp_nondegenerate","line_end":147,"line_start":143,"module_context_as_written":[],"name":"symp_nondegenerate","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.symp_nondegenerate","statement_as_written":"theorem symp_nondegenerate :\n    ∀ x : Label, (∀ y : Label, symp x y = 0) → x = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.Gstd","line_end":154,"line_start":148,"module_context_as_written":[],"name":"Gstd","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.Gstd","statement_as_written":"def Gstd : Matrix (Fin 4) (Fin 4) (ZMod 2)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.P","line_end":162,"line_start":155,"module_context_as_written":[],"name":"P","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.P","statement_as_written":"def P : Matrix (Fin 4) (Fin 4) (ZMod 2)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.Pinv","line_end":169,"line_start":163,"module_context_as_written":[],"name":"Pinv","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.Pinv","statement_as_written":"def Pinv : Matrix (Fin 4) (Fin 4) (ZMod 2)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.darboux_transform","line_end":174,"line_start":170,"module_context_as_written":[],"name":"darboux_transform","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.darboux_transform","statement_as_written":"theorem darboux_transform : P.transpose * G * P = Gstd","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.P_invertible","line_end":177,"line_start":175,"module_context_as_written":[],"name":"P_invertible","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.P_invertible","statement_as_written":"theorem P_invertible : P * Pinv = 1 ∧ Pinv * P = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.hyperplane_card","line_end":186,"line_start":178,"module_context_as_written":[],"name":"hyperplane_card","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.hyperplane_card","statement_as_written":"theorem hyperplane_card :\n    ∀ y : Label, y ≠ 0 →\n      (Finset.univ.filter fun x : Label => x ≠ 0 ∧ symp x y = 0).card\n        = 7","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.self_incidence","line_end":190,"line_start":187,"module_context_as_written":[],"name":"self_incidence","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.self_incidence","statement_as_written":"theorem self_incidence : ∀ y : Label, y ≠ 0 → symp y y = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.hyperplane_pair_card","line_end":197,"line_start":191,"module_context_as_written":[],"name":"hyperplane_pair_card","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.hyperplane_pair_card","statement_as_written":"theorem hyperplane_pair_card :\n    ∀ y z : Label, y ≠ 0 → z ≠ 0 → y ≠ z →\n      (Finset.univ.filter fun x : Label =>\n        x ≠ 0 ∧ symp x y = 0 ∧ symp x z = 0).card = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.pt","line_end":204,"line_start":198,"module_context_as_written":[],"name":"pt","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.pt","statement_as_written":"def pt (i : Fin 15) : Label","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.pt_faithful","line_end":209,"line_start":205,"module_context_as_written":[],"name":"pt_faithful","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.pt_faithful","statement_as_written":"theorem pt_faithful :\n    (∀ i : Fin 15, pt i ≠ 0) ∧\n    (∀ i j : Fin 15, pt i = pt j → i = j)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.B","line_end":214,"line_start":210,"module_context_as_written":[],"name":"B","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.B","statement_as_written":"def B : Matrix (Fin 15) (Fin 15) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.Jmat","line_end":217,"line_start":215,"module_context_as_written":[],"name":"Jmat","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.Jmat","statement_as_written":"def Jmat : Matrix (Fin 15) (Fin 15) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.B_symm_unit_diag","line_end":221,"line_start":218,"module_context_as_written":[],"name":"B_symm_unit_diag","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.B_symm_unit_diag","statement_as_written":"theorem B_symm_unit_diag :\n    B.transpose = B ∧ ∀ i : Fin 15, B i i = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.B_row_sums","line_end":226,"line_start":222,"module_context_as_written":[],"name":"B_row_sums","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.B_row_sums","statement_as_written":"theorem B_row_sums : ∀ i : Fin 15, (∑ j, B i j) = 7","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.B_mul_Bt","line_end":232,"line_start":227,"module_context_as_written":[],"name":"B_mul_Bt","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.B_mul_Bt","statement_as_written":"theorem B_mul_Bt : B * B.transpose = (4 : ℤ) • 1 + (3 : ℤ) • Jmat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.B_sq","line_end":234,"line_start":233,"module_context_as_written":[],"name":"B_sq","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.B_sq","statement_as_written":"theorem B_sq : B * B = (4 : ℤ) • 1 + (3 : ℤ) • Jmat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.B_mulVec_ones","line_end":239,"line_start":235,"module_context_as_written":[],"name":"B_mulVec_ones","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.B_mulVec_ones","statement_as_written":"theorem B_mulVec_ones :\n    B.mulVec (fun _ => 1) = fun _ => 7","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.B_traces","line_end":246,"line_start":240,"module_context_as_written":[],"name":"B_traces","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.B_traces","statement_as_written":"theorem B_traces :\n    (∑ i, B i i) = 15 ∧ (∑ i, (B * B) i i) = 105","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.J_mul_B","line_end":249,"line_start":247,"module_context_as_written":[],"name":"J_mul_B","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.J_mul_B","statement_as_written":"theorem J_mul_B : Jmat * B = (7 : ℤ) • Jmat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.B_annihilated","line_end":260,"line_start":250,"module_context_as_written":[],"name":"B_annihilated","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.B_annihilated","statement_as_written":"theorem B_annihilated :\n    (B * B - (4 : ℤ) • 1) * (B - (7 : ℤ) • 1) = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.B_multiplicity_arithmetic","line_end":267,"line_start":261,"module_context_as_written":[],"name":"B_multiplicity_arithmetic","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.B_multiplicity_arithmetic","statement_as_written":"theorem B_multiplicity_arithmetic :\n    1 + 9 + 5 = 15 ∧ 7 * 1 + 2 * 9 - 2 * 5 = 15 ∧\n    49 * 1 + 4 * 9 + 4 * 5 = 105","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.castHom","line_end":272,"line_start":268,"module_context_as_written":[],"name":"castHom","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.castHom","statement_as_written":"def castHom : ℤ →+* ℚ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.Bq","line_end":275,"line_start":273,"module_context_as_written":[],"name":"Bq","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.Bq","statement_as_written":"def Bq : Matrix (Fin 15) (Fin 15) ℚ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.Jq","line_end":278,"line_start":276,"module_context_as_written":[],"name":"Jq","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.Jq","statement_as_written":"def Jq : Matrix (Fin 15) (Fin 15) ℚ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.K","line_end":281,"line_start":279,"module_context_as_written":[],"name":"K","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.K","statement_as_written":"def K : Matrix (Fin 15) (Fin 15) ℚ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.Pi0","line_end":284,"line_start":282,"module_context_as_written":[],"name":"Pi0","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.Pi0","statement_as_written":"def Pi0 : Matrix (Fin 15) (Fin 15) ℚ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.Bq_sq","line_end":297,"line_start":285,"module_context_as_written":[],"name":"Bq_sq","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.Bq_sq","statement_as_written":"theorem Bq_sq : Bq * Bq = (4 : ℚ) • 1 + (3 : ℚ) • Jq","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.K_sq","line_end":310,"line_start":298,"module_context_as_written":[],"name":"K_sq","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.K_sq","statement_as_written":"theorem K_sq :\n    K * K = (4 / 49 : ℚ) • (1 : Matrix (Fin 15) (Fin 15) ℚ)\n      + (45 / 49 : ℚ) • Pi0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.K_row_sums","line_end":323,"line_start":311,"module_context_as_written":[],"name":"K_row_sums","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.K_row_sums","statement_as_written":"theorem K_row_sums : ∀ i : Fin 15, (∑ j, K i j) = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.chi","line_end":328,"line_start":324,"module_context_as_written":[],"name":"chi","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.chi","statement_as_written":"def chi (c x : Label) : ZMod 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.parity_count_generic","line_end":336,"line_start":329,"module_context_as_written":[],"name":"parity_count_generic","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.parity_count_generic","statement_as_written":"theorem parity_count_generic :\n    ∀ c : Label, c ≠ 0 →\n      (Finset.univ.filter fun x : Label => x ≠ 0 ∧ chi c x = 0).card = 7\n      ∧ (Finset.univ.filter fun x : Label => chi c x = 1).card = 8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.every_character_is_a_point","line_end":343,"line_start":337,"module_context_as_written":[],"name":"every_character_is_a_point","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.every_character_is_a_point","statement_as_written":"theorem every_character_is_a_point :\n    ∀ c : Label, ∃ y : Label, ∀ x : Label, chi c x = symp x y","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.y0","line_end":348,"line_start":344,"module_context_as_written":[],"name":"y0","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.y0","statement_as_written":"def y0 : Label","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.chiNSR","line_end":351,"line_start":349,"module_context_as_written":[],"name":"chiNSR","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.chiNSR","statement_as_written":"def chiNSR (x : Label) : ZMod 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.chiNSR_is_anchor_bit","line_end":355,"line_start":352,"module_context_as_written":[],"name":"chiNSR_is_anchor_bit","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.chiNSR_is_anchor_bit","statement_as_written":"theorem chiNSR_is_anchor_bit : ∀ x : Label, chiNSR x = x 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.chiNSR_count","line_end":362,"line_start":356,"module_context_as_written":[],"name":"chiNSR_count","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.chiNSR_count","statement_as_written":"theorem chiNSR_count :\n    (Finset.univ.filter fun x : Label => x ≠ 0 ∧ chiNSR x = 0).card = 7\n    ∧ (Finset.univ.filter fun x : Label => chiNSR x = 1).card = 8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.so16_decomposition","line_end":369,"line_start":363,"module_context_as_written":[],"name":"so16_decomposition","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.so16_decomposition","statement_as_written":"theorem so16_decomposition :\n    7 * 16 = 112 ∧ 8 * 16 = 128 ∧ 112 + 128 = 240 ∧\n    112 + 8 = 120 ∧ 120 + 128 = 248","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.Gdeg","line_end":379,"line_start":370,"module_context_as_written":[],"name":"Gdeg","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.Gdeg","statement_as_written":"def Gdeg : Matrix (Fin 4) (Fin 4) (ZMod 2)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.sympDeg","line_end":381,"line_start":380,"module_context_as_written":[],"name":"sympDeg","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.sympDeg","statement_as_written":"def sympDeg (x y : Label) : ZMod 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.degenerate_breaks","line_end":388,"line_start":382,"module_context_as_written":[],"name":"degenerate_breaks","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.degenerate_breaks","statement_as_written":"theorem degenerate_breaks :\n    ∃ y : Label, y ≠ 0 ∧\n      (Finset.univ.filter fun x : Label =>\n        x ≠ 0 ∧ sympDeg x y = 0).card = 15","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.sympDot","line_end":391,"line_start":389,"module_context_as_written":[],"name":"sympDot","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.sympDot","statement_as_written":"def sympDot (x y : Label) : ZMod 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean:TfptCarrier.ProjectiveHamming.non_alternating_breaks_diagonal","line_end":403,"line_start":392,"module_context_as_written":[],"name":"non_alternating_breaks_diagonal","path":"experiments/lean4-carrier-rigidity/TfptCarrier/ProjectiveHamming.lean","qualified_name":"TfptCarrier.ProjectiveHamming.non_alternating_breaks_diagonal","statement_as_written":"theorem non_alternating_breaks_diagonal :\n    (Finset.univ.filter fun x : Label =>\n      x ≠ 0 ∧ sympDot x x = 0).card = 7","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean:TfptCarrier.QuarticHalf.I_pow_four","line_end":70,"line_start":65,"module_context_as_written":[{"line":442,"source_text":"variable {R : Type*} [CommRing R]"}],"name":"I_pow_four","path":"experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean","qualified_name":"TfptCarrier.QuarticHalf.I_pow_four","statement_as_written":"theorem I_pow_four : Complex.I ^ 4 = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean:TfptCarrier.QuarticHalf.neg_I_pow_four","line_end":74,"line_start":71,"module_context_as_written":[{"line":442,"source_text":"variable {R : Type*} [CommRing R]"}],"name":"neg_I_pow_four","path":"experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean","qualified_name":"TfptCarrier.QuarticHalf.neg_I_pow_four","statement_as_written":"theorem neg_I_pow_four : (-Complex.I) ^ 4 = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean:TfptCarrier.QuarticHalf.orbit_factor_multiple","line_end":82,"line_start":75,"module_context_as_written":[{"line":442,"source_text":"variable {R : Type*} [CommRing R]"}],"name":"orbit_factor_multiple","path":"experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean","qualified_name":"TfptCarrier.QuarticHalf.orbit_factor_multiple","statement_as_written":"theorem orbit_factor_multiple (d : ℕ) (hd : d % 4 = 0) :\n    (1 : ℂ) + (-Complex.I) ^ d + (-1) ^ d + Complex.I ^ d = 4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean:TfptCarrier.QuarticHalf.orbit_factor_vanishes","line_end":97,"line_start":83,"module_context_as_written":[{"line":442,"source_text":"variable {R : Type*} [CommRing R]"}],"name":"orbit_factor_vanishes","path":"experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean","qualified_name":"TfptCarrier.QuarticHalf.orbit_factor_vanishes","statement_as_written":"theorem orbit_factor_vanishes (d : ℕ) (hd : d % 4 ≠ 0) :\n    (1 : ℂ) + (-Complex.I) ^ d + (-1) ^ d + Complex.I ^ d = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean:TfptCarrier.QuarticHalf.orbit_factor_iff","line_end":108,"line_start":98,"module_context_as_written":[{"line":442,"source_text":"variable {R : Type*} [CommRing R]"}],"name":"orbit_factor_iff","path":"experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean","qualified_name":"TfptCarrier.QuarticHalf.orbit_factor_iff","statement_as_written":"theorem orbit_factor_iff (d : ℕ) :\n    ((1 : ℂ) + (-Complex.I) ^ d + (-1) ^ d + Complex.I ^ d = 0)\n      ↔ d % 4 ≠ 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean:TfptCarrier.QuarticHalf.weight_pair_J","line_end":115,"line_start":109,"module_context_as_written":[{"line":442,"source_text":"variable {R : Type*} [CommRing R]"}],"name":"weight_pair_J","path":"experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean","qualified_name":"TfptCarrier.QuarticHalf.weight_pair_J","statement_as_written":"theorem weight_pair_J (a b : ℂ) :\n    (-b) - Complex.I * a = -Complex.I * (a - Complex.I * b)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean:TfptCarrier.QuarticHalf.orbit_powersum_vanishes","line_end":127,"line_start":116,"module_context_as_written":[{"line":442,"source_text":"variable {R : Type*} [CommRing R]"}],"name":"orbit_powersum_vanishes","path":"experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean","qualified_name":"TfptCarrier.QuarticHalf.orbit_powersum_vanishes","statement_as_written":"theorem orbit_powersum_vanishes (t : ℂ) (d : ℕ) (hd : d % 4 ≠ 0) :\n    t ^ d + (-Complex.I * t) ^ d + (-t) ^ d + (Complex.I * t) ^ d = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean:TfptCarrier.QuarticHalf.vanishing_half_mod_four","line_end":131,"line_start":128,"module_context_as_written":[{"line":442,"source_text":"variable {R : Type*} [CommRing R]"}],"name":"vanishing_half_mod_four","path":"experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean","qualified_name":"TfptCarrier.QuarticHalf.vanishing_half_mod_four","statement_as_written":"theorem vanishing_half_mod_four :\n    ∀ d ∈ ([2, 14, 18, 30] : List ℕ), d % 4 ≠ 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean:TfptCarrier.QuarticHalf.trivial_extras_mod_four","line_end":136,"line_start":132,"module_context_as_written":[{"line":442,"source_text":"variable {R : Type*} [CommRing R]"}],"name":"trivial_extras_mod_four","path":"experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean","qualified_name":"TfptCarrier.QuarticHalf.trivial_extras_mod_four","statement_as_written":"theorem trivial_extras_mod_four :\n    ∀ d ∈ ([6, 10, 22, 26] : List ℕ), d % 4 ≠ 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean:TfptCarrier.QuarticHalf.g31_half_mod_four","line_end":140,"line_start":137,"module_context_as_written":[{"line":442,"source_text":"variable {R : Type*} [CommRing R]"}],"name":"g31_half_mod_four","path":"experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean","qualified_name":"TfptCarrier.QuarticHalf.g31_half_mod_four","statement_as_written":"theorem g31_half_mod_four :\n    ∀ d ∈ ([8, 12, 20, 24] : List ℕ), d % 4 = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean:TfptCarrier.QuarticHalf.deg_we8_mod_four_split","line_end":148,"line_start":141,"module_context_as_written":[{"line":442,"source_text":"variable {R : Type*} [CommRing R]"}],"name":"deg_we8_mod_four_split","path":"experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean","qualified_name":"TfptCarrier.QuarticHalf.deg_we8_mod_four_split","statement_as_written":"theorem deg_we8_mod_four_split :\n    (([2, 8, 12, 14, 18, 20, 24, 30] : List ℕ).filter\n        fun d => d % 4 == 0) = [8, 12, 20, 24] ∧\n    (([2, 8, 12, 14, 18, 20, 24, 30] : List ℕ).filter\n        fun d => d % 4 != 0) = [2, 14, 18, 30]","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean:TfptCarrier.QuarticHalf.vanishing_half_orbit","line_end":155,"line_start":149,"module_context_as_written":[{"line":442,"source_text":"variable {R : Type*} [CommRing R]"}],"name":"vanishing_half_orbit","path":"experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean","qualified_name":"TfptCarrier.QuarticHalf.vanishing_half_orbit","statement_as_written":"theorem vanishing_half_orbit (d : ℕ) (hd : d ∈ ([2, 14, 18, 30] : List ℕ))\n    (t : ℂ) :\n    t ^ d + (-Complex.I * t) ^ d + (-t) ^ d + (Complex.I * t) ^ d = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"abbrev","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean:TfptCarrier.QuarticHalf.Z8","line_end":166,"line_start":156,"module_context_as_written":[{"line":442,"source_text":"variable {R : Type*} [CommRing R]"}],"name":"Z8","path":"experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean","qualified_name":"TfptCarrier.QuarticHalf.Z8","statement_as_written":"abbrev Z8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean:TfptCarrier.QuarticHalf.rdD8","line_end":281,"line_start":167,"module_context_as_written":[{"line":442,"source_text":"variable {R : Type*} [CommRing R]"}],"name":"rdD8","path":"experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean","qualified_name":"TfptCarrier.QuarticHalf.rdD8","statement_as_written":"def rdD8 : List (Z8)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean:TfptCarrier.QuarticHalf.rdSpinor","line_end":413,"line_start":282,"module_context_as_written":[{"line":442,"source_text":"variable {R : Type*} [CommRing R]"}],"name":"rdSpinor","path":"experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean","qualified_name":"TfptCarrier.QuarticHalf.rdSpinor","statement_as_written":"def rdSpinor : List (Z8)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean:TfptCarrier.QuarticHalf.rd240","line_end":416,"line_start":414,"module_context_as_written":[{"line":442,"source_text":"variable {R : Type*} [CommRing R]"}],"name":"rd240","path":"experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean","qualified_name":"TfptCarrier.QuarticHalf.rd240","statement_as_written":"def rd240 : List Z8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean:TfptCarrier.QuarticHalf.rd240_length","line_end":420,"line_start":417,"module_context_as_written":[{"line":442,"source_text":"variable {R : Type*} [CommRing R]"}],"name":"rd240_length","path":"experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean","qualified_name":"TfptCarrier.QuarticHalf.rd240_length","statement_as_written":"theorem rd240_length : rd240.length = 240","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean:TfptCarrier.QuarticHalf.rd240_nodup","line_end":422,"line_start":421,"module_context_as_written":[{"line":442,"source_text":"variable {R : Type*} [CommRing R]"}],"name":"rd240_nodup","path":"experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean","qualified_name":"TfptCarrier.QuarticHalf.rd240_nodup","statement_as_written":"theorem rd240_nodup : rd240.Nodup","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean:TfptCarrier.QuarticHalf.rd240_norm_eight","line_end":430,"line_start":423,"module_context_as_written":[{"line":442,"source_text":"variable {R : Type*} [CommRing R]"}],"name":"rd240_norm_eight","path":"experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean","qualified_name":"TfptCarrier.QuarticHalf.rd240_norm_eight","statement_as_written":"theorem rd240_norm_eight :\n    ∀ p ∈ rd240,\n      p.1 ^ 2 + p.2.1 ^ 2 + p.2.2.1 ^ 2 + p.2.2.2.1 ^ 2\n        + p.2.2.2.2.1 ^ 2 + p.2.2.2.2.2.1 ^ 2 + p.2.2.2.2.2.2.1 ^ 2\n        + p.2.2.2.2.2.2.2 ^ 2 = 8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean:TfptCarrier.QuarticHalf.Jt","line_end":438,"line_start":431,"module_context_as_written":[{"line":442,"source_text":"variable {R : Type*} [CommRing R]"}],"name":"Jt","path":"experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean","qualified_name":"TfptCarrier.QuarticHalf.Jt","statement_as_written":"def Jt (p : Z8) : Z8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean:TfptCarrier.QuarticHalf.rd240_mu4_closed","line_end":443,"line_start":439,"module_context_as_written":[{"line":442,"source_text":"variable {R : Type*} [CommRing R]"}],"name":"rd240_mu4_closed","path":"experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean","qualified_name":"TfptCarrier.QuarticHalf.rd240_mu4_closed","statement_as_written":"theorem rd240_mu4_closed : ∀ p ∈ rd240, Jt p ∈ rd240","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean:TfptCarrier.QuarticHalf.quartic","line_end":452,"line_start":444,"module_context_as_written":[{"line":442,"source_text":"variable {R : Type*} [CommRing R]"}],"name":"quartic","path":"experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean","qualified_name":"TfptCarrier.QuarticHalf.quartic","statement_as_written":"def quartic (x0 x1 x2 x3 x4 x5 x6 x7 : R) (p : Z8) : R","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean:TfptCarrier.QuarticHalf.quartic_d8_block","line_end":473,"line_start":453,"module_context_as_written":[{"line":442,"source_text":"variable {R : Type*} [CommRing R]"}],"name":"quartic_d8_block","path":"experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean","qualified_name":"TfptCarrier.QuarticHalf.quartic_d8_block","statement_as_written":"theorem quartic_d8_block (x0 x1 x2 x3 x4 x5 x6 x7 : R) :\n    (rdD8.map (quartic x0 x1 x2 x3 x4 x5 x6 x7)).sum\n      = 448 * (x0 ^ 4 + x1 ^ 4 + x2 ^ 4 + x3 ^ 4 + x4 ^ 4 + x5 ^ 4\n          + x6 ^ 4 + x7 ^ 4)\n        + 384 * (x0 ^ 2 * x1 ^ 2 + x0 ^ 2 * x2 ^ 2 + x0 ^ 2 * x3 ^ 2\n          + x0 ^ 2 * x4 ^ 2 + x0 ^ 2 * x5 ^ 2 + x0 ^ 2 * x6 ^ 2\n          + x0 ^ 2 * x7 ^ 2 + x1 ^ 2 * x2 ^ 2 + x1 ^ 2 * x3 ^ 2\n          + x1 ^ 2 * x4 ^ 2 + x1 ^ 2 * x5 ^ 2 + x1 ^ 2 * x6 ^ 2\n          + x1 ^ 2 * x7 ^ 2 + x2 ^ 2 * x3 ^ 2 + x2 ^ 2 * x4 ^ 2\n          + x2 ^ 2 * x5 ^ 2 + x2 ^ 2 * x6 ^ 2 + x2 ^ 2 * x7 ^ 2\n          + x3 ^ 2 * x4 ^ 2 + x3 ^ 2 * x5 ^ 2 + x3 ^ 2 * x6 ^ 2\n          + x3 ^ 2 * x7 ^ 2 + x4 ^ 2 * x5 ^ 2 + x4 ^ 2 * x6 ^ 2\n          + x4 ^ 2 * x7 ^ 2 + x5 ^ 2 * x6 ^ 2 + x5 ^ 2 * x7 ^ 2\n          + x6 ^ 2 * x7 ^ 2)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean:TfptCarrier.QuarticHalf.quartic_spinor_block","line_end":484,"line_start":474,"module_context_as_written":[{"line":442,"source_text":"variable {R : Type*} [CommRing R]"}],"name":"quartic_spinor_block","path":"experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean","qualified_name":"TfptCarrier.QuarticHalf.quartic_spinor_block","statement_as_written":"theorem quartic_spinor_block (x0 x1 x2 x3 x4 x5 x6 x7 : R) :\n    (rdSpinor.map (quartic x0 x1 x2 x3 x4 x5 x6 x7)).sum\n      = 384 * (x0 ^ 2 + x1 ^ 2 + x2 ^ 2 + x3 ^ 2 + x4 ^ 2 + x5 ^ 2\n          + x6 ^ 2 + x7 ^ 2) ^ 2\n        - 256 * (x0 ^ 4 + x1 ^ 4 + x2 ^ 4 + x3 ^ 4 + x4 ^ 4 + x5 ^ 4\n          + x6 ^ 4 + x7 ^ 4)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean:TfptCarrier.QuarticHalf.quartic_powersum","line_end":495,"line_start":485,"module_context_as_written":[{"line":442,"source_text":"variable {R : Type*} [CommRing R]"}],"name":"quartic_powersum","path":"experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean","qualified_name":"TfptCarrier.QuarticHalf.quartic_powersum","statement_as_written":"theorem quartic_powersum (x0 x1 x2 x3 x4 x5 x6 x7 : R) :\n    (rd240.map (quartic x0 x1 x2 x3 x4 x5 x6 x7)).sum\n      = 576 * (x0 ^ 2 + x1 ^ 2 + x2 ^ 2 + x3 ^ 2 + x4 ^ 2 + x5 ^ 2\n          + x6 ^ 2 + x7 ^ 2) ^ 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean:TfptCarrier.QuarticHalf.holomorphic_isotropy","line_end":504,"line_start":496,"module_context_as_written":[{"line":442,"source_text":"variable {R : Type*} [CommRing R]"}],"name":"holomorphic_isotropy","path":"experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean","qualified_name":"TfptCarrier.QuarticHalf.holomorphic_isotropy","statement_as_written":"theorem holomorphic_isotropy (w0 w1 w2 w3 : ℂ) :\n    w0 ^ 2 + (-Complex.I * w0) ^ 2 + w1 ^ 2 + (-Complex.I * w1) ^ 2\n      + w2 ^ 2 + (-Complex.I * w2) ^ 2 + w3 ^ 2 + (-Complex.I * w3) ^ 2\n      = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean:TfptCarrier.QuarticHalf.quartic_restriction_vanishes","line_end":516,"line_start":505,"module_context_as_written":[{"line":442,"source_text":"variable {R : Type*} [CommRing R]"}],"name":"quartic_restriction_vanishes","path":"experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean","qualified_name":"TfptCarrier.QuarticHalf.quartic_restriction_vanishes","statement_as_written":"theorem quartic_restriction_vanishes (w0 w1 w2 w3 : ℂ) :\n    (rd240.map (quartic w0 (-Complex.I * w0) w1 (-Complex.I * w1)\n        w2 (-Complex.I * w2) w3 (-Complex.I * w3))).sum = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/Rigidity.lean:TFPT.Carrier.Rigidity.unique_carrier_pair","line_end":47,"line_start":20,"module_context_as_written":[],"name":"unique_carrier_pair","path":"experiments/lean4-carrier-rigidity/TfptCarrier/Rigidity.lean","qualified_name":"TFPT.Carrier.Rigidity.unique_carrier_pair","statement_as_written":"theorem unique_carrier_pair\n    (qm qp : ℤ)\n    (htrace   : 3 * qm + 2 * qp = 0)\n    (hsign_m  : qm < 0)\n    (hsign_p  : 0 < qp)\n    (hgcd     : Int.gcd qm qp = 1) :\n    qm = -2 ∧ qp = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"inductive","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean:TfptCarrier.SeamApplicabilityLedger.Src","line_end":45,"line_start":37,"module_context_as_written":[{"line":111,"source_text":"axiom ContinuumChiralScalingLimit : Prop"},{"line":117,"source_text":"axiom SeamEquiv : Prop"},{"line":120,"source_text":"axiom keystone_from_existence : ContinuumChiralScalingLimit → SeamEquiv"}],"name":"Src","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean","qualified_name":"TfptCarrier.SeamApplicabilityLedger.Src","statement_as_written":"inductive Src\n  | internal\n  | external\n  deriving DecidableEq, Repr","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean:Src.isExternal","line_end":50,"line_start":46,"module_context_as_written":[{"line":111,"source_text":"axiom ContinuumChiralScalingLimit : Prop"},{"line":117,"source_text":"axiom SeamEquiv : Prop"},{"line":120,"source_text":"axiom keystone_from_existence : ContinuumChiralScalingLimit → SeamEquiv"}],"name":"Src.isExternal","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean","qualified_name":"Src.isExternal","statement_as_written":"def Src.isExternal : Src → Bool\n  | .external => true\n  | .internal => false","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean:Src.isInternal","line_end":55,"line_start":51,"module_context_as_written":[{"line":111,"source_text":"axiom ContinuumChiralScalingLimit : Prop"},{"line":117,"source_text":"axiom SeamEquiv : Prop"},{"line":120,"source_text":"axiom keystone_from_existence : ContinuumChiralScalingLimit → SeamEquiv"}],"name":"Src.isInternal","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean","qualified_name":"Src.isInternal","statement_as_written":"def Src.isInternal : Src → Bool\n  | .internal => true\n  | .external => false","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean:TfptCarrier.SeamApplicabilityLedger.sources","line_end":71,"line_start":56,"module_context_as_written":[{"line":111,"source_text":"axiom ContinuumChiralScalingLimit : Prop"},{"line":117,"source_text":"axiom SeamEquiv : Prop"},{"line":120,"source_text":"axiom keystone_from_existence : ContinuumChiralScalingLimit → SeamEquiv"}],"name":"sources","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean","qualified_name":"TfptCarrier.SeamApplicabilityLedger.sources","statement_as_written":"def sources : List Src","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean:TfptCarrier.SeamApplicabilityLedger.total_count","line_end":76,"line_start":72,"module_context_as_written":[{"line":111,"source_text":"axiom ContinuumChiralScalingLimit : Prop"},{"line":117,"source_text":"axiom SeamEquiv : Prop"},{"line":120,"source_text":"axiom keystone_from_existence : ContinuumChiralScalingLimit → SeamEquiv"}],"name":"total_count","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean","qualified_name":"TfptCarrier.SeamApplicabilityLedger.total_count","statement_as_written":"theorem total_count : sources.length = 12","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean:TfptCarrier.SeamApplicabilityLedger.internal_count","line_end":79,"line_start":77,"module_context_as_written":[{"line":111,"source_text":"axiom ContinuumChiralScalingLimit : Prop"},{"line":117,"source_text":"axiom SeamEquiv : Prop"},{"line":120,"source_text":"axiom keystone_from_existence : ContinuumChiralScalingLimit → SeamEquiv"}],"name":"internal_count","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean","qualified_name":"TfptCarrier.SeamApplicabilityLedger.internal_count","statement_as_written":"theorem internal_count : sources.countP Src.isInternal = 11","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean:TfptCarrier.SeamApplicabilityLedger.external_count","line_end":83,"line_start":80,"module_context_as_written":[{"line":111,"source_text":"axiom ContinuumChiralScalingLimit : Prop"},{"line":117,"source_text":"axiom SeamEquiv : Prop"},{"line":120,"source_text":"axiom keystone_from_existence : ContinuumChiralScalingLimit → SeamEquiv"}],"name":"external_count","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean","qualified_name":"TfptCarrier.SeamApplicabilityLedger.external_count","statement_as_written":"theorem external_count : sources.countP Src.isExternal = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean:TfptCarrier.SeamApplicabilityLedger.audit","line_end":90,"line_start":84,"module_context_as_written":[{"line":111,"source_text":"axiom ContinuumChiralScalingLimit : Prop"},{"line":117,"source_text":"axiom SeamEquiv : Prop"},{"line":120,"source_text":"axiom keystone_from_existence : ContinuumChiralScalingLimit → SeamEquiv"}],"name":"audit","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean","qualified_name":"TfptCarrier.SeamApplicabilityLedger.audit","statement_as_written":"theorem audit :\n    sources.length = 12 ∧\n    sources.countP Src.isInternal = 11 ∧\n    sources.countP Src.isExternal = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean:TfptCarrier.SeamApplicabilityLedger.rankE8","line_end":95,"line_start":91,"module_context_as_written":[{"line":111,"source_text":"axiom ContinuumChiralScalingLimit : Prop"},{"line":117,"source_text":"axiom SeamEquiv : Prop"},{"line":120,"source_text":"axiom keystone_from_existence : ContinuumChiralScalingLimit → SeamEquiv"}],"name":"rankE8","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean","qualified_name":"TfptCarrier.SeamApplicabilityLedger.rankE8","statement_as_written":"def rankE8 : Nat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean:TfptCarrier.SeamApplicabilityLedger.cChiral","line_end":97,"line_start":96,"module_context_as_written":[{"line":111,"source_text":"axiom ContinuumChiralScalingLimit : Prop"},{"line":117,"source_text":"axiom SeamEquiv : Prop"},{"line":120,"source_text":"axiom keystone_from_existence : ContinuumChiralScalingLimit → SeamEquiv"}],"name":"cChiral","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean","qualified_name":"TfptCarrier.SeamApplicabilityLedger.cChiral","statement_as_written":"def cChiral : Nat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean:TfptCarrier.SeamApplicabilityLedger.D","line_end":99,"line_start":98,"module_context_as_written":[{"line":111,"source_text":"axiom ContinuumChiralScalingLimit : Prop"},{"line":117,"source_text":"axiom SeamEquiv : Prop"},{"line":120,"source_text":"axiom keystone_from_existence : ContinuumChiralScalingLimit → SeamEquiv"}],"name":"D","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean","qualified_name":"TfptCarrier.SeamApplicabilityLedger.D","statement_as_written":"def D : Nat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean:TfptCarrier.SeamApplicabilityLedger.detE8","line_end":101,"line_start":100,"module_context_as_written":[{"line":111,"source_text":"axiom ContinuumChiralScalingLimit : Prop"},{"line":117,"source_text":"axiom SeamEquiv : Prop"},{"line":120,"source_text":"axiom keystone_from_existence : ContinuumChiralScalingLimit → SeamEquiv"}],"name":"detE8","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean","qualified_name":"TfptCarrier.SeamApplicabilityLedger.detE8","statement_as_written":"def detE8 : Nat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean:TfptCarrier.SeamApplicabilityLedger.detAnyon","line_end":103,"line_start":102,"module_context_as_written":[{"line":111,"source_text":"axiom ContinuumChiralScalingLimit : Prop"},{"line":117,"source_text":"axiom SeamEquiv : Prop"},{"line":120,"source_text":"axiom keystone_from_existence : ContinuumChiralScalingLimit → SeamEquiv"}],"name":"detAnyon","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean","qualified_name":"TfptCarrier.SeamApplicabilityLedger.detAnyon","statement_as_written":"def detAnyon : Nat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean:TfptCarrier.SeamApplicabilityLedger.mmst_range","line_end":106,"line_start":104,"module_context_as_written":[{"line":111,"source_text":"axiom ContinuumChiralScalingLimit : Prop"},{"line":117,"source_text":"axiom SeamEquiv : Prop"},{"line":120,"source_text":"axiom keystone_from_existence : ContinuumChiralScalingLimit → SeamEquiv"}],"name":"mmst_range","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean","qualified_name":"TfptCarrier.SeamApplicabilityLedger.mmst_range","statement_as_written":"theorem mmst_range : rankE8 ≤ cChiral ∧ cChiral ≤ D","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean:TfptCarrier.SeamApplicabilityLedger.npw_outside_bucket","line_end":110,"line_start":107,"module_context_as_written":[{"line":111,"source_text":"axiom ContinuumChiralScalingLimit : Prop"},{"line":117,"source_text":"axiom SeamEquiv : Prop"},{"line":120,"source_text":"axiom keystone_from_existence : ContinuumChiralScalingLimit → SeamEquiv"}],"name":"npw_outside_bucket","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean","qualified_name":"TfptCarrier.SeamApplicabilityLedger.npw_outside_bucket","statement_as_written":"theorem npw_outside_bucket : detE8 = 1 ∧ detAnyon = 4 ∧ detE8 ≠ detAnyon","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"axiom","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean:TfptCarrier.SeamApplicabilityLedger.ContinuumChiralScalingLimit","line_end":116,"line_start":111,"module_context_as_written":[{"line":111,"source_text":"axiom ContinuumChiralScalingLimit : Prop"},{"line":117,"source_text":"axiom SeamEquiv : Prop"},{"line":120,"source_text":"axiom keystone_from_existence : ContinuumChiralScalingLimit → SeamEquiv"}],"name":"ContinuumChiralScalingLimit","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean","qualified_name":"TfptCarrier.SeamApplicabilityLedger.ContinuumChiralScalingLimit","statement_as_written":"axiom ContinuumChiralScalingLimit : Prop","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"axiom","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean:TfptCarrier.SeamApplicabilityLedger.SeamEquiv","line_end":119,"line_start":117,"module_context_as_written":[{"line":111,"source_text":"axiom ContinuumChiralScalingLimit : Prop"},{"line":117,"source_text":"axiom SeamEquiv : Prop"},{"line":120,"source_text":"axiom keystone_from_existence : ContinuumChiralScalingLimit → SeamEquiv"}],"name":"SeamEquiv","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean","qualified_name":"TfptCarrier.SeamApplicabilityLedger.SeamEquiv","statement_as_written":"axiom SeamEquiv : Prop","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"axiom","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean:TfptCarrier.SeamApplicabilityLedger.keystone_from_existence","line_end":125,"line_start":120,"module_context_as_written":[{"line":111,"source_text":"axiom ContinuumChiralScalingLimit : Prop"},{"line":117,"source_text":"axiom SeamEquiv : Prop"},{"line":120,"source_text":"axiom keystone_from_existence : ContinuumChiralScalingLimit → SeamEquiv"}],"name":"keystone_from_existence","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean","qualified_name":"TfptCarrier.SeamApplicabilityLedger.keystone_from_existence","statement_as_written":"axiom keystone_from_existence : ContinuumChiralScalingLimit → SeamEquiv","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean:TfptCarrier.SeamApplicabilityLedger.keystoneReducesToOneFact","line_end":143,"line_start":126,"module_context_as_written":[{"line":111,"source_text":"axiom ContinuumChiralScalingLimit : Prop"},{"line":117,"source_text":"axiom SeamEquiv : Prop"},{"line":120,"source_text":"axiom keystone_from_existence : ContinuumChiralScalingLimit → SeamEquiv"}],"name":"keystoneReducesToOneFact","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean","qualified_name":"TfptCarrier.SeamApplicabilityLedger.keystoneReducesToOneFact","statement_as_written":"theorem keystoneReducesToOneFact : ContinuumChiralScalingLimit → SeamEquiv","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean:TFPT.Carrier.SeamDeckClosure.geom_sum_fourth_root","line_end":66,"line_start":55,"module_context_as_written":[],"name":"geom_sum_fourth_root","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean","qualified_name":"TFPT.Carrier.SeamDeckClosure.geom_sum_fourth_root","statement_as_written":"theorem geom_sum_fourth_root (ζ : ℂ) (h4 : ζ ^ 4 = 1) :\n    (∑ j ∈ range 4, ζ ^ j) = if ζ = 1 then 4 else 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean:TFPT.Carrier.SeamDeckClosure.clock_gen_pow_four","line_end":75,"line_start":67,"module_context_as_written":[],"name":"clock_gen_pow_four","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean","qualified_name":"TFPT.Carrier.SeamDeckClosure.clock_gen_pow_four","statement_as_written":"theorem clock_gen_pow_four : (-Complex.I) ^ 4 = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean:TFPT.Carrier.SeamDeckClosure.clock_gen_pow_ne_one","line_end":90,"line_start":76,"module_context_as_written":[],"name":"clock_gen_pow_ne_one","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean","qualified_name":"TFPT.Carrier.SeamDeckClosure.clock_gen_pow_ne_one","statement_as_written":"theorem clock_gen_pow_ne_one :\n    (-Complex.I) ^ 1 ≠ 1 ∧ (-Complex.I) ^ 2 ≠ 1 ∧ (-Complex.I) ^ 3 ≠ 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean:TFPT.Carrier.SeamDeckClosure.mark_sum_residue_zero","line_end":98,"line_start":91,"module_context_as_written":[],"name":"mark_sum_residue_zero","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean","qualified_name":"TFPT.Carrier.SeamDeckClosure.mark_sum_residue_zero","statement_as_written":"theorem mark_sum_residue_zero :\n    (∑ j ∈ range 4, ((-Complex.I) ^ (0 : ℕ)) ^ j) = 4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean:TFPT.Carrier.SeamDeckClosure.mark_sum_residue_nonzero","line_end":114,"line_start":99,"module_context_as_written":[],"name":"mark_sum_residue_nonzero","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean","qualified_name":"TFPT.Carrier.SeamDeckClosure.mark_sum_residue_nonzero","statement_as_written":"theorem mark_sum_residue_nonzero :\n    (∑ j ∈ range 4, ((-Complex.I) ^ (1 : ℕ)) ^ j) = 0 ∧\n    (∑ j ∈ range 4, ((-Complex.I) ^ (2 : ℕ)) ^ j) = 0 ∧\n    (∑ j ∈ range 4, ((-Complex.I) ^ (3 : ℕ)) ^ j) = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean:TFPT.Carrier.SeamDeckClosure.cls","line_end":120,"line_start":115,"module_context_as_written":[],"name":"cls","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean","qualified_name":"TFPT.Carrier.SeamDeckClosure.cls","statement_as_written":"def cls (n : ℤ) : ZMod 4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean:TFPT.Carrier.SeamDeckClosure.MarkLocal","line_end":126,"line_start":121,"module_context_as_written":[],"name":"MarkLocal","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean","qualified_name":"TFPT.Carrier.SeamDeckClosure.MarkLocal","statement_as_written":"def MarkLocal (S : Finset ℤ) : Prop","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean:TFPT.Carrier.SeamDeckClosure.markLocal_blockDiagonal","line_end":138,"line_start":127,"module_context_as_written":[],"name":"markLocal_blockDiagonal","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean","qualified_name":"TFPT.Carrier.SeamDeckClosure.markLocal_blockDiagonal","statement_as_written":"theorem markLocal_blockDiagonal {S : Finset ℤ} (h : MarkLocal S)\n    {n n' : ℤ} (hmem : (n - n') ∈ S) : cls n = cls n'","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"structure","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean:TFPT.Carrier.SeamDeckClosure.SeamDeckPremise","line_end":155,"line_start":139,"module_context_as_written":[],"name":"SeamDeckPremise","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean","qualified_name":"TFPT.Carrier.SeamDeckClosure.SeamDeckPremise","statement_as_written":"structure SeamDeckPremise","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean:TFPT.Carrier.SeamDeckClosure.SeamDeckPremise.clock_invariant","line_end":165,"line_start":156,"module_context_as_written":[],"name":"clock_invariant","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean","qualified_name":"TFPT.Carrier.SeamDeckClosure.SeamDeckPremise.clock_invariant","statement_as_written":"theorem clock_invariant (P : SeamDeckPremise)\n    {n n' : ℤ} (h : (n - n') ∈ P.modes) : cls n = cls n'","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean:TFPT.Carrier.SeamDeckClosure.SeamDeckPremise.ofMarkSet","line_end":174,"line_start":166,"module_context_as_written":[],"name":"ofMarkSet","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean","qualified_name":"TFPT.Carrier.SeamDeckClosure.SeamDeckPremise.ofMarkSet","statement_as_written":"def ofMarkSet (S : Finset ℤ) (hS : ∀ m ∈ S, cls m = 0) : SeamDeckPremise","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean:TFPT.Carrier.SeamDeckClosure.CommutesClock","line_end":181,"line_start":175,"module_context_as_written":[],"name":"CommutesClock","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean","qualified_name":"TFPT.Carrier.SeamDeckClosure.CommutesClock","statement_as_written":"def CommutesClock (M : ℤ → ℤ → ℂ) : Prop","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean:TFPT.Carrier.SeamDeckClosure.diagonal_commutesClock","line_end":191,"line_start":182,"module_context_as_written":[],"name":"diagonal_commutesClock","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean","qualified_name":"TFPT.Carrier.SeamDeckClosure.diagonal_commutesClock","statement_as_written":"theorem diagonal_commutesClock {M : ℤ → ℤ → ℂ}\n    (hd : ∀ n n', n ≠ n' → M n n' = 0) : CommutesClock M","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean:TFPT.Carrier.SeamDeckClosure.specFun","line_end":197,"line_start":192,"module_context_as_written":[],"name":"specFun","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean","qualified_name":"TFPT.Carrier.SeamDeckClosure.specFun","statement_as_written":"def specFun (g : ℂ → ℂ) (d : ℤ → ℂ) : ℤ → ℤ → ℂ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean:TFPT.Carrier.SeamDeckClosure.specFun_diagonal","line_end":201,"line_start":198,"module_context_as_written":[],"name":"specFun_diagonal","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean","qualified_name":"TFPT.Carrier.SeamDeckClosure.specFun_diagonal","statement_as_written":"theorem specFun_diagonal (g : ℂ → ℂ) (d : ℤ → ℂ) :\n    ∀ n n', n ≠ n' → specFun g d n n' = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean:TFPT.Carrier.SeamDeckClosure.flat_all_orders_clock","line_end":213,"line_start":202,"module_context_as_written":[],"name":"flat_all_orders_clock","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean","qualified_name":"TFPT.Carrier.SeamDeckClosure.flat_all_orders_clock","statement_as_written":"theorem flat_all_orders_clock (g : ℂ → ℂ) (d : ℤ → ℂ) :\n    CommutesClock (specFun g d)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean:TFPT.Carrier.SeamDeckClosure.heatDeviation","line_end":222,"line_start":214,"module_context_as_written":[],"name":"heatDeviation","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean","qualified_name":"TFPT.Carrier.SeamDeckClosure.heatDeviation","statement_as_written":"def heatDeviation {ι : Type*} (s : Finset ι) (W g : ι → ℝ) : ℝ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean:TFPT.Carrier.SeamDeckClosure.heatDeviation_nonneg","line_end":228,"line_start":223,"module_context_as_written":[],"name":"heatDeviation_nonneg","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean","qualified_name":"TFPT.Carrier.SeamDeckClosure.heatDeviation_nonneg","statement_as_written":"theorem heatDeviation_nonneg {ι : Type*} (s : Finset ι) (W g : ι → ℝ)\n    (hW : ∀ k ∈ s, 0 ≤ W k) : 0 ≤ heatDeviation s W g","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean:TFPT.Carrier.SeamDeckClosure.heatDeviation_eq_zero_iff","line_end":247,"line_start":229,"module_context_as_written":[],"name":"heatDeviation_eq_zero_iff","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean","qualified_name":"TFPT.Carrier.SeamDeckClosure.heatDeviation_eq_zero_iff","statement_as_written":"theorem heatDeviation_eq_zero_iff {ι : Type*} (s : Finset ι) (W g : ι → ℝ)\n    (hW : ∀ k ∈ s, 0 < W k) :\n    heatDeviation s W g = 0 ↔ ∀ k ∈ s, g k = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean:TFPT.Carrier.SeamDeckClosure.cls_periodic","line_end":258,"line_start":248,"module_context_as_written":[],"name":"cls_periodic","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean","qualified_name":"TFPT.Carrier.SeamDeckClosure.cls_periodic","statement_as_written":"theorem cls_periodic (n : ℤ) : cls (n + 4) = cls n","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean:TFPT.Carrier.SeamDeckClosure.cls_residues_distinct","line_end":265,"line_start":259,"module_context_as_written":[],"name":"cls_residues_distinct","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean","qualified_name":"TFPT.Carrier.SeamDeckClosure.cls_residues_distinct","statement_as_written":"theorem cls_residues_distinct :\n    cls 0 ≠ cls 1 ∧ cls 0 ≠ cls 2 ∧ cls 0 ≠ cls 3 ∧\n    cls 1 ≠ cls 2 ∧ cls 1 ≠ cls 3 ∧ cls 2 ≠ cls 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean:TfptCarrier.SeamEdgeChern.gCar","line_end":40,"line_start":36,"module_context_as_written":[],"name":"gCar","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean","qualified_name":"TfptCarrier.SeamEdgeChern.gCar","statement_as_written":"def gCar : Nat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean:TfptCarrier.SeamEdgeChern.nFam","line_end":42,"line_start":41,"module_context_as_written":[],"name":"nFam","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean","qualified_name":"TfptCarrier.SeamEdgeChern.nFam","statement_as_written":"def nFam : Nat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean:TfptCarrier.SeamEdgeChern.nMaj","line_end":44,"line_start":43,"module_context_as_written":[],"name":"nMaj","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean","qualified_name":"TfptCarrier.SeamEdgeChern.nMaj","statement_as_written":"def nMaj : Nat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean:TfptCarrier.SeamEdgeChern.nMaj_eq_16","line_end":46,"line_start":45,"module_context_as_written":[],"name":"nMaj_eq_16","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean","qualified_name":"TfptCarrier.SeamEdgeChern.nMaj_eq_16","statement_as_written":"theorem nMaj_eq_16 : nMaj = 16","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean:TfptCarrier.SeamEdgeChern.chern","line_end":56,"line_start":47,"module_context_as_written":[],"name":"chern","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean","qualified_name":"TfptCarrier.SeamEdgeChern.chern","statement_as_written":"def chern : Int → Int\n  | 1  => 1\n  | 3  => 0\n  | -1 => -1\n  | _  => 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean:TfptCarrier.SeamEdgeChern.chern_topological","line_end":58,"line_start":57,"module_context_as_written":[],"name":"chern_topological","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean","qualified_name":"TfptCarrier.SeamEdgeChern.chern_topological","statement_as_written":"theorem chern_topological : chern 1 = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean:TfptCarrier.SeamEdgeChern.chern_trivial","line_end":59,"line_start":59,"module_context_as_written":[],"name":"chern_trivial","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean","qualified_name":"TfptCarrier.SeamEdgeChern.chern_trivial","statement_as_written":"theorem chern_trivial     : chern 3 = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean:TfptCarrier.SeamEdgeChern.chern_opposite","line_end":60,"line_start":60,"module_context_as_written":[],"name":"chern_opposite","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean","qualified_name":"TfptCarrier.SeamEdgeChern.chern_opposite","statement_as_written":"theorem chern_opposite    : chern (-1) = -1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean:TfptCarrier.SeamEdgeChern.bulk_edge","line_end":64,"line_start":61,"module_context_as_written":[],"name":"bulk_edge","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean","qualified_name":"TfptCarrier.SeamEdgeChern.bulk_edge","statement_as_written":"theorem bulk_edge : (chern 1).natAbs = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean:TfptCarrier.SeamEdgeChern.cMinus","line_end":69,"line_start":65,"module_context_as_written":[],"name":"cMinus","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean","qualified_name":"TfptCarrier.SeamEdgeChern.cMinus","statement_as_written":"def cMinus : Nat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean:TfptCarrier.SeamEdgeChern.cMinus_eq_eight","line_end":71,"line_start":70,"module_context_as_written":[],"name":"cMinus_eq_eight","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean","qualified_name":"TfptCarrier.SeamEdgeChern.cMinus_eq_eight","statement_as_written":"theorem cMinus_eq_eight : cMinus = 8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean:TfptCarrier.SeamEdgeChern.two_cMinus_eq","line_end":75,"line_start":72,"module_context_as_written":[],"name":"two_cMinus_eq","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean","qualified_name":"TfptCarrier.SeamEdgeChern.two_cMinus_eq","statement_as_written":"theorem two_cMinus_eq : 2 * cMinus = nMaj * (chern 1).natAbs","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean:TfptCarrier.SeamEdgeChern.cMinus_eq_rank","line_end":79,"line_start":76,"module_context_as_written":[],"name":"cMinus_eq_rank","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean","qualified_name":"TfptCarrier.SeamEdgeChern.cMinus_eq_rank","statement_as_written":"theorem cMinus_eq_rank : cMinus = gCar + nFam","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean:TfptCarrier.SeamEdgeChern.holomorphic","line_end":84,"line_start":80,"module_context_as_written":[],"name":"holomorphic","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean","qualified_name":"TfptCarrier.SeamEdgeChern.holomorphic","statement_as_written":"theorem holomorphic : cMinus % 8 = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean:TfptCarrier.SeamEdgeChern.gcd_c_24","line_end":89,"line_start":85,"module_context_as_written":[],"name":"gcd_c_24","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean","qualified_name":"TfptCarrier.SeamEdgeChern.gcd_c_24","statement_as_written":"theorem gcd_c_24 : Nat.gcd cMinus 24 = 8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean:TfptCarrier.SeamEdgeChern.tphase_order_three","line_end":90,"line_start":90,"module_context_as_written":[],"name":"tphase_order_three","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean","qualified_name":"TfptCarrier.SeamEdgeChern.tphase_order_three","statement_as_written":"theorem tphase_order_three : 24 / Nat.gcd cMinus 24 = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean:TfptCarrier.SeamEdgeChern.ising_weights","line_end":99,"line_start":91,"module_context_as_written":[],"name":"ising_weights","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean","qualified_name":"TfptCarrier.SeamEdgeChern.ising_weights","statement_as_written":"theorem ising_weights :\n    (1 / 16 : ℚ) = 1 / 16 ∧ (1 / 2 : ℚ) = 1 / 2 ∧ (16 : ℚ) * (1 / 2) = cMinus","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify 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SeamIsE8 : Prop"},{"line":52,"source_text":"axiom kitaev_invertibility : GapPositive → InvertibleSRE"},{"line":58,"source_text":"axiom mueger_klm_holomorphy : InvertibleSRE → HolomorphicC8"},{"line":61,"source_text":"axiom conway_sloane_e8 : HolomorphicC8 → SeamIsE8"},{"line":64,"source_text":"axiom recovery_gap : GapPositive"}],"name":"HolomorphicC8","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamEquivChain.lean","qualified_name":"TfptCarrier.SeamEquivChain.HolomorphicC8","statement_as_written":"axiom HolomorphicC8 : Prop","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"axiom","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamEquivChain.lean:TfptCarrier.SeamEquivChain.SeamIsE8","line_end":51,"line_start":50,"module_context_as_written":[{"line":41,"source_text":"axiom GapPositive : Prop"},{"line":46,"source_text":"axiom InvertibleSRE : Prop"},{"line":48,"source_text":"axiom HolomorphicC8 : Prop"},{"line":50,"source_text":"axiom SeamIsE8 : Prop"},{"line":52,"source_text":"axiom kitaev_invertibility : GapPositive → InvertibleSRE"},{"line":58,"source_text":"axiom mueger_klm_holomorphy : InvertibleSRE → HolomorphicC8"},{"line":61,"source_text":"axiom conway_sloane_e8 : HolomorphicC8 → SeamIsE8"},{"line":64,"source_text":"axiom recovery_gap : GapPositive"}],"name":"SeamIsE8","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamEquivChain.lean","qualified_name":"TfptCarrier.SeamEquivChain.SeamIsE8","statement_as_written":"axiom SeamIsE8 : Prop","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify 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GapPositive"}],"name":"kitaev_invertibility","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamEquivChain.lean","qualified_name":"TfptCarrier.SeamEquivChain.kitaev_invertibility","statement_as_written":"axiom kitaev_invertibility : GapPositive → InvertibleSRE","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"axiom","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamEquivChain.lean:TfptCarrier.SeamEquivChain.mueger_klm_holomorphy","line_end":60,"line_start":58,"module_context_as_written":[{"line":41,"source_text":"axiom GapPositive : Prop"},{"line":46,"source_text":"axiom InvertibleSRE : Prop"},{"line":48,"source_text":"axiom HolomorphicC8 : Prop"},{"line":50,"source_text":"axiom SeamIsE8 : Prop"},{"line":52,"source_text":"axiom kitaev_invertibility : GapPositive → 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Prop"},{"line":46,"source_text":"axiom InvertibleSRE : Prop"},{"line":48,"source_text":"axiom HolomorphicC8 : Prop"},{"line":50,"source_text":"axiom SeamIsE8 : Prop"},{"line":52,"source_text":"axiom kitaev_invertibility : GapPositive → InvertibleSRE"},{"line":58,"source_text":"axiom mueger_klm_holomorphy : InvertibleSRE → HolomorphicC8"},{"line":61,"source_text":"axiom conway_sloane_e8 : HolomorphicC8 → SeamIsE8"},{"line":64,"source_text":"axiom recovery_gap : GapPositive"}],"name":"conway_sloane_e8","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamEquivChain.lean","qualified_name":"TfptCarrier.SeamEquivChain.conway_sloane_e8","statement_as_written":"axiom conway_sloane_e8 : HolomorphicC8 → SeamIsE8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify 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GapPositive"}],"name":"recovery_gap","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamEquivChain.lean","qualified_name":"TfptCarrier.SeamEquivChain.recovery_gap","statement_as_written":"axiom recovery_gap : GapPositive","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamEquivChain.lean:TfptCarrier.SeamEquivChain.seamEquivChain","line_end":82,"line_start":71,"module_context_as_written":[{"line":41,"source_text":"axiom GapPositive : Prop"},{"line":46,"source_text":"axiom InvertibleSRE : Prop"},{"line":48,"source_text":"axiom HolomorphicC8 : Prop"},{"line":50,"source_text":"axiom SeamIsE8 : Prop"},{"line":52,"source_text":"axiom kitaev_invertibility : GapPositive → InvertibleSRE"},{"line":58,"source_text":"axiom mueger_klm_holomorphy : InvertibleSRE → HolomorphicC8"},{"line":61,"source_text":"axiom conway_sloane_e8 : HolomorphicC8 → SeamIsE8"},{"line":64,"source_text":"axiom recovery_gap : GapPositive"}],"name":"seamEquivChain","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamEquivChain.lean","qualified_name":"TfptCarrier.SeamEquivChain.seamEquivChain","statement_as_written":"theorem seamEquivChain : SeamIsE8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamEquivChain.lean:TfptCarrier.SeamEquivChain.primariesE8","line_end":87,"line_start":83,"module_context_as_written":[{"line":41,"source_text":"axiom GapPositive : Prop"},{"line":46,"source_text":"axiom InvertibleSRE : Prop"},{"line":48,"source_text":"axiom HolomorphicC8 : Prop"},{"line":50,"source_text":"axiom SeamIsE8 : Prop"},{"line":52,"source_text":"axiom kitaev_invertibility : GapPositive → InvertibleSRE"},{"line":58,"source_text":"axiom mueger_klm_holomorphy : InvertibleSRE → HolomorphicC8"},{"line":61,"source_text":"axiom conway_sloane_e8 : HolomorphicC8 → SeamIsE8"},{"line":64,"source_text":"axiom recovery_gap : GapPositive"}],"name":"primariesE8","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamEquivChain.lean","qualified_name":"TfptCarrier.SeamEquivChain.primariesE8","statement_as_written":"def primariesE8 : Nat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify 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GapPositive"}],"name":"primariesD8","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamEquivChain.lean","qualified_name":"TfptCarrier.SeamEquivChain.primariesD8","statement_as_written":"def primariesD8 : Nat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamEquivChain.lean:TfptCarrier.SeamEquivChain.e8_unique_holomorphic","line_end":102,"line_start":90,"module_context_as_written":[{"line":41,"source_text":"axiom GapPositive : Prop"},{"line":46,"source_text":"axiom InvertibleSRE : Prop"},{"line":48,"source_text":"axiom HolomorphicC8 : Prop"},{"line":50,"source_text":"axiom SeamIsE8 : Prop"},{"line":52,"source_text":"axiom kitaev_invertibility : GapPositive → InvertibleSRE"},{"line":58,"source_text":"axiom mueger_klm_holomorphy 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CollarRealizedAsLatticePhase : Prop"},{"line":221,"source_text":"axiom SeamIsE8 : Prop"},{"line":223,"source_text":"axiom collar_realizes : CollarRealizedAsLatticePhase"},{"line":226,"source_text":"axiom seam_realisation_theorem :"},{"line":248,"source_text":"axiom CollarHasInvariants : Prop"},{"line":258,"source_text":"axiom collar_invariants : CollarHasInvariants"},{"line":260,"source_text":"axiom crossedproduct_route_theorem :"}],"name":"Z2","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamResidualAxiom.lean","qualified_name":"TfptCarrier.SeamResidualAxiom.Z2","statement_as_written":"def Z2 : Nat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify 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SeamIsE8 : Prop"},{"line":223,"source_text":"axiom collar_realizes : CollarRealizedAsLatticePhase"},{"line":226,"source_text":"axiom seam_realisation_theorem :"},{"line":248,"source_text":"axiom CollarHasInvariants : Prop"},{"line":258,"source_text":"axiom collar_invariants : CollarHasInvariants"},{"line":260,"source_text":"axiom crossedproduct_route_theorem :"}],"name":"strict_locality_forbidden","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamResidualAxiom.lean","qualified_name":"TfptCarrier.SeamResidualAxiom.strict_locality_forbidden","statement_as_written":"theorem strict_locality_forbidden : wannierWinding ≠ 0 ∧ cMinus ≠ 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify 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seam_realisation_theorem :"},{"line":248,"source_text":"axiom CollarHasInvariants : Prop"},{"line":258,"source_text":"axiom collar_invariants : CollarHasInvariants"},{"line":260,"source_text":"axiom crossedproduct_route_theorem :"}],"name":"holomorphy_selects_e8","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamResidualAxiom.lean","qualified_name":"TfptCarrier.SeamResidualAxiom.holomorphy_selects_e8","statement_as_written":"theorem holomorphy_selects_e8 :\n    forcedDimV1 = dimE8 ∧ forcedDimV1 ≠ dimA8 ∧ forcedDimV1 ≠ dimD8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify 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CollarHasInvariants : Prop"},{"line":258,"source_text":"axiom collar_invariants : CollarHasInvariants"},{"line":260,"source_text":"axiom crossedproduct_route_theorem :"}],"name":"glueEighths","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamResidualAxiom.lean","qualified_name":"TfptCarrier.SeamResidualAxiom.glueEighths","statement_as_written":"def glueEighths : List Nat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamResidualAxiom.lean:TfptCarrier.SeamResidualAxiom.glue_locality_integers","line_end":197,"line_start":195,"module_context_as_written":[{"line":214,"source_text":"axiom CollarRealizedAsLatticePhase : Prop"},{"line":221,"source_text":"axiom SeamIsE8 : Prop"},{"line":223,"source_text":"axiom collar_realizes : CollarRealizedAsLatticePhase"},{"line":226,"source_text":"axiom seam_realisation_theorem :"},{"line":248,"source_text":"axiom CollarHasInvariants : Prop"},{"line":258,"source_text":"axiom collar_invariants : CollarHasInvariants"},{"line":260,"source_text":"axiom crossedproduct_route_theorem :"}],"name":"glue_locality_integers","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamResidualAxiom.lean","qualified_name":"TfptCarrier.SeamResidualAxiom.glue_locality_integers","statement_as_written":"theorem glue_locality_integers : ∀ h ∈ glueEighths, h % 8 = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamResidualAxiom.lean:TfptCarrier.SeamResidualAxiom.klm_holomorphic","line_end":201,"line_start":198,"module_context_as_written":[{"line":214,"source_text":"axiom CollarRealizedAsLatticePhase : Prop"},{"line":221,"source_text":"axiom SeamIsE8 : Prop"},{"line":223,"source_text":"axiom collar_realizes : CollarRealizedAsLatticePhase"},{"line":226,"source_text":"axiom seam_realisation_theorem :"},{"line":248,"source_text":"axiom CollarHasInvariants : Prop"},{"line":258,"source_text":"axiom collar_invariants : CollarHasInvariants"},{"line":260,"source_text":"axiom crossedproduct_route_theorem :"}],"name":"klm_holomorphic","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamResidualAxiom.lean","qualified_name":"TfptCarrier.SeamResidualAxiom.klm_holomorphic","statement_as_written":"theorem klm_holomorphic : 4 / 2 ^ 2 = 1 ∧ 16 / 4 ^ 2 = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamResidualAxiom.lean:TfptCarrier.SeamResidualAxiom.nuInvariant","line_end":204,"line_start":202,"module_context_as_written":[{"line":214,"source_text":"axiom CollarRealizedAsLatticePhase : Prop"},{"line":221,"source_text":"axiom SeamIsE8 : Prop"},{"line":223,"source_text":"axiom collar_realizes : CollarRealizedAsLatticePhase"},{"line":226,"source_text":"axiom seam_realisation_theorem :"},{"line":248,"source_text":"axiom CollarHasInvariants : Prop"},{"line":258,"source_text":"axiom collar_invariants : CollarHasInvariants"},{"line":260,"source_text":"axiom crossedproduct_route_theorem :"}],"name":"nuInvariant","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamResidualAxiom.lean","qualified_name":"TfptCarrier.SeamResidualAxiom.nuInvariant","statement_as_written":"def nuInvariant : Nat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamResidualAxiom.lean:TfptCarrier.SeamResidualAxiom.sixteenfold_pin","line_end":207,"line_start":205,"module_context_as_written":[{"line":214,"source_text":"axiom CollarRealizedAsLatticePhase : Prop"},{"line":221,"source_text":"axiom SeamIsE8 : Prop"},{"line":223,"source_text":"axiom collar_realizes : CollarRealizedAsLatticePhase"},{"line":226,"source_text":"axiom seam_realisation_theorem :"},{"line":248,"source_text":"axiom CollarHasInvariants : Prop"},{"line":258,"source_text":"axiom collar_invariants : CollarHasInvariants"},{"line":260,"source_text":"axiom crossedproduct_route_theorem :"}],"name":"sixteenfold_pin","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamResidualAxiom.lean","qualified_name":"TfptCarrier.SeamResidualAxiom.sixteenfold_pin","statement_as_written":"theorem sixteenfold_pin : nuInvariant % 16 = 0 ∧ nuInvariant / 2 = cMinus","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamResidualAxiom.lean:TfptCarrier.SeamResidualAxiom.crossedproduct_arithmetic","line_end":213,"line_start":208,"module_context_as_written":[{"line":214,"source_text":"axiom CollarRealizedAsLatticePhase : Prop"},{"line":221,"source_text":"axiom SeamIsE8 : Prop"},{"line":223,"source_text":"axiom collar_realizes : CollarRealizedAsLatticePhase"},{"line":226,"source_text":"axiom seam_realisation_theorem :"},{"line":248,"source_text":"axiom CollarHasInvariants : Prop"},{"line":258,"source_text":"axiom collar_invariants : CollarHasInvariants"},{"line":260,"source_text":"axiom crossedproduct_route_theorem :"}],"name":"crossedproduct_arithmetic","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamResidualAxiom.lean","qualified_name":"TfptCarrier.SeamResidualAxiom.crossedproduct_arithmetic","statement_as_written":"theorem crossedproduct_arithmetic :\n    hSpinorSixteenths % 16 = 0 ∧ (∀ h ∈ glueEighths, h % 8 = 0) ∧\n    (4 / 2 ^ 2 = 1 ∧ 16 / 4 ^ 2 = 1) ∧\n    nuInvariant % 16 = 0 ∧ nuInvariant / 2 = cMinus","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"axiom","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamResidualAxiom.lean:TfptCarrier.SeamResidualAxiom.CollarRealizedAsLatticePhase","line_end":220,"line_start":214,"module_context_as_written":[{"line":214,"source_text":"axiom CollarRealizedAsLatticePhase : Prop"},{"line":221,"source_text":"axiom SeamIsE8 : Prop"},{"line":223,"source_text":"axiom collar_realizes : CollarRealizedAsLatticePhase"},{"line":226,"source_text":"axiom seam_realisation_theorem :"},{"line":248,"source_text":"axiom CollarHasInvariants : Prop"},{"line":258,"source_text":"axiom collar_invariants : CollarHasInvariants"},{"line":260,"source_text":"axiom crossedproduct_route_theorem 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CollarHasInvariants : Prop"},{"line":258,"source_text":"axiom collar_invariants : CollarHasInvariants"},{"line":260,"source_text":"axiom crossedproduct_route_theorem :"}],"name":"SeamIsE8","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamResidualAxiom.lean","qualified_name":"TfptCarrier.SeamResidualAxiom.SeamIsE8","statement_as_written":"axiom SeamIsE8 : Prop","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"axiom","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamResidualAxiom.lean:TfptCarrier.SeamResidualAxiom.collar_realizes","line_end":225,"line_start":223,"module_context_as_written":[{"line":214,"source_text":"axiom CollarRealizedAsLatticePhase : Prop"},{"line":221,"source_text":"axiom SeamIsE8 : Prop"},{"line":223,"source_text":"axiom collar_realizes : CollarRealizedAsLatticePhase"},{"line":226,"source_text":"axiom seam_realisation_theorem :"},{"line":248,"source_text":"axiom CollarHasInvariants : Prop"},{"line":258,"source_text":"axiom collar_invariants : CollarHasInvariants"},{"line":260,"source_text":"axiom crossedproduct_route_theorem :"}],"name":"collar_realizes","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamResidualAxiom.lean","qualified_name":"TfptCarrier.SeamResidualAxiom.collar_realizes","statement_as_written":"axiom collar_realizes : CollarRealizedAsLatticePhase","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify 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CollarRealizedAsLatticePhase"},{"line":226,"source_text":"axiom seam_realisation_theorem :"},{"line":248,"source_text":"axiom CollarHasInvariants : Prop"},{"line":258,"source_text":"axiom collar_invariants : CollarHasInvariants"},{"line":260,"source_text":"axiom crossedproduct_route_theorem :"}],"name":"seamResidualClosed","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamResidualAxiom.lean","qualified_name":"TfptCarrier.SeamResidualAxiom.seamResidualClosed","statement_as_written":"theorem seamResidualClosed : SeamIsE8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify 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collar_realizes : CollarRealizedAsLatticePhase"},{"line":226,"source_text":"axiom seam_realisation_theorem :"},{"line":248,"source_text":"axiom CollarHasInvariants : Prop"},{"line":258,"source_text":"axiom collar_invariants : CollarHasInvariants"},{"line":260,"source_text":"axiom crossedproduct_route_theorem :"}],"name":"crossedproduct_route_theorem","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamResidualAxiom.lean","qualified_name":"TfptCarrier.SeamResidualAxiom.crossedproduct_route_theorem","statement_as_written":"axiom crossedproduct_route_theorem :\n    CollarHasInvariants →\n    (rankE8 ≤ cMinus ∧ cMinus ≤ D) →\n    hSpinorSixteenths % 16 = 0 →\n    (detK_E8 = 1 ∧ detK_SO16 ≠ detK_E8) →\n    SeamIsE8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamResidualAxiom.lean:TfptCarrier.SeamResidualAxiom.seamResidualClosed'","line_end":285,"line_start":278,"module_context_as_written":[{"line":214,"source_text":"axiom CollarRealizedAsLatticePhase : Prop"},{"line":221,"source_text":"axiom SeamIsE8 : Prop"},{"line":223,"source_text":"axiom collar_realizes : CollarRealizedAsLatticePhase"},{"line":226,"source_text":"axiom seam_realisation_theorem :"},{"line":248,"source_text":"axiom CollarHasInvariants : Prop"},{"line":258,"source_text":"axiom collar_invariants : CollarHasInvariants"},{"line":260,"source_text":"axiom crossedproduct_route_theorem :"}],"name":"seamResidualClosed'","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamResidualAxiom.lean","qualified_name":"TfptCarrier.SeamResidualAxiom.seamResidualClosed'","statement_as_written":"theorem seamResidualClosed' : SeamIsE8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamResidualAxiom.lean:TfptCarrier.SeamResidualAxiom.residual_arithmetic","line_end":315,"line_start":286,"module_context_as_written":[{"line":214,"source_text":"axiom CollarRealizedAsLatticePhase : Prop"},{"line":221,"source_text":"axiom SeamIsE8 : Prop"},{"line":223,"source_text":"axiom collar_realizes : CollarRealizedAsLatticePhase"},{"line":226,"source_text":"axiom seam_realisation_theorem :"},{"line":248,"source_text":"axiom CollarHasInvariants : Prop"},{"line":258,"source_text":"axiom collar_invariants : CollarHasInvariants"},{"line":260,"source_text":"axiom crossedproduct_route_theorem :"}],"name":"residual_arithmetic","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamResidualAxiom.lean","qualified_name":"TfptCarrier.SeamResidualAxiom.residual_arithmetic","statement_as_written":"theorem residual_arithmetic :\n    eightC3 = 8 ∧ cMinus = eightC3 ∧ (rankE8 ≤ cMinus ∧ cMinus ≤ D) ∧\n    D / 2 = cMinus ∧ so16 + spinor = adjE8 ∧ cartan + roots = adjE8 ∧\n    rootsInt + rootsHalf = roots ∧ cartan + rootsInt = so16 ∧ rootsHalf = spinor ∧\n    (detK_E8 = 1 ∧ detK_SO16 ≠ detK_E8) ∧\n    wannierWinding = chern.natAbs ∧ wannierWinding ≠ 0 ∧ cMinus ≠ 0 ∧\n    so16Currents = so16 ∧ ramond = 256 ∧ spinorFock = spinor ∧\n    so16Currents + spinorFock = adjE8 ∧\n    (dimA8 = 8 * (1 + hvA8) ∧ dimD8 = 8 * (1 + hvD8) ∧ dimE8 = 8 * (1 + hvE8)) ∧\n    (forcedDimV1 = dimE8 ∧ forcedDimV1 ≠ dimA8 ∧ forcedDimV1 ≠ dimD8)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean:TfptCarrier.SeamRigidityForcing.clock4","line_end":46,"line_start":37,"module_context_as_written":[{"line":93,"source_text":"axiom ClockInvariantOnFullL2 : Prop"},{"line":100,"source_text":"axiom SeamRigidityClosed : Prop"},{"line":102,"source_text":"axiom rigidity_from_clock_invariance : ClockInvariantOnFullL2 → SeamRigidityClosed"}],"name":"clock4","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean","qualified_name":"TfptCarrier.SeamRigidityForcing.clock4","statement_as_written":"def clock4 : Fin 4 → ℤ × ℤ\n  | 0 => (1, 0)\n  | 1 => (0, 1)\n  | 2 => (-1, 0)\n  | 3 => (0, -1)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean:TfptCarrier.SeamRigidityForcing.commutator_zero_iff","line_end":51,"line_start":47,"module_context_as_written":[{"line":93,"source_text":"axiom ClockInvariantOnFullL2 : Prop"},{"line":100,"source_text":"axiom SeamRigidityClosed : Prop"},{"line":102,"source_text":"axiom rigidity_from_clock_invariance : ClockInvariantOnFullL2 → SeamRigidityClosed"}],"name":"commutator_zero_iff","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean","qualified_name":"TfptCarrier.SeamRigidityForcing.commutator_zero_iff","statement_as_written":"theorem commutator_zero_iff : ∀ a b : Fin 4, clock4 a = clock4 b ↔ a = b","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean:TfptCarrier.SeamRigidityForcing.clock_injective","line_end":54,"line_start":52,"module_context_as_written":[{"line":93,"source_text":"axiom ClockInvariantOnFullL2 : Prop"},{"line":100,"source_text":"axiom SeamRigidityClosed : Prop"},{"line":102,"source_text":"axiom rigidity_from_clock_invariance : ClockInvariantOnFullL2 → SeamRigidityClosed"}],"name":"clock_injective","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean","qualified_name":"TfptCarrier.SeamRigidityForcing.clock_injective","statement_as_written":"theorem clock_injective : Function.Injective clock4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean:TfptCarrier.SeamRigidityForcing.four_distinct","line_end":60,"line_start":55,"module_context_as_written":[{"line":93,"source_text":"axiom ClockInvariantOnFullL2 : Prop"},{"line":100,"source_text":"axiom SeamRigidityClosed : Prop"},{"line":102,"source_text":"axiom rigidity_from_clock_invariance : ClockInvariantOnFullL2 → SeamRigidityClosed"}],"name":"four_distinct","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean","qualified_name":"TfptCarrier.SeamRigidityForcing.four_distinct","statement_as_written":"theorem four_distinct :\n    clock4 0 ≠ clock4 1 ∧ clock4 0 ≠ clock4 2 ∧ clock4 0 ≠ clock4 3 ∧\n    clock4 1 ≠ clock4 2 ∧ clock4 1 ≠ clock4 3 ∧ clock4 2 ≠ clock4 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean:TfptCarrier.SeamRigidityForcing.marks","line_end":65,"line_start":61,"module_context_as_written":[{"line":93,"source_text":"axiom ClockInvariantOnFullL2 : Prop"},{"line":100,"source_text":"axiom SeamRigidityClosed : Prop"},{"line":102,"source_text":"axiom rigidity_from_clock_invariance : ClockInvariantOnFullL2 → SeamRigidityClosed"}],"name":"marks","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean","qualified_name":"TfptCarrier.SeamRigidityForcing.marks","statement_as_written":"def marks : Nat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean:TfptCarrier.SeamRigidityForcing.marks_eq_four","line_end":66,"line_start":66,"module_context_as_written":[{"line":93,"source_text":"axiom ClockInvariantOnFullL2 : Prop"},{"line":100,"source_text":"axiom SeamRigidityClosed : Prop"},{"line":102,"source_text":"axiom rigidity_from_clock_invariance : ClockInvariantOnFullL2 → SeamRigidityClosed"}],"name":"marks_eq_four","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean","qualified_name":"TfptCarrier.SeamRigidityForcing.marks_eq_four","statement_as_written":"theorem marks_eq_four : marks = 4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean:TfptCarrier.SeamRigidityForcing.commutant_dim_16","line_end":70,"line_start":67,"module_context_as_written":[{"line":93,"source_text":"axiom ClockInvariantOnFullL2 : Prop"},{"line":100,"source_text":"axiom SeamRigidityClosed : Prop"},{"line":102,"source_text":"axiom rigidity_from_clock_invariance : ClockInvariantOnFullL2 → SeamRigidityClosed"}],"name":"commutant_dim_16","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean","qualified_name":"TfptCarrier.SeamRigidityForcing.commutant_dim_16","statement_as_written":"theorem commutant_dim_16 : 4 * (4 * 4) = 64","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean:TfptCarrier.SeamRigidityForcing.algebra_dim_16","line_end":72,"line_start":71,"module_context_as_written":[{"line":93,"source_text":"axiom ClockInvariantOnFullL2 : Prop"},{"line":100,"source_text":"axiom SeamRigidityClosed : Prop"},{"line":102,"source_text":"axiom rigidity_from_clock_invariance : ClockInvariantOnFullL2 → SeamRigidityClosed"}],"name":"algebra_dim_16","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean","qualified_name":"TfptCarrier.SeamRigidityForcing.algebra_dim_16","statement_as_written":"theorem algebra_dim_16 : 16 * 16 = 256","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean:TfptCarrier.SeamRigidityForcing.proper_16","line_end":75,"line_start":73,"module_context_as_written":[{"line":93,"source_text":"axiom ClockInvariantOnFullL2 : Prop"},{"line":100,"source_text":"axiom SeamRigidityClosed : Prop"},{"line":102,"source_text":"axiom rigidity_from_clock_invariance : ClockInvariantOnFullL2 → SeamRigidityClosed"}],"name":"proper_16","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean","qualified_name":"TfptCarrier.SeamRigidityForcing.proper_16","statement_as_written":"theorem proper_16 : 4 * (4 * 4) < 16 * 16","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean:TfptCarrier.SeamRigidityForcing.order2_dim_16","line_end":79,"line_start":76,"module_context_as_written":[{"line":93,"source_text":"axiom ClockInvariantOnFullL2 : Prop"},{"line":100,"source_text":"axiom SeamRigidityClosed : Prop"},{"line":102,"source_text":"axiom rigidity_from_clock_invariance : ClockInvariantOnFullL2 → SeamRigidityClosed"}],"name":"order2_dim_16","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean","qualified_name":"TfptCarrier.SeamRigidityForcing.order2_dim_16","statement_as_written":"theorem order2_dim_16 : 2 * (8 * 8) = 128","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean:TfptCarrier.SeamRigidityForcing.order_discriminator_16","line_end":83,"line_start":80,"module_context_as_written":[{"line":93,"source_text":"axiom ClockInvariantOnFullL2 : Prop"},{"line":100,"source_text":"axiom SeamRigidityClosed : Prop"},{"line":102,"source_text":"axiom rigidity_from_clock_invariance : ClockInvariantOnFullL2 → SeamRigidityClosed"}],"name":"order_discriminator_16","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean","qualified_name":"TfptCarrier.SeamRigidityForcing.order_discriminator_16","statement_as_written":"theorem order_discriminator_16 : 4 * (4 * 4) < 2 * (8 * 8)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean:TfptCarrier.SeamRigidityForcing.forcing_kernel_facts","line_end":92,"line_start":84,"module_context_as_written":[{"line":93,"source_text":"axiom ClockInvariantOnFullL2 : Prop"},{"line":100,"source_text":"axiom SeamRigidityClosed : Prop"},{"line":102,"source_text":"axiom rigidity_from_clock_invariance : ClockInvariantOnFullL2 → SeamRigidityClosed"}],"name":"forcing_kernel_facts","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean","qualified_name":"TfptCarrier.SeamRigidityForcing.forcing_kernel_facts","statement_as_written":"theorem forcing_kernel_facts :\n    (∀ a b : Fin 4, clock4 a = clock4 b ↔ a = b) ∧\n    Function.Injective clock4 ∧\n    (4 * (4 * 4) = 64) ∧ (4 * (4 * 4) < 16 * 16) ∧\n    (4 * (4 * 4) < 2 * (8 * 8)) ∧ (marks = 4)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"axiom","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean:TfptCarrier.SeamRigidityForcing.ClockInvariantOnFullL2","line_end":99,"line_start":93,"module_context_as_written":[{"line":93,"source_text":"axiom ClockInvariantOnFullL2 : Prop"},{"line":100,"source_text":"axiom SeamRigidityClosed : Prop"},{"line":102,"source_text":"axiom rigidity_from_clock_invariance : ClockInvariantOnFullL2 → SeamRigidityClosed"}],"name":"ClockInvariantOnFullL2","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean","qualified_name":"TfptCarrier.SeamRigidityForcing.ClockInvariantOnFullL2","statement_as_written":"axiom ClockInvariantOnFullL2 : Prop","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"axiom","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean:TfptCarrier.SeamRigidityForcing.SeamRigidityClosed","line_end":101,"line_start":100,"module_context_as_written":[{"line":93,"source_text":"axiom ClockInvariantOnFullL2 : Prop"},{"line":100,"source_text":"axiom SeamRigidityClosed : Prop"},{"line":102,"source_text":"axiom rigidity_from_clock_invariance : ClockInvariantOnFullL2 → SeamRigidityClosed"}],"name":"SeamRigidityClosed","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean","qualified_name":"TfptCarrier.SeamRigidityForcing.SeamRigidityClosed","statement_as_written":"axiom SeamRigidityClosed : Prop","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"axiom","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean:TfptCarrier.SeamRigidityForcing.rigidity_from_clock_invariance","line_end":106,"line_start":102,"module_context_as_written":[{"line":93,"source_text":"axiom ClockInvariantOnFullL2 : Prop"},{"line":100,"source_text":"axiom SeamRigidityClosed : Prop"},{"line":102,"source_text":"axiom rigidity_from_clock_invariance : ClockInvariantOnFullL2 → SeamRigidityClosed"}],"name":"rigidity_from_clock_invariance","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean","qualified_name":"TfptCarrier.SeamRigidityForcing.rigidity_from_clock_invariance","statement_as_written":"axiom rigidity_from_clock_invariance : ClockInvariantOnFullL2 → SeamRigidityClosed","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean:TfptCarrier.SeamRigidityForcing.forcingClosesRigidity","line_end":124,"line_start":107,"module_context_as_written":[{"line":93,"source_text":"axiom ClockInvariantOnFullL2 : Prop"},{"line":100,"source_text":"axiom SeamRigidityClosed : Prop"},{"line":102,"source_text":"axiom rigidity_from_clock_invariance : ClockInvariantOnFullL2 → SeamRigidityClosed"}],"name":"forcingClosesRigidity","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean","qualified_name":"TfptCarrier.SeamRigidityForcing.forcingClosesRigidity","statement_as_written":"theorem forcingClosesRigidity : ClockInvariantOnFullL2 → SeamRigidityClosed","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamScalingLimit.lean:TfptCarrier.SeamScalingLimit.D","line_end":42,"line_start":38,"module_context_as_written":[{"line":62,"source_text":"axiom CollarGappedQuasifree : Prop"},{"line":68,"source_text":"axiom ChiralCFT_c8 : Prop"},{"line":70,"source_text":"axiom SeamIsE8 : Prop"},{"line":72,"source_text":"axiom collar_gapped : CollarGappedQuasifree"},{"line":76,"source_text":"axiom mmst_scaling_limit :"},{"line":87,"source_text":"axiom adamo_holomorphic_e8 :"}],"name":"D","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamScalingLimit.lean","qualified_name":"TfptCarrier.SeamScalingLimit.D","statement_as_written":"def D : Nat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamScalingLimit.lean:TfptCarrier.SeamScalingLimit.c","line_end":44,"line_start":43,"module_context_as_written":[{"line":62,"source_text":"axiom CollarGappedQuasifree : Prop"},{"line":68,"source_text":"axiom ChiralCFT_c8 : Prop"},{"line":70,"source_text":"axiom SeamIsE8 : Prop"},{"line":72,"source_text":"axiom collar_gapped : CollarGappedQuasifree"},{"line":76,"source_text":"axiom mmst_scaling_limit :"},{"line":87,"source_text":"axiom adamo_holomorphic_e8 :"}],"name":"c","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamScalingLimit.lean","qualified_name":"TfptCarrier.SeamScalingLimit.c","statement_as_written":"def c : Nat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamScalingLimit.lean:TfptCarrier.SeamScalingLimit.rankE8","line_end":46,"line_start":45,"module_context_as_written":[{"line":62,"source_text":"axiom CollarGappedQuasifree : Prop"},{"line":68,"source_text":"axiom ChiralCFT_c8 : Prop"},{"line":70,"source_text":"axiom SeamIsE8 : Prop"},{"line":72,"source_text":"axiom collar_gapped : CollarGappedQuasifree"},{"line":76,"source_text":"axiom mmst_scaling_limit :"},{"line":87,"source_text":"axiom adamo_holomorphic_e8 :"}],"name":"rankE8","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamScalingLimit.lean","qualified_name":"TfptCarrier.SeamScalingLimit.rankE8","statement_as_written":"def rankE8 : Nat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamScalingLimit.lean:TfptCarrier.SeamScalingLimit.cMinus","line_end":48,"line_start":47,"module_context_as_written":[{"line":62,"source_text":"axiom CollarGappedQuasifree : Prop"},{"line":68,"source_text":"axiom ChiralCFT_c8 : Prop"},{"line":70,"source_text":"axiom SeamIsE8 : Prop"},{"line":72,"source_text":"axiom collar_gapped : CollarGappedQuasifree"},{"line":76,"source_text":"axiom mmst_scaling_limit :"},{"line":87,"source_text":"axiom adamo_holomorphic_e8 :"}],"name":"cMinus","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamScalingLimit.lean","qualified_name":"TfptCarrier.SeamScalingLimit.cMinus","statement_as_written":"def cMinus : Nat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify 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adamo_holomorphic_e8 :"}],"name":"ChiralCFT_c8","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamScalingLimit.lean","qualified_name":"TfptCarrier.SeamScalingLimit.ChiralCFT_c8","statement_as_written":"axiom ChiralCFT_c8 : Prop","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"axiom","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamScalingLimit.lean:TfptCarrier.SeamScalingLimit.SeamIsE8","line_end":71,"line_start":70,"module_context_as_written":[{"line":62,"source_text":"axiom CollarGappedQuasifree : Prop"},{"line":68,"source_text":"axiom ChiralCFT_c8 : Prop"},{"line":70,"source_text":"axiom SeamIsE8 : Prop"},{"line":72,"source_text":"axiom collar_gapped : CollarGappedQuasifree"},{"line":76,"source_text":"axiom mmst_scaling_limit :"},{"line":87,"source_text":"axiom adamo_holomorphic_e8 :"}],"name":"SeamIsE8","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamScalingLimit.lean","qualified_name":"TfptCarrier.SeamScalingLimit.SeamIsE8","statement_as_written":"axiom SeamIsE8 : Prop","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"axiom","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamScalingLimit.lean:TfptCarrier.SeamScalingLimit.collar_gapped","line_end":75,"line_start":72,"module_context_as_written":[{"line":62,"source_text":"axiom CollarGappedQuasifree : Prop"},{"line":68,"source_text":"axiom ChiralCFT_c8 : Prop"},{"line":70,"source_text":"axiom SeamIsE8 : Prop"},{"line":72,"source_text":"axiom collar_gapped : CollarGappedQuasifree"},{"line":76,"source_text":"axiom mmst_scaling_limit :"},{"line":87,"source_text":"axiom adamo_holomorphic_e8 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adamo_holomorphic_e8 :"}],"name":"mmst_scaling_limit","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamScalingLimit.lean","qualified_name":"TfptCarrier.SeamScalingLimit.mmst_scaling_limit","statement_as_written":"axiom mmst_scaling_limit :\n    CollarGappedQuasifree → (rankE8 ≤ c ∧ c ≤ D) → cMinus ≠ 0 → ChiralCFT_c8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"axiom","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamScalingLimit.lean:TfptCarrier.SeamScalingLimit.adamo_holomorphic_e8","line_end":93,"line_start":87,"module_context_as_written":[{"line":62,"source_text":"axiom CollarGappedQuasifree : Prop"},{"line":68,"source_text":"axiom ChiralCFT_c8 : Prop"},{"line":70,"source_text":"axiom SeamIsE8 : Prop"},{"line":72,"source_text":"axiom collar_gapped : CollarGappedQuasifree"},{"line":76,"source_text":"axiom mmst_scaling_limit :"},{"line":87,"source_text":"axiom adamo_holomorphic_e8 :"}],"name":"adamo_holomorphic_e8","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamScalingLimit.lean","qualified_name":"TfptCarrier.SeamScalingLimit.adamo_holomorphic_e8","statement_as_written":"axiom adamo_holomorphic_e8 :\n    ChiralCFT_c8 → (detK_E8 = 1 ∧ detK_SO16 ≠ detK_E8) → SeamIsE8","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamScalingLimit.lean:TfptCarrier.SeamScalingLimit.seamScalingLimit","line_end":116,"line_start":94,"module_context_as_written":[{"line":62,"source_text":"axiom CollarGappedQuasifree : Prop"},{"line":68,"source_text":"axiom ChiralCFT_c8 : 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seam_continuum_standard_pair : SeamHasStandardPair"}],"name":"reflection_flips_translation","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamStandardPair.lean","qualified_name":"TfptCarrier.SeamStandardPair.reflection_flips_translation","statement_as_written":"theorem reflection_flips_translation : J * P * J = Pplus","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamStandardPair.lean:TfptCarrier.SeamStandardPair.standard_pair_relations","line_end":98,"line_start":92,"module_context_as_written":[{"line":99,"source_text":"axiom SeamHasStandardPair : Prop"},{"line":108,"source_text":"axiom GeometricModularFlow : Prop"},{"line":111,"source_text":"axiom borchers_wiesbrock : SeamHasStandardPair → 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Prop"},{"line":111,"source_text":"axiom borchers_wiesbrock : SeamHasStandardPair → GeometricModularFlow"},{"line":117,"source_text":"axiom seam_continuum_standard_pair : SeamHasStandardPair"}],"name":"borchers_wiesbrock","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamStandardPair.lean","qualified_name":"TfptCarrier.SeamStandardPair.borchers_wiesbrock","statement_as_written":"axiom borchers_wiesbrock : SeamHasStandardPair → GeometricModularFlow","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"axiom","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamStandardPair.lean:TfptCarrier.SeamStandardPair.seam_continuum_standard_pair","line_end":121,"line_start":117,"module_context_as_written":[{"line":99,"source_text":"axiom SeamHasStandardPair : Prop"},{"line":108,"source_text":"axiom GeometricModularFlow : Prop"},{"line":111,"source_text":"axiom borchers_wiesbrock : SeamHasStandardPair → GeometricModularFlow"},{"line":117,"source_text":"axiom seam_continuum_standard_pair : SeamHasStandardPair"}],"name":"seam_continuum_standard_pair","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamStandardPair.lean","qualified_name":"TfptCarrier.SeamStandardPair.seam_continuum_standard_pair","statement_as_written":"axiom seam_continuum_standard_pair : SeamHasStandardPair","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamStandardPair.lean:TfptCarrier.SeamStandardPair.geometricModularFlowFromStandardPair","line_end":132,"line_start":122,"module_context_as_written":[{"line":99,"source_text":"axiom SeamHasStandardPair : Prop"},{"line":108,"source_text":"axiom GeometricModularFlow : Prop"},{"line":111,"source_text":"axiom borchers_wiesbrock : SeamHasStandardPair → GeometricModularFlow"},{"line":117,"source_text":"axiom seam_continuum_standard_pair : SeamHasStandardPair"}],"name":"geometricModularFlowFromStandardPair","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamStandardPair.lean","qualified_name":"TfptCarrier.SeamStandardPair.geometricModularFlowFromStandardPair","statement_as_written":"theorem geometricModularFlowFromStandardPair : GeometricModularFlow","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamStandardPair.lean:TfptCarrier.SeamStandardPair.boost_traceless","line_end":144,"line_start":133,"module_context_as_written":[{"line":99,"source_text":"axiom SeamHasStandardPair : Prop"},{"line":108,"source_text":"axiom GeometricModularFlow : Prop"},{"line":111,"source_text":"axiom borchers_wiesbrock : SeamHasStandardPair → GeometricModularFlow"},{"line":117,"source_text":"axiom seam_continuum_standard_pair : SeamHasStandardPair"}],"name":"boost_traceless","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamStandardPair.lean","qualified_name":"TfptCarrier.SeamStandardPair.boost_traceless","statement_as_written":"theorem boost_traceless : Matrix.trace K = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"structure","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamWindingInterface.lean:TFPT.Carrier.SeamWindingInterface.SeamWindingData","line_end":90,"line_start":55,"module_context_as_written":[{"line":89,"source_text":"variable {m n : ℕ}"}],"name":"SeamWindingData","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamWindingInterface.lean","qualified_name":"TFPT.Carrier.SeamWindingInterface.SeamWindingData","statement_as_written":"structure SeamWindingData (m n : ℕ)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamWindingInterface.lean:TFPT.Carrier.SeamWindingInterface.SeamWindingData.toPrimitiveOrientedDeterminantCarrier","line_end":107,"line_start":91,"module_context_as_written":[{"line":89,"source_text":"variable {m n : ℕ}"}],"name":"toPrimitiveOrientedDeterminantCarrier","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamWindingInterface.lean","qualified_name":"TFPT.Carrier.SeamWindingInterface.SeamWindingData.toPrimitiveOrientedDeterminantCarrier","statement_as_written":"def toPrimitiveOrientedDeterminantCarrier\n    (s : SeamWindingData m n) :\n    TFPT.Carrier.OrientedDeterminantCarrier.PrimitiveOrientedDeterminantCarrier m n","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamWindingInterface.lean:TFPT.Carrier.SeamWindingInterface.SeamWindingData.ofPrimitiveOrientedDeterminantCarrier","line_end":126,"line_start":108,"module_context_as_written":[{"line":89,"source_text":"variable {m n : ℕ}"}],"name":"ofPrimitiveOrientedDeterminantCarrier","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamWindingInterface.lean","qualified_name":"TFPT.Carrier.SeamWindingInterface.SeamWindingData.ofPrimitiveOrientedDeterminantCarrier","statement_as_written":"def ofPrimitiveOrientedDeterminantCarrier\n    (c : TFPT.Carrier.OrientedDeterminantCarrier.PrimitiveOrientedDeterminantCarrier m n) :\n    SeamWindingData m n","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SeamWindingInterface.lean:TFPT.Carrier.SeamWindingInterface.SeamWindingData.sm_pair_eq","line_end":139,"line_start":127,"module_context_as_written":[{"line":89,"source_text":"variable {m n : ℕ}"}],"name":"sm_pair_eq","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SeamWindingInterface.lean","qualified_name":"TFPT.Carrier.SeamWindingInterface.SeamWindingData.sm_pair_eq","statement_as_written":"theorem sm_pair_eq (s : SeamWindingData 3 2) :\n    s.q_minus = -2 ∧ s.q_plus = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SpectralGapAttractor.lean:TFPT.Carrier.SpectralGapAttractor.iter","line_end":46,"line_start":41,"module_context_as_written":[],"name":"iter","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SpectralGapAttractor.lean","qualified_name":"TFPT.Carrier.SpectralGapAttractor.iter","statement_as_written":"def iter (r xstar x0 : ℝ) : ℕ → ℝ\n  | 0     => x0\n  | n + 1 => xstar + r * (iter r xstar x0 n - xstar)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SpectralGapAttractor.lean:TFPT.Carrier.SpectralGapAttractor.iter_sub","line_end":58,"line_start":47,"module_context_as_written":[],"name":"iter_sub","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SpectralGapAttractor.lean","qualified_name":"TFPT.Carrier.SpectralGapAttractor.iter_sub","statement_as_written":"theorem iter_sub (r xstar x0 : ℝ) (n : ℕ) :\n    iter r xstar x0 n - xstar = r ^ n * (x0 - xstar)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SpectralGapAttractor.lean:TFPT.Carrier.SpectralGapAttractor.iter_tendsto","line_end":73,"line_start":59,"module_context_as_written":[],"name":"iter_tendsto","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SpectralGapAttractor.lean","qualified_name":"TFPT.Carrier.SpectralGapAttractor.iter_tendsto","statement_as_written":"theorem iter_tendsto (r xstar x0 : ℝ) (hr0 : 0 ≤ r) (hr1 : r < 1) :\n    Tendsto (iter r xstar x0) atTop (nhds xstar)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SpectralGapAttractor.lean:TFPT.Carrier.SpectralGapAttractor.starts_agree","line_end":84,"line_start":74,"module_context_as_written":[],"name":"starts_agree","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SpectralGapAttractor.lean","qualified_name":"TFPT.Carrier.SpectralGapAttractor.starts_agree","statement_as_written":"theorem starts_agree (r xstar a b : ℝ) (n : ℕ) :\n    iter r xstar a n - iter r xstar b n = r ^ n * (a - b)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SpectralGapAttractor.lean:TFPT.Carrier.SpectralGapAttractor.no_gap_no_forget","line_end":92,"line_start":85,"module_context_as_written":[],"name":"no_gap_no_forget","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SpectralGapAttractor.lean","qualified_name":"TFPT.Carrier.SpectralGapAttractor.no_gap_no_forget","statement_as_written":"theorem no_gap_no_forget (xstar x0 : ℝ) (n : ℕ) :\n    iter 1 xstar x0 n - xstar = x0 - xstar","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SpectralGapAttractor.lean:TFPT.Carrier.SpectralGapAttractor.seam_rate_lt_one","line_end":97,"line_start":93,"module_context_as_written":[],"name":"seam_rate_lt_one","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SpectralGapAttractor.lean","qualified_name":"TFPT.Carrier.SpectralGapAttractor.seam_rate_lt_one","statement_as_written":"theorem seam_rate_lt_one : (0 : ℝ) ≤ (2 / 3) ^ 6 ∧ ((2 / 3 : ℝ)) ^ 6 < 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SpectralGapAttractor.lean:TFPT.Carrier.SpectralGapAttractor.golden_rate_lt_one","line_end":109,"line_start":98,"module_context_as_written":[],"name":"golden_rate_lt_one","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SpectralGapAttractor.lean","qualified_name":"TFPT.Carrier.SpectralGapAttractor.golden_rate_lt_one","statement_as_written":"theorem golden_rate_lt_one : (0 : ℝ) ≤ (5 + Real.sqrt 5) / 8 ∧ (5 + Real.sqrt 5) / 8 < 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SpectralGapAttractor.lean:TFPT.Carrier.SpectralGapAttractor.component_tendsto","line_end":129,"line_start":110,"module_context_as_written":[],"name":"component_tendsto","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SpectralGapAttractor.lean","qualified_name":"TFPT.Carrier.SpectralGapAttractor.component_tendsto","statement_as_written":"theorem component_tendsto (r c : ℝ) (hr : |r| < 1) :\n    Tendsto (fun n : ℕ => r ^ n * c) atTop (nhds 0)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SpectralGapAttractor.lean:TFPT.Carrier.SpectralGapAttractor.deviation_tendsto","line_end":139,"line_start":130,"module_context_as_written":[],"name":"deviation_tendsto","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SpectralGapAttractor.lean","qualified_name":"TFPT.Carrier.SpectralGapAttractor.deviation_tendsto","statement_as_written":"theorem deviation_tendsto {k : ℕ} (r c : Fin k → ℝ) (hr : ∀ i, |r i| < 1) :\n    Tendsto (fun n : ℕ => fun i => (r i) ^ n * c i) atTop (nhds (0 : Fin k → ℝ))","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SpectralGapAttractor.lean:TFPT.Carrier.SpectralGapAttractor.deviation_unique","line_end":151,"line_start":140,"module_context_as_written":[],"name":"deviation_unique","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SpectralGapAttractor.lean","qualified_name":"TFPT.Carrier.SpectralGapAttractor.deviation_unique","statement_as_written":"theorem deviation_unique {k : ℕ} (r c c' : Fin k → ℝ) (hr : ∀ i, |r i| < 1) :\n    Tendsto (fun n : ℕ => fun i => (r i) ^ n * c i - (r i) ^ n * c' i) atTop\n      (nhds (0 : Fin k → ℝ))","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SpectralGapAttractor.lean:TFPT.Carrier.SpectralGapAttractor.flavorRate","line_end":157,"line_start":152,"module_context_as_written":[],"name":"flavorRate","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SpectralGapAttractor.lean","qualified_name":"TFPT.Carrier.SpectralGapAttractor.flavorRate","statement_as_written":"noncomputable def flavorRate : Fin 2 → ℝ\n  | 0 => (2 / 3) ^ 6\n  | 1 => (1 / 3) ^ 6","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SpectralGapAttractor.lean:TFPT.Carrier.SpectralGapAttractor.flavor_rates_lt_one","line_end":163,"line_start":158,"module_context_as_written":[],"name":"flavor_rates_lt_one","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SpectralGapAttractor.lean","qualified_name":"TFPT.Carrier.SpectralGapAttractor.flavor_rates_lt_one","statement_as_written":"theorem flavor_rates_lt_one : ∀ i, |flavorRate i| < 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SpectralGapAttractor.lean:TFPT.Carrier.SpectralGapAttractor.flavor_deviation_tendsto","line_end":171,"line_start":164,"module_context_as_written":[],"name":"flavor_deviation_tendsto","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SpectralGapAttractor.lean","qualified_name":"TFPT.Carrier.SpectralGapAttractor.flavor_deviation_tendsto","statement_as_written":"theorem flavor_deviation_tendsto (c : Fin 2 → ℝ) :\n    Tendsto (fun n : ℕ => fun i => (flavorRate i) ^ n * c i) atTop (nhds (0 : Fin 2 → ℝ))","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SquareParity.lean:TfptCarrier.SquareParity.squareTerm","line_end":45,"line_start":40,"module_context_as_written":[],"name":"squareTerm","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SquareParity.lean","qualified_name":"TfptCarrier.SquareParity.squareTerm","statement_as_written":"def squareTerm (k : ℕ) : Multiset ℕ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SquareParity.lean:TfptCarrier.SquareParity.squareCycleType","line_end":49,"line_start":46,"module_context_as_written":[],"name":"squareCycleType","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SquareParity.lean","qualified_name":"TfptCarrier.SquareParity.squareCycleType","statement_as_written":"def squareCycleType (M : Multiset ℕ) : Multiset ℕ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SquareParity.lean:TfptCarrier.SquareParity.squareCycleType_cons","line_end":53,"line_start":50,"module_context_as_written":[],"name":"squareCycleType_cons","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SquareParity.lean","qualified_name":"TfptCarrier.SquareParity.squareCycleType_cons","statement_as_written":"theorem squareCycleType_cons (k : ℕ) (M : Multiset ℕ) :\n    squareCycleType (k ::ₘ M) = squareTerm k + squareCycleType M","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SquareParity.lean:TfptCarrier.SquareParity.count_squareTerm","line_end":82,"line_start":54,"module_context_as_written":[],"name":"count_squareTerm","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SquareParity.lean","qualified_name":"TfptCarrier.SquareParity.count_squareTerm","statement_as_written":"theorem count_squareTerm {L : ℕ} (hL : Even L) (k : ℕ) :\n    (squareTerm k).count L = 2 * (if 2 * L = k then 1 else 0)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SquareParity.lean:TfptCarrier.SquareParity.count_squareCycleType","line_end":94,"line_start":83,"module_context_as_written":[],"name":"count_squareCycleType","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SquareParity.lean","qualified_name":"TfptCarrier.SquareParity.count_squareCycleType","statement_as_written":"theorem count_squareCycleType (M : Multiset ℕ) {L : ℕ} (hL : Even L) :\n    (squareCycleType M).count L = 2 * M.count (2 * L)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SquareParity.lean:TfptCarrier.SquareParity.even_count_even_length","line_end":101,"line_start":95,"module_context_as_written":[],"name":"even_count_even_length","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SquareParity.lean","qualified_name":"TfptCarrier.SquareParity.even_count_even_length","statement_as_written":"theorem even_count_even_length (M : Multiset ℕ) {L : ℕ} (hL : Even L) :\n    Even ((squareCycleType M).count L)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SquareParity.lean:TfptCarrier.SquareParity.ne_of_odd_even_count","line_end":109,"line_start":102,"module_context_as_written":[],"name":"ne_of_odd_even_count","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SquareParity.lean","qualified_name":"TfptCarrier.SquareParity.ne_of_odd_even_count","statement_as_written":"theorem ne_of_odd_even_count {T : Multiset ℕ} {L : ℕ} (hL : Even L)\n    (hodd : ¬ Even (T.count L)) (M : Multiset ℕ) :\n    squareCycleType M ≠ T","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SquareParity.lean:TfptCarrier.SquareParity.census","line_end":114,"line_start":110,"module_context_as_written":[],"name":"census","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SquareParity.lean","qualified_name":"TfptCarrier.SquareParity.census","statement_as_written":"def census : Multiset ℕ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SquareParity.lean:TfptCarrier.SquareParity.census_count_twelve","line_end":117,"line_start":115,"module_context_as_written":[],"name":"census_count_twelve","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SquareParity.lean","qualified_name":"TfptCarrier.SquareParity.census_count_twelve","statement_as_written":"theorem census_count_twelve : census.count 12 = 19","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/SquareParity.lean:TfptCarrier.SquareParity.census_not_square","line_end":127,"line_start":118,"module_context_as_written":[],"name":"census_not_square","path":"experiments/lean4-carrier-rigidity/TfptCarrier/SquareParity.lean","qualified_name":"TfptCarrier.SquareParity.census_not_square","statement_as_written":"theorem census_not_square (M : Multiset ℕ) : squareCycleType M ≠ census","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/TraceProjection.lean:TFPT.Carrier.TraceProjection.trace_linear_combination_of_idempotents","line_end":68,"line_start":42,"module_context_as_written":[{"line":39,"source_text":"variable {K M : Type*}"},{"line":41,"source_text":"variable [Field K] [AddCommGroup M] [Module K M] [FiniteDimensional K M]"}],"name":"trace_linear_combination_of_idempotents","path":"experiments/lean4-carrier-rigidity/TfptCarrier/TraceProjection.lean","qualified_name":"TFPT.Carrier.TraceProjection.trace_linear_combination_of_idempotents","statement_as_written":"theorem trace_linear_combination_of_idempotents\n    (Pm Pp : M →ₗ[K] M)\n    (hm : IsIdempotentElem Pm)\n    (hp : IsIdempotentElem Pp)\n    (a b : K) :\n    LinearMap.trace K M (a • Pm + b • Pp)\n      = a * (Module.finrank K (LinearMap.range Pm) : K)\n        + b * (Module.finrank K (LinearMap.range Pp) : K)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/TraceProjection.lean:TFPT.Carrier.TraceProjection.trace_carrier_Y_eq_zero","line_end":101,"line_start":69,"module_context_as_written":[{"line":39,"source_text":"variable {K M : Type*}"},{"line":41,"source_text":"variable [Field K] [AddCommGroup M] [Module K M] [FiniteDimensional K M]"}],"name":"trace_carrier_Y_eq_zero","path":"experiments/lean4-carrier-rigidity/TfptCarrier/TraceProjection.lean","qualified_name":"TFPT.Carrier.TraceProjection.trace_carrier_Y_eq_zero","statement_as_written":"theorem trace_carrier_Y_eq_zero\n    [CharZero K]\n    (Pm Pp : M →ₗ[K] M)\n    (hm : IsIdempotentElem Pm)\n    (hp : IsIdempotentElem Pp)\n    (hrank_m : Module.finrank K (LinearMap.range Pm) = 3)\n    (hrank_p : Module.finrank K (LinearMap.range Pp) = 2) :\n    LinearMap.trace K M (-((1 : K)/3) • Pm + ((1 : K)/2) • Pp) = 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WallReducedMinuscule.lean:TfptCarrier.WallReducedMinuscule.wallDegs","line_end":34,"line_start":30,"module_context_as_written":[],"name":"wallDegs","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WallReducedMinuscule.lean","qualified_name":"TfptCarrier.WallReducedMinuscule.wallDegs","statement_as_written":"def wallDegs : List Int","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WallReducedMinuscule.lean:TfptCarrier.WallReducedMinuscule.wobblyDegs","line_end":37,"line_start":35,"module_context_as_written":[],"name":"wobblyDegs","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WallReducedMinuscule.lean","qualified_name":"TfptCarrier.WallReducedMinuscule.wobblyDegs","statement_as_written":"def wobblyDegs : List Int","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WallReducedMinuscule.lean:TfptCarrier.WallReducedMinuscule.posPairings","line_end":43,"line_start":38,"module_context_as_written":[],"name":"posPairings","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WallReducedMinuscule.lean","qualified_name":"TfptCarrier.WallReducedMinuscule.posPairings","statement_as_written":"def posPairings : List Int → List Int\n  | [a, b, c] => [a - b, b - c, a - c]\n  | _ => []","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WallReducedMinuscule.lean:TfptCarrier.WallReducedMinuscule.allPairings","line_end":47,"line_start":44,"module_context_as_written":[],"name":"allPairings","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WallReducedMinuscule.lean","qualified_name":"TfptCarrier.WallReducedMinuscule.allPairings","statement_as_written":"def allPairings (d : List Int) : List Int","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WallReducedMinuscule.lean:TfptCarrier.WallReducedMinuscule.reducedB","line_end":52,"line_start":48,"module_context_as_written":[],"name":"reducedB","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WallReducedMinuscule.lean","qualified_name":"TfptCarrier.WallReducedMinuscule.reducedB","statement_as_written":"def reducedB (d : List Int) : Bool","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WallReducedMinuscule.lean:TfptCarrier.WallReducedMinuscule.affineLength","line_end":56,"line_start":53,"module_context_as_written":[],"name":"affineLength","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WallReducedMinuscule.lean","qualified_name":"TfptCarrier.WallReducedMinuscule.affineLength","statement_as_written":"def affineLength (d : List Int) : Nat","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WallReducedMinuscule.lean:TfptCarrier.WallReducedMinuscule.wall_pos_pairings","line_end":62,"line_start":57,"module_context_as_written":[],"name":"wall_pos_pairings","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WallReducedMinuscule.lean","qualified_name":"TfptCarrier.WallReducedMinuscule.wall_pos_pairings","statement_as_written":"theorem wall_pos_pairings : posPairings wallDegs = [1, 0, 1]","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WallReducedMinuscule.lean:TfptCarrier.WallReducedMinuscule.wall_reduced","line_end":66,"line_start":63,"module_context_as_written":[],"name":"wall_reduced","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WallReducedMinuscule.lean","qualified_name":"TfptCarrier.WallReducedMinuscule.wall_reduced","statement_as_written":"theorem wall_reduced : reducedB wallDegs = true","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WallReducedMinuscule.lean:TfptCarrier.WallReducedMinuscule.wall_length","line_end":69,"line_start":67,"module_context_as_written":[],"name":"wall_length","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WallReducedMinuscule.lean","qualified_name":"TfptCarrier.WallReducedMinuscule.wall_length","statement_as_written":"theorem wall_length : affineLength wallDegs = 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WallReducedMinuscule.lean:TfptCarrier.WallReducedMinuscule.wall_sum","line_end":72,"line_start":70,"module_context_as_written":[],"name":"wall_sum","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WallReducedMinuscule.lean","qualified_name":"TfptCarrier.WallReducedMinuscule.wall_sum","statement_as_written":"theorem wall_sum : wallDegs.sum = 4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WallReducedMinuscule.lean:TfptCarrier.WallReducedMinuscule.wobbly_not_reduced","line_end":78,"line_start":73,"module_context_as_written":[],"name":"wobbly_not_reduced","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WallReducedMinuscule.lean","qualified_name":"TfptCarrier.WallReducedMinuscule.wobbly_not_reduced","statement_as_written":"theorem wobbly_not_reduced : reducedB wobblyDegs = false","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WallReducedMinuscule.lean:TfptCarrier.WallReducedMinuscule.wobbly_length","line_end":81,"line_start":79,"module_context_as_written":[],"name":"wobbly_length","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WallReducedMinuscule.lean","qualified_name":"TfptCarrier.WallReducedMinuscule.wobbly_length","statement_as_written":"theorem wobbly_length : affineLength wobblyDegs = 6","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WallReducedMinuscule.lean:TfptCarrier.WallReducedMinuscule.wall_certificate","line_end":97,"line_start":82,"module_context_as_written":[],"name":"wall_certificate","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WallReducedMinuscule.lean","qualified_name":"TfptCarrier.WallReducedMinuscule.wall_certificate","statement_as_written":"theorem wall_certificate :\n    reducedB wallDegs = true ∧\n    affineLength wallDegs = 2 ∧\n    wallDegs.sum = 4 ∧\n    reducedB wobblyDegs = false","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WallRegularSemisimple.lean:TfptCarrier.WallRegularSemisimple.cuspWeights3","line_end":30,"line_start":28,"module_context_as_written":[],"name":"cuspWeights3","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WallRegularSemisimple.lean","qualified_name":"TfptCarrier.WallRegularSemisimple.cuspWeights3","statement_as_written":"def cuspWeights3 : List Int","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WallRegularSemisimple.lean:TfptCarrier.WallRegularSemisimple.residueSpec","line_end":33,"line_start":31,"module_context_as_written":[],"name":"residueSpec","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WallRegularSemisimple.lean","qualified_name":"TfptCarrier.WallRegularSemisimple.residueSpec","statement_as_written":"def residueSpec : List Int","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WallRegularSemisimple.lean:TfptCarrier.WallRegularSemisimple.irregularSpec","line_end":36,"line_start":34,"module_context_as_written":[],"name":"irregularSpec","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WallRegularSemisimple.lean","qualified_name":"TfptCarrier.WallRegularSemisimple.irregularSpec","statement_as_written":"def irregularSpec : List Int","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WallRegularSemisimple.lean:TfptCarrier.WallRegularSemisimple.cusp_distinct","line_end":41,"line_start":37,"module_context_as_written":[],"name":"cusp_distinct","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WallRegularSemisimple.lean","qualified_name":"TfptCarrier.WallRegularSemisimple.cusp_distinct","statement_as_written":"theorem cusp_distinct : cuspWeights3.Nodup","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WallRegularSemisimple.lean:TfptCarrier.WallRegularSemisimple.residue_spec","line_end":44,"line_start":42,"module_context_as_written":[],"name":"residue_spec","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WallRegularSemisimple.lean","qualified_name":"TfptCarrier.WallRegularSemisimple.residue_spec","statement_as_written":"theorem residue_spec : residueSpec = [1, 2, 3]","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WallRegularSemisimple.lean:TfptCarrier.WallRegularSemisimple.residue_regular_semisimple","line_end":48,"line_start":45,"module_context_as_written":[],"name":"residue_regular_semisimple","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WallRegularSemisimple.lean","qualified_name":"TfptCarrier.WallRegularSemisimple.residue_regular_semisimple","statement_as_written":"theorem residue_regular_semisimple : residueSpec.Nodup","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WallRegularSemisimple.lean:TfptCarrier.WallRegularSemisimple.irregular_control","line_end":51,"line_start":49,"module_context_as_written":[],"name":"irregular_control","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WallRegularSemisimple.lean","qualified_name":"TfptCarrier.WallRegularSemisimple.irregular_control","statement_as_written":"theorem irregular_control : ¬ irregularSpec.Nodup","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WallRegularSemisimple.lean:TfptCarrier.WallRegularSemisimple.wall_regular_and_reduced","line_end":69,"line_start":52,"module_context_as_written":[],"name":"wall_regular_and_reduced","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WallRegularSemisimple.lean","qualified_name":"TfptCarrier.WallRegularSemisimple.wall_regular_and_reduced","statement_as_written":"theorem wall_regular_and_reduced :\n    residueSpec.Nodup ∧\n    residueSpec = [1, 2, 3] ∧\n    cuspWeights3.Nodup ∧\n    WallReducedMinuscule.reducedB WallReducedMinuscule.wallDegs = true","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.Sh","line_end":86,"line_start":77,"module_context_as_written":[],"name":"Sh","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.Sh","statement_as_written":"def Sh : Matrix (Fin 12) (Fin 12) ℤ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.ns_shift_order","line_end":90,"line_start":87,"module_context_as_written":[],"name":"ns_shift_order","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.ns_shift_order","statement_as_written":"theorem ns_shift_order : Sh ^ 12 = -1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.mu4_order_forced_by_ns","line_end":96,"line_start":91,"module_context_as_written":[],"name":"mu4_order_forced_by_ns","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.mu4_order_forced_by_ns","statement_as_written":"theorem mu4_order_forced_by_ns :\n    (Sh ^ 6) * (Sh ^ 6) = -1 ∧ (Sh ^ 6) ^ 4 = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.deck_layer","line_end":102,"line_start":97,"module_context_as_written":[],"name":"deck_layer","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.deck_layer","statement_as_written":"theorem deck_layer :\n    (Sh ^ 4) ^ 3 = -1 ∧ (Sh ^ 4) * (Sh ^ 6) = (Sh ^ 6) * (Sh ^ 4)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"abbrev","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.Zi","line_end":107,"line_start":103,"module_context_as_written":[],"name":"Zi","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.Zi","statement_as_written":"abbrev Zi : Type","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.gi","line_end":110,"line_start":108,"module_context_as_written":[],"name":"gi","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.gi","statement_as_written":"def gi : Zi","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.gi_pow","line_end":112,"line_start":111,"module_context_as_written":[],"name":"gi_pow","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.gi_pow","statement_as_written":"theorem gi_pow : gi * gi = -1 ∧ gi * gi * gi * gi = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.gconj","line_end":115,"line_start":113,"module_context_as_written":[],"name":"gconj","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.gconj","statement_as_written":"def gconj (z : Zi) : Zi","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.adj","line_end":120,"line_start":116,"module_context_as_written":[],"name":"adj","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.adj","statement_as_written":"def adj {n : ℕ} (M : Matrix (Fin n) (Fin n) Zi) :\n    Matrix (Fin n) (Fin n) Zi","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"abbrev","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.M4","line_end":123,"line_start":121,"module_context_as_written":[],"name":"M4","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.M4","statement_as_written":"abbrev M4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.U","line_end":132,"line_start":124,"module_context_as_written":[],"name":"U","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.U","statement_as_written":"def U : M4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.U_unitary","line_end":135,"line_start":133,"module_context_as_written":[],"name":"U_unitary","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.U_unitary","statement_as_written":"theorem U_unitary : U * adj U = 1 ∧ adj U * U = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.U_order_four","line_end":139,"line_start":136,"module_context_as_written":[],"name":"U_order_four","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.U_order_four","statement_as_written":"theorem U_order_four : U ^ 4 = 1 ∧ U ^ 2 ≠ 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.Upow","line_end":142,"line_start":140,"module_context_as_written":[],"name":"Upow","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.Upow","statement_as_written":"def Upow : Fin 4 → M4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.chi","line_end":149,"line_start":143,"module_context_as_written":[],"name":"chi","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.chi","statement_as_written":"def chi : Fin 4 → Fin 4 → Zi","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.Psec","line_end":153,"line_start":150,"module_context_as_written":[],"name":"Psec","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.Psec","statement_as_written":"def Psec : Fin 4 → M4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.Psec_complete","line_end":159,"line_start":154,"module_context_as_written":[],"name":"Psec_complete","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.Psec_complete","statement_as_written":"theorem Psec_complete :\n    (∑ q, Psec q) = 1 ∧\n    ∀ q q' : Fin 4, Psec q * Psec q' = if q = q' then Psec q else 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.sector_projection_fourier","line_end":166,"line_start":160,"module_context_as_written":[],"name":"sector_projection_fourier","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.sector_projection_fourier","statement_as_written":"theorem sector_projection_fourier :\n    ∀ q : Fin 4, (4 : Zi) • Psec q = ∑ j, gconj (chi q j) • Upow j","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.Efix","line_end":170,"line_start":167,"module_context_as_written":[],"name":"Efix","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.Efix","statement_as_written":"def Efix (x : M4) : M4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.Eu","line_end":174,"line_start":171,"module_context_as_written":[],"name":"Eu","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.Eu","statement_as_written":"def Eu (a b : Fin 4) : M4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.pinching_eq_group_average","line_end":183,"line_start":175,"module_context_as_written":[],"name":"pinching_eq_group_average","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.pinching_eq_group_average","statement_as_written":"theorem pinching_eq_group_average :\n    ∀ a b : Fin 4,\n      (∑ j, Upow j * Eu a b * adj (Upow j))\n        = (4 : Zi) • Efix (Eu a b)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.Efix_unital","line_end":186,"line_start":184,"module_context_as_written":[],"name":"Efix_unital","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.Efix_unital","statement_as_written":"theorem Efix_unital : Efix 1 = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.Efix_diagonal","line_end":193,"line_start":187,"module_context_as_written":[],"name":"Efix_diagonal","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.Efix_diagonal","statement_as_written":"theorem Efix_diagonal :\n    ∀ a b : Fin 4, Efix (Eu a b) = if a = b then Eu a a else 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.Efix_idempotent","line_end":197,"line_start":194,"module_context_as_written":[],"name":"Efix_idempotent","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.Efix_idempotent","statement_as_written":"theorem Efix_idempotent :\n    ∀ a b : Fin 4, Efix (Efix (Eu a b)) = Efix (Eu a b)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.Efix_range_fixed","line_end":201,"line_start":198,"module_context_as_written":[],"name":"Efix_range_fixed","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.Efix_range_fixed","statement_as_written":"theorem Efix_range_fixed :\n    ∀ a b : Fin 4, U * Efix (Eu a b) = Efix (Eu a b) * U","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.fixed_units_are_diagonal","line_end":206,"line_start":202,"module_context_as_written":[],"name":"fixed_units_are_diagonal","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.fixed_units_are_diagonal","statement_as_written":"theorem fixed_units_are_diagonal :\n    ∀ a b : Fin 4, (U * Eu a b = Eu a b * U) ↔ a = b","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.quasibasis","line_end":219,"line_start":207,"module_context_as_written":[],"name":"quasibasis","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.quasibasis","statement_as_written":"def quasibasis : List M4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.quasibasis_length","line_end":221,"line_start":220,"module_context_as_written":[],"name":"quasibasis_length","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.quasibasis_length","statement_as_written":"theorem quasibasis_length : quasibasis.length = 13","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.quasibasis_reconstruction","line_end":228,"line_start":222,"module_context_as_written":[],"name":"quasibasis_reconstruction","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.quasibasis_reconstruction","statement_as_written":"theorem quasibasis_reconstruction :\n    ∀ a b : Fin 4,\n      (quasibasis.map fun v => v * Efix (adj v * Eu a b)).sum\n        = Eu a b","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.watatani_index_four","line_end":234,"line_start":229,"module_context_as_written":[],"name":"watatani_index_four","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.watatani_index_four","statement_as_written":"theorem watatani_index_four :\n    (quasibasis.map fun v => v * adj v).sum = (4 : Zi) • 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.index_eq_ramified_norm_sq","line_end":240,"line_start":235,"module_context_as_written":[],"name":"index_eq_ramified_norm_sq","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.index_eq_ramified_norm_sq","statement_as_written":"theorem index_eq_ramified_norm_sq : ((⟨1, 1⟩ : Zi).norm) ^ 2 = 4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.PsecQ","line_end":246,"line_start":241,"module_context_as_written":[],"name":"PsecQ","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.PsecQ","statement_as_written":"def PsecQ : Fin 4 → Matrix (Fin 4) (Fin 4) ℚ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.EfixQ","line_end":250,"line_start":247,"module_context_as_written":[],"name":"EfixQ","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.EfixQ","statement_as_written":"def EfixQ (x : Matrix (Fin 4) (Fin 4) ℚ) : Matrix (Fin 4) (Fin 4) ℚ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.Jmix","line_end":254,"line_start":251,"module_context_as_written":[],"name":"Jmix","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.Jmix","statement_as_written":"def Jmix : Matrix (Fin 4) (Fin 4) ℚ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.EfixQ_mixing","line_end":261,"line_start":255,"module_context_as_written":[],"name":"EfixQ_mixing","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.EfixQ_mixing","statement_as_written":"theorem EfixQ_mixing : EfixQ Jmix = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.Lap4","line_end":265,"line_start":262,"module_context_as_written":[],"name":"Lap4","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.Lap4","statement_as_written":"def Lap4 : Matrix (Fin 4) (Fin 4) ℚ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.pp_pencil_is_laplacian","line_end":274,"line_start":266,"module_context_as_written":[],"name":"pp_pencil_is_laplacian","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.pp_pencil_is_laplacian","statement_as_written":"theorem pp_pencil_is_laplacian : (4 : ℚ) • EfixQ Jmix - Jmix = Lap4","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.pp_pencil_sos","line_end":284,"line_start":275,"module_context_as_written":[],"name":"pp_pencil_sos","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.pp_pencil_sos","statement_as_written":"theorem pp_pencil_sos (v : Fin 4 → ℚ) :\n    ∑ j, ∑ k, v j * ((4 : ℚ) • EfixQ Jmix - Jmix) j k * v k\n      = (v 0 - v 1) ^ 2 + (v 0 - v 2) ^ 2 + (v 0 - v 3) ^ 2\n        + (v 1 - v 2) ^ 2 + (v 1 - v 3) ^ 2 + (v 2 - v 3) ^ 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.pp_bound_at_quarter","line_end":290,"line_start":285,"module_context_as_written":[],"name":"pp_bound_at_quarter","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.pp_bound_at_quarter","statement_as_written":"theorem pp_bound_at_quarter (v : Fin 4 → ℚ) :\n    0 ≤ ∑ j, ∑ k, v j * ((4 : ℚ) • EfixQ Jmix - Jmix) j k * v k","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.onesQ","line_end":294,"line_start":291,"module_context_as_written":[],"name":"onesQ","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.onesQ","statement_as_written":"def onesQ : Fin 4 → ℚ","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.pp_pencil_at_mixing","line_end":302,"line_start":295,"module_context_as_written":[],"name":"pp_pencil_at_mixing","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.pp_pencil_at_mixing","statement_as_written":"theorem pp_pencil_at_mixing (lam : ℚ) :\n    ∑ j, ∑ k, onesQ j * (EfixQ Jmix - lam • Jmix) j k * onesQ k\n      = 4 - 16 * lam","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.pp_constant_sharp","line_end":310,"line_start":303,"module_context_as_written":[],"name":"pp_constant_sharp","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.pp_constant_sharp","statement_as_written":"theorem pp_constant_sharp (lam : ℚ) (hl : 1 / 4 < lam) :\n    ∑ j, ∑ k, onesQ j * (EfixQ Jmix - lam • Jmix) j k * onesQ k < 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.Eu2","line_end":316,"line_start":311,"module_context_as_written":[],"name":"Eu2","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.Eu2","statement_as_written":"def Eu2 (a b : Fin 2) : Matrix (Fin 2) (Fin 2) Zi","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.Efix2","line_end":320,"line_start":317,"module_context_as_written":[],"name":"Efix2","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.Efix2","statement_as_written":"def Efix2 (x : Matrix (Fin 2) (Fin 2) Zi) : Matrix (Fin 2) (Fin 2) Zi","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.quasibasis2","line_end":324,"line_start":321,"module_context_as_written":[],"name":"quasibasis2","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.quasibasis2","statement_as_written":"def quasibasis2 : List (Matrix (Fin 2) (Fin 2) Zi)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.watatani_index_two","line_end":333,"line_start":325,"module_context_as_written":[],"name":"watatani_index_two","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.watatani_index_two","statement_as_written":"theorem watatani_index_two :\n    (quasibasis2.map fun v => v * adj v).sum = (2 : Zi) • 1 ∧\n    ∀ a b : Fin 2,\n      (quasibasis2.map fun v => v * Efix2 (adj v * Eu2 a b)).sum\n        = Eu2 a b","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.Eu3","line_end":337,"line_start":334,"module_context_as_written":[],"name":"Eu3","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.Eu3","statement_as_written":"def Eu3 (a b : Fin 3) : Matrix (Fin 3) (Fin 3) Zi","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.Efix3","line_end":341,"line_start":338,"module_context_as_written":[],"name":"Efix3","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.Efix3","statement_as_written":"def Efix3 (x : Matrix (Fin 3) (Fin 3) Zi) : Matrix (Fin 3) (Fin 3) Zi","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.quasibasis3","line_end":345,"line_start":342,"module_context_as_written":[],"name":"quasibasis3","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.quasibasis3","statement_as_written":"def quasibasis3 : List (Matrix (Fin 3) (Fin 3) Zi)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.watatani_index_three","line_end":355,"line_start":346,"module_context_as_written":[],"name":"watatani_index_three","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.watatani_index_three","statement_as_written":"theorem watatani_index_three :\n    (quasibasis3.map fun v => v * adj v).sum = (3 : Zi) • 1 ∧\n    ∀ a b : Fin 3,\n      (quasibasis3.map fun v => v * Efix3 (adj v * Eu3 a b)).sum\n        = Eu3 a b","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.character_orthogonality","line_end":368,"line_start":356,"module_context_as_written":[],"name":"character_orthogonality","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.character_orthogonality","statement_as_written":"theorem character_orthogonality :\n    ∀ a b : Fin 4,\n      (∑ k, chi k a * gconj (chi k b)) = if a = b then 4 else 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean:TfptCarrier.WatataniIndexFour.Upow_diag_eq_chi","line_end":376,"line_start":369,"module_context_as_written":[],"name":"Upow_diag_eq_chi","path":"experiments/lean4-carrier-rigidity/TfptCarrier/WatataniIndexFour.lean","qualified_name":"TfptCarrier.WatataniIndexFour.Upow_diag_eq_chi","statement_as_written":"theorem Upow_diag_eq_chi : ∀ j a : Fin 4, Upow j a a = chi a j","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"structure","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaPrimitive.lean:TFPT.Carrier.YukawaPrimitive.PrimitiveIndecomposableYukawaCoupling","line_end":112,"line_start":80,"module_context_as_written":[{"line":111,"source_text":"variable {K E : Type*} [Field K] [AddCommGroup E] [Module K E]"}],"name":"PrimitiveIndecomposableYukawaCoupling","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaPrimitive.lean","qualified_name":"TFPT.Carrier.YukawaPrimitive.PrimitiveIndecomposableYukawaCoupling","statement_as_written":"structure PrimitiveIndecomposableYukawaCoupling\n    (K E : Type*) [Field K]\n    [AddCommGroup E] [Module K E]","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"lemma","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaPrimitive.lean:TFPT.Carrier.YukawaPrimitive.PrimitiveIndecomposableYukawaCoupling.nat_dim_eq_choose_two_self","line_end":138,"line_start":113,"module_context_as_written":[{"line":111,"source_text":"variable {K E : Type*} [Field K] [AddCommGroup E] [Module K E]"}],"name":"nat_dim_eq_choose_two_self","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaPrimitive.lean","qualified_name":"TFPT.Carrier.YukawaPrimitive.PrimitiveIndecomposableYukawaCoupling.nat_dim_eq_choose_two_self","statement_as_written":"private lemma nat_dim_eq_choose_two_self (n : ℕ) (hn : 0 < n)\n    (h : n = n.choose 2) : n = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaPrimitive.lean:TFPT.Carrier.YukawaPrimitive.PrimitiveIndecomposableYukawaCoupling.finrank_E_eq_three","line_end":172,"line_start":139,"module_context_as_written":[{"line":111,"source_text":"variable {K E : Type*} [Field K] [AddCommGroup E] [Module K E]"}],"name":"finrank_E_eq_three","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaPrimitive.lean","qualified_name":"TFPT.Carrier.YukawaPrimitive.PrimitiveIndecomposableYukawaCoupling.finrank_E_eq_three","statement_as_written":"theorem finrank_E_eq_three\n    [FiniteDimensional K E]\n    (Y : PrimitiveIndecomposableYukawaCoupling K E) :\n    Module.finrank K E = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaPrimitive.lean:TFPT.Carrier.YukawaPrimitive.PrimitiveIndecomposableYukawaCoupling.toYukawaTopForm","line_end":192,"line_start":173,"module_context_as_written":[{"line":111,"source_text":"variable {K E : Type*} [Field K] [AddCommGroup E] [Module K E]"}],"name":"toYukawaTopForm","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaPrimitive.lean","qualified_name":"TFPT.Carrier.YukawaPrimitive.PrimitiveIndecomposableYukawaCoupling.toYukawaTopForm","statement_as_written":"noncomputable def toYukawaTopForm\n    [FiniteDimensional K E]\n    (Y : PrimitiveIndecomposableYukawaCoupling K E) :\n    TFPT.Carrier.YukawaTopForm.YukawaTopForm K E","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaPrimitive.lean:TFPT.Carrier.YukawaPrimitive.PrimitiveIndecomposableYukawaCoupling.toYukawaRankCertificate","line_end":201,"line_start":193,"module_context_as_written":[{"line":111,"source_text":"variable {K E : Type*} [Field K] [AddCommGroup E] [Module K E]"}],"name":"toYukawaRankCertificate","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaPrimitive.lean","qualified_name":"TFPT.Carrier.YukawaPrimitive.PrimitiveIndecomposableYukawaCoupling.toYukawaRankCertificate","statement_as_written":"noncomputable def toYukawaRankCertificate\n    [FiniteDimensional K E]\n    (Y : PrimitiveIndecomposableYukawaCoupling K E) :\n    TFPT.Carrier.YukawaRank.YukawaRankCertificate K E","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaPrimitive.lean:PrimitiveIndecomposableYukawaCoupling.ofFinrankEqThree","line_end":241,"line_start":202,"module_context_as_written":[{"line":111,"source_text":"variable {K E : Type*} [Field K] [AddCommGroup E] [Module K E]"}],"name":"PrimitiveIndecomposableYukawaCoupling.ofFinrankEqThree","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaPrimitive.lean","qualified_name":"PrimitiveIndecomposableYukawaCoupling.ofFinrankEqThree","statement_as_written":"noncomputable def PrimitiveIndecomposableYukawaCoupling.ofFinrankEqThree\n    {K E : Type*} [Field K] [AddCommGroup E] [Module K E]\n    [FiniteDimensional K E]\n    (h : Module.finrank K E = 3) :\n    PrimitiveIndecomposableYukawaCoupling K E","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaPrimitive.lean:PrimitiveIndecomposableYukawaCoupling.nonempty_iff_finrank_eq_three","line_end":260,"line_start":242,"module_context_as_written":[{"line":111,"source_text":"variable {K E : Type*} [Field K] [AddCommGroup E] [Module K E]"}],"name":"PrimitiveIndecomposableYukawaCoupling.nonempty_iff_finrank_eq_three","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaPrimitive.lean","qualified_name":"PrimitiveIndecomposableYukawaCoupling.nonempty_iff_finrank_eq_three","statement_as_written":"theorem PrimitiveIndecomposableYukawaCoupling.nonempty_iff_finrank_eq_three\n    {K E : Type*} [Field K] [AddCommGroup E] [Module K E]\n    [FiniteDimensional K E] :\n    Nonempty (PrimitiveIndecomposableYukawaCoupling K E)\n      ↔ Module.finrank K E = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"abbrev","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaRank.lean:TFPT.Carrier.YukawaRank.NegativeBlockShadow","line_end":89,"line_start":79,"module_context_as_written":[{"line":77,"source_text":"variable (K : Type*) [Field K]"},{"line":102,"source_text":"variable {K}"},{"line":125,"source_text":"variable {Eminus : Type*} [AddCommGroup Eminus] [Module K Eminus]"}],"name":"NegativeBlockShadow","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaRank.lean","qualified_name":"TFPT.Carrier.YukawaRank.NegativeBlockShadow","statement_as_written":"abbrev NegativeBlockShadow : Type _","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaRank.lean:TFPT.Carrier.YukawaRank.finrank_negativeBlockShadow","line_end":103,"line_start":90,"module_context_as_written":[{"line":77,"source_text":"variable (K : Type*) [Field K]"},{"line":102,"source_text":"variable {K}"},{"line":125,"source_text":"variable {Eminus : Type*} [AddCommGroup Eminus] [Module K Eminus]"}],"name":"finrank_negativeBlockShadow","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaRank.lean","qualified_name":"TFPT.Carrier.YukawaRank.finrank_negativeBlockShadow","statement_as_written":"theorem finrank_negativeBlockShadow :\n    Module.finrank K (NegativeBlockShadow K) = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"structure","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaRank.lean:TFPT.Carrier.YukawaRank.YukawaRankCertificate","line_end":131,"line_start":104,"module_context_as_written":[{"line":77,"source_text":"variable (K : Type*) [Field K]"},{"line":102,"source_text":"variable {K}"},{"line":125,"source_text":"variable {Eminus : Type*} [AddCommGroup Eminus] [Module K Eminus]"}],"name":"YukawaRankCertificate","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaRank.lean","qualified_name":"TFPT.Carrier.YukawaRank.YukawaRankCertificate","statement_as_written":"structure YukawaRankCertificate\n    (K : Type*) [Field K]\n    (Eminus : Type*) [AddCommGroup Eminus] [Module K Eminus]","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaRank.lean:YukawaRankCertificate.finrank_Eminus_eq_three","line_end":149,"line_start":132,"module_context_as_written":[{"line":77,"source_text":"variable (K : Type*) [Field K]"},{"line":102,"source_text":"variable {K}"},{"line":125,"source_text":"variable {Eminus : Type*} [AddCommGroup Eminus] [Module K Eminus]"}],"name":"YukawaRankCertificate.finrank_Eminus_eq_three","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaRank.lean","qualified_name":"YukawaRankCertificate.finrank_Eminus_eq_three","statement_as_written":"theorem YukawaRankCertificate.finrank_Eminus_eq_three\n    (cert : YukawaRankCertificate K Eminus) :\n    Module.finrank K Eminus = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaStageDExistence.lean:TFPT.Carrier.YukawaStageDExistence.ofBasis","line_end":84,"line_start":72,"module_context_as_written":[{"line":69,"source_text":"variable {K : Type*} [Field K]"},{"line":71,"source_text":"variable {E : Type*} [AddCommGroup E] [Module K E]"}],"name":"ofBasis","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaStageDExistence.lean","qualified_name":"TFPT.Carrier.YukawaStageDExistence.ofBasis","statement_as_written":"noncomputable def ofBasis (b : Module.Basis (Fin 3) K E) :\n    TFPT.Carrier.YukawaTrilinearForm.YukawaTrilinearForm K E","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaStageDExistence.lean:TFPT.Carrier.YukawaStageDExistence.ofFinrankEqThree","line_end":97,"line_start":85,"module_context_as_written":[{"line":69,"source_text":"variable {K : Type*} [Field K]"},{"line":71,"source_text":"variable {E : Type*} [AddCommGroup E] [Module K E]"}],"name":"ofFinrankEqThree","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaStageDExistence.lean","qualified_name":"TFPT.Carrier.YukawaStageDExistence.ofFinrankEqThree","statement_as_written":"noncomputable def ofFinrankEqThree\n    [FiniteDimensional K E]\n    (h : Module.finrank K E = 3) :\n    TFPT.Carrier.YukawaTrilinearForm.YukawaTrilinearForm K E","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaStageDExistence.lean:TFPT.Carrier.YukawaStageDExistence.ofBasis_ω_apply_top","line_end":112,"line_start":98,"module_context_as_written":[{"line":69,"source_text":"variable {K : Type*} [Field K]"},{"line":71,"source_text":"variable {E : Type*} [AddCommGroup E] [Module K E]"}],"name":"ofBasis_ω_apply_top","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaStageDExistence.lean","qualified_name":"TFPT.Carrier.YukawaStageDExistence.ofBasis_ω_apply_top","statement_as_written":"theorem ofBasis_ω_apply_top\n    (b : Module.Basis (Fin 3) K E) :\n    (ofBasis b).ω (ιMulti K 3 ![b 0, b 1, b 2]) = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"lemma","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaStageDExistence.lean:TFPT.Carrier.YukawaStageDExistence.contraction_apply_ιMulti","line_end":130,"line_start":113,"module_context_as_written":[{"line":69,"source_text":"variable {K : Type*} [Field K]"},{"line":71,"source_text":"variable {E : Type*} [AddCommGroup E] [Module K E]"}],"name":"contraction_apply_ιMulti","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaStageDExistence.lean","qualified_name":"TFPT.Carrier.YukawaStageDExistence.contraction_apply_ιMulti","statement_as_written":"private lemma contraction_apply_ιMulti\n    (b : Module.Basis (Fin 3) K E) (v : E) (w : Fin 2 → E) :\n    (ofBasis b).contraction v (ιMulti K 2 w) =\n      b.det (Matrix.vecCons v w)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"lemma","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaStageDExistence.lean:TFPT.Carrier.YukawaStageDExistence.det_basis_first_pair12","line_end":162,"line_start":131,"module_context_as_written":[{"line":69,"source_text":"variable {K : Type*} [Field K]"},{"line":71,"source_text":"variable {E : Type*} [AddCommGroup E] [Module K E]"}],"name":"det_basis_first_pair12","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaStageDExistence.lean","qualified_name":"TFPT.Carrier.YukawaStageDExistence.det_basis_first_pair12","statement_as_written":"private lemma det_basis_first_pair12\n    (b : Module.Basis (Fin 3) K E) (v : E) :\n    b.det (Matrix.vecCons v ![b 1, b 2]) = (b.repr v) 0","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"lemma","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaStageDExistence.lean:TFPT.Carrier.YukawaStageDExistence.det_basis_first_pair02","line_end":192,"line_start":163,"module_context_as_written":[{"line":69,"source_text":"variable {K : Type*} [Field K]"},{"line":71,"source_text":"variable {E : Type*} [AddCommGroup E] [Module K E]"}],"name":"det_basis_first_pair02","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaStageDExistence.lean","qualified_name":"TFPT.Carrier.YukawaStageDExistence.det_basis_first_pair02","statement_as_written":"private lemma det_basis_first_pair02\n    (b : Module.Basis (Fin 3) K E) (v : E) :\n    b.det (Matrix.vecCons v ![b 0, b 2]) = -((b.repr v) 1)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"lemma","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaStageDExistence.lean:TFPT.Carrier.YukawaStageDExistence.det_basis_first_pair01","line_end":222,"line_start":193,"module_context_as_written":[{"line":69,"source_text":"variable {K : Type*} [Field K]"},{"line":71,"source_text":"variable {E : Type*} [AddCommGroup E] [Module K E]"}],"name":"det_basis_first_pair01","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaStageDExistence.lean","qualified_name":"TFPT.Carrier.YukawaStageDExistence.det_basis_first_pair01","statement_as_written":"private lemma det_basis_first_pair01\n    (b : Module.Basis (Fin 3) K E) (v : E) :\n    b.det (Matrix.vecCons v ![b 0, b 1]) = (b.repr v) 2","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaStageDExistence.lean:TFPT.Carrier.YukawaStageDExistence.ofBasis_contractionInjective","line_end":251,"line_start":223,"module_context_as_written":[{"line":69,"source_text":"variable {K : Type*} [Field K]"},{"line":71,"source_text":"variable {E : Type*} [AddCommGroup E] [Module K E]"}],"name":"ofBasis_contractionInjective","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaStageDExistence.lean","qualified_name":"TFPT.Carrier.YukawaStageDExistence.ofBasis_contractionInjective","statement_as_written":"theorem ofBasis_contractionInjective\n    (b : Module.Basis (Fin 3) K E) :\n    (ofBasis b).ContractionInjective","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaStageDExistence.lean:TFPT.Carrier.YukawaStageDExistence.ofBasis_contractionSurjective","line_end":278,"line_start":252,"module_context_as_written":[{"line":69,"source_text":"variable {K : Type*} [Field K]"},{"line":71,"source_text":"variable {E : Type*} [AddCommGroup E] [Module K E]"}],"name":"ofBasis_contractionSurjective","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaStageDExistence.lean","qualified_name":"TFPT.Carrier.YukawaStageDExistence.ofBasis_contractionSurjective","statement_as_written":"theorem ofBasis_contractionSurjective\n    [FiniteDimensional K E]\n    (b : Module.Basis (Fin 3) K E) :\n    (ofBasis b).ContractionSurjective","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaStageDExistence.lean:TFPT.Carrier.YukawaStageDExistence.ofBasis_satisfies_condition","line_end":289,"line_start":279,"module_context_as_written":[{"line":69,"source_text":"variable {K : Type*} [Field K]"},{"line":71,"source_text":"variable {E : Type*} [AddCommGroup E] [Module K E]"}],"name":"ofBasis_satisfies_condition","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaStageDExistence.lean","qualified_name":"TFPT.Carrier.YukawaStageDExistence.ofBasis_satisfies_condition","statement_as_written":"theorem ofBasis_satisfies_condition\n    [FiniteDimensional K E]\n    (b : Module.Basis (Fin 3) K E) :\n    (ofBasis b).PrimitiveIndecomposableYukawaCondition","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaStageDExistence.lean:TFPT.Carrier.YukawaStageDExistence.exists_yukawaTrilinearForm_of_finrank_eq_three","line_end":305,"line_start":290,"module_context_as_written":[{"line":69,"source_text":"variable {K : Type*} [Field K]"},{"line":71,"source_text":"variable {E : Type*} [AddCommGroup E] [Module K E]"}],"name":"exists_yukawaTrilinearForm_of_finrank_eq_three","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaStageDExistence.lean","qualified_name":"TFPT.Carrier.YukawaStageDExistence.exists_yukawaTrilinearForm_of_finrank_eq_three","statement_as_written":"theorem exists_yukawaTrilinearForm_of_finrank_eq_three\n    [FiniteDimensional K E]\n    (h : Module.finrank K E = 3) :\n    ∃ Y : TFPT.Carrier.YukawaTrilinearForm.YukawaTrilinearForm K E,\n      Y.ContractionInjective ∧ Y.ContractionSurjective","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaStageDExistence.lean:TFPT.Carrier.YukawaStageDExistence.stage_D_iff_finrank_eq_three","line_end":329,"line_start":306,"module_context_as_written":[{"line":69,"source_text":"variable {K : Type*} [Field K]"},{"line":71,"source_text":"variable {E : Type*} [AddCommGroup E] [Module K E]"}],"name":"stage_D_iff_finrank_eq_three","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaStageDExistence.lean","qualified_name":"TFPT.Carrier.YukawaStageDExistence.stage_D_iff_finrank_eq_three","statement_as_written":"theorem stage_D_iff_finrank_eq_three\n    [FiniteDimensional K E] [Nontrivial E] :\n    (∃ Y : TFPT.Carrier.YukawaTrilinearForm.YukawaTrilinearForm K E,\n        Y.ContractionInjective ∧ Y.ContractionSurjective) ↔\n      Module.finrank K E = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"structure","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTopForm.lean:TFPT.Carrier.YukawaTopForm.YukawaTopForm","line_end":89,"line_start":62,"module_context_as_written":[{"line":59,"source_text":"variable (K : Type*) [Field K]"},{"line":61,"source_text":"variable (E : Type*) [AddCommGroup E] [Module K E]"},{"line":88,"source_text":"variable {K E}"},{"line":171,"source_text":"variable {K E}"}],"name":"YukawaTopForm","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTopForm.lean","qualified_name":"TFPT.Carrier.YukawaTopForm.YukawaTopForm","statement_as_written":"structure YukawaTopForm\n    (K E : Type*) [Field K] [AddCommGroup E] [Module K E]","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTopForm.lean:TFPT.Carrier.YukawaTopForm.YukawaTopForm.finrank_lambda3_eq_one","line_end":101,"line_start":90,"module_context_as_written":[{"line":59,"source_text":"variable (K : Type*) [Field K]"},{"line":61,"source_text":"variable (E : Type*) [AddCommGroup E] [Module K E]"},{"line":88,"source_text":"variable {K E}"},{"line":171,"source_text":"variable {K E}"}],"name":"finrank_lambda3_eq_one","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTopForm.lean","qualified_name":"TFPT.Carrier.YukawaTopForm.YukawaTopForm.finrank_lambda3_eq_one","statement_as_written":"theorem finrank_lambda3_eq_one\n    (Y : YukawaTopForm K E) :\n    Module.finrank K (⋀[K]^3 E) = 1","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTopForm.lean:TFPT.Carrier.YukawaTopForm.YukawaTopForm.finrank_E_eq_three","line_end":128,"line_start":102,"module_context_as_written":[{"line":59,"source_text":"variable (K : Type*) [Field K]"},{"line":61,"source_text":"variable (E : Type*) [AddCommGroup E] [Module K E]"},{"line":88,"source_text":"variable {K E}"},{"line":171,"source_text":"variable {K E}"}],"name":"finrank_E_eq_three","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTopForm.lean","qualified_name":"TFPT.Carrier.YukawaTopForm.YukawaTopForm.finrank_E_eq_three","statement_as_written":"theorem finrank_E_eq_three\n    [FiniteDimensional K E]\n    (Y : YukawaTopForm K E) :\n    Module.finrank K E = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTopForm.lean:TFPT.Carrier.YukawaTopForm.YukawaTopForm.toYukawaRankCertificate","line_end":172,"line_start":129,"module_context_as_written":[{"line":59,"source_text":"variable (K : Type*) [Field K]"},{"line":61,"source_text":"variable (E : Type*) [AddCommGroup E] [Module K E]"},{"line":88,"source_text":"variable {K E}"},{"line":171,"source_text":"variable {K E}"}],"name":"toYukawaRankCertificate","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTopForm.lean","qualified_name":"TFPT.Carrier.YukawaTopForm.YukawaTopForm.toYukawaRankCertificate","statement_as_written":"noncomputable def toYukawaRankCertificate\n    [FiniteDimensional K E]\n    (Y : YukawaTopForm K E) :\n    TFPT.Carrier.YukawaRank.YukawaRankCertificate K E","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTopForm.lean:TFPT.Carrier.YukawaTopForm.YukawaTopForm.ofFinrankEqThree","line_end":187,"line_start":173,"module_context_as_written":[{"line":59,"source_text":"variable (K : Type*) [Field K]"},{"line":61,"source_text":"variable (E : Type*) [AddCommGroup E] [Module K E]"},{"line":88,"source_text":"variable {K E}"},{"line":171,"source_text":"variable {K E}"}],"name":"ofFinrankEqThree","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTopForm.lean","qualified_name":"TFPT.Carrier.YukawaTopForm.YukawaTopForm.ofFinrankEqThree","statement_as_written":"noncomputable def ofFinrankEqThree\n    [FiniteDimensional K E]\n    (h : Module.finrank K E = 3) :\n    YukawaTopForm K E","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTopForm.lean:TFPT.Carrier.YukawaTopForm.YukawaTopForm.nonempty_iff_finrank_eq_three","line_end":204,"line_start":188,"module_context_as_written":[{"line":59,"source_text":"variable (K : Type*) [Field K]"},{"line":61,"source_text":"variable (E : Type*) [AddCommGroup E] [Module K E]"},{"line":88,"source_text":"variable {K E}"},{"line":171,"source_text":"variable {K E}"}],"name":"nonempty_iff_finrank_eq_three","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTopForm.lean","qualified_name":"TFPT.Carrier.YukawaTopForm.YukawaTopForm.nonempty_iff_finrank_eq_three","statement_as_written":"theorem nonempty_iff_finrank_eq_three\n    [FiniteDimensional K E] :\n    Nonempty (YukawaTopForm K E) ↔ Module.finrank K E = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"structure","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTrilinearForm.lean:TFPT.Carrier.YukawaTrilinearForm.YukawaTrilinearForm","line_end":89,"line_start":75,"module_context_as_written":[{"line":72,"source_text":"variable (K : Type*) [Field K]"},{"line":74,"source_text":"variable (E : Type*) [AddCommGroup E] [Module K E]"},{"line":88,"source_text":"variable {K E}"}],"name":"YukawaTrilinearForm","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTrilinearForm.lean","qualified_name":"TFPT.Carrier.YukawaTrilinearForm.YukawaTrilinearForm","statement_as_written":"structure YukawaTrilinearForm\n    (K E : Type*) [Field K] [AddCommGroup E] [Module K E]","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTrilinearForm.lean:TFPT.Carrier.YukawaTrilinearForm.YukawaTrilinearForm.contraction","line_end":115,"line_start":90,"module_context_as_written":[{"line":72,"source_text":"variable (K : Type*) [Field K]"},{"line":74,"source_text":"variable (E : Type*) [AddCommGroup E] [Module K E]"},{"line":88,"source_text":"variable {K E}"}],"name":"contraction","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTrilinearForm.lean","qualified_name":"TFPT.Carrier.YukawaTrilinearForm.YukawaTrilinearForm.contraction","statement_as_written":"noncomputable def contraction (Y : YukawaTrilinearForm K E) :\n    E →ₗ[K] ((⋀[K]^2 E) →ₗ[K] K)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTrilinearForm.lean:TFPT.Carrier.YukawaTrilinearForm.YukawaTrilinearForm.ContractionInjective","line_end":130,"line_start":116,"module_context_as_written":[{"line":72,"source_text":"variable (K : Type*) [Field K]"},{"line":74,"source_text":"variable (E : Type*) [AddCommGroup E] [Module K E]"},{"line":88,"source_text":"variable {K E}"}],"name":"ContractionInjective","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTrilinearForm.lean","qualified_name":"TFPT.Carrier.YukawaTrilinearForm.YukawaTrilinearForm.ContractionInjective","statement_as_written":"def ContractionInjective (Y : YukawaTrilinearForm K E) : Prop","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTrilinearForm.lean:TFPT.Carrier.YukawaTrilinearForm.YukawaTrilinearForm.ContractionSurjective","line_end":146,"line_start":131,"module_context_as_written":[{"line":72,"source_text":"variable (K : Type*) [Field K]"},{"line":74,"source_text":"variable (E : Type*) [AddCommGroup E] [Module K E]"},{"line":88,"source_text":"variable {K E}"}],"name":"ContractionSurjective","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTrilinearForm.lean","qualified_name":"TFPT.Carrier.YukawaTrilinearForm.YukawaTrilinearForm.ContractionSurjective","statement_as_written":"def ContractionSurjective (Y : YukawaTrilinearForm K E) : Prop","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTrilinearForm.lean:TFPT.Carrier.YukawaTrilinearForm.YukawaTrilinearForm.PrimitiveIndecomposableYukawaCondition","line_end":153,"line_start":147,"module_context_as_written":[{"line":72,"source_text":"variable (K : Type*) [Field K]"},{"line":74,"source_text":"variable (E : Type*) [AddCommGroup E] [Module K E]"},{"line":88,"source_text":"variable {K E}"}],"name":"PrimitiveIndecomposableYukawaCondition","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTrilinearForm.lean","qualified_name":"TFPT.Carrier.YukawaTrilinearForm.YukawaTrilinearForm.PrimitiveIndecomposableYukawaCondition","statement_as_written":"def PrimitiveIndecomposableYukawaCondition\n    (Y : YukawaTrilinearForm K E) : Prop","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTrilinearForm.lean:TFPT.Carrier.YukawaTrilinearForm.YukawaTrilinearForm.contractionEquivOfBoth","line_end":166,"line_start":154,"module_context_as_written":[{"line":72,"source_text":"variable (K : Type*) [Field K]"},{"line":74,"source_text":"variable (E : Type*) [AddCommGroup E] [Module K E]"},{"line":88,"source_text":"variable {K E}"}],"name":"contractionEquivOfBoth","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTrilinearForm.lean","qualified_name":"TFPT.Carrier.YukawaTrilinearForm.YukawaTrilinearForm.contractionEquivOfBoth","statement_as_written":"noncomputable def contractionEquivOfBoth\n    [FiniteDimensional K E]\n    (Y : YukawaTrilinearForm K E)\n    (hinj : Y.ContractionInjective)\n    (hsurj : Y.ContractionSurjective) :\n    E ≃ₗ[K] ((⋀[K]^2 E) →ₗ[K] K)","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTrilinearForm.lean:TFPT.Carrier.YukawaTrilinearForm.YukawaTrilinearForm.toPrimitiveIndecomposableYukawaCoupling","line_end":186,"line_start":167,"module_context_as_written":[{"line":72,"source_text":"variable (K : Type*) [Field K]"},{"line":74,"source_text":"variable (E : Type*) [AddCommGroup E] [Module K E]"},{"line":88,"source_text":"variable {K E}"}],"name":"toPrimitiveIndecomposableYukawaCoupling","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTrilinearForm.lean","qualified_name":"TFPT.Carrier.YukawaTrilinearForm.YukawaTrilinearForm.toPrimitiveIndecomposableYukawaCoupling","statement_as_written":"noncomputable def toPrimitiveIndecomposableYukawaCoupling\n    [FiniteDimensional K E] [Nontrivial E]\n    (Y : YukawaTrilinearForm K E)\n    (hinj : Y.ContractionInjective)\n    (hsurj : Y.ContractionSurjective) :\n    TFPT.Carrier.YukawaPrimitive.PrimitiveIndecomposableYukawaCoupling K E","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTrilinearForm.lean:TFPT.Carrier.YukawaTrilinearForm.YukawaTrilinearForm.finrank_E_eq_three","line_end":207,"line_start":187,"module_context_as_written":[{"line":72,"source_text":"variable (K : Type*) [Field K]"},{"line":74,"source_text":"variable (E : Type*) [AddCommGroup E] [Module K E]"},{"line":88,"source_text":"variable {K E}"}],"name":"finrank_E_eq_three","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTrilinearForm.lean","qualified_name":"TFPT.Carrier.YukawaTrilinearForm.YukawaTrilinearForm.finrank_E_eq_three","statement_as_written":"theorem finrank_E_eq_three\n    [FiniteDimensional K E] [Nontrivial E]\n    (Y : YukawaTrilinearForm K E)\n    (hinj : Y.ContractionInjective)\n    (hsurj : Y.ContractionSurjective) :\n    Module.finrank K E = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTrilinearForm.lean:TFPT.Carrier.YukawaTrilinearForm.YukawaTrilinearForm.finrank_E_eq_three_of_condition","line_end":220,"line_start":208,"module_context_as_written":[{"line":72,"source_text":"variable (K : Type*) [Field K]"},{"line":74,"source_text":"variable (E : Type*) [AddCommGroup E] [Module K E]"},{"line":88,"source_text":"variable {K E}"}],"name":"finrank_E_eq_three_of_condition","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTrilinearForm.lean","qualified_name":"TFPT.Carrier.YukawaTrilinearForm.YukawaTrilinearForm.finrank_E_eq_three_of_condition","statement_as_written":"theorem finrank_E_eq_three_of_condition\n    [FiniteDimensional K E] [Nontrivial E]\n    (Y : YukawaTrilinearForm K E)\n    (h : Y.PrimitiveIndecomposableYukawaCondition) :\n    Module.finrank K E = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"theorem","id":"lean-symbol:experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTrilinearForm.lean:TFPT.Carrier.YukawaTrilinearForm.YukawaTrilinearForm.finrank_E_eq_zero_or_three","line_end":253,"line_start":221,"module_context_as_written":[{"line":72,"source_text":"variable (K : Type*) [Field K]"},{"line":74,"source_text":"variable (E : Type*) [AddCommGroup E] [Module K E]"},{"line":88,"source_text":"variable {K E}"}],"name":"finrank_E_eq_zero_or_three","path":"experiments/lean4-carrier-rigidity/TfptCarrier/YukawaTrilinearForm.lean","qualified_name":"TFPT.Carrier.YukawaTrilinearForm.YukawaTrilinearForm.finrank_E_eq_zero_or_three","statement_as_written":"theorem finrank_E_eq_zero_or_three\n    [FiniteDimensional K E]\n    (Y : YukawaTrilinearForm K E)\n    (hinj : Y.ContractionInjective)\n    (hsurj : Y.ContractionSurjective) :\n    Module.finrank K E = 0 ∨ Module.finrank K E = 3","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"checked_by_registry":false,"contains_sorry_or_admit":false,"declaration_kind":"def","id":"lean-symbol:experiments/lean4-carrier-rigidity/lakefile.lean:leanMemoryMb","line_end":31,"line_start":3,"module_context_as_written":[],"name":"leanMemoryMb","path":"experiments/lean4-carrier-rigidity/lakefile.lean","qualified_name":"leanMemoryMb","statement_as_written":"def leanMemoryMb : String","statement_truncated":false,"status_basis":"source declaration only; registry does not run Lean or certify assumptions","type":"lean_declaration"},{"check_labels_as_written":["alpha_* = 0.00729735256220985","alpha^-1 = 137.0359992168407","240 = 16*5*3 (roots = dim S+ * g_car * N_fam)","248 = 240 + 8 (dim E8 = roots + rank)","E8 Coxeter h = 30 = 2*3*5"],"checked_by_registry":false,"heading_as_written":"(* ---- (v3) electromagnetic closure: alpha^-1 ---- *) M = 41; phiseam[a_] := phibase + (dtop Exp[-2 a]) (1 - dtop Exp[-2 a])^(-5/4); F[a_] := a^3 - 2 c3^3 a^2 - (4/5) c3^6 M Log[1/phiseam[a]]; aStar = a /. FindRoot[F[a] == 0, {a, 0.0073}, WorkingPrecision -> 40]; alphaInv = 1/aStar; check[\"alpha_* = 0.00729735256220985\", aStar, 0.00729735256220985, 10^-15]; check[\"alpha^-1 = 137.0359992168407\", alphaInv, 137.0359992168407, 10^-12]; (* ---- (v1) E8 glue arithmetic ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:36","line_end":49,"line_start":36,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v1","v3"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["dim S+ = 2^(g_car-1) = 16","16 = 1 + 5 + 10 = C(5,0)+C(5,1)+C(5,2)","N_fam = 3","rank E8 = g_car + N_fam = 8","M = 40 + N_Phi(=1) = 10 b1 = 41"],"checked_by_registry":false,"heading_as_written":"(* ---- (v2) carrier / Pascal ---- *) checkExact[\"dim S+ = 2^(g_car-1) = 16\", 2^(gcar - 1) == 16]; checkExact[\"16 = 1 + 5 + 10 = C(5,0)+C(5,1)+C(5,2)\", Binomial[5, 0] + Binomial[5, 1] + Binomial[5, 2] == 16]; checkExact[\"N_fam = 3\", Nfam == 3]; checkExact[\"rank E8 = g_car + N_fam = 8\", gcar + Nfam == 8]; (* ---- (v13) M = 41 budget ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:50","line_end":60,"line_start":50,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v13","v2"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["K = R + Q.Sigma","L = R + Q.(I + Sigma)","det ladder (Q,K,R,L) = (3,4,8,20)","det product = 1920 = |W(D5)|","a^T K a = 41 (the EM budget anchor)","c_e = |mu4|^1 / (5/4 - cos(2pi/3)) = 16/7","c_mu = 4/3","product rule 2^g_car/N_fam^2 = 32/9","c_tau = product/(c_e c_mu) = 7/6"],"checked_by_registry":false,"heading_as_written":"(* ---- (v10) K/Q/Sigma determinant ladder ---- *) R = {{1, 3, 0}, {1, 5, 2}, {2, 5, 3}}; W = {{1, 0, 0}, {1, 0, 0}, {1, 0, 0}}; L = R + 6 W; K = {{4, 2, 0}, {4, 3, 2}, {5, 3, 2}}; Q = {{3, 1, 0}, {3, 2, 0}, {3, 2, 1}}; Sig = DiagonalMatrix[{1, -1, -1}]; checkExact[\"K = R + Q.Sigma\", K == R + Q.Sig]; checkExact[\"L = R + Q.(I + Sigma)\", L == R + Q.(IdentityMatrix[3] + Sig)]; checkExact[\"det ladder (Q,K,R,L) = (3,4,8,20)\", {Det[Q], Det[K], Det[R], Det[L]} == {3, 4, 8, 20}]; checkExact[\"det product = 1920 = |W(D5)|\", Det[Q] Det[K] Det[R] Det[L] == 1920]; aVec = {1, 1, 2}; checkExact[\"a^T K a = 41 (the EM budget anchor)\", aVec.K.aVec == 41]; (* ---- (v20/v21) lepton c's: delta=1/2 resolvent + product rule ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:61","line_end":87,"line_start":61,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v10","v20","v21"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["E8 glue norm q(D5) + q(A3) = 2","eps leading q(A3)/(6pi) = 1/(8pi) = c3","sin^2 theta12 = 1/3 - phi0/2 (exact)","anchor e_k(a)=(4,5,2)=(|mu4|,g_car,|Z2|)","c3 = 1/(2 e1 pi) = 1/(8pi)","p_n(a)=2+2^n -> |R(E8)|=p1 p2 p3=240","dim E8 = p1 p2 p3 + (p4 - p3) = 248","binary ladder p_{n+1}-p_n = 2^n"],"checked_by_registry":false,"heading_as_written":"(* ---- (v16/v21) solar angle from the A3 glue-norm q(A3) = 3/4 ---- *) qA3 = 3/4; qD5 = 5/4; checkExact[\"E8 glue norm q(D5) + q(A3) = 2\", qA3 + qD5 == 2]; checkExact[\"eps leading q(A3)/(6pi) = 1/(8pi) = c3\", Simplify[qA3/(6 Pi) - c3] == 0]; s12 = 1/3 - (2/3) qA3 phi0; checkExact[\"sin^2 theta12 = 1/3 - phi0/2 (exact)\", Simplify[s12 - (1/3 - phi0/2)] == 0]; (* ---- (v23) anchor generator a=(1,1,2) ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:88","line_end":104,"line_start":88,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v16","v21","v23"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["c_u/c_d = g_car*11/(N_fam^2 Delta_Q) = 55/117","c_c/c_s = p_5(a)/(Omega_adm-1) = 34/47","c_t/c_b = N_fam/(2 Delta_Q) = 3/26","m_c/m_s = (34/47)/phi0 = 13.605","m_t/m_b = (3/26)/phi0^2 = 40.81","G2: a2 = -R/3 (Einstein-Hilbert emerges)","G2: a4|R^2 = R^2/72 (Starobinsky R^2 emerges)","G2: scalaron ratio M^2/Mbar^2 = 6(4pi)^2/f0 fixed by c3^7 (f0 = 6(4pi)^2/c3^7)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v24) quark ratio closure ---- *) checkExact[\"c_u/c_d = g_car*11/(N_fam^2 Delta_Q) = 55/117\", (gcar*11)/(Nfam^2*13) == 55/117]; checkExact[\"c_c/c_s = p_5(a)/(Omega_adm-1) = 34/47\", pn[5]/(48 - 1) == 34/47]; checkExact[\"c_t/c_b = N_fam/(2 Delta_Q) = 3/26\", Nfam/(2*13) == 3/26]; check[\"m_c/m_s = (34/47)/phi0 = 13.605\", (34/47)/phi0, 13.605, 10^-3]; check[\"m_t/m_b = (3/26)/phi0^2 = 40.81\", (3/26)/phi0^2, 40.81, 10^-2]; (* ---- (v36) G2: spectral-action Seeley-DeWitt coefficients -> R + R^2 ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:105","line_end":121,"line_start":105,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v24","v36"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["Pl(K) = (-1,6,4) and ||Pl(K)||_1 = 11 (the '11' localised in K)","Pl_R(K)=(12,12,-2), ||Pl_R(K)||_1=26; sum Pl_R(L)=60 (cascade start)","pencil det(K + x Q) = 3x^3 + 7x^2 + 6x + 4 = (N_fam,7,|R+A3|,|mu4|)","lepton-up duality: K_e - K_u = a = (1,1,2)","lepton-up duality: L_e - L_u = Exp(A3) = (1,2,3)","lepton ring: c_e c_tau = |Z2| c_mu (= 8/3)","Spec(Q_+) = {1,2,3} (A3 exponents)","Spec(Q_+) = 3 alpha + 1, alpha = cusp weights {0,1/3,2/3}","det R = 8 selector; splitting type = anchor a = (1,1,2)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v37) anchor-plane Plücker apparatus + K+xQ pencil + dualities ---- *) oneV = {1, 1, 1}; aVc = {1, 1, 2}; plLeft[Mat_] := Module[{r1 = oneV.Mat, r2 = aVc.Mat}, {r1[[1]] r2[[2]] - r1[[2]] r2[[1]], r1[[1]] r2[[3]] - r1[[3]] r2[[1]], r1[[2]] r2[[3]] - r1[[3]] r2[[2]]}]; plRight[Mat_] := Module[{c1 = Mat.oneV, c2 = Mat.aVc}, {c1[[1]] c2[[2]] - c1[[2]] c2[[1]], c1[[1]] c2[[3]] - c1[[3]] c2[[1]], c1[[2]] c2[[3]] - c1[[3]] c2[[2]]}]; checkExact[\"Pl(K) = (-1,6,4) and ||Pl(K)||_1 = 11 (the '11' localised in K)\", plLeft[K] == {-1, 6, 4} && Total[Abs[plLeft[K]]] == 11]; checkExact[\"Pl_R(K)=(12,12,-2), ||Pl_R(K)||_1=26; sum Pl_R(L)=60 (cascade start)\", plRight[K] == {12, 12, -2} && Total[Abs[plRight[K]]] == 26 && Total[plRight[L]] == 60]; checkExact[\"pencil det(K + x Q) = 3x^3 + 7x^2 + 6x + 4 = (N_fam,7,|R+A3|,|mu4|)\", Expand[Det[K + x Q]] === 3 x^3 + 7 x^2 + 6 x + 4]; checkExact[\"lepton-up duality: K_e - K_u = a = (1,1,2)\", K[[3]] - K[[1]] == {1, 1, 2}]; checkExact[\"lepton-up duality: L_e - L_u = Exp(A3) = (1,2,3)\", L[[3]] - L[[1]] == {1, 2, 3}]; checkExact[\"lepton ring: c_e c_tau = |Z2| c_mu (= 8/3)\", ce ctau == 2 cmu]; (* ---- (v39) (U_wall) selectors read off the bundle (algebraic) ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:122","line_end":147,"line_start":122,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v37","v39"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["scalar leg necessity: u,d share (r,w)=(1,1) => c_u/c_d (scalar) = 1","anchor microcode: p_0=3=N_fam, p_2=6, p_3=10; Delta_Q=2p_2+1=13; ||Pl(K)||_1=p_3+1=11","c_u/c_d = e_2(a)(p_3+1)/(p_0^2(2p_2+1)) = 55/117 (Lambda^2 F readout)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v42) Exterior Leg Lemma: u/d leg is a Lambda^2 F area, not a scalar ---- *) (* u,d share (r,w)=(1,1): the C6 resolvent reads only (r,w) => scalar ratio = 1. *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:148","line_end":160,"line_start":148,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v42"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["16 = Lambda^even(5) = C(5,0)+C(5,2)+C(5,4) = 1+10+5","exterior degrees: deg(u)+deg(d)=2+4=6=|R^+(A3)|, deg(d)-deg(u)=2=|Z2|"],"checked_by_registry":false,"heading_as_written":"(* ---- (v44) exterior leg = carrier exterior-algebra grading ---- *) checkExact[\"16 = Lambda^even(5) = C(5,0)+C(5,2)+C(5,4) = 1+10+5\", {Binomial[5, 0], Binomial[5, 2], Binomial[5, 4]} == {1, 10, 5}]; (* u^c in 10=Lambda^2(5) deg 2 ; d^c in 5bar=Lambda^4(5) deg 4 *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:161","line_end":167,"line_start":161,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v44"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["Lambda^k(4)=Pascal row 4=(1,4,6,4,1), sum=2^4=16=dim S+","|Pl(K)|={1,4,6}={Lambda^0,Lambda^1,Lambda^2}(mu4); ||Pl(K)||_1=11=sum_{k<=2}C(4,k)=16-g_car","family(x)carrier=15=dim su(4)=Lambda^2(5)+Lambda^4(5)=10+5=N_fam*g_car","sector det exponents = K row sums (6,9,10)=(|R+A3|,N_fam^2,A_Lambda); total 25=g_car^2","Q row sums (4,5,6) sum 15=dim A3; 25+15=40=sum L=|R(D5)|"],"checked_by_registry":false,"heading_as_written":"(* ---- (v45) the '11' = exterior algebra of the family fundamental 4=mu4 (Pascal) ---- *) checkExact[\"Lambda^k(4)=Pascal row 4=(1,4,6,4,1), sum=2^4=16=dim S+\", Table[Binomial[4, k], {k, 0, 4}] == {1, 4, 6, 4, 1} && Total[Table[Binomial[4, k], {k, 0, 4}]] == 16]; checkExact[\"|Pl(K)|={1,4,6}={Lambda^0,Lambda^1,Lambda^2}(mu4); ||Pl(K)||_1=11=sum_{k<=2}C(4,k)=16-g_car\", Sort[Abs[plLeft[K]]] == {1, 4, 6} && Total[Abs[plLeft[K]]] == Sum[Binomial[4, k], {k, 0, 2}] == 16 - gcar]; checkExact[\"family(x)carrier=15=dim su(4)=Lambda^2(5)+Lambda^4(5)=10+5=N_fam*g_car\", 4^2 - 1 == Binomial[5, 2] + Binomial[5, 4] == Nfam gcar == 15]; (* ---- (v46) Grand Mass Volume: absolute mass-scaling = det ~ u^25 ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:168","line_end":183,"line_start":168,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v45","v46"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["q(D5)+q(A3)=5/4+3/4=2 (E8 root norm); glue index sqrt(4*4/1)=4=|mu4|","only n=5 gives 16-dim D_n half-spinor (2^{n-1}=16) => D5","transport coeff 8 b1 = (4/5) M = (4/5)(40+1) = 164/5; -5/4 = q(D5)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v47) Boundary Carrier Selection Theorem (Theorem A) ---- *) checkExact[\"q(D5)+q(A3)=5/4+3/4=2 (E8 root norm); glue index sqrt(4*4/1)=4=|mu4|\", 5/4 + 3/4 == 2 && Sqrt[4*4/1] == 4]; checkExact[\"only n=5 gives 16-dim D_n half-spinor (2^{n-1}=16) => D5\", Select[Range[2, 8], 2^(# - 1) == 16 &] == {5}]; (* ---- (v48) EM boundary Ward decomposition (Theorem C) ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:184","line_end":193,"line_start":184,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v47","v48"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["Q_+ char poly = (t-1)(t-2)(t-3) => Spec(Q_+)={1,2,3}","Q_- char poly = t(t^2-3) => Q_-^2 eigenvalues {0,3} (3=N_fam)","Readout Rigidity: c_u/c_d = g_car*||Pl(K)||_1/(N_fam^2 Delta_Q) = 55/117 (stratum-constant)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v50) Q geometry (Theorem Q): Sigma-split char polys ---- *) Qp = (Q + Sig.Q.Sig)/2; Qm = (Q - Sig.Q.Sig)/2; checkExact[\"Q_+ char poly = (t-1)(t-2)(t-3) => Spec(Q_+)={1,2,3}\", Sort[Eigenvalues[Qp]] == {1, 2, 3}]; checkExact[\"Q_- char poly = t(t^2-3) => Q_-^2 eigenvalues {0,3} (3=N_fam)\", Sort[Eigenvalues[Qm]] == Sort[{0, Sqrt[3], -Sqrt[3]}] && Sort[Eigenvalues[Qm.Qm]] == {0, 3, 3}]; (* ---- (v49) Readout Rigidity: c_u/c_d constant on the selector stratum ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:194","line_end":204,"line_start":194,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v49","v50"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["glue norms = (g_car,N_fam)/|mu4|: q(D5)=5/4=gcar/4, q(A3)=3/4=Nfam/4","four ops forced: sum=2(root), diff=1/2(delta=|Z2|/4), prod=15/16(su4/S+), ratio=5/3(gcar/Nfam)","delta=1/2 reproduces leptons: 4*1/(5/4-cos(2 Pi/3))=16/7, 1/(5/4-cos(Pi/3))=4/3","pencil P(x)=det(K+xQ): P(-1)=2=|Z2|, P(0)=4=|mu4|, P(1)=20=det L, P(2)=68=2 p5(a)","det(K-Q)=2=|Z2|, trace(K-Q)=3=N_fam"],"checked_by_registry":false,"heading_as_written":"(* ---- (v51) delta=1/2 glue-norm origin + (g_car,N_fam)/|mu4| unification ---- *) checkExact[\"glue norms = (g_car,N_fam)/|mu4|: q(D5)=5/4=gcar/4, q(A3)=3/4=Nfam/4\", 5/4 == gcar/4 && 3/4 == Nfam/4]; checkExact[\"four ops forced: sum=2(root), diff=1/2(delta=|Z2|/4), prod=15/16(su4/S+), ratio=5/3(gcar/Nfam)\", {5/4 + 3/4, 5/4 - 3/4, 5/4*3/4, (5/4)/(3/4)} == {(gcar + Nfam)/4, (gcar - Nfam)/4, gcar*Nfam/16, gcar/Nfam} == {2, 1/2, 15/16, 5/3}]; checkExact[\"delta=1/2 reproduces leptons: 4*1/(5/4-cos(2 Pi/3))=16/7, 1/(5/4-cos(Pi/3))=4/3\", 4*1/(5/4 - Cos[2 Pi/3]) == 16/7 && 1/(5/4 - Cos[Pi/3]) == 4/3]; (* ---- (v52) K+xQ pencil endpoints ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:205","line_end":221,"line_start":205,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v51","v52"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["rank E8=g+n=8, |Z2|=g-n=2, |mu4|=(g+n)/2=4; five core ints {2,3,4,5,8} from (5,3)","Pythagorean mass-volume: Delta_Y=g^2=25=N_fam^2 + (g-n)(g+n)=9+16; up+lep=|Z2|*rank E8=dim S+","anchor char-poly: (t-1)^2(t-2)=t^3-|mu4|t^2+g_car t-|Z2|; e_k(1,1,2)=(4,5,2)","8 overdetermined: 2|mu4| = rank E8 = h(D5) = phi(30) = 8","both pi-coeffs are 2pi*integer: phi_tree=1/(6pi)=(|mu4|/N_fam) c3, 6=2 N_fam, 8=2|mu4|","one transfer operator: spec {1,(2/3)^6,(1/3)^6}; flavor gap=-log(2/3)^6=6 log(3/2); same lambda2 in horizon","de Sitter: 128 c3^4 = 1/(32 pi^4); T_dS coeff 16=|mu4|^2; S_BH 1/4=1/|mu4|"],"checked_by_registry":false,"heading_as_written":"(* ---- (v53) compiler core: everything from (g_car,N_fam)=(5,3) ---- *) checkExact[\"rank E8=g+n=8, |Z2|=g-n=2, |mu4|=(g+n)/2=4; five core ints {2,3,4,5,8} from (5,3)\", gcar + Nfam == 8 && gcar - Nfam == 2 && (gcar + Nfam)/2 == 4 && Sort[{gcar - Nfam, Nfam, 4, gcar, gcar + Nfam}] == {2, 3, 4, 5, 8}]; checkExact[\"Pythagorean mass-volume: Delta_Y=g^2=25=N_fam^2 + (g-n)(g+n)=9+16; up+lep=|Z2|*rank E8=dim S+\", Module[{rs = Total /@ K}, gcar^2 == Nfam^2 + 4^2 == 25 && rs == {6, 9, 10} && rs[[2]] == Nfam^2 == 9 && (rs[[1]] + rs[[3]]) == (gcar - Nfam)(gcar + Nfam) == 16]]; checkExact[\"anchor char-poly: (t-1)^2(t-2)=t^3-|mu4|t^2+g_car t-|Z2|; e_k(1,1,2)=(4,5,2)\", Module[{tt}, Expand[(tt - 1)^2 (tt - 2)] == tt^3 - 4 tt^2 + gcar tt - 2] && {1 + 1 + 2, 1*1 + 1*2 + 1*2, 1*1*2} == {4, 5, 2}]; (* ---- (v54) seam=horizon keystones: triply-forced 8 + shared transfer operator ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:222","line_end":244,"line_start":222,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v53","v54"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["E8 exponents {1,7,11,13,17,19,23,29} = totatives of 30; count phi(30)=8=rank E8","cycle order 30 = |Z2|*N_fam*g_car = 2*3*5","one alpha^-1: S_dS*rho_Lambda = 1/(128 c3^4) = 32 pi^4 (de Sitter entropy ~ 1/Lambda)","S_dS = 2^g_car pi^|mu4| e^{2 ainv}: 32=2^g_car=dim Dirac(D5)=16+16; 128=2^7, 7=g+n-1","spectral gap Delta = -log(2/3)^6 = 6 log(3/2) > 0 => unique dominant eigenvector (Perron-Frobenius)","exponents pair m+(30-m)=30 => rank/2 = 4 = |mu4| invariant planes; sum exps=120=|R+(E8)|; rank*h=240"],"checked_by_registry":false,"heading_as_written":"(* ---- (v55) cyclic element in the hull: E8 Coxeter order 30 + one-alpha cross-sector ---- *) checkExact[\"E8 exponents {1,7,11,13,17,19,23,29} = totatives of 30; count phi(30)=8=rank E8\", {1, 7, 11, 13, 17, 19, 23, 29} == Select[Range[1, 29], CoprimeQ[#, 30] &] && EulerPhi[30] == 8 == gcar + Nfam]; checkExact[\"cycle order 30 = |Z2|*N_fam*g_car = 2*3*5\", 30 == 2*Nfam*gcar == 2*3*5]; checkExact[\"one alpha^-1: S_dS*rho_Lambda = 1/(128 c3^4) = 32 pi^4 (de Sitter entropy ~ 1/Lambda)\", Simplify[1/(128 (1/(8 Pi))^4) - 32 Pi^4] == 0]; checkExact[\"S_dS = 2^g_car pi^|mu4| e^{2 ainv}: 32=2^g_car=dim Dirac(D5)=16+16; 128=2^7, 7=g+n-1\", 32 == 2^gcar == 16 + 16 && 128 == 2^7 && 7 == gcar + Nfam - 1]; (* ---- (v56) unique attractor: gapped transport, Coxeter planes ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:245","line_end":262,"line_start":245,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v55","v56"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["c3=1/(8pi) Einstein/Jacobson: 1/(16pi)=c3/2; 1/4=1/|mu4|; 1/(2pi)=4c3","Hod QNM omega_R/T_H = ln(3) = ln(N_fam); Hawking power denom 1920=|W(D5)|=2^4*5!","one-sided S^2 Gauss-Bonnet: c3 = 1/(|Z2| * 2pi chi(S^2)) = 1/(2*4pi) = 1/(8pi)","seam units: 1/(2c3)=4pi (S_BH=M^2/2c3), 1/(4c3)=2pi (RT), 1/(2pi)=4c3 (KMS)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v57) horizon cross-links: Jacobson 8pi, Hod ln(3), Hawking |W(D5)| ---- *) checkExact[\"c3=1/(8pi) Einstein/Jacobson: 1/(16pi)=c3/2; 1/4=1/|mu4|; 1/(2pi)=4c3\", Simplify[1/(16 Pi) - (1/(8 Pi))/2] == 0 && 1/4 == 1/4 && Simplify[1/(2 Pi) - 4/(8 Pi)] == 0]; checkExact[\"Hod QNM omega_R/T_H = ln(3) = ln(N_fam); Hawking power denom 1920=|W(D5)|=2^4*5!\", Nfam == 3 && 1920 == 2^4 * 5!]; (* ---- (v58) seam-horizon chain: one-sided Gauss-Bonnet, KMS, S_BH, RT in seam units ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:263","line_end":275,"line_start":263,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v57","v58"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["8 = |Z2|*|mu4| (sheet x glue); chaos-bound/seam unit 2pi = 1/(4 c3)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v59) area-law evidence: exact seam-unit parts (the EE area-law is numerical, Python-only) ---- *) checkExact[\"8 = |Z2|*|mu4| (sheet x glue); chaos-bound/seam unit 2pi = 1/(4 c3)\", 2*4 == 8 && Simplify[2 Pi - 1/(4*(1/(8 Pi)))] == 0]; (* NOTE: the free-field entanglement area-law of v59 is a numerical computation (numpy symplectic spectra), Python-only by design -- not mirrored here. *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:276","line_end":281,"line_start":276,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v59"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["delta_top=48 c3^4=3/(256 pi^4); (8pi)^2 delta_top=3/(4 pi^2); 2c3/delta_top=64 pi^3/3 (G_N pinned)","action exponents (1,5,10) = K5 counts (5 vertices, C(5,2)=10 edges); Pascal 16=1+5+10","WZW level-1 central charges: c(E8)=248/31=8, c(D5)=45/9=5, c(A3)=15/5=3 = (rank E8,g_car,N_fam)","conformal embedding: c_coset = c(E8)-c(D5)-c(A3) = 8-5-3 = 0; additivity 5+3=8=c(E8)","reconciliation: N_fam = |mu4|-1 = 3 (P^1\\\\mu4 homology); SU(3) triality {0,1/3,2/3} != SU(4)_1 {0,3/8,1/2}"],"checked_by_registry":false,"heading_as_written":"(* ---- (v60) Lambda branch selection: prefactor 3/(4pi^2), branch mis-scale 64pi^3/3 ---- *) checkExact[\"delta_top=48 c3^4=3/(256 pi^4); (8pi)^2 delta_top=3/(4 pi^2); 2c3/delta_top=64 pi^3/3 (G_N pinned)\", With[{c3 = 1/(8 Pi), dt = 48 (1/(8 Pi))^4}, Simplify[dt - 3/(256 Pi^4)] == 0 && Simplify[(8 Pi)^2 dt - 3/(4 Pi^2)] == 0 && Simplify[2 c3/dt - 64 Pi^3/3] == 0]]; checkExact[\"action exponents (1,5,10) = K5 counts (5 vertices, C(5,2)=10 edges); Pascal 16=1+5+10\", {1, 5, Binomial[5, 2]} == {1, 5, 10} && 1 + 5 + 10 == 16]; (* ---- (v61) boundary-CFT bridge: WZW central charges = atoms, conformal embedding ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:282","line_end":299,"line_start":282,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v60","v61"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["||V||=248 c3^2=31/(8pi^2); 2||V||=31/(4pi^2); 248=dim E8, 31=1+h^v(E8)","Xi = 2||V||/Delta = 31/(24 pi^2 log(3/2)); Delta_eff = Delta - 2||V|| > 0","E8 degrees {2,8,12,14,18,20,24,30}: clean atoms 2=|Z2|,8=rank,14=dimG2,20=detL,24=4!,30=h(E8)","sum(degrees)=128=2^7 (dS prefactor, 7=g+n-1); sum(exponents)=120=|R+(E8)|; prod=|W(E8)|"],"checked_by_registry":false,"heading_as_written":"(* ---- (v63) Seam-Engineering Index: exact closed form ---- *) checkExact[\"||V||=248 c3^2=31/(8pi^2); 2||V||=31/(4pi^2); 248=dim E8, 31=1+h^v(E8)\", With[{c3 = 1/(8 Pi)}, Simplify[248 c3^2 - 31/(8 Pi^2)] == 0 && 248/8 == 31 == 1 + 30]]; checkExact[\"Xi = 2||V||/Delta = 31/(24 pi^2 log(3/2)); Delta_eff = Delta - 2||V|| > 0\", Simplify[(31/(4 Pi^2))/(6 Log[3/2]) - 31/(24 Pi^2 Log[3/2])] == 0 && N[6 Log[3/2] - 31/(4 Pi^2)] > 1]; (* ---- (v66) compiler atoms = E8 Casimir invariant degrees ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:300","line_end":314,"line_start":300,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v63","v66"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["Fursaev-Solodukhin: k=c3/2=1/(16pi); S=4pi k A=2pi c3 A; 2pi c3=1/4 => S=A/4 (BH)","theorem (inverse): S=A/4 & S=4pi k A & k=c3/2 => c3=1/(8pi) UNIQUE","Seeley-DeWitt a2 = (1/(4pi)^2)(1/6)(R d + 6(-R/4)d) = -d/(192 pi^2) R (Dirac, carrier dof d)","1/(16 pi G)=f2 Lambda^2 d/(192 pi^2) is UV-sensitive: d/dLambda = f2 d Lambda/(96 pi^2) != 0"],"checked_by_registry":false,"heading_as_written":"(* ---- (v67) central theorem structural closure: replica area-law coeff => c3=1/(8pi) ---- *) checkExact[\"Fursaev-Solodukhin: k=c3/2=1/(16pi); S=4pi k A=2pi c3 A; 2pi c3=1/4 => S=A/4 (BH)\", With[{c3 = 1/(8 Pi)}, Simplify[c3/2 - 1/(16 Pi)] == 0 && Simplify[2 Pi c3 - 1/4] == 0 && Simplify[4 Pi (c3/2) - 1/4] == 0]]; checkExact[\"theorem (inverse): S=A/4 & S=4pi k A & k=c3/2 => c3=1/(8pi) UNIQUE\", Module[{ksol = 1/(4 (4 Pi))}, Simplify[ksol - 1/(16 Pi)] == 0 && Simplify[2*ksol - 1/(8 Pi)] == 0]]; (* ---- (v68) Seeley-DeWitt a2 for the carrier; 1/G UV-sensitive => k=c3/2 is a normalization ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:315","line_end":328,"line_start":315,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v67","v68"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["Z4 4-cycle eigenvalues {1,i,-1,-i}; H_1(sum=0) families = {i,-1,-i}","Q_+=3 diag(0,1/3,2/3)+1=diag(1,2,3): Spec{1,2,3}; Q_-=E-coupling sqrt3: Spec{0,+-sqrt3}","Z4 puncture action R unimodular (det=-1, eigenvalues {-1,i,-i}); det Q=3=N_fam (transport)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v69) D4-equivariant Q-geometry: Q_+ from cusp weights, Q_- E-block coupling ---- *) checkExact[\"Z4 4-cycle eigenvalues {1,i,-1,-i}; H_1(sum=0) families = {i,-1,-i}\", Sort[Eigenvalues[{{0,0,0,1},{1,0,0,0},{0,1,0,0},{0,0,1,0}}]] == Sort[{1, I, -1, -I}]]; checkExact[\"Q_+=3 diag(0,1/3,2/3)+1=diag(1,2,3): Spec{1,2,3}; Q_-=E-coupling sqrt3: Spec{0,+-sqrt3}\", Sort[Eigenvalues[3 DiagonalMatrix[{0, 1/3, 2/3}] + IdentityMatrix[3]]] == {1, 2, 3} && Sort[Eigenvalues[{{0, 0, 0}, {0, 0, Sqrt[3]}, {0, Sqrt[3], 0}}]] == Sort[{0, Sqrt[3], -Sqrt[3]}]]; (* ---- (v70) integer-lift of Q: Z4 puncture action unimodular, det Q = N_fam ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:329","line_end":341,"line_start":329,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v69","v70"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["det ladder (Q,K,R,L)=(3,4,8,20)=(N_fam,|mu4|,rank E8,det L); det R=8=rank E8=g+n; det Q=3=N_fam","selector stratum derived => c_u/c_d=55/117 is a pure integer Plucker readout (13=8+5=9+4)","det Q=3=|coker Q|=cusp-class order=denominator of cusp weights {0,1/3,2/3}=N_fam (same data as Spec Q_+)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v71) SIMPLE R-bridge: selector stratum derived => ratios are integer Plucker, no monodromy ---- *) checkExact[\"det ladder (Q,K,R,L)=(3,4,8,20)=(N_fam,|mu4|,rank E8,det L); det R=8=rank E8=g+n; det Q=3=N_fam\", {Det[Q], Det[K], Det[R], Det[L]} == {3, 4, 8, 20} && Det[R] == 8 == gcar + Nfam && Det[Q] == Nfam]; checkExact[\"selector stratum derived => c_u/c_d=55/117 is a pure integer Plucker readout (13=8+5=9+4)\", (gcar*11)/(Nfam^2*13) == 55/117 && 13 == 8 + 5 == Nfam^2 + 4]; (* ---- (v72) det Q = N_fam from the cusp class: order = weight denominator = |coker Q| ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:342","line_end":351,"line_start":342,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v71","v72"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["k=c3/2=1/(16pi)=(1/2)*(1/(|Z2|*2pi*chi(S2))), chi(S2)=2; Fursaev-Solodukhin 4pi k = 1/4","pencil P(x)=det(K+xQ) endpoints (2,4,20,68); consecutive differences (2,16,48)=(|Z2|,dim S+,Omega_adm)","anchor QF: 1^TK1=25=g_car^2, a^TKa=41=10 b1, a^TKa-1^TK1=16=dim S+ (EM budget = mass vol + one gen)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v73) k=c3/2 forced: variational factor x Gauss-Bonnet topology; Fursaev-Solodukhin S=A/4 ---- *) checkExact[\"k=c3/2=1/(16pi)=(1/2)*(1/(|Z2|*2pi*chi(S2))), chi(S2)=2; Fursaev-Solodukhin 4pi k = 1/4\", Module[{c3 = 1/(8 Pi), chi = 2, Z2 = 2}, (c3/2 == 1/(16 Pi)) && (c3 == 1/(Z2*2 Pi*chi)) && (4 Pi*(c3/2) == 1/4)]]; (* ---- (v74) compiler micro-lemmas: pencil differences 2->16->48; anchor QF 41-25=16 ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:352","line_end":364,"line_start":352,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v73","v74"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["lepton c-product 16/7*4/3*7/6 = 32/9 = 2^g_car/N_fam^2; (ratios,product)=>(individuals) bijection rebuilds (16/7,4/3,7/6)","||V||<=248 c3^2 = 31/(8pi^2) (31=2^g_car-1); 2||V||=31/(4pi^2); Delta_eff=6log(3/2)-31/(4pi^2)>0"],"checked_by_registry":false,"heading_as_written":"(* ---- (v75) Gate 1: U_point -> v_geo. lepton product 32/9; (ratios,product)<=>(individuals) bijection ---- *) checkExact[\"lepton c-product 16/7*4/3*7/6 = 32/9 = 2^g_car/N_fam^2; (ratios,product)=>(individuals) bijection rebuilds (16/7,4/3,7/6)\", Module[{c = {16/7, 4/3, 7/6}, P, r, c0}, P = Times @@ c; r = c/c[[1]]; c0 = (P/(Times @@ r))^(1/3); (P == 32/9 == 2^gcar/Nfam^2) && (c0*r === c)]]; (* ---- (v76) Gate 2: decoupling margin Delta_eff = 6log(3/2) - 31/(4pi^2) > 0 ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:365","line_end":375,"line_start":365,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v75","v76"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["level-1 c=dim/(1+h^v): c(E8)=248/31=8=rank E8, c(D5)=45/9=5, c(A3)=15/5=3; embedding 5+3=8 => coset c=0","S_dS * rho_Lambda = 1/(128 c3^4) = 32 pi^4 (cosmological pinning of the single scale)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v77) G6 via E8 level-1 net: level-1 central charges + conformal embedding c-sum ---- *) checkExact[\"level-1 c=dim/(1+h^v): c(E8)=248/31=8=rank E8, c(D5)=45/9=5, c(A3)=15/5=3; embedding 5+3=8 => coset c=0\", Module[{cE8 = 248/(1 + 30), cD5 = 45/(1 + 8), cA3 = 15/(1 + 4)}, (cE8 == 8) && (cD5 == 5) && (cA3 == 3) && (cD5 + cA3 == cE8)]]; (* ---- (v78) v_geo floor: S_dS*rho_Lambda = 1/(128 c3^4) = 32 pi^4 (one scale pinned by one measurement) ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:376","line_end":384,"line_start":376,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v77","v78"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["Lucas-Binet D_n=(3^n-(-2)^n)/5 = {1,1,7,13,55,133}; c_u/c_d = D_5/(N_fam^2 D_4) = 55/117","1^T M^-1 1 = 1/atom (Q->1/3,R=K->1/4,L->1/10); a^T R^-1 a = a^T K^-1 a = a^T L^-1 a = 1 (a^T Q^-1 a=7/3)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v79) hypercharge Lucas-Binet D_n + the quark-ratio reading ---- *) checkExact[\"Lucas-Binet D_n=(3^n-(-2)^n)/5 = {1,1,7,13,55,133}; c_u/c_d = D_5/(N_fam^2 D_4) = 55/117\", Module[{D}, D = Table[(3^n - (-2)^n)/5, {n, 1, 6}]; D == {1, 1, 7, 13, 55, 133} && D[[5]]/(Nfam^2 D[[4]]) == 55/117]]; (* ---- (v79) Inverse Anchor Theorem: 1^T M^-1 1 = 1/atom; a^T M^-1 a = 1 for R,K,L ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:385","line_end":396,"line_start":385,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v79"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["anchor singularity: det B(K+xQ)=(3x+2)(3x+5); type checker det B = (9,10,16,40) for (Q,K,R,L)","F4xG2 shadow: det B_{R+Q}=52=dim F4; 248 = 52 + 14 + 26*7 (real E8->F4xG2 branching)","double cover y^2=det B(K+xQ)=(3x+2)(3x+5): branch points {-5/3,-2/3}, discriminant 81=N_fam^4, separation 1","clearing matrices: C_{2/3}=3K-2Q (tr=15,sum=45,det=60), B=(5,7)^T(9,11) sum=240; C_{5/3}=3K-5Q neutral chi=(l+2)(l^2+l+6)","branch divisor = (scalaron,A_Lambda): sum roots=-7/3=-scalaron/N_fam, product=10/9=A_Lambda/N_fam^2; {2,5} sum=7 prod=10 diff=3"],"checked_by_registry":false,"heading_as_written":"(* ---- (v80) operator-pencil geometry: anchor singularity + block-det type checker + F4xG2 shadow ---- *) checkExact[\"anchor singularity: det B(K+xQ)=(3x+2)(3x+5); type checker det B = (9,10,16,40) for (Q,K,R,L)\", Module[{one = {1, 1, 1}, av = {1, 1, 2}, bb, dbx}, bb[M_] := {{one.M.one, one.M.av}, {av.M.one, av.M.av}}; dbx = Det[bb[K + xx*Q]]; (Factor[dbx] == (3 xx + 2) (3 xx + 5)) && (Det[bb[Q]] == 9) && (Det[bb[K]] == 10) && (Det[bb[R]] == 16) && (Det[bb[L]] == 40)]]; checkExact[\"F4xG2 shadow: det B_{R+Q}=52=dim F4; 248 = 52 + 14 + 26*7 (real E8->F4xG2 branching)\", Module[{one = {1, 1, 1}, av = {1, 1, 2}, F = R + Q, bb}, bb[M_] := {{one.M.one, one.M.av}, {av.M.one, av.M.av}}; (Det[bb[F]] == 52) && (52 + 14 + 26*7 == 248)]]; (* ---- (v81) double cover: det B(K+xQ) quadratic, branch points {-2/3,-5/3}, disc=81=N_fam^4 ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:397","line_end":443,"line_start":397,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v80","v81"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v983 NORMS+WEIGHT [E]: |omega_s|^2=5/4, |omega_f|^2=3/4, |lambda|^2=2, h_lambda=1","v983 ORDER FOUR [E]: 4*lambda in D5(+)A3, lambda and 2*lambda not -- [lambda] generates the diagonal Z4","v983 ISOTROPY+UNIMODULAR [E]: lambda.L0 subset Z on a generator set; det(D5)*det(A3)=16, index-4 glue => det L=1","v983 COSET ROOT CENSUS [E]: norm-2 vectors per fusion power k=0..3 = {52,64,60,64}, total 240; odd powers 64+64=128","v983 KILLS+HOLOMORPHY SHADOW [E]: vector glue (v,omega_f) norm 7/4 and mismatched (omega_s, omega_2) norm 9/4 not in 2Z; det Cartan D8=4 vs glued det=1","v985 SPECTRA [E]: jump circ(2,-1,0,-1) -> {0,2,4,2} (kernel k=0); mark circ(0,1,2,1) -> {4,-2,0,-2} (kernel k=2)","v985 DECK SWAP [E]: r->r+2 maps |jump| onto |mark| exactly; odd swap r->r+1 does NOT (Z2 deck, not arbitrary)","v985 GRADED DET' [E]: gr(jump)-gr(mark)=log(ln2/4) exactly, c3-free","v985 UNIFORM RATIO [E]: after deck swap, (16 c3 |lambda^J_{r+2}|)/(4 c3 ln2 |lambda^M_r|)=4/ln2 in every matched nonzero channel"],"checked_by_registry":false,"heading_as_written":"(* ---- (v983) SEAM.SIMPLECURRENT.GENERATOR.01: glue vector lambda = (omega_s, omega_f) ---- *) Module[{omegaS, omegaF, lam, inD5, inA3, inL0, gensD5, gensA3, dots, cosetRoots, census, lamV, omega2, nV, n2, cartanD8}, omegaS = ConstantArray[1/2, 5]; omegaF = {3/4, -1/4, -1/4, -1/4}; lam = Join[omegaS, omegaF]; inD5[x_] := (And @@ (IntegerQ /@ x)) && EvenQ[Total[x]]; inA3[y_] := (And @@ (IntegerQ /@ y)) && Total[y] === 0; inL0[z_] := inD5[Take[z, 5]] && inA3[Take[z, {6, 9}]]; checkExact[\"v983 NORMS+WEIGHT [E]: |omega_s|^2=5/4, |omega_f|^2=3/4, |lambda|^2=2, h_lambda=1\", Total[omegaS^2] === 5/4 && Total[omegaF^2] === 3/4 && Total[lam^2] === 2 && Total[lam^2]/2 === 1]; checkExact[\"v983 ORDER FOUR [E]: 4*lambda in D5(+)A3, lambda and 2*lambda not -- [lambda] generates the diagonal Z4\", inL0[4 lam] && ! inL0[2 lam] && ! inL0[lam]]; gensD5 = {{1, 1, 0, 0, 0}, {1, -1, 0, 0, 0}, {0, 1, 1, 0, 0}, {0, 0, 1, 1, 0}, {0, 0, 0, 1, 1}}; gensA3 = {{1, -1, 0, 0}, {0, 1, -1, 0}, {0, 0, 1, -1}}; dots = Join[omegaS . # & /@ gensD5, omegaF . # & /@ gensA3]; checkExact[\"v983 ISOTROPY+UNIMODULAR [E]: lambda.L0 subset Z on a generator set; det(D5)*det(A3)=16, index-4 glue => det L=1\", (And @@ (IntegerQ /@ dots)) && 16/4^2 === 1]; cosetRoots[k_] := Module[{t = k lam, d5, a3}, d5 = Counts @ Select[ Total[(# + Take[t, 5])^2] & /@ Select[Tuples[Range[-5, 3], 5], EvenQ[Total[#]] &], # <= 2 &]; a3 = Counts @ Select[ Total[(Join[#, {-Total[#]}] + Take[t, {6, 9}])^2] & /@ Tuples[Range[-6, 6], 3], # <= 2 &]; Total[KeyValueMap[#2 Lookup[a3, 2 - #1, 0] &, d5]]]; census = Table[cosetRoots[k], {k, 0, 3}]; checkExact[\"v983 COSET ROOT CENSUS [E]: norm-2 vectors per fusion power k=0..3 = {52,64,60,64}, total 240; odd powers 64+64=128\", census === {52, 64, 60, 64} && Total[census] === 240 && census[[2]] + census[[4]] === 128]; lamV = Join[{1, 0, 0, 0, 0}, omegaF]; omega2 = {1/2, 1/2, -1/2, -1/2}; nV = Total[lamV^2]; n2 = Total[omegaS^2] + Total[omega2^2]; cartanD8 = {{2, -1, 0, 0, 0, 0, 0, 0}, {-1, 2, -1, 0, 0, 0, 0, 0}, {0, -1, 2, -1, 0, 0, 0, 0}, {0, 0, -1, 2, -1, 0, 0, 0}, {0, 0, 0, -1, 2, -1, 0, 0}, {0, 0, 0, 0, -1, 2, -1, -1}, {0, 0, 0, 0, 0, -1, 2, 0}, {0, 0, 0, 0, 0, -1, 0, 2}}; checkExact[\"v983 KILLS+HOLOMORPHY SHADOW [E]: vector glue (v,omega_f) norm 7/4 and mismatched (omega_s, omega_2) norm 9/4 not in 2Z; det Cartan D8=4 vs glued det=1\", nV === 7/4 && n2 === 9/4 && Det[cartanD8] === 4 && 16/4^2 === 1]; ]; (* ---- (v985) ALPHA.QUILLEN.EXACT.01: mu4 circulant spectra + graded channel swap ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:444","line_end":519,"line_start":444,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v983","v985"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v987 SPECTRAL [E]: B=P1+(2/3)P2+(1/3)P3 with orthogonal projectors summing to I","v987 H=-log B [E]: spectrum {0, log(3/2), log 3}, gap log(3/2), H.u1=0","v987 WICK ANCHOR [E]: U(-i n)=B^n for n=1..6","v987 CONGRUENCE+MUST-FAIL [E]: K^{1/2} B K^{1/2} symmetric (Sylvester: B SPD with eigs {1,2/3,1/3}); mutant K.B not symmetric; v971 negative kernel det<0"],"checked_by_registry":false,"heading_as_written":"(* ---- (v987) DYN.UNITARY.DILATION.01: B spectral decomp, H=-log B, Wick, congruence ---- Python-only: size-uniform free-band D2/LR (numeric collision), interacting gap plateau, quantum SWAP coupling. *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:520","line_end":556,"line_start":520,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v987"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v993 SNF TEXTBOOK [E]: A_n=Z_{n+1} (n=1..8); D_n=Z4 (n odd)/Z2xZ2 (n even) (n=2..8); E6=Z3, E7=Z2, E8=1; D3 cong A3","v993 ADE RANK-8 CENSUS [E]: only diagonal cyclic-Z4 isotropic unimodular glue is (D5,A3), up to D3 cong A3","v993 KILLS [X]: (D4,A4) not cyclic Z4; (A4,A4) prod 25; (E7,A1) prod 4; (D4,D4) Klein no order-4; (A7,A1) A1=Z2; (E6,A2)=Z3xZ3; isotropic q(D5)+q(A3)=5/4+3/4=2","v993 [lambda]^2=[v] [E]: 2[omega_s]=[v] in disc(D5); 4*lambda in L0, 2*lambda not; order-2 vector glue norm 7/4 not in 2Z","v993 UNIQUE-CE DIMS [E]: bimodule deviations force D=0 (n_free=0 at d=4,8); dropping the module property leaves kernel 36 (d=4) / 720 (d=8)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v993) AX.P2.01 census: SNF disc groups, unique (D5,A3), [lambda]^2=[v], CE dims ---- Python-only: random CE axiom sampling on M_d^{Z4} / crossed product. *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:557","line_end":679,"line_start":557,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v993"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v994 THETA_E8/eta^8 [E]: SeriesCoefficient of (EllipticTheta[2]^8+EllipticTheta[3]^8+EllipticTheta[4]^8)/2 / Product[(1-q^n)^8] = {1,248,4124,34752}; Jacobi theta_E8 matches E4=1+240 Sum sigma_3 (DedekindEta^8 = q^{1/3} Product)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v994) SEAM.EQUIV.MMST.01 C3: Theta_E8 / eta^8 = {1,248,4124,34752} ---- Python-only: C1 entropy, C2 QWZ spectrum, C4 two-point numeric, C5 sector recombination beyond det, C6 cited, C7 open, GSO/N=8 must-fail combinatorics. *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:680","line_end":698,"line_start":680,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v994"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v997 BARNES-RIVERS [E]: projector algebra P_i P_j=delta_ij P_i, sum=I_10; ranks (spin-2, spin-1, 0s, 0w)=(5,3,1,1) at p=(0,0,0,1)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v997) GRAV.SPIN2.EMERGENCE.01: Barnes-Rivers ranks (5,3,1,1) ---- Python-only: Weyl^2 ghost residues, random-p numeric, SMG N=8 Fidkowski-Kitaev toy (spectrum / Spin(7) / Schmidt / edge). *)","id":"wolfram-section:verification/wolfram/tfpt_readouts.wl:699","line_end":739,"line_start":699,"path":"verification/wolfram/tfpt_readouts.wl","python_identifiers_in_heading":["v997"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v84 ALPHA_INV frozen","v84 SIN2_THETA12_SEED frozen","v84 SIN2_THETA13 frozen","v84 BETA_BIREFRINGENCE_DEG frozen","v84 OMEGA_B frozen","v84 LAMBDA_C frozen","v84 S23_CKM frozen","v84 S13_CKM frozen","v84 DELTA_CKM_RAD frozen","v84 MMU_OVER_MTAU frozen","v84 ME_OVER_MMU frozen","v84 MU_OVER_MD = 55/117 exactly","v84 MC_OVER_MS frozen","v84 MT_OVER_MB frozen","v84 MSCAL_OVER_MBAR frozen","v84 RHOL_OVER_MBAR4 frozen","v84 theta12 variants distinct (seed < seam < nonlin band)","v85 master cover det B(K+xQ) = (3x+2)(3x+5), disc 81","v85 GL(2) covariance (exact symbolic identity)","v85 disc transforms as 81 det(G)^2","v85 negative controls: disc(R+xQ)=153, disc(K+xR)=201 (non-square)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v84) frozen registry decimals recompute from the axioms ---- *) phiseam[a_] := phibase + (dtop Exp[-2 a]) (1 - dtop Exp[-2 a])^(-5/4); FU1[a_] := a^3 - 2 c3^3 a^2 - (4/5) c3^6 41 Log[1/phiseam[a]]; aStar = a /. FindRoot[FU1[a] == 0, {a, 0.0073}, WorkingPrecision -> 40]; check[\"v84 ALPHA_INV frozen\", 1/aStar, 137.0359992168407125035379`30, 10^-20]; lamC = Sqrt[phi0 (1 - phi0)]; check[\"v84 SIN2_THETA12_SEED frozen\", 1/3 - phi0/2, 0.3067473572449105696786871`30, 10^-20]; check[\"v84 SIN2_THETA13 frozen\", phi0 Exp[-5/6], 0.02310843515888110429328466`30, 10^-20]; check[\"v84 BETA_BIREFRINGENCE_DEG frozen\", (phi0/(4 Pi)) (180/Pi), 0.2424350309009295284924315`30, 10^-20]; check[\"v84 OMEGA_B frozen\", (1 - 1/(4 Pi)) phi0, 0.04894066266545011220054565`30, 10^-20]; check[\"v84 LAMBDA_C frozen\", lamC, 0.2243762368847217731120972`30, 10^-20]; check[\"v84 S23_CKM frozen\", phi0/(1 + lamC), 0.04342778843220215630289116`30, 10^-20]; check[\"v84 S13_CKM frozen\", lamC^3/3, 0.003765384454486429837965432`30, 10^-20]; check[\"v84 DELTA_CKM_RAD frozen\", Pi/3 + 3 lamC^2, 1.198231638232244084651243`30, 10^-20]; check[\"v84 MMU_OVER_MTAU frozen\", (8/7) phi0, 0.06076794534496631692490568`30, 10^-20]; check[\"v84 ME_OVER_MMU frozen\", (12/7) phi0^2, 0.004846725425651567674771059`30, 10^-20]; checkExact[\"v84 MU_OVER_MD = 55/117 exactly\", 55/117 == 55/117]; check[\"v84 MC_OVER_MS frozen\", (34/47)/phi0, 13.60499710285539356302651`30, 10^-20]; check[\"v84 MT_OVER_MB frozen\", (3/26)/phi0^2, 40.8115130177002629681607`30, 10^-20]; check[\"v84 MSCAL_OVER_MBAR frozen\", c3^(7/2), 0.00001256494208322844896998079`30, 10^-20]; check[\"v84 RHOL_OVER_MBAR4 frozen\", (3/(4 Pi^2)) Exp[-2/aStar], 7.125329526706216792033797`30 10^-121, 10^-15]; checkExact[\"v84 theta12 variants distinct (seed < seam < nonlin band)\", (1/3 - phi0/2) < (1/3 - 1/(12 Pi))]; (* ---- (v85) master cover: GL(2) covariance on the anchor plane ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:38","line_end":82,"line_start":38,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v84","v85"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v86 Gamma = 4 M^3/(48 pi Mbar^2) = 128.1 GeV","v86 T_reh = 9.55e9 GeV (g*=106.75)","v86 A_s(51.4406) = 1.764e-9 (the A_s-disfavoured slow point)","v86 A_s-preferred N_star = 56.198","v86 dichotomy: matching A_s at 51.44 needs M x 1.0925","v87 modularity: S^2 = I, (ST)^3 = I","v87 all six modular invariants commute with S and T (Z00=1)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v86) reheating arithmetic (scale chain; pivot solve stays Python) ---- *) Mbar = 2.435323203`20 10^18; Mscal = c3^(7/2) Mbar; GammaScal = 4 Mscal^3/(48 Pi Mbar^2); check[\"v86 Gamma = 4 M^3/(48 pi Mbar^2) = 128.1 GeV\", GammaScal, 128.146562596`12, 10^-6]; check[\"v86 T_reh = 9.55e9 GeV (g*=106.75)\", (30 (3 GammaScal^2 Mbar^2)/(Pi^2 106.75))^(1/4), 9.55048669665`12 10^9, 10^-6]; AsOf[n_] := n^2 c3^7/(24 Pi^2); check[\"v86 A_s(51.4406) = 1.764e-9 (the A_s-disfavoured slow point)\", AsOf[51.4406], 1.7637`5 10^-9, 10^-3]; check[\"v86 A_s-preferred N_star = 56.198\", Sqrt[2.105`10 10^-9 24 Pi^2/c3^7], 56.198`6, 10^-4]; check[\"v86 dichotomy: matching A_s at 51.44 needs M x 1.0925\", Sqrt[2.105`10 10^-9/AsOf[51.4406]], 1.09248`6, 10^-4]; (* ---- (v87) SO(16)_1 modular data and its six invariants ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:83","line_end":116,"line_start":83,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v86","v87"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v89 KLM: mu(D5xA3)=16, mu(E8)=1 => index 4 = |mu4| = |Z2|^2","v89 branching 248 = 45+15+64+64+60; glue sectors h = 1","v89 mu-additivity: 16/4^2 = 1 (holomorphy follows)","v90 cap Gauss-Bonnet = 2 pi (1 - cos theta0), smoothing-independent","v90 replica S = 4 pi k A (smooth part drops out)","v90 S = A/4 forces c3 = 1/(8 pi) uniquely"],"checked_by_registry":false,"heading_as_written":"(* ---- (v89) carrier index lemma ---- *) checkExact[\"v89 KLM: mu(D5xA3)=16, mu(E8)=1 => index 4 = |mu4| = |Z2|^2\", (4*4 == 16) && (Sqrt[16/1] == 4) && (4 == mu4) && (4 == 2^2)]; checkExact[\"v89 branching 248 = 45+15+64+64+60; glue sectors h = 1\", (45 + 15 + 16*4 + 16*4 + 10*6 == 248) && (1/2 + 1/2 == 1) && (5/8 + 3/8 == 1)]; checkExact[\"v89 mu-additivity: 16/4^2 = 1 (holomorphy follows)\", 16/4^2 == 1]; (* ---- (v90) conical defect chain ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:117","line_end":135,"line_start":117,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v89","v90"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v91 edges/faces/volume of {2,3,4,5}","v91 graph reading 240 = |mu4| |E(K4)| |E(K5)|; breaks at K6","v91 chi_T audit: coeffs (14,71,154,120); chi(0)=chi(7)=120, chi(1)=chi(6)=24","v92 the two Lagrangian glues are isotropic (q = 0 on all elements)","v92 isotropic order-4 ELEMENTS are exactly (1,1),(1,3),(3,1),(3,3)","v92 Klein subgroup not isotropic ((2,0): q=1/2); halfway {(0,0),(2,2)} isotropic","v92 halfway extension has det 16/2^2 = 4 (D8); Lagrangian det 16/4^2 = 1 (E8)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v91) spine tetrahedron ---- *) spine = {2, 3, 4, 5}; checkExact[\"v91 edges/faces/volume of {2,3,4,5}\", (Sort[Times @@@ Subsets[spine, {2}]] == {6, 8, 10, 12, 15, 20}) && (Sort[Times @@@ Subsets[spine, {3}]] == {24, 30, 40, 60}) && (Times @@ spine == 120) && (120 == Total[{1, 7, 11, 13, 17, 19, 23, 29}])]; checkExact[\"v91 graph reading 240 = |mu4| |E(K4)| |E(K5)|; breaks at K6\", (4 Binomial[4, 2] Binomial[5, 2] == 240) && (Binomial[6, 2] == 15) && (1 + 1 + 2^4 != 15)]; chiT[t_] := (t - 2) (t - 3) (t - 4) (t - 5); checkExact[\"v91 chi_T audit: coeffs (14,71,154,120); chi(0)=chi(7)=120, chi(1)=chi(6)=24\", (Expand[chiT[t]] == t^4 - 14 t^3 + 71 t^2 - 154 t + 120) && (chiT[0] == 120) && (chiT[7] == 120) && (chiT[1] == 24) && (chiT[6] == 24)]; (* ---- (v92) glue uniqueness ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:136","line_end":164,"line_start":136,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v91","v92"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v93 F fixes branch points; F'(2)=(2/3)^6, F'(5)=(3/2)^6","v93 Q_src = 0.6644638161 from the exact ladder","v93 basin lemma: Q in [1/3,1] -> q = 3Q in [1,3]: attractor 2 in, repeller 5 out","v93 rho_src = -phi0/24 to 0.8% (v25 conjecture in attractor coordinates)","v94 corners: R=M(0,0), K=M(1,-1), L=M(2,0), F=M(1,1)","v94 global invariants det M and det B_M (exact polynomials)","v94 pencil cut (1+x, x-1) refactorises the master cover (3x+2)(3x+5)","v94 diagonal cut disc = 153 NON-square (negative control)","v94 winding line: det B = 2 det for ALL s (8+2s vs 16+4s)","v94 cofactor seam normal n=(5,-9,6): n.1=2=|Z2|, n.R=(8,0,0), n.L=(20,0,0)","v94 Pluecker canonicalisation: ||Pi_L(K)||_1 = 11 and ||Pi_R(K)||_1 = 26"],"checked_by_registry":false,"heading_as_written":"(* ---- (v93) Koide relaxation toy ---- *) FK[q_] := 2 (569 q - 3325)/(665 q - 3517); checkExact[\"v93 F fixes branch points; F'(2)=(2/3)^6, F'(5)=(3/2)^6\", (FK[2] == 2) && (FK[5] == 5) && (Simplify[FK'[2]] == (2/3)^6) && (Simplify[FK'[5]] == (3/2)^6)]; Qsrc = Module[{me = (16/7) phi0^5, mm = (4/3) phi0^3, mt = (7/6) phi0^2}, (me + mm + mt)/(Sqrt[me] + Sqrt[mm] + Sqrt[mt])^2]; check[\"v93 Q_src = 0.6644638161 from the exact ladder\", Qsrc, 0.664463816123`12, 10^-10]; checkExact[\"v93 basin lemma: Q in [1/3,1] -> q = 3Q in [1,3]: attractor 2 in, repeller 5 out\", (3 (1/3) == 1) && (3*1 == 3) && (1 < 2 < 3) && ! (1 < 5 < 3)]; rhoOf[q_] := (q - 2)/(5 - q); check[\"v93 rho_src = -phi0/24 to 0.8% (v25 conjecture in attractor coordinates)\", rhoOf[3 Qsrc]/(-phi0/24), 0.992105906542`12, 10^-8]; (* ---- (v94) sheet diamond & winding line ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:165","line_end":203,"line_start":165,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v25","v93","v94"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v95 centered cross: Q=U+V; R=C-U, L=C+U, K=C-V, F=C+V","v95 axes spectra: Spec U = {3,0,0} (winding), Spec V = {0,1,2} = N_fam*cusp","v95 center invariants: tr C=12, det C=14, sum C=31=2^g_car-1, det B_C=28","v95 ray alignment: Pi_R(C)=7(2,3,1), Pi_R(L)=10(2,3,1)","v96 B(x) = [[15x+25,16x+29],[21x+35,23x+41]], det = (3x+2)(3x+5)","v96 integer kernels: Koide w=(2,2,-7), v=(2,2,-3); carrier w=1, v=(1,1,-6)","v96 collapse lemma: P(-2/3).w = (20/3)(1,-1,0), P(-5/3).w = (2/3)(-1,1,0)","v96 generation side: v.P prop (-1,1,0) at both branch points","v96 sector ladder: Koide kernel -> (8x+12, 10x, 3x+2); carrier kernel -> (4x+6, 5x+9, 6x+10)","v96 lepton pairings ARE the det-B factors; up-row of P(-3/2) = (-1/2)(1,-1,0)","v96 controls: anchor (2,1,1) det B = (x+2)(9x+11) (split, disc 49); (1,2,1) disc 40 non-square"],"checked_by_registry":false,"heading_as_written":"(* ---- (v95) centered flavor diamond ---- *) Uop = Q.DiagonalMatrix[{1, 0, 0}]; Vop = Q.DiagonalMatrix[{0, 1, 1}]; Cc = R + Uop; Lop = R + 2 Uop; Fop = R + Q; checkExact[\"v95 centered cross: Q=U+V; R=C-U, L=C+U, K=C-V, F=C+V\", (Q == Uop + Vop) && (R == Cc - Uop) && (Lop == Cc + Uop) && (K == Cc - Vop) && (Fop == Cc + Vop)]; checkExact[\"v95 axes spectra: Spec U = {3,0,0} (winding), Spec V = {0,1,2} = N_fam*cusp\", (Sort[Eigenvalues[Uop]] == {0, 0, 3}) && (Sort[Eigenvalues[Vop]] == {0, 1, 2})]; checkExact[\"v95 center invariants: tr C=12, det C=14, sum C=31=2^g_car-1, det B_C=28\", (Tr[Cc] == 12) && (Det[Cc] == 14) && (Total[Cc, 2] == 31) && (31 == 2^gcar - 1) && (Det[bb[Cc]] == 28)]; checkExact[\"v95 ray alignment: Pi_R(C)=7(2,3,1), Pi_R(L)=10(2,3,1)\", (plR[Cc] == 7 {2, 3, 1}) && (plR[Lop] == 10 {2, 3, 1})]; (* ---- (v96) branch-kernel selection (P1) ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:204","line_end":248,"line_start":204,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v95","v96"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v97 Q_+ eigenvectors e1=(0,0,1) [l=1], e2=(0,1,2) [l=2], e3=(1,0,0) [l=3]","v97 T_A integer involution, det -1, fixes 1 and a; T_A swaps e2 <-> e3, fixes e1","v97 anchor = conjugation-symmetric vector: a = e2+e3, 1 = a-e1; odd line e2-e3","v97 one deck action: T_A = -1 on R^3/span{1,a} (like sigma_12); parity det T_A = det sigma_12 = -1, det Sigma = +1","v97 D4 closure: G = T_A.Sigma has order 4, char (t+1)(t^2+1) = char(v70 R_rot)","v97 sheet-index lemma: det S always EVEN on the integer intertwiner space, minimum |det| = 2 = |Z2|","v97 Q (det = N_fam) does NOT intertwine G -> R_rot (independent bridge)","v98 integer mu4 on the cusp basis: G e1 = -e1, G e3 = e2, G e2 = -e3; G^4 = I","v98 dictionary: cusp-0 line = the self-conjugate Z4-class-2 line (-1 eigenspace of G)","v98 T_A G T_A^-1 = G^-1 (discriminant conjugation k -> -k); Sigma = T_A G","v98 q_A3 respects the swap: q(1) = q(3) = 3/8, q(2) = 1/2, q(0) = 0","v98 reflection classes separated: T_A e1 = +e1 (det -1, glue-swapping) vs Sigma e1 = -e1 (det +1, glue-fixing)","v98 audit: G a = e2 - e3; dihedral (T_A G)^2 = I"],"checked_by_registry":false,"heading_as_written":"(* ---- (v97) sheet-conjugation bridge (P1 -> one [P]) ---- *) TA = {{0, 1, 0}, {1, 0, 0}, {2, -2, 1}}; SigM = DiagonalMatrix[{1, -1, -1}]; sig12 = {{0, 1, 0}, {1, 0, 0}, {0, 0, 1}}; e1v = {0, 0, 1}; e2v = {0, 1, 2}; e3v = {1, 0, 0}; QPm = (Q + SigM.Q.SigM)/2; checkExact[\"v97 Q_+ eigenvectors e1=(0,0,1) [l=1], e2=(0,1,2) [l=2], e3=(1,0,0) [l=3]\", (QPm.e1v == 1 e1v) && (QPm.e2v == 2 e2v) && (QPm.e3v == 3 e3v)]; checkExact[\"v97 T_A integer involution, det -1, fixes 1 and a; T_A swaps e2 <-> e3, fixes e1\", (TA.TA == IdentityMatrix[3]) && (Det[TA] == -1) && (TA.one == one) && (TA.av == av) && (TA.e2v == e3v) && (TA.e3v == e2v) && (TA.e1v == e1v)]; checkExact[\"v97 anchor = conjugation-symmetric vector: a = e2+e3, 1 = a-e1; odd line e2-e3\", (av == e2v + e3v) && (one == av - e1v) && (TA.(e2v - e3v) == -(e2v - e3v))]; ddir = {-1, 1, 0}; coeffs = LinearSolve[Transpose[{one, av, ddir}], TA.ddir]; checkExact[\"v97 one deck action: T_A = -1 on R^3/span{1,a} (like sigma_12); parity det T_A = det sigma_12 = -1, det Sigma = +1\", (coeffs[[3]] == -1) && (sig12.ddir == -ddir) && (Det[sig12] == -1) && (Det[SigM] == 1)]; Gm = TA.SigM; RrotM = {{0, 0, -1}, {1, 0, -1}, {0, 1, -1}}; checkExact[\"v97 D4 closure: G = T_A.Sigma has order 4, char (t+1)(t^2+1) = char(v70 R_rot)\", (MatrixPower[Gm, 4] == IdentityMatrix[3]) && (MatrixPower[Gm, 2] != IdentityMatrix[3]) && (Expand[CharacteristicPolynomial[Gm, t] + (t + 1) (t^2 + 1)] === 0) && (Expand[CharacteristicPolynomial[Gm, t] - CharacteristicPolynomial[RrotM, t]] === 0)]; Svars = Array[sv, {3, 3}]; solS = Quiet[Solve[Flatten[Svars.Gm - RrotM.Svars] == 0, Flatten[Svars]], Solve::svars]; Sgen = Svars /. First[solS]; detSgen = Factor[Det[Sgen]]; checkExact[\"v97 sheet-index lemma: det S always EVEN on the integer intertwiner space, minimum |det| = 2 = |Z2|\", Module[{vars = Variables[detSgen], vals}, vals = Select[Abs[detSgen /. Thread[vars -> #]] & /@ Tuples[Range[-2, 2], Length[vars]], # =!= 0 &]; (And @@ (EvenQ /@ vals)) && (Min[vals] == 2)]]; checkExact[\"v97 Q (det = N_fam) does NOT intertwine G -> R_rot (independent bridge)\", Q.Gm != RrotM.Q]; (* ---- (v98) discriminant dictionary derived ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:249","line_end":302,"line_start":249,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v70","v97","v98"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v99 canonical generator: time-1 map of the rho-scaling flow IS the v82 Moebius F (exact symbolic identity)","v99 e^{-Delta} = (2/3)^6 exactly (the gap is the multiplier)","v99 flow time at PDG central m_tau = 1776.93: t = 2.8385","v99 t(-1 sigma) = 2.347 (data fragility)","v99 Q = 2/3 exactly at m_tau = 1776.9690 (+0.43 sigma, inside the band)","v99 conditional n=3 (= N_fam steps): m_tau = 1776.9427 MeV","v99 n=2 excluded: m_tau = 1776.6690 MeV (-2.9 sigma)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v99) Koide flow time ---- *) DeltaGap = 6 Log[3/2]; rhoK[q_] := (q - 2)/(5 - q); qOfRho[r_] := (2 + 5 r)/(1 + r); checkExact[\"v99 canonical generator: time-1 map of the rho-scaling flow IS the v82 Moebius F (exact symbolic identity)\", Simplify[FK[q] - qOfRho[(2/3)^6 rhoK[q]]] === 0]; checkExact[\"v99 e^{-Delta} = (2/3)^6 exactly (the gap is the multiplier)\", Simplify[Exp[-DeltaGap] - (2/3)^6] === 0]; koideQ[a_, b_, c_] := (a + b + c)/(Sqrt[a] + Sqrt[b] + Sqrt[c])^2; mE = 0.51099895069`20; mMU = 105.6583755`20; (* PDG 2024 pole masses, MeV *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:303","line_end":325,"line_start":303,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v82","v99"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":[],"checked_by_registry":false,"heading_as_written":"(* v100_numerology_null_mc.py is Python-only by design: it is a STATISTICAL module (exact integer census of a declared formula grammar + deterministic Monte-Carlo pseudo-theories + RNG-seeded negative controls + 94500 float root-solves), not an exact algebraic identity -- same convention as the Python-only v62/v64/v65. No Wolfram mirror is required; flagged in README.md and ledger GATE.WOLFRAM.02. *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:326","line_end":332,"line_start":326,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v62","v64","v65"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v101 Nariai double root: M_N = 1/(3 Sqrt[L]) = 1/(N_fam Sqrt[L]), r_N = 1/Sqrt[L]","v101 Nariai cubic = t^3 - 3t + 2 = (t-1)^2(t+2): roots (1,1,-2) = traceless anchor","v101 Koide 2/3 = Nariai entropy bound: S_N/S_dS = 2/3, per horizon 1/3, deficit 1/3","v101 interpolation S_tot/S_dS = (x^2+1)/(x^2+x+1) (denominator = Phi_3), min at merge","v101 three-sheet conservation: Sum r_i^2 = 2(rb^2+rb rc+rc^2) for roots (rb, rc, -(rb+rc))","v101 Q_geom range: pure dS -> 1/2 = delta, Nariai -> 3/8 = p2(a)/e1(a)^2 = SU(4)_1 weights","v101 mass-line double cover: disc = (108/L^3)(1-9 L M^2) -> (1-3m)(1+3m), branch +-1/N_fam","v101 temperature lemma: |kappa_b/kappa_c| = (2x+1)/(x(x+2)), = 1 iff x = 1","v101 seam-unit mechanics: 1/(8Pi) = c3; Smarr 1/(4Pi) = 2c3; Bekenstein 2Pi = 1/(4c3); P_H 15360 Pi = 1920/c3; lifetime 5120 Pi = 128*5/c3; Kerr A_ext = M^2/c3; 4 Log[3] = Log[81]","v102 flavor gradient flow: V' = -(Delta/3)(q-2)(q-5), critical points = the branch points {2,5}","v102 stationary curvatures = +-the gap: V''(2) = +Delta, V''(5) = -Delta; inflection at q = 7/2","v102 Lyapunov rate: d(-ln rho)/dt = Delta exactly along the flow","v102 gravity: dS/dx = (x-1)(x+1)/Phi_3^2 -- Nariai is the unique physical stationary point","v102 stationary curvature S''(1) = 2/9 = |Z2|/N_fam^2 = (2/3)(1/3)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v101) horizon anchor: SdS in seam units ---- *) fSdS = 1 - 2 mm/rr - LL rr^2/3; cubicSdS = Expand[-fSdS 3 rr/LL]; narSol = Solve[{cubicSdS == 0, D[cubicSdS, rr] == 0}, {rr, mm}, Assumptions -> LL > 0]; checkExact[\"v101 Nariai double root: M_N = 1/(3 Sqrt[L]) = 1/(N_fam Sqrt[L]), r_N = 1/Sqrt[L]\", MemberQ[Simplify[{rr, mm} /. narSol], {1/Sqrt[LL], 1/(3 Sqrt[LL])}]]; checkExact[\"v101 Nariai cubic = t^3 - 3t + 2 = (t-1)^2(t+2): roots (1,1,-2) = traceless anchor\", (Expand[(t - 1)^2 (t + 2)] == t^3 - 3 t + 2) && (Simplify[{1, 1, 2} - (4/3) {1, 1, 1} - (-1/3) {1, 1, -2}] == {0, 0, 0})]; checkExact[\"v101 Koide 2/3 = Nariai entropy bound: S_N/S_dS = 2/3, per horizon 1/3, deficit 1/3\", ((2 Pi/LL)/(3 Pi/LL) == 2/3) && ((Pi/LL)/(3 Pi/LL) == 1/3)]; checkExact[\"v101 interpolation S_tot/S_dS = (x^2+1)/(x^2+x+1) (denominator = Phi_3), min at merge\", (Simplify[(xx^2 + 1)/(xx^2 + xx + 1) - (Pi (xx^2 + 1) 3/(LL (xx^2 + xx + 1)))/(3 Pi/LL)] === 0) && (Cyclotomic[3, xx] == xx^2 + xx + 1) && (((xx^2 + 1)/(xx^2 + xx + 1) /. xx -> 0) == 1) && (((xx^2 + 1)/(xx^2 + xx + 1) /. xx -> 1) == 2/3)]; checkExact[\"v101 three-sheet conservation: Sum r_i^2 = 2(rb^2+rb rc+rc^2) for roots (rb, rc, -(rb+rc))\", Expand[rbb^2 + rcc^2 + (rbb + rcc)^2 - 2 (rbb^2 + rbb rcc + rcc^2)] === 0]; checkExact[\"v101 Q_geom range: pure dS -> 1/2 = delta, Nariai -> 3/8 = p2(a)/e1(a)^2 = SU(4)_1 weights\", Module[{Qg = (xx^2 + (xx + 1)^2 + 1)/(4 (xx + 1)^2)}, ((Qg /. xx -> 0) == 1/2) && ((Qg /. xx -> 1) == 3/8) && (6/16 == 3/8)]]; checkExact[\"v101 mass-line double cover: disc = (108/L^3)(1-9 L M^2) -> (1-3m)(1+3m), branch +-1/N_fam\", (Simplify[Discriminant[cubicSdS, rr] - 108/LL^3 (1 - 9 LL mm^2)] === 0) && (Expand[(1 - 3 md) (1 + 3 md) - (1 - 9 md^2)] === 0)]; checkExact[\"v101 temperature lemma: |kappa_b/kappa_c| = (2x+1)/(x(x+2)), = 1 iff x = 1\", Module[{ff, kb, kc}, ff = -LL/(3 rr) (rr - rbb) (rr - rcc) (rr + rbb + rcc); kb = D[ff, rr] /. rr -> rbb; kc = D[ff, rr] /. rr -> rcc; Simplify[(kb/-kc /. rbb -> xx rcc) - (2 xx + 1)/(xx (xx + 2)), Assumptions -> rcc > 0 && xx > 0 && xx < 1] === 0]]; checkExact[\"v101 seam-unit mechanics: 1/(8Pi) = c3; Smarr 1/(4Pi) = 2c3; Bekenstein 2Pi = 1/(4c3); P_H 15360 Pi = 1920/c3; lifetime 5120 Pi = 128*5/c3; Kerr A_ext = M^2/c3; 4 Log[3] = Log[81]\", (1/(8 Pi) == c3) && (Simplify[1/(4 Pi) - 2 c3] === 0) && (Simplify[2 Pi - 1/(4 c3)] === 0) && (Simplify[1/(15360 Pi) - c3/1920] === 0) && (Simplify[5120 Pi - 128*5/c3] === 0) && (Simplify[8 Pi - 1/c3] === 0) && (Simplify[4 Log[3] - Log[81]] === 0)]; (* ---- (v102) seam orientation: anchor = stationary repeller, both sectors ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:333","line_end":391,"line_start":333,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v101","v102"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v103 trisection: r = 2 cos(theta) => r^3 - 3r = 2 cos(3 theta) exactly","v103 centered angle: m = cos(psi)/3; roots sum 0, e2 = -3; Nariai roots (1,1,-2) at psi = 0","v103 NORMAL FORM: sigma(psi) = 4/3 - (2/3) cos(2 psi/3); sigma(0) = 2/3, sigma(pi/2) = 1","v103 canonical curvature sigma''(0) = 8/27 = (2/3)^3 (the Koide constant to the family power)","v103 invariant base slope: dsigma/dm = -(4/3) sin(2 psi/3)/sin(psi), limit -8/9 = -rank(E8)/N_fam^2","v103 x-coordinate cross-check: m(x) deck-invariant, m''(1) = -1/4, sigma''(1)/m''(1) = -8/9","v103 bridge: (2/3)^6 = ((2/3)^3)^2 -- same base, exponent ratio 2 = |Z2|","v104 static pin: phi = rho solves d/drho[(1-L rho^2) phi'] = -2 L phi exactly","v104 horizon split: r_{b,c} = 1 -+ psi/Sqrt[3] - psi^2/18 + O(psi^3) (coefficient 1/Sqrt[N_fam])","v104 Ginsparg-Perry tower (l(l+1)-2): {-2, 0, 4, 10} -- exactly one negative mode = -|Z2|","v104 THE CLOCK: lambda^2 + lambda - 2 = (lambda-1)(lambda+2) = the anchor quadratic; Nariai cubic = (t-1) x clock","v104 entropy-deviation rate: d/dt log((1/2)(2/3)^3 (psi0 e^{H t})^2) = 2H = |Z2| H"],"checked_by_registry":false,"heading_as_written":"(* ---- (v103) trisection normal form ---- *) checkExact[\"v103 trisection: r = 2 cos(theta) => r^3 - 3r = 2 cos(3 theta) exactly\", Simplify[(2 Cos[th])^3 - 3 (2 Cos[th]) - 2 Cos[3 th]] === 0]; rcT = 2 Cos[(ps + Pi)/3]; rbT = 2 Cos[(ps - Pi)/3]; r3T = 2 Cos[(ps + 3 Pi)/3]; checkExact[\"v103 centered angle: m = cos(psi)/3; roots sum 0, e2 = -3; Nariai roots (1,1,-2) at psi = 0\", (Simplify[-Cos[ps + Pi]/3 - Cos[ps]/3] === 0) && (Simplify[rcT + rbT + r3T] === 0) && (Simplify[rcT rbT + rcT r3T + rbT r3T + 3] === 0) && (Simplify[{rcT, rbT, r3T} /. ps -> 0] == {1, 1, -2})]; sigT = Simplify[(rbT^2 + rcT^2)/3]; checkExact[\"v103 NORMAL FORM: sigma(psi) = 4/3 - (2/3) cos(2 psi/3); sigma(0) = 2/3, sigma(pi/2) = 1\", (Simplify[sigT - (4/3 - (2/3) Cos[2 ps/3])] === 0) && (Simplify[sigT /. ps -> 0] == 2/3) && (Simplify[sigT /. ps -> Pi/2] == 1)]; checkExact[\"v103 canonical curvature sigma''(0) = 8/27 = (2/3)^3 (the Koide constant to the family power)\", (Simplify[D[sigT, {ps, 2}] /. ps -> 0] == 8/27) && ((2/3)^3 == 8/27)]; checkExact[\"v103 invariant base slope: dsigma/dm = -(4/3) sin(2 psi/3)/sin(psi), limit -8/9 = -rank(E8)/N_fam^2\", (Simplify[D[sigT, ps]/D[Cos[ps]/3, ps] + (4/3) Sin[2 ps/3]/Sin[ps]] === 0) && (Limit[D[sigT, ps]/D[Cos[ps]/3, ps], ps -> 0] == -8/9)]; checkExact[\"v103 x-coordinate cross-check: m(x) deck-invariant, m''(1) = -1/4, sigma''(1)/m''(1) = -8/9\", Module[{mxw = Sqrt[3]/2 xx (1 + xx)/(xx^2 + xx + 1)^(3/2), sxw = (xx^2 + 1)/(xx^2 + xx + 1)}, (Simplify[(mxw /. xx -> 1/xx) - mxw, Assumptions -> xx > 0] === 0) && (Simplify[D[mxw, xx] /. xx -> 1] == 0) && (Simplify[D[mxw, {xx, 2}] /. xx -> 1] == -1/4) && (Simplify[(D[sxw, {xx, 2}] /. xx -> 1)/(D[mxw, {xx, 2}] /. xx -> 1)] == -8/9)]]; checkExact[\"v103 bridge: (2/3)^6 = ((2/3)^3)^2 -- same base, exponent ratio 2 = |Z2|\", (2/3)^6 == ((2/3)^3)^2]; (* ---- (v104) the classical Nariai clock ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:392","line_end":434,"line_start":392,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v103","v104"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v105 one-constant inventory (exact items): Koide branch -2/3; gap base (2/3)^6; Nariai bound 2/3; branch separation 2/3; canonical amplitude/frequency 2/3; curvature (2/3)^3","v105 anchor triptych: chi_a = (t-1)^2(t-2); Nariai = (t-1)^2(t+2) = (t-1) x clock (lam-1)(lam+2)","v105 relocation: eps = (8/24Pi) * 7.125e-121 = 7.56e-122 (deficient ~121.5 orders vs Delta)","v105 residual table: exactly FIVE structural objects + 2 irreducibles (typing contract)","v106 seed normal form: phi0 = (4/3) c3 + 48 c3^4 with 4/3 = |mu4|/N_fam, 48 = N_fam dim S+, exponent = |mu4|","v106 anchor ladder: p_n = 2+2^n; (3,4,6,10); 240; 8; 248","v106 hypercharge moment: Tr X = 0, Tr X^2 = 120 = 5! (X = 6Y, 16 states)","v106 factorial spine: 5! = 120 = sum E8 exponents; 240 = 2x120; 1920 = 2^4 x 5!","v106 degree-2 inventory: Pascal K=2 closure unique at g=5 (1..40); 5/4+3/4 = 2; (1/2)(1/(4Pi)) = 1/(8Pi); C(5,2) = 10","v106 audit: 240 = 16x15 = 16x5x3 (two readings, non-unique)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v105) residual inventory ---- *) checkExact[\"v105 one-constant inventory (exact items): Koide branch -2/3; gap base (2/3)^6; Nariai bound 2/3; branch separation 2/3; canonical amplitude/frequency 2/3; curvature (2/3)^3\", ((3 (-2/3) + 2) == 0) && ((2/3)^6 == 64/729) && ((4/3 - (2/3) Cos[0]) == 2/3) && ((1/3) - (-1/3) == 2/3) && (Coefficient[4/3 - (2/3) Cos[2 ps/3], Cos[2 ps/3]] == -2/3) && (((2/3)^3) == 8/27)]; checkExact[\"v105 anchor triptych: chi_a = (t-1)^2(t-2); Nariai = (t-1)^2(t+2) = (t-1) x clock (lam-1)(lam+2)\", (Expand[(t - 1)^2 (t - 2)] == t^3 - 4 t^2 + 5 t - 2) && (Expand[(t - 1)^2 (t + 2) - (t - 1) (t^2 + t - 2)] === 0)]; check[\"v105 relocation: eps = (8/24Pi) * 7.125e-121 = 7.56e-122 (deficient ~121.5 orders vs Delta)\", (8/(24 Pi)) 7.125329526706`20 10^-121 / (6 Log[3/2]), 10^-121.5076, 10^-3]; checkExact[\"v105 residual table: exactly FIVE structural objects + 2 irreducibles (typing contract)\", Length[{\"R1clock\", \"R2holc8\", \"R3seamEH\", \"R4H2\", \"R5Qreal\"}] == 5]; (* ---- (v106) review validation ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:435","line_end":470,"line_start":435,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v105","v106"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v107 per-l clock: l=0 (la-1)(la+2), l=1 la(la+1); l>=2 complex Re=-1/2","v107 cusp-ladder cross-link: decay set {0,-1,-2} = -Spec(Q diag(0,1,1)) = -N_fam x cusp","v107 exact target: (1/3)^6 = ((2/3)^6)^{log_{3/2}3}; ratio = 1 + log_{3/2}2","v107 bend log_{9/4}(3) = 1.354756; seam coupling 1/(3Pi) = 0.106103","v108 ladder: closure 2^{g-1} = sum_{k<=K} C(g,k) solved exactly by g = 2K+1 (K=1..6, g<=60)","v108 even-g straddle: sum_{k<g/2} < 2^{g-1} < sum_{k<=g/2} for g = 2..16 even","v108 neighbour worlds: K=1 -> N_fam 1; K=2 -> 3; K=3 -> 9; K=4 -> 255/9 not integer; only K=2 has g+N_fam = 8"],"checked_by_registry":false,"heading_as_written":"(* ---- (v107) quantum-clock target ---- *) checkExact[\"v107 per-l clock: l=0 (la-1)(la+2), l=1 la(la+1); l>=2 complex Re=-1/2\", (Factor[la^2 + la + (0 - 2)] == (la - 1) (la + 2)) && (Factor[la^2 + la + (2 - 2)] == la (la + 1)) && (Re[la /. Solve[la^2 + la + 4 == 0, la]] == {-1/2, -1/2})]; checkExact[\"v107 cusp-ladder cross-link: decay set {0,-1,-2} = -Spec(Q diag(0,1,1)) = -N_fam x cusp\", Module[{Vw = Q.DiagonalMatrix[{0, 1, 1}]}, Sort[Eigenvalues[Vw]] == {0, 1, 2}]]; checkExact[\"v107 exact target: (1/3)^6 = ((2/3)^6)^{log_{3/2}3}; ratio = 1 + log_{3/2}2\", (FullSimplify[-6 Log[3] - (Log[3]/Log[3/2]) (6 Log[2] - 6 Log[3])] === 0) && (FullSimplify[Log[3]/Log[3/2] - (1 + Log[2]/Log[3/2])] === 0)]; check[\"v107 bend log_{9/4}(3) = 1.354756; seam coupling 1/(3Pi) = 0.106103\", Log[3]/Log[9/4], 1.3547556457`10, 10^-9]; (* ---- (v108) Pascal ladder ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:471","line_end":498,"line_start":471,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v107","v108"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v109 no scalar within a sheet: zero-weight mult of S+xS+ and S-xS- is 0","v109 cross-sheet zero-weight mult = 16 = 1+5+10 (Pascal triple)","v109 EXACT multiset: S+xS- = Lambda^0+Lambda^2+Lambda^4 (256 = 1+45+210)","v109 sheet-diagonal = odd forms: (S+xS+)u(S-xS-) = 2L1+2L3+L5 (512)","v109 zero-mode grading (L0,L2,L4) -> (1,5,10) = the carrier code; tower tops at 2K = 4","v110 sheet-block zero-weight counts (++, --, +-, -+) = (0, 0, 16, 16)","v110 selection theorem: sheet-ODD involution certifies 1+1 = 2 = |Z2| scalar kernels, sheet-EVEN certifies 0 (scalar datum <=> sheet-odd)","v110 ladder genericity: g = 3,5,7 -> within-sheet 0, cross 2^{g-1} = (4,16,64), K = (g-1)/2 = (1,2,3) - half-spinor relation, not g-selection"],"checked_by_registry":false,"heading_as_written":"(* ---- (v109) sheet pairing ---- *) Module[{splus, sminus, vecw, lamW, addW, crossT, formsEven, diagT, formsOdd, zmult}, splus = Select[Tuples[{1/2, -1/2}, 5], EvenQ[Count[#, -1/2]] &]; sminus = Select[Tuples[{1/2, -1/2}, 5], OddQ[Count[#, -1/2]] &]; vecw = Flatten[Table[s UnitVector[5, i], {i, 5}, {s, {1, -1}}], 1]; lamW[k_] := If[k == 0, {ConstantArray[0, 5]}, Total /@ Subsets[vecw, {k}]]; checkExact[\"v109 no scalar within a sheet: zero-weight mult of S+xS+ and S-xS- is 0\", (Count[Flatten[Outer[Plus, splus, splus, 1], 1], ConstantArray[0, 5]] == 0) && (Count[Flatten[Outer[Plus, sminus, sminus, 1], 1], ConstantArray[0, 5]] == 0)]; crossT = Sort[Flatten[Outer[Plus, splus, sminus, 1], 1]]; checkExact[\"v109 cross-sheet zero-weight mult = 16 = 1+5+10 (Pascal triple)\", Count[crossT, ConstantArray[0, 5]] == 16]; formsEven = Sort[Join[lamW[0], lamW[2], lamW[4]]]; checkExact[\"v109 EXACT multiset: S+xS- = Lambda^0+Lambda^2+Lambda^4 (256 = 1+45+210)\", crossT === formsEven && Length[crossT] == 256]; diagT = Sort[Join[Flatten[Outer[Plus, splus, splus, 1], 1], Flatten[Outer[Plus, sminus, sminus, 1], 1]]]; formsOdd = Sort[Join[lamW[1], lamW[1], lamW[3], lamW[3], lamW[5]]]; checkExact[\"v109 sheet-diagonal = odd forms: (S+xS+)u(S-xS-) = 2L1+2L3+L5 (512)\", diagT === formsOdd && Length[diagT] == 512]; zmult[k_] := Count[lamW[k], ConstantArray[0, 5]]; checkExact[\"v109 zero-mode grading (L0,L2,L4) -> (1,5,10) = the carrier code; tower tops at 2K = 4\", ({zmult[0], zmult[2], zmult[4]} == {1, 5, 10}) && (4 == 2*2)]; ]; (* ---- (v110) Calderon-sheet selection ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:499","line_end":541,"line_start":499,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v109","v110"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v111 model: 45 quadratics = dim so(10); 10 linears sheet-ODD, 45 quadratics sheet-EVEN (exact block-zero)","v111 GENERATION: quadratic words of length <= 2 span all 16 code states from the vacuum","v111 COMPLETENESS: products of length <= 2 of the 45 quadratics span End(S+) = 256 (transport degree exactly 2)","v111 ladder genericity: g=3 world identical (15 quadratics -> End(S+) = 16) - degree selected, not rank","v111 channel reading: certified tower 256 = 1 + 45 + 210 = norm + transport generators + pair sector","v112 canonical bijection: w -> -w maps S+ into S-; # neutral kernels = dim S+ = 2^{g-1} (4, 16, 64)","v112 Pascal partition: channel pair-grading = (C(g,m))_{m<=K}; g=5 -> (1,5,10)","v112 the closure is an identity: 2^{g-1} = Sum_{m<=K} C(g,m) for all odd g = 3..13","v112 Hodge fold: code minus-grading C(g,2j) = C(g,min(2j,g-2j)), same multiset as the channel grading"],"checked_by_registry":false,"heading_as_written":"(* ---- (v111) quadratic transport ---- *) Module[{jwOps, evensOf, buildQuads, runWorld}, jwOps[g_] := Module[{eye = IdentityMatrix[2], zee = {{1, 0}, {0, -1}}, am = {{0, 1}, {0, 0}}}, Table[KroneckerProduct @@ Join[ConstantArray[zee, i - 1], {am}, ConstantArray[eye, g - i]], {i, g}]]; evensOf[g_] := Select[Range[2^g], EvenQ[DigitCount[# - 1, 2, 1]] &]; buildQuads[g_] := Module[{a = jwOps[g], ad}, ad = Transpose /@ a; Join[ Flatten[Table[{ad[[i]] . ad[[j]], a[[i]] . a[[j]]}, {i, g}, {j, i + 1, g}], 2], Flatten[Table[ad[[i]] . a[[j]], {i, g}, {j, g}], 1]]]; runWorld[g_] := Module[{a = jwOps[g], ad, ev = evensOf[g], od, quads, vac, d1, d2, orbit, qr, words}, ad = Transpose /@ a; od = Complement[Range[2^g], ev]; quads = buildQuads[g]; vac = UnitVector[2^g, 1]; d1 = (# . vac) & /@ quads; d2 = Flatten[Outer[Dot, quads, d1, 1], 1]; orbit = (#[[ev]]) & /@ Join[{vac}, d1, d2]; qr = (#[[ev, ev]]) & /@ quads; words = Join[{IdentityMatrix[Length[ev]]}, qr, Flatten[Outer[Dot, qr, qr, 1], 1]]; {Length[quads], And @@ ((Max[Abs[#[[ev, ev]]]] == 0 && Max[Abs[#[[od, od]]]] == 0) & /@ Join[a, ad]), And @@ ((Max[Abs[#[[ev, od]]]] == 0 && Max[Abs[#[[od, ev]]]] == 0) & /@ quads), MatrixRank[orbit], MatrixRank[Flatten /@ words], Length[ev]}]; Module[{r5 = runWorld[5], r3 = runWorld[3]}, checkExact[\"v111 model: 45 quadratics = dim so(10); 10 linears sheet-ODD, 45 quadratics sheet-EVEN (exact block-zero)\", r5[[1]] == 45 && r5[[2]] && r5[[3]]]; checkExact[\"v111 GENERATION: quadratic words of length <= 2 span all 16 code states from the vacuum\", r5[[4]] == 16]; checkExact[\"v111 COMPLETENESS: products of length <= 2 of the 45 quadratics span End(S+) = 256 (transport degree exactly 2)\", r5[[5]] == 256]; checkExact[\"v111 ladder genericity: g=3 world identical (15 quadratics -> End(S+) = 16) - degree selected, not rank\", r3[[1]] == 15 && r3[[5]] == 16]; checkExact[\"v111 channel reading: certified tower 256 = 1 + 45 + 210 = norm + transport generators + pair sector\", 1 + 45 + 210 == 256]; ]; ]; (* ---- (v112) self-counting channel ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:542","line_end":606,"line_start":542,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v111","v112"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v113 Majorana bookkeeping: c(D5)1 = 45/9 = 5 = g_car, c(A3)1 = 15/5 = 3 = N_fam, c(SO16)1 = 8, c(E8)1 = 248/31 = 8; carrier = 10+6 = 16 free Majoranas; tower index 2x2 = 4 = |mu4|","v113 kernel = Calderon involution of rank g: M = I+iA, A integer antisym, A^2 = -I, P = M/2 projection of rank 5 = g_car, eps = iA involution","v113 Wick/Pfaffian: all 210 vacuum 4-point AND all 210 6-point functions equal the Pfaffian of the single 2-point kernel","v113 one kernel <=> one state: joint annihilator kernel exactly 1-dimensional","v113 seam level: 16-Majorana kernel rank 8 = rank E8 = c (the central charge is the rank of the one kernel)","v114 flatness = mu4 torsion: prod_k U^k M U^{-k} = (MU)^4 for generic symbolic M","v114 delta theorem (construction): T^2 = 1, M = TU^-1 unitary, tr M = 0, diag M = (0, i/2, -i/2), char poly = lam^3 - 1 (cusp class automatic)","v114 delta theorem (necessity): cusp trace condition splits into |v1|^2 = 1/2 (real) and |v2| = |v3| (imaginary)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v113) quasi-free kernel ---- *) Module[{jwOps, g = 5, a, ad, cs, vac, vev, m2, amat, pol, k10, pf, ok4, ok6, a16, p16}, jwOps[gg_] := Module[{eye = IdentityMatrix[2], zee = {{1, 0}, {0, -1}}, am = {{0, 1}, {0, 0}}}, Table[KroneckerProduct @@ Join[ConstantArray[zee, i - 1], {am}, ConstantArray[eye, gg - i]], {i, gg}]]; checkExact[\"v113 Majorana bookkeeping: c(D5)1 = 45/9 = 5 = g_car, c(A3)1 = 15/5 = 3 = N_fam, c(SO16)1 = 8, c(E8)1 = 248/31 = 8; carrier = 10+6 = 16 free Majoranas; tower index 2x2 = 4 = |mu4|\", 45/9 == 5 && 15/5 == 3 && 120/15 == 8 && 248/31 == 8 && 10 + 6 == 16 && Sqrt[16/4] Sqrt[4/1] == 4]; a = jwOps[g]; ad = Transpose /@ a; cs = Flatten[Table[{a[[i]] + ad[[i]], I (ad[[i]] - a[[i]])}, {i, g}], 1]; vac = UnitVector[2^g, 1]; vev[ops_] := vac . (Dot @@ ops) . vac; m2 = Table[vev[{cs[[j]], cs[[k]]}], {j, 10}, {k, 10}]; amat = (m2 - IdentityMatrix[10])/I; pol = (IdentityMatrix[10] + I amat)/2; checkExact[\"v113 kernel = Calderon involution of rank g: M = I+iA, A integer antisym, A^2 = -I, P = M/2 projection of rank 5 = g_car, eps = iA involution\", amat == -Transpose[amat] && AllTrue[Flatten[amat], IntegerQ] && amat . amat == -IdentityMatrix[10] && pol . pol == pol && MatrixRank[pol] == 5 && (I amat) . (I amat) == IdentityMatrix[10]]; k10 = Table[If[x < y, vev[{cs[[x]], cs[[y]]}], 0], {x, 10}, {y, 10}]; pf[idx_] := If[idx === {}, 1, Sum[(-1)^(t - 1) k10[[idx[[1]], idx[[t + 1]]]] pf[Delete[Rest[idx], t]], {t, Length[idx] - 1}]]; ok4 = AllTrue[Subsets[Range[10], {4}], (vev[cs[[#]]] == pf[#]) &]; ok6 = AllTrue[Subsets[Range[10], {6}], (vev[cs[[#]]] == pf[#]) &]; checkExact[\"v113 Wick/Pfaffian: all 210 vacuum 4-point AND all 210 6-point functions equal the Pfaffian of the single 2-point kernel\", ok4 && ok6]; checkExact[\"v113 one kernel <=> one state: joint annihilator kernel exactly 1-dimensional\", 2^g - MatrixRank[Join @@ a] == 1]; a16 = SparseArray[Join[Table[{2 i - 1, 2 i} -> 1, {i, 8}], Table[{2 i, 2 i - 1} -> -1, {i, 8}]], {16, 16}] // Normal; p16 = (IdentityMatrix[16] + I a16)/2; checkExact[\"v113 seam level: 16-Majorana kernel rank 8 = rank E8 = c (the central charge is the rank of the one kernel)\", p16 . p16 == p16 && MatrixRank[p16] == 8]; ]; (* ---- (v114) torsion normal form + delta = 1/2 theorem ---- The [N] branch census (scipy Nelder-Mead sampling of the D4-fixed flat cusp locus) is Python-only by convention; the exact statements are mirrored here. *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:607","line_end":667,"line_start":607,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v113","v114"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v115 mu4-average lemma: sum_k U^k X U^{-k} = 4 diag(X) (anchor splitting <=> diag A0 = (2,1,1)/4 = a/|mu4|)","v115 the (8,0,5)/144 lemma: unique solution (|a12|^2, |a23|^2) = (8/144, 5/144); 8+5 = 13 = Delta_Q, 144 = (|mu4| N_fam)^2","v115 exact residue normal form: char poly of A0* = -lam(lam-1/3)(lam-2/3) exactly (eigenvalues = cusp weights)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v115) anchor residue ---- The [N] Riemann-Hilbert parts (scipy ODE monodromy of the Fuchsian system, multi-seed uniqueness scan) are Python-only by convention; the exact lemmas are mirrored here. *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:668","line_end":686,"line_start":668,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v115"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v116 twisted-average lemma: B0 = 4 diag(A0), B1 = 4 a12 E_12 + 4 conj(a13) E_31 (only ratio -i cells survive)","v116 resonance theorem: singular cells {(2,1),(3,1)}; obstruction (0, 4 conj(a13)); k >= 2 non-resonant => M_inf = 1 <=> a13 = 0","v116 uniqueness corollary: diagonal gauge commutes with U, fixes the diagonal, rotates arg(a12), arg(a23) freely => one gauge orbit"],"checked_by_registry":false,"heading_as_written":"(* ---- (v116) resonance theorem ---- The [N] falsification control (scipy ODE) is Python-only by convention; the exact statements are mirrored here. *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:687","line_end":712,"line_start":687,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v116"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v117 exact monodromy: M0 unitary, det 1, tr 0, char poly lam^3 - 1, M0^3 = 1, diag = (0, -i/2, i/2) => d1 = 0 and delta = 1/2 exact","v117 torsion/flatness: (M0 U)^4 = 1, tr(M0 U) = 1, prod_k U^k M0 U^{-k} = 1","v117 the group is W(A3) = S4: order 24, order statistics (1,9,8,6), character values (3,-1,0,1) with counts (1,9,8,6); 24 = |W(A3)| = 4!"],"checked_by_registry":false,"heading_as_written":"(* ---- (v117) monodromy = W(A3) ---- The [N] ODE identification (scipy monodromy of the exact A0* system) is Python-only by convention; the exact statements are mirrored here. *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:713","line_end":748,"line_start":713,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v117"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v118 sign-twist lemma: (-M0)^3 = -1 and spec(M0) u spec(-M0) = mu_6 (the hexagon); denominators 5/4 - cos(r pi/3) = |1 - zeta_6^r/2|^2","v118 cyclotomic determinant: det(1 - t M0) = 1 - t^3; det(1 -+ M0/2) = (7/8, 9/8)","v118 lepton coefficients = resolvent determinants: c_e = 4/(2 det-) = 16/7, c_mu = 3/(2 det+) = 4/3, c_tau = 4 det-/3 = 7/6, product = 4/det+ = 32/9","v118 sheet-extended group: <U, M0, -1> has order 48 = Omega_adm = 3 x 16 = |S4 x Z2|","v119 micro-identities: Omega_adm = 2 p1 p2 = 48, 10b1 = 1 + p1 p3 = 41, Delta_Y = 25 = p0^2 + 16, h(E8) = 30, rank = 8, 240 = p1 p2 p3, 248","v119 anchor ratio triad: (e3,e1,e2)/p0 = (2/3, 4/3, 5/3); flow critical points (2,5) = (e3,e2), inflection 7/2","v119 the 121 audit lemma: (1+a).R.(1+a) = 121 = 11^2 = ||Pl(K)||_1^2 = (p3+1)^2; orderings give {105,121,135}; 1.R.1 = 22, a.R.a = 40 = p1 p3"],"checked_by_registry":false,"heading_as_written":"(* ---- (v118) hexagon-family dictionary ---- *) Module[{m0, usym, t, z6, specU, mu6, detm, detp, elems, frontier, newE}, m0 = {{0, -(1 + I)/2, (1 - I)/2}, {-(1 + I)/2, -I/2, -1/2}, {(1 - I)/2, -1/2, I/2}}; usym = DiagonalMatrix[{1, I, -I}]; z6 = Exp[I Pi/3]; specU = Sort[Join[Eigenvalues[m0], -Eigenvalues[m0]], LessEqual[Arg[#1], Arg[#2]] &]; mu6 = Sort[Table[Exp[I Pi k/3], {k, 0, 5}], LessEqual[Arg[#1], Arg[#2]] &]; checkExact[\"v118 sign-twist lemma: (-M0)^3 = -1 and spec(M0) u spec(-M0) = mu_6 (the hexagon); denominators 5/4 - cos(r pi/3) = |1 - zeta_6^r/2|^2\", Simplify[MatrixPower[-m0, 3]] === -IdentityMatrix[3] && AllTrue[Transpose[{FullSimplify[specU], FullSimplify[mu6]}], FullSimplify[#[[1]] - #[[2]]] === 0 &] && AllTrue[Range[0, 5], FullSimplify[(5/4 - Cos[# Pi/3]) - (1 - z6^#/2) (1 - Conjugate[z6^#]/2)] === 0 &]]; t = \\[FormalT]; detm = Det[IdentityMatrix[3] - m0/2]; detp = Det[IdentityMatrix[3] + m0/2]; checkExact[\"v118 cyclotomic determinant: det(1 - t M0) = 1 - t^3; det(1 -+ M0/2) = (7/8, 9/8)\", FullSimplify[Det[IdentityMatrix[3] - t m0] - (1 - t^3)] === 0 && Simplify[detm] == 7/8 && Simplify[detp] == 9/8]; checkExact[\"v118 lepton coefficients = resolvent determinants: c_e = 4/(2 det-) = 16/7, c_mu = 3/(2 det+) = 4/3, c_tau = 4 det-/3 = 7/6, product = 4/det+ = 32/9\", Simplify[4/(2 detm)] == 16/7 && Simplify[3/(2 detp)] == 4/3 && Simplify[4 detm/3] == 7/6 && Simplify[4/detp] == 32/9 && Abs[m0[[2, 2]]] == 1/2]; elems = <|Expand[IdentityMatrix[3]] -> True|>; frontier = {IdentityMatrix[3]}; While[frontier =!= {}, newE = {}; Do[Module[{xg = Expand[g . e]}, If[! KeyExistsQ[elems, xg], elems[xg] = True; AppendTo[newE, xg]]], {e, frontier}, {g, {usym, m0, -IdentityMatrix[3]}}]; frontier = newE]; checkExact[\"v118 sheet-extended group: <U, M0, -1> has order 48 = Omega_adm = 3 x 16 = |S4 x Z2|\", Length[elems] == 48 && 3*16 == 48]; ]; (* ---- (v119) second review validation ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:749","line_end":798,"line_start":749,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v118","v119"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v120 lepton words = compiler atoms: (8,5,3) = (rank E8, g_car, N_fam) = (p0+e2, e2, p0); sum = 16 = dim S+","v120 addresses = division by hexagon p2 = 6: (r,w) = {(2,1),(5,0),(3,0)}; sum r = 10 = p3","v120 quark sum rules: up = 10 = p3, down = 14 = p1+p3, quarks = 24 = |W(A3)|, all nine = 40 = p1 p3; top at vacuum site (0,0)","v121 word table = residue operator: L = R + 2U; R col 1 = anchor (1,1,2); margins rows (4,8,10) = (e1, rank, p3), cols (4,13,5) = (e1, Delta_Q, g_car)","v121 pinning theorem: exactly 17 hexagon matrices with the atom margins; exactly ONE with det = 8 = rank E8 - and it is R; all 17 dets distinct"],"checked_by_registry":false,"heading_as_written":"(* ---- (v120) address table ---- *) Module[{pp, llep, lqrk, addr, up, down}, pp[n_] := 2 + 2^n; llep = {8, 5, 3}; lqrk = {7, 7, 5, 3, 2, 0}; checkExact[\"v120 lepton words = compiler atoms: (8,5,3) = (rank E8, g_car, N_fam) = (p0+e2, e2, p0); sum = 16 = dim S+\", llep == {3 + 5, 5, 3} && Total[llep] == 16]; addr = {Mod[#, 6], Quotient[#, 6]} & /@ llep; checkExact[\"v120 addresses = division by hexagon p2 = 6: (r,w) = {(2,1),(5,0),(3,0)}; sum r = 10 = p3\", addr == {{2, 1}, {5, 0}, {3, 0}} && Total[addr[[All, 1]]] == pp[3] && pp[2] == 6]; up = 7 + 3 + 0; down = 7 + 5 + 2; checkExact[\"v120 quark sum rules: up = 10 = p3, down = 14 = p1+p3, quarks = 24 = |W(A3)|, all nine = 40 = p1 p3; top at vacuum site (0,0)\", up == pp[3] && down == pp[1] + pp[3] && up + down == 24 && Total[llep] + up + down == pp[1] pp[3] && Mod[0, 6] == 0 && Quotient[0, 6] == 0]; ]; (* ---- (v121) address pinning ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:799","line_end":833,"line_start":799,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v120","v121"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v122 census: 4 x 4 x 4 = 64 annihilator candidates, det 8 leaves 12, det K = 4 leaves exactly ONE = R","v122 corollary: margins are theorems - rows (4,8,10), cols (4,13,5), anchor column (1,1,2); bonus: det(M+2U) = 20 on ALL 12 candidates"],"checked_by_registry":false,"heading_as_written":"(* ---- (v122) margin theorem ---- *) Module[{rmat, qmat, sig, uax, colsT, c8, c0, cands, final}, rmat = {{1, 3, 0}, {1, 5, 2}, {2, 5, 3}}; qmat = {{3, 1, 0}, {3, 2, 0}, {3, 2, 1}}; sig = DiagonalMatrix[{1, -1, -1}]; uax = 3 Outer[Times, {1, 1, 1}, {1, 0, 0}]; colsT[t_] := Select[Tuples[Range[0, 5], 3], 5 #[[1]] - 9 #[[2]] + 6 #[[3]] == t &]; c8 = colsT[8]; c0 = colsT[0]; cands = Select[Flatten[Table[Transpose[{a, b, c}], {a, c8}, {b, c0}, {c, c0}], 2], Det[#] == 8 &]; final = Select[cands, Det[# + qmat . sig] == 4 &]; checkExact[\"v122 census: 4 x 4 x 4 = 64 annihilator candidates, det 8 leaves 12, det K = 4 leaves exactly ONE = R\", Length[c8] == 4 && Length[c0] == 4 && Length[cands] == 12 && Length[final] == 1 && final[[1]] == rmat]; checkExact[\"v122 corollary: margins are theorems - rows (4,8,10), cols (4,13,5), anchor column (1,1,2); bonus: det(M+2U) = 20 on ALL 12 candidates\", (Total /@ final[[1]]) == {4, 8, 10} && Total[final[[1]]] == {4, 13, 5} && final[[1]][[All, 1]] == {1, 1, 2} && AllTrue[cands, Det[# + 2 uax] == 20 &]]; ]; (* ---- (v123) inventory update: ledger-bookkeeping module (CSV parsing of status_ledger.csv, typing contract) -- Python-only by nature, like the statistical v100; no algebraic content to mirror. ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:834","line_end":855,"line_start":834,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v100","v122","v123"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v124 spectrum reads (1-n/3)^6: eigenvalues {1, (2/3)^6, (1/3)^6}","v124 closed-form clock: rates {0, Delta, 6 ln 3}; bend rate(2)/rate(1) = log_{3/2}3","v124 linearisation carries the sheet: series 2x + x^2/3 + 2x^3/27 (slope |Z2| = 2); pole at n = N_fam = 3","v125 Q-system axioms: associativity, unit, Frobenius, specialness m m* = |Z4| id => Jones index 4 = |mu4|; KLM 16 = 4^2","v125 locality = isotropy: q(k(1,1)) = k^2 integer for all k; halfway {0,2} closes (SO(16)_1 step), 4 = 2x2"],"checked_by_registry":false,"heading_as_written":"(* ---- (v124) resummed clock ---- *) Module[{lams, rate, ser}, lams = Table[((3 - n)/3)^6, {n, 0, 2}]; checkExact[\"v124 spectrum reads (1-n/3)^6: eigenvalues {1, (2/3)^6, (1/3)^6}\", lams == {1, (2/3)^6, (1/3)^6}]; rate[n_] := -6 Log[(3 - n)/3]; checkExact[\"v124 closed-form clock: rates {0, Delta, 6 ln 3}; bend rate(2)/rate(1) = log_{3/2}3\", Simplify[rate[1] - 6 Log[3/2]] === 0 && Simplify[rate[2] - 6 Log[3]] === 0 && FullSimplify[rate[2]/rate[1] - Log[3]/Log[3/2]] === 0]; ser = Normal[Series[-6 Log[1 - x/3], {x, 0, 3}]]; checkExact[\"v124 linearisation carries the sheet: series 2x + x^2/3 + 2x^3/27 (slope |Z2| = 2); pole at n = N_fam = 3\", Expand[ser - (2 x + x^2/3 + 2 x^3/27)] === 0 && Limit[-6 Log[1 - x/3], x -> 3, Direction -> \"FromBelow\"] === Infinity]; ]; (* ---- (v125) glue Q-system ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:856","line_end":889,"line_start":856,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v124","v125"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v126 the weights are the parabolic weights: spec A0* = {0, 1/3, 2/3} = n/N_fam; bridge (1-alpha)^6 = {1, (2/3)^6, (1/3)^6}","v126 checkpoint 1 + determinant: linear coefficient p2/N = 2 = |Z2| (= v104 entropy rate 2H); det(1 - A0*) = 2/9 = |Z2|/N^2 (v102 curvature); tr(1 - A0*) = 2; det A0* = 0"],"checked_by_registry":false,"heading_as_written":"(* ---- (v126) clock-wall bridge ---- *) Module[{a0, spec, lams}, a0 = {{1/2, Sqrt[2]/6, 0}, {Sqrt[2]/6, 1/4, Sqrt[5]/12}, {0, Sqrt[5]/12, 1/4}}; spec = Sort[Eigenvalues[a0]]; checkExact[\"v126 the weights are the parabolic weights: spec A0* = {0, 1/3, 2/3} = n/N_fam; bridge (1-alpha)^6 = {1, (2/3)^6, (1/3)^6}\", spec == {0, 1/3, 2/3} && Sort[((1 - #)^6 &) /@ spec, Greater] == {1, (2/3)^6, (1/3)^6}]; checkExact[\"v126 checkpoint 1 + determinant: linear coefficient p2/N = 2 = |Z2| (= v104 entropy rate 2H); det(1 - A0*)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:890","line_end":902,"line_start":890,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v104","v126"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v127 log-det identity: det(1 - a P) = 1 - a (rank-1 P); series -ln(1-a) = a + a^2/2 + a^3/3 + ...","v127 ring ladder: k=1 ring = classical (2, 4 at weights 1, 2); k=2 ring = 1/3 at weight 1; partials below exact and monotone","v127 coupling cross-link + wall: kappa_seam = 8/24 = 1/3 = alpha_1 (kappa = alpha_1/pi); ring series diverges at alpha -> 1","v128 explicit coset construction: 240 = 52 + 64 + 60 + 64 over the glue Z4, all norm 2","v128 the grading is exact on all 6720 root-pair sums: E8 is a Z4-graded Lie algebra over the carrier (grading = the glue Q-system); zero-mode multiplicity 2(2l+1) = 6 = p2 at l = 1"],"checked_by_registry":false,"heading_as_written":"(* ---- (v127) ring resummation ---- *) Module[{proj, partial}, proj = {{1, 0, 0}, {0, 0, 0}, {0, 0, 0}}; checkExact[\"v127 log-det identity: det(1 - a P) = 1 - a (rank-1 P); series -ln(1-a) = a + a^2/2 + a^3/3 + ...\", Simplify[Det[IdentityMatrix[3] - a proj] - (1 - a)] === 0 && Normal[Series[-Log[1 - a], {a, 0, 3}]] === a + a^2/2 + a^3/3]; partial[al_, kmax_] := 6 Sum[al^j/j, {j, kmax}]; checkExact[\"v127 ring ladder: k=1 ring = classical (2, 4 at weights 1, 2); k=2 ring = 1/3 at weight 1; partials below exact and monotone\", partial[1/3, 1] == 2 && partial[2/3, 1] == 4 && 6 (1/3)^2/2 == 1/3 && partial[1/3, 8] < -6 Log[1 - 1/3] && partial[1/3, 2] > partial[1/3, 1]]; checkExact[\"v127 coupling cross-link + wall: kappa_seam = 8/24 = 1/3 = alpha_1 (kappa = alpha_1/pi); ring series diverges at alpha -> 1\", 8/24 == 1/3 && Limit[-Log[1 - a], a -> 1, Direction -> \"FromBelow\"] === Infinity]; ]; (* ---- (v128) graded hull ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:903","line_end":947,"line_start":903,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v127","v128"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v129 entropy power law: S/S_dS = {1, 2/3, 1/3} = 1 - n/N; lambda = (S/S_dS)^6 = frozen spectrum; rates = {0, Delta, 6 ln 3}; alpha = deficit fraction; p2 = 6 = 2 N_fam","v130 Born square: n_zero = 6; amplitude weight h = n_zero/2 = 3 = N_fam; probability exponent 2h = 6 = p2; l=1 dim = 3 = proper CKVs of S^2; x2 = horizon pair"],"checked_by_registry":false,"heading_as_written":"(* ---- (v129) entropy power law ---- *) Module[{levels, lams, rates}, levels = Table[(3 - n)/3, {n, 0, 2}]; lams = levels^6; rates = 6 Log[1/levels]; checkExact[\"v129 entropy power law: S/S_dS = {1, 2/3, 1/3} = 1 - n/N; lambda = (S/S_dS)^6 = frozen spectrum; rates = {0, Delta, 6 ln 3}; alpha = deficit fraction; p2 = 6 = 2 N_fam\", levels == {1, 2/3, 1/3} && lams == {1, (2/3)^6, (1/3)^6} && Simplify[rates[[2]] - 6 Log[3/2]] === 0 && Simplify[rates[[3]] - 6 Log[3]] === 0 && Table[n/3, {n, 0, 2}] == 1 - levels && 6 == 2*3 && rates[[1]] === 0 && levels[[1]] > levels[[2]] > levels[[3]]]; ]; (* ---- (v130) Born square ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:948","line_end":967,"line_start":948,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v129","v130"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v131 zero-mode norm = area: all three l=1 norms^2 = r^2 = A/(4pi); Jacobian bookkeeping (x^3)^2 = x^6; c3 = (1/2)(1/4pi)","v132 det-ratio anomaly: a1 = 1/N_fam + |Z2| = 7/3; zeta(0)|det' = 7/3 - 3 = -2/3 = -|Z2|/N_fam (numeric heat-trace constant agrees to ~1e-3 at t = 1/3000)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v131) measure is area ---- *) Module[{pref, harms, norms}, pref = Sqrt[3/(4 Pi)]; harms = {pref Cos[\\[Theta]], pref Sin[\\[Theta]] Cos[\\[Phi]], pref Sin[\\[Theta]] Sin[\\[Phi]]}; norms = Table[Integrate[Integrate[y^2 rr^2 Sin[\\[Theta]], {\\[Theta], 0, Pi}], {\\[Phi], 0, 2 Pi}], {y, harms}]; checkExact[\"v131 zero-mode norm = area: all three l=1 norms^2 = r^2 = A/(4pi); Jacobian bookkeeping (x^3)^2 = x^6; c3 = (1/2)(1/4pi)\", AllTrue[norms, Simplify[# - rr^2] === 0 &] && Simplify[(4 Pi rr^2)/(4 Pi) - rr^2] === 0 && Simplify[(x^3)^2 - x^6] === 0 && 1/2 * 1/(4 Pi) == 1/(8 Pi)]; ]; (* ---- (v132) det-ratio anomaly ---- The numerical heat-trace continuation is Python-only (mpmath); the exact arithmetic is mirrored here, plus an independent exact check of the constant term via the full heat-trace expansion. *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:968","line_end":993,"line_start":968,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v131","v132"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v133 zeta budget: reduced route = -2/3 per sector, -4/3 total = -e1/p0 (seed gain); 4d route a2 = 161/45, zeta(0) = -109/45 (no atom); zero modes 3+3 = 6","v133 numeric spot-check (WL): 4d constant term at t = 1/2000 within 2e-2 of -109/45"],"checked_by_registry":false,"heading_as_written":"(* ---- (v133) zeta budget ---- Numerical continuations are Python-only (mpmath); the exact arithmetic of both routes is mirrored, plus a numeric spot-check in WL. *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:994","line_end":1009,"line_start":994,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v133"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v134 dual anchor: a.R^-1 = a.L^-1 = (-1/2,-1/2,1); d.1 = 0, d.a = 1; (1,1,-2) = -2d; d = (3/2)(a - (4/3)1)","v134 Sherman-Morrison: L = R + 6*1 e1^T; R^-1 1 = (1,1,-1)/4; a on the invariance plane, 1/e1/n not (1/4, 1/4, -5/2); n.1 = 2","v135 surface: det M = 3s(t+1)(t+2) + t^2+5t+8; walls t=-2 -> 2, t=-1 -> 4 (s-independent); winding line 6s+8 -> (8,14,20); det F = 32 = 2^5","v135 anchor block: det B = 6s(t+2)+3t^2+15t+16; det B(s,0) = 2 det M(s,0); B-wall at t=-2 -> -2; micro-identities 41 = 16+25, 52 = 16+36","v135 row budgets: C = (7,11,13), U = (3,3,3), V = (1,2,3) = Spec(Q+)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v134) dual anchor ---- *) Module[{rmat, lmat, qmat, av, onev, e1v, nv, d, rinv1}, rmat = {{1, 3, 0}, {1, 5, 2}, {2, 5, 3}}; lmat = {{7, 3, 0}, {7, 5, 2}, {8, 5, 3}}; av = {1, 1, 2}; onev = {1, 1, 1}; e1v = {1, 0, 0}; nv = {5, -9, 6}; d = av . Inverse[rmat]; rinv1 = Inverse[rmat] . onev; checkExact[\"v134 dual anchor: a.R^-1 = a.L^-1 = (-1/2,-1/2,1); d.1 = 0, d.a = 1; (1,1,-2) = -2d; d = (3/2)(a - (4/3)1)\", d == av . Inverse[lmat] && d == {-1/2, -1/2, 1} && d . onev == 0 && d . av == 1 && {1, 1, -2} == -2 d && d == 3/2 (av - 4/3 onev)]; checkExact[\"v134 Sherman-Morrison: L = R + 6*1 e1^T; R^-1 1 = (1,1,-1)/4; a on the invariance plane, 1/e1/n not (1/4, 1/4, -5/2); n.1 = 2\", lmat == rmat + 6 Outer[Times, onev, e1v] && rinv1 == {1/4, 1/4, -1/4} && av . rinv1 == 0 && onev . rinv1 == 1/4 && e1v . rinv1 == 1/4 && nv . rinv1 == -5/2 && nv . onev == 2]; ]; (* ---- (v135) determinant surface ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1010","line_end":1049,"line_start":1010,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v134","v135"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v136 column normal form: d.c_j = a_j, n.c_j = 8 delta_1j; kernel (6,8,7); each column UNIQUE in {0..5}^3 (1 of 216)","v136 honesty: K not pinned by (d,n) (d.K = (1,1/2,1), n.K = (14,1,-6)); det K = 4 via the diamond","v136 spectral normal: A0* zero mode signed squares = -(2,-9,5); ||v||^2 = 16/9; adj(A0*) = (2/9) projector; sigma.1 = -2, sigma.a = 3, n.sigma = 121","v136 orbit control: |W(A3)| = 24; real orbit images of sigma = signed copies only; none proportional to n"],"checked_by_registry":false,"heading_as_written":"(* ---- (v136) dual-normal selector ---- *) Module[{dv, nv, av, rmat, qmat, kmat, sols, a0, v0, sigma, adjA0, grp, gens, reals}, dv = {-1/2, -1/2, 1}; nv = {5, -9, 6}; av = {1, 1, 2}; rmat = {{1, 3, 0}, {1, 5, 2}, {2, 5, 3}}; qmat = {{3, 1, 0}, {3, 2, 0}, {3, 2, 1}}; kmat = rmat + qmat . DiagonalMatrix[{1, -1, -1}]; sols = Table[Select[Tuples[Range[0, 5], 3], dv . # == av[[j]] && nv . # == 8 Boole[j == 1] &], {j, 3}]; checkExact[\"v136 column normal form: d.c_j = a_j, n.c_j = 8 delta_1j; kernel (6,8,7); each column UNIQUE in {0..5}^3 (1 of 216)\", (dv . #) & /@ Transpose[rmat] == av && (nv . #) & /@ Transpose[rmat] == {8, 0, 0} && 7 First[NullSpace[{dv, nv}]] == {6, 8, 7} && Length /@ sols == {1, 1, 1} && (First /@ sols) == Transpose[rmat]]; checkExact[\"v136 honesty: K not pinned by (d,n) (d.K = (1,1/2,1), n.K = (14,1,-6)); det K = 4 via the diamond\", dv . kmat == {1, 1/2, 1} && nv . kmat == {14, 1, -6} && Det[kmat] == 4]; a0 = {{1/2, Sqrt[2]/6, 0}, {Sqrt[2]/6, 1/4, Sqrt[5]/12}, {0, Sqrt[5]/12, 1/4}}; v0 = First[NullSpace[a0]]; v0 = v0/v0[[2]] 3; sigma = {2, -9, 5}; adjA0 = Transpose[Table[(-1)^(i + j) Det[Drop[a0, {i}, {j}]], {i, 3}, {j, 3}]]; checkExact[\"v136 spectral normal: A0* zero mode signed squares = -(2,-9,5); ||v||^2 = 16/9; adj(A0*)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1050","line_end":1085,"line_start":1050,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v0","v136"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v137 characters + residues: omega_k has mu_4 character i^k (k=1,2,3); residue vector = zeta^k/4 exactly","v137 grading: Spec(Q+) = {1,2,3}; cusp weights {0,1/3,2/3} = spec(A0*); (1,2,3) = A3 exponents, h(A3) = 4 = |mu_4|"],"checked_by_registry":false,"heading_as_written":"(* ---- (v137) Q+ cohomology grading ---- *) Module[{omchar, resok, qp, a0c}, omchar = Table[Simplify[((I z)^(k - 1)/((I z)^4 - 1)) I/(z^(k - 1)/(z^4 - 1))], {k, 3}]; resok = And @@ Flatten[Table[ Simplify[Residue[z^(k - 1)/(z^4 - 1), {z, zeta}] - zeta^k/4] === 0, {k, 3}, {zeta, {1, -1, I, -I}}]]; checkExact[\"v137 characters + residues: omega_k has mu_4 character i^k (k=1,2,3); residue vector = zeta^k/4 exactly\", omchar === {I, -1, -I} && resok]; qp = DiagonalMatrix[3 {0, 1/3, 2/3} + 1]; a0c = {{1/2, Sqrt[2]/6, 0}, {Sqrt[2]/6, 1/4, Sqrt[5]/12}, {0, Sqrt[5]/12, 1/4}}; checkExact[\"v137 grading: Spec(Q+) = {1,2,3}; cusp weights {0,1/3,2/3} = spec(A0*)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1086","line_end":1101,"line_start":1086,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v137"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v138 external datum + edge match: 22/45 - 8/3 = -98/45 (VW hep-th/0003081 / arXiv:2506.02142); edge = -8/3 = 2 x (-4/3) = two copies of the v133 reduced seam budget; diff -38/45, 38 = 2*19, no atom","v139 selector triangle: d = (3/2)a - 2*1; det(1|a|sigma) = 11; n unique from pairings (2, 8, 121); pairing line 11(11+t) square only at t = 0; review lift n = reverse(sigma) + 4 e3"],"checked_by_registry":false,"heading_as_written":"(* ---- (v138) VW firewall ---- *) checkExact[\"v138 external datum + edge match: 22/45 - 8/3 = -98/45 (VW hep-th/0003081 / arXiv:2506.02142); edge = -8/3 = 2 x (-4/3) = two copies of the v133 reduced seam budget; diff -38/45, 38 = 2*19, no atom\", 22/45 - 8/3 == -98/45 && -8/3 == 2 (-4/3) && -98/45 + 60/45 == -38/45 && FactorInteger[38] == {{2, 1}, {19, 1}} && ! MemberQ[{2/3, 4/3, 1/3, 8/9, 2/9, 16/9, 13/144}, 98/45] && ! MemberQ[{2/3, 4/3, 1/3, 8/9, 2/9, 16/9, 13/144}, 38/45]]; (* ---- (v139) selector triangle ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1102","line_end":1121,"line_start":1102,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v133","v138","v139"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v140 canonical map: deck U chars (0,1,3) miss 2; -U = (2,3,1) and i^Q+ = (1,2,3) both have SET {1,2,3} = H^1; i^Q+ assignment = Q+, -U assignment = Q+ o rho (one Z3 rotation apart)","v141 deck selection: integer deck G = TA.Sigma has the Q+=1 line as exact (-1)-eigenline (character 2, self-conjugate) and {+i,-i} on the E-plane; only the sheet-twisted rotation (2,3,1) is compatible -- i^{Q+} excluded; G^4 = 1","v141 sheet robustness: under k -> -k the assignment (2,3,1) -> (2,1,3): B1 pairing (1->2) and plane set {1,3} invariant; (1,2,3) -> (3,2,1) is not a Z3 rotation"],"checked_by_registry":false,"heading_as_written":"(* ---- (v140) canonical map ---- *) Module[{charf, cu, cmu, cw}, charf[m_] := Mod[Round[Arg[#]/(Pi/2)], 4] & /@ Diagonal[m]; cu = charf[DiagonalMatrix[{1, I, -I}]]; cmu = charf[-DiagonalMatrix[{1, I, -I}]]; cw = charf[DiagonalMatrix[{I, I^2, I^3}]]; checkExact[\"v140 canonical map: deck U chars (0,1,3) miss 2; -U = (2,3,1) and i^Q+ = (1,2,3) both have SET {1,2,3} = H^1; i^Q+ assignment = Q+, -U assignment = Q+ o rho (one Z3 rotation apart)\", cu == {0, 1, 3} && cmu == {2, 3, 1} && cw == {1, 2, 3} && Sort[cmu] == {1, 2, 3} == Sort[cw] && cmu == (cw[[#]] & /@ {2, 3, 1})]; ]; (* ---- (v141) deck selection ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1122","line_end":1155,"line_start":1122,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v140","v141"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v142 frame integrality: 11 m = (m.1)(a x s) + (m.a)(s x 1) + (m.s)(1 x a); integer covectors <=> x - 3y + z = 0 mod 11 (index 11 = ||Pl(K)||_1); with (2,8) the third pairing is forced = 0 mod 11; odd t non-primitive; Cramer: n.a = det R = 8, n.1 = 8 (R^-1 1)_1 = 2","v143 graded Frobenius: coset(-r) = -coset(r) mod 4 for all 240 roots (-C1 = C3, C0/C2 self-dual) => Killing pairing nondegenerate per g_k x g_-k; glue average = carrier projector (Sum_k i^(k d)/4 = KroneckerDelta); sectors single Weyl orbits with 64 = 16*4, 60 = 10*6"],"checked_by_registry":false,"heading_as_written":"(* ---- (v142) frame integrality ---- *) Module[{onev, av, sigma, nv, axs, sx1, oxa, congOK, mref, rmat, rinv}, onev = {1, 1, 1}; av = {1, 1, 2}; sigma = {2, -9, 5}; nv = {5, -9, 6}; axs = Cross[av, sigma]; sx1 = Cross[sigma, onev]; oxa = Cross[onev, av]; mref = {2, -5, 7}; congOK = And @@ Flatten[Table[ (AllTrue[x axs + y sx1 + z oxa, Mod[#, 11] == 0 &]) == (Mod[x - 3 y + z, 11] == 0), {x, 0, 10}, {y, 0, 10}, {z, 0, 10}]]; rmat = {{1, 3, 0}, {1, 5, 2}, {2, 5, 3}}; rinv = Inverse[rmat]; checkExact[\"v142 frame integrality: 11 m = (m.1)(a x s) + (m.a)(s x 1) + (m.s)(1 x a); integer covectors <=> x - 3y + z = 0 mod 11 (index 11 = ||Pl(K)||_1); with (2,8) the third pairing is forced = 0 mod 11; odd t non-primitive; Cramer: n.a = det R = 8, n.1 = 8 (R^-1 1)_1 = 2\", 11 mref == (mref . onev) axs + (mref . av) sx1 + (mref . sigma) oxa && congOK && Mod[2 - 3*8 + 121, 11] == 0 && AllTrue[Range[-21, 21, 2], GCD @@ ({5 + #, -9 - #, 6}) > 1 &] && Det[rmat] == 8 && rinv . onev == {1/4, 1/4, -1/4} && 8 (rinv . onev)[[1]] == 2 == nv . onev && nv . av == 8]; ]; (* ---- (v143) graded Frobenius ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1156","line_end":1206,"line_start":1156,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v142","v143"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v144 det-ratio family cancellation: e2-rigidity r_b r_c = 1 - Delta^2/3 exact (traceless cubic, e2 = -3); ratio = (1 - Delta^2/3)^(4/3) has NO first-order term, quadratic coefficient -4/9; eps = (3/8) Delta^2 => coefficient -32/27 = -|mu4| (2/3)^3","v145 pairing atoms: n = w0(sigma) + 4 e3; n.1 = -|Z2|+|mu4| = 2; sigma.w0(a) = 0 <=> |mu4|+g = N^2 (4+5=9) => n.a = 4*2 = 8; ||sigma||^2 = 110 = 2*5*11; n.sigma = 110-9+20 = 121 = 11^2"],"checked_by_registry":false,"heading_as_written":"(* ---- (v144) det-ratio family cancellation ---- *) Module[{s, p, rb, rc, ro, poly, ratio, ser, cpar, epsSer}, s = 2 Sqrt[1 - \\[CapitalDelta]^2/12]; p = 1 - \\[CapitalDelta]^2/3; rb = (s + \\[CapitalDelta])/2; rc = (s - \\[CapitalDelta])/2; ro = -s; poly = Collect[Expand[(t - rb)(t - rc)(t - ro)], t, Simplify]; ratio = (rb rc)^(4/3); ser = Normal[Series[ratio, {\\[CapitalDelta], 0, 3}]]; cpar = Simplify[p s/2]; epsSer = Normal[Series[1 - cpar, {\\[CapitalDelta], 0, 3}]]; checkExact[\"v144 det-ratio family cancellation: e2-rigidity r_b r_c = 1 - Delta^2/3 exact (traceless cubic, e2 = -3); ratio = (1 - Delta^2/3)^(4/3) has NO first-order term, quadratic coefficient -4/9; eps = (3/8) Delta^2 => coefficient -32/27 = -|mu4| (2/3)^3\", Simplify[rb rc - p] == 0 && Simplify[Coefficient[poly, t, 2]] == 0 && Simplify[Coefficient[poly, t, 1]] == -3 && Coefficient[ser, \\[CapitalDelta], 1] == 0 && Coefficient[ser, \\[CapitalDelta], 2] == -4/9 && Coefficient[epsSer, \\[CapitalDelta], 2] == 3/8 && (-4/9)/(3/8) == -32/27 == -4 (2/3)^3]; ]; (* ---- (v145) pairing atoms ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1207","line_end":1238,"line_start":1207,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v144","v145"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v146 Moebius D4: delta* omega_k = i^k omega_k; iota* omega_(1,2,3) = omega_(3,2,1) (+1 on chi2, det -1); dihedral relations; T_A (cusp basis, char-2 line first) = the same reflection class as iota (fixes the self-conjugate line with +1, swaps the pair, det -1); Sigma = the delta-iota class","v147 clock Gaussian: Born^2 ratio = (1-alpha)^6, rate = -6 ln(1-alpha), ln series = ring sum; bend = ln3/ln(3/2) with (1/3)^6 = ((2/3)^6)^bend; kappa = 8/(24 pi) = 1/(3 pi); spectrum {1,(2/3)^6,(1/3)^6}"],"checked_by_registry":false,"heading_as_written":"(* ---- (v146) Moebius D4 realisation ---- *) Module[{om, deckOK, invOK, ta, sig, p, tac, sigc, delta, iota}, om[k_] := z^(k - 1)/(z^4 - 1); deckOK = And @@ Table[ Simplify[(om[k] /. z -> I w) I - I^k (om[k] /. z -> w)] === 0, {k, 1, 3}]; invOK = Simplify[(om[1] /. z -> 1/w) (-1/w^2) - (om[3] /. z -> w)] === 0 && Simplify[(om[2] /. z -> 1/w) (-1/w^2) - (om[2] /. z -> w)] === 0 && Simplify[(om[3] /. z -> 1/w) (-1/w^2) - (om[1] /. z -> w)] === 0; ta = {{0, 1, 0}, {1, 0, 0}, {2, -2, 1}}; sig = DiagonalMatrix[{1, -1, -1}]; p = Transpose[{{0, 0, 1}, {0, 1, 2}, {1, 0, 0}}]; tac = Inverse[p] . ta . p; sigc = Inverse[p] . sig . p; delta = DiagonalMatrix[{I, -1, -I}]; iota = {{0, 0, 1}, {0, 1, 0}, {1, 0, 0}}; checkExact[\"v146 Moebius D4: delta* omega_k = i^k omega_k; iota* omega_(1,2,3) = omega_(3,2,1) (+1 on chi2, det -1); dihedral relations; T_A (cusp basis, char-2 line first) = the same reflection class as iota (fixes the self-conjugate line with +1, swaps the pair, det -1); Sigma = the delta-iota class\", deckOK && invOK && iota . iota == IdentityMatrix[3] && Simplify[iota . delta . Inverse[iota] - Inverse[delta]] == ConstantArray[0, {3, 3}] && tac == {{1, 0, 0}, {0, 0, 1}, {0, 1, 0}} && Det[tac] == -1 && tac[[1, 1]] == 1 == iota[[2, 2]] && sigc == DiagonalMatrix[{-1, -1, 1}] && Simplify[(delta . iota)[[2, 2]]] == -1 && Simplify[Det[delta . iota]] == 1]; ]; (* ---- (v147) clock Gaussian model ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1239","line_end":1279,"line_start":1239,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v146","v147"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v148 NS/R census (corrected): NS supports only even classes {(0,0),(2,0),(0,2),(2,2)} (integer weights); R zero-mode module = four odd pairs of 64; R splits 128+128 into the odd sectors of the two Lagrangian glues; 248 = 120 NS + 128 R","v149 cusp normal: n pairs with the cusp eigenbasis to (6,3,5) = (p2,p0,e2)(a); cusp matrix unimodular => unique; d = (3/2)a - 2*1; equivalences (2,8,121) + w0-lift; sigma -> (5,1,2); 6+3+5 = 14 = dim G2"],"checked_by_registry":false,"heading_as_written":"(* ---- (v148) NS/R sector census (corrected) ---- *) Module[{nsClasses, rCounts, glueA, glueB, inA, inB}, nsClasses = Union[Flatten[Table[ {2 Mod[Total[v], 2], 2 Mod[Total[w], 2]}, {v, Tuples[Range[-1, 1], 5]}, {w, Tuples[Range[-1, 1], 3]}], 1]]; rCounts = <||>; Do[Module[{qd = If[EvenQ[Count[s5, -1]], 1, 3]}, Do[Module[{qa = If[EvenQ[Count[s3, -1]], 1, 3]}, rCounts[{qd, qa}] = Lookup[rCounts, Key[{qd, qa}], 0] + 1], {s3, Tuples[{1, -1}, 3]}]], {s5, Tuples[{1, -1}, 5]}]; glueA = {{0, 0}, {1, 1}, {2, 2}, {3, 3}}; glueB = {{0, 0}, {1, 3}, {2, 2}, {3, 1}}; inA = Total[Lookup[rCounts, Key[#], 0] & /@ glueA]; inB = Total[Lookup[rCounts, Key[#], 0] & /@ glueB]; checkExact[\"v148 NS/R census (corrected): NS supports only even classes {(0,0),(2,0),(0,2),(2,2)} (integer weights); R zero-mode module = four odd pairs of 64; R splits 128+128 into the odd sectors of the two Lagrangian glues; 248 = 120 NS + 128 R\", Sort[nsClasses] == Sort[{{0, 0}, {2, 0}, {0, 2}, {2, 2}}] && ! MemberQ[nsClasses, {1, 1}] && ! MemberQ[nsClasses, {3, 3}] && Values[KeySort[rCounts]] == {64, 64, 64, 64} && Total[Values[rCounts]] == 256 && inA == 128 && inB == 128 && 120 + 128 == 248]; ]; (* ---- (v149) cusp normal ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1280","line_end":1320,"line_start":1280,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v148","v149"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v150 replica EH model: image sum exact (N=2..8); orbifold deficit = C(2pi/N); Mellin Delta-zeta(s) = C m^-2s => Delta log det' = 2C ln m (cutoff-independent); dC/dgamma|_{2pi} = -1/(12pi) => EH form with k = ln m/(12pi); target k = c3/2 <=> ln m = 3/4 = q(A3)","v151 BFK split: Cheeger form match; doubling => C_N(theta) = C_D(theta) (Kac corner boundary-condition independent); conical deficit of the Calderon/DtN jump determinant = C_cone(g) - 2 C_D(g/2) = 0 IDENTICALLY; dC/dg|_{2pi} = -1/(12pi); target ln m = 3/4 = q(A3) unchanged"],"checked_by_registry":false,"heading_as_written":"(* ---- (v150) replica EH model ---- *) Module[{cdef, imgOK, convOK, mellin, dz0, dC, target}, cdef[g_] := (1/12) (2 Pi/g - g/(2 Pi)); imgOK = And @@ Table[ FullSimplify[Sum[1/Sin[Pi k/n]^2, {k, 1, n - 1}] - (n^2 - 1)/3] === 0, {n, 2, 8}]; convOK = Simplify[(1/(4 nn)) (nn^2 - 1)/3 - cdef[2 Pi/nn]] === 0; mellin = Integrate[tt^(ss - 1) Exp[-mm^2 tt], {tt, 0, Infinity}, Assumptions -> ss > 0 && mm > 0]; dz0 = D[mm^(-2 ss), ss] /. ss -> 0; dC = D[cdef[gg], gg] /. gg -> 2 Pi; target = Simplify[12 Pi (1/2) (1/(8 Pi))]; checkExact[\"v150 replica EH model: image sum exact (N=2..8); orbifold deficit = C(2pi/N); Mellin Delta-zeta(s) = C m^-2s => Delta log det' = 2C ln m (cutoff-independent); dC/dgamma|_{2pi} = -1/(12pi) => EH form with k = ln m/(12pi); target k = c3/2 <=> ln m = 3/4 = q(A3)\", imgOK && convOK && Simplify[mellin - Gamma[ss] mm^(-2 ss)] === 0 && Simplify[dz0 + 2 Log[mm]] === 0 && Simplify[dC + 1/(12 Pi)] === 0 && target == 3/4]; ]; (* ---- (v151) BFK split ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1321","line_end":1354,"line_start":1321,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v150","v151"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v152 R3 normalisation = anchor: Delta log det' = 2 C ln(m/mu) (scale-ambiguous ln m; only m/mu physical); k = c3/2 <=> ln(m/mu) = 3/4 => m/mu = e^{3/4}; 1/(16 pi G)|_{G=1} = c3/2 (induced 1/G = the v68 anchor); audit: 3/4 = q(A3) is the target value, not a derivation","v153 No-Unit Theorem: dimensionless data (g_car,N_fam,|mu4|,rank E8,det-ladder 1920,c3,2pi c3=1/4) invariant under L->lambda L; a mass scales as lambda^-1 (contradiction unless the unit is introduced); collapse U_point~v_geo, 1/G~v_geo^2, m/mu=e^{3/4}"],"checked_by_registry":false,"heading_as_written":"(* ---- (v152) R3 normalisation = the anchor ---- *) Module[{c3, k, lnratio, dlogdet}, c3 = 1/(8 Pi); k = c3/2; lnratio = Simplify[12 Pi k]; dlogdet = -D[(mm/muu)^(-2 ss), ss] /. ss -> 0; checkExact[\"v152 R3 normalisation = anchor: Delta log det' = 2 C ln(m/mu) (scale-ambiguous ln m; only m/mu physical); k = c3/2 <=> ln(m/mu) = 3/4 => m/mu = e^{3/4}; 1/(16 pi G)|_{G=1} = c3/2 (induced 1/G = the v68 anchor); audit: 3/4 = q(A3) is the target value, not a derivation\", Simplify[dlogdet - 2 Log[mm/muu]] === 0 && k == 1/(16 Pi) && lnratio == 3/4 && Simplify[1/(16 Pi) - c3/2] === 0 && 3/4 == 3/4]; ]; (* ---- (v153) No-Unit Theorem ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1355","line_end":1379,"line_start":1355,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v152","v153","v68"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v154 Simple-Current Extension: |L|=4=|mu4| (isotropic q(k(1,1))=k^2 in Z); c(B)=5+3=8; mu(B)=mu(A)/|L|^2=16/16=1 => holomorphic => B=(E8)1 (unique even-unimodular rank-8; SO(16)1 mu=4 excluded)","v156 seam-net construction: DtN of the 2d Laplacian = |k| (free chiral dispersion); c=16/2=8=5+3; E8 currents 248=120+128 (dim SO(16)+spinor 2^7); (E8)_1 character E4/eta^8 = q^{-1/3}(1+248q+4124q^2+34752q^3+213126q^4) = j^{1/3}; NS level-1 = 112, 112+128 = 240 roots, 248 = 240+8"],"checked_by_registry":false,"heading_as_written":"(* ---- (v154) Simple-Current Extension Theorem ---- *) Module[{Lord = 4, cB, muA, muB}, cB = 5 + 3; muA = 4*4; muB = muA/Lord^2; checkExact[\"v154 Simple-Current Extension: |L|=4=|mu4| (isotropic q(k(1,1))=k^2 in Z); c(B)=5+3=8; mu(B)=mu(A)/|L|^2=16/16=1 => holomorphic => B=(E8)1 (unique even-unimodular rank-8; SO(16)1 mu=4 excluded)\", AllTrue[Range[0, 3], IntegerQ[5 #^2/8 + 3 #^2/8] &] && Lord == 4 && cB == 8 && muA == 16 && muB == 1 && 4 != muB]; ]; (* ---- (v156) seam-net construction: DtN = |k| + the (E8)_1 character ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1380","line_end":1410,"line_start":1380,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v154","v156"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v157 rigid fixed point: DtN symbol |k| homogeneous degree 1 (universal, Lee-Uhlmann); holomorphic c=8 has no (1,1) marginal (hbar=0) => isolated/rigid; |Z2| triple role: c3 = 1/(|Z2|*2pi*chi(S2)) = 1/(8pi), and the same |Z2| = Ramond projection giving 248 = 120 + 128 (mu=1)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v157) freeness as the rigid boundary fixed point ---- *) Module[{symbolHomog, c3}, symbolHomog = Simplify[Abs[lam kk] - lam Abs[kk], (lam | kk) \\[Element] Reals && lam > 0]; c3 = 1/(2*2 Pi*2); (* 1/(|Z2| * 2pi * chi(S^2)) , chi=2 *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1411","line_end":1420,"line_start":1411,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v157"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v158 fixed-point stability: Majorana h=1/2, current h=1, quartic h=2; relevant window (0,1) for bosonic ops EMPTY; currents chiral (hbar=0, 248=120+128); quartic h=2>1 irrelevant => free chiral c=8 fixed point isolated/stable"],"checked_by_registry":false,"heading_as_written":"(* ---- (v158) free chiral c=8 fixed point is stable ---- *) Module[{hpsi, hcur, hquart, bosonic, relevant}, hpsi = 1/2; hcur = 2 hpsi; hquart = 4 hpsi; bosonic = {1, 2, 3}; (* integer-h bosonic chiral ops *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1421","line_end":1431,"line_start":1421,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v158"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v159 PyR@TE gauge cross-check: carrier/SM content -> (b1,b2,b3)=(41/10,-19/6,-7) [GUT norm]; 10 b1 = g_car 2^(g_car-2)+1 = 41 = 40(ferm)+1(Higgs); matches PyR@TE 3 beta_g{1,2,3} verbatim"],"checked_by_registry":false,"heading_as_written":"(* ---- (v159) PyR@TE gauge cross-check: carrier content -> SM 1-loop b_i ---- *) Module[{fields, pre, u1, su2, su3, b1, b2, b3, fermIdx, scalIdx}, (* {Y, dimSU2, dimSU3, nGen, kind}: kind 1 = Weyl fermion, 2 = complex scalar *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1432","line_end":1451,"line_start":1432,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v159"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v168 QGEO rigidity: mu4={1,i,-1,-i} cross-ratio 2; omega_k=z^{k-1}dz/(z^4-1) (k=1,2,3) are mu4-eigenforms with character i^k = chi_1,chi_2,chi_3; Spec(Q+)={1,2,3}=A3 exponents (b1=N_fam=3)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v168) QGEO rigidity: mu4 square cross-ratio, mu4 characters = A3 exponents ---- *) Module[{mu4, cross, zz, eig, qspec}, mu4 = {1, I, -1, -I}; cross = Simplify[(mu4[[1]] - mu4[[3]]) (mu4[[2]] - mu4[[4]]) / ((mu4[[1]] - mu4[[4]]) (mu4[[2]] - mu4[[3]])) ]; (* omega_k = z^{k-1}/(z^4-1); pullback z->i z eigenvalue should be i^k *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1452","line_end":1464,"line_start":1452,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v168"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v170 E8 slice compression: P=(3,4,6,10), D=(3,4,8,14,20,32) sum 81=N_fam^4; K4 edges {12,18,30,24,40,60}; all seven E8 slices = 248; 78 = p2 Delta = dim E6","v171 OS moment + Sugawara: spec(T)={1,64/729,1/729}; cluster 1/(1-r)=729/665; 31=1+h^v(E8); c(E8)_1=248/31=8; Delta_eff=6log(3/2)-31/(4pi^2)>0"],"checked_by_registry":false,"heading_as_written":"(* ---- (v170) E8 slice compression: seven slices from two alphabets ---- *) Module[{p, p0, p1, p2, p3, Delta, e1, e2, dimSp, dQ, dK, dR, dC, dL, dF, slices}, p = Table[2 + 2^n, {n, 0, 3}]; {p0, p1, p2, p3} = p; Delta = p0 + p3; e1 = 4; e2 = 5; dimSp = 16; {dQ, dK, dR, dC, dL, dF} = {3, 4, 8, 14, 20, 32}; slices = { p0 p1 p3 + p1 dF, (p1 p3 + e2) + (p0 p1 + p0) + p2 p3 + 2 e1 dimSp, p2 Delta + dR + 81 + 81, (p0 p1 p3 + Delta) + p0 + dR dC, (p1^2 + p2^2) + dC + Delta dC, 2 p1 p2 + 4 e2 p3, dK dL + 2 p2 dC}; checkExact[\"v170 E8 slice compression: P=(3,4,6,10), D=(3,4,8,14,20,32) sum 81=N_fam^4; K4 edges {12,18,30,24,40,60}; all seven E8 slices = 248; 78 = p2 Delta = dim E6\", p === {3, 4, 6, 10} && Total[{dQ, dK, dR, dC, dL, dF}] == 81 && {p0 p1, p0 p2, p0 p3, p1 p2, p1 p3, p2 p3} === {12, 18, 30, 24, 40, 60} && AllTrue[slices, # == 248 &] && p2 Delta == 78]; ]; (* ---- (v171) atomic OS moment + Sugawara gap safety ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1465","line_end":1495,"line_start":1465,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v170","v171"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v172 trace-anomaly seed: c*chi/6=8/3 halved by |Z2| = 4/3 = 16/12 (dim S+/dim g_SM); QCD b3=11-2/3 N_f=7 = scalaron exp 48-41; Volkov-Wipf -98/45 = -2*7^2/45"],"checked_by_registry":false,"heading_as_written":"(* ---- (v172) trace-anomaly seed 4/3 + shared integer 7 ---- *) Module[{cc, chi, anomaly, half, b3, scal, vw}, cc = 8; chi = 2; anomaly = cc chi/6; (* 8/3 *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1496","line_end":1508,"line_start":1496,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v172"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v174 seam Fock-space readings: CAR cone 2^15=32768 -> 16 one-particle (2^15/16=2^11); Witten index sum_{k<=2}C(4,k)=11=dim S+ - g_car (full 2^4=16), c_u/c_d=5*11/(9*13)=55/117; g-theorem c_UV=5+3=8=c_IR((E8)1), Delta c=0"],"checked_by_registry":false,"heading_as_written":"(* ---- (v174) seam Fock-space readings: cone compression, Witten index, g-theorem ---- *) Module[{cone, blocks, trunc, disc, cUV, cIR}, cone = 2^15; blocks = {Binomial[16, 4], Binomial[16, 6], Binomial[16, 8]}; trunc = Sum[Binomial[4, k], {k, 0, 2}]; (* 11 *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1509","line_end":1521,"line_start":1509,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v174"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v175 net existence + full-cone RP: E8 Cartan even (diag 2) with det 1 = unique rank-8 even unimodular lattice; (E8)_1 character E4/eta^8 coeff at q^5 = 1057504 (extends v156 to order 5); Gamma(t)=(+)Lambda^m(t) on the complete Fock space dim 2^16=65536, eigenvalue-1 multiplicity 2^8=256, sub-leading = one-particle gap (2/3)^6, exterior-square C(16,2)=120"],"checked_by_registry":false,"heading_as_written":"(* ---- (v175) net existence + full-cone RP: E8 Cartan even unimodular, character order 5, Gamma(t) functoriality integers ---- *) Module[{cartan, det, evenDiag, sig3, E4, prodv, chi, c5, fockDim, fixedMult, gap, pairCount}, (* E8 Cartan matrix (Bourbaki): even (diag 2) and det 1 = unique rank-8 even unimodular lattice *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1522","line_end":1545,"line_start":1522,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v175"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v183 Koide 53/54 operator origin: 1^T R a = 27 (E6xA2 cubic block, 248=78+8+2*27*3); F=R+Q missing Sheet-Diamond corner, det B_F=52=dim F4, a^T(R+Q)1=53=52+1; ratio a^T(R+Q)1/(2 1^T R a)=53/54=1-1/(2*3^3); negative control: a^T M 1 for {R,Q,K,L}={32,21,35,56}, only F gives 53"],"checked_by_registry":false,"heading_as_written":"(* ---- (v183) Koide 53/54 = a^T(R+Q)1 / (2 1^T R a): missing Sheet-Diamond corner ---- *) Module[{R, Q, K, L, one, a, F, f, cubic, corner, ratio, detBF, others}, R = {{1, 3, 0}, {1, 5, 2}, {2, 5, 3}}; Q = {{3, 1, 0}, {3, 2, 0}, {3, 2, 1}}; K = {{4, 2, 0}, {4, 3, 2}, {5, 3, 2}}; L = {{7, 3, 0}, {7, 5, 2}, {8, 5, 3}}; one = {1, 1, 1}; a = {1, 1, 2}; F = R + Q; f[m_, u_, v_] := u . m . v; cubic = f[R, one, a]; (* 1^T R a = 27 *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1546","line_end":1563,"line_start":1546,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v183"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v189 Riemann-Roch carrier: from D=mu4 (deg 4) on P^1, h^0(O(mu4))=deg+1=5=g_car=rank(D5) and rank H_1(P^1\\\\mu4)=deg-1=3=N_fam; rank D5+rank A3=5+3=8=rank E8 (one object, two canonical invariants)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v189) Riemann-Roch carrier: (g_car,N_fam)=(5,3) from the mu4 divisor ---- *) Module[{degD, h0, rkH1, rankD5, rankA3}, degD = 4; (* |mu4| = deg D *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1564","line_end":1573,"line_start":1564,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v189"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v190 Nariai entropy bound: S_tot/S_dS=(x^2+1)/Phi3(x), value 2/3 at x=1; 3(x^2+1)-2 Phi3(x)=(x-1)^2>=0 so ratio>=2/3 with equality iff x=1 (variation-free floor); global min on x>0 = 2/3"],"checked_by_registry":false,"heading_as_written":"(* ---- (v190) Nariai entropy bound: S_tot/S_dS >= 2/3 via (x-1)^2 ---- *) Module[{x, ratio, val1, gap, mn}, ratio = (x^2 + 1)/(x^2 + x + 1); (* denom = Phi_3(x), the N_fam cyclotomic *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1574","line_end":1583,"line_start":1574,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v190"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v191 universal branch line (alignment, NOT a theorem): q=7/2+(N^2/2)m maps m=-1/3,0,1/3 -> 2,7/2,5 = {|Z2|, scalaron/2, g_car}; the affine map exists for ANY pair (decoy {3,4} -> midpoint 7/2, slope 3/2), so it is a relabeling exhibiting the known 2/3 ramification -- recorded [C], not [E]"],"checked_by_registry":false,"heading_as_written":"(* ---- (v191) Universal branch line: exact affine RELABELING (NOT a theorem) ---- *) Module[{Nfam, q, qm, q0, qp, decoyA, decoyB}, Nfam = 3; q[mm_] := 7/2 + (Nfam^2/2) mm; qm = q[-1/Nfam]; q0 = q[0]; qp = q[1/Nfam]; decoyA = (3 + 4)/2; decoyB = (4 - 3)/(2/Nfam); (* decoy {3,4}: midpoint 7/2, slope 3/2 *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1584","line_end":1593,"line_start":1584,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v191"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v193 QGEO.ENERGY.02 EH-rigidity: induced k=(ln m)/(12 pi) reproduces c3/2=1/(16 pi) iff ln m = q(A3)=3/4 (FAMILY norm); the carrier norm q(D5)=5/4 gives k=5/(48 pi) != 1/(16 pi), off by q(D5)/q(A3)=g_car/N_fam=5/3 -- the energy form must reproduce the family norm (gravity family-geometry-induced)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v193) QGEO.ENERGY.02 EH-rigidity rider: the EH coeff selects q(A3), not q(D5) ---- *) Module[{gcar, Nfam, mu4, c3, qA3, qD5, kFamily, kCarrier, kTarget}, gcar = 5; Nfam = 3; mu4 = 4; c3 = 1/(8 Pi); qA3 = Nfam/mu4; (* 3/4 family glue norm *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1594","line_end":1606,"line_start":1594,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v193"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v195 QGEO.MARKS.02: rho:z->iz on H^1 gives characters i^k={I,-1,-I}, Tr(rho|H^1)=i+i^2+i^3=-1, no trivial component; rank H_1=n-1=3 => n=4 punctures, all off the fixed locus {0,inf} => one free mu4 orbit {1,i,-1,-i} (closed under *i), Moebius cross-ratio 2"],"checked_by_registry":false,"heading_as_written":"(* ---- (v195) QGEO.MARKS.02: Lefschetz/character forcing of the free mu4 orbit ---- *) Module[{chars, trace, noTrivial, orbit, orbitClosed, nPunct}, chars = I^Range[1, 3]; (* {I, -1, -I} *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1607","line_end":1618,"line_start":1607,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v195"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v196 QGEO.VARI.01: on the mu4 H^1 block (rho=diag(i,-1,-i), Lambda diagonal, Theta=conj) all three E_fail terms vanish exactly -- [rho,Lambda]=0, rho^4=I, conj(rho)=rho^{-1} -- so E_fail=0 (the seam-deck conditions of QGEO.SYM.01)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v196) QGEO.VARI.01: E_fail = 0 on the mu4 block (exact finite vanishing) ---- *) Module[{rho, Lam, comm, order4, twist}, rho = DiagonalMatrix[{I, -1, -I}]; Lam = DiagonalMatrix[{1, 2, 3}]; (* any real diagonal (mu4-equivariant) DtN *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1619","line_end":1629,"line_start":1619,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v196"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v197 ARCH.RRCAR.02: dim Lambda^even(C_car=C^5) = C(5,0)+C(5,2)+C(5,4) = 1+10+5 = 16 = 2^(g_car-1) = dim S^+ = the so(10)=D5 half-spinor; so the 5-dim Riemann-Roch carrier mode space generates D5 by its even Clifford algebra (chain mu4->g_car->D5)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v197) ARCH.RRCAR.02: even Clifford of the 5-dim carrier = the D5 half-spinor ---- *) Module[{h0, lamEven}, h0 = 4 + 1; (* h^0(P^1,O(mu4)) = deg+1 = 5 = g_car *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1630","line_end":1637,"line_start":1630,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v197"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v198 QGEO.MODULAR.01: the DtN principal symbol |k|=sqrt(-d^2/dt^2)=diag(|n|) and the clock rho:z->iz=diag(i^n) are both diagonal in the Fourier basis, so [rho,|k|]=0 EXACTLY on all of L^2 (not just H^1) -- the leading-order commutation is free on the whole boundary; the residual reduces (Tomita-Takesaki) to the state-invariance omega o rho = omega, removing the BW circularity"],"checked_by_registry":false,"heading_as_written":"(* ---- (v198) QGEO.MODULAR.01: principal symbol |k| commutes with the clock rho EXACTLY ---- *) Module[{nn, rho1, absK, comm}, nn = Range[-8, 8]; rho1 = DiagonalMatrix[I^nn]; (* z->iz: e^{in t} -> i^n e^{in t} *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1638","line_end":1647,"line_start":1638,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v198"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v199 QGEO.STATE.01: rho^4=1 (carrier clock), and [rho,H]=0 <=> H is block-diagonal in the four mu4-character classes {n=r mod 4} -- a character-block-diagonal H commutes with rho, an off-character entry (class 0<->1) breaks it; so omega o rho=omega reduces to 'H has no off-character matrix elements'"],"checked_by_registry":false,"heading_as_written":"(* ---- (v199) QGEO.STATE.01: [rho,H]=0 <=> H is mu4-character-block-diagonal ---- *) Module[{nn, rho, idx, Hbd, Hoff, classOf}, nn = Range[-6, 6]; rho = DiagonalMatrix[I^nn]; (* carrier clock, order 4 *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1648","line_end":1664,"line_start":1648,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v199"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v201 QGEO.SUBPRIN.01: a mu4-mark sum sum_{j=0}^3 e^{-i m 2pi j/4} = 4 on multiples of 4 and 0 otherwise (Z4-invariant), so a mark-sourced curvature f has Fourier support only on modes ≡0 (mod 4); the multiplication operator M_f is then mu4-character-block-diagonal ([rho,M_f]=0), while an off-character (mode-1) entry breaks it -- block-diagonality is FORCED by the mu4 marks (v195), not postulated"],"checked_by_registry":false,"heading_as_written":"(* ---- (v201) QGEO.SUBPRIN.01: a mu4-mark sum is Z4-invariant => sub-principal block-diagonal ---- *) Module[{markSum, nn, rho, fmodes, Mf, Moff, gprof}, (* exact: the mu4-mark Fourier weight sum_{j=0}^3 e^{-i m 2pi j/4} = 4 [m=0 mod 4], else 0 *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1665","line_end":1684,"line_start":1665,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v201"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v203 HOR.EHT.01: the EHT achromatic polarization coupling beta_BH = 16 c3^4 (Q_e Q_m/r^2) has 16 c3^4 = 1/(256 pi^4) EXACTLY (c3=1/8pi), and equals delta_top/3 with delta_top = 48 c3^4 = 3/(256 pi^4) -- the SAME top-form coefficient that fixes the alpha-kernel precision-zone correction; the EHT coupling and the alpha correction are one compiler number (no free coupling)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v203) HOR.EHT.01: the EHT polarization coupling 16 c3^4 = 1/(256 pi^4) = delta_top/3 ---- *) Module[{c3, dtop}, c3 = 1/(8 Pi); dtop = 48 c3^4; (* = 3/(256 pi^4) *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1685","line_end":1694,"line_start":1685,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v203"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v204 FR.MUONG2.01: the muon anomalous moment a_mu^seam = delta_2/(2 pi) with delta_2 = (B gamma) delta_top^2 = (5/4)(48 c3^4)^2 is the EXACT compiler number 45/(524288 pi^9) ~ 2.879e-9 (c3=1/8pi); delta_2 = 45/(262144 pi^8) = 4! * 120 * c3^8 (trace 2880 = 24 * 120 = 4! * 5!); the value is exact, the vertex projection is the [C] bridge"],"checked_by_registry":false,"heading_as_written":"(* ---- (v204) FR.MUONG2.01: the muon seam-vertex value a_mu = 45/(524288 pi^9) ---- *) Module[{c3, dtop, Bgamma, delta2, amu}, c3 = 1/(8 Pi); dtop = 48 c3^4; (* = 3/(256 pi^4) *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1695","line_end":1707,"line_start":1695,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v204"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v205 GRAV.XI.01: the torsion-compression factor xi = c3/phi_tree = (1/8pi)/(1/6pi) = 3/4 EXACTLY; the Einstein-limit reduction 8 pi c3^2 = c3 makes G an output (xi = c3/phi0); and 3/4 = 12 pi (c3/2) = ln(m/mu) = q(A3) (v152) -- the torsion-compression and the gapped EH replica are two independent appearances of the same gravitational 3/4","v208 HOR.BHTHERMO.01: the induced f(R)=R+R^2/(6 Ms^2) gives f_R = 1 + R/(3 Ms^2), so the Wald entropy S_W = (f_R A)/(4 G) = (A/4G)(1 + R_h/(3 Ms^2)) -- an exact scalaron correction to the area law; the modular beta 2 pi = 1/(4 c3) (T_H = kappa/2pi), and the leading area law S_BH = M^2/(2 c3) = 4 pi M^2 = A/(4 G)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v205) GRAV.XI.01: xi = c3/phi_tree = 3/4, the independent gravitational 3/4 ---- *) Module[{c3, phitree}, c3 = 1/(8 Pi); phitree = 1/(6 Pi); checkExact[\"v205 GRAV.XI.01: the torsion-compression factor xi = c3/phi_tree = (1/8pi)/(1/6pi) = 3/4 EXACTLY; the Einstein-limit reduction 8 pi c3^2 = c3 makes G an output (xi = c3/phi0); and 3/4 = 12 pi (c3/2) = ln(m/mu) = q(A3) (v152) -- the torsion-compression and the gapped EH replica are two independent appearances of the same gravitational 3/4\", Simplify[c3/phitree - 3/4] == 0 && Simplify[8 Pi c3^2 - c3] == 0 && Simplify[12 Pi (c3/2) - 3/4] == 0]; ]; (* ---- (v208) HOR.BHTHERMO.01: scalaron Wald factor + modular 2 pi = 1/(4 c3) ---- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1708","line_end":1725,"line_start":1708,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v152","v205","v208"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v214 QGEO.PILLOW.01: the pillowcase reduction of QGEO.SYM.01 -- (i) the orbifold S^2(2,2,2,2) is Euclidean, chi_orb = 2-4(1-1/2) = 0 (Troyanov flat metric; Gauss-Bonnet four cone deficits pi = 4pi = 2pi chi(S^2) => flat away from the marks = the v201 conformal-deck residual); (ii) NEW LINK cross-ratio(mu4)=2 (v168) => j(2)=1728 via j(l)=256(l^2-l+1)^3/(l^2(l-1)^2), and all six harmonic cross-ratios {2,-1,1/2} give 1728, so the square modulus (hence the order-4 clock) is FORCED by cross-ratio 2, not assumed; (iii) the lemniscatic CM (x,y)->(-x,iy) on y^2=x^3-x negates the defining polynomial (same zero locus) and has order 4 = the z->iz isometry; (iv) NEG CONTROL j(3)=21952/9 not in {0,1728} => a generic config has only Z/2. Unifies QGEO.ISO.01 (v180) + QGEO.SUBPRIN.01 (v201) into one canonical flat-pillowcase-metric premise; does NOT close QGEO.SYM.01. The Klein-J modular values (J(i)=1) are mpmath-numerical (Python-only)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v214) QGEO.PILLOW.01: pillowcase reduction -- cross-ratio 2 => j=1728 => order-4 CM ---- *) Module[{chiorb, jl, x, y, curve, auto, xx, yy}, chiorb = 2 - 4 (1 - 1/2); (* orbifold Euler char of S^2(2,2,2,2) *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1726","line_end":1739,"line_start":1726,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v214"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v216 QGEO.MARKS.03: the four seam marks emerge from Gauss-Bonnet -- Z2 branch points (cone angle pi, deficit pi) on a flat sphere (chi=2) give n*pi = 2pi*chi = 4pi => n = 2 chi = 4 = |mu4| = N_fam+1; the closed Euclidean sphere 2-orbifolds (sum(1-1/m_i)=2) are exactly {(2,3,6),(2,4,4),(3,3,3),(2,2,2,2)}; all-order-2 (the |Z2| branch) selects (2,2,2,2) uniquely, and N_fam=3 (rank H^1=#marks-1) selects it too (the 4-mark square over the 3-mark hexagonal); only the square modulus (cross-ratio 2 => j=1728, v214) stays the order-4 input"],"checked_by_registry":false,"heading_as_written":"(* ---- (v216) QGEO.MARKS.03: the four marks from Gauss-Bonnet + Euclidean-orbifold uniqueness ---- *) Module[{orbs, gb, nn}, orbs = {{2, 3, 6}, {2, 4, 4}, {3, 3, 3}, {2, 2, 2, 2}}; gb = nn /. Solve[nn (2 Pi - Pi) == 2 Pi 2, nn][[1]]; (* Z2 deficit pi, chi(S^2)=2 *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1740","line_end":1750,"line_start":1740,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v216"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v218 DIAMOND.AXIS/PLUCKER/SPECTRAL.01: the Sheet Diamond (v94) is a discrete geometry with two axes around the centered cross (v95: C center, U winding, V sheet); F is the transfer completion. (1) AXIS CURVATURE: det(C+xU)=14+6x is LINEAR (winding flat, slope 6=|R^+(A3)|), det(C+yV)=14+14y+4y^2 is QUADRATIC with 2nd difference 8=rank E8; det B(C+xU)=2 det(C+xU); the anchor-block sheet 2nd difference is 6=|R^+(A3)| -- two curvatures (8 det, 6 anchor)=(rank E8, |R^+(A3)|). (2) PLUCKER TRANSFER LADDER: Pl(K)=(-1,6,4)->Pl(C)=(0,14,14)->Pl(F)=(1,22,30), steps (1,8,10)=(N_Phi,rank E8,A_Lambda) and (1,8,16)=(N_Phi,rank E8,dim S+) -- decuple 10 then full generation 16. (3) SPECTRAL RAMIFICATION: for Q,K,C,F the cubic discriminant factors as q(r)^2 Disc(q); squares |q(r)|={1,3,4,6}=(N_Phi,N_fam,|mu4|,|R^+(A3)|), kernels Disc(q)={13,48,65,105}=(Delta_Q,Omega_adm,g_car Delta_Q,N_fam g_car 7), F carries 105=3*5*7. NO new numbers -- it organises the existing operators; the G2/F4 pair-sum labels stay audit-only and F=transfer-corner stays a heuristic (Python-only audit blocks)"],"checked_by_registry":false,"heading_as_written":"(* ---- (v218) DIAMOND.AXIS/PLUCKER/SPECTRAL.01: the diamond axis geometry ---- *) Module[{R, Q, a, one, Cc, U, V, K, L, F, anc, plL, ram, x, y, dU, dV, bU, bV, sd, bsd, sq, ker}, R = {{1, 3, 0}, {1, 5, 2}, {2, 5, 3}}; Q = {{3, 1, 0}, {3, 2, 0}, {3, 2, 1}}; one = {1, 1, 1}; a = {1, 1, 2}; Cc = R + Q.DiagonalMatrix[{1, 0, 0}]; (* center C = M(1,0) (v95) *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1751","line_end":1779,"line_start":1751,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v218","v95"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v219 MCKAY.E8.01: 2I (order 120) irrep degrees {1,2,2,3,3,4,4,5,6} -- "],"checked_by_registry":false,"heading_as_written":"(* ==== v219-v230 round: icosahedral McKay, CM-norm duality, structural finds ==== *) Module[{labels, edges, A, Ni, Nw, RRm, QQm, Cc2, Mst, s, t, d, nvec, one, av, KKm, Lm}, (* v219 McKay: affine E8 marks = 2I irrep degrees, sums 30 and 120 *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1780","line_end":1792,"line_start":1780,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v219","v230"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v222 CMNORM.DUAL.01: N_Z[i](5+4i)=5^2+4^2=41=10 b1 (EM index), "],"checked_by_registry":false,"heading_as_written":"(* v222 CM-norm duality: 41 (square), 7 (hex), 13 (square) *) Ni[a_, b_] := a^2 + b^2; (* Gaussian Z[i] norm *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1793","line_end":1803,"line_start":1793,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v222"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v223 COX.CLOCK.01: (Z/30)^x = {1,7,11,13,17,19,23,29} = E8 exponents, ","v227 E8.CHAN.01: E8 exponents {1,7,11,13,17,19,23,29} sum 120=|R^+(E8)| "],"checked_by_registry":false,"heading_as_written":"(* v223 Coxeter totative clock: (Z/30)^x = E8 exponents, order-4 element 7 *) checkExact[\"v223 COX.CLOCK.01: (Z/30)^x = {1,7,11,13,17,19,23,29} = E8 exponents, \" <> \"phi(30)=8=rank E8, 30=2*3*5; mult-by-7 has order 4 (7^2=19, 7^4=1 mod 30): a \" <> \"mu4 clock <7>={1,7,13,19}; the conjugate pairs split into 4 invariant planes\", Select[Range[29], CoprimeQ[#, 30] &] == {1, 7, 11, 13, 17, 19, 23, 29} && EulerPhi[30] == 8 && PowerMod[7, 2, 30] == 19 && PowerMod[7, 4, 30] == 1 && Sort[Mod[7^Range[0, 3], 30]] == {1, 7, 13, 19} && Length[Union[Sort /@ ({#, 30 - #} & /@ {1, 7, 11, 13, 17, 19, 23, 29})]] == 4]; (* v227 degree/exponent channel split: 248 = 120 + 128 *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1804","line_end":1820,"line_start":1804,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v223","v227"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v228 QGEO.RR.01: deg D=4=|mu4| on P^1 => h0=deg+1=5=g_car, ","v229 LEP.FROB.01: (c_e,c_mu,c_tau)=(16/7,4/3,7/6), ring closure "],"checked_by_registry":false,"heading_as_written":"(* v228 Riemann-Roch index gate: degree-4 divisor on P^1 *) checkExact[\"v228 QGEO.RR.01: deg D=4=|mu4| on P^1 => h0=deg+1=5=g_car, \" <> \"rank H1(P^1 minus 4)=4-1=3=N_fam; h0+H1=8=rank E8, h0-H1=2=|Z2|; \" <> \"Lambda^even(C^5)=C(5,0)+C(5,2)+C(5,4)=16=dim S^+; controls deg 3->(4,2), deg 5->(6,4)\", (4 + 1) == 5 && (4 - 1) == 3 && (5 + 3) == 8 && (5 - 3) == 2 && (Binomial[5, 0] + Binomial[5, 2] + Binomial[5, 4]) == 16 && {3 + 1, 3 - 1} == {4, 2} && {5 + 1, 5 - 1} == {6, 4}]; (* v229 lepton etale Frobenius algebra *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1821","line_end":1837,"line_start":1821,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v228","v229"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v230 CENTER.NORM.01: C=R+Q diag(1,0,0) row sums (7,11,13) = ","v224 FTR.PATH.01: K=M(1,-1),C=M(1,0),F=M(1,1) on the sheet axis; "],"checked_by_registry":false,"heading_as_written":"(* v230 center budget (7,11,13) = three local norms *) RRm = {{1, 3, 0}, {1, 5, 2}, {2, 5, 3}}; QQm = {{3, 1, 0}, {3, 2, 0}, {3, 2, 1}}; Cc2 = RRm + QQm.DiagonalMatrix[{1, 0, 0}]; checkExact[\"v230 CENTER.NORM.01: C=R+Q diag(1,0,0) row sums (7,11,13) = \" <> \"(N_Z[omega](3+2w)=7 hex, C(4,0)+C(4,1)+C(4,2)=11 QBL Fock, N_Z[i](3+2i)=13 square) \" <> \"= (hex norm, boundary Fock count, square norm)\", Total /@ Cc2 == {7, 11, 13} && {Nw[3, 2], Binomial[4, 0] + Binomial[4, 1] + Binomial[4, 2], Ni[3, 2]} == {7, 11, 13}]; (* v224 diamond F_transfer path: sheet axis curved, winding axis flat, Plucker steps *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1838","line_end":1860,"line_start":1838,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v224","v230"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v225 DUAL.FRAME.01: d=a.R^{-1}=(-1/2,-1/2,1)=-1/2(1,1,-2) (Nariai normal; ","v231 CP.MU6.01: both CP phases are mu6 powers of the one hexagonal CM unit rho=e^{i pi/3} "],"checked_by_registry":false,"heading_as_written":"(* v225 dual normal frame (d,n) and oriented volume *) d = av.Inverse[RRm]; nvec = {5, -9, 6}; KKm = {{4, 2, 0}, {4, 3, 2}, {5, 3, 2}}; Lm = KKm + QQm; checkExact[\"v225 DUAL.FRAME.01: d=a.R^{-1}=(-1/2,-1/2,1)=-1/2(1,1,-2) (Nariai normal; \" <> \"d.1=0, d.a=1); n=(5,-9,6) with n.R=(det R,0,0)=(8,0,0), n.L=(det L,0,0)=(20,0,0); \" <> \"oriented volume det(1,d,n)=21=N_fam*scalaron=3*7\", d == {-1/2, -1/2, 1} && d == -1/2 {1, 1, -2} && d.one == 0 && d.av == 1 && nvec.RRm == {Det[RRm], 0, 0} == {8, 0, 0} && nvec.Lm == {Det[Lm], 0, 0} == {20, 0, 0} && Det[{{1, 1, 1}, d, nvec}] == 21 == 3*7]; ]; (* ==== v231: both CP phases are mu6 powers of one hexagonal unit, split by the sheet ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1861","line_end":1893,"line_start":1861,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v225","v231"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v232 TOPO.E8.01: the seam as the E8 Kleinian singularity (du Val side of McKay, v219). "],"checked_by_registry":false,"heading_as_written":"(* ==== v232: the seam as the E8 Kleinian singularity (du Val resolution + link) ==== *) Module[{labels, e8edges, A8, C8, degs}, labels = {1, 2, 3, 4, 5, 6, 4, 2, 3}; (* affine E8 Kac marks *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1894","line_end":1914,"line_start":1894,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v232"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v233 CP.TRIALITY.01: the CP phase is the universal family/triality phase, sheet-split. ","v234 GATE.HOLO.01: the structural residual is ONE condition (no nontrivial abelian sector) "],"checked_by_registry":false,"heading_as_written":"(* ==== v233: CP = the universal family/triality phase, sheet-split (mu6 = mu3 x mu2) ==== *) Module[{rho, omega}, rho = Exp[I Pi/3]; omega = Exp[2 I Pi/3]; checkExact[\"v233 CP.TRIALITY.01: the CP phase is the universal family/triality phase, sheet-split. \" <> \"mu6 = mu3(triality) x mu2(sheet): omega=e^{2pi i/3} the Z3 triality centre (2/3 cusp weight), \" <> \"rho = omega^2*(-1). Since rho^4 = rho^1*rho^3 with rho^3 in mu2, the quark (rho^1) and lepton \" <> \"(rho^4) CP phases share the SAME family class and differ only by the sheet: rho^1*(-1)=omega^2 \" <> \"(quark family part), rho^4=omega^2 (lepton). So CP = the universal triality phase + the sheet, \" <> \"not a free power choice; omega is the mu3 factor of the order-30 (2,3,5) monodromy (v232).\", Simplify[omega^3] == 1 && Simplify[rho^3 + 1] == 0 && Simplify[rho - omega^2 (-1)] == 0 && Simplify[rho^4 - rho^1 rho^3] == 0 && Simplify[rho^1 (-1) - omega^2] == 0 && Simplify[rho^4 - omega^2] == 0]; ]; (* ==== v234: Seam-Holomorphy selection -- one condition, three faces, E8 ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1915","line_end":1949,"line_start":1915,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v232","v233","v234"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v235 GATE.HOLO.02: the closing step in abelian Chern-Simons -- a free gapped bosonic 2+1d ","v236 TOPO.BRIESKORN.01: the (2,3,5) Brieskorn singularity x^2+y^3+z^5 (exponents = the atoms "],"checked_by_registry":false,"heading_as_written":"(* ==== v235: the closing step in abelian Chern-Simons -- holomorphic <=> det K = 1 ==== *) Module[{cartanA, cartanD, e8edges, A3, D5, D8, E8, carrier}, cartanA[n_] := SparseArray[{{i_, i_} -> 2, {i_, j_} /; Abs[i - j] == 1 -> -1}, {n, n}] // Normal; cartanD[n_] := Module[{K}, K = 2 IdentityMatrix[n]; Do[K[[i, i + 1]] = K[[i + 1, i]] = -1, {i, n - 2}]; K[[n - 2, n]] = K[[n, n - 2]] = -1; K]; e8edges = {{1, 2}, {2, 3}, {3, 4}, {4, 5}, {5, 6}, {6, 7}, {5, 8}}; E8 = 2 IdentityMatrix[8] - Table[If[i != j && MemberQ[e8edges, Sort[{i, j}]], 1, 0], {i, 8}, {j, 8}]; A3 = cartanA[3]; D5 = cartanD[5]; D8 = cartanD[8]; carrier = ArrayFlatten[{{D5, 0}, {0, A3}}]; checkExact[\"v235 GATE.HOLO.02: the closing step in abelian Chern-Simons -- a free gapped bosonic 2+1d \" <> \"bulk = an even integer K-matrix with #anyons=|det K|, edge c=signature(K), holomorphic <=> det=1. \" <> \"The TFPT tower (v92) read by det: carrier D5(+)A3 (even, det 16, 16 anyons) -> SO(16)_1=D8 (det 4) \" <> \"-> (E8)_1 (det 1, holomorphic), all rank 8, c=signature=8=g_car+N_fam. Holomorphic <=> det 1 <=> E8 \" <> \"= the Kitaev E8 quantum-Hall state. Condensation: a Lagrangian glue of order sqrt(16)=|mu4|=4 takes \" <> \"det 16->1; an order-2 isotropic only ->4=D8. NEG: D8 free+bosonic but 4 anyons (not holomorphic). \" <> \"Residual: condense the |mu4| Lagrangian glue = the sheet/QGEO selection.\", Det[E8] == 1 && Det[D8] == 4 && Det[carrier] == 16 && Det[A3] == 4 && Det[D5] == 4 && And @@ (EvenQ[#] & /@ Join[Diagonal[E8], Diagonal[D8], Diagonal[carrier]]) && Min[Eigenvalues[N[E8]]] > 0 && Min[Eigenvalues[N[D8]]] > 0 && Min[Eigenvalues[N[carrier]]] > 0 && Length[E8] == Length[D8] == Length[carrier] == 8 && 16/4^2 == 1 && 16/2^2 == 4 && (5 + 3 == 8)]; ]; (* ==== v236: the (2,3,5) Brieskorn singularity generates the skeleton ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1950","line_end":1990,"line_start":1950,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v235","v236","v92"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v237 GATE.HOLO.03: the closing step as a physical condition -- the abelian K-matrix ","v259 PS.SPECACT.02: the seam KMS cutoff f(u)=e^{-u} (beta=1 by Tomita-Takesaki/BW + the seam "],"checked_by_registry":false,"heading_as_written":"(* ==== v237: closing step as physics -- no topological degeneracy <=> det K=1 <=> SRE ==== *) Module[{cartanA, cartanD, e8edges, E8, D8, A3, D5, carrier, gsd}, cartanA[n_] := SparseArray[{{i_, i_} -> 2, {i_, j_} /; Abs[i - j] == 1 -> -1}, {n, n}] // Normal; cartanD[n_] := Module[{K}, K = 2 IdentityMatrix[n]; Do[K[[i, i + 1]] = K[[i + 1, i]] = -1, {i, n - 2}]; K[[n - 2, n]] = K[[n, n - 2]] = -1; K]; e8edges = {{1, 2}, {2, 3}, {3, 4}, {4, 5}, {5, 6}, {6, 7}, {5, 8}}; E8 = 2 IdentityMatrix[8] - Table[If[i != j && MemberQ[e8edges, Sort[{i, j}]], 1, 0], {i, 8}, {j, 8}]; A3 = cartanA[3]; D5 = cartanD[5]; D8 = cartanD[8]; carrier = ArrayFlatten[{{D5, 0}, {0, A3}}]; gsd[K_, g_] := Abs[Det[K]]^g; checkExact[\"v237 GATE.HOLO.03: the closing step as a physical condition -- the abelian K-matrix \" <> \"ground-state degeneracy on a genus-g surface is |det K|^g (torus: carrier D5(+)A3 -> 16, D8 -> 4, \" <> \"E8 -> 1), so 'no topological ground-state degeneracy on any closed surface' <=> det K = 1 <=> the \" <> \"seam bulk is short-range-entangled (the unique bosonic SRE c=8 phase = the Kitaev E8 state, edge \" <> \"holomorphic). A unique vacuum on the plane (genus 0, always 1) is necessary but not sufficient; the \" <> \"torus sees |det K|. NEG: an LRE bulk (D8, det 4) has 4-fold torus degeneracy + non-holomorphic edge.\", gsd[carrier, 1] == 16 && gsd[D8, 1] == 4 && gsd[E8, 1] == 1 && gsd[carrier, 2] == 256 && gsd[E8, 2] == 1 && gsd[carrier, 0] == 1 && gsd[E8, 0] == 1 && Det[E8] == 1 && (5 + 3 == 8)]; ]; (* ==== v259: the modular/KMS spectral-action cutoff fixes f_2/f_0 = 1 (PS.SPECACT.02) ==== v258 (Dirac as covariance induction) is numerical matrix-log linear algebra -> Python-only. *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:1991","line_end":2031,"line_start":1991,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v237","v258","v259"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v260 ARCH.K3.01: one Kummer/K3 surface carries seam + carrier-16 + E8. E8 Cartan even, det 1, ","v267 QGEO.SYM.02: the rigidity / minimal-axiom form of QGEO.SYM.01 -- an order-4 Moebius "],"checked_by_registry":false,"heading_as_written":"(* ==== v260: one Kummer/K3 carries seam + carrier-16 + E8 (ARCH.K3.01) ==== *) Module[{e8edges, E8, U, L, sig, nodes, marks}, e8edges = {{1, 2}, {2, 3}, {3, 4}, {4, 5}, {5, 6}, {6, 7}, {5, 8}}; E8 = 2 IdentityMatrix[8] - Table[If[i != j && MemberQ[e8edges, Sort[{i, j}]], 1, 0], {i, 8}, {j, 8}]; U = {{0, 1}, {1, 0}}; L = ArrayFlatten[{{U, 0, 0, 0, 0}, {0, U, 0, 0, 0}, {0, 0, U, 0, 0}, {0, 0, 0, -E8, 0}, {0, 0, 0, 0, -E8}}]; sig = {Count[Eigenvalues[N[L]], x_ /; x > 0], Count[Eigenvalues[N[L]], x_ /; x < 0]}; nodes = 2^4; marks = 2^2; checkExact[\"v260 ARCH.K3.01: one Kummer/K3 surface carries seam + carrier-16 + E8. E8 Cartan even, det 1, \" <> \"positive-definite (the unique even unimodular pos-def rank-8 lattice); the K3 lattice U^3(+)E8(-1)^2 \" <> \"has rank 22=b_2, det -1 (unimodular), even, signature (3,19) with E8(-1)^2 an orthogonal summand; the \" <> \"seam T^2/(z->-z) has 4=|(Z/2)^2| marks (pillowcase); the carrier-16 = Kummer nodes |A[2]|=2^4=16 = \" <> \"dim S+ = 4x4 = (seam marks)^2. So the v1 glue D5(+)A3+mu4=>E8 is the lattice shadow of one object.\", Det[E8] == 1 && AllTrue[Diagonal[E8], EvenQ] && PositiveDefiniteMatrixQ[E8] && Length[L] == 22 && Det[L] == -1 && AllTrue[Diagonal[L], EvenQ] && sig == {3, 19} && nodes == 16 && marks == 4 && nodes == marks^2]; ]; (* ==== v267: QGEO rigidity / minimal-axiom form of QGEO.SYM.01 (QGEO.SYM.02) ==== v262 (alpha_s RG), v263 (seesaw numpy), v264 (DtN FFT), v265 (RG+text guard), v266 (proton RG) are numerical -> Python-only; v267's exact cross-ratio/j core is mirrored here (the DtN/FFT part of v267 stays Python-only). *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2032","line_end":2068,"line_start":2032,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v1","v260","v262","v263","v264","v265","v266","v267"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v268 FLAV.TH13.01: the theta_13 exponent is the carrier hypercharge trace -- ","v271 QFT4D.SPERT.02: a concrete Epstein-Glaser one-loop quartic renormalization -- "],"checked_by_registry":false,"heading_as_written":"(* ==== v268: reactor-angle exponent = carrier hypercharge trace (FLAV.TH13.01) ==== *) Module[{Yvec, trY2, roots}, roots = Sort[Y /. Solve[6 Y^2 - Y - 1 == 0, Y]]; Yvec = {-1/3, -1/3, -1/3, 1/2, 1/2}; trY2 = Total[Yvec^2]; checkExact[\"v268 FLAV.TH13.01: the theta_13 exponent is the carrier hypercharge trace -- \" <> \"tr_E Y^2 = 3(1/3)^2 + 2(1/2)^2 = 5/6 over the 5-slot carrier hypercharge \" <> \"Y=diag(-1/3,-1/3,-1/3,1/2,1/2) (the anomaly-free roots {-1/3,1/2} of 6Y^2-Y-1=0), so \" <> \"sin^2 theta_13 = phi0 e^{-5/6} = phi0 e^{-tr_E Y^2}; complement 1 - 5/6 = 1/6 = the neutrino ratio. \" <> \"theta_13 is its own carrier-trace channel (the mu-tau breaking gives only ~1e-3, not 0.023).\", roots === Sort[{-1/3, 1/2}] && trY2 === 5/6 && (1 - trY2) === 1/6]; ]; (* ==== v271: concrete Epstein-Glaser one-loop quartic renormalization (QFT4D.SPERT.02) ==== v269 (S_pert skeleton) + v270 (PMNS Jarlskog, numerical) are Python-only; v271's exact EG core (scaling degree, counterterm count, loop factor) is mirrored here. *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2069","line_end":2101,"line_start":2069,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v268","v269","v270","v271"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v273 QFT4D.SPERT.03: the EG one-loop gauge self-energy gives the SM beta coefficients "],"checked_by_registry":false,"heading_as_written":"(* ==== v273: EG one-loop gauge self-energy -> (b1,b2,b3) (QFT4D.SPERT.03) ==== v272 (nu-scale, numerical) + v274 (over-determination, numerical) + v275 (QG roadmap) are Python-only; v273's exact one-loop beta coefficients from the content are mirrored. *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2102","line_end":2118,"line_start":2102,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v272","v273","v274","v275"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v277 QGAMB.TIERB.01: the seam-Calderon -> (E8)_1 matching certificate -- the discriminator is "],"checked_by_registry":false,"heading_as_written":"(* ==== v277: seam-Calderon -> (E8)_1 matching certificate (QGAMB.TIERB.01) ==== v276 (flat-pillowcase commutator, numerical) is Python-only; v277's exact lattice discriminator (det E8 vs det D8) + the (E8)_1 character 248 are mirrored. *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2119","line_end":2140,"line_start":2119,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v276","v277"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v278 QFT4D.SPERT.04: the one-loop optical theorem -- the s-channel bubble discontinuity "],"checked_by_registry":false,"heading_as_written":"(* ==== v278: S_pert -> S_phys LSZ bridge, one-loop optical theorem (QFT4D.SPERT.04) ==== *) Module[{xs, measureSq, phaseSq}, xs = x /. Solve[s x (1 - x) == m^2, x]; (* x_+ , x_- *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2141","line_end":2152,"line_start":2141,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v278"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v281 QGAMB.MODULAR.01: #anyons = |det Gram| -- E8->1 (holomorphic), D8=SO(16)->4, "],"checked_by_registry":false,"heading_as_written":"(* ==== v281: anyon-condensation tower + Gauss-Milgram (QGAMB.MODULAR.01) ==== *) Module[{cE8, cD8, cD5, cA3, dE8, dD8, dcar, gm}, cE8 = {{2,-1,0,0,0,0,0,0},{-1,2,-1,0,0,0,0,0},{0,-1,2,-1,0,0,0,0},{0,0,-1,2,-1,0,0,0}, {0,0,0,-1,2,-1,0,-1},{0,0,0,0,-1,2,-1,0},{0,0,0,0,0,-1,2,0},{0,0,0,0,-1,0,0,2}}; cD8 = {{2,-1,0,0,0,0,0,0},{-1,2,-1,0,0,0,0,0},{0,-1,2,-1,0,0,0,0},{0,0,-1,2,-1,0,0,0}, {0,0,0,-1,2,-1,0,0},{0,0,0,0,-1,2,-1,-1},{0,0,0,0,0,-1,2,0},{0,0,0,0,0,-1,0,2}}; cD5 = {{2,-1,0,0,0},{-1,2,-1,0,0},{0,-1,2,-1,-1},{0,0,-1,2,0},{0,0,-1,0,2}}; cA3 = {{2,-1,0},{-1,2,-1},{0,-1,2}}; dE8 = Det[cE8]; dD8 = Det[cD8]; dcar = Det[cD5] Det[cA3]; gm = Sum[Exp[2 Pi I h], {h, {0, 1/2, 1, 1}}]; (* D8 anyons 1,v,s,c *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2153","line_end":2169,"line_start":2153,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v281"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v282 QGAMB.UNIFY.01: tau=i is the order-4 CM point (cross-ratio 2 => j=1728), and the "],"checked_by_registry":false,"heading_as_written":"(* ==== v282: E8-at-tau=i unification, chi_E8(i)=12 (QGAMB.UNIFY.01) ==== *) Module[{jf, jorder4, chiI}, jf[x_] := 256 (x^2 - x + 1)^3/(x^2 (x - 1)^2); jorder4 = jf[2]; (* cross-ratio 2 => j = 1728 = the tau=i CM point *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2170","line_end":2181,"line_start":2170,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v282"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v313 GOLD.ATOMS.01: affine-E8 charpoly = x(x^2-4)(x^2-1)(x^2-x-1)(x^2+x-1) -- the golden minimal polynomial x^2-x-1 divides it (phi=2cos(pi/5) an exact eigenvalue); the leading sign tracks Mathematica's Det[A-xI] convention for odd n","v313 the (2,3,5) atoms ARE the spectral angles 2cos(pi/k): 2cos(pi/2)=0=|Z2|, 2cos(pi/3)=1=Nfam, 2cos(pi/5)=golden phi=gcar","v313 icosahedral selection 1/|Z2|+1/Nfam+1/gcar = 31/30; 31 = 2^gcar-1 = 248/8 = 1+h(E8); 30 = h(E8) = |Z2| Nfam gcar"],"checked_by_registry":false,"heading_as_written":"(* ==== v313-v320: the cyclotomic / Galois arithmetic arc (exact) ==== *) Module[{edges, cAff, x, units, maxord, z6, z30, gauss}, (* v313 GOLD.ATOMS.01 -- the golden ratio is the g_car=5 spectral signature *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2182","line_end":2194,"line_start":2182,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v313","v320"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v314 RATE.TRANSLATE.01: the discrete kernel rates {1/2,1/3,2/3,(2/3)^6} are rational (Q); the dynamic golden rate uses phi=2cos(pi/5), MinimalPolynomial x^2-x-1, living in Q(sqrt5) = the real subfield of Q(zeta5) ([Q(zeta5):Q]=4); since Q(sqrt5) cap Q = Q, exact translation acts only on the rational (2,3)-fold sector","v315 COX.COUPLE.01: 30 = gcar(2 Nfam) = 5*6, gcd(5,6)=1; [Q(zeta30):Q]=EulerPhi[30]=8=rank E8; |(Z/30)^x|=8 with max element order 4 (NOT cyclic Z/8) => Galois = mu4 x Z2, (Z/5)^x=mu4 (ord 4), (Z/3)^x=Z2 (ord 2)","v315 carrier generator sqrt5 = phi + 1/phi = the quadratic Gauss sum (zeta5 - zeta5^2 - zeta5^3 + zeta5^4) in Q(zeta5), g^2 = 5"],"checked_by_registry":false,"heading_as_written":"(* v314 RATE.TRANSLATE.01 -- the number-field split between discrete kernel and dynamic rates *) checkExact[\"v314 RATE.TRANSLATE.01: the discrete kernel rates {1/2,1/3,2/3,(2/3)^6} are rational (Q); the dynamic golden rate uses phi=2cos(pi/5), MinimalPolynomial x^2-x-1, living in Q(sqrt5) = the real subfield of Q(zeta5) ([Q(zeta5):Q]=4); since Q(sqrt5) cap Q = Q, exact translation acts only on the rational (2,3)-fold sector\", Element[1/2, Rationals] && Element[(2/3)^6, Rationals] && MinimalPolynomial[2 Cos[Pi/5], x] == x^2 - x - 1 && EulerPhi[5] == 4 && Simplify[2 Cos[2 Pi/5] - (Sqrt[5] - 1)/2] == 0]; (* v315 COX.COUPLE.01 -- the order-30 Coxeter sectors couple as a cyclotomic field *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2195","line_end":2205,"line_start":2195,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v314","v315"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v316 GALOIS.READOUT.01: the CP unit rho=zeta6=zeta30^5 (the order-6 family factor c^5); rho^4=-rho (sheet flip); Gal(Q(zeta6)/Q)=Z2 with zeta6->zeta6^5=conj(zeta6) = CP conjugation","v317 GALOIS.FAMILY.01: Nfam=3 = the mu3 orbit {1,zeta3,zeta3^2} (cube roots of unity), 1+zeta3+zeta3^2=0 (democratic); Gal(Q(zeta3)/Q)=Z2 fixes 1 (the attractor generation) and swaps the conjugate pair {zeta3,zeta3^2} = the Galois-refined 1+2 hierarchy split"],"checked_by_registry":false,"heading_as_written":"(* v316 GALOIS.READOUT.01 -- CP phases are the family-factor cyclotomic data *) z6 = Exp[I Pi/3]; z30 = Exp[2 Pi I/30]; checkExact[\"v316 GALOIS.READOUT.01: the CP unit rho=zeta6=zeta30^5 (the order-6 family factor c^5); rho^4=-rho (sheet flip); Gal(Q(zeta6)/Q)=Z2 with zeta6->zeta6^5=conj(zeta6) = CP conjugation\", Simplify[z6 - z30^5] == 0 && Simplify[z6^4 + z6] == 0 && Simplify[Conjugate[z6] - z6^5] == 0]; (* v317 GALOIS.FAMILY.01 -- the three generations are the mu3 orbit, Galois-refined 1+2 *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2206","line_end":2212,"line_start":2206,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v316","v317"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v318 ARITH.CAPSTONE.01: phi0 = (|mu4|/Nfam) c3 + Omega_adm c3^4 = (4/3)c3 + 48 c3^4 = 1/(6 Pi) + 3/(256 Pi^4) (a pure function of Pi => 0 dimensionless free parameters)","v320 GALOIS.CP.PREDICT.01: delta_PMNS = arg(rho^4) = 4Pi/3 = delta_CKM,lead (=arg(rho)=Pi/3) + Pi = 240 deg -- the Galois CP lock (rho^4=-rho)"],"checked_by_registry":false,"heading_as_written":"(* v318 ARITH.CAPSTONE.01 -- the magnitude seed reduces to a pure pi-function *) checkExact[\"v318 ARITH.CAPSTONE.01: phi0 = (|mu4|/Nfam) c3 + Omega_adm c3^4 = (4/3)c3 + 48 c3^4 = 1/(6 Pi) + 3/(256 Pi^4) (a pure function of Pi => 0 dimensionless free parameters)\", Simplify[(4/3) c3 + 48 c3^4 - (1/(6 Pi) + 3/(256 Pi^4))] == 0 && Simplify[(4/3) c3 + 48 c3^4 - phi0] == 0]; (* v320 GALOIS.CP.PREDICT.01 -- the falsifiable CP lock *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2213","line_end":2219,"line_start":2213,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v318","v320"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v325 QGEO.KEYSTONE.01: the four order-2 cone points give the Euclidean orbifold S^2(2,2,2,2) (the pillowcase), chi_orb = 2 - 4(1-1/2) = 0 => flat, uniformised at tau=i (the keystone hypothesis; marks=4, j=1728, det Cartan E8=1 already mirrored via v216/v214/v277)"],"checked_by_registry":false,"heading_as_written":"(* ==== v325/v327: the keystone pillowcase orbifold + the cusp-weight rewrite (exact) ==== *) Module[{chiOrb, M, evs, edges, cAff, x, p23}, (* v325 QGEO.KEYSTONE.01: the flat pillowcase orbifold S^2(2,2,2,2) has chi_orb = 0 *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2220","line_end":2226,"line_start":2220,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v325","v327"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v327 HYP.REWRITE.01: the minimal 3-channel/1-absorbing rewrite M has spectrum {0,2/3,1}; the recovery survival 2/3 = (Nfam-1)/Nfam = |Z2|/Nfam emerges from the rule arity, and over the order-6 = 2 Nfam hand (2/3)^(2 Nfam) = 64/729 = the recovery gap","v327 NON-GRAPH-SPECTRAL (proof): 2/3 is NOT a root of the affine-E8 charpoly -- p(2/3) != 0 -- so the recovery rate cannot be an adjacency eigenvalue (the v312 negative, now a proof)"],"checked_by_registry":false,"heading_as_written":"(* v327 HYP.REWRITE.01: the minimal 3-channel/1-absorbing rewrite M has spectrum {0,2/3,1} *) M = {{1, 0, 0}, {0, 1/3, 1/3}, {0, 1/3, 1/3}}; evs = Sort[Eigenvalues[M]]; checkExact[\"v327 HYP.REWRITE.01: the minimal 3-channel/1-absorbing rewrite M has spectrum {0,2/3,1}; the recovery survival 2/3 = (Nfam-1)/Nfam = |Z2|/Nfam emerges from the rule arity, and over the order-6 = 2 Nfam hand (2/3)^(2 Nfam) = 64/729 = the recovery gap\", evs == {0, 2/3, 1} && 2/3 == (Nfam - 1)/Nfam && (2/3)^(2 Nfam) == 64/729]; (* v327 NON-GRAPH-SPECTRAL: 2/3 is NOT a root of the affine-E8 charpoly (sharpens v312) *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2227","line_end":2239,"line_start":2227,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v312","v327"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v337 DECOUPLING.THEOREM.01: the ambient back-reaction scale 2*dim(E8)*c3^2 = 2*248/(8pi)^2 = 496/(64 pi^2) = 31/(4 pi^2) exactly; the decoupling margin Delta - 31/(4pi^2) = 6 log(3/2) - 31/(4pi^2) > 0 (the gapped admissible spectrum {1,(2/3)^6,(1/3)^6} has finite susceptibility chi=1/(1-(2/3)^6)=729/665), so every readout is independent of the un-built ambient measure"],"checked_by_registry":false,"heading_as_written":"(* ==== v337 DECOUPLING.THEOREM.01: the ambient back-reaction scale identity ==== *) Module[{ambient}, (* the largest ambient back-reaction scale 2*dim(E8)*c3^2 = 31/(4 pi^2) exactly (c3=1/(8pi)) *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2240","line_end":2247,"line_start":2240,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v337"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v341 ALPHA.QUILLEN.01: phi_base = 1/(6pi) = (4/3) c3 so c3/phi_base = 3/4 = q(A3), the exponent -5/4 = -q(D5), and q(D5)+q(A3) = 5/4+3/4 = 2 = E8 root norm; the anomaly counterterm coefficient (4/5)M = 8 b1 = 8*(41/10) = (rank E8) b1 (the EM Ward, v48) -- so the F_U(1) determinant-line form has only index/heat-kernel/discriminant atoms, no free knob"],"checked_by_registry":false,"heading_as_written":"(* ==== v341 ALPHA.QUILLEN.01: the seam-form discriminant identities ==== *) Module[{c3v, phib}, c3v = 1/(8 Pi); phib = 1/(6 Pi); (* phi_base = (4/3) c3 carries q(A3): c3/phi_base = 3/4; with -5/4 = -q(D5) the F_U(1) seam response carries BOTH glue forms, q(D5)+q(A3)=2 = E8 root norm; counterterm coefficient (4/5)M = 8 b1 = 8*(41/10) with b1 the U(1)_Y one-loop beta (rank E8 = 8) *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2248","line_end":2258,"line_start":2248,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v341"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v342 EM.WARD.02: c3 = 1/(|Z2| oint_{S^2} K) = 1/(2*4pi) = 1/(8pi) (boundary Gauss-Bonnet, chi=2); the Gilkey a4 gauge-curvature coeff is 30 Omega^2/360 = 1/12 (=> an alpha^2 term in log det Delta_U(1), the Calderon -2 c3^3 a^2); the c3-ladder {0,3,6} is arithmetic step 3; 2 c3^3 = 1/(256 pi^3) carries pi^3 (THREE boundary insertions, not a single bulk a4); 8 b1 = (4/5)*41 = (rank E8)(41/10) -- the term STRUCTURE is heat-kernel-forced (the exact value [C], the cubic alpha^3 [O])"],"checked_by_registry":false,"heading_as_written":"(* ==== v342 EM.WARD.02: the heat-kernel origin of the F_U(1) terms ==== *) Module[{c3v, ointK, c3gb, gilkey, q2}, c3v = 1/(8 Pi); (* c3 = boundary Gauss-Bonnet coefficient: oint_{S^2} K = 2 pi chi = 4 pi (chi=2), c3 = 1/(|Z2| oint K) *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2259","line_end":2270,"line_start":2259,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v342"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v344 SEAM.DETK.01: the ADE |det Cartan| = |H_1(link)| = #(1-dim irreps) sequence -- A2=3 (=n+1), A3=4, D4=4, D5=4, E8=1; ONLY E8 -> 1 (the binary icosahedral 2I is the unique perfect ADE group, H_1=0), so det K=1 (holomorphy) <=> homology-sphere link <=> E8. The one open keystone bit, six equivalent faces (v232/v235/v219/v281/v282)"],"checked_by_registry":false,"heading_as_written":"(* ==== v344 SEAM.DETK.01: the ADE |det Cartan| = |H_1(link)| sequence, only E8 -> 1 ==== *) Module[{cartanA, cartanD, E8, detADE}, cartanA[n_] := SparseArray[{{i_, i_} -> 2, {i_, j_} /; Abs[i - j] == 1 -> -1}, {n, n}]; cartanD[n_] := Module[{M = Normal[cartanA[n]]}, M[[n, n - 1]] = M[[n - 1, n]] = 0; M[[n, n - 2]] = M[[n - 2, n]] = -1; M]; E8 = {{2,-1,0,0,0,0,0,0},{-1,2,-1,0,0,0,0,0},{0,-1,2,-1,0,0,0,0},{0,0,-1,2,-1,0,0,0}, {0,0,0,-1,2,-1,0,-1},{0,0,0,0,-1,2,-1,0},{0,0,0,0,0,-1,2,0},{0,0,0,0,-1,0,0,2}}; (* |det Cartan| = |H_1(link)| = #(1-dim irreps): A_n->n+1, D_n->4, E6->3, E7->2, E8->1; only E8 -> 1 *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2271","line_end":2283,"line_start":2271,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v344"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v345 SEAM.DETK.02: the plumbing link H_1 = coker(Cartan) via Smith normal form -- |coker(E8)| = 1 (Smith normal form = identity => the E8-graph plumbing boundary is an INTEGRAL HOMOLOGY SPHERE, the genus-1 meaning of det E8=1), while |coker(D5)| = 4 (Z/4, not a homology sphere); only E8 among ADE gives a homology-sphere link, and with pi_1 = 2I=SL(2,5) perfect it is THE Poincare sphere (det K=1). Executes the combinatorial core of route R3 (v344); the geometric realisation bridge stays SEAM.EQUIV.01"],"checked_by_registry":false,"heading_as_written":"(* ==== v345 SEAM.DETK.02: the plumbing-link H_1 = coker(Cartan) via Smith normal form ==== *) Module[{cartanD, E8, sfE8, sfD5, cokerE8, cokerD5}, cartanD[n_] := Module[{M = Normal[SparseArray[{{i_, i_} -> 2, {i_, j_} /; Abs[i - j] == 1 -> -1}, {n, n}]]}, M[[n, n - 1]] = M[[n - 1, n]] = 0; M[[n, n - 2]] = M[[n - 2, n]] = -1; M]; E8 = {{2,-1,0,0,0,0,0,0},{-1,2,-1,0,0,0,0,0},{0,-1,2,-1,0,0,0,0},{0,0,-1,2,-1,0,0,0}, {0,0,0,-1,2,-1,0,-1},{0,0,0,0,-1,2,-1,0},{0,0,0,0,0,-1,2,0},{0,0,0,0,-1,0,0,2}}; (* coker = product of invariant factors > 1 = |H_1(plumbing link)|; E8 -> 1 (homology sphere), D5 -> 4 *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2284","line_end":2296,"line_start":2284,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v345"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v347 SEAM.EQUIV.CLOSURE.01: the open arrow L2 must bridge the seam pillowcase base S^2(2,2,2,2) -- chi_orb = 2-4(1-1/2) = 0 (EUCLIDEAN/flat) -- to the 2I/E8 Seifert base S^2(2,3,5) -- chi_orb = 2-(1/2+2/3+4/5) = 1/30 (SPHERICAL); two different geometric types, the precise locus of why L2 needs the carrier (2,3,5) input. Closure modes: A construct (analytic wall) / B rigidity (only theorem-route) / C axiom P3 / D empirical -- no free theorem"],"checked_by_registry":false,"heading_as_written":"(* ==== v347 SEAM.EQUIV.CLOSURE.01: the flat seam base vs the spherical icosahedral base ==== *) Module[{chiSeam, chi2I}, (* seam pillowcase S^2(2,2,2,2): chi_orb = 0 (Euclidean/flat); 2I Seifert base S^2(2,3,5): chi_orb = 1/30 (spherical) *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2297","line_end":2305,"line_start":2297,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v347"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v348 SEAM.EQUIV.RIGID.01 (Route B): the crystallographic restriction allows only rotation orders {1,2,3,4,6} (the 5-fold is NON-crystallographic), so mu4 (order 4, crystallographic) needs the golden ratio phi = 2 cos(pi/5) to extend to the icosahedral 2I (5-fold, non-crystallographic, the quasicrystal); and E8 = the ring of icosians (Conway-Sloane, rank 8) makes 2I->E8 a lattice identity. So the whole keystone reduces to ONE question: does the raw seam carry phi? (rigidity closes the rest); NOT closed"],"checked_by_registry":false,"heading_as_written":"(* ==== v348 SEAM.EQUIV.RIGID.01: phi bridges crystallographic mu4 to non-crystallographic 2I ==== *) Module[{cryst, phi}, cryst = {1, 2, 3, 4, 6}; (* crystallographic restriction: lattice-compatible rotation orders *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2306","line_end":2313,"line_start":2306,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v348"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v349 SEAM.EQUIV.GOLDEN.01: the RAW carrier is NOT golden -- D5 (h=8) gives 2cos(2pi/8)=sqrt2 and A3 (h=4) gives 2cos(2pi/4)=0, neither in Q(sqrt5); the golden ratio 2cos(pi/5) needs a 5-fold rotation (5|h), which holds ONLY on the output/icosahedral side {5(SU5),10(H3),30(E8)}. So phi is the icosahedral INPUT, not a hidden feature of the raw seam; the keystone L2 reduces to 'is g_car=5 a pentagon (5-fold) or a count (rank D5)?' -- NOT closed"],"checked_by_registry":false,"heading_as_written":"(* ==== v349 SEAM.EQUIV.GOLDEN.01: the raw carrier is NOT golden (D5 h=8 -> sqrt2); 5|h only on the output side ==== *) Module[{eigD5, eigA3, goldenHs}, (* Coxeter eigenvalue 2cos(2pi/h): D5 (h=8) -> sqrt2, A3 (h=4) -> 0; golden needs 5|h *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2314","line_end":2322,"line_start":2314,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v349"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v350 SEAM.EQUIV.BOOTSTRAP.01 (correcting v349): g_car=5 is NOT the D5 rank but the BOOTSTRAP fixed point -- the largest prime of h(E8)=30, and FactorInteger[30]={2,3,5} ARE the icosahedral axes (the atoms |Z2|,N_fam,g_car). The golden ratio is EMERGENT from the mu4-glue: D5(h=8) and A3(h=4) are non-golden, but D5(+)A3 -> E8 (v154) gives h=30 (golden, 5|30). So the inputs are over-determined fixed points (not free axioms) and the golden is intrinsic to the fixed point; the residual is the physical continuum realisation, not the golden ratio"],"checked_by_registry":false,"heading_as_written":"(* ==== v350 SEAM.EQUIV.BOOTSTRAP.01: g_car=5 IS the icosahedral 5 of h(E8)=30 (the v349 correction) ==== *) Module[{primes30, maxPrime, piecesGolden, glueGolden}, primes30 = Sort[FactorInteger[30][[All, 1]]]; (* {2,3,5} = the icosahedral axes *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2323","line_end":2333,"line_start":2323,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v349","v350"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v351 SEAM.EQUIV.CONTINUUM.02: the c=8 which-net ambiguity (E8 det 1 vs SO(16)=D8 det 4) is RESOLVED by the seam's ORDER-4 mu4 clock -- index-4 extension of D5(+)A3 = E8 (full mu4 condensation 16->4->1), index-2 = SO(16) (partial Z2 16->4); the order (4 not 2) selects E8. The bootstrap agrees: h(E8)=30 max prime 5=g_car, h(D8)=14 max prime 7, so SO(16) fails the Coxeter-match. The residual of SEAM.EQUIV.01 is then PURELY the chiral-edge existence, not which-net","v352 TFPT.IRREDUCIBLE.01: BOTH axioms are bootstrap-forced fixed points -- the 8 in c3=1/(8pi) is over-determined (rank E8 = h(D5)=2*5-2 = phi(30) = 8) and g_car=5 = max prime of h(E8)=30 (Coxeter-match), with c=g_car+N_fam=8 forcing the unique even-unimodular rank-8 E8 hull; so the ONLY irreducibles are the FRAMEWORK (discrete RP boundary + finite carrier) and the transcendental pi -- 'the inputs are not free axioms' confirmed"],"checked_by_registry":false,"heading_as_written":"(* ==== v351 SEAM.EQUIV.CONTINUUM.02: the order-4 clock + Coxeter-match pin E8 over SO(16) ==== *) Module[{cE8, cD8}, cE8 = {{2,-1,0,0,0,0,0,0},{-1,2,-1,0,0,0,0,0},{0,-1,2,-1,0,0,0,0},{0,0,-1,2,-1,0,0,0}, {0,0,0,-1,2,-1,0,-1},{0,0,0,0,-1,2,-1,0},{0,0,0,0,0,-1,2,0},{0,0,0,0,-1,0,0,2}}; cD8 = {{2,-1,0,0,0,0,0,0},{-1,2,-1,0,0,0,0,0},{0,-1,2,-1,0,0,0,0},{0,0,-1,2,-1,0,0,0}, {0,0,0,-1,2,-1,0,0},{0,0,0,0,-1,2,-1,-1},{0,0,0,0,0,-1,2,0},{0,0,0,0,0,-1,0,2}}; checkExact[\"v351 SEAM.EQUIV.CONTINUUM.02: the c=8 which-net ambiguity (E8 det 1 vs SO(16)=D8 det 4) is RESOLVED by the seam's ORDER-4 mu4 clock -- index-4 extension of D5(+)A3 = E8 (full mu4 condensation 16->4->1), index-2 = SO(16) (partial Z2 16->4); the order (4 not 2) selects E8. The bootstrap agrees: h(E8)=30 max prime 5=g_car, h(D8)=14 max prime 7, so SO(16) fails the Coxeter-match. The residual of SEAM.EQUIV.01 is then PURELY the chiral-edge existence, not which-net\", Det[cE8] == 1 && Det[cD8] == 4 && Max[FactorInteger[30][[All,1]]] == 5 && Max[FactorInteger[14][[All,1]]] == 7]; ]; (* ==== v352 TFPT.IRREDUCIBLE.01: both axioms bootstrap-forced; irreducibles = framework + pi ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2334","line_end":2351,"line_start":2334,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v351","v352"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v354 E8.REVERSE.AUDIT.01: the reverse numerology audit -- E8's 8 Casimir degrees {2,8,12,14,18,20,24,30} (=exponents+1); exactly THREE feed a physical readout (2 metric, 8 rank->c3, 30 Coxeter->g_car) and FIVE are UNMAPPED {12,14,18,20,24}, the hull overhead. A small fixed invariant set generates all readouts (economy, not promiscuity = anti-numerology); the golden ratio 2cos(pi/5) is in the unmapped structure (the 5-fold of h=30=2*3*5), so it cannot be numerology"],"checked_by_registry":false,"heading_as_written":"(* ==== v354 E8.REVERSE.AUDIT.01: 3 of 8 E8 Casimir degrees are load-bearing, 5 unmapped ==== *) Module[{exps, degs, mapped, unmapped}, exps = {1, 7, 11, 13, 17, 19, 23, 29}; (* E8 exponents *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2352","line_end":2361,"line_start":2352,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v354"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v355 E8.UNMAPPED.BANDWIDTH.01: disciplined bandwidth search -- the unmapped region's genuine structure is COLLECTIVE and forced: sum(degrees)=128=dim S^+ (the spinor half of 248=120+128; theorem sum=#pos roots+rank=120+8), sum(exponents)=120=#pos roots, product(degrees)=|W(E8)|=696729600, exponents = the phi(30)=8 totatives of 30 (so the unmapped degrees' exponents are part of the forced set), max(degree)=30=h(E8). The per-degree atom matches and the |W| prime 7 are UNFORCED and declined; no new physical hit. Reconciles v66 and v354"],"checked_by_registry":false,"heading_as_written":"(* ==== v355 E8.UNMAPPED.BANDWIDTH.01: the unmapped region's forced content is COLLECTIVE ==== *) Module[{exps, degs, totatives}, exps = {1, 7, 11, 13, 17, 19, 23, 29}; degs = exps + 1; (* {2,8,12,14,18,20,24,30} *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2362","line_end":2370,"line_start":2362,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v355"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v358 GRAV.ENTROPY.EQUILIBRIUM.01: the entanglement first law delta S = delta<K> with TFPT atoms gives the LINEARISED Einstein equation parameter-free -- 1/c3 = 8pi (Unruh 1/(2pi)=4c3, EH 1/(16pi)=c3/2, Bekenstein 1/4=1/|mu4|); THERMO=GEO coincidence 2pi/eta = |Z2|2pi chi iff |mu4|=|Z2|chi=4; J3 matter flux = CHM 3-ball weight integral int w d^3x = 4pi R^4/15 so delta<K_B>=8pi^2 R^4/15 delta<T_00>"],"checked_by_registry":false,"heading_as_written":"(* ==== v358 GRAV.ENTROPY.EQUILIBRIUM.01: parameter-free linearised Einstein + thermo=geo ==== *) Module[{c3, eta, Z2, mu4, chi, r, R, w, wint}, c3 = 1/(8 Pi); eta = 1/4; Z2 = 2; mu4 = 4; chi = 2; w = (R^2 - r^2)/(2 R); wint = Integrate[w * 4 Pi r^2, {r, 0, R}]; (* CHM 3-ball weight integral *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2371","line_end":2381,"line_start":2371,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v358"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v359 GRAV.NONLINEAR.01: the fixed-volume entanglement equilibrium gives the FULL covariant G_ab + Lambda g_ab = (1/c3) T_ab with BOTH coefficients parameter-free -- Einstein-tensor trace g^{ab}G_ab=(1-d/2)R=-R in d=4 (the trace structure carrying Lambda, via Jacobson 2015 + Lovelock); coeff 1: 8pi=1/c3 (2pi/eta, eta=1/|mu4|); coeff 2: Lambda from alpha, prefactor (8pi)^2*48c3^4 = 3/(4pi^2) (v60)"],"checked_by_registry":false,"heading_as_written":"(* ==== v359 GRAV.NONLINEAR.01: full covariant Einstein eq, both coefficients parameter-free ==== *) Module[{c3, eta, d, Rs, traceG, dtop, prefactor}, c3 = 1/(8 Pi); eta = 1/4; traceG = (1 - d/2); (* g^{ab}G_ab = (1-d/2) R; coefficient of R *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2382","line_end":2392,"line_start":2382,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v359"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v410 SHEET.GEN.BINARY.01: V = Q diag(0,1,1) powers print the binary spine -- V^n = {{0,2^(n-1),0},{0,2^n,0},{0,2^(n+1)-2,1}} and V^n.1 = (2^(n-1),2^n,2^(n+1)-1) for n=1..8 = (1,2,3),(2,4,7),(4,8,15),(8,16,31),...; bilinears 1.V^n.1=7 2^(n-1)-1, 1.V^n.a=7 2^(n-1), a.V^n.a=11 2^(n-1), a.V^n.1=11 2^(n-1)-2; readouts (6,7,9,11),13,27=1.R.a,55,56=dim 56_E7; theta sigma3(2)=9=a.V.1, sigma3(3)=28=1.V^3.a=det(I+R), sigma3(5)=126"],"checked_by_registry":false,"heading_as_written":"(* ==== v410-v414 round: the sheet generator V as a binary internal compiler ==== *) Module[{R, Q, V, C, J, one, a, I3, t, lam, Mt, e1, e2, e3, d1, d2, en, num, den}, R = {{1, 3, 0}, {1, 5, 2}, {2, 5, 3}}; Q = {{3, 1, 0}, {3, 2, 0}, {3, 2, 1}}; V = Q . DiagonalMatrix[{0, 1, 1}]; C = R + Q . DiagonalMatrix[{1, 0, 0}]; J = C - 2 V; one = {1, 1, 1}; a = {1, 1, 2}; I3 = IdentityMatrix[3]; (* v410: closed form V^n, binary spine, bilinear families, theta cross-link *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2393","line_end":2416,"line_start":2393,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v410","v414"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v411 FLAV.UD.VPOWER.01: c_u/c_d = (1.V^4.1)/((a.V.1)(1.V^2.1)) = 55/(9*13) = 55/117, identical to g_car*||Pl(K)||_1/(N_fam^2 Delta_Q) = 5*11/(9*13); RE-ENCODING, value stays [C]","v412 DIAMOND.SHEET.SOURCE.J.01: J = M(1,-2) = C - 2V = {{4,1,0},{4,1,2},{5,1,1}} on the Z2 wall (det=2); chi_J = lam^3-6 lam^2+3 lam-2 => (tr,e2,det)=(6,3,2); a.J.a=30=h(E8), det(I+J)=12=dim g_SM=chi_E8(i), det(2I+J)=40=|R(D5)|"],"checked_by_registry":false,"heading_as_written":"(* v411: u/d ratio as a pure V-power readout *) num = one . MatrixPower[V, 4] . one; den = (a . V . one)(one . MatrixPower[V, 2] . one); checkExact[\"v411 FLAV.UD.VPOWER.01: c_u/c_d = (1.V^4.1)/((a.V.1)(1.V^2.1)) = 55/(9*13) = 55/117, identical to g_car*||Pl(K)||_1/(N_fam^2 Delta_Q) = 5*11/(9*13); RE-ENCODING, value stays [C]\", num == 55 && a . V . one == 9 && one . MatrixPower[V, 2] . one == 13 && num/den == 55/117 && (5*11)/(9*13) == 55/117]; (* v412: the sheet source corner J = M(1,-2) on the Z2 wall *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2417","line_end":2429,"line_start":2417,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v411","v412"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v413 DIAMOND.SHEET.CALCULUS.01: on M_t=C+tV, e1=3t+12, e2=2t^2+15t+25, e3=4t^2+14t+14 => Delta e1=3=N_fam, Delta^2 e2=4=|mu4|, Delta^2 e3=8=rank E8; anchor energy a.M_t.a = 52+11t (30->41->52->63)","v414 DIAMOND.CENTER.RESOLVENT.01: tr C=12=dim g_SM=chi_E8(i), det C=14=dim G2, sum C=31=2^g_car-1=248/8; resolvent ladder det(C)=14, det(I+C)=52=dim F4, det(2I+C)=120=|R^+(E8)| (G2->F4->E8^+)"],"checked_by_registry":false,"heading_as_written":"(* v413: the sheet axis is a characteristic-difference calculator *) Mt = C + t V; e1 = Tr[Mt]; e3 = Det[Mt]; e2 = (Tr[Mt]^2 - Tr[Mt . Mt])/2; d1[f_] := (f /. t -> t + 1) - f; d2[f_] := d1[d1[f]]; en = a . Mt . a; checkExact[\"v413 DIAMOND.SHEET.CALCULUS.01: on M_t=C+tV, e1=3t+12, e2=2t^2+15t+25, e3=4t^2+14t+14 => Delta e1=3=N_fam, Delta^2 e2=4=|mu4|, Delta^2 e3=8=rank E8; anchor energy a.M_t.a = 52+11t (30->41->52->63)\", Simplify[e1 - (3 t + 12)] == 0 && Simplify[e2 - (2 t^2 + 15 t + 25)] == 0 && Simplify[e3 - (4 t^2 + 14 t + 14)] == 0 && Simplify[d1[e1] - 3] == 0 && Simplify[d2[e2] - 4] == 0 && Simplify[d2[e3] - 8] == 0 && Simplify[en - (52 + 11 t)] == 0]; (* v414: the center C is a resolvent portal G2 -> F4 -> E8 *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2430","line_end":2446,"line_start":2430,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v413","v414"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v415 DIAMOND.GAUSS.01 (i): J=[U,V]/3={{-1,1,0},{-2,1,0},{-3,1,0}} integer, Spec(J)={i,-i,0}, J^3+J=0 (J^2=-I on the rank-2 image), MatrixRank=2 -- a mu4 quarter-turn from [binary V, ternary U]"],"checked_by_registry":false,"heading_as_written":"(* ==== v415-v416 round: Gaussian operator + atom trichotomy ==== *) Module[{R, Q, U, V, J, I3, one, a, Pi2, D, x, neis}, R = {{1, 3, 0}, {1, 5, 2}, {2, 5, 3}}; Q = {{3, 1, 0}, {3, 2, 0}, {3, 2, 1}}; U = Q . DiagonalMatrix[{1, 0, 0}]; V = Q . DiagonalMatrix[{0, 1, 1}]; J = (U . V - V . U)/3; I3 = IdentityMatrix[3]; one = {1, 1, 1}; a = {1, 1, 2}; (* v415 (1): J = [U,V]/3 is an integer mu4 quarter-turn complex structure *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2447","line_end":2462,"line_start":2447,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v415","v416"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v415 DIAMOND.GAUSS.01 (ii): 3I+2J has spectrum {3+2i,3-2i,3} and 5I+4J has {5+4i,5-4i,5}; |3+2i|^2=13=Delta_Q, |5+4i|^2=41=10 b1 -- the Gaussian integers are literal operator eigenvalues","v415 DIAMOND.GAUSS.01 (iii): (3I+2J)(3I-2J)=9I-4J^2 has Spec {13,13,9} (13=Delta_Q, 9=N_fam^2); (5I+4J)(5I-4J)=25I-16J^2 has Spec {41,41,25} (41=10 b1, 25=g_car^2) -- the v222/v230 norms as operators"],"checked_by_registry":false,"heading_as_written":"(* v415 (2): the Gaussian integers 3+2i, 5+4i are eigenvalues *) checkExact[\"v415 DIAMOND.GAUSS.01 (ii): 3I+2J has spectrum {3+2i,3-2i,3} and 5I+4J has {5+4i,5-4i,5}; |3+2i|^2=13=Delta_Q, |5+4i|^2=41=10 b1 -- the Gaussian integers are literal operator eigenvalues\", Sort[Eigenvalues[3 I3 + 2 J]] == Sort[{3 + 2 I, 3 - 2 I, 3}] && Sort[Eigenvalues[5 I3 + 4 J]] == Sort[{5 + 4 I, 5 - 4 I, 5}] && 3^2 + 2^2 == 13 && 5^2 + 4^2 == 41]; (* v415 (3): the square-norm dictionary as operator identities *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2463","line_end":2475,"line_start":2463,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v415"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v415 DIAMOND.GAUSS.01 (iv): the intrinsic deck D=-I+J-J^2={{-1,1,0},{-2,1,0},{-4,3,-1}} is order 4 (D^4=I), Spec(D)={i,-1,-i} (the seam-deck spectrum, v146); chi2 line = ker[U,V] = NullSpace = {(0,0,1)} = a-1","v416 ARITH.TRICHOTOMY.01 (Z[i], square/seam): 2 RAMIFIES (2=-i(1+i)^2), 3 INERT (3 mod 4=3, norm 9=N_fam^2), 5 SPLITS (5=(2+i)(2-i), 5 mod 4=1) -- g_car=5 factors on the seam"],"checked_by_registry":false,"heading_as_written":"(* v415 (4): the intrinsic order-4 mu4 deck D = -I + J - J^2 *) Pi2 = I3 + J . J; D = J - Pi2; checkExact[\"v415 DIAMOND.GAUSS.01 (iv): the intrinsic deck D=-I+J-J^2={{-1,1,0},{-2,1,0},{-4,3,-1}} is order 4 (D^4=I), Spec(D)={i,-1,-i} (the seam-deck spectrum, v146); chi2 line = ker[U,V] = NullSpace = {(0,0,1)} = a-1\", D == {{-1, 1, 0}, {-2, 1, 0}, {-4, 3, -1}} && MatrixPower[D, 4] == I3 && Sort[Eigenvalues[D]] == Sort[{I, -I, -1}] && NullSpace[J] == {{0, 0, 1}} && a - one == {0, 0, 1}]; (* v416 (1): the Z[i] (square/seam) trichotomy *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2476","line_end":2488,"line_start":2476,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v146","v415","v416"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v416 ARITH.TRICHOTOMY.01 (Z[omega], hex/flavor): 3 RAMIFIES (N(1-omega)=3), 2 INERT (2 mod 3=2, norm 4), 5 INERT (5 mod 3=2, norm 25=g_car^2); the ramified prime of each ring is its atom (Z[i]<->2, Z[omega]<->3)","v416 ARITH.TRICHOTOMY.01 (facets, v403): Q(i)/Q(sqrt-3)/Q(sqrt5) have disc -4,-3,5, ramified over exactly {2},{3},{5}; product 2*3*5=30=h(E8); 2 imaginary (CM) + 1 real (RM)"],"checked_by_registry":false,"heading_as_written":"(* v416 (2): the Z[omega] (hex/flavor) trichotomy + ramified prime = own atom *) neis[aa_, bb_] := aa^2 - aa bb + bb^2; checkExact[\"v416 ARITH.TRICHOTOMY.01 (Z[omega], hex/flavor): 3 RAMIFIES (N(1-omega)=3), 2 INERT (2 mod 3=2, norm 4), 5 INERT (5 mod 3=2, norm 25=g_car^2); the ramified prime of each ring is its atom (Z[i]<->2, Z[omega]<->3)\", neis[1, -1] == 3 && Mod[2, 3] == 2 && neis[2, 0] == 4 && Mod[5, 3] == 2 && neis[5, 0] == 25]; (* v416 (3): the three facets ramify over one atom each (v403) *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2489","line_end":2500,"line_start":2489,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v403","v416"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":[],"checked_by_registry":false,"heading_as_written":"(* ==== v417 round: the Eisenstein/CP operator + the order-30 clock ==== *) Module[{P, W, I3, ones3, omega, zeta6, z30}, P = {{0, 0, 1}, {1, 0, 0}, {0, 1, 0}}; (* family rotation (1 2 3) *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2501","line_end":2507,"line_start":2501,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v417"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v417 DIAMOND.EISEN.01 (i): P=(1 2 3) Eisenstein deck (P^3=I, P^2+P+I=ONES); (3I+2P)(3I+2P^2)=7I+6 ONES with Spec {7,7,25} (7=N_omega(3+2omega)=scalaron, 25=g_car^2) -- the dual of v415's {13,13,9}; NEG (5I+4P)(5I+4P^2)->{21,21,81}, N_omega(5,4)=21!=41","v417 DIAMOND.EISEN.01 (ii): the CP clock W=-P^2 (=rho v233) has W^3=-I, W^2=P, Spec {-1,zeta6,zeta6^-1}; delta_CKM,lead=arg(zeta6)=pi/3 (eigenvalue of W), delta_PMNS=arg(zeta6^4)=4pi/3 (eigenvalue of W^4=P^2); W^3=-I the Z2 sheet flip"],"checked_by_registry":false,"heading_as_written":"(* v417 (1): the family rotation = Eisenstein deck + the hex norm 7 *) checkExact[\"v417 DIAMOND.EISEN.01 (i): P=(1 2 3) Eisenstein deck (P^3=I, P^2+P+I=ONES); (3I+2P)(3I+2P^2)=7I+6 ONES with Spec {7,7,25} (7=N_omega(3+2omega)=scalaron, 25=g_car^2) -- the dual of v415's {13,13,9}; NEG (5I+4P)(5I+4P^2)->{21,21,81}, N_omega(5,4)=21!=41\", MatrixPower[P, 3] == I3 && MatrixPower[P, 2] + P + I3 == ones3 && (3 I3 + 2 P) . (3 I3 + 2 MatrixPower[P, 2]) == 7 I3 + 6 ones3 && Sort[Eigenvalues[(3 I3 + 2 P) . (3 I3 + 2 MatrixPower[P, 2])]] == Sort[{7, 7, 25}] && (3^2 - 3*2 + 2^2) == 7 && Sort[Eigenvalues[(5 I3 + 4 P) . (5 I3 + 4 MatrixPower[P, 2])]] == Sort[{21, 21, 81}] && (5^2 - 5*4 + 4^2) == 21]; (* v417 (2): the CP clock W = -P^2 and both CP phases *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2508","line_end":2523,"line_start":2508,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v415","v417"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v417 DIAMOND.EISEN.01 (iii): all flavor clocks are powers of zeta30 (h(E8)=30): z30^15=-1 (mu2), z30^10=omega (mu3), z30^6=zeta5 (mu5), z30^5=zeta6 (mu6); the seam mu4 (i) is NOT a power (4 nmid 30), it is the Galois side (Z/30)^x of order phi(30)=8=rank E8"],"checked_by_registry":false,"heading_as_written":"(* v417 (3): one order-30 Coxeter clock; seam mu4 is the Galois side *) checkExact[\"v417 DIAMOND.EISEN.01 (iii): all flavor clocks are powers of zeta30 (h(E8)=30): z30^15=-1 (mu2), z30^10=omega (mu3), z30^6=zeta5 (mu5), z30^5=zeta6 (mu6); the seam mu4 (i) is NOT a power (4 nmid 30), it is the Galois side (Z/30)^x of order phi(30)=8=rank E8\", Simplify[z30^15 + 1] == 0 && Simplify[z30^10 - omega] == 0 && Simplify[z30^6 - Exp[2 Pi I/5]] == 0 && Simplify[z30^5 - zeta6] == 0 && Mod[30, 4] != 0 && EulerPhi[30] == 8 && Length[Select[Range[29], GCD[#, 30] == 1 &]] == 8]; ]; (* ==== v418 round: the cyclotomic norm triple (7,13,55) over the atom-rings ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2524","line_end":2538,"line_start":2524,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v417","v418"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v418 ARITH.NORMTRIPLE.01 (i): the carrier-5 clock C5 (Phi5-companion, 4x4) has C5^5=I, tr=-1, det=1 (the four primitive 5th roots); the golden ratio is its real-part data 2cos(72)=1/phi, 2cos(144)=-phi (output-side, v313/v349; dim 4, not 3 -- refines v417's gap)","v418 ARITH.NORMTRIPLE.01 (ii): N_Z[zeta5](3+2 zeta5)=det(3I+2 C5)=55=5*11=quark numerator (v410/v411)"],"checked_by_registry":false,"heading_as_written":"(* v418 (1): the carrier-5 clock C5 + the golden ratio *) checkExact[\"v418 ARITH.NORMTRIPLE.01 (i): the carrier-5 clock C5 (Phi5-companion, 4x4) has C5^5=I, tr=-1, det=1 (the four primitive 5th roots); the golden ratio is its real-part data 2cos(72)=1/phi, 2cos(144)=-phi (output-side, v313/v349; dim 4, not 3 -- refines v417's gap)\", MatrixPower[C5, 5] == I4 && Tr[C5] == -1 && Det[C5] == 1 && Simplify[2 Cos[2 Pi/5] - 1/phi] == 0 && Simplify[2 Cos[4 Pi/5] + phi] == 0]; (* v418 (2): the carrier norm = the quark numerator *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2539","line_end":2547,"line_start":2539,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v313","v349","v417","v418"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v418 ARITH.NORMTRIPLE.01 (iii): det(3I+2 Comp(Phi_{3,4,5}))=(7,13,55) over Z[omega],Z[i],Z[zeta5] (atoms 3,2,5); NEG control anchor (5,4)->(21,41,461) (461 prime, only the carrier ring distinguishes); (3,2) FORCED not unique, (2,1)->(3,5,11)"],"checked_by_registry":false,"heading_as_written":"(* v418 (3): the triple + negative controls *) checkExact[\"v418 ARITH.NORMTRIPLE.01 (iii): det(3I+2 Comp(Phi_{3,4,5}))=(7,13,55) over Z[omega],Z[i],Z[zeta5] (atoms 3,2,5); NEG control anchor (5,4)->(21,41,461) (461 prime, only the carrier ring distinguishes); (3,2) FORCED not unique, (2,1)->(3,5,11)\", {Det[3 I2 + 2 C3], Det[3 I2 + 2 C4], Det[3 I4 + 2 C5]} == {7, 13, 55} && {Det[5 I2 + 4 C3], Det[5 I2 + 4 C4], Det[5 I4 + 4 C5]} == {21, 41, 461} && PrimeQ[461] && {Det[2 I2 + C3], Det[2 I2 + C4], Det[2 I4 + C5]} == {3, 5, 11}]; ]; (* ==== v419 round: the seam mu4 = Gal(Q(zeta5)) = (Z/5)^x ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2548","line_end":2562,"line_start":2548,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v418","v419"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v419 SEAM.GALOIS.01 (i): 30=2*3*5 squarefree => Z/30 has orders {1,2,3,5,6,10,15,30}, NO order 4; the seam mu4 is forced onto the Galois side","v419 SEAM.GALOIS.01 (ii): (Z/30)^x = mu4 x Z2, phi(30)=8=rank E8; mu4=(Z/5)^x (carrier 5), Z2=(Z/3)^x (family/CP); order-4 totatives {7,13,17,23} are (Z/5)^x generators"],"checked_by_registry":false,"heading_as_written":"(* v419 (1): 30 squarefree => no order-4 on the cyclic clock *) checkExact[\"v419 SEAM.GALOIS.01 (i): 30=2*3*5 squarefree => Z/30 has orders {1,2,3,5,6,10,15,30}, NO order 4; the seam mu4 is forced onto the Galois side\", SquareFreeQ[30] && Union[Table[30/GCD[k, 30], {k, 0, 29}]] == {1, 2, 3, 5, 6, 10, 15, 30} && ! MemberQ[Table[30/GCD[k, 30], {k, 0, 29}], 4]]; (* v419 (2): (Z/30)^x = mu4 x Z2 = (Z/5)^x x (Z/3)^x *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2563","line_end":2574,"line_start":2563,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v419"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v419 SEAM.GALOIS.01 (iii): the seam mu4 = Gal(Q(zeta5)): the Frobenius G (zeta5->zeta5^2) has G C5 G^-1 = C5^2, G^4=I, G^2 C5 G^-2 = C5^-1 (complex conj)","v422 SEAM.GALOIS.NET.01 (i): disc(A3)=disc(D5)=Z/4 cyclic (Smith invariant factors {4}, det 4); D_n disc is Z/4 for n ODD, Z2xZ2 for n EVEN -- D5 (rank 5=g_car odd) cyclic, D8 (rank 8 even) Klein {2,2}","v422 SEAM.GALOIS.NET.01 (ii): Gal(Q(zeta5))=(Z/5)^x=<2> cyclic order 4; among the atoms only 5 gives order 4 (EulerPhi 5=4, 3=2, 2=1)","v422 SEAM.GALOIS.NET.01 (iii): in disc(D5(+)A3)=Z4xZ4 (16) the glue (1,1) is order 4 (cyclic) => 16/4^2=1=disc(E8) (det 1); the halfway (2,2) is order 2 => 16/2^2=4=disc(D8) (det 4); cyclic Z/4 -> E8, Klein/order-2 -> D8"],"checked_by_registry":false,"heading_as_written":"(* v419 (3): the seam mu4 = Gal(Q(zeta5)) via the explicit Frobenius G *) checkExact[\"v419 SEAM.GALOIS.01 (iii): the seam mu4 = Gal(Q(zeta5)): the Frobenius G (zeta5->zeta5^2) has G C5 G^-1 = C5^2, G^4=I, G^2 C5 G^-2 = C5^-1 (complex conj)\", G . C5 . Inverse[G] == C5 . C5 && MatrixPower[G, 4] == I4 && MatrixPower[G, 2] . C5 . Inverse[MatrixPower[G, 2]] == MatrixPower[C5, 4] && G != I4 && MatrixPower[G, 2] != I4]; ]; (* ==== v422 round: the Galois<->Net bridge (mu4 = Gal(Q(zeta5)) = (E8)_1 glue) ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2575","line_end":2601,"line_start":2575,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v419","v422"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v429 DM.AXION.PENTAGON.01 (i): N_fam=g_car-2, so theta_i=pi N_fam/g_car=(g_car-2)pi/g_car = the interior angle of the regular g_car-gon; for g_car=5 the PENTAGON, theta_i=3 pi/5=108 deg"],"checked_by_registry":false,"heading_as_written":"(* ==== v429 round: theta_i = the carrier-pentagon interior angle = golden ==== *) Module[{phi, gc, Nf}, phi = (1 + Sqrt[5])/2; gc = 5; Nf = 3; (* v429 (1): theta_i = interior angle of the regular g_car-gon (pentagon) *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2602","line_end":2610,"line_start":2602,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v429"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v429 DM.AXION.PENTAGON.01 (ii): cos(3 pi/5)=(1-Sqrt5)/4=-1/(2 phi); 2 cos(2 pi/5)=1/phi=phi-1; phi=2 cos(pi/5)=(1+Sqrt5)/2 -- the 'unmapped' golden ratio IS theta_i's angular data","v429 DM.AXION.PENTAGON.01 (iii): among small regular n-gons only n=5 has an IRRATIONAL interior-angle cosine -- cos((n-2)pi/n)=1/2,0,-1/2 for n=3,4,6 (rational), only n=5 gives -1/(2 phi); theta_i golden BECAUSE carrier=5 (P2)"],"checked_by_registry":false,"heading_as_written":"(* v429 (2): cos(theta_i) is golden *) checkExact[\"v429 DM.AXION.PENTAGON.01 (ii): cos(3 pi/5)=(1-Sqrt5)/4=-1/(2 phi); 2 cos(2 pi/5)=1/phi=phi-1; phi=2 cos(pi/5)=(1+Sqrt5)/2 -- the 'unmapped' golden ratio IS theta_i's angular data\", Simplify[Cos[3 Pi/5] - (1 - Sqrt[5])/4] == 0 && Simplify[Cos[3 Pi/5] + 1/(2 phi)] == 0 && Simplify[2 Cos[2 Pi/5] - 1/phi] == 0 && Simplify[2 Cos[2 Pi/5] - (phi - 1)] == 0 && Simplify[2 Cos[Pi/5] - phi] == 0]; (* v429 (3): the golden character is unique to g_car=5 *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2611","line_end":2623,"line_start":2611,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v429"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":[],"checked_by_registry":false,"heading_as_written":"(* ==== v430 round: the 'other side' (double-cover deck / conjugate sheet S^-) vs the unmapped E8 degrees ==== *) Module[{exps, degs, matched, unmapped, sheet, spinor}, exps = {1, 7, 11, 13, 17, 19, 23, 29}; degs = exps + 1; (* {2,8,12,14,18,20,24,30} *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2624","line_end":2632,"line_start":2624,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v430"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v430 E8.OTHERSIDE.AUDIT.01 (i): the one-sided cover gives |Z2|=2 (the 1/2 in c3=1/(2*4pi)=1/(8pi)); 2=Min(E8 degrees)=the metric, one of the matched {2,8,30}, NOT one of the unmapped {12,14,18,20,24}","v430 E8.OTHERSIDE.AUDIT.01 (ii): dim S^+=dim S^-=16, the spinor block 128=rank*dim S^+=8*16=2^(rank-1)=Total[degrees], the spinor half of 248=120+128; S^- the conjugate (16-bar,4-bar), 128=2*64"],"checked_by_registry":false,"heading_as_written":"(* v430 (1): the deck is the matched degree-2 invariant, not one of the unmapped degrees *) checkExact[\"v430 E8.OTHERSIDE.AUDIT.01 (i): the one-sided cover gives |Z2|=2 (the 1/2 in c3=1/(2*4pi)=1/(8pi)); 2=Min(E8 degrees)=the metric, one of the matched {2,8,30}, NOT one of the unmapped {12,14,18,20,24}\", 1/8 == 1/(2*4) && Min[degs] == 2 && MemberQ[matched, 2] && ! MemberQ[unmapped, 2] && matched == {2, 8, 30} && unmapped == {12, 14, 18, 20, 24}]; (* v430 (2): the two sheets are the 128-spinor (matched, collective) *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2633","line_end":2642,"line_start":2633,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v430"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v430 E8.OTHERSIDE.AUDIT.01 (iii): the sheet/deck integer set {2,16,32,128} has EMPTY intersection with the unmapped degrees {12,14,18,20,24}; its only degree-alphabet contact is the matched 2"],"checked_by_registry":false,"heading_as_written":"(* v430 (3): the sheet/deck set is forced-disjoint from the unmapped region *) checkExact[\"v430 E8.OTHERSIDE.AUDIT.01 (iii): the sheet/deck integer set {2,16,32,128} has EMPTY intersection with the unmapped degrees {12,14,18,20,24}; its only degree-alphabet contact is the matched 2\", sheet == {2, 16, 32, 128} && Intersection[sheet, unmapped] == {} && Intersection[sheet, degs] == {2}]; ]; (* ==== v431 round: E8.DEGREE.LADDER.01 -- unmapped degrees = 6*spine U det-ladder ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2643","line_end":2662,"line_start":2643,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v430","v431"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v431 E8.DEGREE.LADDER.01 (i): E8 exponents = phi(30)=8 totatives of h=30=2*N_fam*g_car; coprime to 6 => +-1 mod 6, so degrees occupy ONLY {0,2} mod 6","v431 E8.DEGREE.LADDER.01 (ii): degrees==0 mod 6 = {12,18,24,30}; /6 = {2,3,4,5} = v91 spine {e3,p0,e1,e2}(a=(1,1,2)); 30=6*g_car matched"],"checked_by_registry":false,"heading_as_written":"(* v431 (1): two-family split forced by 30 = 2*3*5 *) checkExact[\"v431 E8.DEGREE.LADDER.01 (i): E8 exponents = phi(30)=8 totatives of h=30=2*N_fam*g_car; coprime to 6 => +-1 mod 6, so degrees occupy ONLY {0,2} mod 6\", exps == tot30 && EulerPhi[h] == 8 && h == 2*3*5 && expMod6 == {1, 5} && degMod6 == {0, 2}]; (* v431 (2): 6k family = 6 x spine {2,3,4,5} = v91 anchor a=(1,1,2) *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2663","line_end":2677,"line_start":2663,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v431","v91"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v431 E8.DEGREE.LADDER.01 (iii): degrees==2 mod 6 = {2,8,14,20}; {8,14,20}=(det R,det C,det L)=winding line det M(s,0)=6s+8 (v135); 2=matched metric, 8=rank E8","v431 E8.DEGREE.LADDER.01 (iv): 18=6*3=6*N_fam is spine-family 6*p0, NOT on det-ladder (6s+8=18 has no integer s); no orphan degree"],"checked_by_registry":false,"heading_as_written":"(* v431 (3): 6k+2 family = {2} U det-ladder {8,14,20} on winding line 6s+8 *) fam2 = Sort[Select[degs, Mod[#, 6] == 2 &]]; R = {{1, 3, 0}, {1, 5, 2}, {2, 5, 3}}; Q = {{3, 1, 0}, {3, 2, 0}, {3, 2, 1}}; C = R + Q . DiagonalMatrix[{1, 0, 0}]; L = R + Q . DiagonalMatrix[{2, 0, 0}]; ladder = {Det[R], Det[C], Det[L]}; surf = Table[6 s + 8, {s, 0, 2}]; checkExact[\"v431 E8.DEGREE.LADDER.01 (iii): degrees==2 mod 6 = {2,8,14,20}; {8,14,20}=(det R,det C,det L)=winding line det M(s,0)=6s+8 (v135); 2=matched metric, 8=rank E8\", fam2 == {2, 8, 14, 20} && ladder == {8, 14, 20} && ladder == surf && ladder[[1]] == 8]; (* v431 (4): 18 = 6*N_fam spine member, not det-ladder holdout *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2678","line_end":2692,"line_start":2678,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v135","v431"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v431 E8.DEGREE.LADDER.01 (v): clean {0,2}-mod-6 split (6|h AND exponents=totatives) holds for E8 but FAILS for E6,E7,D5; F4/G2 share split but not spine+flavor-det content","v431 E8.DEGREE.LADDER.01 (vi): all five unmapped {12,14,18,20,24} have forced FAMILY home (6*spine or det-ladder); degrees=6*spine U ({2} U det-ladder) exact [I]; functorial flavor map stays [P]"],"checked_by_registry":false,"heading_as_written":"(* v431 (5): clean {0,2} split special to E8 among exceptionals *) cleanSplit[name_] := Module[{ex, hh, dm}, ex = Switch[name, \"A4\", {1, 2, 3, 4}, \"D5\", {1, 3, 5, 7, 4}, \"E6\", {1, 4, 5, 7, 8, 11}, \"E7\", {1, 5, 7, 9, 11, 13, 17}, \"E8\", exps, \"F4\", {1, 5, 7, 11}, \"G2\", {1, 5}]; hh = Switch[name, \"A4\", 5, \"D5\", 8, \"E6\", 12, \"E7\", 18, \"E8\", 30, \"F4\", 12, \"G2\", 6]; dm = DeleteDuplicates[Mod[ex + 1, 6]]; Sort[ex] == Select[Range[1, hh - 1], CoprimeQ[#, hh] &] && SubsetQ[{0, 2}, dm] && Mod[hh, 6] == 0]; e8Clean = cleanSplit[\"E8\"]; e67Fail = ! (cleanSplit[\"E6\"] && cleanSplit[\"E7\"] && cleanSplit[\"D5\"]); checkExact[\"v431 E8.DEGREE.LADDER.01 (v): clean {0,2}-mod-6 split (6|h AND exponents=totatives) holds for E8 but FAILS for E6,E7,D5; F4/G2 share split but not spine+flavor-det content\", e8Clean && e67Fail && cleanSplit[\"F4\"] && cleanSplit[\"G2\"]]; (* v431 (6): all five 'unmapped' degrees homed; v355 functorial line upheld [P] *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2693","line_end":2713,"line_start":2693,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v355","v431"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v437 E8.DEGREE.JOINT.01 (i): E8 fixed by its degrees -- rank=#deg=8=2nd deg, h=max=30, #posroots=sum(exp)=120, #roots=240, dim=248, |W|=prod(deg)=696729600, sum(deg)=128=2^7"],"checked_by_registry":false,"heading_as_written":"(* ==== v437 round: E8.DEGREE.JOINT.01 -- (g_car,N_fam)=unique roots of x^2-8x+15; E8 fixed by its degrees ==== *) Module[{degs, exps, rank, h, nPos, nRoots, dim, x, quad, roots, factorPairs, pairsSum8, mapped, canonical}, degs = {2, 8, 12, 14, 18, 20, 24, 30}; exps = degs - 1; rank = Length[degs]; h = Max[degs]; nPos = Total[exps]; nRoots = 2 nPos; dim = nRoots + rank; (* v437 (1): all of E8 fixed by its degree multiset *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2714","line_end":2728,"line_start":2714,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v437"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v437 E8.DEGREE.JOINT.01 (ii): (g_car,N_fam)=(5,3) are the UNIQUE roots of x^2-(rank)x+(h/2)=x^2-8x+15=(x-3)(x-5); sum=rank E8=8, product=h/2=15=g_car*N_fam; {3,5} unique factor pair of 15 summing to 8","v437 E8.DEGREE.JOINT.01 (iii): 3 primary-readout degrees {2,8,30}={min deg (quadratic Casimir), rank, max deg (Coxeter h)}; g_car=5=max prime of 30, N_fam=3=h/(2 g_car)"],"checked_by_registry":false,"heading_as_written":"(* v437 (2): the joint quadratic -- (g_car,N_fam) unique roots, coeffs (rank, h/2) *) quad = x^2 - rank x + h/2; roots = Sort[x /. Solve[quad == 0, x]]; factorPairs = Select[Divisors[h/2], # <= (h/2)/# &]; pairsSum8 = Select[factorPairs, # + (h/2)/# == rank &]; checkExact[\"v437 E8.DEGREE.JOINT.01 (ii): (g_car,N_fam)=(5,3) are the UNIQUE roots of x^2-(rank)x+(h/2)=x^2-8x+15=(x-3)(x-5); sum=rank E8=8, product=h/2=15=g_car*N_fam; {3,5} unique factor pair of 15 summing to 8\", roots == {3, 5} && h/2 == 15 && Factor[quad] == (x - 3) (x - 5) && pairsSum8 == {3}]; (* v437 (3): the three mapped degrees are the canonical invariants *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2729","line_end":2743,"line_start":2729,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v437"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v445 SEAM.RIGIDITY.FORCING.01 (i): entrywise forcing -- [rho,E_ab]=(i^a-i^b)E_ab=0 IFF a==b mod 4, verified for ALL a,b in 0..31 (residue-only => uniform in N; the converse of v442, commuting FORCES mu4-block-diagonality)"],"checked_by_registry":false,"heading_as_written":"(* ==== v445 round: SEAM.RIGIDITY.FORCING.01 -- commuting with the order-4 clock FORCES mu4-block-diagonality (the converse of v442; mirrors v445_seam_rigidity_forcing.py) ==== *) Module[{forcingIff, sec, sec2, dim4, dim2, sweepOK}, (* v445 (i): entrywise forcing -- [rho,E_ab]=(i^a-i^b)E_ab=0 <=> a==b mod 4 *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2744","line_end":2751,"line_start":2744,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v442","v445"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v445 SEAM.RIGIDITY.FORCING.01 (ii): exact commutant dim = sum n_s^2 = 4*4^2 = 64 (N=16, four sectors {4,4,4,4}), a PROPER subspace of N^2=256 -- a genuine quantitative restriction","v445 SEAM.RIGIDITY.FORCING.01 (iii): THE ORDER IS THE DISCRIMINATOR -- order-2 commutant (N=16: 2*8^2=128) STRICTLY LARGER than order-4 (64); swept N=4..64; the four marks |mu4|=4=h(A3) force strictly more structure than two; only index-4 is (E8)_1 (det 1 vs SO(16) det 4, mirrored v281/v344)"],"checked_by_registry":false,"heading_as_written":"(* v445 (ii): exact commutant dimension = sum n_s^2, a PROPER subspace of N^2 (N=16) *) sec = Table[Count[Range[0, 16 - 1], k_ /; Mod[k, 4] == s], {s, 0, 3}]; dim4 = Total[sec^2]; checkExact[\"v445 SEAM.RIGIDITY.FORCING.01 (ii): exact commutant dim = sum n_s^2 = 4*4^2 = 64 (N=16, four sectors {4,4,4,4}), a PROPER subspace of N^2=256 -- a genuine quantitative restriction\", sec == {4, 4, 4, 4} && dim4 == 64 && dim4 < 16^2]; (* v445 (iii): the order is the discriminator -- order-2 commutant strictly larger; marks=4 *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2752","line_end":2768,"line_start":2752,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v445"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v452 SEAM.EQUIV.E8.MODULAR.01 (i): S-invariance chi(-1/tau)=chi(tau) (E4 wt4/eta^8 wt4 => chi wt0) -- ONE primary, S-matrix=[1]","v452 SEAM.EQUIV.E8.MODULAR.01 (ii): T-phase chi(tau+1)/chi(tau)=e^{-2pi i/3}=e^{-2pi i c/24} (c=8)","v452 SEAM.EQUIV.E8.MODULAR.01 (iii): leading power chi*q^{1/3}->1 => q^{-c/24}=q^{-1/3} => c=8=g_car+N_fam","v452 SEAM.EQUIV.E8.MODULAR.01 (iv): holomorphic c=8=0 mod 8 (even unimodular rank-8 E8) and T-phase order 24/gcd(8,24)=3 (primitive cube root e^{-2pi i/3}); c=8=g_car+N_fam=rank E8"],"checked_by_registry":false,"heading_as_written":"(* ==== v452 round: SEAM.EQUIV.E8.MODULAR.01 -- the (E8)_1 torus modular data (one primary, S-invariant, T-phase e^{-2pi i/3}, holomorphic c=8); mirrors v452_seam_e8_modular.py. EisensteinE is left unevaluated by some engines, so E4 is built from its q-series; the modular T-branch e^{i pi/12} is carried correctly by the native DedekindEta. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2769","line_end":2791,"line_start":2769,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v452"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v450 SEAM.EQUIV.EDGE.ENTANGLEMENT.01: c per Majorana=1/2 (Calabrese-Cardy: Dirac c=1=2*1/2), N_Maj=2^(g_car-1)=16, c_-=N_Maj*(1/2)=8=g_car+N_fam=rank E8 -- the entanglement reading of the edge central charge (third observable after v444/v447)","v451 SEAM.EQUIV.EDGE.CARDY.01: the edge is the Ising minimal model M(3,4) -- c=1-6(p-q)^2/(pq)=1/2, Kac weights h_{2,2}=1/16 (sigma) and h_{1,3}=1/2 (epsilon); {c,h_sigma,h_epsilon}={1/2,1/16,1/2} uniquely names the free-Majorana CFT, 16 copies => c_-=16*(1/2)=8"],"checked_by_registry":false,"heading_as_written":"(* ==== v450/v451 round: SEAM.EQUIV.EDGE.* -- the edge central charge c_-=8 from entanglement (c=1/2 per Majorana) and the Ising minimal-model Kac weights (Cardy tower); mirrors v450_seam_edge_entanglement.py / v451_seam_edge_cardy_tower.py (the numerical fits are Python-only; the c_-=8 assembly and the Kac weights are exact and mirrored here). ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2792","line_end":2807,"line_start":2792,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v450","v451"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v453 SEAM.RIGIDITY.MU4FROMMARKS.01 (i): the four Gauss-Bonnet marks ARE mu4=roots of z^4-1; z->iz sends (1,i,-1,-i)->(i,-1,-i,1), a 4-cycle of order 4 (fixes the configuration setwise, the order-4 clock of v445)","v453 SEAM.RIGIDITY.MU4FROMMARKS.01 (ii): the form basis omega_k=z^{k-1}dz/(z^4-1) -> i^k omega_k under z->iz (k=1,2,3 -> {i,-1,-i}, the three nontrivial mu4 characters; weights (1,2,3)=A3 exponents=Spec(Q_+)) -- the natural basis is mu4-graded, so any geometric datum is mu4-covariant","v453 SEAM.RIGIDITY.MU4FROMMARKS.01 (iii): cross-ratio lambda(1,i,-1,-i)=2 is preserved by z->iz (in the D4 stabiliser, v168) => QGEO.SYM.01 ('seam RP data mu4-symmetric') follows from marks=mu4 + the existing QGEO.REALIZE.01, NO new premise; SEAM.EQUIV.01 stays [O]"],"checked_by_registry":false,"heading_as_written":"(* ==== v453 round: SEAM.RIGIDITY.MU4FROMMARKS.01 -- the mu4-symmetry of the seam RP data (QGEO.SYM.01) derived from the four marks; mirrors v453_seam_mu4_from_marks.py. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2808","line_end":2826,"line_start":2808,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v453"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":[],"checked_by_registry":false,"heading_as_written":"(* ==== v454/v456/v457/v459 round (G-block): the edge current-algebra/Sugawara c=8, the S3-from-P1 one-sided arithmetic, the (E8)_1 character/sector kill-test, and the lattice-VOA second route; mirrors v454/v456/v457/v459. The Casimir + Kac-Moody fits (v454), the Chern flip (v456) and the Tomita-Takesaki tower (v455) are numerical, Python-only; the exact algebra is mirrored here. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2827","line_end":2834,"line_start":2827,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v454","v455","v456","v457","v459"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v454 SEAM.EQUIV.EDGE.VIRASORO.01: level-1 Sugawara c=dim G/(1+h^v)=8 for BOTH SO(16)_1 (120/15) and (E8)_1 (248/31); 16 Majoranas => c_-=8=g_car+N_fam (the Casimir c and Kac-Moody central term <J_n J_-n>=n are numerical, Python-only)","v456 SEAM.S3.FROM-P1.01: c3's '8' is the one-sided count |Z2|*(intK/pi)=2*4=8; a reflection sends Chern C->-C so two-sided forces C=0 (Solve[c==-c]=>c=0), one-sided (no reflection) allows C!=0; c_-=8=g_car+N_fam shares the 8 (the Chern computation is numerical, Python-only)"],"checked_by_registry":false,"heading_as_written":"(* v454: level-1 Sugawara c = dim G/(1+h^v) = 8 for both SO(16)_1 and (E8)_1 *) cSO16 = 120/(1 + 14); cE8 = 248/(1 + 30); checkExact[\"v454 SEAM.EQUIV.EDGE.VIRASORO.01: level-1 Sugawara c=dim G/(1+h^v)=8 for BOTH SO(16)_1 (120/15) and (E8)_1 (248/31); 16 Majoranas => c_-=8=g_car+N_fam (the Casimir c and Kac-Moody central term <J_n J_-n>=n are numerical, Python-only)\", cSO16 == 8 && cE8 == 8 && cSO16 == cE8 && 8 == gcar + Nfam]; (* v456: c3's '8' is the one-sided count; reflection C->-C so two-sided forces C=0 *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2835","line_end":2846,"line_start":2835,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v454","v456"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v457 SEAM.EQUIV.KILLTEST.01 (i): the (E8)_1 character tower chi=E4/eta^8=q^{-1/3}(1+248q+4124q^2+34752q^3+...); E4/Product(1-q^n)^8 q-series coeffs {1,248,4124,34752} -- the exact (E8)_1 conformal-tower degeneracies","v457 SEAM.EQUIV.KILLTEST.01 (ii): the kill-test discriminators -- weight-1 count 248=dim E8=120(SO16)+128(spinor); |det Cartan(E8)|=1 (invertible, one sector) vs |det Cartan(D8=SO16)|=4 (four sectors); a measured 120 or 4 would FALSIFY (E8)_1, the data give 248/1","v459 SEAM.EQUIV.LATTICEVOA.01 (i): E8 even unimodular -- det Cartan(E8)=1; the 240 roots split 112 integer (D8) + 128 half-integer (spinor): #{norm-2 in {-1,0,1}^8}=112, #{(+-1/2)^8 even #signs}=128","v459 SEAM.EQUIV.LATTICEVOA.01 (ii): the (E8)_1 weight-1 content in BOTH decompositions 248=8+240 (lattice: 8 Cartan + 240 roots) = 120+128 (fermionic: 120 so(16) bilinears + 128 spinor); the lattice route supplies the 128 spinor MMST (v458) leaves open"],"checked_by_registry":false,"heading_as_written":"(* v457: the (E8)_1 character tower {1,248,4124,34752} and the kill-test discriminators *) cartanE8 = {{2, -1, 0, 0, 0, 0, 0, 0}, {-1, 2, -1, 0, 0, 0, 0, 0}, {0, -1, 2, -1, 0, 0, 0, 0}, {0, 0, -1, 2, -1, 0, 0, 0}, {0, 0, 0, -1, 2, -1, 0, -1}, {0, 0, 0, 0, -1, 2, -1, 0}, {0, 0, 0, 0, 0, -1, 2, 0}, {0, 0, 0, 0, -1, 0, 0, 2}}; cartanD8 = {{2, -1, 0, 0, 0, 0, 0, 0}, {-1, 2, -1, 0, 0, 0, 0, 0}, {0, -1, 2, -1, 0, 0, 0, 0}, {0, 0, -1, 2, -1, 0, 0, 0}, {0, 0, 0, -1, 2, -1, 0, 0}, {0, 0, 0, 0, -1, 2, -1, -1}, {0, 0, 0, 0, 0, -1, 2, 0}, {0, 0, 0, 0, 0, -1, 0, 2}}; E4q = 1 + 240 Sum[DivisorSigma[3, n] q^n, {n, 1, 6}]; inv8 = Series[Product[(1 - q^n)^-8, {n, 1, 6}], {q, 0, 4}]; chiSeries = Series[E4q inv8, {q, 0, 4}]; coeffs = CoefficientList[Normal[chiSeries], q]; checkExact[\"v457 SEAM.EQUIV.KILLTEST.01 (i): the (E8)_1 character tower chi=E4/eta^8=q^{-1/3}(1+248q+4124q^2+34752q^3+...); E4/Product(1-q^n)^8 q-series coeffs {1,248,4124,34752} -- the exact (E8)_1 conformal-tower degeneracies\", Take[coeffs, 4] == {1, 248, 4124, 34752}]; checkExact[\"v457 SEAM.EQUIV.KILLTEST.01 (ii): the kill-test discriminators -- weight-1 count 248=dim E8=120(SO16)+128(spinor); |det Cartan(E8)|=1 (invertible, one sector) vs |det Cartan(D8=SO16)|=4 (four sectors); a measured 120 or 4 would FALSIFY (E8)_1, the data give 248/1\", 120 + 128 == 248 && Det[cartanE8] == 1 && Abs[Det[cartanD8]] == 4]; (* v459: E8 even unimodular + the 240 roots split 112+128; 248=8+240=120+128 *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2847","line_end":2873,"line_start":2847,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v457","v459"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":[],"checked_by_registry":false,"heading_as_written":"(* ==== v461/v462 round: the Kapustin-Fidkowski strict-locality obstruction (integer logic; the Wilson-loop winding/Chern themselves are numerical, Python-only) and the 128-spinor extension at character level -- the Jacobi/E8 theta identity theta2^8+theta3^8+theta4^8=2E4 (so the (E8)_1 character is the SO(16)_1 vacuum+spinor sum) and the 120+128=248 sector + finite 16-Majorana Fock counts; mirrors v461/v462. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2874","line_end":2880,"line_start":2874,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v461","v462"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v461 SEAM.S3.LOCALITY.01: the Kapustin-Fidkowski strict-locality obstruction (integer logic) -- the Wannier/Wilson-loop winding=|C|=1!=0 and c_-=2^(g_car-1)*|C|/2=8=g_car+N_fam=rank E8!=0; a strictly finite-range commuting projector would force winding 0 => C=-C => C=0 (Solve[c==-c]={c->0}), contradicting C=1, so it is forbidden (the Wilson-loop winding/Chern themselves are numerical, Python-only)"],"checked_by_registry":false,"heading_as_written":"(* v461: tied obstruction integers + the reflection forcing (strict-local => C=-C => C=0) *) cMinus = 2^(gcar - 1)*1/2; (* 16*|C|/2 = 8, |C|=1 *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2881","line_end":2885,"line_start":2881,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v461"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v462 SEAM.EQUIV.SPINOR.01 (i): the Jacobi/E8 theta identity theta2^8+theta3^8+theta4^8 = 2 E4 => chi_{(E8)_1}=E4/eta^8 = chi_o^{SO16}+chi_s^{SO16} (the holomorphic (E8)_1 character IS the SO(16)_1 vacuum + spinor sector sum, the conformal embedding SO(16)_1 in (E8)_1)","v462 SEAM.EQUIV.SPINOR.01 (ii): the (E8)_1 weight-1 multiplicity 248 = SO(16)_1 vacuum 120 (C(16,2) bilinear so(16) currents) + spinor 128 (=2^{16/2}/2, half the Ramond ground space); 2^{16/2}=256=128+128, 120+128=248=dim E8 -- the 128 spinor fills the (E8)_1 - SO(16)_1 deficit"],"checked_by_registry":false,"heading_as_written":"(* v462 (i): the Jacobi/E8 theta identity theta2^8+theta3^8+theta4^8 = 2 E4 (numerical at q=1/50) *) qq = N[1/50, 50]; th2 = 2 qq^(1/8) Sum[qq^(n (n + 1)/2), {n, 0, 30}]; th3 = 1 + 2 Sum[qq^(n^2/2), {n, 1, 30}]; th4 = 1 + 2 Sum[(-1)^n qq^(n^2/2), {n, 1, 30}]; qE4 = 1 + 240 Sum[DivisorSigma[3, n] qq^n, {n, 1, 40}]; check[\"v462 SEAM.EQUIV.SPINOR.01 (i): the Jacobi/E8 theta identity theta2^8+theta3^8+theta4^8 = 2 E4 => chi_{(E8)_1}=E4/eta^8 = chi_o^{SO16}+chi_s^{SO16} (the holomorphic (E8)_1 character IS the SO(16)_1 vacuum + spinor sector sum, the conformal embedding SO(16)_1 in (E8)_1)\", th2^8 + th3^8 + th4^8, 2 qE4, 10^-20]; (* v462 (ii): (E8)_1 weight-1 = SO(16)_1 vacuum 120 + spinor 128; finite 16-Majorana Fock *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2886","line_end":2903,"line_start":2886,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v462"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":[],"checked_by_registry":false,"heading_as_written":"(* ==== v463 round: the c=8 holomorphic-uniqueness pin -- c=8 has THREE level-1 candidates (A8/80, D8/120, E8/248), but holomorphy forces dim V_1 = E4/eta^8 q^1 coeff = 248 => E8 uniquely; mirrors v463 (the c8 candidates + the forced 248 + the E4/eta^8 tower). v464 (one-particle realization rigidity) is numerical (symbol convergence), Python-only. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2904","line_end":2909,"line_start":2904,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v463","v464"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v463 SEAM.EQUIV.UNIQ.01 (i): c=8 is NOT unique at level 1 -- A8 (dim 80), D8=so(16) (dim 120), E8 (dim 248) all satisfy dim=8*(1+h^v) (c=dim/(1+h^v)=8); holomorphy forces dim V_1 = (E4/eta^8 q^1 coeff) = 248 = dim E8, EXCLUDING the gleich-c rivals A8 (80) and D8 (120) -- 'c=8' is promoted to 'E8' uniquely"],"checked_by_registry":false,"heading_as_written":"(* v463 (i): c=dim/(1+h^v)=8 has three simple solutions; holomorphy forces 248=dim E8 *) cand = {{\"A8\", 80, 9}, {\"D8\", 120, 14}, {\"E8\", 248, 30}}; forced = 248; (* the E4/eta^8 q^1 coefficient *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2910","line_end":2915,"line_start":2910,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v463"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v463 SEAM.EQUIV.UNIQ.01 (ii): the holomorphic c=8 partition function is the unique j^{1/3}=E4/eta^8, whose q-coefficients are the (E8)_1 tower {1,248,4124,34752,213126} -- the q^1=248 is the forced weight-1 dimension (Dong-Mason/Schellekens: the holomorphic c=8 VOA is unique = V_{E8})"],"checked_by_registry":false,"heading_as_written":"(* v463 (ii): the (E8)_1 tower = E4/eta^8 coefficients {1,248,4124,34752,213126} *) inv8 = Series[Product[(1 - q^n)^-8, {n, 1, 6}], {q, 0, 5}]; chiSer = Series[(1 + 240 Sum[DivisorSigma[3, n] q^n, {n, 1, 6}]) inv8, {q, 0, 5}]; tower = CoefficientList[Normal[chiSer], q][[1 ;; 5]]; checkExact[\"v463 SEAM.EQUIV.UNIQ.01 (ii): the holomorphic c=8 partition function is the unique j^{1/3}=E4/eta^8, whose q-coefficients are the (E8)_1 tower {1,248,4124,34752,213126} -- the q^1=248 is the forced weight-1 dimension (Dong-Mason/Schellekens: the holomorphic c=8 VOA is unique = V_{E8})\", tower == {1, 248, 4124, 34752, 213126}]; ]; (* ==== v469 round: the net-level crossed-product certification -- the LR locality integers (h_s(SO(16)_1) = 16/16 = 1 in Z; the mu4 glue h(J^k) = {1,1,1} all integer), the KLM mu-index arithmetic (4/2^2 = 1 and 16/4^2 = 1, both holomorphic) and the Kitaev 16-fold-way pin (nu = 16 x |C| = 16 = 0 mod 16, c_- = nu/2 = 8 = g_car+N_fam); mirrors v469 (the FHS Chern itself is numerical, Python-only). ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2916","line_end":2929,"line_start":2916,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v463","v469"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v469 SEAM.EQUIV.CROSSEDPRODUCT.01 (i): the LR locality integers -- the SO(16)_1 spinor has h_s = 16/16 = 1 in Z (statistics phase +1, the Longo-Rehren locality criterion for the Z2 simple-current crossed product), and the index-4 mu4 glue J = (s,Lambda1) of (D5)_1 x (A3)_1 has h(J^k) = {1,1,1} for k = 1,2,3 ALL integer (5/8+3/8 = 1, 1/2+1/2 = 1) -- the v125 isotropy q(k(1,1)) = k^2 at net level"],"checked_by_registry":false,"heading_as_written":"(* v469 (i): the LR locality integers of both extension routes *) hs = 16/16; (* so(N)_1 spinor weight N/16, N = 16 *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2930","line_end":2936,"line_start":2930,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v469"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v469 SEAM.EQUIV.CROSSEDPRODUCT.01 (ii): KLM mu-index -- both routes land holomorphic, mu = 4/2^2 = 1 (index-2 SO(16)_1 route) and mu = 16/4^2 = 1 (index-4 mu4 route); and the Kitaev 16-fold-way pin nu = 16 x |C| = 16 = 0 mod 16 with c_- = nu/2 = 8 = g_car + N_fam = rank E8 (the class-D phase whose edge is the purely bosonic (E8)_1 state)","v470 ALPHA.QUILLEN.INFLOW.01: the embedding-index rigidity -- k_Y = tr_5bar(Y^2)/tr(T3^2) = (5/6)/(1/2) = 5/3 (Ginsparg 1987), so (1/k_Y) x 41/6 = 3/5 x 41/6 = 41/10 = b1 (the 'GUT 3/5' IS the inverse embedding index); carrier decomposition 41/6 = 20/3 (fermions, 3 generations x 16-content) + 1/6 (Higgs doublet)"],"checked_by_registry":false,"heading_as_written":"(* v469 (ii): KLM mu-index + the 16-fold-way pin *) muI2 = 4/2^2; muI4 = 16/4^2; nu = 16*1; cminus = nu/2; checkExact[\"v469 SEAM.EQUIV.CROSSEDPRODUCT.01 (ii): KLM mu-index -- both routes land holomorphic, mu = 4/2^2 = 1 (index-2 SO(16)_1 route) and mu = 16/4^2 = 1 (index-4 mu4 route); and the Kitaev 16-fold-way pin nu = 16 x |C| = 16 = 0 mod 16 with c_- = nu/2 = 8 = g_car + N_fam = rank E8 (the class-D phase whose edge is the purely bosonic (E8)_1 state)\", muI2 == 1 && muI4 == 1 && Mod[nu, 16] == 0 && cminus == 8 && cminus == 5 + 3]; ]; (* ==== v470 round: the alpha^3 level / embedding-index rigidity -- the exact k_Y = 5/3 arithmetic (tr Y^2 / tr T3^2 over the 5bar), the b1 conversion (3/5)(41/6) = 41/10, and the carrier decomposition 41/6 = 20/3 + 1/6; mirrors v470 (the FHS Chern and the alpha^-1 root re-verification are numerical, Python-only). ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2937","line_end":2956,"line_start":2937,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v469","v470"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":[],"checked_by_registry":false,"heading_as_written":"(* ==== v473 round: the entropic-action bridge (Bianconi, PRD 111, 066001 (2025); arXiv:2408.14391) -- the exact algebraic content: the carrier Hodge count 1+5+10 = 16 = 2^(g_car-1) (vs the 4d fiber 11), the coefficient pin beta'_B = c3/6 = 1/(48 pi) from 3 beta' = 1/(16 pi), the entropy potential s(x) = x-1-ln x (nonnegative, quadratic minimum), the Lambda-channel target Tr Q^2 = 32 c3^4 = 1/(128 pi^4) = (2/3) delta_top, and the R^2 kill-test gap 3 c3^-9 = 3 (8 pi)^9; mirrors v473 (the Frullani quadrature is numerical, Python-only). ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2957","line_end":2967,"line_start":2957,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v473"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v473 GRAV.ENTROPIC.ACTION.01 (i): the carrier Hodge count -- dim Omega^{0,1,2}(C^5) = 1+5+10 = 16 = 2^(g_car-1) = dim S+_{D5} (Hodge-folded onto L^even C^5 = 1+10+5), while on 4d spacetime the fiber is only 1+4+6 = 11 (the 16 REQUIRES the five-slot carrier); and the coefficient pin -- her weak-coupling 3 beta' R matched to the TFPT EH normalisation 1/(16 pi G) = c3/(2G) fixes beta'_B = c3/6 = 1/(48 pi) exactly (the 6 = 3 form blocks x 2 = p2 = |R+(A3)|)","v473 GRAV.ENTROPIC.ACTION.01 (ii): the entropy potential s(x) = x-1-ln x has s(1) = 0, s''(1) = 1, series eps^2/2 - eps^3/3 (Lambda_G nonnegative, QUADRATIC at the fixed point); with eps_* = e^{-1/alpha} Q and beta' = c3/6, l_P^2 Mbar^2 = c3, the v60 branch (3/4 pi^2) e^{-2/alpha} forces the EXACT target Tr Q^2 = 32 c3^4 = 1/(128 pi^4) = (2/3) delta_top"],"checked_by_registry":false,"heading_as_written":"(* v473 (i): carrier Hodge count + coefficient pin *) dims = Table[Binomial[5, k], {k, 0, 2}]; fiber4d = Total[Table[Binomial[4, k], {k, 0, 2}]]; betaP = bp /. First[Solve[3 bp == 1/(16 Pi), bp]]; checkExact[\"v473 GRAV.ENTROPIC.ACTION.01 (i): the carrier Hodge count -- dim Omega^{0,1,2}(C^5) = 1+5+10 = 16 = 2^(g_car-1) = dim S+_{D5} (Hodge-folded onto L^even C^5 = 1+10+5), while on 4d spacetime the fiber is only 1+4+6 = 11 (the 16 REQUIRES the five-slot carrier); and the coefficient pin -- her weak-coupling 3 beta' R matched to the TFPT EH normalisation 1/(16 pi G) = c3/(2G) fixes beta'_B = c3/6 = 1/(48 pi) exactly (the 6 = 3 form blocks x 2 = p2 = |R+(A3)|)\", Total[dims] == 16 && dims == {1, 5, 10} && Total[{1, 10, 5}] == 16 && fiber4d == 11 && betaP == c3v/6 && betaP == 1/(48 Pi) && Binomial[4, 2] == 6]; (* v473 (ii): entropy potential + Lambda-channel target *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2968","line_end":2984,"line_start":2968,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v473"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v473 GRAV.ENTROPIC.ACTION.01 (iii): the R^2 kill-test gap -- raw log-expansion coefficient (c3/6)^2 vs the TFPT Starobinsky 1/(12 c3^7) (M_scal^2 = c3^7 Mbar^2) mismatch EXACTLY 3 c3^-9 = 3 (8 pi)^9 ~ 1.2e13 (13 orders): direct identification FALSE without a mechanism -- the pre-registered kill test"],"checked_by_registry":false,"heading_as_written":"(* v473 (iii): the R^2 kill-test gap *) gap = Simplify[(1/(12 c3v^7))/((c3v/6)^2)]; checkExact[\"v473 GRAV.ENTROPIC.ACTION.01 (iii): the R^2 kill-test gap -- raw log-expansion coefficient (c3/6)^2 vs the TFPT Starobinsky 1/(12 c3^7) (M_scal^2 = c3^7 Mbar^2) mismatch EXACTLY 3 c3^-9 = 3 (8 pi)^9 ~ 1.2e13 (13 orders): direct identification FALSE without a mechanism -- the pre-registered kill test\", gap == 3 (8 Pi)^9 && Abs[N[gap] - 1.2002728758784*^13]/1.2*^13 < 10^-3]; ]; (* ==== v474 round: the operator level of the entropic-action bridge -- the exact arithmetic content: the Q-target enumeration d k^2 = 32 with integer k has exactly the supports (2,4), (8,2), (32,1) = {|Z2|, rank E8, 2^g_car} with the 10/16 blocks excluded (irrational multipliers) and the mode-ratio identity Tr Q^2/delta_top = 32/48 = 2/3; and the fold-is-conjugation weight identity: the traceless u(5) weights of Lambda^4 are the negatives of those of Lambda^1 (5 -> 5bar), with the Pascal blocks {1,5,10} vs {1,10,5}; mirrors v474 (the 32x32 Fock/Clifford matrix checks are Python-only). ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:2985","line_end":2999,"line_start":2985,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v473","v474"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v474 GRAV.ENTROPIC.HODGE.01 (i): the Q-target enumeration -- Tr Q^2 = d k^2 c3^4 = 32 c3^4 with INTEGER k has exactly the supports (d,k) = (2,4), (8,2), (32,1) = {|Z2|, g_car+N_fam = rank E8, 2^g_car = dim Lambda^* C^5}; the two-form block d = 10 needs Sqrt[16/5] and the fiber d = 16 needs Sqrt[2] (both irrational, the naive pair-block reading KILLED); minimal uniform q = c3^2 = 1/(64 pi^2); mode-ratio identity 32 c3^4 / delta_top = 32/48 = 2/3","v474 GRAV.ENTROPIC.HODGE.01 (ii): the fold is the 5 -> 5bar conjugation -- the traceless u(5) weights of Lambda^4 C^5 are EXACTLY the negatives of those of Lambda^1 (multisets equal), so the Hodge fold conjugates the vector block and Bianconi's fiber 1+5+10 becomes the GUT half-spinor 16 = 1 + 5bar + 10; Pascal blocks {1,5,10} (fiber) vs {1,10,5} (even)"],"checked_by_registry":false,"heading_as_written":"(* v474 (i): Q-target enumeration + mode-count ratio *) sols = Select[Table[{d, Sqrt[32/d]}, {d, 1, 32}], IntegerQ[#[[2]]] &]; q32 = (1/(8 Pi))^2; checkExact[\"v474 GRAV.ENTROPIC.HODGE.01 (i): the Q-target enumeration -- Tr Q^2 = d k^2 c3^4 = 32 c3^4 with INTEGER k has exactly the supports (d,k) = (2,4), (8,2), (32,1) = {|Z2|, g_car+N_fam = rank E8, 2^g_car = dim Lambda^* C^5}; the two-form block d = 10 needs Sqrt[16/5] and the fiber d = 16 needs Sqrt[2] (both irrational, the naive pair-block reading KILLED); minimal uniform q = c3^2 = 1/(64 pi^2); mode-ratio identity 32 c3^4 / delta_top = 32/48 = 2/3\", sols == {{2, 4}, {8, 2}, {32, 1}} && ! Element[Sqrt[32/10], Rationals] && ! Element[Sqrt[32/16], Rationals] && Simplify[q32 - 1/(64 Pi^2)] == 0 && 32/48 == 2/3]; (* v474 (ii): the fold is the 5 -> 5bar conjugation (traceless u(5) weights) *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:3000","line_end":3015,"line_start":3000,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v474"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":[],"checked_by_registry":false,"heading_as_written":"(* ==== v475 round: the R^2 kill test of the entropic-action bridge, executed -- the exact content: the maximally-symmetric eigenvalues {R, R/4 x4, R/6 x6} of R~ g~^-1 (incl. the 6x6 two-form flattening), the exact vacuum f(R) series 3 b R + (17/24) b^2 R^2, the raw scalaron mass m^2 = 4608 pi^2/17 Mbar^2 with the enhancement (72/17)(8 pi)^9, the domain pole 384 pi^2 Mbar^2, and the Lorentzian timelike witness 1 - alpha v^2; mirrors v475 (all exact). ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:3016","line_end":3024,"line_start":3016,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v475"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v475 GRAV.ENTROPIC.SCALARON.01 (i): maximally symmetric eigenvalues of the relative curvature operator -- on a general diagonal 4d metric with R_munurhosigma = (R/12)(gg - gg), the Ricci block is (R/4) Id_4 and the flattened 6x6 Riemann-on-2-forms block is (R/6) Id_6 (Bianconi's Appendix-B flattening verified); with the scalar block R the eigenvalues are exactly {R; R/4 x4; R/6 x6}","v475 GRAV.ENTROPIC.SCALARON.01 (ii): the exact vacuum f(R) = 3 b R + (17/24) b^2 R^2 + O(R^3) (the 3 re-derives Eq. (45) = the v473 pin; 17/24 = (1/2)(1+1/4+1/6) the exact tensorial factor); with beta' = c3/6 the EH normalisation matches identically and BOTH routes give the raw scalaron m^2 = 4608 pi^2/17 Mbar^2 (~51.7 Mbar, trans-Planckian); required enhancement EXACTLY (72/17)(8 pi)^9 -- v473's interpretation 2 killed in naive form; domain pole 1/beta = 384 pi^2 Mbar^2"],"checked_by_registry":false,"heading_as_written":"(* v475 (i): maximally symmetric eigenvalues incl. the 6x6 flattening *) gm = DiagonalMatrix[{gg0, gg1, gg2, gg3}]; ginv = Inverse[gm]; riem[m_, n_, r_, s_] := (RR/12) (gm[[m, r]] gm[[n, s]] - gm[[m, s]] gm[[n, r]]); ricci = Table[Sum[riem[m, a, n, b] ginv[[a, b]], {a, 4}, {b, 4}], {m, 4}, {n, 4}]; n1 = Simplify[ricci . ginv]; prs = Subsets[Range[4], {2}]; g2f = Table[gm[[prs[[A, 1]], prs[[B, 1]]]] gm[[prs[[A, 2]], prs[[B, 2]]]] - gm[[prs[[A, 1]], prs[[B, 2]]]] gm[[prs[[A, 2]], prs[[B, 1]]]], {A, 6}, {B, 6}]; r2f = Table[2 riem[prs[[A, 1]], prs[[A, 2]], prs[[B, 1]], prs[[B, 2]]], {A, 6}, {B, 6}]; n2 = Simplify[r2f . Inverse[g2f]]; checkExact[\"v475 GRAV.ENTROPIC.SCALARON.01 (i): maximally symmetric eigenvalues of the relative curvature operator -- on a general diagonal 4d metric with R_munurhosigma = (R/12)(gg - gg), the Ricci block is (R/4) Id_4 and the flattened 6x6 Riemann-on-2-forms block is (R/6) Id_6 (Bianconi's Appendix-B flattening verified); with the scalar block R the eigenvalues are exactly {R; R/4 x4; R/6 x6}\", n1 == (RR/4) IdentityMatrix[4] && n2 == (RR/6) IdentityMatrix[6]]; (* v475 (ii): exact vacuum f(R) series + the raw scalaron mass, two routes *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:3025","line_end":3051,"line_start":3025,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v475"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v475 GRAV.ENTROPIC.SCALARON.01 (iii): the Lorentzian-positivity witness -- on Minkowski a TIMELIKE gradient gives G g^-1 eigenvalues {1 - alpha v^2, 1, 1, 1} (nonpositive for v^2 >= 1/alpha, ln undefined) while a SPACELIKE gradient gives {1 + alpha v^2, 1, 1, 1} (positive for all v) -- the v473 caveat exhibited, the OS route sturdier"],"checked_by_registry":false,"heading_as_written":"(* v475 (iii): the Lorentzian timelike positivity witness *) gL = DiagonalMatrix[{-1, 1, 1, 1}]; mM = Outer[Times, {vv, 0, 0, 0}, {vv, 0, 0, 0}]; evT = Sort[Eigenvalues[(gL + aal mM) . Inverse[gL]]]; evS = Sort[Eigenvalues[(gL + aal Outer[Times, {0, vv, 0, 0}, {0, vv, 0, 0}]) . Inverse[gL]]]; checkExact[\"v475 GRAV.ENTROPIC.SCALARON.01 (iii): the Lorentzian-positivity witness -- on Minkowski a TIMELIKE gradient gives G g^-1 eigenvalues {1 - alpha v^2, 1, 1, 1} (nonpositive for v^2 >= 1/alpha, ln undefined) while a SPACELIKE gradient gives {1 + alpha v^2, 1, 1, 1} (positive for all v) -- the v473 caveat exhibited, the OS route sturdier\", Sort[evT] == Sort[{1 - aal vv^2, 1, 1, 1}] && Sort[evS] == Sort[{1 + aal vv^2, 1, 1, 1}]]; ]; (* ==== v477 round: the scale-flow representation of the entropic action -- the exact content: the Frullani identity Integrate[(e^{-a t}-e^{-t})/t] = -Log[a], the moment dictionary (flat weight = unit moments = the v475 raw coefficients 3 b R + (17/24) b^2 R^2), the ONE moment condition mu2/mu1^2 = (72/17)(8 pi)^9 with the exact closure (4608 pi^2/17)/((72/17)(8 pi)^9) = c3^7, and the v36 consistency f0 = 6 (4 pi)^2/c3^7 <=> M^2 = c3^7 Mbar^2; mirrors v477 (the chi-form quadrature is numerical, Python-only). ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:3052","line_end":3070,"line_start":3052,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v36","v473","v475","v477"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v477 GRAV.ENTROPIC.SCALEFLOW.01 (i): the Frullani/scale-flow identity -Log[a] = Integrate[(e^{-a t}-e^{-t})/t] (symbolic) and the moment dictionary -- at the FLAT weight the maximally-symmetric relative trace integrates to exactly the v475 raw coefficients 3 b R + (17/24) b^2 R^2 (unit moments mu1 = mu2 = 1): the raw entropic action is the unit-moment point of a scale-measure family","v477 GRAV.ENTROPIC.SCALEFLOW.01 (ii): the ONE moment condition -- demanding m^2 = c3^7 Mbar^2 forces mu2/mu1^2 = (72/17)(8 pi)^9 (the v475 kill-test number IS a moment ratio), and the closure identity (4608 pi^2/17)/((72/17)(8 pi)^9) = c3^7 holds IDENTICALLY; v36 consistency: f0 = 6(4 pi)^2/c3^7 <=> M^2/Mbar^2 = c3^7 -- one KMS moment, two parametrisations, zero new dials"],"checked_by_registry":false,"heading_as_written":"(* v477 (i): Frullani + the moment dictionary at flat weight *) frul = Integrate[(Exp[-aa tt] - Exp[-tt])/tt, {tt, 0, Infinity}, Assumptions -> aa > 0]; eig = Join[{1}, Table[1/4, 4], Table[1/6, 6]]; tr = Total[Exp[-tt (1 - bb # RR)] & /@ eig] - 11 Exp[-tt]; serR = Normal[Series[tr, {RR, 0, 2}]]; mu1f = Integrate[Coefficient[serR, RR, 1]/tt, {tt, 0, Infinity}]; mu2f = Integrate[Coefficient[serR, RR, 2]/tt, {tt, 0, Infinity}]; checkExact[\"v477 GRAV.ENTROPIC.SCALEFLOW.01 (i): the Frullani/scale-flow identity -Log[a] = Integrate[(e^{-a t}-e^{-t})/t] (symbolic) and the moment dictionary -- at the FLAT weight the maximally-symmetric relative trace integrates to exactly the v475 raw coefficients 3 b R + (17/24) b^2 R^2 (unit moments mu1 = mu2 = 1): the raw entropic action is the unit-moment point of a scale-measure family\", frul == -Log[aa] && Simplify[mu1f - 3 bb] == 0 && Simplify[mu2f - (17/24) bb^2] == 0]; (* v477 (ii): the one moment condition + closure + v36 consistency *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:3071","line_end":3087,"line_start":3071,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v36","v475","v477"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v479 SEAM.KRONHEIMER.01 (i): the Kac marks {1,2,2,3,3,4,4,5,6} are simultaneously the null vector of the affine-E8 Cartan matrix (C_aff delta = 0) and the Perron eigenvector of the McKay graph (A delta = 2 delta) -- the v312 rewrite-attractor vector, i.e. Kronheimer's quiver dimension vector","v479 SEAM.KRONHEIMER.01 (ii): the Kronheimer hyper-Kaehler quotient dimension count -- dim_R M - 4 dim_R G = 4(sum_edges d_i d_j - sum d_i^2 + 1) = 4 (the C^2/Gamma geometry), with sum_edges d_i d_j = sum d_i^2 = 120 = |2I| = |mu4| h(E8) forced by the null identity (h(E8) = 30 = 2*3*5); and the finite-E8 Cartan is unimodular with Smith normal form = identity (the Poincare-sphere link = the det K = 1 face) with 3*8 = 24 deformation parameters"],"checked_by_registry":false,"heading_as_written":"(* ==== v479 round: the Kronheimer quiver bridge -- the exact content: the Kac marks are the null vector of the affine-E8 Cartan matrix AND the Perron vector (A delta = 2 delta) with multiset {1,2,2,3,3,4,4,5,6} = 2I irrep dims; the hyper-Kaehler quotient dimension count dim_R M - 4 dim_R G = 4 with sum_edges d_i d_j = sum d_i^2 = 120 = |mu4| h(E8), h(E8) = 30 = 2*3*5; and the finite-E8 Cartan is unimodular with Smith normal form = identity (the Poincare-sphere link, the det K = 1 face); mirrors v479. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:3088","line_end":3115,"line_start":3088,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v479"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v491 P2.PARTITION.01 (i): 4 into exactly 3 positive integer parts is UNIQUELY {1,1,2}; e = (e1,e2,e3) = (4,5,2), so g_car = e2 = 5, |Z2| = e3 = 2, N_fam = e2 - e3 = 3 are corollaries, and the carrier formula closes as a fixed point (2^4-1)/5 = 3 = rank H^1 = #marks - 1","v491 P2.PARTITION.01 (ii): negative controls -- drop positivity: 4 solutions, e2 ambiguous {0,3,4,5}; sum 3: unique but e2 = 3; sum 5: NOT unique; 2 parts: e2 in {3,4}; 4 parts: e2 = 6 -- every assumption is load-bearing","v491 P2.PARTITION.01 (iii): integrality control -- Mehta-Seshadri RATIONAL weights (sum 1, scaled by 4) give e2 = 16/3 resp. 44/9 != 5 (integrality = the Birkhoff-Grothendieck splitting-type typing); v53 sharpening -- all-three-targets search == only-e1=4 search == {1,1,2}; sum rule 4(N-1)/2 = 4 iff N = 3, and |a|_1 = |mu4| tr(A0) = 4(0 + 1/3 + 2/3) = 4"],"checked_by_registry":false,"heading_as_written":"(* ==== v491 round: P2.PARTITION.01 -- g_car = 5 as the partition corollary of the four marks (the sharpening of v53). Exact content: 4 into exactly 3 positive integer parts is uniquely {1,1,2} => e = (4,5,2) => g_car = e2 = 5, |Z2| = e3 = 2, N_fam = e2 - e3 = 3 as corollaries; every assumption load-bearing (positivity / sum / part count / integrality negative controls); v53 needs all three targets, the partition only e1 = 4; sum rule 4(N-1)/2 = 4 iff N = 3; mirrors v491. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:3116","line_end":3146,"line_start":3116,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v491","v53"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v493 CELEST.WP2.01 (i): P(iZ) = P(Z) forces a3 = a2 = a1 = 0 (SHARP, two-sided: prod_k (Z - i^k w) = Z^4 - w^4), disc(Z^4 + a0) = 256 a0^3, and the branch points of Z^4 = t^4 are ONE free mu4 orbit with cross-ratio 2 and j(2) = 1728 -- the clock-invariant deformation is the 1-parameter family XY = Z^4 + a0 with the tau = i pillowcase configuration in every fibre","v493 CELEST.WP2.01 (ii): PILLOWCASE FROZEN -- w^2 = Z^4 + a0 has I = 12 a0, J = 0 IDENTICALLY, so j = 6912 I^3/(4I^3 - J^2) = 1728 for every a0 != 0 (a0 = pure scale, no shape modulus); negative controls: the a1-deformation has I = 0 (j = 0, hexagonal CM point) and the a2-instance u = 1, v = 2 gives cross-ratio 8/9 with j = 1556068/81 != 1728 -- the clock-variant directions move the shape, a0 never does","v493 CELEST.WP2.01 (iii): COXETER MONODROMY -- the clock acts on H2 as A with A^4 = 1, char poly x^3+x^2+x+1, eigenvalues {i,-1,-i} = the A3 exponents (h(A3) = 4 = |mu4| = N_fam + 1), det(A - 1) = -4 (no invariant cycle); the period point Pi = t(i-1)(1,i,i^2) sits on the chi_1-Fourier eigenline (A^T v = i v); the versal clock weights are (a3,a2,a1,a0) -> (i,-1,-i,1) = the regular mu4 representation with invariant line a0 alone","v493 CELEST.WP2.01 (iv): S-ALGEBRA CORRECTIONS -- the reduction Z^r Z^r' mod (Z^4 - XY + a0) picks up corrections exactly at the Z4 wrap r+r' >= 4 (6 of 16 basic products), each exactly LINEAR in a0; the EH k = 2 analogue reduces Z*Z to XY - c^2 (one wrap pair, linear in c^2) -- the BHS c^2 pattern transfers to k = 4 with a0 in the weight-0 slot"],"checked_by_registry":false,"heading_as_written":"(* ==== v493 round: CELEST.WP2.01 -- the clock-invariant deformation XY = Z^4 + a0 of the A3 seam orbifold (WP2 of CELEST.SEAM.01). Exact content mirrored: clock-invariance selects the 1-parameter slice sharply (P(iZ) = P(Z) forces a3 = a2 = a1 = 0; prod(Z - i^k w) = Z^4 - w^4); disc = 256 a0^3; binary-quartic invariants I = 12 a0, J = 0 identically => j = 1728 frozen (tau = i pillowcase), cross-ratio 2; negative controls a1 (j = 0) and a2-instance (j = 1556068/81); clock on H2 = Coxeter element of W(A3) (char x^3+x^2+x+1, eigenvalues {i,-1,-i}, no invariant cycle, chi_1-Fourier eigenline, period point t(i-1)(1,i,i^2)); versal weights (1,2,3,0) = regular mu4 rep; S-algebra corrections linear in a0 at the Z4 wrap (6/16 pairs) with the EH k = 2 analogue; mirrors v493. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:3147","line_end":3208,"line_start":3147,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v493"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v495 CELEST.WP3.01 (i): DELIGNE CLOSED FORM -- lambda~^2 = 10 h_vee^2/(dim+2) = h_vee + 6 EXACTLY for all 8 algebras on Costello's list, values (8,9,10,12,15,18,24,36); dimension formula dim = 2(5h_vee-6)(h_vee+1)/(h_vee+6) exact; fundamental-trace lambda^2 = (h_vee+6)/i^2 = (8,9,5/2,3,5/12,1/2,1/6,1/100) with i_R = (1,1,2,2,6,6,12,60); E8: lambda~ = 6, lambda_fund = 1/10 exact","v495 CELEST.WP3.01 (ii): E8 ALIGNMENT -- kappa = lambda_g/(8 pi sqrt 3) gives (kappa/c3)^2 = lambda^2/3 = 36/3 = 12 = |mu4| N_fam (unit-trace) resp. (1/100)/3 = 1/300 (adjoint-trace), both exact anchor rationals; kappa/c3 ITSELF is irrational (2 sqrt 3 resp. 1/(10 sqrt 3)); anchors h_vee = 30 = 2*3*5 (all three atoms once), EulerPhi(30) = 8 = rank, dim+2 = 250 = 2*5^3, lambda~ = 6 = |Z2| N_fam, lambda_fund = 1/10 = 1/(|Z2| g_car); so8 slip: Costello's own weight content gives Sum w^4 = 192, lambda^2 = 192/64 = 3 (Okubo-consistent 12/4), NOT the printed 3/2","v495 CELEST.WP3.01 (iii): LOOK-ELSEWHERE PASS COUNTS (alignment != selection) -- '(kappa/c3)^2 rational' passes 8/8 by construction and 'h_vee {2,3,5}-smooth' 8/8 (zero selectivity); 'lambda~ integer' 2/8 (positions {2,8} = sl3, e8); 'g_car = 5 | h_vee' 1/8 (position {8} = e8 ONLY); 'phi(h_vee) = rank' 4/8 (sl2, sl3, g2, e8); 'phi(h) = rank' 5/8 (+f4); e8 exponents = totatives of 30 = {1,7,11,13,17,19,23,29}, sum 120 = #positive roots, degrees product 696729600 = |W(E8)|"],"checked_by_registry":false,"heading_as_written":"(* ==== v495 round: CELEST.WP3.01 -- the Green-Schwarz axion coefficient lambda_g (Costello) vs c3 = 1/(8 pi) (WP3 of CELEST.SEAM.01, alignment test only). Exact content mirrored: the Deligne closed form lambda~^2 = 10 h_vee^2/(dim+2) = h_vee + 6 for all 8 algebras on Costello's list, with the dimension formula dim = 2(5h_vee-6)(h_vee+1)/(h_vee+6) and the fundamental-index values (h_vee+6)/i^2; the E8 alignment (kappa/c3)^2 = lambda^2/3 = 12 = |mu4| N_fam resp. 1/300 with kappa/c3 itself irrational; the so8 factor-2 slip (exact 3, printed 3/2); the look-elsewhere pass counts (smooth 8/8, lambda-integrality 2/8 = {sl3, e8}, g_car | h_vee 1/8 = {e8}, phi(h_vee) = rank 4/8, phi(h) = rank 5/8) and the e8 exponents = totatives of 30; mirrors v495. The Okubo root-sum identity itself is polynomial (verified in Python from explicit root systems); its arithmetic consequence lambda~^2 = h_vee + 6 is mirrored here. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:3209","line_end":3256,"line_start":3209,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v495"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v496 CELEST.WP4.01 (i): CHARACTER SIDE EXACT -- chi_(E8)_1 = E4/eta^8 = (1, 248, 4124, 34752, 213126, 1057504, 4530744) through q^6 (the v377/v492 series extended); machinery cross-check q j(tau) = E4^3/eta^24 = (1, 744, 196884, 21493760); Sugawara c = 248/31 = 8 = 2|mu4| and the null-ideal bookkeeping 4124 = 1 + 248 + 3875, Sym^2(248) = 1 + 3875 + 27000 = 30876","v496 CELEST.WP4.01 (ii): EQUIVARIANT HILBERT SERIES -- chi_sp(t) = (60 + 128 t + 60 t^2)/(1-t^2)^2 reproduces the tower D[d] = 60(d+1) even / 64(d+1) odd exactly (d <= 12), palindromic numerator with 60+128+60 = 248 at t = 1; cumulative generator count QUADRATIC 31 s^2 + 92 s + 60 (even) / 31 s^2 + 94 s + 63 (odd) with 31 = k + h_vee and 31*8 = 248; the SU(2)_+ primary slice (60+64t)/(1-t^2) cycles (60,64,60,64) -- bounded but never (1, 248, ...)","v496 CELEST.WP4.01 (iii): MISMATCH LOCALISED -- equivariant jet Fock f = (1, 128, 8436, 381056) vs chi = (1, 248, 4124, 34752): TWO-SIDED failure (f1 = 128 < 248 undercount, f2 = 8436 > 4124 overcount); f_n/chi_n strictly increasing for n = 1..12 (exact cross-multiplication); free-current level-2 count 31124 = 248 + Sym^2(248), character keeps 4124, deficit EXACTLY 27000 = 30^3 = h_vee^3 (the (E8)_1 null ideal, absent from the jets; level 1 agrees 248 = 248)","v496 CELEST.WP4.01 (iv): BOUNDARY BRIDGES -- one full mu4 period of loop energies carries dim g_(n mod 4) = (64,60,64,60), sum = 248 EXACTLY (the single-particle level of the 248q stage); 248 is NOT a jet-tower dimension (no d <= 100 with 60(d+1) or 64(d+1) = 248) -- only the period collapse produces it; BUT the free loop Fock at integer level 1 (u^4) counts 897266 >> 248: the rational truncation must be imposed in the limit (the SEAM.EQUIV.01 scaling-limit shape)"],"checked_by_registry":false,"heading_as_written":"(* ==== v496 round: CELEST.WP4.01 -- the (E8)_1 character E4/eta^8 vs the glue-equivariant E8[C^2] S-algebra (WP4 of CELEST.SEAM.01, the type mismatch head-on). Exact content mirrored: the character coefficients through q^6 with the q j = E4^3/eta^24 cross-check; the equivariant Hilbert series (60+128t+60t^2)/(1-t^2)^2 with the quadratic cumulative count 31 s^2 + 92 s + 60 and the SU(2)_+ slice; the two-sided jet-Fock mismatch f = (1,128,8436,381056) with strictly increasing f_n/chi_n (n = 1..12); the level-2 null ideal 27000 = 30^3 = h_vee^3; the boundary bridges (mu4 period sum 248, 248 not a tower dimension, loop Fock 897266); mirrors v496. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:3257","line_end":3311,"line_start":3257,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v496"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v497 CELEST.WP5A.01 (i): STABILISATION THEOREM -- the chi_w family (chiral jet generators, E_w = m + w r in quarter units) has u^n coefficient EQUAL to the quarter-moded loop Fock for ALL w >= n+1 and STRICTLY larger for every w <= n (n <= 8, w <= 10); the w = 2 member IS the chiral jet grading (generator counts 64,120,128,180,192,240,256,300 = the p >= q monomial count); loop Fock at u^4 = INTEGER level 1 counts 897266 (the limit alone does NOT give the 248 of the character)","v497 CELEST.WP5A.01 (ii): NULL IDEAL DERIVED (Weyl dimension formula, standard E8 frame) -- 240 roots, 120 positive, MemberQ theta; dim V(theta) = 248 (unit test), dim V(2 theta) = 27000 = 30^3 = h_vee^3 EXACTLY, dim V(omega) = 3875, Sym^2(248) count 30876 = 1 + 3875 + 27000; Casimirs C2 = (60, 124, 96) = (2 h_vee, ., .), Dynkin indices 6750/750 integers; level-1 integrability <2 theta,theta_vee> = 4 > 1, <omega,theta_vee> = 2 > 1; quotient 31124 - 27000 = 4124 = 1 + 248 + 3875 = chi_2","v497 CELEST.WP5A.01 (iii): TWO ROUTES, ONE NUMBER -- the mu4 theta-split sector characters Theta_Cj/eta^8 give currents (60,64,60,64) at q^1, (1036,1024,1040,1024) at q^2 summing to 4124 = 31124 - 27000 EXACTLY (the independent lattice route hits the Fock quotient), and 34752 = chi_3 at q^3; glue-diagonal weights h = (0,1,1,1) INTEGER (one-block fusion)","v497 CELEST.WP5A.01 (iv): NEGATIVE CONTROLS -- SO(16)_1 through the SAME pipeline: dim V(theta) = 120 (unit test), Sym^2(120) = 5304 + 1820 + 135 + 1 (Weyl dims of the FOUR components), 5304 != 14^3 = 2744 (h_vee^3 NOT generic), quotient 7380 - 5304 = 2076 = Theta_D8/eta^8 at q^2 (D8 shells (1,112,1136)); block weights h = (0,1/2,1,1) -- h_vector = 1/2 NON-integer, no one-block fusion (vs E8's (0,1,1,1)); false periodisation P = 1/2/4/8 -> 64/124/248/496 (only P = |mu4| = 4 gives the 248 layer); swapped glue breaks the zero-mode anchor (64 != 60)"],"checked_by_registry":false,"heading_as_written":"(* ==== v497 round: CELEST.WP5A.01 -- WP5a of CELEST.SEAM.01, \"the null ideal from the limit\" (the v496 boundary-limit shadow made precise). Exact content mirrored: (i) the chi_w stabilisation family (threshold w = n+1, w = 2 = the chiral jet grading, loop Fock 897266 at u^4); (ii) the null ideal DERIVED via the Weyl dimension formula in the standard E8 frame (Sym^2(248) = 27000 + 3875 + 1, 27000 = h_vee^3, Casimirs/Dynkin indices, level-1 integrability, quotient 31124 - 27000 = 4124); (iii) the two-route identity (mu4 theta-split sector sum at q^2 = (1036,1024,1040,1024) = 4124, q^3 = 34752, glue diagonal h = (0,1,1,1)); (iv) the negative controls (SO(16)_1: 5304 + 1820 + 135 + 1, 5304 != 14^3, quotient 2076 = Theta_D8/eta^8, block weights (0,1/2,1,1); false periodisation; swapped glue). The Freudenthal/peeling residual-zero derivation itself is Python-side (v497 S3); the Weyl-dimension and orbit-independent counting consequences are what is mirrored here. Mirrors v497. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:3312","line_end":3462,"line_start":3312,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v496","v497"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v498 CELEST.WP5B.01 (i): CASE CLASSIFICATION of the J^a_1 condition over the 248-element basis, from the standard-frame E8 root data -- theta-grading dims (1,56,134,56,1) (roots (1,56,126,56,1) + 8 Cartan in g_0); a + theta never a root for the 120 positives (theta highest); a + 2 theta re-enters the root system for EXACTLY one root (a = -theta); tally (first bracket, second bracket, central term) = (190, 57, 1) -- exactly ONE case sees the level k, and 190 + 57 + 1 = 248","v498 CELEST.WP5B.01 (ii): LEVEL DIAL DERIVED from the affine sl2 commutation -- F^theta_1 (E^theta_{-1})^n|0> = n(k-n+1) (E_{-1})^(n-1)|0> (summed central/Cartan cascade); square coefficient c(2,k) = 2(k-1) = -2(1-k): values (-2, 0, 2) at k = 0, 1, 2 -- zero EXACTLY at k = 1 (no deletion operator in the centerless k = 0 loop algebra); Shapovalov <s|s> ~ c(2,k) c(1,k) = 2k(k-1): 0 at k = 1, 4 at k = 2; the CUBE coefficient c(3,k) = 3(k-2) vanishes exactly at k = 2 -- the (E^theta)^(k+1) pattern is generic Kac level mechanics","v498 CELEST.WP5B.01 (iii): MU4 GLUE DATA -- 240 glue-frame roots with classes (52,64,60,64); inner grading <alpha,h> = glue class mod 4 for ALL 240 roots (h = (2,2,2,2,2;0^4), v492 S1); theta_glue = the phi-maximal root with <theta,h> = 5 => glue class j(theta) = 1, clock phase on |s> = i^(2j) = -1 (class(2 theta) = 2, SHEET-EVEN), the theta-sl2 pair in the sheet-ODD classes (1,3); cross-table row sums over <alpha,theta_vee> = (1,56,126,56,1)","v498 CELEST.WP5B.01 (iv): THE 27000 MATCH + COMARK DISCRIMINATOR -- weight 2 theta has multiplicity 1 in the level-2 Fock (unique unordered pair theta + theta => U(g)|s> is THE 27000 = 30^3 = h_vee^3, dim V(2 theta) by Weyl); lattice reading (2 theta, 2 theta)/2 = 4 > 2 (no momentum-2theta state at q^2 in E4/eta^8 -- |s> IS the kernel generator); E8 comarks <omega_i,theta_vee> = (2,2,3,3,4,4,5,6) all >= 2 (vacuum the ONLY level-1 primary: one-block closure), D8 comarks (1,1,1,2,2,2,2,2) keep 3 comark-1 weights with h = (1/2,1,1) -- h = 1/2 NON-integer breaks one-block fusion; dim V(2 theta_D8) = 5304 != 14^3 = 2744","v498 CELEST.WP5B.01 (v): TWISTED-SLOT TENSION (the honest [O] handover to WP5c) -- in the quarter-SLOT moding of the chi_w limit Fock the sector-C_1 modes sit at n = -j(theta) = 3 mod 4 (mode fraction 1/4 = j/4): two such modes NEVER sum to 8 quarters (0 solutions; minimum total 6 quarters = q^(3/2)) -- the per-PERIOD dictionary (one mu4 period = 248 = the level-1 currents; E^theta_{-1} = 4 quarters, |s> = 8 = q^2), not the per-slot identification, carries |s> to q^2"],"checked_by_registry":false,"heading_as_written":"(* ==== v498 round: CELEST.WP5B.01 -- WP5b of CELEST.SEAM.01, \"the singular vector as an operator\" (the deleting object of the v497 null ideal made explicit). Exact content mirrored: (i) the case classification of the J^a_1 condition over the 248-element basis (190/57/1, exactly one case sees the level k) from the standard E8 root data + the theta-grading (1,56,134,56,1); (ii) the LEVEL DIAL derived from the affine sl2 commutation -- F^theta_1 (E^theta_{-1})^n|0> = n(k-n+1) (E_{-1})^{n-1}|0>, square coefficient 2(k-1) = -2(1-k) with values (-2,0,2) at k = 0,1,2, Shapovalov 2k(k-1) (0 at k = 1, 4 at k = 2), cube singular exactly at k = 2; (iii) the glue frame -- 240 roots with classes (52,64,60,64), inner grading <r,h> = class mod 4 on all 240, theta_glue = argmax with <theta,h> = 5 => j(theta) = 1, clock phase i^(2j) = -1, cross-table rows (1,56,126,56,1); (iv) multiplicity 1 of weight 2 theta in the level-2 Fock (U(g)|s> is THE 27000 = 30^3), lattice reading (2t,2t)/2 = 4 > 2, and the comark discriminator (E8 comarks all >= 2 -- vacuum the only level-1 primary; D8 has three comark-1 weights with h = (1/2,1,1)); (v) the twisted-slot tension (two sector-C_1 modes never sum to 8 quarters, minimum 6 = q^(3/2)) + the per-period 248. The full Chevalley/PBW singularity run (J^a_1|s> = 0 on all 248 basis elements, engine unit tests on all 61504 pairs) is Python-side (v498 S1-S3); the counting/dial/grading consequences are what is mirrored here. Mirrors v498. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:3463","line_end":3619,"line_start":3463,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v497","v498"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v499 P2.TYPING.01 (i): PARTITION UNDER THE FULL TYPING -- {a in Z^3 : a_i >= 1 (h^0 = 0), sum 4 (deg E = -4), 3 parts (rank 3)} = {{1,1,2}} unique with e2 = 5 = g_car; BG dictionary h^0(O(-a1)+O(-a2)+O(-a3)) = 0 <=> all a_i >= 1 (window [-3,6] exhaustive); naive-typing control: h^1(E') = 3 with h^0 = 0 forces sum a_i = 6 (deg -6 != -4) and loses uniqueness ({1,1,4},{1,2,3},{2,2,2}, e2 = {9,11,12} never 5); the h^1 discrepancy is real: h^1(O(-2)+O(-1)^2) = 1 != 3 = h^1(O(-4)) (the L-side carries the generations)","v499 P2.TYPING.01 (ii): DELIGNE RESIDUE-TRACE DEGREE -- the cusp exponents {0,1/3,2/3} are the unique lift of spec(lam^3 - 1) to [0,1) (cube roots of unity, distinct mod Z => canonical extension unique, no Jordan ambiguity); residue trace 1 per mark x 4 marks => deg E = -4, par-deg = -4 + 4(0+1/3+2/3) = 0 (the (U) consistency); the explicit witness A0* has char poly lam(lam-1/3)(lam-2/3) exactly","v499 P2.TYPING.01 (iii): SCHUR-HORN LATTICE POINTS -- the integer points of the permutohedron of 4 spec(A0) = (8/3, 4/3, 0) with sum 4 are exactly {(2,1,1),(2,2,0)} (the two options of the tfpt_2 'Global computation' theorem); h^0 = 0 kills {2,2,0} (it contains an O(0) summand, h^0 = 1) => (2,1,1) alone survives -- the 'balanced' selection is TYPED as positivity/stability, and the Schur-Horn and Deligne/BG routes converge on {1,1,2}","v499 P2.TYPING.01 (iv): BISWAS Z3-COVER DEGREE ARITHMETIC -- equal local monodromies impossible (4c != 0 mod 3 for c = 1,2); m = (1,1,2,2) works (sum 6 = 0 mod 3, unramified over infinity), Riemann-Hurwitz genus 2; eigensheaves deg V_j = sum floor(j m_i/3) - 2j = (-2,-2) => p_* O_Y = O + O(-2)^2 with chi cross-check -1 = 1 - g(Y); regular-rep weights {j m_i/3 mod 1} = {0,1/3,2/3} at every mark; the decomposable model bundle {0,2,2}: deg -4 OK, par-deg 0 OK but h^0 = 1 (the UNSTABLE Schur-Horn companion) -- integrality + sum rule come out of the correspondence, stability is the selector; deck double w^2 = z^4-1: genus 1, cross-ratio 2 => j = 1728 (denominator 2 = |Z2|, not the weight cover)","v499 P2.TYPING.01 (v): N-MARK FORMULA -- n marks => n-1 positive parts summing to n; {1,..,1,2} is unique for EVERY n >= 3 (uniqueness is generic), but e2 = (n-2)(n+1)/2 = (2,5,9,14,20,27) for n = 3..8 -- e2 = 5 = g_car picks out n = 4 ALONE: the VALUE, not the uniqueness, is the n = 4 content"],"checked_by_registry":false,"heading_as_written":"(* ==== v499 round: P2.TYPING.01 -- the P2 weight-typing postulate hardened: the anchor a = (1,1,2) as the Birkhoff-Grothendieck splitting exponents of the Deligne canonical extension E of the flavor connection (types the v491 check-9 residual). Exact content mirrored: (i) partition enumeration under the full typing (BG dictionary h^0 = 0 <=> a_i >= 1, exhaustive window) + the naive- typing negative control (h^1(E') = 3 forces deg -6, three splittings, e2 never 5) + the h^1 discrepancy (h^1(anchor bundle) = 1 != 3); (ii) the Deligne residue-trace degree (cusp exponents {0,1/3,2/3} = the unique lift of spec(lam^3 - 1) to [0,1), trace 1 per mark, deg E = -4, par-deg 0, witness A0* charpoly); (iii) the Schur-Horn permutohedron integer points {(2,2,0),(2,1,1)} with h^0 = 0 killing {2,2,0}; (iv) the Biswas Z3-cover degree arithmetic (genus 2, eigensheaves O(-2)^2, chi cross-check, regular-rep weights, the decomposable model {0,2,2} with h^0 = 1 = the unstable companion; deck double genus 1, j = 1728); (v) the n-mark formula e2 = (n-2)(n+1)/2 = 5 only at n = 4. The sympy symbolic parts (H^1 residue basis, monodromy group closure |<U,M0>| = 24, the 324-case stability skeleton) stay Python-side (v499). Mirrors v499. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:3620","line_end":3708,"line_start":3620,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v491","v499"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v500 CELEST.WP5C.01 (i): LEVEL-2 BLOCK CENSUS from the E8 root data -- 31124 = 248 (one J_{-2}) + 30876 (two J_{-1}, unordered with repetition) monomials fall into 9361 weight blocks with dim profile {164:1, 37:240, 7:2160, 1:6960}; orbit census by lattice norm (8,6,4,2,0) -> sizes (240, 6720, 2160, 240, 1) with CONSTANT block dims (1,1,7,37,164) along each norm class -- the exact block structure of the omega_inf level-2 Gram","v500 CELEST.WP5C.01 (ii): RANK/KERNEL ARITHMETIC -- the Python-side exact Gram gives rank per norm orbit (8,6,4,2,0) -> (0,0,1,8,44); total GNS level-2 dimension 240*0 + 6720*0 + 2160*1 + 240*8 + 44 = 4124 = 1 + 248 + 3875 = chi_2 EXACTLY (dim V(omega) = 3875 recomputed by Weyl from the unique dominant norm-4 weight); kernel per orbit = dim - rank = (1,1,6,29,120), total 240 + 6720 + 12960 + 6960 + 120 = 27000 = 30^3 = dim V(2 theta) (Weyl) -- the kernel is V(2 theta) orbit by orbit","v500 CELEST.WP5C.01 (iii): CLOCK-CLASS SPLIT AT THE STATE LEVEL (two routes) -- the same 31124-monomial census in the GLUE frame (class(lambda) = <lambda,h> mod 4, h = (2,2,2,2,2;0^4)) with the rank table (0,0,1,8,44) gives the GNS level-2 rank split by clock class (1036, 1024, 1040, 1024) = Theta_Cj/eta^8 at q^2 (the per-period lattice theta-split, v497 route) summing to 4124; level 1 splits as root classes + Cartan = (52+8, 64, 60, 64) = (60,64,60,64) -- the state-level GNS grading reproduces the lattice split EXACTLY","v500 CELEST.WP5C.01 (iv): THRESHOLD + LEVEL DIAL + D8 CONTROL -- the radial x-adic orders w*r satisfy 'w r >= N+1 for all r >= 1 iff w >= N+1' (N = 8; enumerated w, r <= 12), SHARP at w = N via the r = 1 mode: the WP5a character threshold holds identically at the state level; level dial: root-mode level-1 norm = k kappa (no 248 layer at k = 0), <s|s> = 2k(k-1) = 0 at k = 1 and +4 at k = 2 (v498 derivation reused -- the deletion is a k = 1 state fact); D8/SO(16)_1 census: 7380 = 120 + 120*121/2 monomials in 2705 weight blocks, quotient 7380 - 5304 = 2076 = Theta_D8/eta^8 at q^2 (one GNS block of the FOUR-block theory, h = 1/2 non-integer)"],"checked_by_registry":false,"heading_as_written":"(* ==== v500 round: CELEST.WP5C.01 -- WP5c of CELEST.SEAM.01, \"the GNS limit state\" (the state whose GNS kernel contains the v497/v498 null ideal). Exact content mirrored: (i) the LEVEL-2 BLOCK CENSUS from the standard E8 root data -- 31124 = 248 + 30876 monomials in 9361 weight blocks with dim profile {164:1, 37:240, 7:2160, 1:6960}, orbit census by lattice norm (8,6,4,2,0) -> (240, 6720, 2160, 240, 1) with constant block dims (1,1,7,37,164); (ii) the RANK/KERNEL ARITHMETIC of the full Gram -- rank table per orbit (0,0,1,8,44) (the Python-side Gram result) gives total rank 4124 = 1 + 248 + 3875 = chi_2 (dim V(omega) = 3875 recomputed by Weyl from the dominant norm-4 weight) and kernel per orbit (1,1,6,29,120) summing to 27000 = 30^3 = dim V(2 theta) (Weyl); (iii) the CLOCK-CLASS SPLIT at the state level -- the same census in the glue frame with class(lambda) = <lambda,h> mod 4 turns the rank table into the split (1036,1024,1040,1024) = Theta_Cj/eta^8 at q^2, and level 1 gives (52+8,64,60,64) = (60,64,60,64); (iv) the THRESHOLD + LEVEL-DIAL + D8 arithmetic -- x-adic order w*r >= N+1 for all r >= 1 iff w >= N+1 (sharp at w = N via r = 1), level-1 root-mode norm = k (no 248 layer at k = 0), <s|s> = 2k(k-1) (0 at k = 1, +4 at k = 2), D8 census 7380 = 120 + 7260 in 2705 blocks with quotient 7380 - 5304 = 2076. The exact Gram computation itself (9361 blocks over Fractions, PSD inertia, the highest-weight norms (3844, 49, 2, 0), the contravariance and anti-involution machine checks on 61504 pairs) is Python-side (v500 S1-S4). Mirrors v500. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:3709","line_end":3829,"line_start":3709,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v497","v498","v500"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v501 CELEST.WP5D.01 (i): CARTAN DETERMINANTS (v378 replication, explicit matrices) -- det Cartan(D5) = 4, det Cartan(A3) = 4, product 16 = mu(carrier D5 x A3); det Cartan(D8) = 4 = mu(SO(16)_1); det Cartan(E8) = 1 = mu((E8)_1): the KLM two-interval index chain starts at 16 and must end at 1","v501 CELEST.WP5D.01 (ii): KLM/LONGO-REHREN QUOTIENTS -- mu/|L|^2 with |L| = |mu4| = 4 gives 16/16 = 1 (the one-step mu4 glue to (E8)_1); |L| = 2 gives 16/4 = 4 = mu(SO(16)_1), then the theta_v = 1 simple current 4/2^2 = 1: BOTH routes land exactly on mu = 1 -- the 16 -> 4 -> 1 condensation chain","v501 CELEST.WP5D.01 (iii): SIGMA d^2 CROSS-CHECK + INDEX READING -- KLM mu = Sigma d_i^2: Ising 1 + 1 + (Sqrt 2)^2 = 4; SO(16)_1 four abelian sectors = 4; (E8)_1 one sector = 1 (matches the Cartan-det chain exactly); index reading arithmetic: [F : F_even] = e^(ln 2) = 2, mu_gauged = e^(2 ln 2) = 4, per-layer gauging 16 ln 2 = ln 2^16 (the offset measures ln[index]), complementary-pair budget ln 4 = ln mu(SO(16)_1)","v501 CELEST.WP5D.01 (iv): 16-FOLD-WAY CONDENSABILITY -- theta_v = e^(2 pi i nu/16) = 1 EXACTLY at nu = 2 c_- = 16 (c_- = 8 = g_car + N_fam; the seam carrier is 16 = 2^(g_car-1) Majorana layers): the vortex is bosonic and condensable (v490); the rivals nu = 1, 2, 8 give theta_v = e^(i pi/8), e^(i pi/4), -1, all != 1 -- the Ising-class offset is NOT removable (the kill discriminator has teeth)"],"checked_by_registry":false,"heading_as_written":"(* ==== v501 round: CELEST.WP5D.01 -- WP5d-alpha of CELEST.SEAM.01, \"the two-interval index from the lattice\" (the local-net question, alpha stage). Exact content mirrored: (i) the Cartan determinants det(D5) = det(A3) = 4, product 16 = mu(carrier), det(D8) = 4 = mu(SO(16)_1), det(E8) = 1 = mu((E8)_1) (v378 replication, explicit matrices); (ii) the KLM/Longo-Rehren quotients mu/|L|^2 -- 16/4^2 = 1 (one-step mu4 glue, |L| = |mu4| = 4) and 16/2^2 = 4 -> 4/2^2 = 1 (via SO(16)_1), both routes exact; (iii) the Sigma d_i^2 cross-checks (Ising 1+1+2 = 4, SO(16)_1 four abelian sectors = 4, (E8)_1 one sector = 1) + the index reading arithmetic ([F:F_even] = e^(ln 2) = 2, mu_gauged = e^(2 ln 2) = 4, per-layer gauging 16 ln 2 = ln 2^16, budget ln 4 = ln mu(SO(16)_1)); (iv) the 16-fold-way condensability theta_v = e^(2 pi i nu/16) = 1 EXACTLY at nu = 2 c_- = 16 (c_- = 8 = g_car + N_fam, 16 layers = 2^(g_car - 1)) vs the rivals nu = 1, 2, 8. The lattice curves (Peschel covariance, Renyi-2 offsets, the ln 2 plateau, the duality-asymmetry witness, all ED validations) are numerical and stay Python-only (v501 S0-S4, S6). Mirrors v501. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:3830","line_end":3892,"line_start":3830,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v378","v501"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v502 CELEST.WP5E.ALPHA.01 (i): HURWITZ-ZETA VACUUM ENERGIES -- zeta(-1,theta) = -B2(theta)/2 exactly at all rational twists n/8, so E_b(theta) = (1/4)[zeta(-1,th) + zeta(-1,1-th)] = -1/24 + theta(1-theta)/4 EXACTLY; values (0,1/4,1/2,3/4) -> (-1/24, 1/192, 1/48, 1/192); fermion shift E_R - E_NS = 1/24 - (-1/48) = 1/16 per Majorana (Ising h_sigma); untwisted vacuum 8 x (-1/24) = -1/3 = -c/24 at c = 8 = Sugawara 248/(1+30); eta^8 = q^{8/24} = q^{1/3} x (product): the q^{-1/3} prefactor is the c = 8 vacuum energy","v502 CELEST.WP5E.ALPHA.01 (ii): DISCRIMINANT FORM = CASIMIR ENERGY -- exact lattice coset minima give h_D5 = (0,5/8,1/2,5/8), h_A3 = (0,3/8,1/2,3/8), glue diagonal h = (0,1,1,1) INTEGER; spectral flow j^2 (h,h)/32 with (h,h) = 20, (h',h') = 12, sum 32 reproduces both tables mod 1 (sum j^2 = 0 mod 1 = isotropy); free-fermion route EXACT: R-NS shift n/16 on 10 (D5) + 6 (A3 = D3) = 16 = 2^(g_car-1) Majoranas gives 5/8, 3/8, 1; the geometric deck diag(i,i^-1) gives 3/16 != 3/8 -- the rotation reading fails (clock != deck at the Casimir level)","v502 CELEST.WP5E.ALPHA.01 (iii): k = 1 FIXING EQUATIONS -- simple-current closed forms h(k om_s) = 5k/8, h(k om_1) = 3k/8, h(k om_v) = h(k om_2) = k/2 (affine formula, symbolic); glue-diagonal integrality 5k/8 + 3k/8 = k INTEGER FOR ALL k = 1..8 (fixes nothing -- the honest finding); current condition h(J) = k = 1 unique; conformal embedding 47k^2 + 219k - 266 = (k-1)(47k + 266), unique positive root k = 1; D8 route 120k(k+30) - 248k(k+14) = -128k(k-1); central charge 248k/(k+30) = 8 <=> 240(k-1) = 0, k = 1; Shapovalov 2k(k-1) = (0,4,12,24) for k = 1..4; Weyl dims 248/3875/27000 recomputed from E8 root data, level-2 count 31124 - 27000 = 4124","v502 CELEST.WP5E.ALPHA.01 (iv): CHARACTER SUMS -- exact glue-coset theta enumeration (norms <= 6): sum of the four Theta_Cj = E4 = (1,240,2160,6720); sector characters Theta_Cj x 1/prod(1-q^n)^8 (P8 = 1,8,44,192) have leading coefficients (1,64,60,64) and level-1 currents (60,64,60,64), and sum EXACTLY to E4/eta^8 = q^{-1/3}(1, 248, 4124, 34752); D8/SO(16)_1 control: Theta_D8 = (1,112,1136,...), Theta_s = (0,128,1024,...), sum = E4 (the {1,s} Lagrangian extension IS E8) with the vector-class minimum norm 1 => h_v = 1/2 NON-integer (the discriminator is glue-h integrality, not the prefactor)"],"checked_by_registry":false,"heading_as_written":"(* ==== v502 round: CELEST.WP5E.ALPHA.01 -- WP5e-alpha of CELEST.SEAM.01, \"prefactor and level bookkeeping\" (the CFT-side anchor of the twistor uplift). Exact content mirrored: (i) the HURWITZ-ZETA vacuum energies -- zeta(-1,theta) = -B2(theta)/2 at rational twists, E_b(theta) = -1/24 + theta(1-theta)/4, Ising shift E_R - E_NS = 1/16 per Majorana, the untwisted vacuum 8 x (-1/24) = -1/3 = -c/24 with the Sugawara route 248/(1+30) = 8, and the eta^8 exponent 8/24 = 1/3; (ii) DISCRIMINANT FORM = CASIMIR ENERGY -- coset minima h_D5 = (0,5/8,1/2,5/8), h_A3 = (0,3/8,1/2,3/8), glue diagonal (0,1,1,1) INTEGER (exact lattice enumeration), spectral flow j^2 (h,h)/32 with (h,h) = 20, (h',h') = 12, sum 32 (mod-1 identity), free-fermion route n/16 = 5/8, 3/8, 1 on 10 + 6 = 16 = 2^(g_car-1) Majoranas, and the deck failure 3/16 != 3/8; (iii) the k = 1 FIXING EQUATIONS -- simple-current closed forms 5k/8, 3k/8, glue-diagonal integrality for ALL k = 1..8 (the honest 'fixes nothing' finding), current condition h(J) = k = 1 unique, conformal embedding 47k^2 + 219k - 266 = (k-1)(47k+266) with unique positive root 1, D8 route 128k(1-k) = 0, central charge 248k/(k+30) = 8 <=> 240(k-1) = 0, Shapovalov values 2k(k-1) = (0,4,12,24), and the Weyl-dim count 31124 - 27000 = 4124 (dims 248/3875/27000 recomputed); (iv) the CHARACTER SUMS -- the four glue-coset thetas sum to E4 = (1,240,2160, 6720), the sector characters (leading coefficients (1,64,60,64), currents (60,64,60,64)) sum to E4/eta^8 = q^{-1/3}(1,248,4124,34752), and the D8 control Theta_D8 + Theta_s = E4 with h_v = 1/2 non-integer. The sympy symbolic manipulations and the PBW engine are Python-side (v502 S1/S5). Mirrors v502. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:3893","line_end":4052,"line_start":3893,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v502"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v503 QGEO.EMERGE.LIGHT.01 (i): CM-POINT IDENTITIES -- the q-series E2 reproduces the classical closed forms E2(i) = 3/Pi and E2(rho) = 2 Sqrt[3]/Pi to 30 digits, hence the almost-holomorphic completion vanishes EXACTLY at both exceptional-automorphism points: E2*(i) = 3/Pi - 3/(Pi tau2) = 0 at tau2 = 1 and E2*(rho) = 2 Sqrt[3]/Pi - 3/(Pi Sqrt[3]/2) = 0 (the ONLY critical points of the det' functional are the CM points); j(i) = 1728 and j(rho) = 0 exactly (KleinInvariantJ); DedekindEta[I] = Gamma[1/4]/(2 Pi^(3/4)) exact","v503 QGEO.EMERGE.LIGHT.01 (ii): NO DYNAMICAL SELECTION -- logF(tau) = log(tau2 |eta(tau)|^4) (the OPS scale-invariant log det' of the torus; pillowcase = half of it) is exactly S-invariant (logF(-1/tau) = logF(tau) to 30 digits at a generic point, so t = 1 is symmetry-forced critical on tau = it); the HEXAGONAL point wins globally: logF(rho) - logF(i) = 0.02116... > 0 (free dynamics does NOT select the square); tau = i is a SADDLE: a maximum along the rectangular family (logF(i) > logF(0.9 i), logF(1.1 i)) and a minimum along the tau1-direction (logF(+-0.1 + i) > logF(i))","v503 QGEO.EMERGE.LIGHT.01 (iii): PILLOWCASE = HALF TORUS -- exact N = 8 discrete-torus spectrum (algebraic eigenvalues 4 - 2cos(2 pi m/8) - 2cos(2 pi n/8)): the Z2 map (m,n) -> (-m,-n) has EXACTLY 3 nonzero self-paired cone modes (+ the zero mode: the 4 marks in frequency space), 30 genuine +- pairs, dim(even) = 1 + 3 + 30 = 34 = (N^2+4)/2; det'_even^2 = det'_torus x prod_self EXACTLY (algebraic identity) -- the orbifold spectrum is one copy of each pair, zeta_pillow = zeta_torus/2, so every tau-conclusion transfers verbatim to the pillowcase","v503 QGEO.EMERGE.LIGHT.01 (iv): CLOCK => SQUARE + COXETER -- P(iZ) = P(Z) forces a3 = a2 = a1 = 0 (SolveAlways, exact), and the surviving family Z^4 + a0 has binary-quartic invariants I = 12 a0, J = 0, hence j = 6912 I^3/(4 I^3 - J^2) = 1728 IDENTICALLY (given the clock, the modulus freezes -- not a second input); the order-4 element on H^1 has char poly lam^3 + lam^2 + lam + 1 = the Coxeter element of W(A3) (A^4 = 1, order 4 = |mu4| = N_fam + 1 -- the P2 cusp-class carrier datum: QGEO-R1 == P2-R1); Aut(hexagonal) = Z6 has element orders {1,2,3,6} -- NO order-4 element (the dynamical winner cannot carry the clock)"],"checked_by_registry":false,"heading_as_written":"(* ==== v503 round: QGEO.EMERGE.LIGHT.01 -- the v215 deferred emergence test (lever 7) executed light + the residual convergence QGEO-R1 == P2-R1. Exact/numeric content mirrored: (i) the CM-POINT IDENTITIES -- E2(i) = 3/Pi and E2(rho) = 2 Sqrt[3]/Pi (30-digit q-series vs the classical closed forms), hence E2*(i) = E2*(rho) = 0 EXACTLY by arithmetic; j(i) = 1728, j(rho) = 0 (KleinInvariantJ); DedekindEta[I] = Gamma[1/4]/(2 Pi^(3/4)) exact; (ii) NO DYNAMICAL SELECTION -- logF = log(tau2 |eta|^4) is S-invariant (30 digits at a generic point), the HEXAGONAL point wins (logF(rho) > logF(i)) and tau = i is a saddle (max along it, min along tau1 + i, sampled); (iii) the PILLOWCASE HALVING -- exact N = 8 discrete-torus spectrum (algebraic eigenvalues), Z2 pairing with exactly 4 self-paired cone modes, dim(even) = (N^2+4)/2 = 34, and det'_even^2 = det'_torus x prod_self EXACTLY; (iv) CLOCK => SQUARE + COXETER -- P(iZ) = P(Z) forces a3 = a2 = a1 = 0 (SolveAlways), j = 6912 I^3/(4 I^3 - J^2) = 1728 identically for Z^4 + a0, the order-4 element on H^1 has char poly lam^3 + lam^2 + lam + 1 (Coxeter of W(A3), order 4 = |mu4| = N_fam + 1), and Z6 = Aut(hexagonal) has element orders {1,2,3,6} -- no order 4. The v280-style lattice DtN curves (mod-4 off-character weights, sqrtm/expm) are numerical and stay Python-only (v503 B3-B5). Mirrors v503. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:4053","line_end":4131,"line_start":4053,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v215","v280","v503"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v504 CELEST.WP5DB.01 (i): GF2 SPAN THEOREM -- Majorana monomials multiply as GF(2) labels (c_S c_T = +- c_{S xor T}), so the strong-additivity span is an exact set count: WITH the shared boundary Majorana Even(A) v Even(B) = Even(A u B) EXACTLY (span/target 64/64, 256/256, 1024/1024 at sizes 4+4, 5+5, 6+6 -- the lattice strong-additivity witness for the orbifold algebra); DISJOINT intervals give EXACTLY HALF (64/128, 256/512, 1024/2048 = index 2; the missing sector is odd(x)odd, the single ln 2 bit of v501, localised at the split point)","v504 CELEST.WP5DB.01 (ii): PIMSNER-POPA IDENTITY + ATTAINMENT -- E(a) = (a + PaP)/2 gives E(a) - a/2 = PaP/2 IDENTICALLY on a fully symbolic 4x4 matrix (the one-line PP inequality: PaP >= 0 for a >= 0, so E(a) >= a/2 with lambda = 1/2 = 1/[F:F_even]); attainment on explicit gamma matrices: h = c_1 (odd, h^2 = 1, Tr h = 0, PhP = -h exactly), x = 1 + h has x*x = 2 + 2h and E(x*x) - lam x*x = 2(1-lam) - 2 lam h with spec(h) = {+-1}: eigenvalues {2 - 4 lam, 2} -- nonnegative iff lam <= 1/2: lambda_PP = 1/2 EXACTLY","v504 CELEST.WP5DB.01 (iii): TWO-INTERVAL GROUP + INDEX CONSISTENCY -- E4 over {1, P_A, P_B, P_AB} on the uniform 4-sector vector gives E4(vv+) = I/4 EXACTLY (the four sectors are orthogonal characters), so the Pimsner-Popa constant of the two-interval orbifold inclusion is lambda_E4 = 1/4 = 1/mu (PSD at 1/4, not PSD above); index consistency of the two routes: 1/lambda_PP = 2 = [F:F_even] (the v501 entropic offset exp(Delta_inf) = 2) and (1/lambda_PP)^2 = 4 = 1/lambda_E4 = mu(SO(16)_1) = det Cartan(D8) -- the Longo-Rehren index witnessed operator-algebraically and entropically","v504 CELEST.WP5DB.01 (iv): LAMBDA^2 COMPOUND -- the Wick cross-Gram of even bilinears c_i c_j (A) x c_k c_l (B) is the second compound Minors[C, 2]: Cauchy-Binet functoriality Minors[A.B, 2] = Minors[A, 2].Minors[B, 2] holds exactly on explicit integer matrices (so Lambda^2(U Sigma V) factors and the singular values are the pair products), Minors[diag(s), 2] = diag(s_a s_b) symbolically ({sigma_a sigma_b} -- the SAME ladder at doubled rate), and Minors[-C, 2] == Minors[C, 2] IDENTICALLY on a rational matrix: the parity flip C -> -C is invisible to the even bilinears -- the exact orbifold split-inheritance mechanism (the lattice shadow of Longo heredity)","v504 CELEST.WP5DB.01 (v): U(1) PP CONTROL -- charge dephasing on m modes has m + 1 sectors; on the uniform-spread vector the dephasing map gives E_U(vv+) = P_diag/(m + 1) exactly, so the Pimsner-Popa constant is lambda = 1/(m + 1) EXACTLY (verified m = 2, 3: PSD at 1/(m + 1), not PSD above) -- lambda -> 0 with region size: INFINITE index, the operator-algebraic twin of the divergent U(1) touching deficit (the divergence itself is a lattice curve, Python-only)"],"checked_by_registry":false,"heading_as_written":"(* ==== v504 round: CELEST.WP5DB.01 -- WP5d-beta \"split + strong additivity from the lattice\", the two remaining KLM legs of complete rationality (the mu-index is v501). Exact content mirrored: (i) the GF2 SPAN THEOREM -- Majorana monomials multiply as labels in GF(2)^n (c_S c_T = +- c_{S xor T}), so span dims are exact set counts: with the shared boundary Majorana Even(A) v Even(B) = Even(A u B) EXACTLY (64/64, 256/256, 1024/1024), disjoint EXACTLY half (64/128, 256/512, 1024/2048) = index 2; (ii) the PIMSNER-POPA IDENTITY -- E(a) = (a + PaP)/2 gives E(a) - a/2 = PaP/2 symbolically on a full 4x4 matrix, and the attainment x = 1 + h (h = c_1 odd, h^2 = 1, PhP = -h, explicit gamma matrices) has E(x*x) - lam x*x = 2(1 - lam) - 2 lam h with spec(h) = {+-1}: nonnegative iff lam <= 1/2 = 1/[F:F_even] EXACTLY; (iii) the TWO-INTERVAL GROUP -- E4 over {1,PA,PB,PAB} on the uniform 4-sector vector gives E4(vv+) = I/4 exactly, so lam_E4 = 1/4 = 1/mu, and the index consistency (1/lam_PP)^2 = 4 = 1/lam_E4 = mu(SO(16)_1) = det Cartan(D8); (iv) the LAMBDA^2 COMPOUND -- the Wick cross-Gram of even bilinears is the second compound Minors[C, 2]: Cauchy-Binet functoriality Minors[A.B, 2] = Minors[A, 2].Minors[B, 2] on explicit integer matrices, Minors[diag(s), 2] = diag(s_a s_b) symbolically (singular values = products, the same ladder at doubled rate), and Minors[-C, 2] == Minors[C, 2] IDENTICALLY (the parity flip C -> -C is invisible to the even bilinears -- the exact orbifold split-inheritance mechanism); (v) the U(1) PP CONTROL -- charge dephasing on m modes has m + 1 sectors and the uniform-spread vector gives E_U(vv+) = P_diag/(m + 1), so lam = 1/(m + 1) -> 0 EXACTLY (m = 2, 3): infinite index. The lattice curves (deficit tables, Ising exponent p = 0.2444, elliptic-nome ladder, Klich-Levitov slope, ED validations) are numerical and stay Python-only (v504 S0/S2/S3/S5). Mirrors v504. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:4132","line_end":4243,"line_start":4132,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v501","v504"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v505 CELEST.WP5E.BETA.01 (i): AB DENOMINATORS + EQUIVARIANT CHARACTERS -- det(1 - g_j^{-1}|_{T0}) = (1-i^{-j})(1-i^j) = (2,4,2) for j = 1,2,3 (real, positive: the deck diag(i,i^{-1}) is in SU(2)); Dedekind sum 1/2+1/4+1/2 = 5/4 = (|Z4|^2-1)/12 exactly; the 240 glue-frame roots split (52,64,60,64), graded dims (60,64,60,64), and the equivariant characters tr_{g_j}(Ad E8) = (248,0,-8,0) by TWO routes (graded dims and the explicit root sum 8 + sum_alpha i^{j class}); invariant average 60 = the D5+A3 carrier; Frobenius sum 61568 = 4(60^2+64^2+60^2+64^2); tr_{g_2} = -8 = 120 - 128 (so16 adjoint-minus-spinor)","v505 CELEST.WP5E.BETA.01 (ii): THE INDEX BRIDGE -- intersection form = -Cartan(A3) with det 4 = |Z4|; ch2(T_m) = -(C^{-1})_mm/2 = (-3/8, -1/2, -3/8) = MINUS the A3 discriminant weights j(4-j)/8 (the v502 sector Casimir energies); the per-character Atiyah-Bott sum f(m) = (1/4) sum_j (i^{jm}-1)/det_j = (0, -3/8, -1/2, -3/8) = ch2(T_m) EXACTLY (fixed-point ledger = McKay/Kronheimer intersection ledger); the glue-bundle ch2 defect is -78 by BOTH routes (AB route (1/4) sum_j (chi_j - 248)/det_j and intersection route 64(-3/8)+60(-1/2)+64(-3/8), per class (-24,-30,-24), the middle -30 = -h_vee); bridge identity sum_m h_A3(m) = 5/4 = sum_j 1/det_j","v505 CELEST.WP5E.BETA.01 (iii): OKUBO PER SECTOR + THE RIGID 32 T3 RESIDUAL -- the invariant quartic sum over the 240 glue roots is EXACTLY Q^{(0)} = 36 <x,x>^2 (36 = lambda~^2_e8: the v495 Okubo identity re-derived through the mu4-glue grading); the twisted quartics are NOT squares: Q^{(1)} = Q^{(3)} = 12P1 - 24P2 - 24P3 - 8T5 + 48T3 and Q^{(2)} = -12P1 - 24P2 + 36P3 + 32T5 - 64T3 exactly (irreducible T5/T3 content); the Atiyah-Bott-weighted sum Q^{(1)}/2 + Q^{(2)}/4 + Q^{(3)}/2 = 9P1 - 30P2 - 15P3 + 32T3 EXACTLY: the D5 quartic cancels, the rigid residual 32 T3 remains -- the fixed-point ledger is not a perfect square","v505 CELEST.WP5E.BETA.01 (iv): LEVEL DIALS, k = 1 GEOMETRIC -- the lattice current count (norm-2/k vectors in the glue cosets under the pairing (0,s,v,c) <-> classes (0,1,2,3)) is 240 at k = 1 and EXACTLY 0 at k = 2, 3, 4 (the seam lattice realises the (E8)_1 adjoint closure at k = 1 only); the conformal-embedding residual 47k^2 + 219k - 266 = (0, 360, 814, 1362) for k = 1..4; det(Coxeter - 1) = -4 != 0: no invariant flux vector on H2 -- one scale => one level (v493 lockstep periods)","v505 CELEST.WP5E.BETA.01 (v): AXION-SLOT WEIGHT ARITHMETIC + TWISTED SLOTS -- the mu4 clock acts on the versal moduli (a3,a2,a1,a0) with weights (i,-1,-i,1) = the regular representation (a0 the unique invariant); the volume form has weight 2+1+1 = 4 = -deg K_PT and the moduli weights are a_m in O(8-2m) (a0 in O(8) = O(2|Z4|)); the Poisson bracket O(a) x O(b) -> O(a+b-2) puts the a0 Hamiltonian in O(2) (the s = 2 GRAVITON slot: Y = +2) while the untwisted axion is iota_V Omega with V in T(x)O(-4), Hamiltonian weight X = -4+2 = -2 (the s = 0 slot O(-2)): X != Y with mismatch Y - X = 4 = |mu4| -- a0 is NOT the GS axion; the Coxeter eigenvalues on H2(ALE) are {i,-1,-i} = exactly the three twisted sector characters (bijection; det(A-1) = -4: no invariant class); slot count 1 + 3 = 4 = |mu4|"],"checked_by_registry":false,"heading_as_written":"(* ==== v505 round: CELEST.WP5E.BETA.01 -- WP5e-beta \"the equivariant anomaly ledger on twistor space\" (the Atiyah-Bott/Lefschetz skeleton of the one-loop inflow on C^2/Z4 with the E8 mu4-glue monodromy; the CFT side is v502). Exact content mirrored: (i) the AB DENOMINATORS + CHARACTERS -- det(1 - g_j^{-1}) = (2,4,2), Dedekind sum 5/4 = (|Z4|^2-1)/12, equivariant characters (248,0,-8,0) by TWO routes (graded dims / explicit root sum), invariant average 60 = carrier, Frobenius 61568; (ii) the INDEX BRIDGE -- f(m) = (1/4) sum_j (i^{jm}-1)/det_j = ch2(T_m) = -(C^{-1})_mm/2 exactly, glue defect -78 by both routes with classes (-24,-30,-24), bridge identity sum_m h_A3(m) = 5/4; (iii) OKUBO PER SECTOR -- the invariant quartic sum over the 240 glue roots is EXACTLY 36 <x,x>^2 (36 = lambda~^2_e8), the twisted quartics are NOT proportional to squares (T5/T3 content), and the AB-weighted sum leaves the rigid residual 32 T3; (iv) the LEVEL DIALS -- lattice current count 240/0/0/0 for k = 1..4, embedding residual 47k^2+219k-266 = (0,360,814,1362), det(A-1) = -4 (one scale => one level); (v) the AXION-SLOT WEIGHTS -- a0 fills the graviton slot O(2) (Hamiltonian weight arithmetic X = -2 != +2 = Y, mismatch 4 = |mu4|), the clock weights on (a3,a2,a1,a0) are the regular mu4 representation, and the Coxeter eigencharacters {i,-1,-i} = the three twisted sector characters. Mirrors v505. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:4244","line_end":4393,"line_start":4244,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v502","v505"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v506 SEAM.CLOCK.RIGIDITY.01 (i): COMPLETE SQUARE-ROOT SOLVE -- g^2 = deck (z -> -z) in PGL2(C): the trace != 0 branch forces b = 0 and c = 0 (diagonal) with (a/d)^2 = -1, i.e. a/d = +-i (g = z -> +iz or z -> -iz, EXACTLY TWO solutions); the trace = 0 branch is impossible: a traceless M has M^2 = (a^2 + bc) x IDENTITY (a scalar matrix, never proportional to diag(1,-1) except with factor 0), and the factor-0 case a^2 + bc = 0 forces det M = 0; both roots have projective ORDER 4 automatically, are mutually inverse (the Aut(Z4) pair), and square to the deck -- 'order 4' is NOT an input once 'square root of the deck' is given","v506 SEAM.CLOCK.RIGIDITY.01 (ii): D4 CENTER + ORDER-4 COUNT + COUNTEREXAMPLE -- the mu4 stabiliser {i^k z, i^k/z} (8 elements, all preserving {1,i,-1,-i}) has order profile {1,2,2,2,2,2,4,4}: EXACTLY 2 order-4 elements, both squaring to the deck (the clock pair), and center = {id, deck} (deck CENTRAL <=> clock exists); the silver counterexample {+-1, +-(3+2 sqrt 2)} is harmonic (cross-ratio 1/2, j = 1728) with a full D4 of 8 exact elements preserving it, BUT its two order-4 elements square to the CENTRAL crossing involution z -> -v/z, NOT the deck (which sits edge-type/non-centrally): the number of marks-preserving square roots of the deck is EXACTLY ZERO -- harmonicity alone is insufficient, the residual datum is deck-centrality (one bit)","v506 SEAM.CLOCK.RIGIDITY.01 (iii): THE Cl(16) IDENTITY U^2 = (-1)^F -- on explicit 256x256 Jordan-Wigner gamma matrices (gamma_a^2 = 1, all anticommuting), the NS deck implementer Utilde = prod_j (1 - gamma_j gamma_{j+8}) satisfies Utilde^2 = 256 gamma_1...gamma_16 EXACTLY, i.e. U^2 = (-1)^F with (-1)^F = the volume element (squares to 1, NOT a scalar, anticommutes with every gamma_a): the Z4 lift of the deck is FORCED (nonsplit extension -- (cU)^2 = c^2 (-1)^F is never 1); the R-sector implementer U_R = prod_j (gamma_j - gamma_{j+8}) squares to +256 x 1 EXACTLY (split Z2 control: the forcing rests on the NS/bounding spin structure)","v506 SEAM.CLOCK.RIGIDITY.01 (iv): N-ARITHMETIC + GENERIC KILL -- S4 element orders = {1,2,3,4}, so any Moebius Z_n preserving 4 marks faithfully dies for n >= 5 (max cyclic image order = (1,3,1,4) < n for n = 5..8); a free Z_n orbit forces n | 4 (n in {1,2,4}); n = 6 is killed independently by the cusp side (deg(lam^5 - 1) = 5 != 3 = deg(lam^3 - 1) = N_fam, v117) with transfer spectrum {1, 64/729, 1/729} and gap (2/3)^6; the generic 4-set stabiliser V4 = {+-z, +-2/z} has exponent 2 (every square = id): not even the deck has a marks-preserving square root at generic modulus -- the stabiliser trichotomy V4/D4/A4 carries order-4 counts (0, 2, 0)"],"checked_by_registry":false,"heading_as_written":"(* ==== v506 round: SEAM.CLOCK.RIGIDITY.01 -- clock rigidity, Route B of the v503 classification (Part A Moebius + Part B Fock). Exact content mirrored: (i) the COMPLETE SQUARE-ROOT SOLVE -- g^2 = deck in PGL2(C) has exactly two solutions z -> +-iz (tr != 0 forces diagonal with (a/d)^2 = -1; tr = 0 forces det = 0), both automatically of projective order 4; (ii) the D4 CENTER + ORDER-4 COUNT + the COUNTEREXAMPLE -- the mu4 stabiliser D4 = {i^k z, i^k/z} has exactly 2 order-4 elements (the clocks), both squaring to the deck, center = {id, deck}; the silver harmonic set {+-1, +-(3+2 sqrt 2)} has j = 1728 and full D4 but its 4-cycle squares to the CROSSING involution v/z, not the deck (deck non-central: 0 roots -- harmonicity alone insufficient); (iii) the Cl(16) IDENTITY -- on explicit 256x256 Jordan-Wigner gamma matrices, Utilde = prod_j (1 - g_j g_{j+8}) satisfies Utilde^2 = 256 g_1...g_16 EXACTLY (U^2 = (-1)^F, the forced nonsplit Z4), the R implementer squares to +256 (split control), and the volume element anticommutes with every gamma; (iv) the N-ARITHMETIC -- S4 element orders {1,2,3,4} (faithfulness kills n >= 5: max cyclic image order < n for n = 5..8), free orbits force n | 4, the cusp side kills n = 6 (deg(lam^5-1) = 5 != 3 = deg(lam^3-1)), transfer spectrum {1, 64/729, 1/729} with gap (2/3)^6, and the generic 4-set stabiliser V4 = {+-z, +-2/z} has exponent 2 (not even the deck has a root). The full 24-triple stabiliser enumeration and the A4/hexagonal profile stay Python-side (v506 Part A). Mirrors v506. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:4394","line_end":4544,"line_start":4394,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v503","v506"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v507 SEAM.BIT.ORIGIN.01 (i): HALF-PERIOD DESCENT -- the fixed points of the hyperelliptic involution w -> -w on C/(Z + tau Z) are EXACTLY the 4 half-periods Lambda/2Lambda (2w in Lambda <=> both coefficients in {0, 1/2}; on the 6-point control grid with a 1/3-coefficient exactly the 4 genuine ones survive); a translation t_c commutes with w -> -w iff 2c in Lambda: TRUE for all 3 nonzero half-periods, FALSE for the control c = 1/3; the descended map sigma_i(x) = e_i + (e_i-e_j)(e_i-e_k)/(x-e_i) satisfies the exact curve-lift identity prod(sigma_i - e_l) = psi_i^2 prod(x - e_l) with RATIONAL psi_i = (e_i-e_j)(e_i-e_k)/(x-e_i)^2 (symbolic e1, e2, e3, all three cyclic assignments -- the p-function addition formula as pure algebra, no unit i needed), and {id, sigma_1, sigma_2, sigma_3} closes to Klein V4 projectively (sigma_i sigma_j = sigma_k, all commuting) -- the deck candidates for EVERY modulus","v507 SEAM.BIT.ORIGIN.01 (ii): THE CORE SOLVE -- a marks-preserving PGL2 square root of the half-period deck sigma_c exists iff its two deck pairs separate HARMONICALLY (pair cross-ratio = -1), and the condition solves EXACTLY to lambda = -1 (sigma_1: pairs {0,inf},{1,lambda}), lambda = 2 (sigma_2: {1,inf},{0,lambda}), lambda = 1/2 (sigma_3: {lambda,inf},{0,1}) -- per half-period c exactly ONE solution; the union over c is the harmonic orbit {-1, 2, 1/2} with j(-1) = j(2) = j(1/2) = 1728 (tau = i), against the controls j(3) = 21952/9 (generic) and j(hexagonal) = 0 -- 'which sigma_c aligns' is the modulus-plus-alignment choice","v507 SEAM.BIT.ORIGIN.01 (iii): STABILISER COUNTS -- the complete 24-ordered-triple enumeration of the 4-mark stabiliser gives (|Stab|, #involutions, #freely-acting involutions) = (4,3,3) at the generic modulus lambda = 3 (Klein V4), (8,5,3) at the harmonic lambda = -1 (D4: 5 involutions, only 3 free), (12,3,3) at the hexagonal point (A4), and in ALL THREE types the freely-acting involutions are EXACTLY the three half-period involutions sigma_c -- EVERY mark-free collar deck descends from a half-period translation of the seam double: the CLASS of the deck is forced by the origin, only WHICH half-period is not","v507 SEAM.BIT.ORIGIN.01 (iv): THE CM FIXED POINT -- on the half-periods mod 2 the CM action mult-by-i = [[0,-1],[1,0]] fixes EXACTLY ONE nonzero half-period, the vector (1,1) = c* = (1+tau)/2 (the intrinsically distinguished translation), while mult-by-rho = [[0,-1],[1,1]] 3-CYCLES all three (zero fixed -- at the hexagonal point NO half-period is distinguished, matching A4 with zero order-4 elements); on the lemniscatic curve the clock ghat: x -> (x-1)/(x+1) has projective order 4 and ghat^2 = -1/x = the CENTRAL half-period involution, and its curve lift REQUIRES psi = 2i/(x+1)^2 (exact identity prod(phi - e) = psi^2 prod(x - e) with ratio -4/(x+1)^4; t^2+1 irreducible over Q) -- half-period decks lift rationally, the clock root exists only WITH the CM unit i <=> tau = i","v507 SEAM.BIT.ORIGIN.01 (v): THE Cl(16) DICHOTOMY -- on explicit 256x256 Jordan-Wigner gamma matrices the CENTRAL implementer Utilde = prod_j (1 - gamma_j gamma_{j+8}) squares to 256 gamma_1...gamma_16 = 256 (-1)^F (NONSPLIT Z4, v506 reproduced), while the EDGE implementer Utilde_e = P_3 (g1+g5)(g2+g4)(g6-g16)(g7-g15)(g8-g14)(g9-g13)(g10-g12) implements the NS edge reflection j -> 4-j on ALL 16 generators (the implementation does NOT break) and squares to the SCALAR +2^7 x 1 EXACTLY (U_e^2 = +1: the extension SPLITS -- the fermions measure the alignment); in the 32-element NS dihedral lift group the central deck has EXACTLY 2 square roots (the +-quarter shifts, lift indices 5 and 13 = shifts by 4 and 12: the clock pair) while the edge deck has 0 (no Z8 tower over the edge deck) -- the Moebius root count 2 vs 0 reappears fermionically","v507 SEAM.BIT.ORIGIN.01 (vi): THE SILVER BIJECTION CENSUS -- among all 24 ordered mark triples exactly 8 Moebius maps carry the silver counterexample {+-1, +-(3+2 sqrt 2)} onto the Legendre marks {0, 1, -1, inf}, and EVERY one conjugates the deck z -> -z to an EDGE half-period involution sigma_2 or sigma_3, NEVER the central sigma_1 = -1/x (the silver set IS 'tau = i with deck = a non-CM-fixed half-period translation' -- the in-family witness that refutes the tautology); the control: all 8 bijections mu4 -> Legendre carry the v506 seam deck to the CENTRAL sigma_1 ONLY -- the common torus origin does NOT force the alignment, the bit is the position choice among the half-periods"],"checked_by_registry":false,"heading_as_written":"(* ==== v507 round: SEAM.BIT.ORIGIN.01 -- the tautology attack on the v506 alignment bit, executed and refuted (Part A torus origin + Part B fermion dichotomy). Exact content mirrored: (i) the HALF-PERIOD DESCENT -- the fixed points of w -> -w on C/(Z + tau Z) are the 4 half-periods (2w in Lambda <=> coefficients in {0, 1/2}; the 1/3-control fails), a translation t_c descends iff 2c in Lambda (exactly the 3 nonzero half-periods), and the descended map sigma_i(x) = e_i + (e_i-e_j)(e_i-e_k)/(x-e_i) satisfies the exact curve-lift identity prod(sigma_i - e_l) = psi_i^2 prod(x - e_l) with RATIONAL psi_i, closing to Klein V4 symbolically; (ii) the CORE SOLVE -- the pair cross-ratio condition CR = -1 solves to lambda = -1 (sigma_1), 2 (sigma_2), 1/2 (sigma_3) exactly, union = the harmonic orbit with j = 1728, against j(3) = 21952/9 and j(hex) = 0; (iii) the STABILISER COUNTS -- the complete 24-triple enumeration gives (|Stab|, #involutions, #free) = (4,3,3) generic / (8,5,3) harmonic / (12,3,3) hexagonal, and in ALL three types the free involutions are EXACTLY the three sigma_c (the deck CLASS is forced); (iv) the CM FIXED POINT -- mult-by-i mod 2 fixes exactly the half-period (1,1) = c* = (1+tau)/2 while mult-by-rho 3-cycles all three, the lemniscatic clock ghat: x -> (x-1)/(x+1) needs the curve-lift factor psi = 2i/(x+1)^2 (the CM unit; t^2+1 irreducible over Q) and squares to the central -1/x; (v) the Cl(16) DICHOTOMY -- on explicit 256x256 Jordan-Wigner gammas the central implementer squares to 256 gamma_1...gamma_16 = 256 (-1)^F (nonsplit) while the EDGE implementer Utilde_e = P_3 (g1+g5)(g2+g4)(g6-g16)(g7-g15)(g8-g14) (g9-g13)(g10-g12) implements the NS edge reflection and squares to the SCALAR +2^7 (split), and in the 32-element NS dihedral lift group the central deck has EXACTLY 2 square roots (the +-quarter shifts) vs 0 for the edge deck; (vi) the SILVER BIJECTION CENSUS -- all 8 mark bijections {+-1, +-(3+2 sqrt 2)} -> {0, 1, -1, inf} carry the deck z -> -z to the EDGE sigma_2/sigma_3 (never the central sigma_1), while all 8 mu4 bijections carry it to the CENTRAL sigma_1. The v493 circularity-audit direction and the 28/21 arrangement census stay Python-side (v507). Mirrors v507. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:4545","line_end":4783,"line_start":4545,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v493","v506","v507"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v508 CELEST.WP5E.GAMMA.01 (i): VERTEX-SPACE DIMS -- the W(D5) x W(A3)-invariant quadratics on the 8-dim glue Cartan have bidegree dims (x^2, xy, y^2) = (1, 0, 1), total 2 = span{s5, s3} (the COMPLETE gauge-invariant quadratic vertex basis), and the invariant quartics have bidegree dims (4,0)/(3,1)/(2,2)/(1,3)/(0,4) = (2, 0, 1, 0, 2), total 5 = span{P1, P2, P3, T5, T3} (the complete anomaly bookkeeping space) -- exact Weyl nullspace arithmetic over all bidegrees, generator by generator","v508 CELEST.WP5E.GAMMA.01 (ii): TWISTED QUADRATICS + THE EVEN-SECTOR COLLAPSE -- K^{(0)} = 60(s5+s3), K^{(1)} = K^{(3)} = 4 s5 - 12 s3, K^{(2)} = -4(s5+s3) exactly (the v505 sector quadratics recomputed), and the SIDE DISCOVERY K^{(0)} = -15 K^{(2)}: the two even-sector quadratics are PARALLEL -- this collapse reduces the charge-0 product span to 2 dims and drives the Phi_P obstruction","v508 CELEST.WP5E.GAMMA.01 (iii): THE PRODUCT THEOREM (the master kill) -- (a s5 + b s3)(c s5 + d s3) = ac P1 + (ad+bc) P2 + bd P3 IDENTICALLY (symbolic a, b, c, d): the product of ANY two invariant quadratics has identically ZERO T5- and T3-content, so every scalar-exchange image (any axion count, any selection rule, any couplings) is annihilated by Phi_T3 while Phi_T3(A_fix) = 32 != 0 -- the pairing is decided before enumeration","v508 CELEST.WP5E.GAMMA.01 (iv): THE RANK-3 CERTIFICATE -- exchange channels E13 = K^{(3)}K^{(1)} = (16, -96, 144, 0, 0), E22 = (K^{(2)})^2 = (16, 32, 16, 0, 0), bulk E00 = (K^{(0)})^2 = 225 E22 (parallel); the exchange matrix M (5 x 2) has rank 2 with kernel 0 and rank([M | A_fix]) = 3 > 2: UNSOLVABLE, with A_fix = (9, -30, -15, 0, 32) and annihilator certificate (Phi_T5, Phi_T3, Phi_P)(A_fix) = (0, 32, 72) (each functional annihilates E13, E22, E00); the naturalness anchors miss identically: ch2-natural couplings (9/64, 1/4) give (25/4, -11/2, 97/4, 0, 0) and AB-weight couplings (1/2, 1/4) give (12, -40, 76, 0, 0), BOTH with certificate (0, 0) vs required (32, 72) -- scale- and coupling-independent","v508 CELEST.WP5E.GAMMA.01 (v): THE SO(16) NEGATIVE CONTROL -- restricting to the even classes {0, 2} (the so16 glue: a mere Z2 monodromy, odd McKay nodes EMPTY -- there are NO twisted sphere-axion partners at all), the Atiyah-Bott-weighted sum is (15, -18, -15, -4, 40) in (P1, P2, P3, T5, T3): the D5 quartic does NOT even cancel (T5 = -4, unlike E8's exact T5 = 0) and 40 T3 stands with zero axions available -- the mechanism is structurally BROKEN, not merely obstructed; the E8 mu4 glue is special on both counts","v508 CELEST.WP5E.GAMMA.01 (vi): THE D8 NATIVE QUARTIC -- on the D8 Cartan the 112 so16 roots give sum <alpha,z>^2 = 28 s8 (2 h_vee(D8) = 28 Killing) and sum <alpha,z>^4 = 16 T8 + 12 s8^2 exactly: the independent quartic coefficient 16 != 0 (no Okubo reduction) and there is NO A3 block at all -- no T3 structure, no sphere classes, nothing to pair: the gamma question cannot even be posed for the D8 route"],"checked_by_registry":false,"heading_as_written":"(* ==== v508 round: CELEST.WP5E.GAMMA.01 -- WP5e-gamma \"the sphere-axion pairing check\", an honest rigid NEGATIVE result (the exchange route for pairing the three twisted sphere axions with the rigid 32 T3 residual of the v505 Atiyah-Bott ledger is killed with a certificate). Exact content mirrored: (i) the VERTEX-SPACE DIMS -- the W(D5) x W(A3)-invariant quadratics on the 8-dim glue Cartan have bidegree dims (1,0,1), total 2 = span{s5, s3}, and the invariant quartics have bidegree dims (2,0,1,0,2), total 5 = span{P1,P2,P3,T5,T3} (Weyl nullspace arithmetic, generator by generator); (ii) the TWISTED QUADRATICS + the K^(0) = -15 K^(2) collapse (the two even-sector quadratics are PARALLEL); (iii) the PRODUCT THEOREM -- (a s5 + b s3)(c s5 + d s3) = ac P1 + (ad+bc) P2 + bd P3 identically (zero T5/T3 content of every exchange image); (iv) the RANK-3 CERTIFICATE -- channels E13 = (16,-96,144,0,0), E22 = (16,32,16,0,0), E00 = 225 E22, exchange matrix rank 2 with kernel 0, rank([M | A_fix]) = 3, annihilator certificate (Phi_T5, Phi_T3, Phi_P)(A_fix) = (0, 32, 72), and the naturalness images (25/4,-11/2,97/4,0,0) / (12,-40,76,0,0) with certificate (0,0); (v) the SO(16) AB SUM (15,-18,-15,-4,40) -- T5 does not even cancel, odd classes empty; (vi) the D8 NATIVE QUARTIC 16 T8 + 12 s8^2 with Killing 28 s8 -- no T3 structure. Mirrors v508. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:4784","line_end":4979,"line_start":4784,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v505","v508"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v509 CELEST.WP5E.EPS2.01 (i): CPS PERIOD INTEGRALS -- the S^3 period of the brane backreaction 3-form int d^2v ^ [vbar dvbar] on |v| = 1 has pullback density -sin(2 theta) exactly (phases cancel) and integral (2 pi)^2 x (-1) = -4 pi^2 = (2 pi i)^2 (CPS eq. 3.33: ONE quantum per brane, large-gauge invariance quantises N); the exceptional-sphere Kahler flux from K = |u|^2 + N log|u|^2 is int i ddbar N log(1+|z|^2) = 2 pi N EXACTLY with density N/(1+|z|^2)^2, while the flat part i ddbar t^2|zeta|^2 = t^2 -> 0 at t -> 0 -- level = flux quantum (CPS secs. 2, 3.3)","v509 CELEST.WP5E.EPS2.01 (ii): LEVEL ~ FLUX, EXACT CONTRACTION + DYNKIN NORMALISATION -- the Sp(N) symplectic-boson double contraction Om_ij Om_kl P^ik P^jl = +2N with crossed term -2N for N = 1, 2, 3 (the so(k) current-algebra level magnitude is LINEAR in the brane/flux number, CPS eq. 9.4: level -2N); so(8) vector sum_weights <l,x>^2 = 2<x,x> => T(vector) = 1 and adjoint sum_roots = 12<x,x> = 2 h_vee(so8) => T(adj) = 6 -- 'level = flux quantum x Dynkin index of the boundary matter'","v509 CELEST.WP5E.EPS2.01 (iii): PAIRING-MATRIX ENUMERATION 48 -> 2 -- the v505 ch2 ledger targets (C^-1)_mm give integer row candidates (8, 6, 8) per sphere; the FULL form condition P C^-1 P^T = C^-1 with |det P| = 1 has exactly 48 unimodular solutions, and effectivity P >= 0 cuts them to EXACTLY 2 = {identity, A3 diagram flip}: P_mi = c1(T_m).[Sigma_i] = delta_mi up to the sphere relabeling -- the McKay/Kronheimer normalisation is DERIVED from ch2 + integrality + unimodularity + effectivity, not postulated","v509 CELEST.WP5E.EPS2.01 (iv): THE THREE FLUXES -- 240 roots split (52, 64, 60, 64), graded dims (60, 64, 60, 64); glue fluxes F_i = sum_m dim(g_m) c1(T_m).[Sigma_i] = (64, 60, 64) = dim g_i with total 188 = 248 - 60 (all non-carrier currents), INVARIANT under the diagram flip; every charged root current carries deg(L_alpha|Sigma_i) = delta_mi: exactly ONE flux quantum through exactly one sphere -- and the three UNEQUAL numbers (64, 60, 64) kill the naive reading 'level = total open-string flux' by the lockstep consistency test itself (F_i = flavour multiplicity), while flux per adjoint current = F_i/dim g_i = (1, 1, 1)","v509 CELEST.WP5E.EPS2.01 (v): THE SECTOR-COUNTER DIAL -- #primaries((E8)_k) from the affine marks (2, 3, 4, 6, 5, 4, 3, 2) is (1, 3, 5, 10, 15, 27) for k = 1..6: EXACTLY ONE sector iff k = 1 (quantum dims >= 1, so the condensed two-interval index mu = sum d_i^2 = 1 iff #prim = 1) -- the KLM-condensed flux-sector count 1 (mu = 16 = ord^2 -> 16/4^2 = 1 through the Lagrangian mu4 glue) PINS the level k = 1 among all levels, independent of the CPS transplantation","v509 CELEST.WP5E.EPS2.01 (vi): THE LOCKSTEP THEOREM + THE 0/24 NEGATIVE PROBE -- clock invariance P(iZ) = P(Z) forces a3 = a2 = a1 = 0 (unique solution: the clock-invariant family is XY = Z^4 + a0 alone); the branch points are ONE mu4 orbit {i^k t} with periods Pi_j = t(i-1)(1, i, i^2) and squared moduli 2t^2 EQUAL on all three spheres; the monodromy t -> it multiplies the period vector by the pure phase i, and the Coxeter clock A has A^4 = 1 with det(A - 1) = -4 != 0 (NO invariant flux vector) -- k1 = k2 = k3 IS A THEOREM of clock invariance; NEGATIVE PROBE: the clock-forbidden family Z^4 - Z (disc = -27, smooth) has branch points {0, 1, w, w^2} that are NOT a mu4 orbit, and over ALL 24 orderings ZERO chains give three equal period moduli (1 vs sqrt 3): non-lockstep => unequal k_i => no single (E8)_k boundary","v509 CELEST.WP5E.EPS2.01 (vii): NEGATIVE CONTROLS -- SO(16) glue (Z4 classes (60, 0, 60, 0), a mere Z2 monodromy): fluxes (0, 60, 0) leave spheres 1 and 3 FLUX-DARK, the ch2 defect is -30 != -78, and the condensation stops at 16/2^2 = 4 = det Cartan(D8) (four sectors survive, no holomorphic single-sector net); the WRONG intersection form A2: det = 3 != 4 = |Z4| (McKay bijection broken), ch2 = (-1/3, -1/3) (wrong denominators), Dedekind sum 2/3 != 5/4, glue diagonal 5/8 + 1/3 = 23/24 NOT integer (non-isotropic), mu = 12 is not a perfect square (NO Lagrangian subgroup exists at all), and the A2 Coxeter has order 3 != 4 = |mu4| -- the clock cannot even act"],"checked_by_registry":false,"heading_as_written":"(* ==== v509 round: CELEST.WP5E.EPS2.01 -- WP5e-epsilon-2 \"the CPS level-from-flux dial\" (verdict B; k = 1 from flux quantisation on the lockstep spheres, Costello-Paquette-Sharma Burns holography). Exact content mirrored: (i) the CPS PERIOD INTEGRALS -- the S^3 period of the brane backreaction 3-form = (2 pi i)^2 (pullback density -sin 2 theta) and the exceptional-sphere Kahler flux = 2 pi N exactly (flat part dies at t -> 0); (ii) the LEVEL ~ FLUX contraction 2N (symplectic bosons, N = 1, 2, 3) with the Dynkin normalisation T(so8 vector) = 1, T(adj) = 6; (iii) the PAIRING-MATRIX ENUMERATION -- row candidates (8, 6, 8), 48 unimodular solutions of P C^-1 P^T = C^-1, with effectivity P >= 0 exactly 2 = {identity, A3 diagram flip}; (iv) the FLUXES (64, 60, 64) = dim g_i with total 188 = 248 - 60, flip-invariant, one quantum per charged current; (v) the SECTOR-COUNTER dial #primaries((E8)_k) = (1, 3, 5, 10, 15, 27) for k = 1..6 from the affine marks -- exactly one sector iff k = 1; (vi) the LOCKSTEP THEOREM -- clock invariance forces a3 = a2 = a1 = 0, periods t(i-1)(1, i, i^2) with squared moduli 2t^2 equal on all three spheres, monodromy = pure phase i, det(A-1) = -4, and the negative probe Z^4 - Z (disc -27): 0/24 orderings lockstep; (vii) the NEGATIVE CONTROLS -- SO(16) fluxes (0, 60, 0) with ch2 defect -30 and condensation stuck at 4, A2 form det 3, glue diagonal 23/24 not integer, mu = 12 not a perfect square, Coxeter order 3 != 4. Mirrors v509. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:4980","line_end":5154,"line_start":4980,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v509"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v510 SEAM.BIT.FREEDOM.01 (i): DIHEDRAL CENSUS + QUOTIENT TOPOLOGY -- on the refined 2N-point seam circle D_16 has EXACTLY 17 involutions with exactly ONE free (the antipodal shift by 8) and all 16 reflections have exactly 2 circle fixed points (8 site-axis + 8 edge-axis: a reflection is NEVER free); robustness (9,1,4,4) at N = 8 and (13,1,6,6) at N = 12; odd control N = 9: (9,0,...) -- ZERO free involutions (no antipode at odd N, even carrier count needed); quotient topology: chi(circle/antipode) = 0 with 0 boundary points (a CLOSED circle) vs chi(circle/reflection) = 1 with 2 fixed corners (an INTERVAL, both axis types) -- the 6pi = 3 x 2pi Gauss-Bonnet budget counts closed circles, so deck freeness IS the established 'seam = closed circle' datum","v510 SEAM.BIT.FREEDOM.01 (ii): AUT COMPLETENESS -- Aut(C_8) computed by BRUTE FORCE over all 8! = 40320 permutations has exactly 16 elements and equals D_8 (no exotic circle automorphism exists); Aut(C_16) by degree-2 propagation: an adjacency-preserving map is DETERMINED by (image of 0, image of 1), all 32 = 16 x 2 candidates propagate consistently and equal D_16 exactly -- the dihedral census of mirror (i) covers ALL circle symmetries: the unique free involution of the seam circle IS the antipode, with no loophole","v510 SEAM.BIT.FREEDOM.01 (iii): THE Cl(16) DICHOTOMY CENSUS -- on explicit 256x256 Jordan-Wigner gammas the free deck's NS implementer Utilde = prod_j (1 - gamma_j gamma_{j+8}) squares to 256 gamma_1...gamma_16 = 256 (-1)^F (NONSPLIT, v507 reproduced), while for EVERY reflection axis k = 0..15 the NS implementer exists (implements one of the two spin lifts +-R on all 16 generators -- the v507 F2.2 lift ambiguity) and squares to a SCALAR in {2^7 (site-axis), 2^8 (edge-axis)}: the extension SPLITS for every non-free involution -- NONSPLIT <=> FREE over the COMPLETE 17-involution census, no exception; root dichotomy in the 32-element dihedral lift group: the free deck has EXACTLY 2 square roots (the +-quarter shifts = the Z8 clock tower) while ALL 16 reflections together have 0 -- no clock tower over any non-free arrangement","v510 SEAM.BIT.FREEDOM.01 (iv): THE REAL-STRUCTURE TABLE -- the deck-commuting condition M D = lam D M solves symbolically to exactly TWO families (lam = +1: M diagonal, sigma = mu conj z with |mu| = 1, fix locus = a LINE through the deck poles {0, inf} -- deck NOT free on it; lam = -1: M antidiagonal, sigma = mu/conj z with mu real, mu > 0 giving the fix circle |z| = sqrt mu that avoids the poles -- deck FREE on it); the unique mark-fixing antiholomorphic involution per deck-invariant configuration {+-1, +-b}: mu4 (b = i) -> the EQUATORIAL 1/conj z, deck FREE (v506 A-S2.9 reproduced); silver (b = 3+2 sqrt 2) -> the REAL AXIS through the poles, deck NOT free; generic-real (b = 3) -> real axis, NOT free; generic-unit (b = (3+4i)/5) -> equatorial, FREE without harmonicity; hexagonal (b = i(2 - sqrt 3), the j = 0 frame) -> NO mark-fixing real structure at all (marks not concyclic: RP-INCOMPATIBLE) -- the edge class exists only on circles through the deck poles","v510 SEAM.BIT.FREEDOM.01 (v): HARMONIC + FREE => mu4 EXACTLY -- the deck-pair cross-ratio condition (1-b)^2/(1+b)^2 = -1 solves EXACTLY to b = +-i: on a free-deck seam circle 'deck pairs harmonically separated' (the v507 tetrad face) forces the marks to be the mu4 orbit {+-1, +-i}, so GIVEN freeness harmonicity becomes SUFFICIENT (the silver family 'harmonic AND edge' is EMPTY on free circles); the lambda table 4b/(1+b)^2: mu4 -> 2 (the v168 value), silver -> 1/2 (harmonic!), generic-real -> 3/4, generic-unit -> 5/4 -- all real (concyclic), while the hexagonal frame has Im lambda = sqrt(3)/2 != 0 (not concyclic: no seam circle at all)","v510 SEAM.BIT.FREEDOM.01 (vi): THE HONEST COUNTERWITNESSES -- 'nonsplit => clock' is FALSE: the discrete witness {0,1,8,9} is shift-8-invariant with CROSSING deck pairing (the same nonsplit Fock lift applies, mark-independent), yet the quarter shift does NOT preserve it (while it does preserve the equally-spaced marks {0,4,8,12}); the continuous witness {+-1, +-(3+4i)/5} sits on a free-deck equatorial circle in the central class, yet its pair cross-ratio is -1/4 != -1, lambda = 5/4, j = 148176/25 != 1728, and the clock z -> iz does NOT preserve it -- freeness forces the CLASS (crossing/central, nonsplit), NOT the square modulus: 'tau = i' survives as the one continuous carrier datum"],"checked_by_registry":false,"heading_as_written":"(* ==== v510 round: SEAM.BIT.FREEDOM.01 -- the freedom attack on the v506/v507 alignment bit: the POSITION half of the bit is topology. Exact content mirrored: (i) the DIHEDRAL CENSUS -- on the refined 2N-point seam circle D_16 has 17 involutions with EXACTLY ONE free (the antipodal shift by 8) and all 16 reflections have exactly 2 circle fixed points (8 site-axis + 8 edge-axis; robustness N = 8, 12; odd control N = 9: zero free), plus the quotient topology chi(C/antipode) = 0 (circle) vs chi(C/reflection) = 1 (interval, 2 boundary corners); (ii) the AUT COMPLETENESS -- Aut(C_8) = D_8 by brute force over all 8! = 40320 permutations and Aut(C_16) = D_16 by degree-2 propagation (all 32 candidates), so the census covers ALL circle symmetries; (iii) the Cl(16) DICHOTOMY CENSUS -- on explicit 256x256 Jordan-Wigner gammas the free deck's NS implementer squares to 256 gamma_1...gamma_16 = 256 (-1)^F (nonsplit) while the implementers of ALL 16 reflections exist (one of the two spin lifts +-R) and square to SCALARS {2^7 (site-axis), 2^8 (edge-axis)} (split): NONSPLIT <=> FREE over the complete census; root dichotomy 2 (the +-quarter shifts) vs 0 total over all 16 reflections; (iv) the REAL-STRUCTURE TABLE -- the deck-commuting antiholomorphic involutions solve symbolically to exactly two families (M diagonal: mu conj z, fix line through the poles; M antidiagonal: mu/conj z, fix circle |z| = sqrt mu), and the unique mark-fixing real structure per configuration is equatorial/FREE for mu4 and generic-unit, real-axis/NOT-free for silver and generic-real, and NONEXISTENT for the hexagonal frame; (v) HARMONIC + FREE => mu4 -- the deck-pair cross-ratio (1-b)^2/(1+b)^2 = -1 solves exactly to b = +-i, with the lambda table (2, 1/2, 3/4, 5/4) real and the hexagonal lambda complex; (vi) the HONEST COUNTERWITNESSES -- the discrete witness {0,1,8,9} (shift-invariant, crossing, but not quarter-shift-invariant) and the continuous witness {+-1, +-(3+4i)/5} (pair cross-ratio -1/4, j = 148176/25 != 1728, clock does not preserve): the Fock dichotomy measures the CLASS, not the modulus. The Moebius/Klein covering models and the pillowcase branch control stay Python-side (v510). Mirrors v510. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:5155","line_end":5378,"line_start":5155,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v506","v507","v510"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v511 CELEST.WP5E.DELTA2.01 (i): INNERNESS COUNT + g0 STRUCTURE -- 240 glue roots of norm 2 with class split (52, 64, 60, 64); h = (2,2,2,2,2;0^4) AND h' = (0^5;1,1,1,-3) read <alpha,.> = class mod 4 on ALL 240 roots (the Z4 charge is inner, h in the Cartan of g0 -- the engine of the charge theorem); the 52 class-0 roots split 40 pure D5 + 12 pure A3 with NO mixed root and root span rank 8 = rank E8 (g0 = d5 (+) a3 SEMISIMPLE, no u(1)); class(-alpha) = -class(alpha) (the Killing pairing is charge-0)","v511 CELEST.WP5E.DELTA2.01 (ii): THE BILINEAR HOM TABLE (full tensor, exact Kostant) -- dim Hom_{g0}(g_j (x) g_j') over all 16 sector pairs is nonzero ONLY at j' = -j: (0,0) = 2 (K_d5, K_a3), (1,3) = (3,1) = (2,2) = 1 (Killing blocks), ALL 12 pairs with j + j' != 0 mod 4 vanish -- the inner-torus theorem at arity 2: the sphere axions (m = 1, 2, 3) have NO invariant bilinear vertex on the FULL algebra, the v508 Cartan collapse is a full-tensor statement","v511 CELEST.WP5E.DELTA2.01 (iii): THE TRILINEAR HOM TABLE -- ALL 15 sector triples with a+b+c != 0 mod 4 have Hom = 0 (the inner-torus theorem holds at arity 3: eta_m has no invariant trilinear vertex on the full algebra either) and the five neutral multisets carry dims {0,0,0}: 3, {0,1,3}: 2, {0,2,2}: 2, {1,1,2}: 1, {2,3,3}: 1 -- 9 independent trilinear structures: brackets/Killing composites plus exactly ONE more","v511 CELEST.WP5E.DELTA2.01 (iv): THE UNIQUE SYMMETRIC SURVIVOR -- Inv(S^3 adj) = (0, 1) for (d5, a3): so(10) has NO symmetric cubic invariant (Casimir degrees 2,4,5,6,8 -- protects T5), su(4) HAS exactly one (the d-symbol); Inv(L^3 adj) = (1, 1) (the structure constants), Inv(S^2 adj) = (1, 1) (Killing); on g0 = d5 (+) a3: Inv(S^3 g0) = 1 and Inv(L^3 g0) = 2 -- of the three g0-trilinears exactly ONE is totally symmetric, the su(4) d-symbol (the full-tensor object the Cartan-quadratic ansatz of v508 could not see); machinery guard: 4 x 4 = 0 vs 4 x 4bar = 1","v511 CELEST.WP5E.DELTA2.01 (v): THE CONTROLS -- SO(16)/D8 glue: bilinears (adj adj, adj spin, spin spin) = (1, 0, 1) (Killing + the real spinor pairing, nothing off-diagonal), trilinears (adj^3, adj^2 spin, adj spin^2, spin^3) = (1, 0, 1, 0), Inv(S^3 adj_d8) = 0 and Inv(L^3 adj_d8) = 1: D8 has NO symmetric cubic (no cubic Casimir) and no A3 block -- the delta-2 channel cannot even be posed (E8/mu4 doubly special); FALSE g0 = d5+a2+u(1): bilinear entries (0,0)/(1,3)/(2,2) = (5, 2, 2) != (2, 1, 1) and Inv(S^3 g0_false) = 6 != 1 (breaking a3 inflates every Hom dimension); FALSE sector content (16_s, 4bar): fake-g1 x g3 = 0 and fake-g1 x fake-g1 = 0 vs the true g1-g3 value 1 -- the (16_s, 4)/(16_c, 4bar) content is forced","v511 CELEST.WP5E.DELTA2.01 (vi): Q_dd BY TWO ROUTES -- explicit su(4) matrices (3 Cartan + 12 root vectors, exact trace Gram): bracket vertices f(x, x, B_a) = 0 for all 15 basis elements (antisymmetry kills every bracket-type vertex with two identical legs), root-direction contractions d(x, x, E_ij) = 0 (zero-weight matching), the tadpole sum G^{-1}_ab d(x, B_a, B_b) = 0 (the d-symbol is trace-free), and the exchange quartic Q_dd = sum_ab d(x,x,B_a)(60 G)^{-1}_ab d(x,x,B_b) = (0, 0, -1/240, 0, 1/60) = (1/60)(T3 - P3/4) in (P1, P2, P3, T5, T3), agreeing EXACTLY with the independent hand route |x^2 - (tr x^2/4) 1|^2/60 -- Phi_T3(Q_dd) = 1/60 != 0: the v508 master kill does NOT extend to cubic vertices; and Tr X^3 = 0 for antisymmetric X (no T5 analogue, Phi_T5 stays a universal annihilator)","v511 CELEST.WP5E.DELTA2.01 (vii): THE PSI CERTIFICATE + THE RELAXED SOLUTION -- v508 replication E13 = (16, -96, 144, 0, 0), E22 = (16, 32, 16, 0, 0), E00 = 225 E22, A_fix = (9, -30, -15, 0, 32); the enlarged exchange matrix M = [E13, E22, E00, Q_dd] has rank 3 with rank([M | A_fix]) = 4: STILL UNSOLVABLE, but Phi_T3 is no longer an annihilator (Phi_T3(Q_dd) = 1/60) -- the surviving certificate is {Phi_T5, psi = Phi_P - Phi_T3/4} with psi annihilating ALL FOUR channels and psi(A_fix) = 72 - 8 = 64 (= dim g1, [C] fence); the RELAXED system {u, v, w, Q_dd} (charge bookkeeping dropped on the bilinear P-block) has rank 4 and solves EXACTLY: A_fix = -1 u + 8 v + 2 w + 1920 Q_dd with residual 0 -- c_d = 1920 = 32 x 60 = |W(D5)| = 8 x 240 ([C] fence)"],"checked_by_registry":false,"heading_as_written":"(* ==== v511 round: CELEST.WP5E.DELTA2.01 -- WP5e-delta-2 \"the full-tensor ledger\" (the named escape route of the v508 exchange no-go, executed: the collapse is CONFIRMED full-tensorially, and one cubic door opens). Exact content mirrored: (i) the INNERNESS COUNT -- 240 glue roots with class split (52, 64, 60, 64), h = (2,2,2,2,2;0^4) and h' = (0^5;1,1,1,-3) reading the class mod 4 on ALL 240 roots, the class-0 roots splitting 40 pure D5 + 12 pure A3 with NO mixed root (g0 = d5 (+) a3 semisimple, NO u(1); root span rank 8), and class(-alpha) = -class(alpha); (ii) the BILINEAR HOM TABLE -- dim Hom_{g0}(g_j (x) g_j') by exact Kostant alternating sums on integer-scaled minuscule weight orbits: nonzero ONLY at j' = -j with dims (2, 1, 1, 1), all 12 charged pairs ZERO (the inner-torus theorem at arity 2); (iii) the TRILINEAR HOM TABLE -- all 15 non-neutral sector triples have Hom = 0 (arity 3) and the five neutral multisets carry dims (3, 2, 2, 1, 1); (iv) the UNIQUE SYMMETRIC SURVIVOR -- Inv(S^3 adj) = (0, 1) for (d5, a3) (so(10) has NO cubic Casimir, su(4) has exactly one), Inv(L^3 adj) = (1, 1), Inv(S^2 adj) = (1, 1), and on g0: Inv(S^3 g0) = 1, Inv(L^3 g0) = 2 (of the three g0-trilinears exactly ONE is totally symmetric: the su(4) d-symbol), with the dual machinery guard 4 x 4 = 0 vs 4 x 4bar = 1; (v) Q_dd BY TWO ROUTES -- explicit su(4) matrices: bracket vertices f(x,x,B) = 0, root-direction contractions d(x,x,E_ij) = 0, tadpole sum G^{-1}_ab d(x,B_a,B_b) = 0, and the exchange quartic Q_dd = sum d(x,x,B_a)(60 G)^{-1}_ab d(x,x,B_b) = (0, 0, -1/240, 0, 1/60) = (1/60)(T3 - P3/4) agreeing exactly with the hand route |x^2 - (tr x^2/4) 1|^2/60, so Phi_T3(Q_dd) = 1/60 != 0; plus Tr X^3 = 0 for antisymmetric X (no T5 analogue); (vi) the PSI CERTIFICATE + THE RELAXED SOLUTION -- E13 = (16, -96, 144, 0, 0), E22 = (16, 32, 16, 0, 0), E00 = 225 E22, A_fix = (9, -30, -15, 0, 32); M = [E13, E22, E00, Q_dd] has rank 3 with rank([M | A_fix]) = 4 (still unsolvable), psi = Phi_P - Phi_T3/4 annihilates all four channels with psi(A_fix) = 72 - 8 = 64, and the relaxed system {u, v, w, Q_dd} solves EXACTLY: A_fix = -u + 8v + 2w + 1920 Q_dd (rank 4, c_d = 1920 = |W(D5)| = 8 x 240); (vii) the CONTROLS -- SO(16)/D8: bilinears (adj adj, adj spin, spin spin) = (1, 0, 1), trilinears (1, 0, 1, 0), Inv(S^3 adj_d8) = 0 and Inv(L^3 adj_d8) = 1 (NO symmetric cubic, no odd sectors, no A3 block -- the delta-2 channel cannot even be posed); false g0 = d5+a2+u(1): bilinear entries (5, 2, 2) != (2, 1, 1) and Inv(S^3 g0_false) = 6 != 1; false sector content (16_s, 4bar): both pairings die (0, 0) vs the true value 1. Mirrors v511. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:5379","line_end":5674,"line_start":5379,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v508","v511"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v512 SEAM.TAU.FLAG.01 (i): THE V4/D4 CENSUS TABLE -- five exact members delta in {pi/6, pi/4, arctan(4/3) [the v510 counterwitness (3+4i)/5], pi/3, pi/2}: every generic member has |G| = 4 = V4 with 2 rotations, IS mark-transitive (pair-exchanging inversions z -> +-b/z: bare transitivity is delta-BLIND -- the falsification), 2 flag orbits and 2 arc orbits; ONLY delta = pi/2 has |G| = 8 = D4, 4 rotations (the clock), 1 flag orbit and 1 arc orbit -- the discrete datum is exactly the V4 -> D4 symmetry-lift bit (flag transitivity), nothing else moves","v512 SEAM.TAU.FLAG.01 (ii): THE SOLVESET EQUIVALENCES + FAMILY IDENTITIES -- on (0, pi/2]: b^2 = -1 (order-4 rotation) <=> delta = pi/2 EXACTLY, b^2 = +1 impossible, mark mirror cos delta = 0 <=> pi/2, odd-split zero tan(delta/2) = 1 <=> pi/2, equal arcs delta = pi - delta <=> pi/2 (five faces, one solveset); family identities lambda = 4b/(1+b)^2 = sec^2(delta/2) and pair cross-ratio = -tan^2(delta/2) = 1 - lambda exact; mu4 member lambda = 2, j = 1728, cross-ratio -1 (harmonic); counterwitness member lambda = 5/4, j = 148176/25 != 1728, cross-ratio -1/4 != -1 -- the v510 counterwitness lives INSIDE the family","v512 SEAM.TAU.FLAG.01 (iii): THE SPECTRAL FACES IN CLOSED FORM -- the free seam covariance G(theta) = -(1/pi) log(2 sin(theta/2)) restricted to the 4 marks has exact deck-adapted eigenvectors, and the DECK-ODD doublet splits by 2(u - v) with exp(pi split/2) = cot(delta/2) EXACTLY (zero iff delta = pi/2; counterwitness tan(delta_cw/2) = 1/2, split = (2/pi) log 2 != 0); the arc-weighted seam Laplacian has exact spectrum {0, 2/delta, 2/(pi-delta), sum} with the SAME degeneracy criterion (mu4: doubly 4/pi); the v215-K3/v503 mod-4 indicator restricted to the marks is ||[G4, P_clock]||_F^2 = 8(u - v)^2, i.e. (2 sqrt 2/pi)|log tan(delta/2)| in closed form -- the v503 lattice curve's isolated zero at tau = i, analytically","v512 SEAM.TAU.FLAG.01 (iv): THE TWIST MODE IDENTITY + AB delta-BLINDNESS + j-RATIONALITY CONTROL -- the order-4 twist rho needs [rho, Delta_tau] = 0 with mode identity lam_mn - lam_rho(mn) = (m^2 - n^2)(t - 1/t), zero for all modes iff t = 1 (Reduce: {1} on t > 0) -- the rho-twist EXISTS iff tau = i; the deck twist sigma has d sigma = -Id on EVERY torus, |det(1 - d sigma)| = 4, so Tr(sigma e^(t Delta)) = 4 x 1/4 = 1 exactly rational for ALL delta (Atiyah-Bott rationality selects NOTHING); and j_cw = 148176/25 is rational with denominator 25 != 1 (not an algebraic integer, hence non-CM) yet != 1728: even j-rationality does not select -- H3 is the clock postulate in trace clothing","v512 SEAM.TAU.FLAG.01 (v): H4 RIGIDITY (Schur) -- the v117 cusp quadruple M_k = U^k M0 U^-k is unitary with char poly lam^3 - 1 at every mark and product 1 (existence is position-blind: a pi_1 relation); but the joint CENTRALISER of the four blocks is the scalars (nullspace dim 1, prop Id), every implementer of the cusp 4-cycle W M_k W^-1 = M_(k+1) is W = c U (nullspace dim 1, prop U), and U^2 = diag(1, -1, -1) is NONSCALAR: no projective involution implements the 4-cycle -- the implementer has projective order exactly 4 (the Z8/clock-tower shadow); group level: V4 has element orders {1,2,2,2} while the 4-cycle has order 4 -- V4 cannot induce it, 'the cusp 4-cycle is geometrically realised' <=> the clock","v512 SEAM.TAU.FLAG.01 (vi): THE NEGATIVE CONTROLS -- hexagonal: |b_hex| = 2 - sqrt(3) != 1 (not on the free circle) and j = 0 (Aut(E_rho) = Z6, no order-4 element): fails the battery PRECONDITIONS; silver {+-1, +-(3+2 sqrt 2)}: all marks real, lambda = 1/2, j = 1728 -- HARMONIC but the mark circle passes through the deck poles (topologically dead, the v510 edge class): position and modulus halves independent; Z16 free-deck census: 0 invariant 3-subsets vs 28 = C(8,2) invariant 4-subsets (odd mark counts impossible on the free circle); n = 3 on a plain circle: scalene (|G|, transitive) = (1, False), isosceles (2, False), equilateral (6, True) -- at n = 3 bare transitivity ALREADY forces equal spacing; it is the deck-pairing at n = 4 that makes bare transitivity free of charge: '4 counts'"],"checked_by_registry":false,"heading_as_written":"(* ==== v512 round: SEAM.TAU.FLAG.01 -- \"the flag-transitivity equivalence web\": the tau = i attack on the free RP seam circle. Test family M(delta) = {+-1, +-e^(i delta)}; bare mark-transitivity is delta-blind (pair-exchanging V4), FLAG transitivity <=> delta = pi/2 <=> tau = i. Six exact mirrors: (i) the V4/D4 census over five exact members incl. flag/arc orbit counts, (ii) the solveset equivalences + family identities, (iii) the odd-split closed form + arc Laplacian + K3 indicator, (iv) the twist mode identity + AB delta-blindness + j-rationality control, (v) the H4 centraliser rigidity (Schur), and (vi) the negative controls (hexagonal/silver/Z16 census/n = 3). Mirrors v512. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:5675","line_end":5858,"line_start":5675,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v512"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v513 CELEST.DTERM.NONDERIV.01 (i): THE PROPAGATOR ANCHOR + T3-SLOT PINNING -- sum over all 240 glue roots of <alpha, e>^2 = 120 = 2 h_vee(E8) <e,e> for the a3-block direction e (the e8 Killing form restricts to 60 x the fundamental trace form: the 60 in Q_dd is [E]-DERIVED, not chosen); the relaxed P-directions {u, v, w} span the full (P1, P2, P3) block (det = -64 != 0) and carry no T5/T3, so the Q_dd coefficient is pinned by the T3 slot ALONE: c_d = Phi_T3(A_fix)/Phi_T3(Q_dd) = 32/(1/60) = 1920 = 32 x 60","v513 CELEST.DTERM.NONDERIV.01 (ii): THE CONVENTION TABLE -- c_d = (1920, 120, 256, 32, 69120) in the five normalisations (probe tr-fund d + e8-Killing 60G; Gell-Mann d_abc = 2tr(T{T,T}) with tr(TT) = 1/2 + e8-Killing 30 delta; tr-fund d + su(4)-Killing 8G; tr-fund d + plain trace G; ch3-normalised d/6 + e8-Killing): EXACTLY ONE convention hits |W(D5)| = 1920 -- the Weyl-order fingerprint is normalisation-CONTINGENT; the convention-stable content is c_d x Phi_T3(Q^conv) = 32 = Phi_T3(A_fix) in ALL five, i.e. the factorisation c_d = Phi_T3(A_fix) x 2 h_vee(E8) = 32 x 60 -- everything beyond it (incl. '= |W(D5)|') is convention decoration","v513 CELEST.DTERM.NONDERIV.01 (iii): FLUX ENUMERATION + LOOK-ELSEWHERE LEDGER -- the charge-LEGAL sphere pairings (m + m' = 0 mod 4) are (1,3) and (2,2) with flux products F_m F_m'/2 = (2048, 1800): they BRACKET 1920 and both MISS; the only flux hit 64*60/2 = 1920 is the (1,2) pairing with charge 3 mod 4, FORBIDDEN by the v511 innerness theorem; pre-declared catalog of 21 [E] numbers x grammar {a*b, a*b/2, a*b/4, a+b} = 924 expressions with 11 distinct hits on 1920, while the control targets score 1800 -> 8, 2016 -> 0, 2048 -> 5: any smooth number near 2000 is easy to hit -- K1 is numerology","v513 CELEST.DTERM.NONDERIV.01 (iv): THE K2 QUANTISATION LATTICES -- tr(h^3) on the su(4) COROOT lattice is valued in 6Z with minimal nonzero quantum 6 (x^3 = x mod 6, tr h = 0), while on the WEIGHT lattice it is fractional (fundamental weight: 3/8) -- the quantum is lattice-dependent; integer couplings in tr-fund units + e8-Killing propagator give c_d in 60 Z with 1920/60 = 32: ON the lattice but the 32ND multiple, no minimality; strict ch3-unit couplings (6 Z) give 2160 Z and 1920/2160 = 8/9 NOT integer: EXCLUDED; and the residual integer 32 has 12 signed factorisations lambda_1 lambda_3 -- nothing selects one: K2 delivers a lattice, never the value 1920","v513 CELEST.DTERM.NONDERIV.01 (v): THE K3 PROVENANCE CLASH + WEYL DATA -- the su(4) cubic power sums per class from the actual roots are A_m = (0, 16, 0, -16) (total 0: e8 has NO cubic Casimir) with twisted sum sum_m i^m A_m = 32i, NUMERICALLY equal to Phi_T3(A_fix) = 32; but the quartic T3 coefficients per class are (8, 16, -40, 16) and the AB-weighted contributions to Phi_T3(A_fix) are (10, -4, 30, -4) -- DOMINATED by classes 0/2 with classes 1/3 contributing NEGATIVELY (-8), while the cubic 32 is built 16 + 16 from classes 1/3 ONLY: same number, disjoint mechanism = coincidence exposed; Weyl data: exactly |W(D5)| = 1920 = 2^4 5! and the ACCIDENTAL |W(E8)|/|W(A8)| = 1920 hit (A8 is not a carrier factor), the d-symbol is an A3-side object with |W(A3)| = 24, and |W(D8)| = 5160960 != 1920","v513 CELEST.DTERM.NONDERIV.01 (vi): THE K4 NEGATIVE CONTROLS -- SO(16)/D8: the cubic class sums vanish identically (adjoint AND spinor: all reps real), the fluxes (0, 60, 0) give charge-legal flux products {0, 1800} (dark spheres) and |W(D8)| = 5160960 != 1920: every candidate formula fails or is undefined; k = 2 flux doubling scales the flux-product formula x4 to 7680 != 1920 while c_d = Phi_T3(A_fix)/Phi_T3(Q_dd) is root-theoretic and STATIC (this control kills K1 but honestly cannot discriminate the Weyl fence, which is also static); the false g0 = d5+a2+u(1) carries SIX symmetric cubics (v511 D7.3) -- no unique channel, the derivation question cannot even be posed there"],"checked_by_registry":false,"heading_as_written":"(* ==== v513 round: CELEST.DTERM.NONDERIV.01 -- \"the c_d negative certificate\": can geometry derive c_d = 1920? Anti-numerology battery on the v511 [C] fence 1920 = |W(D5)|. Six exact mirrors: (i) the propagator anchor + T3-slot pinning, (ii) the five-way convention table + the convention-stable factorisation 32 x 60, (iii) the flux enumeration + look-elsewhere ledger with control targets, (iv) the K2 quantisation lattices, (v) the K3 provenance clash + Weyl data, and (vi) the negative controls. Mirrors v513. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:5859","line_end":6055,"line_start":5859,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v511","v513"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v514 CELEST.WP5E.EPS1.01 (i): THE EQUIVARIANT PENROSE LEDGER -- on PT' = tot(O(1)+O(1) -> P^1) the pushforward ledger pi_* O(-2) gives per spacetime degree d exactly (d+1)^2 twistor classes = the exact nullspace dimension of the wave operator Box = d_a d_e - d_b d_c on degree-d polynomials (1, 4, 9, 16, 25, 36, 49 for d = 0..6); with the incidence-forced column weights (+1, +1, -1, -1) the PER-CHARACTER kernels EQUAL the twistor block counts (d+1) x #{(p,q): p+q = d, p-q = m mod 4} for ALL d = 0..6 and ALL four characters m: the equivariant Penrose accounting closes block by block -- the O(-2) slot is a CONSTRUCTION","v514 CELEST.WP5E.EPS1.01 (ii): THE CHARACTER SERIES + THE SURVIVING BULK AXION -- the character-valued Hilbert series H(t, g_j) = (1 - t^2)/((1 - i^j t)^2 (1 - i^-j t)^2) equal the closed forms ((1+t)/(1-t)^3, (1-t^2)/(1+t^2)^2, (1-t)/(1+t)^3, dito); the per-character series are P_0 = 1 + 3t^2 + 15t^4 + 21t^6 + 45t^8, P_1 = P_3 = 2t + 8t^3 + 18t^5 + 32t^7, P_2 = 6t^2 + 10t^4 + 28t^6 + 36t^8 (all coefficients to t^8); the d = 0 slot has multiplicity (1, 0, 0, 0): THE BULK AXION SURVIVES the Z4 projection with invariant density lim (1-t)^3 P_0 = 1/2 = (1/4) x 2; the twisted characters {i, -1, -i} carry the minimal content (2t, 6t^2, 2t) and NO degree-0 mode = the E3 bijection per character","v514 CELEST.WP5E.EPS1.01 (iii): THE MOLIEN HYPERSURFACE + THE VERONESE CONTROL -- the invariant fibre ring has Molien series (1/4) sum_j 1/((1-i^j t)(1-i^-j t)) = (1 - t^8)/((1 - t^4)^2 (1 - t^2)) EXACTLY: generators Z = mu1 mu2 in O(2), X = mu1^4, Y = mu2^4 in O(4), ONE relation XY = Z^4 in degree 8 = the a0 weight (the v492/v493 hypersurface from the slot); NEGATIVE CONTROL diag(i, i): invariant Molien = (1 + 3t^4)/(1 - t^4)^2 = the quartic VERONESE cone (degree-4 slice dim 5 => five generators, not a hypersurface) and the harmonic character is DEGREE-LOCKED (series 1 + 25t^4 + 81t^8); the Coxeter clock A on H^2(ALE) has eigenvalues {i, -1, -i} = the twisted characters and det(A - 1) = -4 (no invariant sphere class)","v514 CELEST.WP5E.EPS1.01 (iv): THE OKUBO RESIDUE, A PERFECT SQUARE -- on the 240 glue roots (norm 2, classes 52 + 64 + 60 + 64) the exact polynomial identities Tr_adj X^2 = 60 <x,x> = 2 h_vee <x,x> (Killing anchor) and Tr_adj X^4 = 36 <x,x>^2 = (6 <x,x>)^2 hold: the box anomaly is the PERFECT SQUARE of 6 <x,x> -- the residue on the single axion channel is lambda~ = 6 = |Z2| N_fam, with 36 = h_vee + 6 = 10 h_vee^2/(dim+2); NEGATIVE CONTROL so8: Killing 12 <x,x> and Okubo 12 <x,x>^2 hold exactly (so8 IS on Costello's list) but lambda~^2 = 12 is NOT a perfect square (lambda~ = 2 sqrt 3 irrational); perfect squares among the Deligne-series values (8, 9, 10, 12, 15, 18, 24, 36) are exactly {9, 36} = {sl3, e8}","v514 CELEST.WP5E.EPS1.01 (v): THE MEASURE CANCELLATION EXCLUDING 3 AND 12 + THE FLUX DIAL -- on PT/Z4 the quotient measure mu = 1/4 enters the GS chain three times (vertex^2 = mu^2, invariant-mode propagator = 1/mu, anomaly = mu) and cancels EXACTLY: lam_eff^2 (mu v)^2 (G/mu) = mu 36 v^2 G solves to lam_eff^2 = 36 for ARBITRARY mu -- lambda~_eff(PT/Z4) = 6; the WRONG bookings are quantified and EXCLUDED: anomaly-only reduction gives 36 mu = 9 at mu = 1/4 (lambda~ = 3 = N_fam), missing propagator renormalisation gives 36/mu = 144 (lambda~ = 12 = |mu4| N_fam); FLUX SIDE: #primaries((E8)_k) = (1, 3, 5, 10) for k = 1..4 from the affine marks -- a SINGLE exchange channel iff k = 1, minimal CPS quantum N = 1; (kappa/c3)^2 = 36/3 = 12 = |mu4| N_fam exact with sqrt 48 = 4 sqrt 3 (48 = 2 x 4!)","v514 CELEST.WP5E.EPS1.01 (vi): THE GH CENTRE DICHOTOMY RE-DERIVES THE v493 FAMILY -- on the GH base C x R the clock (z, h) -> (iz, h) has orbit sizes {1 (axis), 4 (free)} (i^j z = z forces z = 0 for j = 1, 2, 3), so a clock-invariant FOUR-centre set is either four axis points (pure RESOLUTION) or ONE free mu4 orbit at a common height (pure DEFORMATION) -- exactly 2 branches; the free orbit gives prod_p (Z - i^p z0) = Z^4 - z0^4 EXACTLY (e1 = e2 = e3 = 0), i.e. XY = Z^4 + a0 with a0 = -z0^4 = the v493 clock-invariant family, independently confirmed by P(iZ) = P(Z) forcing b3 = b2 = b1 = 0; the monodromy a0 -> e^{2 pi i} a0 moves z0 -> e^{i pi s/2} z0 (exact) and at s = 1 is the cyclic shift of the four centres = ONE mu4 clock step","v514 CELEST.WP5E.EPS1.01 (vii): THE PERIOD LOCKSTEP + THE COXETER CLOCK FROM GEOMETRY -- the charge-k GH point (V = k/r, r = R^2/(4k)) is EXACTLY the flat cone R^4/Z_k (V dr^2 = dR^2, V r^2 = R^2/4, fibre R^2/(4k^2); k = 4 => seam boundary S^3/Z4 = |mu4|) with the monopole equation dA = -*dV exact (k sin th both sides); the free-orbit holomorphic periods are Pi_j = 4 pi t0 (i-1)(1, i, i^2) with |Pi_j| = 4 sqrt(2) pi t0 EQUAL on all three spheres (LOCKSTEP, the v509 counter-check from GH geometry); the closure sum_p (x_{p+1} - x_p) = 0 induces on H_2 the map A = [[0,0,-1],[1,0,-1],[0,1,-1]] with A^4 = 1, det(A - 1) = -4 and Pi . A = i Pi (pure phase): the Coxeter clock RE-DERIVED from the centre geometry","v514 CELEST.WP5E.EPS1.01 (viii): THE MULTIPOLE SELECTION RULE + THE EH LOG LEDGER -- the free-orbit GH potential V = 4/r + sum_l t0^l/r^{l+1} S_l has DIPOLE = OCTUPOLE = 0, quadrupole S_2 = 3 sin^2 th - 2 (m = 0, clock-invariant), and the FIRST symmetry-breaking multipole is (l, m) = (4, +-4) with amplitude (35/16) sin^4 th carried by t0^4 e^{4 i phi0} = -a0 (selection rule m = 0 mod 4 exact: all m = 1, 2, 3 Fourier integrals vanish; Legendre generating identity verified to l = 4; source flux -4 pi per centre, total charge 4 = |mu4|); THE EH LOG LEDGER: u K' = sqrt(u^2 + a^4) solves det g = K'^2 + u K' K'' = 1 exactly, at infinity the 1/u coefficient is 0 (NO asymptotic log on the Ricci-flat ALE -- the honest sharpening) while at u -> 0 the log coefficient is a^2 with exceptional-sphere flux 2 pi a^2; Burns contrast K = u + N log u: det g = 1 + N/u != 1 (scalar-flat, brane-SOURCED)"],"checked_by_registry":false,"heading_as_written":"(* ==== v514 round: CELEST.WP5E.EPS1.01 -- \"the O(-2) bulk-axion slot\": WP5e-epsilon-1 executed (verdict B). Eight exact mirrors: (i) the equivariant Penrose ledger (pushforward blocks = wave-operator kernels, block by block, all d <= 6, all 4 characters), (ii) the character series P_m with the surviving bulk-axion zero mode and the twisted minimal content, (iii) the Molien hypersurface + the diag(i,i) Veronese control, (iv) the Okubo residue (6<x,x>)^2 on the 240 glue roots + the so8 irrationality control, (v) the measure cancellation excluding 3 and 12 + the flux/sector dial, (vi) the GH centre dichotomy re-deriving the v493 family, (vii) the period lockstep + the Coxeter clock from geometry, and (viii) the multipole selection rule + the EH log ledger. Mirrors v514. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:6056","line_end":6270,"line_start":6056,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v493","v514"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v515 CELEST.WP5E.M1.01 (i): THE RESIDUE-FORM IDENTITIES -- the Poincare residue omega2 = dX^dZ/X of the A3 family F = XY - P(Z) pulls back along the invariant cover (X, Y, Z) = (z1^4, z2^4, z1 z2) at a0 = 0 to EXACTLY 4 dz1^dz2 = |mu4| x (flat form): the residue normalisation CARRIES the source charge 4 = |mu4| (degree of the invariant map); the deck diag(i, i^-1) leaves the pullback invariant while the clock diag(i, 1) multiplies it by i (the v492 S5 phase det = i replicated at Omega level); the weight ledger closes: omega2 weight 4+4+2-8 = 2 = the O(2) fibre symplectic slot, Omega = omega2 ^ <la dla> weight 4 = -deg K_PT, and the wrong weight Z in O(4) gives 8+8+4-16 = 4 != 2 (no CY volume: 4+2 = 6 != 4); THE EH/Z2 ANCHOR from the same residue: the A1 cover (z1^2, z2^2, z1 z2) gives 2 dz1^dz2 = |Z2| x (flat form) -- charge per quotient = deck order","v515 CELEST.WP5E.M1.01 (ii): THE TWISTOR FAMILY, CLOSED FORM -- the four O(2) centre sections q_p(la) = i^p t0 - i^-p t0 la^2 satisfy the O(2) reality condition la_bar^2 q(-1/la_bar) = -conj(q(la)) for all four centres, and their product closes EXACTLY: prod_p (Z - q_p(la)) = Z^4 + 4 t0^2 la^2 Z^2 - t0^4 (1 - la^4)^2 (e1 = e3 = 0 identically, a2 = 4 t0^2 la^2 in O(4), a0 in O(8)); the seam fibre la = 0 is EXACTLY the v493 clock family XY = Z^4 - t0^4 and a2 vanishes at BOTH clock-fixed fibres (the a2 slot opens only off-seam); the la -> 1/la patch (Z -> Z/la^2, x la^8) returns the SAME form (self-mirror); the clock lift gamma: (Z, la) -> (iZ, -i la) preserves the family exactly, gamma^4 = 1, and with omega2 -> i omega2, dla -> -i dla the CY volume transforms as Omega -> +Omega (the CY-compatible lift)","v515 CELEST.WP5E.M1.01 (iii): PERIOD REDUCTION + LOCKSTEP + CLOCK COVARIANCE -- the fibre-sphere period reduces generically to int_{S_j} omega2 = 2 pi i (q_b - q_a) (the phi residue circle x the path endpoint difference; profile and path drop identically), so Pi_j(la) = 2 pi i t0 [(i-1) i^j + (1+i) i^-j la^2]; at the seam fibre la = 0: Pi = 2 pi i t0 (i-1)(1, i, i^2) with ALL squared moduli EQUAL to 8 pi^2 t0^2 (LOCKSTEP) and phase ratios (1, i, i^2); the clock covariance Pi_{j+1}(-i la) = i Pi_j(la) holds for ALL four segments and ALL la, Pi . A = i Pi at la = 0 and the chain closure sum_j Pi_j = 0 (v493 replicated on the twistor family); Pi_j(la) is POLYNOMIAL with residue 0 at la = 0: the undeformed Omega_0 carries NO quantised 3-flux -- all (2 pi i)^2 flux must be SOURCED","v515 CELEST.WP5E.M1.01 (iv): THE COLLISION LEDGER = 12 NODES ON Z8 -- adjacent centre pairs (j, j+1) collide exactly at la^2 = i^{2j+3} (all 8 candidate roots verified), non-adjacent pairs (0,2) at la = +-1 and (1,3) at la = +-i, and the antipodal identity q_{p+2} = -q_p forces DOUBLE nodes on every adjacent fibre; the la-support of all 12 nodes is EXACTLY the set of 8 eighth roots of unity (8 of 8 hit; 8 = 2|mu4| = the Z8 seam bridge); the clock la -> -i la permutes the adjacent node fibres cyclically j -> j+1 and the non-adjacent set in one 4-cycle: clock orbits 4 + 4 + 4 -- the lockstep phase structure ON the la-sphere","v515 CELEST.WP5E.M1.01 (v): THE BM ANCHOR (2 pi i)^2 + THE LENS FORCING N IN 4Z -- the CPS/Bochner-Martinelli kernel K = d^2 v ^ (vb1 dvb2 - vb2 dvb1)/|v|^4 has S^3 pullback density EXACTLY -sin(2 theta) (both Hopf phases cancel: the period is an ITERATED two-circle residue 2 pi x 2 pi x (-1)) and int_{S^3} K = -4 pi^2 = (2 pi i)^2 (CPS eq. 3.33 / v509 S1.1 replicated); the deck diag(i, i^-1) acts freely, everything descends to the lens S^3/Z4 with lens period (2 pi i)^2/4 per unit upstairs charge, so quotient large-gauge quantisation demands (2 pi i)^2 N/4 in (2 pi i)^2 Z: N/4 = (1/4, 1/2, 3/4, 1, 2) for N = (1, 2, 3, 4, 8) -- ONLY N = 0 mod 4 passes: THE SOURCE CHARGE 4 = |mu4| IS FORCED, minimal invariant charge 4 <-> lens period (2 pi i)^2 x 1 = the minimal CPS quantum N = 1 <-> level k = 1 (the v509 bridge); fractional seam charges N = 1, 2, 3 are EXCLUDED (the quantum knows the deck order; dK = 0 and the scale-degree-0 statement stay Python-side)","v515 CELEST.WP5E.M1.01 (vi): THE SOURCE CURVE -- FOUR LINES, ONE CHARGE -- the centre twistor lines L_p = {X = Y = 0, Z = q_p(la)} lie on the family (P4(q_p) = 0 identically for all four); the clock lift maps L_p -> L_{p+1} exactly (i q_p(i la') = q_{p+1}(la')); ALL 6 pairs of lines intersect (each q_p - q_r is quadratic in la with nonzero discriminant: 6 edges, 12 intersection points): the union is CONNECTED (the K4 graph) -- a single charge N is forced TWICE OVER (clock orbit + connectivity): flux vector N x (1, 1, 1, 1) = LOCKSTEP STRUCTURAL, boundary period 4 N (2 pi i)^2 by Stokes, orbifold-limit cover count 4 lines x 4 deck images = 16 = |mu4|^2 (the v509 mu = 16 resonance in Omega clothes)","v515 CELEST.WP5E.M1.01 (vii): NODES = CONIFOLD POINTS = SPHERE BRANES -- at the adjacent collision (la0 = e^{3 i pi/4}, Z = q_0 = q_1 = t0(1 + i)): (P4, P4_Z, P4_la) = (0, 0, 0), so dF = 0 and the 3-fold {XY = P4} is SINGULAR there; the (Z, la)-Hessian has det = 512 t0^6 != 0 and the full 4x4 quadric (XY block + Hessian) has rank 4: an ORDINARY DOUBLE POINT (conifold node), whose small-resolution exceptional curve is the sphere class -- indeed Pi_0(la0) = 0 (the sphere volume vanishes exactly at its node) and the collision is transversal (d(q_0 - q_1)/dla != 0); branes on the exceptional curves inherit ONE N per clock orbit: the per-sphere flux vector N (1, 1, 1)","v515 CELEST.WP5E.M1.01 (viii): THE KILL PROBE + NEGATIVE CONTROLS -- the clock-forbidden family (centres {0, 1, w, w^2}, seam fibre Z^4 - Z, e3 = 1 != 0, section set NOT clock-covariant): 0 of 24 orderings lockstep (vs 8/24 for the mu4 orbit = the 8 Hamiltonian paths of the 4-cycle), the node positions la^2 = the 6 SIXTH roots of unity (all distinct) => la-support = 12 twelfth roots, NOT the Z8 seam set (la^8 != 1 occurs), no antipodal pairing -- the HONEST verdict: the (2 pi i)^2 quantisation itself holds there too (gauge invariance is local), INTEGRALITY ALONE IS NOT THE DISCRIMINATOR -- the discriminator is the lockstep phase structure + the clock forcing (the v509 dial survives, the KILL does not fire); EH/Z2 ANCHOR: centres +-t0 give XY = Z^2 - t0^2(1 - la^2)^2 with exactly 2 nodes at la = +-1 and lens quantisation N in 2Z = |Z2| (N/2 integer only for N = 2, 4); diag(i, i) CONTROL: d^2v -> (i x i) d^2v = -d^2v (not SU(2), no invariant 3-form: the deformation problem collapses at step ZERO)"],"checked_by_registry":false,"heading_as_written":"(* ==== v515 round: CELEST.WP5E.M1.01 -- \"the A3 Omega_N\": milestone M1 of the CELEST.SEAM.01 back-reaction programme executed (SUCCESS on the preregistered v514 S8.1 criterion). Eight exact mirrors: (i) the residue-form identities (cover pullback 4 = |mu4|, clock phase i, weight ledger, EH anchor 2 = |Z2|), (ii) the twistor family closed (XY = Z^4 + 4 t0^2 la^2 Z^2 - t0^4 (1 - la^4)^2, O(2) reality, seam fibre = v493, self-mirror, CY-compatible clock lift), (iii) the period reduction + lockstep + clock covariance, (iv) the collision ledger (12 nodes exactly on the 8 eighth roots of unity, antipodal double nodes, clock orbits), (v) the BM anchor (2 pi i)^2 + the lens forcing N in 4Z, (vi) the source curve (four lines, K4 connectivity, forced uniform flux), (vii) the conifold nodes (Hessian det 512 t0^6, quadric rank 4, transversality), and (viii) the KILL probe + negative controls (forbidden family 0/24 vs 8/24, twelfth-root support, EH charge 2, diag(i,i) collapse). The exterior-derivative identity dK = 0 and the generic-profile sphere parametrisation stay Python-side in v515 (dict-based exterior algebra). Mirrors v515. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:6271","line_end":6503,"line_start":6271,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v493","v514","v515"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v516 CELEST.WP5E.M2.01 (i): THE COMPLETION-WEIGHT IDENTITY -- the index bridge f(m) = (1/4) sum_j (i^{jm} - 1)/det_j = (0, -3/8, -1/2, -3/8) = ch2(T_m) = -(C^-1)_mm/2 = -h_m with h_m = m(4-m)/8 the v502 sector Casimir energies (v505 S4.3 replicated), and the completion weights w_m = sum_j (1 - i^{jm})/det_j = (0, 3/2, 2, 3/2) = 4 h_m = |mu4| h_m = -4 ch2(T_m) EXACTLY for all m -- under the declared completion reading the per-class contact weight is FORCED: the three sphere axions pair through their OWN McKay ch2 charges, the 4 = |mu4| is the group order in the identity, not a dial; ratio h_2 : h_1 = 4 : 3 = the delta-1-forced leading ratio","v516 CELEST.WP5E.M2.01 (ii): ROOT/QUARTIC REPLICATION -- 240 glue roots with class split (52, 64, 60, 64); class quartics in (P1, P2, P3, T5, T3): Q_0 = (12, 0, 6, 4, 8), Q_1 = Q_3 = (12, 24, 0, -8, 16), Q_2 = (0, 24, 30, 12, -40) (v505 S3.1); A_fix = sum_j Q^{(j)}/det_j = (9, -30, -15, 0, 32) by characters AND by class weights (5/4, -1/4, -3/4, -1/4) -- the rigid twisted residual is +32 T3; bulk Okubo: K^{(0)} = 60<x,x> and Q^{(0)} = 36<x,x>^2 = (K^{(0)})^2/100 as exact polynomial identities (lambda~^2 = 36 = h_vee + 6), Q^{(0)} = (36, 72, 36, 0, 0) -- ZERO independent quartic in the summed trace","v516 CELEST.WP5E.M2.01 (iii): PARAMETER-FREE LOCKS -- with weights c (h_1, h_2, h_3): the T5 total vanishes IDENTICALLY for symbolic c (the ch2 pattern alone kills T5), the T3 total is -8c so the 32 T3 budget forces c = 4 = |mu4| uniquely, and the 2x2 leading system (T5, T3) x (w13, w2) has det 256 != 0 with unique solution (w13, w2) = (3/2, 2) = (4h_1, 4h_2): the delta-1-forced unique leading weights are REPRODUCED, not fitted","v516 CELEST.WP5E.M2.01 (iv): THE CONTACT TERM + THE SUCCESS TABLE -- channel form sum_j (Q^{(0)} - Q^{(j)})/det_j = class form sum_m 4 h_m Q_m = (36, 120, 60, 0, -32) EXACTLY (one object, two bases); PER-SECTOR PERFECT SQUARES: skeleton_j + contact_j = Q^{(0)}/det_j = 36<x,x>^2/det_j in EVERY twisted channel ((18, 36, 18, 0, 0), (9, 18, 9, 0, 0), (18, 36, 18, 0, 0): T5 = T3 = 0 in every sector -- the preregistered KILL does NOT fire); total A_fix + contact = (45, 90, 45, 0, 0) = 45<x,x>^2 = (5/4) x 36<x,x>^2 = Dedekind x Okubo (the v505 S3.8 unique quartic-free weighting); CERTIFICATES KILLED: Phi_T3 32 + (-32) = 0, Phi_P 72 + (-72) = 0, psi = Phi_P - Phi_T3/4: 64 + (-64) = 0 (the v511 psi = 64 slice SUPPLIED EXACTLY -- no cubic d-channel needed); remainder inside the exchange span (45<x,x>^2 = (45/16) E22 = (1/80) E00, per channel (36/(16 det_j)) E22, Phi_P(remainder) = 0); the measure chain is mu-BLIND: lam_eff^2 (mu v)^2 (G/mu) = mu 36 v^2 G => lam_eff^2 = 36 for symbolic mu","v516 CELEST.WP5E.M2.01 (v): NEGATIVE CONTROLS -- wrong scale: leftover T3(c) = 32 - 8c = (24, 16, 8, 0, -8) for c = 1..5, only c = 4 = |mu4| clears the budget; shuffled weights (h_1 <-> h_2) leave T5 = -14 != 0 AND T3 = 36 != 0 (the ch2 PATTERN carries the cancellation); SO(16) glue (classes {0, 2} only): AB sum (15, -18, -15, -4, 40) and completion total (5/4)(Q_0 + Q_2) = (15, 30, 45, 20, -40) -- leftover T5 = 20, T3 = -40: the KILL branch FIRES for so16 (Okubo failure inherited, E8 doubly special); diag(i, i) fake zero modes (2i, 4, -2i): the skeleton DEGENERATES to the Z2 target A_2 = (-3, -6, 9, 8, -16) and the fake weights (0, -1/2, 0, 3/2) break the conjugation pairing (w_1 != w_3) and the index bridge; Z2/EGUCHI-HANSON ANCHOR: A_2 + |Z2| h^{A1} (Q_1 + Q_3) = (9, 18, 9, 0, 0) = 9<x,x>^2 = (1/4) x 36<x,x>^2 -- perfect square, coupling scale 2 = |Z2| = centre count: the published anchor PASSES with the same mechanism","v516 CELEST.WP5E.M2.01 (vi): THE MULTIPLIER NOTE (cross-reference to the delta-1d strand) -- the A3 discriminant T-phases e(3a^2/8) have orders (1, 8, 2, 8) (8th roots, 8 = 2|mu4|) and their SQUARES have orders (1, 4, 1, 4) = a finite mu4 system (the order <= 4 multiplier delta-1c diagnosed); the contact weights 4h = (0, 3/2, 2, 3/2) themselves are REAL RATIONALS with no multiplier phase; Gauss sums: A3 slice sum = 2 e(3/8), D5 slice sum = 2 e(5/8), full 16-component Weil sum = 4 (signature 0 mod 8)"],"checked_by_registry":false,"heading_as_written":"(* ==== v516 round: CELEST.WP5E.M2.01 -- \"the twisted Kodaira-Spencer measure\": milestone M2 of the CELEST.SEAM.01 back-reaction programme executed (SUCCESS on the preregistered v514 S8.2 criterion, on the DECLARED completion measure -- the completion reading itself is the [C] fence, everything mirrored here is exact arithmetic). Six exact mirrors: (i) the completion-weight identity w_m = sum_j (1 - i^{jm})/det_j = (0, 3/2, 2, 3/2) = 4 h_m = |mu4| h_m = -4 ch2(T_m) with the index bridge f(m) = -h_m = ch2 (no free scale), (ii) the root/quartic replication (class quartics Q_m, A_fix two routes, bulk Okubo 36<x,x>^2 = (K^(0))^2/100), (iii) the parameter-free locks (T5 = 0 for symbolic scale, 4:3 ratio, T3 budget forces c = 4 = |mu4|, unique leading weights det 256), (iv) the contact term two forms + the per-sector SUCCESS TABLE (perfect Okubo squares 36<x,x>^2/det_j, total 45<x,x>^2 = (5/4) x 36, certificates 32/72/psi = 64 all killed, exchange-span remainder, mu-blind chain), (v) the negative controls (wrong scale 32 - 8c, shuffled weights, SO(16) KILL, diag(i,i) degeneration, Z2/EH anchor), and (vi) the multiplier note (discriminant T-phase orders (1,8,2,8) squaring to (1,4,1,4), Gauss sums 2e(3/8), 2e(5/8), full Weil 4). Mirrors v516. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:6504","line_end":6677,"line_start":6504,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v514","v516"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v517 CELEST.WP5E.M3.01 (i): THE GH MULTIPOLE LEDGER + THE FAMILY AT GENERAL PHASE -- for the four mu4 centres the dipole S_1 and octupole S_3 vanish identically, the quadrupole is the m = 0 form 3 sin^2 th - 2, and the FIRST symmetry-breaking multipole is (4, +-4) with cos 4(ph - phi0) amplitude EXACTLY (35/16) sin^4 th (the m = 1, 2, 3 Fourier integrals of S_4 all vanish: selection rule m = 0 mod 4, v514 S6.2 replicated); the twistor family at general orbit phase: prod_p (eta - q_p) = eta^4 + a2 eta^2 + a0(zeta) with e1 = e3 = 0 identically, a2 = 4 z0 zb0 zeta^2 (clock-invariant O(4) slot), a0(zeta) = -(z0^2 - zb0^2 zeta^4)^2 in O(8), seam value a0(0) = -z0^4 = -t0^4 e^{4 i phi0}; the phi0 = 0 slice is EXACTLY the v515 closed form XY = Z^4 + 4 t0^2 la^2 Z^2 - t0^4 (1 - la^4)^2","v517 CELEST.WP5E.M3.01 (ii): THE KERNEL BRIDGE -- the O(2) section distance eta_p = (z - z_p) + 2(x - x_p) zeta - (zb - zb_p) zeta^2 is a NULL coordinate: Laplacian(3d) G(eta_p) = G'' [4 (d_z eta)(d_zb eta) + (d_x eta)^2] = 0 IDENTICALLY for an ARBITRARY kernel G (every contour transform of every kernel lands in the V-ledger's harmonic function space: the uplift is well-typed); the RESIDUE V-LEDGER IDENTITY: eta_p(zeta_-) = 0 at zeta_- = (dx - r)/dzb and Res = 1/eta_p'(zeta_-) = 1/(2 r_p) EXACTLY, so with d_x log eta_p = 2 zeta/eta_p the contour transform of chi_p = log eta_p obeys d_x [transform] = 1/r_p: the GH potential V = sum_p 1/r_p IS the x-derivative of the transform of chi = log P4 (the contour prescription is the [C] GLT dictionary); source ledger: flux of each 1/r_p through S^2 = -4 pi per centre, total source charge 4 = |mu4| = centre count","v517 CELEST.WP5E.M3.01 (iii): THE ASYMPTOTIC KERNEL LOG + THE GLT TOWER -- chi = log P4 = 4 log eta + log(1 + a2/eta^2 + a0/eta^4) with LOG COEFFICIENT 4 = |mu4| = centre count (the CPS 'N log' analogue at kernel level): corrections c2 = a2, c4 = a0 - a2^2/2, all odd powers vanish, and the tower is a PURE Laurent series (no log x power terms -- the v514 honest zero preserved, the a0 correction is power-law at infinity); at the clock-fixed seam fibre zeta = 0 the a2 slot closes and the first correction is EXACTLY a0/eta^4 = the (4, +-4) multipole in kernel clothes; exact m-grading of c4(zeta) = -z0^4 - 6 z0^2 zb0^2 zeta^4 - zb0^4 zeta^8: the m = +-4 pieces are PURE a0 with clock phase -+4i t0^4 and the m = 0 piece -6 t0^4 is phi0-FREE (the U(1) -> Z4 breaking sits exclusively in the a0 pieces); GLT KERNEL TOWER: the power sums p_n = sum_p (i^p z0)^n vanish unless n = 0 mod 4 (selection rule at potential level), p_4 = 4 z0^4 = -4 a0, p_8 = 4 z0^8 = 4 a0^2, and sum_p eta_p log eta_p = 4 eta log eta + p_4/(12 eta^3) + p_8/(56 eta^7) + ...: coefficients z0^4/3 and z0^8/14 EXACTLY -- every correction carries the prefactor 4 = centre count through p_{4k} = 4 (-a0)^k","v517 CELEST.WP5E.M3.01 (iv): THE EXCEPTIONAL-LOCUS LOG -- chi(eta = 0) = log P4(0, 0) = log a0 = 4 log t0 + i(4 phi0 + pi) EXACTLY (exponential match), with t0 d/dt0 chi(0) = 4 = |mu4| = centre count and d/dphi0 chi(0) = 4i = the clock charge: the first nontrivial log structure generated by the a0 direction sits AT the exceptional locus with coefficient EXACTLY the centre count ('log-type correction tied to the source charge 4' -- the preregistered SUCCESS wording); WHERE THE LOG LIVES: the modulus response a0 d/da0 chi = a0/(eta^4 + a0) equals 1 at the exceptional locus and falls off as a0/eta^4 at infinity (no constant term, no log term): the asymptotic region sees only the power-law (4, +-4) tail -- the v514 S6.3 EH log ledger uplifted to the A3 kernel","v517 CELEST.WP5E.M3.01 (v): THE PERIOD RESPONSE = 1/|mu4| => CLOCK MONODROMY -- Pi_j(la) is LINEAR in t0 for all j and all la (Euler remainders 0): the a0 perturbation shifts every sphere period by the SAME relative amount (lockstep + phase ratios (1, i, i^2) preserved EXACTLY at first order, v515 S3.2 undisturbed); the holomorphic first-order response d log Pi_j / d log a0 = 1/4 = 1/|mu4| (Pi ~ z0, a0 = -z0^4), and integrating around the a0 circle gives e^{2 pi i/4} = i = ONE Coxeter clock step (the v493 monodromy reproduced from the perturbative shift); the finite monodromy z0 -> i z0 permutes the O(2) sections q_p -> q_{p+1} exactly and Pi_{j+1}(0) = i Pi_j(0); a0-RIGID FLUX STRUCTURE: (q_{j+1} - q_j)/t0 is t0-FREE for all adjacent pairs and (q_1 - q_0)(e^{3 i pi/4}) = 0 (the Z8 node support does NOT move under the a0 deformation), all 6 pair discriminants are nonzero and ~ t0^2 (the K4 connectivity that forces the uniform flux vector persists for every t0 > 0)","v517 CELEST.WP5E.M3.01 (vi): NEGATIVE CONTROLS -- the (4, 0) multipole (m = 0 component of S_4) is (105 sin^4 th - 120 sin^2 th + 24)/16, phi0-INDEPENDENT: clock- and U(1)-invariant, it breaks nothing (its kernel-side uplift is the m = 0 piece -6 t0^4); Z2/EGUCHI-HANSON ANALOGUE: two centres +-z0 give dipole 0, first symmetry-breaking multipole (2, +-2) with amplitude (3/2) sin^2 th, kernel log coefficient 2 = |Z2| with first correction a0^EH/eta^2, exceptional log t0-coefficient 2, period response 1/2 = 1/|Z2|, monodromy e^{pi i} = -1 = the Z2 clock: EVERY dial reads 2 -- the coefficient is COUPLED to the centre count, not universal; WRONG CENTRE COUNTS k = 3, 5: kernel log coefficient k with modulus slot O(6)/O(10) != O(8) -- the observable MOVES with the centre count (the KILL 'decoupled' does NOT fire), only k = 4 = |mu4| hits the O(8) a0 slot; the CLOCK-FORBIDDEN FAMILY {0, 1, w, w^2}: power sums (0, 0, 3) -- p3 = 3 != 0 breaks the m = 0 mod 4 selection rule (the first kernel correction -u^3 sits in the forbidden m = 3 slot) and e4 = 0 kills the a0-log at the exceptional locus: the forbidden family fails BOTH uplift dials"],"checked_by_registry":false,"heading_as_written":"(* ==== v517 round: CELEST.WP5E.M3.01 -- \"the a0 uplift\": milestone M3 of the CELEST.SEAM.01 back-reaction programme executed (SUCCESS on the preregistered v514 S8.3 criterion). Six exact mirrors: (i) the GH multipole ledger (selection rule m = 0 mod 4, (4, +-4) amplitude (35/16) sin^4 th) + the twistor family at general orbit phase (e1 = e3 = 0, a2 = 4 z0 zb0 zeta^2, a0(zeta), v515 slice), (ii) the kernel bridge (null coordinate: any kernel harmonic; residue V-ledger identity 1/(2r); source flux -4 pi per centre), (iii) the asymptotic kernel log (coefficient 4 = |mu4|, first seam correction a0/eta^4, exact m-grading, GLT tower p_{4k} = 4(-a0)^k with the n = 0 mod 4 selection rule, no log x power terms), (iv) the exceptional-locus log (chi(0) = log a0 = 4 log t0 + i(4 phi0 + pi), modulus response 1 at the locus vs power-law at infinity), (v) the period response (linear in t0, d log Pi/d log a0 = 1/4 = 1/|mu4|, integrated monodromy i = one Coxeter clock step, centre permutation, a0-rigid node support, K4 discriminants ~ t0^2), and (vi) the negative controls ((4,0) clock-invariant, Z2/EH reads 2 on every dial, k = 3/5 orbits move the coefficient, the forbidden family fails both dials). The contour-transform typing itself is the [C] GLT dictionary; the BM kernel anchor is already mirrored in the v515 round. Mirrors v517. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:6678","line_end":6874,"line_start":6678,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v514","v515","v517"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v518 CELEST.WP5E.DELTA1.01 (i): THE 16-COMPONENT WEIL SYSTEM, EXACT -- the discriminant module of D5 (+) A3 is Z4 x Z4 with q = (5x^2 + 3y^2)/8 mod 1; Gauss sums: sum e(5x^2/8) = 2 zeta_8^5 (sig D5 = 5 mod 8), sum e(3y^2/8) = 2 zeta_8^3 (sig A3 = 3 mod 8), total 4 = sqrt(16) e(0) (signature 0 mod 8 = rank E8: the signature factor in S is exactly 1); T = diag e(q), S = (1/4) e(-(mu,nu)) satisfy S symmetric, S unitary, S^2 = C (the conjugation permutation), (ST)^3 = S^2, S^4 = 1, T^8 = 1 (level 8); tensor split S = S_D5 (x) S_A3 with the factor signature phases e(-5/8) and e(-3/8) (5 + 3 = 8 = 0 mod 8) -- the completion that closes the delta-1b E1.5 obstruction is forced Weil data, not a choice","v518 CELEST.WP5E.DELTA1.01 (ii): THE TWO LAGRANGIANS + WHY THE 4-RULE FAILED -- exactly 6 of 16 classes are isotropic; the glue diagonal H = {(a,a)} and the anti-diagonal H' = {(0,0),(1,3),(2,2),(3,1)} are BOTH Lagrangian (q = 0 on them) and their indicator vectors e_H, e_H' are EXACTLY S- and T-invariant: two E8 gluings inside one Weil system (the v502 block is the invariant slice); the S-block on the diagonal classes is P_H S P_H = (1/4) J (EVERY entry exactly 1/4 -- not the naive (1/2) i^{-aa'}), and 3/4 of the S-image weight of a diagonal basis vector sits on the 12 SHIFTED classes: the 4-character rule cannot close, the 16-component completion is mandatory (the delta-1b E1.5 residual 2.91 -> ~1e-39 lives on the Python side, numerical theta certificate)","v518 CELEST.WP5E.DELTA1.01 (iii): THE KOBOUNDARY TEST, EXACT -- on the recorded exact transport phases (t_p, s_p) of the dressed gauge blocks (T-fixed pairs (0,b): t = e(1/2) = -1, the naked level-matching defect; sectors 1/3: t = e(11/16); sector 2: t = e(3/4) = -i; s-phases e(1/8)/e(7/8) on the four (odd, odd) pairs, else 1), the three SL(2,Z) relation defects c_{S^4}(p), c_{(ST)^3 S^-2}(p), c_{[S^2,T]}(p) -- gauge- and character-invariant pure scalars, exact rational phase arithmetic -- are (1, 1, 1) on ALL 15 sector pairs (every word returns to its base pair): the mu4 multiplier system is a CHARACTER of the orbit stabilisers Gamma_1(4) / Gamma_0(2)+-, NOT a genuine 2-cocycle on SL(2,Z) -- the exact precondition for the f1 f3 cancellation","v518 CELEST.WP5E.DELTA1.01 (iv): THE CHARACTER FORMULA lambda(gamma) = i^{2B + C/4} ON Gamma_1(4) -- every recorded loop matrix gamma = [[A,B],[C,D]] of the gcd-1 transport groupoid lies in Gamma_1(4) (C = 0 mod 4, D = 1 mod 4, det 1: exact integer check on all six distinct holonomy classes incl. [[5,2],[-8,-3]] and [[-3,-1],[4,1]]), every measured multiplier lies in mu_4, and lambda(gamma) = i^{2B + C/4} reproduces ALL of them ((2,1,0,0) among the four equivalent monomial solutions in the residues (B, C/4, (A-1)/4, (D-1)/4) mod 4 -- all four agree on the recorded loops): the finite obstruction of the derived Harvey-Moore measure is this explicit character, the exact datum the f1 f3 dressing must cancel","v518 CELEST.WP5E.DELTA1.01 (v): THE T-FIX MECHANISM, EXACT PHASES -- v502 vacuum energies E(theta) = -1/24 + theta(1-theta)/4 at theta = (0, 1/4, 1/2, 3/4) give (-1/24, 1/192, 1/48, 1/192) exactly (the axion Coxeter characters {i, -1, -i} = weights (1,2,3) = the A3 exponents); at every T-fixed pair (0,b) each twisted axion factor contributes e(2E(0)) = e(-1/12), so the f1 f3 dressing shifts uniformly by e(-1/6) and (-1) x e(-1/6) = e(1/3) = chi_4(T) at ALL THREE nodes -- ONE character; the three-sphere-axion candidate f1 f2 f3 demands chi_3 (b odd, f2 twisted) but chi_4 (b = 2, f2 untwisted) and f2 alone demands chi_5/chi_6: INCONSISTENT at the T-fixed nodes alone -- only the twisted fibre block f1 f3 = G (the exact gauge-block identity, verified to 30+ digits Python-side) supplies a single SL(2,Z) character (the full residual-order table none/f1f2f3 -> 4, f2 -> 6, f1f3 -> 1 and the loop-level scan live in v518, exact phase arithmetic on the 1/960 grid)","v518 CELEST.WP5E.DELTA1.01 (vi): MISASSIGNMENT CONTROLS, EXACT -- wrong discriminant form q = (x^2 + y^2)/4 on the same group: the Gauss sum has |G|^2 = 64 != 16 (no unit signature factor can exist -- the form is not the discriminant form of an even unimodular gluing) and forcing sigma = 1 breaks S^2 = C EXACTLY; the correct form with the WRONG signature factor sigma = e(-1/4) (a signature-2 pretence) gives S^2 = e(-1/2) C exactly instead of C: the Weil data of the completion is rigid -- both controls separate at O(1), and the O(1) failure of their S-rules on the true 16 coset thetas is the numerical twin (Python-side)"],"checked_by_registry":false,"heading_as_written":"(* ==== v518 round: CELEST.WP5E.DELTA1.01 -- \"the delta-1 chain decided: the derived chiral measure kills the delta-1 route\" (delta-1b/1c/1d consolidated; an honest, decided NEGATIVE result with the v516 tension stated). Six exact mirrors: (i) the 16-component Weil system of the D5 (+) A3 discriminant module Z4 x Z4 with q = (5x^2 + 3y^2)/8 -- Gauss sums 2 zeta_8^5 x 2 zeta_8^3 = 4 = sqrt(16) (signature 0 mod 8 = rank E8), S symmetric + unitary, S^2 = C, (ST)^3 = S^2, S^4 = 1, T^8 = 1, tensor split S = S_D5 (x) S_A3 with factor signatures e(-5/8), e(-3/8); (ii) the two invariant Lagrangians (diagonal H and anti-diagonal H', both S- and T-fixed = two E8 gluings), 6 isotropic classes, P_H S P_H = (1/4) J and 3/4 of every S-image weight on the 12 shifted classes (why the naive 4-character rule fails); (iii) the KOBOUNDARY TEST on the recorded exact transport phases (t_p, s_p) of the dressed gauge blocks M = G[a,b] eta^{-8}: the SL(2,Z) relation defects c_{S^4}, c_{(ST)^3 S^-2}, c_{[S^2,T]} are (1, 1, 1) EXACTLY on all 15 sector pairs -- the mu4 multiplier system is a CHARACTER of the orbit stabilisers, not a genuine 2-cocycle; (iv) the Gamma_1(4) CHARACTER FORMULA lambda(gamma) = i^{2B + C/4} on the recorded loop matrices (all in Gamma_1(4), exact integer check), with all four equivalent monomial solutions agreeing; (v) the T-FIX MECHANISM: v502 vacuum energies E_b exact, the f1 f3 dressing shifts every T-fixed node by e(2E + 2E) = e(-1/6) and (-1) x e(-1/6) = e(1/3) = chi_4(T) UNIFORMLY, while f1f2f3 demands {chi_3, chi_4} and f2 demands {chi_5, chi_6} (inconsistent: only the twisted fibre block supplies one character); (vi) the misassignment controls (wrong form (x^2+y^2)/4: |Gauss|^2 = 64 != 16 and S^2 != C exactly; wrong signature sigma = e(-1/4): S^2 = e(-1/2) C exactly). The Harvey-Moore integrals, the SVD contraction solves, the theta covariance certificates and the block transport measurements are numerical (mpmath 30+ digits / numpy) and stay Python-only, flagged here. Mirrors v518. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:6875","line_end":7076,"line_start":6875,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v502","v516","v518"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v519 WOIT.THETA.FREE.01 (i): THE TWO-FAMILY CLASSIFICATION -- anti-linear Theta = C o M on C^2 with Theta rho Theta^-1 = lam rho^-1 forces M DIAGONAL with lam = 1 (Solve: {b -> 0, c -> 0, lam -> 1}; the off-diagonal branch collapses to a = d = 0) and Theta rho Theta^-1 = lam rho forces M ANTIDIAGONAL with lam = -i (family A centralises the clock only projectively, NEVER inverts it): no third family exists; family D relations EXACT for symbolic mu (Theta_D rho Theta_D^-1 = rho^-1 at matrix level, deck inverted, Theta_D^2 = diag(mu conj mu, 1) -- POSITIVE diagonal, the Kramers case -1 is IMPOSSIBLE in the clock-inverting family); family A: Theta_A rho Theta_A^-1 = -i rho, deck centralised exactly, Theta_A^2 = diag(mu, conj mu) -- the role separation (A defines the euclidean section, D reflects it) at the sphere level","v519 WOIT.THETA.FREE.01 (ii): MARK PINNING + THE mu4 TORSOR -- z -> mu conj(z) preserves the mu4 mark set {1, i, -1, -i} iff mu in mu4 (all 4 members pass, the controls e^(i pi/3) and zeta8 fail): the mark-compatible clock-inverting reflections form a 4-element mu4-TORSOR; clock conjugation maps rho Theta_mu rho^-1 = Theta_{-mu} (ratio = -mu exactly) => exactly 2 clock orbits {1,-1} (mark axes, each fixing 2 marks) and {i,-i} (silver-midpoint axes, fixing 0 marks -- permutation fixed-point counts (2,0,2,0)); each torsor member is the seam-circle REFLECTION e^(i th) -> mu e^(-i th) with EXACTLY 2 cut points (e^(2 i th) = mu on the eighth-grid: 2 solutions for mu = 1 and mu = i, none elsewhere) -- the euclidean cut is a great circle through the deck poles","v519 WOIT.THETA.FREE.01 (iii): THE C^4 TWISTOR LEVEL -- Woit's rho_tw = diag(J, J) o conj reproduced EXACTLY: Theta_tw^2 = M conj(M) = -1 on C^4 (rho_tw^2 = -1 upstairs, +1 projectively, NO real points), it centralises the blockwise clock lift only projectively (Theta_tw rho4 Theta_tw^-1 = -i rho4) and centralises the deck exactly -- rho_tw IS family A globalised (the EUCLIDEAN structure); the standard conjugation sigma_std inverts the clock lift exactly (conj(rho4) = rho4^-1), inverts the deck, squares to +1 with real points RP^3 -- sigma_std IS family D globalised: Theta^2 = +1 AND Theta rho Theta = rho^-1 hold on the twistor level (the OS-quotient interpretation stays contract work, only the group relations are settled)","v519 WOIT.THETA.FREE.01 (iv): THE Z8 SPIN LEVEL -- conj(zeta8^k) = zeta8^-k for ALL k = 0..7 (inversion of the whole Z8 = 2|mu4| tower is pure Galois conjugation: no sign/phase leaks anywhere in the 8 steps, so the Theta relation propagates through clock^2 = deck without correction terms); Theta_D s Theta_D^-1 = s^-1 EXACTLY for the Z8 spin lift s = diag(zeta8, zeta8^-1) and ANY diagonal mu (no Kramers obstruction at the spin level), while the equatorial family-A member centralises s exactly -- the role separation persists upstairs","v519 WOIT.THETA.FREE.01 (v): THE Cl(16) FOCK LEVEL, 2^7 vs (-1)^F -- on explicit 256x256 Jordan-Wigner gammas both pinned mu4-torsor reflection axes have EVEN NS implementers (k = 0 fixing the marks {0,8}, k = 4 fixing the silver midpoints {2,10}; both commute with Gamma) with U_r^2 = 128 = 2^7 > 0 exactly, so Theta_Fock = U_r o K squares to +1 after unitary normalisation (Kramers-free); the v506 quarter-shift clock lift V (per-block nullspace element on the four mu4-orbits of sites) implements the wrap-signed shift-4 and U_r V U_r V = 2^19 exactly -- i.e. Theta_Fock V Theta_Fock^-1 = 4096 V^-1: the anti-unitary lift of the seam-circle reflection INVERTS the Fock clock tower; the deck lift Utilde (shift-8 implementer) has Utilde^2 = 256 Gamma = 256 (-1)^F (NOT a scalar: the deck-induced anti-linear candidate is the KRAMERS class -- the v510 split/nonsplit dichotomy IS the Theta^2 = +1 vs (-1)^F dichotomy) and Utilde V = V Utilde exactly (the antipodal/euclidean structure CENTRALISES the clock tower, family A at Fock level): the deck does NOT furnish the OS Theta, the seam-circle reflection does","v519 WOIT.THETA.FREE.01 (vi): FREE-RP PRECONDITIONS + THE SITE-CUT DEGENERATION + THE CONTINUUM CONTROL, EXACT -- the chiral NS kernel C(d) = (2/N)/sin(pi d/N) (odd d, 0 even) has C^2 = -1 EXACTLY at N = 8 (pure state); at N = 16 every NS reflection lift gives R C R^T = -C exactly (k = 15, 3, 0 -- the OS precondition omega o theta = conj o omega), the quarter-shift clock lift preserves the state (S C S^T = C) with R S R^-1 = S^-1 (theta inverts the clock on the state side), and the ANTIPODE/deck S^2 FAILS anti-invariance (S^2 C S^2T = +C != -C: the deck is not an OS reflection of the chiral vacuum); the cut THROUGH sites degenerates exactly (7x7 one-particle Gram C(16-a-b): ZERO diagonal -- reflected distances even, chiral checkerboard C(even) = 0 -- with 24 nonzero off-diagonal entries and det = 0 exactly, bipartite 4+3); the continuum mark-cut kernel is strictly PD (1/sin((s+t)/2) = positive diagonal x Cauchy-Stieltjes 1/(x+y), identity exact; leading minors 1/2, 1/72, 1/43200, 1/423360000 all > 0): the site-cut failure is a LATTICE-PLACEMENT artifact -- RP selects the site placement relative to the marks (bond midpoints); the 40-digit PD inertia certificates of the bond-cut Grams ((8,0,0)/(29,0,0)/full N = 8 half-algebra, min eigenvalue 1.888e-3) are Python-only"],"checked_by_registry":false,"heading_as_written":"(* ==== v519 round: WOIT.THETA.FREE.01 -- the WOIT-alpha milestone of the OS twistor bridge: the real structure exists (two-family classification, mu4 torsor, Z8/C^4/Cl(16) levels) and the exact free-RP preconditions + site-cut degeneration + continuum control. The 40-digit positive- definiteness inertia certificates of the bond-cut Grams (R3/R5) are Python-only by the suite convention (mpmath eigh at dps 40). Mirrors v519. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:7077","line_end":7269,"line_start":7077,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v519"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v520 CELEST.WP5E.MEASURE.01 (i): THE 16-COMPONENT WEIL DATA, EXACT -- on the discriminant module Z4 x Z4 of D5 (+) A3 with q = (5x^2 + 3y^2)/8: S symmetric + unitary, S^2 = C, (ST)^3 = S^2, S^4 = 1, T^8 = 1 exactly in Q(zeta_8); the glue diagonal e_H and the anti-diagonal e_H' are EXACTLY T- and S-fixed and all their classes are isotropic (q = 0 mod 8) -- the two invariant Lagrangian gluings of the dressed Weil system, the arena of the measure decision","v520 CELEST.WP5E.MEASURE.01 (ii): THE INVARIANT-SUBSPACE FORCING, EXACT -- the joint fixed space {v : rho(T) v = v, rho(S) v = v} of the 16-dim Weil representation has dimension EXACTLY 2 over the field (= dim_Q 8 = 4 x 2 Python-side), and it is EXACTLY the span of the two Lagrangian gluings {e_H, e_H'} (rank of the joint span stays 2): every single-valued lattice factor at physical weight is FORCED onto the two Lagrangian thetas, both = E4 = the UNPHASED sector trace -- with single-valuedness derived (F-lemma + Quillen pairing), this forcing decides the measure question for the v516 completion reading","v520 CELEST.WP5E.MEASURE.01 (iii): THE CHARACTER ARITHMETIC OF THE TWO SOURCES, EXACT -- chi_4(T) = e(1/3) and chi_10(T) = e(5/6) are NONTRIVIAL (source-1: a character-covariant integrand has no fundamental-domain-independent nonzero moduli integral, so every chiral option dies under TP-1 + TP-2); |chi_4(T)|^2 = 1 exactly while the one-sided square chi_4(T)^2 = e(2/3) != 1 (source-2: only the CONJUGATE Quillen pairing hol x conj(hol) cancels the multiplier -- on the exact 1/960 grid the squared T-fixed defects are 2 x 480 = 0 mod 960 for the gauge block but 2 x 800 = 640 != 0 = e(2/3) for the fibre); the T-fix mechanism (-1) x e(-1/6) = chi_4(T) replicated -- real tau_2 powers carry no phase","v520 CELEST.WP5E.MEASURE.01 (iv): A-CORE + Z2/EH ANCHOR TARGETS, EXACT -- Q^{(0)} = (36, 72, 36, 0, 0) = 36<x,x>^2; A_fix = (9, -30, -15, 0, 32); completion weights w_m = sum_j (1 - i^{jm})/det_j = (0, 3/2, 2, 3/2) = 4 h_m with h_2 : h_1 = 4 : 3; contact total = (36, 120, 60, 0, -32); per-sector perfect squares (18, 9, 18) <x,x>^2; psi(A_fix) = +64, psi(contact) = -64 (v516 replicated inside the decision module); Z2 ANCHOR: A_2 = Q^{(g^2)}/4 = (-3, -6, 9, 8, -16), contact_2 = (1/2)(Q_1 + Q_3) = Q_1, A_2 + contact_2 = (9, 18, 9, 0, 0) = 9<x,x>^2 = (1/4) x 36<x,x>^2 (coupling scale 2 = |Z2|), psi(A_2) = -8; SCALE TEETH: of c in {1/4, 1/2, 1, 2} ONLY c = 1/2 = |Z2| h^{A1} clears both (T5, T3) leftovers -- the anchor the derived instantiations all fail (integral side Python-only)","v520 CELEST.WP5E.MEASURE.01 (v): BOTH LAGRANGIAN GLUINGS ARE E4 AND OKUBO AT LEVEL 1, EXACT -- the anti-diagonal gluing H' (D5 spinor x A3 class 3, vector x 2, cospinor x 1) also has EXACTLY 240 norm-2 vectors (all norm 2) and its summed quartic equals 36<x,x>^2 = Q^{(0)} as an exact polynomial identity: the invariant subspace of (ii) carries the SAME unphased Okubo numerator on both gluings -- the forced single-valued lattice factor is E4 either way (the levelwise n <= 8 4-design and the J-weighted closure psi(skeleton) = -psi(contact) are Python-only: exact Fraction ledgers + 30-digit kernels)","v520 CELEST.WP5E.MEASURE.01 (vi): NEGATIVE CONTROLS, EXACT -- SO(16)/D8: the summed unphased trace (5/4)(Q_0 + Q_2) = (15, 30, 45, 20, -40) leaves T5 = 20, T3 = -40 (NO Okubo square even with single-valuedness granted: the KILL fires for so16, E8 stays doubly special) and on the derived side all even-sector fibre b-characters lie in mu_2 (the order-4 supply is structurally absent); SHUFFLED WEIGHTS h_1 <-> h_2 leave T5 = -14 != 0 AND T3 = 36 != 0 (the ch2 pattern carries the levelwise cancellation); diag(i, i) FAKE ZERO MODES (2i, 4, -2i): the skeleton degenerates to the Z2 target A_2 = (-3, -6, 9, 8, -16) and the fake weights (0, -1/2, 0, 3/2) break the conjugation pairing (w_1 != w_3) and the index bridge (w != 4h) -- the wrong-form/wrong-signature Weil controls are mirrored under v518 (vi); the planted-family and hol (x) hol SVD controls are Python-only"],"checked_by_registry":false,"heading_as_written":"(* ==== v520 round: CELEST.WP5E.MEASURE.01 -- \"the WP5e BCOV measure question decided at probe level\" (delta-1e + delta-1f consolidated): the exact Weil data, the invariant-subspace forcing, the character arithmetic behind the two constructive sources (F-independence + Quillen pairing), the completion/contact/psi and Z2-anchor targets, the level-1 4-design of BOTH Lagrangian gluings, and the exact negative controls. The Harvey-Moore integrals, SVD memberships and J-weighted closures are numerical (mpmath/numpy) and stay Python-only by the suite convention. Mirrors v520. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:7270","line_end":7478,"line_start":7270,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v520"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v521 SEAM.BIT.RPBLIND.01 (i): THE ANTI-LINEAR CENSUS ON M(delta), EXACT SOLVESETS -- for EVERY delta the two mark-SWAPPING reflections Theta_{+-e^(i delta)}(z) = +-e^(i delta) conj(z) preserve the mark set {+-1, +-e^(i delta)} identically (symbolic delta); the mark-FIXING conjugations mu = +-1 need cos delta = 0 (solveset {pi/2}) or sin delta = 0 (EMPTY on (0, pi/2]) -- they exist EXACTLY at the clock point; the v510/v512 counterwitness {+-1, +-(3+4i)/5} carries the swap pair exactly (exact rationals) and NO mark-fixing reflection (conj((3+4i)/5) not a mark); family A doubles 2 -> 4 exactly at pi/2 too (b^2 = -1 solveset {pi/2}, b^2 = +1 empty): the census is 2 generic -> 4 at the clock, and OS-reflection EXISTENCE never sees the side datum","v521 SEAM.BIT.RPBLIND.01 (ii): CLOSURE / FACE #13, EXACT SYMBOLIC -- Theta_b o Theta_{-b} = the deck z -> -z and Theta_b^2 = id for symbolic delta: the admissible OS reflections generate {id, deck, Theta_b, Theta_{-b}} ~= V4 for EVERY delta; at delta = pi/2 the extra mark-fixing pair joins and Theta_i o Theta_1 = the CLOCK z -> iz with clock^2 = deck: the OS-reflection group closes to D4 (8 elements) EXACTLY at the clock point -- 'the OS-reflection group generates the clock' <=> delta = pi/2 is FACE #13 of the v512 equivalence web (12 -> 13), a typed [C] REFORMULATION of the alignment bit, not a derivation from positivity","v521 SEAM.BIT.RPBLIND.01 (iii): CUT INCIDENCE + THE EPS JUMP + THE LATTICE FRAME, EXACT -- all 20 swap-cut/mark incidence solvesets on (0, pi/2] are EMPTY (the mark-swapping cut points {delta/2 + k pi/2} never hit a mark); the eps-ladder sin(eps) = 0 on [0, pi/2) has solveset {0}: the mark-fixing reflection is lost IMMEDIATELY off the clock point, no continuous transition; lattice frame (units of pi/16 resp. pi/32): the marks {0, m pi/8, pi, pi + m pi/8} sit on BOND midpoints for every m (never on a half-offset site), the swap reflection preserves them with NO fixed mark for m < 4, at m = 4 the mark-fixing axis fixes exactly {1, -1}, and at N = 32 every swap axis k = 2m - 1 is a bond axis -- the v519 axes reproduced, the odd-m N = 16 failure is pre-diagnosed as placement (PD inertia certificates Python-only)","v521 SEAM.BIT.RPBLIND.01 (iv): CONTINUUM AXIS ELIMINATION + THE COUNTERWITNESS CUT, EXACT -- the continuum chiral OS kernel for the reflection about ANY axis alpha, in axis-adapted coordinates theta = alpha + s, theta' = alpha + t, is 1/sin((s+t)/2) with alpha dropping out IDENTICALLY (d/d alpha = 0 exactly); it factorises through the Cauchy-Stieltjes kernel 1/(x+y) (identity exact; leading minors 1/2, 1/72, 1/43200, 1/423360000 all > 0): continuum free RP holds for EVERY cut position, hence for EVERY delta member -- the strongest possible delta-blindness; the counterwitness cut at delta_cw/2 = arctan(4/3)/2 sits strictly between 0 and the mark arctan(4/3) (exact ordering 0 < delta_cw/2 < delta_cw < pi/2), avoiding all marks -- its 6-point PD Gram certificate is Python-only (40 digits)","v521 SEAM.BIT.RPBLIND.01 (v): THE CLOCK-TOWER CLAUSE PRESUPPOSES THE BIT + PRECONDITION CONTROLS, EXACT -- the quarter rotation z -> iz preserves the deformed lattice mark set iff m = 4 (census {False, False, False, True}) and 'i M(delta) = M(delta)' solves to {pi/2} exactly (v512 H1.1): the candidate sharpening 'RP + clock-tower compatibility' (and the whole v519 Z8/Theta-rho chain) is delta-sensitive ONLY through the clock-existence face -- a REFORMULATION of the bit, not a derivation; hexagonal control: |b_hex| = 2 - sqrt(3) != 1 and Im lambda = sqrt(3)/2 != 0 (marks not concyclic, no seam circle -- the battery preconditions fail before positivity is asked); silver control: all four marks real (the mark circle passes through the deck poles, the deck is not free there) -- both excluded exactly as established (v510/v512)","v521 SEAM.BIT.RPBLIND.01 (vi): THE SIDE CONDITIONS ARE delta-BLIND, THE CLOCK CLAUSE IS NOT FORMULABLE OFF pi/2 -- Theta_mu^2 = diag(mu conj(mu), 1) = +1 for every unit mu (the whole family-D ladder is Kramers-free, symbolic); the v519 defining relation Theta rho Theta = rho^-1 holds for the whole mu4 torsor at the clock point (all four members, exact 2x2 matrix identity), but it NEEDS the mark-compatible order-4 rotation, whose existence solves to {pi/2} EXACTLY: for delta != pi/2 the clock clause is not violated -- it is NOT FORMULABLE; the only delta-sensitive clause of the v519 battery presupposes the bit itself (the Cl(16) Fock implementer squares U^2 = 2^7/2^8 > 0 are mirrored under v519 (v); the 40-digit spectra-blindness certificates are Python-only)"],"checked_by_registry":false,"heading_as_written":"(* ==== v521 round: SEAM.BIT.RPBLIND.01 -- \"free OS positivity does not see delta\": the anti-linear census solvesets on M(delta), the counterwitness census, the V4 -> D4 closure (face #13), the cut/mark incidence, the continuum axis elimination + Cauchy-Stieltjes factorisation, the clock-tower clause and the hex/silver precondition controls. The 40-digit lattice Gram inertia spectra (N = 16 / N = 32) are Python-only by the suite convention. Mirrors v521. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:7479","line_end":7608,"line_start":7479,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v521"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v522 WOIT.BETA1.GSO.01 (i): THE GAUGE DATUM IS THE NS CLOCK TOWER, EXACT -- the NS quarter-shift lift (wrap -1) has S^4 = -1, so <alpha_S> is the Z8 tower with alpha_S^4 = (-1)^F, and the chiral NS vacuum is tower-invariant (S C S^T = C exactly, N = 16 and N = 8); RAMOND CONTROL: the wrap +1 lift is a true Z4 (S_R^4 = +1) but FAILS state invariance with exact witness entry S_R C S_R^T - C = 1/(4 sin(5 pi/16)) != 0 at (0, 5) -- the 'genuine Z4' gauge lift is NOT a symmetry of the chiral NS vacuum: the Z8/NS tower is forced, fermion parity is contained in the mu4 gauge datum","v522 WOIT.BETA1.GSO.01 (ii): INVARIANT DIMENSIONS, EXACT RANKS -- on the 120 quadratic monomials of the 16-Majorana circle the clock-tower average has rank 32 (orbit census: 28 free shift-4 quadruples + 4 halved antipodal doublets -- the first frozen run preregistered 30, a combinatorial error corrected by the machine), the deck-only average rank 64, the parity-only average rank 120: the chain parity > deck > clock is STRICT -- the three candidate 'gauge' groups project to genuinely different invariant sectors, and only parity survives the Hermiticity census of (iv)/(v)","v522 WOIT.BETA1.GSO.01 (iii): THE CLOCK IS EUCLIDEAN-TIME-LIKE, EXACT CENSUS -- ALL 16 dihedral reflection axes of the NS seam circle INVERT the clock lift (R S R^-1 = S^-1 as exact integer matrices) and NONE commutes with it; same for all 8 axes at N = 8: there is no 'space-like' OS reflection for which the mu4 clock is an internal symmetry -- with the seam circle as Euclidean time, the clock is the time translation itself (Woit's euclidean rotation), Gamma_ALE = Z4 equivariance is ROTATION data, and a pre-quotient 'gauge average' over the clock has no OS meaning","v522 WOIT.BETA1.GSO.01 (iv): THE HERMITICITY WITNESS, EXACT -- the one-step clock insertion T_1 = <theta(e_a), alpha_S(e_b)> on the even deg <= 2 bond-cut basis (29 elements) has the EXACT witness entry T_1[(8,12), (8,15)] = -i/(8 sin(5 pi/16)) while the conjugate transpose demands +i/(8 sin(5 pi/16)); the full entrywise census gives conj(T_1^T) = +-T_1 with 745 Hermitian-matching, 96 ANTI-matching and 0 violations (the pairing is complex-SYMMETRIC, strictly weaker than Hermitian), and the full clock average (T_0 + T_1 + T_2 + T_3)/4 stays NON-Hermitian: 'positivity after gauge fixing' is NOT well-posed for the clock reading -- the quarter-turn insertion is a chiral transfer step, exactly what the time-like census (iii) predicts","v522 WOIT.BETA1.GSO.01 (v): THE GAUGEABLE SUBGROUP IS EXACTLY {1, (-1)^F}, EXACT CENSUS -- on the even 29-basis the insertions T_k are Hermitian for k = 0 ONLY (census {True, False, False, False}; on even monomials alpha^4 = id so k and k+4 coincide); on the odd one-particle basis they are Hermitian for k = 0 and k = 4 ONLY, with T_{k+4} = -T_k pairwise (alpha^4 = (-1)^F) and vanishing full 8-term average (the odd sector is gauge-VARIANT: the v519 one-particle PD certificate projects to zero): the theta-compatible subgroup of the Z8 clock tower is its 2-torsion {1, alpha^4} = {1, (-1)^F} = the GSO/fermion-parity Z2 -- the free-fermion shadow of the E8 glue; the clock and deck averages are NOT pre-quotient gauge fixings (the GSO-fixed PD inertia (29,0,0)/(8,0,0) is Python-only, 40 digits)","v522 WOIT.BETA1.GSO.01 (vi): FAMILY A BREAKS THE GAUGE EQUIVARIANCE, EXACT -- the clock-centralising antipode candidate theta_c(g_a) = i (-1)^a g_{a+8} keeps the state anti-invariant with the alternating dressing (the dressed antipodal kernel equals -C exactly), but it does NOT normalise the NS clock tower: theta_c o alpha_S matches alpha_S^j o theta_c for NO j in {1, 3, 5, 7} (exact coefficient comparison on all 16 generators, census {False, False, False, False}) -- the dressing that saves the state BREAKS the gauge equivariance; RP still separates the two real-structure families ON the gauge-invariant sector (family A indefinite (17,12,0) vs family D PD (29,0,0) -- the inertia certificates are Python-only, 40 digits): the alpha-stage triangulation survives gauge fixing"],"checked_by_registry":false,"heading_as_written":"(* ==== v522 round: WOIT.BETA1.GSO.01 -- \"the clock is time-like, GSO is the gauge datum\": the Z8/NS tower + Ramond control, the invariant- dimension chain, the time-like reflection census, the exact Hermiticity witness of the clock insertion, the GSO 2-torsion census and the family-A tower-normalisation failure. The 40-digit GSO-fixed RP inertia certificates ((29,0,0)/(8,0,0)/(7,9,6)/(17,12,0)) are Python-only by the suite convention. Mirrors v522. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:7609","line_end":7791,"line_start":7609,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v522"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v523 CELEST.WP5E.WM.01 (i): THE EQUIVARIANT MODE LEDGER IS THE CLOSED FORM, ABEL VALUE = 1/det_j -- the direct fibre ledger c_n = sum_{a+b=n} i^{j(a-b)} equals the series coefficient of 1/((1-q i^j)(1-q i^{-j})) = the reciprocal characteristic polynomial of g^j at EVERY order n <= 40 for j = 1, 2, 3 (exact in Q(i)); the closed form is REGULAR at q = 1 (no volume pole in the twisted sectors) with Abel value (1/2, 1/4, 1/2) = 1/det_j, det_j = det(1 - g^j) = (2, 4, 2); Dedekind sum 5/4 = (|Z4|^2 - 1)/12 and product 16 = |Z4|^2 -- the fixed-point weight of the w_m derivation is COMPUTED from the mode ledger, not chosen (the Cesaro truncation means are numerical, Python-only)","v523 CELEST.WP5E.WM.01 (ii): THE ZETA/QUILLEN ROUTE -- the reflection formula (2 pi/(Gamma(a) Gamma(1-a)))^2 = 4 sin^2(pi a) holds SYMBOLICALLY on 0 < a < 1 (the Lerch closed form of the twisted circle determinant), so det_zeta(a = j/4) = 4 sin^2(pi j/4) = (2, 4, 2) = det_j EXACTLY -- the spectral determinant of the g^j-twisted fibre Laplacian IS the Atiyah-Bott denominator; the Quillen split over the two fibre directions (twists a and 1-a) gives det Delta_j = det_j^2 = (4, 16, 4), and the AB holomorphic section (1-i^j)(1-i^{-j}) = det_j is REAL POSITIVE (SU(2) conjugation pairing) so the positive square root det dbar = det_j is unique and canonical; diag(i, i) CONTROL: the fake denominators (1-i^j)^2 = (2i, 4, -2i) are COMPLEX (arg((1-i)^2) = -pi/2, no real Quillen section) and the fake weights (0, -1/2, 0, 3/2) break the pairing w_1 != w_3 -- the zeta = AB agreement REQUIRES the SU(2) pairing (the Hurwitz 40-digit certificates are numerical, Python-only)","v523 CELEST.WP5E.WM.01 (iii): THE DERIVED-WEIGHT CONTACT VECTORS + THE SUCCESS TABLE ON THE 240 GLUE ROOTS -- with det_j = (2, 4, 2) DERIVED (checks (i)/(ii)), the Abel-limit contact vectors contact_j = (Q^(0) - Q^(j))/det_j = (12, 48, 30, 4, -24)/(12, 24, 0, -8, 16)/(12, 48, 30, 4, -24) are the v516 contact vectors COMPUTED; per sector skeleton_j + contact_j = Q^(0)/det_j = the perfect Okubo squares (18, 9, 18) x <x,x>^2 with T5 = T3 = 0 in EVERY channel; total A_fix + contact = (45, 90, 45, 0, 0) = 45<x,x>^2 = (5/4) x 36<x,x>^2; certificates Phi_T3: 32 -> 0, Phi_P: 72 -> 0, psi: +64/-64; Z2/EGUCHI-HANSON ANCHOR with the SAME derivation (det(1-(-1)) = 4, derived weight 1/2 = |Z2| h^{A1}): A_2 + (1/2)(Q_1 + Q_3) = (9, 18, 9, 0, 0) = 9<x,x>^2 = (1/4) x 36<x,x>^2 with psi(A_2) = -8 -- the published anchor passes with the constructive weight","v523 CELEST.WP5E.WM.01 (iv): THE CONSISTENCY CHAIN UNDER THE DERIVED WEIGHT + WRONG-WEIGHT CONTROLS -- index bridge f(m) = (1/4) sum_j (i^{jm}-1)/det_j = (0, -3/8, -1/2, -3/8) = ch2(T_m) = -h_m; weights w_m = sum_j (1-i^{jm})/det_j = (0, 3/2, 2, 3/2) = 4 h_m with ratio h_2 : h_1 = 4 : 3; the T3 budget 32 - 8c leaves (24, 16, 8, 0, -8) for c = 1..5 and Solve forces c = 4 = |mu4| uniquely; NC-1 (wrong weight 1/det^2): w' = (0, 5/8, 1, 5/8) with ratio 8 : 5 != 4 : 3 and the totals keep (T5, T3) = (2, 12) != (0, 0) against the v505-forced skeleton, while the zeta side CONTRADICTS it (det dbar = det^2 would demand det Delta = det^4 = (16, 256, 16) != measured det^2 = (4, 16, 4)); NC-2 (wrong weight 1/|1-i^j|): w''_1 = 1 + sqrt2 IRRATIONAL (leaves Q, the index bridge w = 4h unreachable), contact T5 = 8 sqrt2 - 16 != 0 and total T3 = 64 - 48 sqrt2 != 0 exactly in Q(sqrt2) -- both wrong weights break the chain QUANTIFIABLY","v523 CELEST.WP5E.WM.01 (v): THE k = 3, 5 WANDERING CONTROLS, EXACT CYCLOTOMIC -- the SAME constructive derivation on C^2/Z_k (g = diag(zeta_k, zeta_k^-1)): the derived weights w_m^(k) = sum_j (1 - zeta_k^{jm})/det_j^(k) = m(k-m)/2 = k h_m^(k) = -k ch2(T_m^{A_{k-1}}) EXACTLY (k = 3: w = (1, 1); k = 5: w = (2, 3, 3, 2)); the Dedekind sum is (k^2-1)/12 and the product of denominators k^2; the zeta determinants 4 sin^2(pi j/k) match the AB denominators per j -- the constructive weight moves CORRECTLY with the centre count (cf. v517 S5.3), so only k = 4 = |mu4| carries the E8-glue chain of (iii)/(iv): the derivation is geometry-tracking, not tuned"],"checked_by_registry":false,"heading_as_written":"(* ==== v523 round: CELEST.WP5E.WM.01 -- \"the constructive w_m derivation\": the residual [O] of v516/v520 closed at the fibre-zero-mode level (verdict ERFOLG; the typed premises TP-REG/TP-Q/TP-NUM/TP-CH are the [C] fence, a typing, not mirrorable). Five exact mirrors: (i) the equivariant mode ledger = the closed form 1/((1-q i^j)(1-q i^{-j})) at every order n <= 40 with the Abel value (1/2, 1/4, 1/2) = 1/det_j, Dedekind sum 5/4 and product 16; (ii) the zeta-determinant route (reflection formula symbolic, det_zeta = 4 sin^2(pi j/4) = det_j, Quillen split det Delta = det_j^2, the unique REAL POSITIVE section, the diag(i,i) control breaking realness and the conjugation pairing); (iii) the derived-weight contact vectors + per-sector Okubo squares + total 45<x,x>^2 + psi certificates on the 240 glue roots + the Z2/EH anchor; (iv) the consistency chain w = 4h = -4 ch2 with the T3 budget c = 4 and the two wrong-weight negative controls (1/det^2 leftovers (2, 12) + Quillen contradiction; 1/|1-i^j| irrational with T5/T3 leftovers in Q(sqrt2)); (v) the k = 3, 5 cyclotomic wandering controls w_m = m(k-m)/2 = k h_m. The (C,2) Cesaro truncation means, the Hurwitz/Lerch 40-digit certificates and the delta-1f stripped block limits are numerical (mpmath), Python-only, flagged here. Mirrors v523. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:7792","line_end":7964,"line_start":7792,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v516","v520","v523"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v524 WOIT.BETA2.OS.01 (i): EUCLIDEAN-ROTATION PRECONDITIONS + THE EXACT PD CERTIFICATE -- the one-step NS rotation alpha_1 (2 pi/N) wound N times around the seam circle picks up EXACTLY one wrap sign per generator: alpha_1^N = (-1)^F at N = 16 AND N = 8 (lattice spin-statistics: the 2 pi seam rotation is the GSO element, the exact integer wrap arithmetic mirrored generator by generator); and the exact certificate identity sin^2(3 pi/8) - sin(pi/8) sin(5 pi/8) = 1/2 that makes the N = 8 one-particle checkerboard determinants exactly positive (the H_phys nondegeneracy witness of the quotient construction)","v524 WOIT.BETA2.OS.01 (ii): THE KLEIN-LANDAU LOCAL TRANSFER FORMS, EXACT -- the one-particle insertions tau_k(a, b) = <theta(g_a) alpha_k(g_b)> on the shrinking domains D_k = {8, ..., 15-k} of the N = 16 bond cut are EXACTLY Hermitian for ALL k = 1..7 (entrywise RootReduce zero -- the OS-quotient cure of the v522 pre-quotient Hermiticity failure); the ODD steps have EXACTLY ZERO diagonal (the chiral checkerboard C(even) = 0 lands the effective reflection on a site axis: the one-step transfer is NOT positive -- the free chirality/staggering datum); and the EVEN steps obey the exact square identity tau_2j(a, b) = <alpha_j g_a, alpha_j g_b> ENTRYWISE for j = 1, 2, 3 (T(2j) = A_j* A_j: even powers of the transfer are manifestly PSD) -- the v519 site/bond RP dichotomy resurfacing INSIDE the reconstructed semigroup (the 40-digit inertia certificates are Python-only)","v524 WOIT.BETA2.OS.01 (iii): THE CLOCK = T^{N/4}, EXACT SPECTRUM -- at N = 8 the compressed clock on the one-particle Klein-Landau domain {4, 5} has generalized eigenvalues det(tau_2 - lambda G) = 0 solving to EXACTLY {1, sqrt(2) - 1} = {1, 1/delta_Silver} (the silver-midpoint axes of the v519 mu4 torsor return as the exact clock-transfer eigenvalue; sin(pi/8)/sin(3 pi/8) = sqrt(2) - 1 exactly); at N = 16 the quarter-turn one-particle block is exactly PD via the kernel identities C(9) = C(7), C(11) = C(5) and the TRANSPARENCY product formula sin(7 pi/16) - sin(5 pi/16) = 2 cos(3 pi/8) sin(pi/16) > 0 -- the TRUE pi/16 identity that sympy simplify missed on run 1, certified here symbolically (RootReduce on the exponential rewrite; no criterion changed)","v524 WOIT.BETA2.OS.01 (iv): THE PRE-DECLARED KMS WITNESSES, EXACT -- the local clock step EXPANDS the N = 8 edge mode by exactly the SILVER RATIO C(1)/C(3) = sin(3 pi/8)/sin(pi/8) = 1 + sqrt(2) = delta_S (while the compressed spectrum is {1, 1/delta_S}: no contraction on the compact euclidean circle -- the reconstruction is THERMAL/KMS, dim H_phys = 4^2); and at N = 16 the odd one-particle clock block has det(G - tau_4) = -(C5 - C7)((C3 - C7) + (C5 - C7)) < 0 EXACTLY (kernel monotonicity C3 > C5 > C7 > 0), so the compressed clock exceeds 1 -- contraction failure with EXACTLY the pre-declared witnesses, a typed KMS finding, not a beta2 failure (the compressed lambda_max = 1.6414 is numerical, Python-only)"],"checked_by_registry":false,"heading_as_written":"(* ==== v524 round: WOIT.BETA2.OS.01 -- \"the OS quotient of the free system made explicit\" (verdict SUCCESS, [C]-typed per contract precision (iii)). Four exact mirrors: (i) the euclidean-rotation preconditions (alpha_1^N = (-1)^F wrap arithmetic at N = 16 and N = 8) + the exact PD certificate identity sin^2(3pi/8) - sin(pi/8) sin(5pi/8) = 1/2; (ii) the Klein-Landau one-particle transfer forms tau_k on the shrinking domains at N = 16, k = 1..7: exactly Hermitian, odd k with exactly ZERO diagonal (the C(even) = 0 checkerboard), even k = 2j obeying the exact square identity tau_2j(a, b) = <alpha_j a, alpha_j b> entrywise; (iii) the clock identities (C(9) = C(7), C(11) = C(5), the transparency product formula sin(7pi/16) - sin(5pi/16) = 2 cos(3pi/8) sin(pi/16) > 0) + the N = 8 compressed clock spectrum EXACTLY {1, sqrt(2)-1} = {1, 1/delta_S} via the generalized eigenvalues of (tau_2, G) on the one-particle domain, with sin(pi/8)/sin(3pi/8) = sqrt(2)-1; (iv) the pre-declared KMS witnesses (C(1)/C(3) = 1 + sqrt(2) = delta_S at N = 8; -(C5-C7)((C3-C7)+(C5-C7)) < 0 exactly at N = 16, i.e. det(G - tau_4) < 0 on the odd one-particle clock block). The 37x37/16x16 H_phys Grams, the 40-digit inertia certificates, the spectral projections and the reconstructed rotation group are numerical (mpmath eighe), Python-only, flagged here. Mirrors v524. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:7965","line_end":8057,"line_start":7965,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v524"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v525 SEAM.BIT.TWISTBLIND.01 (i): THE INTEGER FRAME + THE sigma o r = +-sigma CONGRUENCE MECHANISM, EXACT -- on the N = 32 ladder (delta = m pi/8, m = 1..7, incl. pi/2 +- pi/8): the four marks sit on bond midpoints (never on the odd-unit sites), sigma flips exactly at the 4 marks, |D_short| = mu, the two mark-swapping axes k = 2m-1 and k = 2m+15 are BOND axes preserving the mark set, the mu4 defect planes are pairwise disjoint; the MECHANISM: sigma o r = sigma EXACTLY on every swap axis (so the twisted Gram is the diagonal unitary congruence D M D of the untwisted one = RP-spectrally INVISIBLE -- the exact reason the sigma decoration is delta-blind), while on the mark-fixing axes k = 31, 15 (existing iff delta = pi/2) sigma o r = -sigma EXACTLY (the odd-sector negation = the eta flip +i -> -i: twist-visible, but only formulable at pi/2 -- presupposes-the-bit class)","v525 SEAM.BIT.TWISTBLIND.01 (ii): THE pi/2 EXISTENCE SOLVESET + THE COUNTERWITNESS CENSUS, EXACT -- mark-FIXING reflections on M(delta) exist exactly at cos(delta) = 0, i.e. delta = pi/2 (the v521 S1.1 solveset: every twist-visible clause of v525 lives on axes that exist iff delta = pi/2 -- the presupposes-the-bit fence is a theorem about the frame, not a convention); and the v512/v510 counterwitness mark (3 + 4i)/5 is UNIMODULAR but not a root of unity of ANY order k = 1..64 (exact power census), so it never carries a lattice mark-compatible reflection at any dyadic refinement -- no decorated-state selector can exclude it without excluding a blind lattice member (its N = 16 arc content is IDENTICAL to the blind member delta = pi/4)","v525 SEAM.BIT.TWISTBLIND.01 (iii): THE delta <-> pi - delta MIRROR EQUIVARIANCE, EXACT INTEGER -- the lattice reflection u -> -u maps the m-mark set {0, 4m, 32, 32 + 4m} EXACTLY onto the (8-m)-mark set for every m = 1..7 (and the deck u -> u + n preserves every mark set): the family equivariance delta <-> pi - delta is an exact lattice symmetry, so EVERY invariant readout of a mark decoration is mirror-symmetric under m <-> 8 - m with pi/2 the SYMMETRIC POINT -- the exact mechanism behind the measured Casimir mirror symmetry ln|omega(D)|(m) = ln|omega(D)|(8 - m) (spread 1.15e-40, Python-only) and behind 'measuring, never selecting': the twisted data can gauge delta but cannot pick a side of pi/2"],"checked_by_registry":false,"heading_as_written":"(* ==== v525 round: SEAM.BIT.TWISTBLIND.01 -- \"the twist-state kill\": the NINTH side-blind test on the v512 scoreboard (8 -> 9); the free-plus-twist class is exhausted. Three exact mirrors: (i) the integer incidence frame + the sigma o r = +-sigma congruence mechanism (swap axes: sigma o r = sigma => the twisted Gram is the diagonal unitary congruence D M D = spectrally invisible; fixing axes at pi/2: sigma o r = -sigma = the eta flip); (ii) the pi/2-existence solveset of the mark-fixing axes + the exact counterwitness census ((3+4i)/5 unimodular but NEVER a root of unity up to order 64 -- no lattice mark-compatible reflection at any dyadic refinement); (iii) the delta <-> pi - delta mirror equivariance (the lattice reflection maps the m-mark set EXACTLY to the (8-m)-mark set -- the exact mechanism behind the Casimir mirror symmetry ln|omega(D)|(m) = ln|omega(D)|(8-m) and behind pi/2 as the symmetric point of every invariant readout). The Pfaffian insertion spectra, the Bogoliubov 2-of-16 pattern census, the defect energy and the 40-digit inertia certificates are numerical (mpmath), Python-only, flagged here. Mirrors v525. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:8058","line_end":8138,"line_start":8058,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v512","v525"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v526 SEAM.THERMAL.KMS.01 (i): N = 8 DETAILED-BALANCE / Q-POLYNOMIAL -- the palindromic Prony recurrence closes with b = (C1+C3)/C3 = 2 + Sqrt[2] exactly; C3/C1 = 1/(1+Sqrt[2]) exactly (the Q-polynomial identity with weight-pairing kappa = q^{-8} => beta = 8 = N); omega = arcsinh(2^{-3/4}) satisfies sinh^2 omega = Sqrt[2]/4; silver expansion C1/C3 = 1 + Sqrt[2] -- beta is MEASURED, not assumed","v526 SEAM.THERMAL.KMS.01 (ii): THE c3 THIRD-LEG CHAIN, EXACT -- beta_angle = 2 pi = 1/(4 c3) EXACTLY (c3 = 1/(8 pi)); T_seam = 1/(2 pi) = 4 c3 (Bisognano-Wichmann/Hawking modular normalisation); Schwarzschild T_H = c3/M = 1/(8 pi M) -- the axiom IS the Hawking coefficient; SdS 1/(4 pi) = 2 c3; Nariai T_N = 4 c3 Sqrt[Lambda]; v104 cross-link 2H/T_N = 4 pi = 1/(2 c3) exactly -- temperature joins geometry and anomaly as the third leg of c3 (class-1 identity r = 1)","v526 SEAM.THERMAL.KMS.01 (iii): MODULAR CLOSED FORMS AT N = 8, EXACT -- char poly of the half covariance: nu^2 = (4 + Sqrt[2] +- Sqrt[6])/8 with nu1 = cos(pi/24), nu2 = cos(7 pi/24); spectrum p = {(1+-nu1)(1+-nu2)/4} sums to 1; single-particle energies via (1+nu)/(1-nu) = Cot[theta/2]^2 at theta = pi/24, 7 pi/24 (i.e. eps = 2 ln cot(theta/2)) -- the modular Hamiltonian K = eps1 n1 + eps2 n2 is closed (Tomita 40-digit residuals Python-only)"],"checked_by_registry":false,"heading_as_written":"(* ==== v526 round: SEAM.THERMAL.KMS.01 -- the thermal seam / third leg of c3. Exact mirrors: (i) Q-polynomial / measured beta = N at N = 8; (ii) beta_angle = 2 pi = 1/(4 c3) chain + Hawking/Nariai identities; (iii) nu char-poly / closed modular spectrum at N = 8. Tomita 40-digit residuals and the entropy tower are Python-only. Mirrors v526. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:8139","line_end":8186,"line_start":8139,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v526"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v527 SEAM.CLOCK.SILVER.01 (i): THE CLOSED CHAIN / tan(pi/8) PENCIL, EXACT -- at N = 8 the quarter-turn Hankel pencil is diagonal on the odd sector and the compressed clock eigenvalue is the pure kernel ratio C(3)/C(1) = sin(pi/8)/sin(3 pi/8) = tan(pi/8) = Sqrt[2] - 1 = 1/delta_S exactly; the gap DeltaK = -ln(Sqrt[2]-1) = ln(1+Sqrt[2]) = arcsinh(1) with sinh(DeltaK) = 1 exactly -- structure SUCCESS","v527 SEAM.CLOCK.SILVER.01 (ii): N-SCALING -- SILVER IS AN N = 8 LATTICE DATUM, EXACT WITNESS -- at N = 16 and N = 24 the kernel ratio C(N/2-1)/C(1) differs from Sqrt[2]-1 (FullSimplify =!= 0): the exact silver eigenvalue does NOT recur at the next mod-8 levels; the silver spectrum is a 16-Majorana/N = 8 lattice datum, not a continuum datum","v527 SEAM.CLOCK.SILVER.01 (iii): GAP = INVERSE GUDERMANNIAN OF THE SILVER-MIDPOINT ANGLE, EXACT -- DeltaK = arcsinh(1) = ln tan(pi/8 + pi/4) = gd^{-1}(pi/4) exactly; |arcsinh(1) - pi/4| > 0.09 (not the naive continuum NS mode gap) -- lattice half-angle geometry"],"checked_by_registry":false,"heading_as_written":"(* ==== v527 round: SEAM.CLOCK.SILVER.01 -- silver explained / demystified. Exact mirrors: (i) tan(pi/8) Hankel pencil; (ii) N-scaling witness; (iii) gap = arcsinh(1) = gd^{-1}(pi/4). Census Python-only. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:8187","line_end":8212,"line_start":8187,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v527"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v528 SEAM.BIT.TWISTCLASS.01 (i): THE CARDINALITY LEMMA, EXACT -- sigma o f = -sigma for ANY bijection f forces |A+| = |A-|, and |A+| = 4m vs |A-| = 32 - 4m are equal IFF m = 4; equivalently the continuum arc-exchange solveset delta = pi - delta -> {pi/2} -- the (=>)-backbone of facets #14 and #15","v528 SEAM.BIT.TWISTCLASS.01 (ii): COMPLETE g-CLASS CENSUS OVER ALL 224 AXES, EXACT -- the global flip class g = -1 occurs EXACTLY at the mark-fixing axes {15, 31} for m = 4 and NOWHERE else on the N = 32 ladder x all 32 reflections (7 x 32 = 224) -- facet #14 (=>) generalized kill","v528 SEAM.BIT.TWISTCLASS.01 (iii): ORDER PARAMETER O ON THE N = 32 LADDER, EXACT -- O := (#flip axes)/(#mark-compatible axes) equals 1/2 EXACTLY at m = 4 and 0 at every other m = 1..7; O != 0 <=> bit set"],"checked_by_registry":false,"heading_as_written":"(* ==== v528 round: SEAM.BIT.TWISTCLASS.01 -- bit = twist-class choice. Exact mirrors: (i) cardinality lemma; (ii) 224-axis flip census; (iii) O-values. Pfaffian spectra Python-only. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:8213","line_end":8244,"line_start":8213,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v528"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v529 SEAM.INT.FKTOY.01 (i): Z8 / THETA BACKBONE IDENTITIES, EXACT INTEGER -- U_r^2 = 2^8 = 256 (bond-axis class); conj_V V = 4096 = 2^{12} (clock-tower inversion under Theta); Utilde^2 = 256 Gamma = 256 (-1)^F (nonsplit) and V^2 = 256 Utilde (the tower IS a square root of the deck) -- Kill-Test 1's object exists on the interacting-capable algebra (full Cl(16) matrix certificates Python-only)","v529 SEAM.INT.FKTOY.01 (ii): STRADDLE-LAW COMBINATORICS, EXACT -- over the mark-swap axis pairs of even members {2,4,6}, the quartet-STRADDLED cuts are exactly {(m,k) = (2,1), (6,13)} and the quartet-AVOIDING cuts are the rest; the Python battery confirms RP fails exactly on the straddled cuts and stays PD on the avoiding ones for all g in {1/4,1/2,1,2} (24/24) -- the concrete hurdle for beta3/gamma (inertias Python-only)","v529 SEAM.INT.FKTOY.01 (iii): FK ANCHOR BINOMIAL LADDER, EXACT -- a single quartet has spectrum {-1,+1} x 128; the m = 4 (delta = pi/2) mark-anchored interaction of 4 DISJOINT commuting quartets has the exact binomial ladder E in {-4,-2,0,2,4} with multiplicities {16,64,96,64,16} = Table[Binomial[4,k]*16,{k,0,4}] -- the g -> infinity FK fixed-point structure (Total = 256)"],"checked_by_registry":false,"heading_as_written":"(* ==== v529 round: SEAM.INT.FKTOY.01 -- interacting FK toy / Kill-Test-2 shadow. Exact mirrors: (i) Z8 integer identities; (ii) straddle combinatorics; (iii) FK binomial ladder multiplicities. 256-dim spectra Python-only. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:8245","line_end":8262,"line_start":8245,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v529"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v530 DIAMOND.CENTER.QUOTIENT.01 (i): FIXED PRIMITIVE LINE, EXACT -- C.v = v for v = (-1,1,0) and GCD(v) = 1","v530 DIAMOND.CENTER.QUOTIENT.01 (ii): THE QUOTIENT IS THE ATOM MATRIX, EXACT -- Det[P] = -1 (unimodular), P^-1.C.P = {{1,4,2},{0,8,2},{0,5,3}}, quotient A = {{8,2},{5,3}} = {{rank E8,|Z2|},{g_car,N_fam}}","v530 DIAMOND.CENTER.QUOTIENT.01 (iii): QUOTIENT INVARIANTS, EXACT -- tr A = 11, det A = 14 = det C, disc = 65 = 5*13, perm A = 34 = p5(a), prod entries = 240 = |R(E8)|, det(A-I) = 4 = |mu4|","v530 DIAMOND.CENTER.QUOTIENT.01 (iv): SELF-CODE + CP CODE, EXACT -- row sums C.1 = (7,11,13) = (det A/|Z2|, tr A, disc/g_car); with the fixed eigenvalue 1: (1,7,11,13) = the positive CP-pair representatives Min[m,30-m] of the E8 exponents (Z/30)^x","v530 DIAMOND.CENTER.QUOTIENT.01 (v): RESOLVENT FACTORISATION, EXACT POLYNOMIAL IDENTITY -- Det[C + k I] = (k+1) Det[A + k I] identically; quotient ladder (14,26,40,56) with differences (12,14,16); center ladder (14,52,120,224), 224 = 248 - 24","v530 DIAMOND.CENTER.QUOTIENT.01 (vi): HONEST UNIQUENESS CONTROLS, EXACT -- K and Q also fix a line (K.(2,-3,-1) = (2,-3,-1); Q.e3 = e3) but the K quotient {{14,8},{-11,-6}} (tr 8, det 4, 5 does not divide disc 48) and the Q quotient {{3,1},{3,2}} (tr 5, det 3, det/|Z2| = 3/2 not integer) are NOT the atom matrix and cannot self-code -- C is unique in the conjunction"],"checked_by_registry":false,"heading_as_written":"(* ==== v530 round: DIAMOND.CENTER.QUOTIENT.01 -- the center quotient compiler. Exact mirrors: fixed line, unimodular quotient = atom matrix, invariants, self-coding row sums, CP code, resolvent factorisation, K/Q controls. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:8263","line_end":8299,"line_start":8263,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v530"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v531 COX.STAGEA.TENSOR.01 (i): THE TENSOR CLOCK, EXACT -- T30 = Comp(Phi5) (x) Comp(Phi6) is 8x8 integer with CharacteristicPolynomial = Phi30 = x^8+x^7-x^5-x^4-x^3+x+1","v531 COX.STAGEA.TENSOR.01 (ii): EXACT ORDER 30 -- MatrixPower[T30,30] = I and MatrixPower[T30,k] != I for every proper divisor step k < 30","v531 COX.STAGEA.TENSOR.01 (iii): RAMANUJAN TRACE TOMOGRAPHY, EXACT -- tr(T30^k) = c_30(k) for ALL k = 1..30, c_30 = c_5 c_6, signed divisor table (-1,1,2,4,-2,-4,-8,8) at k = (1,2,3,5,6,10,15,30), atom readout (|c(3)|,|c(5)|,|c(15)|) = (2,4,8)","v531 COX.STAGEA.TENSOR.01 (iv): HONEST KILL SCOPE, EXACT -- Comp(Phi15) passes the unsigned triple (Phi30(x) = Phi15(-x)) but fails the signed table (c_15(1) = +1 vs c_30(1) = -1); Phi16/Phi20/Phi24 die on the triple (traces 0,0,0)","v531 COX.STAGEA.TENSOR.01 (v): COPRIMALITY CONTROLS, EXACT -- C6 (x) C6 has order 3 (not 36), C5 (x) C5 has order 5 (not 25): gcd(5,6) = 1 / CRT is load-bearing"],"checked_by_registry":false,"heading_as_written":"(* ==== v531 round: COX.STAGEA.TENSOR.01 -- the Stage A tensor clock. Exact mirrors: order 30, chi = Phi30, Ramanujan trace tomography, honest Phi15 scope, coprimality controls. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:8300","line_end":8333,"line_start":8300,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v531"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v532 E8.DEGREE.MODULAR.01 (i): DUAL PRODUCTS, EXACT -- d_i + d_{9-i} = 32 = h+2; (60,192,240,252): sum 744 = 3*248, product 696729600 = |W(E8)|, gcd 12, /12 = (5,16,20,21)","v532 E8.DEGREE.MODULAR.01 (ii): MODULAR ANCHOR, EXACT q-SERIES -- q j = E4^3/Prod(1-q^n)^24 = 1 + 744 q + 196884 q^2 + ... (j = q^-1 + 744 + 196884 q)","v532 E8.DEGREE.MODULAR.01 (iii): D16 NEGATIVE CONTROL, EXACT -- same duality d+d' = 32, dual-product sum 1488 = 3*496 = 2*744 (the checksum is heterotic, NOT E8-exclusive; 496 = dim E8xE8 = dim SO(32))","v532 E8.DEGREE.MODULAR.01 (iv): NON-HETEROTIC CONTROLS FAIL, EXACT -- A8 100/240, D8 200/360, E6 117/234, E7 316/399, F4 72/156, G2 12/42 (half-pair convention; E8 gives 744 under the same rule)","v532 E8.DEGREE.MODULAR.01 (v): PRIME-TOTATIVE FINGERPRINT, EXACT [audit] -- {2,3,5} u (Exp(E8) minus {1}) = all primes < 30; every totative of 30 except 1 is prime; 30 is the LARGEST such n (scan to 10^4, full list {1,2,3,4,6,8,12,18,24,30})"],"checked_by_registry":false,"heading_as_written":"(* ==== v532 round: E8.DEGREE.MODULAR.01 -- the dual-degree checksum 744. Exact mirrors: dual products, j-series constant 744, D16 control, non-heterotic controls, prime-totative fingerprint. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:8334","line_end":8371,"line_start":8334,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v532"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v533 FTR.DISC7.NORM.01 (i): NORM IDENTITY, EXACT -- D(t) = det M(1,t) = 4t^2+14t+14 = ((4t+7)^2+7)/4 = N(alpha_t), alpha_t = (4t+7+Sqrt[-7])/2 integral (-7 = 1 mod 4, 4t+7 odd)","v533 FTR.DISC7.NORM.01 (ii): TRANSLATION ORBIT, EXACT -- alpha_{t+1} = alpha_t + 2 = alpha_t + |Z2|; norms at t = -2..1 are (2,4,14,32) = (det J, det K, det C, det F)","v533 FTR.DISC7.NORM.01 (iii): CONSTANT DISCRIMINANT -7 + VERTEX, EXACT -- Discriminant[x^2-(4t+7)x+D(t), x] = -7 for every t; vertex t = -7/4, D_min = 7/4 > 0; curvature D'' = 8 = rank E8; 2 splits in Q(Sqrt[-7]) (-7 = 1 mod 8)","v533 FTR.DISC7.NORM.01 (iv): NEGATIVE CONTROLS, EXACT -- the winding axis det M(s,0) = 6s+8 is LINEAR; the anchor block det B(1,t) = 3t^2+21t+28 has POSITIVE discriminant 105 (real roots) -- only the sheet determinant is a complex norm line"],"checked_by_registry":false,"heading_as_written":"(* ==== v533 round: FTR.DISC7.NORM.01 -- the disc -7 norm line. Exact mirrors: norm identity, translation, norms (2,4,14,32), constant discriminant -7, vertex, negative controls. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:8372","line_end":8400,"line_start":8372,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v533"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v534 SEAM.STRADDLE.CONE.01 (i): STABILIZER CENSUS, EXACT -- the pi/2 member m = 4 carries the FULL clock+mirror stabilizer (rotations {0,4,8,12}, reflection axes {3,7,11,15} = four admissible bond cuts); every other member has rotations {0,8} and axes {m-1, m+7}; odd members carry NO bond (odd) axis, m = 2/6 carry {1,9}/{5,13}","v534 SEAM.STRADDLE.CONE.01 (ii): PARTITION + STRADDLE INCIDENCE, EXACT -- the four m = 4 quartets TILE the 16-circle (disjoint union = all 16 sites; every other member overlaps); straddled cuts: m = 4 exactly {7,15} (quartets {4,12}/{0,8}), m = 2 exactly {1}, m = 6 exactly {13}, the avoiding axes {3,11}/{9}/{5} carry no straddling quartet","v534 SEAM.STRADDLE.CONE.01 (iii): REFLECTION-CLOSURE SIGNS, EXACT -- every m = 4 straddling quartet is reflection-CLOSED across its own cut with signed-permutation sign +1 (theta_c(Q_q) = +Q_q: the symmetric straddle), while NO m = 2/6 straddling quartet is closed (asymmetric straddle) -- the dichotomy that separates pi/2 from the rest","v534 SEAM.STRADDLE.CONE.01 (iv): EQUIVARIANT Fix RAYS, EXACT -- the signed stabilizer action on the four quartet couplings has a ONE-dimensional fixed space for every member: the UNIFORM ray (1,1,1,1) for m = 2..6 and the NS-wrap-TWISTED signed rays (1,-1,1,1) / (-1,-1,-1,1) for the tight members m = 1/7 -- the cone question reduces to the sign of one uniform coupling on every well-posed member"],"checked_by_registry":false,"heading_as_written":"(* ==== v534 round: SEAM.STRADDLE.CONE.01 -- the RP cone on the interacting FK quartets (the first dynamical selection of the alignment bit). Exact mirrors: the stabilizer census of the mark family, the pi/2 partition + straddle incidence, the reflection-closure signs of the straddling quartets, and the equivariant Fix rays (uniform on m=2..6, NS-wrap-twisted on m=1,7). The 256-dim Fock spectra, the PT Gram corrections and the finite-g survival scan are Python-only (numpy), flagged per GATE.WOLFRAM.02. ==== *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:8401","line_end":8477,"line_start":8401,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v534"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v535 HECKE.GEOM.01 (i): KNESER COUNT IDENTITY, EXACT -- #iso_lines = (pts-1)/(p-1) = sigma3(p)*#P^3(F_p) = (1+p^3)*(p^4-1)/(p-1) = (p+1)^2 (p^2+1)(p^2-p+1) identically","v535 HECKE.GEOM.01 (ii): KNESER ENUMERATION ANCHORS, EXACT -- #iso_lines at p=2,3,5,7 = (135,1120,19656,137600); #iso_pts = (136,2241,78625,825601)","v535 HECKE.GEOM.01 (iii): AFFINE HECKE LAW (a,b), EXACT -- b=sigma3+a_p, a=#lines-b*sigma3; at p=3,5 with a_p=(-4,-2) gives (448,24) and (4032,124); a+b*sigma3=#lines","v535 HECKE.GEOM.01 (iv): LAMBDA / CUSP RULE, EXACT -- lambda_odd = #lines - sigma3^2 + a_p^2 equals (352,3784,19840) at p=3,5,7; a_p = b-sigma3 recovers (-4,-2); |a_7|=24 from disc","v535 HECKE.GEOM.01 (v): OLDFORM / PROJECTOR ARITHMETIC, EXACT -- dim V = 5+2 = 7; pi_Eis=(T+4)/32 and pi_cusp=(28-T)/32 complementary idempotents on diag(28x5,-4x2); new quotients 5-4=1 and 2-1=1; 2-adic levels {1,2,4,8,16} u {8,16}"],"checked_by_registry":false,"heading_as_written":"(* ==== v535 round: HECKE.GEOM.01 -- Hecke from geometry (exact identities). Live p=3 FP census and q-series builds stay Python-only. *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:8478","line_end":8518,"line_start":8478,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v535"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v536 HECKE.GEOM.EICHLER.01 (i): WITT LAMBDA_EIS, EXACT -- lambda_Eis = L - sigma3^2 = sigma3*(#P3-sigma3) = p(p^4+p^3+p+1); anchors (336,3780,19264) at p=3,5,7","v536 HECKE.GEOM.EICHLER.01 (ii): EICHLER ANCHORS / N_PERP, EXACT -- N_perp=(p^6-1)/(p-1) = (364,3906,19608); lambda_geom = lambda_Eis + a_p^2 = (352,3784,19840) at a_p=(-4,-2,24); N_perp - lambda_Eis = sigma3","v536 HECKE.GEOM.EICHLER.01 (iii): LOCAL DENSITIES N_A/N_B, EXACT -- N_A=min(240(1+p^3),#iso-1); algebra shell-(#iso-1)=(1+p^3)(241-p^4); p=3 => (2240,0); p=7 => (82560,743040); B empty iff p^4<241","v536 HECKE.GEOM.EICHLER.01 (iv): SIGNED a_p / b TABLE, EXACT -- a_p=(-4,-2,24) at p=3,5,7; b=sigma3+a_p in {24,124,368}; R=a_p^2 in {16,4,576}","v536 HECKE.GEOM.EICHLER.01 (v): ASSEMBLER / RAMANUJAN, EXACT -- R = sigma3 - 1 - c(p^2)/8 with c=-8 a(p^2), a(p^2)=a_p^2-p^3 equals a_p^2; |a_p|<=2 p^{3/2} at p=3,5,7,11,13"],"checked_by_registry":false,"heading_as_written":"(* ==== v536 round: HECKE.GEOM.EICHLER.01 -- Eichler trace layer (exact identities). Live FP Shell(p)/Shell(p^2) stays Python-only. *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:8519","line_end":8557,"line_start":8519,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v536"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v537 HECKE.GEOM.HALFINT.01 (i): f8 a_p HEAD TABLE, EXACT -- a_p(f8) at p=3,5,7,11,13 = (-4,-2,24,-44,22)","v537 HECKE.GEOM.HALFINT.01 (ii): SHIMURA SCALE / WEIGHT, EXACT -- k=2 => weight 5/2 -> 4; signed preimage scale -8; related monoid scales {+8,-16,+16}","v537 HECKE.GEOM.HALFINT.01 (iii): KOHNEN SCOPE FENCE, EXACT -- level 32=4*8 has M=8 even (not odd squarefree); W(4) condition 4a-M b c=1 unsolvable with b≡1 mod 4","v537 HECKE.GEOM.HALFINT.01 (iv): TWIST ROOT NUMBER, EXACT -- eps_d = chi_d(8) = +1 on d≡1 mod 8 and -1 on d≡5 mod 8 (sample fund. discriminants)","v537 HECKE.GEOM.HALFINT.01 (v): SIGNED-SCALE UNIQUENESS CARDINALITY, EXACT -- among related scales {-8,+8,-16,+16} exactly one equals -8 (the T38 witness scale)"],"checked_by_registry":false,"heading_as_written":"(* ==== v537 round: HECKE.GEOM.HALFINT.01 -- half-integral bridge (exact identities). q-series builds, AFE/L-values and R-constancy stay Python-only. *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:8558","line_end":8584,"line_start":8558,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v537"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v538 HECKE.GEOM.RTF.01 (i): R1 TRACE ANCHORS, EXACT -- Tr_V(nu_p) at p=3,5,7 = (6304,105848,727680); f8-channel (352,3784,19840)","v538 HECKE.GEOM.RTF.01 (ii): R1 PROJECTOR TABLE, EXACT -- full (Id,Eis,cusp,E4,f8) anchors at p=5 and p=7","v538 HECKE.GEOM.RTF.01 (iii): R2 ORBIT DICTIONARY, EXACT -- lambda_Eis=(336,3780,19264), a_p^2=(16,4,576), lambda_geom=lambda_Eis+a_p^2","v538 HECKE.GEOM.RTF.01 (iv): NU_LAW (a,b) ANCHORS, EXACT -- (a,b)=(448,24)/(4032,124)/(11008,368) at p=3,5,7","v538 HECKE.GEOM.RTF.01 (v): FINITE RTF SCOPE, EXACT -- p-set {3,5,7}; 5 projectors; dim V=7=5+2; ONE-FORMULA cardinality 3-of-3 pillars"],"checked_by_registry":false,"heading_as_written":"(* ==== v538 round: HECKE.GEOM.RTF.01 -- compiler relative-trace identity (exact). q-series builds, AFE/L-values and R-constancy stay Python-only. *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:8585","line_end":8622,"line_start":8585,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v538"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v539 RTF.GNS.WEIL.01 (i): G_0 ALGEBRAIC, EXACT -- G_0=(1+Y)/(1-Y)=zeta_p(w-3)^2/zeta_p(2w-6); witness (1+Y)=(1-Y^2)/(1-Y)","v539 RTF.GNS.WEIL.01 (ii): PHI CHARACTER EXPANSIONS, EXACT -- Phi1=chi0+chi2, Phi2=chi4-chi2, Phi3=2chi0-chi4+chi6, Phi4=chi8-chi6","v539 RTF.GNS.WEIL.01 (iii): CORE SERIES c_k0, EXACT -- c_k0=[1,0,2,0,2,0] = coeffs of Y dlog G_0 - Y","v539 RTF.GNS.WEIL.01 (iv): DIRICHLET 2^omega HEAD, EXACT -- a(n)=2^omega(n) for n=1..30 equals multiplicative Euler of G_0","v539 RTF.GNS.WEIL.01 (v): OBSTRUCTION (c) e^{-Y} DLOG, EXACT -- Y D[Log[Exp[-Y]],Y] = -Y (non-automorphic EXTRA TERM)"],"checked_by_registry":false,"heading_as_written":"(* ==== v539 round: RTF.GNS.WEIL.01 -- Weil structure of the compiler family (exact). Arch digamma / numeric Q assembly stay Python-only. *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:8623","line_end":8670,"line_start":8623,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v539"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v540 RTF.GNS.AMP.01 (i): CAUCHY-LITTLEWOOD WINDOW LEMMA, EXACT -- Sum h_k(s,t)h_k(u,v)X^k = (1-stuvX^2)/[(1-suX)(1-svX)(1-tuX)(1-tvX)] (k<=6, free Satake symbols); st=uv=p^3 => numerator 1-p^6X^2 pair-INDEPENDENT","v540 RTF.GNS.AMP.01 (ii): THREE SQUARE CHANNELS, EXACT -- b^2 (f8xf8), Theta^2 (EisxEis floor), Theta*g (f8xEis, Rankin) all carry the deletion numerator 1-p^6X^2 (series vs closed form, k<=6, chi=0)","v540 RTF.GNS.AMP.01 (iii): TOWER DOUBLE-COUNTING, EXACT -- fam[1,0,2,0]+2flat[0,2,0,2]+Plancherel delta_k1 = FULL[2,2,2,2] (generating functions; flat = zeta_p(2u) layer; mixed = deletion isolated with minus)","v540 RTF.GNS.AMP.01 (iv): LINEAR CARRIER FULL WEIGHTS + PLUS KERNEL, EXACT -- lambda_k = 1+p^{3k}-(chi p)^k (k<=6, layer [1,1,1,1] chi-free); pole-kernel collapse (e^{u/2}+e^{-u/2})2cosh(3u/2) = e^{2u}+e^u+e^{-u}+e^{-2u}; FE centre 5/4=(0+5/2)/2, plus-locus offset 1/4, tilts {-3/2,3/2} -> mirror {-5/2,1/2}","v540 RTF.GNS.AMP.01 (v): SQUARE SIEVE + COHEN SEED, EXACT -- 2^omega = mu_sq * d and d = 1_sq * 2^omega (n<=30); Theta(1)=4=-48 zeta(-1); Theta(17)=192, S2(17)=136, 17 Theta(17)=24 S2(17)=3264 (Cohen H(2,d)=L(-1,chi_d))"],"checked_by_registry":false,"heading_as_written":"(* ==== v540 round: RTF.GNS.AMP.01 -- amplitude route and positive linear carrier (exact). Lattice enumeration, FFT autocorrelations and the mpmath split-Mellin FE stay Python-only. *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:8671","line_end":8759,"line_start":8671,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v540"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v541 RTF.GNS.LEDGER.01 (i): CHARACTER DECOMPOSITION, EXACT -- character system (residues 1,3,5,7 mod 8) solves to (chi0,chi-4,chi8,chi-8) coefficients (0,1,1/4,1/4); 4(-psi(n)) = [4 chi_-4 + chi_8 + chi_-8](n) Theta(n) on all odd n<=33 from the theta heads","v541 RTF.GNS.LEDGER.01 (ii): PSI W-TABLE, EXACT -- the three 2-adic w-families satisfy w(8x) = 9 w(x) - 8 w(x/8) (roots {1,8} of y^2 = 9y - 8) with first steps -3/2 / -1/2 / +1","v541 RTF.GNS.LEDGER.01 (iii): DUPLICATION BRIDGE, EXACT -- Gamma(2z) = 2^{2z-1} Pi^{-1/2} Gamma(z)Gamma(z+1/2); (2Pi)^{-s}Gamma(s) = (1/2)Gamma_R(s)Gamma_R(s+1); kernel anchor at t=0: 2 psi(1/2) - 2 log 2Pi = [psi(3/4) - log Pi] + [psi(1/4) - log Pi] (Gauss digamma values)","v541 RTF.GNS.LEDGER.01 (iv): CERTIFICATE HEAD, EXACT -- 7 S(j) < 40 A(j) with S(j) = Sum_{d|j, d=0,1 mod 4, d>=4} (j/d)Theta(j/d)|psi(d)| and A(j) = j Theta(j) at j in {12,24,48,60} (integer theta heads); sign law sign psi(n) = (-1)^{floor(n/2)+1} on n<=60 (the 10^6 full enumeration stays Python-only)","v541 RTF.GNS.LEDGER.01 (v): CM CARRIER HEAD, EXACT -- g_lambda lattice sums c1(5)=-14, c1(13)=-238=pi^4+pibar^4 (split, pi=3+2i), c1(3)=c1(7)=0 and c1(9)=3^4=81 (inert), c1(2^r)=(-4)^r for r<=4 (ramified); canonical weight mu1(5) = c1(5)/((r2/4) 25) = -7/25 in [-1,1] (r2(5)=8)"],"checked_by_registry":false,"heading_as_written":"(* ==== v541 round: RTF.GNS.LEDGER.01 -- matching lemma and transport ledger package (exact). The 10^6 integer sieves, FFT autocorrelation batteries, Cornacchia tables and the mpmath digamma/erfc quadratures stay Python-only. *)","id":"wolfram-section:verification/wolfram/tfpt_readouts_extension.wl:8760","line_end":8831,"line_start":8760,"path":"verification/wolfram/tfpt_readouts_extension.wl","python_identifiers_in_heading":["v541"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v1027 signed determinant M a (1+c a)","v1027 physical kernel remains one-dimensional at a=0","v1028 exact factorwise Frobenius identity mod 5","v1028 full 192-mode one-site Gauss dimension is 3 mod 5"],"checked_by_registry":false,"heading_as_written":"(* v1027: exact signed-wall determinant and unsquared low branch. *) {a, delta, lambda, g} = Unique /@ {\"a\", \"delta\", \"lambda\", \"g\"}; mass = delta + lambda; beta = lambda g^2; eta = lambda g; c = beta - eta^2/mass; h = {{a + beta a^2, eta a}, {eta a, mass}}; check[\"v1027 signed determinant M a (1+c a)\", Together[Det[h] - mass a (1 + c a)] === 0]; check[\"v1027 physical kernel remains one-dimensional at a=0\", NullSpace[h /. a -> 0] === {{1, 0}}]; (* v1028: exact characteristic-five reduction of the full 192-mode one-site character. P^12 == P^2 P(z^5)^2 mod 5 is evaluated by coefficient dictionaries, never by floating group quadrature. *)","id":"wolfram-section:verification/wolfram/tfpt_round4.wl:28","line_end":111,"line_start":28,"path":"verification/wolfram/tfpt_round4.wl","python_identifiers_in_heading":["v1027","v1028"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v1028 ordinary D4 relations on selected even pair space","v1028 D4-invariant selected-space cap has rank 11 and gap one","v1028 invariant-ray space is two-dimensional, not oriented"],"checked_by_registry":false,"heading_as_written":"(* v1028: exact ordinary D4 cap on the selected 12D even pair space. *) cs = DiagonalMatrix[{1, -I, -1, I}]; cf = DiagonalMatrix[{-I, -1, I}]; js = SparseArray[Table[{Mod[-kk, 4] + 1, kk + 1} -> 1, {kk, 0, 3}], {4, 4}]; jf = {{0, 0, 1}, {0, 1, 0}, {1, 0, 0}}; rot = KroneckerProduct[cs, cf]; refl = KroneckerProduct[js, jf]; check[\"v1028 ordinary D4 relations on selected even pair space\", zeroQ[MatrixPower[rot, 4] - IdentityMatrix[12]] && zeroQ[refl.refl - IdentityMatrix[12]] && zeroQ[refl.rot.refl - ConjugateTranspose[rot]]]; (* One-based flattened slots for (k,g)=(1,3),(2,2),(3,1). *)","id":"wolfram-section:verification/wolfram/tfpt_round4.wl:112","line_end":134,"line_start":112,"path":"verification/wolfram/tfpt_round4.wl","python_identifiers_in_heading":["v1028"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v1029 generic local tensor constraint identities","v1029 periodic k=0 trace mode has exact energy -3 r^2/4","v1030 connected-sector actual-word frame spans all 16 matrix units","v1030 connected/disconnected commutant ranks are 3 and 2"],"checked_by_registry":false,"heading_as_written":"(* v1029: exact generic local tensor identities and the k=0 instability. *) {x, y, z} = Unique /@ {\"x\", \"y\", \"z\"}; k = {x, y, z}; basis = Join[ Table[Outer[Times, UnitVector[3, ii], UnitVector[3, ii]], {ii, 1, 3}], Table[With[{ii = pair[[1]], jj = pair[[2]]}, (Outer[Times, UnitVector[3, ii], UnitVector[3, jj]] + Outer[Times, UnitVector[3, jj], UnitVector[3, ii]])/Sqrt[2]], {pair, {{2, 3}, {1, 3}, {1, 2}}}] ]; bmat = Transpose[(#.k) & /@ basis]; trace = {1, 1, 1, 0, 0, 0}; k2 = k.k; v = Transpose[bmat].k; scalar = v - k2 trace; kp = IdentityMatrix[6] - Outer[Times, trace, trace]/2; kq = k2 (IdentityMatrix[6] - Outer[Times, trace, trace]) - 2 Transpose[bmat].bmat + Outer[Times, trace, v] + Outer[Times, v, trace]; check[\"v1029 generic local tensor constraint identities\", zeroQ[bmat.Transpose[bmat] - (k2 IdentityMatrix[3] + Outer[Times, k, k])/2] && zeroQ[kq.Transpose[bmat]] && zeroQ[kp.scalar - Transpose[bmat].k] && PossibleZeroQ[scalar.scalar - 2 k2^2]]; r = Unique[]; zeroEnergy = Expand[(r trace).kp.(r trace)/2]; check[\"v1029 periodic k=0 trace mode has exact energy -3 r^2/4\", zeroEnergy === -3 r^2/4]; (* v1030: actual connected-sector words span M4; a disconnected mutant leaves one extra commutant degree. *)","id":"wolfram-section:verification/wolfram/tfpt_round4.wl:135","line_end":189,"line_start":135,"path":"verification/wolfram/tfpt_round4.wl","python_identifiers_in_heading":["v1029","v1030"],"status_basis":"source section and check labels only; no execution or equivalence assertion","type":"wolfram_section"},{"check_labels_as_written":["v1031 C=r^4 PTT with a symmetric rank-two projector","v1031 exact PSD factorization has spectrum {0^4,r^4,r^4}","v1032 de Donder numerator is symmetric with inertia (6+,4-)","v1032 curvature annihilates all four exact pure-gauge columns","v1032 null de Donder sandwich is PSD of physical rank two"],"checked_by_registry":false,"heading_as_written":"(* v1031: exact rational-fibre curvature projector and positivity. *) p = {1, 2, 2}; {r2, b, trace, scalar, kp, kq, c} = tensorData[p]; ptt = Simplify[explicitPTT[p, r2]]; check[\"v1031 C=r^4 PTT with a symmetric rank-two projector\", zeroQ[c - r2^2 ptt] && zeroQ[ptt - Transpose[ptt]] && zeroQ[ptt.ptt - ptt] && MatrixRank[ptt] === 2]; cFactor = r2 ptt; check[\"v1031 exact PSD factorization has spectrum {0^4,r^4,r^4}\", zeroQ[c - cFactor.Transpose[cFactor]] && MatrixRank[c] === 2 && Sort[Simplify[Eigenvalues[c]]] === {0, 0, 0, 0, r2^2, r2^2}]; (* v1032: a separate Lorentz-covariant curvature calculation at one exact nonzero null momentum. 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not exact)","claim_id":"FR.KOIDE.01","dependencies_as_recorded":"-","external_data_as_recorded":"PDG lepton masses","id":"claim:FR.KOIDE.01","location_as_recorded":"tfpt_4","path":"verification/status_ledger.csv","row_number":50,"scripts_as_recorded":"-","status_as_recorded":"Physical (near-miss)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open (relic scale)","checked_by_registry":false,"claim_excerpt":"dark matter: axion candidate fixed; relic scale (f_a; m_a) open","claim_id":"FR.DM.01","dependencies_as_recorded":"strong-CP determinant-line","external_data_as_recorded":"-","id":"claim:FR.DM.01","location_as_recorded":"tfpt_4","path":"verification/status_ledger.csv","row_number":51,"scripts_as_recorded":"-","status_as_recorded":"Open (relic scale)","type":"claim_ledger_row"},{"active_as_recorded":"false","canonical_status_as_recorded":"SUPERSEDED -> FLAV.QGEO.02 + v69/v70: Q-geometry derived (D4-equivariant); residual sharpened to det Q = N_fam","checked_by_registry":false,"claim_excerpt":"RESIDUAL GATE (5.0 review, B3): geometric origin of Q -- Q_+ spectrum {1,2,3}=A3 exponents and Q_-^2|supp=N_fam algebraically forced; deriving Q_+/Q_- from D4-equivariant parabolic geometry on P1\\mu4 is open; do NOT promote [2026-08-01 XXIII, GATE AUDIT after the cover program v597-v605 -- the OPERATOR half of this gate is now MODEL-COMPLETE: on the mu3-cover y^3 = x^4-1 the pair (U, V) hence Q = U+V, Q_+/Q_-, H, the","claim_id":"GATE.QGEO.01","dependencies_as_recorded":"FLAV.QGEO.01; FLAV.UFSTAR.01","external_data_as_recorded":"-","id":"claim:GATE.QGEO.01","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":52,"scripts_as_recorded":"v13_open_gates.py;v19_monodromy_moduli.py;v22_open_gates_audit.py","status_as_recorded":"Open","type":"claim_ledger_row"},{"active_as_recorded":"false","canonical_status_as_recorded":"UPDATED -> v69/v70 + FLAV.RIGID: R selector derived (det R=8 lattice, Spec Q+ from D4); ratios rigid (v49)","checked_by_registry":false,"claim_excerpt":"RESIDUAL GATE (5.0 review, A2/B4): R derived only up to Mehta-Seshadri unitarity (U); parabolic scaffolding forced (deg E=-4, split 2+1+1 unique, det R=8); 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local equation closed v359)","checked_by_registry":false,"claim_excerpt":"RESIDUAL GATE (5.0 review, B6/C7) -- RESCOPED 2026-06-24: the LOCAL covariant metric-sector field equation is now CLOSED parameter-free (G_ab+Lambda g_ab=(1/c3)T_ab, both coefficients fixed, Einstein tensor via Lovelock; GRAV.NONLINEAR.01/v359, extending v358); c3=1/8pi is the gravitational seam constant and R+R^2/scalaron (M=c3^{7/2}Mbar) is the heat-kernel-grounded IR shadow. What remains OPEN is ONLY the GLOBAL no","claim_id":"GATE.METRIC.01","dependencies_as_recorded":"QG.AMB.01; GRAV.NONLINEAR.01","external_data_as_recorded":"-","id":"claim:GATE.METRIC.01","location_as_recorded":"tfpt_2;tfpt_4","path":"verification/status_ledger.csv","row_number":55,"scripts_as_recorded":"v22_open_gates_audit.py","status_as_recorded":"Open (global measure only; local equation closed v359)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical (structural grounding)","checked_by_registry":false,"claim_excerpt":"G2 grounded: spectral-action Seeley-DeWitt for Dirac (E=-R/4, tr I=4) gives a2~-R/3 (Einstein-Hilbert) + a4~R^2/72 (R^2), i.e. R+R^2 STRUCTURE convention-independently; M^2/Mbar^2=6(4pi)^2/f0, TFPT closure c3^7 fixes f0; M=c3^{7/2}Mbar=3.06e13 GeV","claim_id":"QG.G2.01","dependencies_as_recorded":"GATE.METRIC.01; v28","external_data_as_recorded":"standard Gilkey/Chamseddine-Connes","id":"claim:QG.G2.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":56,"scripts_as_recorded":"v36_spectral_action_g2.py","status_as_recorded":"Numerical (structural grounding)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Physical (conditional reframe)","checked_by_registry":false,"claim_excerpt":"SIMPLER resolution: gap decoupling. 2||V_metric||=0.785<Delta=6log(3/2)=2.433 => Delta_eff=1.648>0; admissible sector keeps positive gap under metric dressing => decoupled from un-built ambient; physical QG = closed admissible-sector measure, ambient (G6) = math completeness, gap-decoupled & inert","claim_id":"QG.GAPDEC.01","dependencies_as_recorded":"GATE.METRIC.01; G5","external_data_as_recorded":"-","id":"claim:QG.GAPDEC.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":57,"scripts_as_recorded":"v36_spectral_action_g2.py","status_as_recorded":"Physical (conditional reframe)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical (second path) ROUND-4 2026-09-05: 11 representative exact checks in wolfram/tfpt_round4.wl are wired into the base runner, but execution is UNVERIFIED_NO_KERNEL (wolframscript exit255: no WolframKernel location). Last verified base count remains116/116; native Arb/Fourier/cube regressions are not claimed as Wolfram verified. ROUND-7 2026-09-05: 14 exact representative blocks in wolfram/tfpt_round7.wl are included but UNVERIFIED_LICENSE_INACTIVE; explicit installed kernel selection fails license activation. Verified count remains116/116; no new engine success claimed.","checked_by_registry":false,"claim_excerpt":"second [C] path VERIFIED RUNNING: Wolfram Engine 14.3 reproduces alpha^-1, E8 glue, M=41, K/Q ladder, lepton c, solar angle, anchor generator, quark ratios, G2 heat-kernel (a2=-R/3,a4|R2=R2/72), Plucker apparatus (11,26,60 + pencil + dualities + lepton ring), (U_wall) selectors (Spec Q+, det R=8), Exterior Leg Lemma (scalar leg=>c_u/c_d=1; anchor microcode 55/117), carrier exterior grading (16=Lambda^even(5), exterio","claim_id":"GATE.WOLFRAM.01","dependencies_as_recorded":"mirrors v1;v2;v3;v10;v13;v16;v20;v21;v23;v24;v36;v37;v39;v42;v44;v45;v46;v47;v48;v49;v50;v51;v52;v53;v54;v55;v56;v57;v58;v59 (algebra only);v60;v61;v62 (data-confrontation, Python-only);v63;v64 (no-CTC core numerical, Python-only);v65 (falsification layer, Python-only);v66;v67;v68;v69;v70;v71;v72;v73;v74;v75;v76;v77;v78;v79;v80;v81;v983;v985;v987;v993;v994;v997","external_data_as_recorded":"-","id":"claim:GATE.WOLFRAM.01","location_as_recorded":"verification/wolfram","path":"verification/status_ledger.csv","row_number":58,"scripts_as_recorded":"wolfram/tfpt_readouts.wl","status_as_recorded":"Numerical (second path)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity (audit layer)","checked_by_registry":false,"claim_excerpt":"anchor-plane Plucker apparatus (anti-numerology): left/right 2x2 minors of B_M=(1^T M; a^T M) and C_M=(M1 Ma) for R,Q,K,L are compiler atoms; ||Pl(K)||_1=11 (localizes the '11' in K), ||Pl_R(K)||_1=Pl(L)_13=26, sum Pl_R(L)=60=cascade start; inverse col-sums {1,5,6}; quark ratios are anchor-plane Plucker readouts. Identities [I]; physical amplitudes STAY [P]","claim_id":"FLAV.PLUCKER.01","dependencies_as_recorded":"FLAV.QRATIO.01; AX anchor a","external_data_as_recorded":"-","id":"claim:FLAV.PLUCKER.01","location_as_recorded":"tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":59,"scripts_as_recorded":"v37_plucker_anchor.py","status_as_recorded":"Identity (audit layer)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity","checked_by_registry":false,"claim_excerpt":"K+xQ pencil: L=K+Q => mass and transport are one pencil P(x)=K+xQ with det(K+xQ)=3x^3+7x^2+6x+4=(N_fam, scalaron 7, |R^+(A3)|, |mu4|); chi_K=t^3-9t^2+12t-4; [K,L]=[L,Q]=[K,Q], chi_[K,Q]=t^3+5t+14 (5=g_car,14=dim G2 audit); K_e-K_u=a, L_e-L_u=Exp(A3); lepton ring c_e c_tau=|Z2| c_mu","claim_id":"FLAV.PENCIL.01","dependencies_as_recorded":"v10 K=R+Q*Sigma","external_data_as_recorded":"-","id":"claim:FLAV.PENCIL.01","location_as_recorded":"tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":60,"scripts_as_recorded":"v37_plucker_anchor.py","status_as_recorded":"Identity","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Physical (conjecture)","checked_by_registry":false,"claim_excerpt":"sharper Koide source->pole conjecture: multiplicative seed transfer u->(1-1/(2 N_fam^3))u=(53/54)u (54=2*3^3=|Z2| N_fam^3, no new free number) gives Q=0.66666610, dev -5.7e-7 from 2/3 (10x better than additive phi0/24); research gate: derive the leptonic seed transfer","claim_id":"FR.KOIDE.03","dependencies_as_recorded":"FR.KOIDE.01; lepton c","external_data_as_recorded":"PDG lepton masses","id":"claim:FR.KOIDE.03","location_as_recorded":"tfpt_4","path":"verification/status_ledger.csv","row_number":61,"scripts_as_recorded":"v37_plucker_anchor.py","status_as_recorded":"Physical (conjecture)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical (survival hardened)","checked_by_registry":false,"claim_excerpt":"(U_wall) U2 kill-switch HARDENED: kill-switch fires iff D4-cusp rep reducible; across 400 random cusp-class generators M_k=U^{k-1}MU^{1-k} commutant is scalar at every point (irreducible 400/400), reducible locus measure-zero (codim>=1), mixing strength >=0.35 => case A (nontrivial SU(3)_F mixing) is GENERIC not anecdotal; (U_wall) survives its cheapest falsification test. RESIDUAL: amplitude dictionary Gamma^min (Hi","claim_id":"GATE.UWALL.02","dependencies_as_recorded":"CONTRACT.U.01; v33","external_data_as_recorded":"-","id":"claim:GATE.UWALL.02","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":62,"scripts_as_recorded":"v38_uwall_killswitch.py","status_as_recorded":"Numerical (survival hardened)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical (selector side closed)","checked_by_registry":false,"claim_excerpt":"(U_wall) SELECTOR side closed on the explicit point (algebraic, no PDE): exponents at inf eig(sum A_k)={2,1,1}=anchor a => splitting O(-2)+O(-1)^2; pardeg=0 (deg E=-4=-|mu4| + 4 weight-sums of 1) => polystable; det R=8=n.a (anchor pairing on splitting type); Spec(Q_+)={1,2,3}=3*alpha+1 (alpha=cusp weights {0,1/3,2/3}) => both U4 selectors read off the bundle. RESIDUAL: amplitudes c_u/c_d are the finer harmonic-metric","claim_id":"GATE.UWALL.03","dependencies_as_recorded":"GATE.UWALL.02; v33; FLAV.R.01","external_data_as_recorded":"-","id":"claim:GATE.UWALL.03","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":63,"scripts_as_recorded":"v39_uwall_selectors.py","status_as_recorded":"Numerical (selector side closed)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical (Hitchin reduced to finite)","checked_by_registry":false,"claim_excerpt":"(U_wall) harmonic metric = FINITE linear algebra, NOT a transcendental Hitchin PDE: polystable point is unitary (Mehta-Seshadri) => Phi=0, harmonic metric = constant invariant form H. Explicit bundle: raw M_k non-unitary (||M^dag M-I||~0.83) but UNIQUE invariant Hermitian form H (null dim 1) is POSITIVE-DEFINITE => unitarisable; unitarised M~_k=H^{1/2}M_k H^{-1/2} unitary (1e-8), cusp class, prod=I, clean elements {0","claim_id":"GATE.UWALL.04","dependencies_as_recorded":"GATE.UWALL.03; v31; v33; Mehta-Seshadri","external_data_as_recorded":"-","id":"claim:GATE.UWALL.04","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":64,"scripts_as_recorded":"v40_harmonic_metric.py","status_as_recorded":"Numerical (Hitchin reduced to finite)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical (honest negative + suggestive link)","checked_by_registry":false,"claim_excerpt":"(U_wall) FINAL leg-assignment test (honest result): (i) delta=1/2 resolvent reproduces lepton c=(16/7,4/3,7/6) exactly => Lambda=(0.475,1.107,0.917); (ii) Lambda_mu=1.107>1 RULES OUT amplitudes=unitary holonomy moduli (modulus bound); (iii) SUGGESTIVE: harmonic-frame |diag M~_0|=(0,1/2,1/2), the 1/2 = delta=1/2 => geometry supplies delta (point observation, genericity future); (iv) CLEAN NEGATIVE: (I-1/2 M~)^-1 != am","claim_id":"GATE.UWALL.05","dependencies_as_recorded":"GATE.UWALL.04; v20; v40","external_data_as_recorded":"PDG lepton ratios","id":"claim:GATE.UWALL.05","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":65,"scripts_as_recorded":"v41_leg_assignment.py","status_as_recorded":"Numerical (honest negative + suggestive link)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I] + Physical [P]","checked_by_registry":false,"claim_excerpt":"EXTERIOR LEG LEMMA (re-types the v41 negative as a category error): u,d share hexagon-radial (r,w)=(1,1) and the C6 resolvent reads only (r,w) => ANY scalar leg gives c_u/c_d=1 identically (scalar sees radius not orientation). The u/d split is the smallest non-scalar invariant = exterior square Lambda^2 F = oriented anchor-plane area Pl_{1,a}(K). The '11' is GENERATED: (K,1,a)->B_K=[[13,8,4],[18,11,6]]->Pl(K)=(-1,6,4","claim_id":"GATE.UWALL.15","dependencies_as_recorded":"GATE.UWALL.05; FLAV.PLUCKER.01; v37","external_data_as_recorded":"-","id":"claim:GATE.UWALL.15","location_as_recorded":"tfpt_research_contracts;tfpt_2","path":"verification/status_ledger.csv","row_number":66,"scripts_as_recorded":"v42_exterior_leg.py","status_as_recorded":"Identity [I] + Physical [P]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I] (rigidity) + [A] (U_point)","checked_by_registry":false,"claim_excerpt":"Readout Rigidity (Theorem U2): c_u/c_d is CONSTANT on the discrete selector stratum S_{8,Q}={det R=8, SNF(R)=(1,1,8), Spec(Q+)={1,2,3}}, independent of the continuous D4 position => c_u/c_d=55/117 needs NO point-uniqueness. (U_wall) splits into U_unitary (v40, Phi=0 finite) + U_H2 (v39, R/Q/K from bundle) + U_Lambda2 (v42/v45, exterior Plucker 55/117) + U_point (open, only for full U_f* matrix). D4 fixes the chamber,","claim_id":"FLAV.RIGID.01","dependencies_as_recorded":"GATE.UWALL.03; v39; v40; v42","external_data_as_recorded":"-","id":"claim:FLAV.RIGID.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":67,"scripts_as_recorded":"v49_readout_rigidity.py","status_as_recorded":"Identity [I] (rigidity) + [A] (U_point)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/Lattice [I]/[L] + [P] geometry","checked_by_registry":false,"claim_excerpt":"Q geometry (Theorem Q): Sigma-split Q_+=(Q+SigQSig)/2=[[3,0,0],[0,2,0],[0,2,1]] (chi=(t-1)(t-2)(t-3), Spec={1,2,3}=A3 exponents), Q_-=[[0,1,0],[3,0,0],[3,0,0]] (chi=t(t^2-3), Q_-^2|supp=3=N_fam). UNIQUE nonneg-integer Q with rows(4,5,6), cols(9,5,1), chi_Q+, chi_Q- (enumeration) => K=R+Q*Sigma is the second Sigma-shadow of the same parabolic flavor operator. Algebraic normal form [I]/[L]; D4-equivariant parabolic rea","claim_id":"FLAV.QGEO.02","dependencies_as_recorded":"FLAV.KQ.01; GATE.QGEO.01","external_data_as_recorded":"-","id":"claim:FLAV.QGEO.02","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":68,"scripts_as_recorded":"v50_q_geometry.py","status_as_recorded":"Identity/Lattice [I]/[L] + [P] geometry","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Lattice [L] + selection [P]","checked_by_registry":false,"claim_excerpt":"Boundary Carrier Selection Theorem (Theorem A): admissible boundary-carrier data SELECT (D5+A3)+mu4=E8 uniquely. Boundary mu4->H1=Z^3->A3,N_fam=3; minimal 16-spinor->D5 (only n=5); disc(D5)=disc(A3)=Z4 cyclic anti-isometric, q(D5)+q(A3)=5/4+3/4=2=E8 root norm, glue index 4=|mu4|, E8 unique even unimodular rank 8. Four simultaneous conditions (16-spinor, N_fam=3, cyclic Z4, q-sum 2) met ONLY by D5+A3; D8 (non-cyclic, ","claim_id":"SEL.THM.01","dependencies_as_recorded":"E8.GLU.01; BOOT.CLASS.01; v1; v15","external_data_as_recorded":"-","id":"claim:SEL.THM.01","location_as_recorded":"tfpt_1","path":"verification/status_ledger.csv","row_number":69,"scripts_as_recorded":"v47_selection_theorem.py","status_as_recorded":"Lattice [L] + selection [P]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I] + physical origin [P]","checked_by_registry":false,"claim_excerpt":"EM Boundary Ward decomposition (Theorem C): F_U(1)=0 read as reduced boundary U(1) Ward identity in three terms - Maxwell alpha^3 + Calderon -2c3^3 alpha^2 (2=|Z2|) + transport -8b1 c3^6 log(1/phi_seam). Coefficient identities EXACT [I]: 8b1=(4/5)M=(4/5)(sumL+N_Phi)=164/5; seam exponent -5/4=-q(D5); transport power c3^6=C6 hexagon. Root reproduces alpha^-1=137.0359992 (v3). Physical Ward ORIGIN (EM1/EM2/EM3: d_tau lo","claim_id":"EM.WARD.01","dependencies_as_recorded":"EM.FP.01; v3; v341; v342","external_data_as_recorded":"-","id":"claim:EM.WARD.01","location_as_recorded":"tfpt_1","path":"verification/status_ledger.csv","row_number":70,"scripts_as_recorded":"v48_em_ward.py","status_as_recorded":"Identity [I] + physical origin [P] (sharpened to a Quillen form by v341; to a heat-kernel origin by v342)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the order-4 clock + Coxeter-match jointly pin E8 over SO(16), resolving the which-net ambiguity non-circularly; [O] the chiral-edge/scaling-limit existence (v336) is the remaining residual. A sharpening; does NOT close SEAM.EQUIV.01.","checked_by_registry":false,"claim_excerpt":"THE CONTINUUM REALISATION SHARPENED BY THE BOOTSTRAP (2026-06-22): the 'c=8 ambiguity' flagged open in v277/v344 (E8 vs SO(16) both have c=8) is RESOLVED, non-circularly, by the seam's ORDER-4 mu4 clock; so the continuum residual of SEAM.EQUIV.01 is no longer 'which c=8 net?' but PURELY the existence of the chiral edge / massless scaling limit. [E] two c=8 lattices: E8 (det Cartan 1, holomorphic, 1 primary) and D8=SO","claim_id":"SEAM.EQUIV.CONTINUUM.02","dependencies_as_recorded":"SEAM.EQUIV.GEOM.01; v277; v344; v216; v154; v281; v336","external_data_as_recorded":"-","id":"claim:SEAM.EQUIV.CONTINUUM.02","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":71,"scripts_as_recorded":"v351_continuum_realisation_sharpened.py","status_as_recorded":"Sharpening [E]/[O] (the order-4 clock + Coxeter-match pin E8 over SO(16); the residual is purely the chiral-edge existence)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the dimensionless-compiler / gravity-adds-no-scale / final-tally facts; [O] the irreducible-primitive status of v_geo (No-Unit consequence) + the Sakharov UV-sensitivity of 1/G. A capstone sharpening of v153 after the parameter-free gravity; v_geo stays the one declared unit (not a gap). Direction 6 closed -- clarity, not a new derivation.","checked_by_registry":false,"claim_excerpt":"v_geo IS THE SINGLE DIMENSIONFUL INPUT OF THE WHOLE THEORY (2026-06-23, Direction 6 of next-plan.md), now confirmed across matter AND gravity, and irreducibly primitive. The No-Unit Theorem (v153) already established that the dimensionless compiler cannot output an absolute scale, so v_geo is a forced metrology primitive, with the matter residuals collapsing onto it (U_point~v_geo, 1/G~v_geo^2, m/mu=e^{3/4} a pure ra","claim_id":"VGEO.SHARPEN.01","dependencies_as_recorded":"v153; v358; v359; v361; v60; v68; v78","external_data_as_recorded":"-","id":"claim:VGEO.SHARPEN.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":72,"scripts_as_recorded":"v364_vgeo_sharpen.py","status_as_recorded":"v_geo capstone [E]/[O] (Direction 6: v_geo the single dimensionful input across matter+gravity, irreducibly primitive by No-Unit; final tally 0 dimensionless dials + 1 unit + pi vs SM ~26)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the carrier gravitational anomaly c_-=8 + the finite-backreaction-to-Lambda loop closure + the explicit J3 coupling; [C] the SM trace-anomaly reproduction; [O] the decline of a new per-quantum-number read-out. A disciplined consolidation (positive content + an honest decline): the backreaction is finite and forced (c_-=8, Lambda), but adds no new free quantity. Nothing over-claimed.","checked_by_registry":false,"claim_excerpt":"THE MATTER-GRAVITY BACKREACTION WITH THE EXPLICIT J3 FLUX (2026-06-23, Direction 5 of next-plan.md). With the parameter-free Einstein equation (v359, G_ab+Lambda g_ab=(1/c3)T_ab) and the matter boost flux (v358, delta<K_B>=(8 pi^2 R^4/15) delta<T_00>), feed TFPT's carrier stress tensor in and ask what is FORCED about the backreaction of the SM content on the metric. Run with the v354/v355 discriminator: two genuine f","claim_id":"GRAV.BACKREACT.01","dependencies_as_recorded":"GRAV.NONLINEAR.01; v359; v358; v60; v337; v159; v354; v355","external_data_as_recorded":"-","id":"claim:GRAV.BACKREACT.01","location_as_recorded":"tfpt_4","path":"verification/status_ledger.csv","row_number":73,"scripts_as_recorded":"v361_grav_backreaction.py","status_as_recorded":"Backreaction result [E]/[C]/[O] (Direction 5: carrier gravitational anomaly c_-=8 forced + finite backreaction -> Lambda from alpha, loop closes; no new SM-quantum-number read-out -> declined per v354/v355)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the scalaron-as-leading-correction + its existing n_s/r kill test + the gap-is-dimensionless/Planck-scale reasoning; [C] the Wald-first-law consistency; [O] the explicit decline of a manufactured new coefficient. A disciplined-search record (like v355): the positive content is that the calculable GR deviation is the scalaron; the decline is the anti-numerology outcome. No new prediction added; nothing over-claimed.","checked_by_registry":false,"claim_excerpt":"THE GAP-INDUCED HIGHER-CURVATURE CORRECTION TO GR -- THE DISCIPLINED RESULT (2026-06-23, Direction 2 of next-plan.md). Question: does the seam transfer gap {1,(2/3)^6,(1/3)^6} yield a NEW, calculable, FORCED deviation from GR (a near-term kill test) beyond the known R^2 scalaron? Run with the v354/v355 anti-numerology discriminator (a coefficient counts only if atom-forced, never a fit), the honest answer is NO -- an","claim_id":"GRAV.GAPCORR.01","dependencies_as_recorded":"GRAV.NONLINEAR.01; v359; v358; v36; v28; v354; v355","external_data_as_recorded":"-","id":"claim:GRAV.GAPCORR.01","location_as_recorded":"tfpt_4","path":"verification/status_ledger.csv","row_number":74,"scripts_as_recorded":"v360_grav_gap_corrections.py","status_as_recorded":"Gap-correction result [E]/[C]/[O] (Direction 2 declined: the calculable GR deviation is the R^2 scalaron already falsifiable via n_s/r; a new gap coefficient is not atom-forced -> declined per v354/v355)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the Einstein-tensor structure (trace=-R d=4) + Lovelock conservation + both parameter-free coefficients (8pi=1/c3, Lambda prefactor 3/(4pi^2)); [C] the Jacobson-2015 fixed-volume machinery + the all-directions quantifier; [O] the equation-of-state status + the global measure (C7). Delivers the full LOCAL covariant equation parameter-free; advances B6/GATE.METRIC from 'linearised (v358)' to 'full covariant local'; does NOT claim a from-action QG quantisation.","checked_by_registry":false,"claim_excerpt":"THE FULL COVARIANT EINSTEIN EQUATION, PARAMETER-FREE (2026-06-23, Direction 1 of next-plan.md, extends GRAV.ENTROPY.EQUILIBRIUM.01/v358). v358 ran the entanglement first law at fixed radius -> the Ricci-level (linearised) equation. Jacobson 2015 (PRL 116, 201101) shows that demanding stationarity of the small-ball entanglement entropy at fixed VOLUME brings in the EINSTEIN TENSOR G_ab (not just R_ab) -- the unique sy","claim_id":"GRAV.NONLINEAR.01","dependencies_as_recorded":"GRAV.ENTROPY.EQUILIBRIUM.01; v358; v60; v323; v57; v58; v216","external_data_as_recorded":"-","id":"claim:GRAV.NONLINEAR.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":75,"scripts_as_recorded":"v359_grav_nonlinear_einstein.py","status_as_recorded":"Full covariant Einstein equation [E]/[C]/[O] (parameter-free: 8pi=1/c3 + Lambda from alpha; Einstein tensor via fixed-volume equilibrium + Lovelock conservation; B6 closed at local level; residual = equation-of-state status + C7 global measure)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the parameter-free Einstein coefficient + the thermo=geo coincidence (the new exact result) + the entropy-density atom-fixing; [C] J3 (cited CHM/BW ball modular Hamiltonian applied to TFPT's matter) + the area-law form; [O] linear->non-linear (B6 full) + the v_geo unit. Closes the LINEARISED Einstein equation parameter-free; advances B6/GATE.METRIC substantially; does NOT claim the full non-linear closure.","checked_by_registry":false,"claim_excerpt":"THE ENTANGLEMENT-EQUILIBRIUM DERIVATION OF THE LINEARISED EINSTEIN EQUATION, PARAMETER-FREE (2026-06-23). Carries out the Jacobson-2015 / Faulkner-et-al. 'first law of entanglement => Einstein equation' (delta S = delta<K>) with TFPT's atoms, and closes the two pieces that the bridge analysis (v356) left open (the matter boost flux J3 and the entropy-density coefficient). [E] PARAMETER-FREE EINSTEIN COEFFICIENT: delt","claim_id":"GRAV.ENTROPY.EQUILIBRIUM.01","dependencies_as_recorded":"SEAM.EQUIV.CONTINUUM.03; v356; v57; v58; v59; v216; v221; v323; v76","external_data_as_recorded":"-","id":"claim:GRAV.ENTROPY.EQUILIBRIUM.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":76,"scripts_as_recorded":"v358_grav_entropy_equilibrium.py","status_as_recorded":"Entanglement-equilibrium gravity [E]/[C]/[O] (parameter-free linearised Einstein 8pi=1/c3; thermo=geo coincidence via |mu4|=|Z2|chi; J3 assembled; entropy density atom-fixed; residual = nonlinear + v_geo)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[C] the MMST range + edge-existence-from-invertibility + chirality=one-sidedness=c3-origin; [E] chain-closes-modulo-S3; [O] the one lattice-realization input. A genuine assembly reducing SEAM.EQUIV.01 to one realization input tied to the seam one-sidedness; does NOT close it. Direction B found already closed by v40 (harmonic metric = finite linear algebra, not a PDE); no redundant B module shipped.","checked_by_registry":false,"claim_excerpt":"DIRECTION A (2026-06-23): the continuum chain of SEAM.EQUIV.01 assembled theorem-by-theorem, with the residual reduced to ONE lattice-realization input tied to the seam's one-sidedness (the c3 origin). After the reverse-audit/bandwidth work showed no hidden DISCRETE lever remains, the only fundamental progress is to assemble the CONTINUUM chain -- which this does. THE CHAIN: S1 the gapped (Delta=6 ln(3/2)>0, v302) qu","claim_id":"SEAM.EQUIV.CONTINUUM.03","dependencies_as_recorded":"SEAM.EQUIV.01; v301; v302; v336; v351; v297; v58; v40","external_data_as_recorded":"-","id":"claim:SEAM.EQUIV.CONTINUUM.03","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":77,"scripts_as_recorded":"v356_continuum_mmst_applicability.py","status_as_recorded":"Continuum chain assembly [C]/[E]/[O] (edge-existence reduced via anomaly inflow; residual = lattice realization tied to seam one-sidedness; B already closed by v40)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] fixed quadratic form (1/c3=8pi) + gap-controlled convergence (Delta_eff~1.648>0) + finite model log-det (6 ln(9/2)) + tightness (chi=729/665) + 0 dials; [C] the GHP conformal contour + the one-loop Gaussian measure on the admissible sector; [O] the full non-perturbative projective limit. Sharpens C7; does NOT close it.","checked_by_registry":false,"claim_excerpt":"Direction 3 (2026-06-23): the QG measure (gate C7/QG.AMB.01) as one-loop GAUSSIAN fluctuations around the PARAMETER-FREE saddle (v358/v359). Before v358 fluctuations around the gravitational saddle were not even dimensionlessly well-posed (the Newton coupling was a free dial); with the parameter-free saddle the path integral organises as a Gaussian one-loop determinant whose convergence and dimensionless content are ","claim_id":"QGAMB.SADDLE.01","dependencies_as_recorded":"QG.AMB.01; v358; v359; v76; v337; v330; v334; v364; v59","external_data_as_recorded":"-","id":"claim:QGAMB.SADDLE.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":78,"scripts_as_recorded":"v365_qg_oneloop_saddle.py","status_as_recorded":"QG measure reduced to a one-loop Gaussian problem around the parameter-free saddle [E]/[C]/[O] (residual = the non-perturbative projective limit)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] class arithmetic 8<=8<=16 + derived gap + chirality c_-=8 + (E8)_1 pinning; [C] the CAR-class typing + the MMST scaling-limit theorem (cited); [O] the S3 lattice realisation. Verifies MMST in-class; ADVANCES SEAM.EQUIV.01, does not close it.","checked_by_registry":false,"claim_excerpt":"Direction 7 (2026-06-23): the seam collar is IN MMST's free-lattice-fermion scaling-limit class, so the chiral scaling limit is a chiral CFT of central charge 8 pinned to (E8)_1 -- reducing SEAM.EQUIV.01 to the single S3 lattice-realisation input. the cited theorem (Osborne-Stottmeister, arXiv:2107.13834, CMP 398 (2023) 219; the internal 'MMST' code-token/claim-id is LEGACY and denotes THIS Osborne-Stottmeister theor","claim_id":"SEAM.MMST.INCLASS.01","dependencies_as_recorded":"SEAM.EQUIV.01; v336; v356; v351; v302; v155; v160; v297; v301","external_data_as_recorded":"-","id":"claim:SEAM.MMST.INCLASS.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":79,"scripts_as_recorded":"v366_mmst_seam_collar.py","status_as_recorded":"SEAM.EQUIV.01 reduced to the single S3 lattice-realisation input; MMST in-class verified for the collar [E]/[C]/[O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the Barnes-Rivers projector completeness + EH structure + the spin-2 pole algebra; [C] the entire form factor (inherits v304) + GHP (v334) + the sector-by-sector unitarity conclusion; [O] perturbative-only + the open analyticity assumption. Extends v304 to the tensor sector; does NOT close QG.AMB.01. tr P2=5 != g_car (declined).","checked_by_registry":false,"claim_excerpt":"Track 2 (2026-06-23): the Barnes-Rivers spin decomposition of the graviton propagator -- perturbative graviton unitarity SECTOR-BY-SECTOR. Extends v304 (scalar pole algebra) to the tensor spin structure and combines it with v334 (spin-0 conformal mode); does not re-derive v304 and does not close QG.AMB.01. [E] PROJECTOR COMPLETENESS: tr P2=(d-2)(d+1)/2, tr P1=d-1, tr P0s=tr P0w=1 sum to d(d+1)/2 (the symmetric-tensor","claim_id":"GRAV.SPIN2.UNITARITY.01","dependencies_as_recorded":"QG.AMB.01; v304; v334; v332; v259; v278; v354","external_data_as_recorded":"-","id":"claim:GRAV.SPIN2.UNITARITY.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":80,"scripts_as_recorded":"v370_grav_spin2_unitarity.py","status_as_recorded":"perturbative graviton unitarity sector-by-sector (spin-2 ghost-free via the entire KMS form factor, spin-0 via GHP) [E]/[C]/[O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the gapped Chern model + the c_-=8 counting + the det K discriminators (numerical Chern + lattice arithmetic); [C] the mu4 condensation to (E8)_1; [O] the continuum scaling limit. Reduces S3 to a runnable lattice model; does NOT close SEAM.EQUIV.01.","checked_by_registry":false,"claim_excerpt":"Track 1 (2026-06-23): the EXPLICIT lattice realisation of the S3 input -- a concrete gapped chiral-Majorana (p+ip) lattice model whose edge is the 16-Majorana SO(16)_1 carrier, mu4-condensed to (E8)_1. Turns the abstract S3 residual of v356/v366 ('the collar realised as a genuine lattice chiral free-fermion invertible phase') into a RUNNABLE model with a numerically computed topological invariant, not a re-assertion ","claim_id":"SEAM.S3.LATTICE.01","dependencies_as_recorded":"SEAM.EQUIV.01; v356; v366; v351; v369; v301; v302; v154","external_data_as_recorded":"-","id":"claim:SEAM.S3.LATTICE.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":81,"scripts_as_recorded":"v367_seam_s3_lattice.py","status_as_recorded":"S3 realised as an explicit gapped chiral-Majorana lattice model (numerical Chern |C|=1, c_-=8, det K 4->1) [E]/[C]/[O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the strip edge spectrum + localisation + bulk-edge correspondence + the trivial neg control; [C] the anomaly-inflow edge-existence argument; [O] the continuum scaling limit. Discharges the S4 'edge exists' leg on the lattice; does NOT close SEAM.EQUIV.01.","checked_by_registry":false,"claim_excerpt":"Track 1 (2026-06-23): the bulk-edge / anomaly-inflow leg (S4 of the v356 chain) made CONCRETE on the v367 lattice model -- a finite STRIP of the gapped p+ip model has a REALISED, non-gappable chiral edge, so edge EXISTENCE is a CONSEQUENCE of the bulk being a nontrivial invertible phase (anomaly inflow), NOT a separate assumption. This directly discharges the v336/v351 'does the gapped collar HAVE a chiral edge?' res","claim_id":"SEAM.S3.INFLOW.01","dependencies_as_recorded":"SEAM.EQUIV.01; v367; v356; v336; v351; v301","external_data_as_recorded":"-","id":"claim:SEAM.S3.INFLOW.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":82,"scripts_as_recorded":"v368_seam_s3_inflow.py","status_as_recorded":"edge existence forced by the invertible bulk (anomaly inflow) -- realised non-gappable chiral edge on the lattice strip [E]/[C]/[O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the Koide coincidence + the QED-wrong-way sign + the negative required eps (PDG poles + exact ladder ratios, no fit); [C] the verdict that the true transfer is the non-QED generator. A typed solver with a kill test; does NOT promote Q_pole to [E].","checked_by_registry":false,"claim_excerpt":"Track 3 (2026-06-23, F_transfer): the Koide source->pole transfer as a TYPED solver -- promotes experiments/ftransfer/koide_source_to_pole into the ledger with a kill test. Does NOT re-prove the 53/54 operator factor (v183, [E]) or Q*=2/3 (v82/v101); answers the one open question: is the physical source->pole transfer standard QED/EW running? A clean NEGATIVE. [E] Q_pole=Koide(PDG poles)=2/3 to 3e-6; Q_src(phi0-ladde","claim_id":"FR.POLE.SOLVE.01","dependencies_as_recorded":"FR.POLE.01; v183; v82; v93; v101","external_data_as_recorded":"PDG 2024 lepton pole masses","id":"claim:FR.POLE.SOLVE.01","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":83,"scripts_as_recorded":"v371_ftransfer_pole.py","status_as_recorded":"Koide source->pole: standard QED running EXCLUDED (wrong sign) -- the transfer is the non-QED 53/54 operator/Moebius generator [E]/[C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the integrated efficiency; [C] the frozen-scale eta_B near-hit (washout anchored m~1=m3/A_Lambda, M1 via the scalaron route v212); [X] the branch kill test. A typed solver, not a toy; eta_B stays [C] (a transfer target, not a compiler power).","checked_by_registry":false,"claim_excerpt":"Track 3 (2026-06-23, F_transfer): eta_B from the INTEGRATED Buchmueller-Di Bari-Pluemacher Boltzmann network at the TFPT-frozen heavy scale -- promotes experiments/ftransfer/leptogenesis_boltzmann, replacing the v326 toy washout (kappa=0.3 tuned). Does NOT re-derive the viability band (v169) or the decuple anchoring (v212); integrates the ODE at the frozen inputs and checks eta_B. Frozen (NO free M_R dial): M1=M_scal","claim_id":"FR.BOLTZMANN.SOLVE.01","dependencies_as_recorded":"FR.ETAB.01; v169; v212; v9; v7","external_data_as_recorded":"Planck eta_B=6.1e-10","id":"claim:FR.BOLTZMANN.SOLVE.01","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":84,"scripts_as_recorded":"v372_ftransfer_boltzmann.py","status_as_recorded":"eta_B from the integrated BDP Boltzmann ODE at the frozen M1 -- near-hit (factor ~1.1) with no M_R dial [C]/[X]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[I] the candidate scales; [C] the spine in-band relic (finite-T misalignment + lattice chi(T)); [X] the hilltop over-production + the spine kill test. A typed solver that decides the branch; the relic stays [C] (lattice chi(T) + cosmology inputs).","checked_by_registry":false,"claim_excerpt":"Track 3 (2026-06-23, F_transfer): the axion relic abundance from the FINITE-T misalignment ODE -- promotes experiments/ftransfer/axion_relic and DECIDES the two competing TFPT angle branches, replacing the v326 adiabatic toy. Does NOT re-fix the candidate scales (f_a=M_scal/128, m_a; v185/v211); integrates the nonlinear ODE theta'' + (3+dlnH/dN)theta' + (m_a(T)/H)^2 sin theta = 0 with the lattice topological suscepti","claim_id":"FR.RELIC.SOLVE.01","dependencies_as_recorded":"v185; v211; v25","external_data_as_recorded":"Planck Omega_DM h2=0.12","id":"claim:FR.RELIC.SOLVE.01","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":85,"scripts_as_recorded":"v373_ftransfer_relic.py","status_as_recorded":"axion relic finite-T solve DECIDES the branch -- spine 3pi/5 lands on Omega_DM (in band), hilltop 170deg over-produces [C]/[X]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] b3=-7; [N] the two externals; [C] the observed ratio inside the propagated band (no dial); [X] the lattice-tightening kill test. An uncertainty-budget/falsifiability solver, distinct from v262's point estimate; m_p/m_e stays [C].","checked_by_registry":false,"claim_excerpt":"Track 3 (2026-06-23, F_transfer): the m_p/m_e transfer as a TYPED uncertainty-budget + kill test -- the falsifiability companion to v262 (the precise 2-loop point), replacing the v326 toy (which hardcodes 1836.15). Does NOT re-derive Lambda^(3) or the b3=-7 beta (v164/v262, [E]); propagates the two declared externals through the transfer m_p/m_e=C_p Lambda^(3)/m_e. [E] b3=-(11-2 n_f/3)=-7 (n_f=6 carrier). [N] two dec","claim_id":"FR.QCD.BUDGET.01","dependencies_as_recorded":"FR.MPME.02; v262; v164; v339","external_data_as_recorded":"PDG alpha_s(M_Z), lattice C_p, CODATA m_p/m_e","id":"claim:FR.QCD.BUDGET.01","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":86,"scripts_as_recorded":"v374_ftransfer_qcd.py","status_as_recorded":"m_p/m_e uncertainty budget: the observed 1836.15 is inside the propagated +-7.5% (alpha_s, C_p) band; lattice-tightening is the kill [C]/[N]/[X]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the completeness + atom re-derivation + integrity; [N] the live data scorecard (the sigma-distances are data, updated as experiments report). Tooling that verifies the prediction surface; introduces no new physics claim.","checked_by_registry":false,"claim_excerpt":"Track 4 (2026-06-23): the prediction OBSERVATORY -- a status-typed CI over the frozen prediction registry (verification/freeze_file.csv) that makes the falsifiability surface machine-checkable. Does NOT re-derive the physics; verifies (a) the registry is COMPLETE (every frozen signal has a kill criterion), (b) the headline numerical predictions re-derive from the atoms {phi0}, (c) the live scorecard (each headline pr","claim_id":"OBSERVATORY.REGISTRY.01","dependencies_as_recorded":"v3; v9; v268; v328; v86; v60","external_data_as_recorded":"JUNO first run; NuFIT 6.0; ACT DR6; BK18","id":"claim:OBSERVATORY.REGISTRY.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":87,"scripts_as_recorded":"v375_observatory_registry.py","status_as_recorded":"a status-typed CI over freeze_file.csv -- falsifiability complete + the live scorecard (theta13 flagged at 2.0 sigma) [E]/[N]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the numerical c=1 per mode (EE scaling) + additive c=8 + the chirality cross-link; [O] the specific-net identification (v377/v378) + the continuum existence (v336). Numerical evidence that the scaling limit has c=8; does NOT close SEAM.EQUIV.01.","checked_by_registry":false,"claim_excerpt":"S3 closure stack (2026-06-23): the central charge c=8 extracted NUMERICALLY from the lattice via the Calabrese-Cardy finite-size entanglement-entropy scaling of the critical free-fermion content -- the standard, rigorous lattice->CFT central-charge diagnostic (the quantitative core of the MMST scaling-limit claim), on OUR model, not a re-assertion. [E] the Peschel correlation-matrix EE of one critical tight-binding c","claim_id":"SEAM.S3.CENTRALCHARGE.01","dependencies_as_recorded":"SEAM.EQUIV.01; v367; v368; v336","external_data_as_recorded":"-","id":"claim:SEAM.S3.CENTRALCHARGE.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":88,"scripts_as_recorded":"v376_seam_s3_centralcharge.py","status_as_recorded":"central charge c=8 from finite-size entanglement scaling of the lattice (chiral, c_-=8) [E]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the exact character q-series (c=8, 248, 4124) + the integer promotion identities (248=240+8=120+128, 240=16*5*3) + the 1-vs-4 primary discriminator; [O] the continuum existence (v336) + the mu4 projection = S3. Pins the target net (E8)_1; does NOT close SEAM.EQUIV.01.","checked_by_registry":false,"claim_excerpt":"S3 closure stack (2026-06-23): the chiral c=8 content of the seam is the SPECIFIC net (E8)_1, not just 'some c=8' -- shown by the exact affine character q-series and the mu4/GSO promotion SO(16)_1 -> (E8)_1 (the genus-0 character discriminator that pins the target of the scaling limit). [E] chi = E4/eta^8 = q^{-1/3}(1+248q+4124q^2+...): eta^8=q^{1/3}prod(1-q^n)^8 gives the prefactor q^{-c/24}=q^{-1/3} => c=8; the lev","claim_id":"SEAM.S3.E8CHARACTER.01","dependencies_as_recorded":"SEAM.EQUIV.01; v336; v351; v83; v1","external_data_as_recorded":"-","id":"claim:SEAM.S3.E8CHARACTER.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":89,"scripts_as_recorded":"v377_seam_s3_e8character.py","status_as_recorded":"the chiral c=8 content is (E8)_1 (248 currents, 1 primary) via the exact character + mu4/GSO promotion [E]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the KLM condensation 16->1, the det-Cartan #primaries (1 vs 4), the modular T-eigenvalue / 1-dim rep, and the genus-0-vs-genus-1 distinction; [O] the continuum existence (v336). Pins the net at genus-1; does NOT close SEAM.EQUIV.01.","checked_by_registry":false,"claim_excerpt":"S3 closure stack (2026-06-23): the GENUS-1 discriminator -- the torus ground-state degeneracy of the seam net is 1 (holomorphic = (E8)_1), via the KLM index condensation and the modular invariance of the single (E8)_1 character. This is exactly the 'hard part' v344 flagged: the genus-0 arguments (a unique plane vacuum) are necessary but NOT sufficient (a plane vacuum is always 1, v87); det K=1 is the torus (genus-1) ","claim_id":"SEAM.S3.MODULAR.01","dependencies_as_recorded":"SEAM.EQUIV.01; v344; v154; v369; v83; v87","external_data_as_recorded":"-","id":"claim:SEAM.S3.MODULAR.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":90,"scripts_as_recorded":"v378_seam_s3_modular.py","status_as_recorded":"torus GSD=1 / modular uniqueness -- the genus-1 holomorphy discriminator closes the v344 hard part [E]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the positive spectral rep + the EXACT positive-mixture Gram identity for RP (symbolic PSD; the min-eigenvalue check retained as a DIAGNOSTIC measurement of the assembled float matrix, T133) + the non-vacuous neg control; [C] the OS reconstruction + the C7 discharge via v369; [O] the full constructive measure. Verifies the RP axiom for the explicit collar; does NOT by itself construct C7. Marker unchanged [E] (the Gram rescue carries; no upgrade).","checked_by_registry":false,"claim_excerpt":"S3 closure stack / C7 (2026-06-23): reflection positivity (the Osterwalder-Schrader axiom) of the EXPLICIT gapped collar measure, verified numerically -- the remaining constructive-QFT ingredient for the OS reconstruction of the boundary net, after which C7/QG.AMB.01 is discharged by the redundancy theorem v369 (its first premise, SEAM.EQUIV.01, being the S3 stack), not built from scratch. [E] Kaellen-Lehmann/OS posi","claim_id":"SEAM.S3.RP.01","dependencies_as_recorded":"QG.AMB.01; v367; v369; v240; v76; v376; v377; v378; T133","external_data_as_recorded":"-","id":"claim:SEAM.S3.RP.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":91,"scripts_as_recorded":"v379_seam_s3_rp.py","status_as_recorded":"reflection positivity (OS axiom) of the explicit collar verified by an EXACT positive-mixture Gram identity (symbolic PSD: M = V^T diag(1/K) V, sum of squares; eigenvalue check retained as diagnostic, T133 hardening); C7 then discharged via v369 [E]/[C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Formal [F]: the S3 continuum leg machine-formalised as 'closed modulo cited theorems' -- the collar's MMST hypotheses kernel-proved (decide, no axioms), the MMST/Adamo theorems named axioms, the composition's #print axioms clean. The honest closure ceiling for SEAM.EQUIV.01.","checked_by_registry":false,"claim_excerpt":"LEAN 4 FORMALISATION of the S3 / SEAM.EQUIV.01 continuum leg (the MMST scaling-limit theorem applied to the seam collar), 2026-06-23 -- new module TfptCarrier/SeamScalingLimit.lean, lake build OK (target TfptCarrier.SeamScalingLimit, 230ms), #print axioms CLEAN. It formalises the status 'CLOSED MODULO A CITED THEOREM': (1) [F] the MMST applicability HYPOTHESES for the collar are PROVABLE arithmetic facts by kernel de","claim_id":"FORM.SEAM.MMST.01","dependencies_as_recorded":"SEAM.EQUIV.01; v336; v366; v376; v377; v378; v379; FORM.GLUE.01","external_data_as_recorded":"MMST (CMP 2022); Adamo-Moriwaki-Tanimoto (2024)","id":"claim:FORM.SEAM.MMST.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":92,"scripts_as_recorded":"lean4-carrier-rigidity/TfptCarrier/SeamScalingLimit.lean","status_as_recorded":"Formal [F] (Lean kernel; closed modulo the cited MMST/Adamo theorems)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the truncation-artefact mechanism (each finite Taylor truncation of e^u has a zero, e^u has none) + the decoupling (nearest truncation-zero modulus grows monotonically with order); [C] the identification with the full off-shell curved-space Hessian (cited heat-kernel resummation); [O] perturbative-only. Closes the v304/v370 analyticity gap at the truncation-tower level; does NOT change QG.AMB.01.","checked_by_registry":false,"claim_excerpt":"The KMS Entire Hessian (2026-06-23): the Stelle ghost is EXACTLY the Seeley-DeWitt truncation, and resummation pushes it to infinity -- upgrading v304/v370 from the ASSUMPTION 'the resummed graviton form factor is entire' to a DERIVED truncation-artefact + decoupling statement. [E] SEAM CUTOFF -> ENTIRE FORM FACTOR: f(u)=e^{-u} (the beta=1 seam KMS weight, v259) gives the dressed spin-2 propagator e^{-p^2/M^2}/p^2 = ","claim_id":"GRAV.KMS.HESSIAN.01","dependencies_as_recorded":"QG.AMB.01; v259; v304; v370; v334","external_data_as_recorded":"Tomboulis 1997; Biswas-Mazumdar-Siegel 2006","id":"claim:GRAV.KMS.HESSIAN.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":93,"scripts_as_recorded":"v380_grav_kms_hessian.py","status_as_recorded":"the Stelle ghost = the Seeley-DeWitt truncation; resummation decouples it (root modulus -> infinity) => entire spin-2 form factor [E]/[C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] det K=1 => DHR=Vec (no superselection) + no torus GSD + finite Petz recovery (2/3)^6 + gap margin Delta_eff~1.648>0; [C] the BW reconstruction map + the redundancy statement O_phys^bulk/Diff ~= A_Sigma^{mu4}; [O] the two premises (SEAM.EQUIV.01 + BW intrinsicality). The holographic route to Gravity-complete; does NOT construct the ambient measure.","checked_by_registry":false,"claim_excerpt":"Track 2 (2026-06-23, next-plan v2): the AMBIENT REDUNDANCY statement -- the holographic route to Gravity-complete that SIDESTEPS building the general Euclidean QG measure (C7/QG.AMB.01). Instead of constructing the non-perturbative ambient measure (the conformal-factor swamp, v332/v334), assemble the established discriminators that prove the ambient sector carries NO physical d.o.f. relative to the holomorphic bounda","claim_id":"QGAMB.REDUNDANCY.01","dependencies_as_recorded":"QG.AMB.01; SEAM.EQUIV.01; v366; v329; v221; v76; v337; v258; v309; v323; v344; v83","external_data_as_recorded":"-","id":"claim:QGAMB.REDUNDANCY.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":94,"scripts_as_recorded":"v369_qgamb_redundancy.py","status_as_recorded":"Ambient measure proved boundary-REDUNDANT (the holographic route); QG.AMB.01 reframed as a non-fundamental certification object [C]/[O] (conditional on SEAM.EQUIV.01 + BW)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the set-level forced identities and the reconciliation; [C] the subchain Coxeter pattern; [O] the explicit declines. A self-critical search whose main finding is that there is nothing forced left to find per-number -- the correct outcome of an honest reverse audit; sharpens v354 (no PRIMARY readout, not 'unmapped'), reconciles v66.","checked_by_registry":false,"claim_excerpt":"A DISCIPLINED BANDWIDTH SEARCH OF THE UNMAPPED E8 REGION (2026-06-22, the next step after v354). The natural follow-up -- 'search that region for hits and structures we overlooked' -- is itself the numerology temptation v354 warns about: a rich object like E8 yields a numerical match for almost anything. So this scan uses a STRICT discriminator: a candidate is real ONLY if it is a FORCED identity (a theorem about E8)","claim_id":"E8.UNMAPPED.BANDWIDTH.01","dependencies_as_recorded":"E8.REVERSE.AUDIT.01; v354; v66; v223; v219; v305","external_data_as_recorded":"-","id":"claim:E8.UNMAPPED.BANDWIDTH.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":95,"scripts_as_recorded":"v355_e8_unmapped_bandwidth.py","status_as_recorded":"Bandwidth search [E]/[C]/[O] (forced set-level structure sum=128=spinor/product=|W|/exponents=totatives; subchain flagged; per-degree matches declined; no new physical hit; reconciles v66+v354)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the reverse audit (3/8 mapped, 5/8 unmapped), the economy signature (small fixed invariant set -> all readouts), and phi-as-unmapped-structure (so not numerology); [O] the honest reading of the unmapped remainder as hull overhead. A self-critical anti-numerology audit -- the reverse complement of v305; closes nothing, flags the hull overhead plainly.","checked_by_registry":false,"claim_excerpt":"THE REVERSE NUMEROLOGY AUDIT + WHAT THE GOLDEN RATIO MEANS (2026-06-22). TFPT's forward discipline (v305) is one-directional: every physical READOUT must map onto an E8 structure (anti-fitting). The reverse question (rightly asked): how much E8 structure is mapped onto NOTHING, and why? -- and is the recurring golden ratio numerology? [E] THE REVERSE AUDIT: E8 has 8 Casimir invariant degrees {2,8,12,14,18,20,24,30} (","claim_id":"E8.REVERSE.AUDIT.01","dependencies_as_recorded":"WITNESS.INDEP.01; v305; v100; v312; v348; v54","external_data_as_recorded":"-","id":"claim:E8.REVERSE.AUDIT.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":96,"scripts_as_recorded":"v354_e8_reverse_audit.py","status_as_recorded":"Reverse anti-numerology audit [E]/[O] (3/8 Casimir invariants mapped, 5/8 hull overhead; economy not promiscuity; phi is unmapped structure not numerology)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the deck=degree-2 (matched) and two-sheets=128-spinor (matched, =sum(deg)) identities, and the forced-disjointness {2,16,32,128} cap {12,14,18,20,24}=empty; [O] the disciplined decline (no forced sheet->unmapped identity, v355 discriminator) and the honest residual (the 128 phase/glue dark-sector question concerns matched structure). The sheet/deck complement of v354/v355; closes nothing, records the structural negative.","checked_by_registry":false,"claim_excerpt":"THE 'OTHER SIDE OF THE SEAM' AUDITED AGAINST THE UNMAPPED E8 STRUCTURE (2026-06-27, v430): the sheet/deck complement of the reverse audit v354/v355. The reverse audit found FIVE Casimir degrees {12,14,18,20,24} with no primary readout ('hull overhead'); the double cover has an 'other side' (the one-sided Z2 collar / conjugate half-spinor S^-). Does that other side correlate with the unmapped E8 structure -- is the le","claim_id":"E8.OTHERSIDE.AUDIT.01","dependencies_as_recorded":"E8.REVERSE.AUDIT.01; E8.UNMAPPED.BANDWIDTH.01; E8.CHAN.01; E8.CAS.01; v58; v109","external_data_as_recorded":"-","id":"claim:E8.OTHERSIDE.AUDIT.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":97,"scripts_as_recorded":"v430_other_side_reverse_audit.py","status_as_recorded":"Sheet/deck reverse audit [E]/[O] (the double-cover 'other side' = degree-2 + the 128-spinor, forced-disjoint from the 5 unmapped degrees; the complement of v354/v355)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E]/[I] the forced two-family decomposition (the {0,2}-mod-6 split from h=30=2*3*5, 6k=6*spine, 6k+2={2} U det-ladder) and the '18'=6*N_fam + E8-specialness facts; [P] the functorial flavor-sheet identification (rep-theoretic map open, 12/24 multiplicity). Reclassifies the v354/v355 overhead to zero orphan degrees; closes nothing.","checked_by_registry":false,"claim_excerpt":"THE REVERSE-AUDIT 'UNMAPPED' E8 CASIMIR DEGREES ARE THE FORCED TWO-FAMILY DECOMPOSITION (2026-06-27, v431): the structural complement of v354/v355/v430. The reverse audit found FIVE 'unmapped' degrees {12,14,18,20,24} ('hull overhead'); this module shows they are NOT diffuse overhead but the forced two-family decomposition deg(E8) = 6*spine{2,3,4,5} U ({2} U flavor-det-ladder{8,14,20}). [E] TWO-FAMILY SPLIT FORCED BY","claim_id":"E8.DEGREE.LADDER.01","dependencies_as_recorded":"E8.REVERSE.AUDIT.01; E8.UNMAPPED.BANDWIDTH.01; E8.OTHERSIDE.AUDIT.01; E8.CAS.01; v91; v135","external_data_as_recorded":"-","id":"claim:E8.DEGREE.LADDER.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":98,"scripts_as_recorded":"v431_e8_degree_ladder.py","status_as_recorded":"E8 degree-ladder structure theorem [E]/[I] + [P] functorial residual (degrees = 6*spine U det-ladder, forced by 2,3,5; reclassifies v354/v355 overhead)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the joint quadratic lock (both structural integers as the unique roots of one degree-invariant quadratic) and the 'E8 fixed by its degrees' reconstruction; a consolidation of v6/v66/v355/v431 that respects the v354/v355 anti-numerology discipline (no new per-degree coincidence). Closes no gate; strengthens the over-determination of g_car and N_fam.","checked_by_registry":false,"claim_excerpt":"THE TWO STRUCTURAL INTEGERS ARE JOINTLY FORCED BY E8 DEGREE-INVARIANTS, AND E8 IS FIXED BY ITS DEGREES (2026-06-29, v437): a CONSOLIDATION of v6/v66/v355/v431 deriving more from the E8 Casimir degrees WITHOUT crossing the v354/v355 anti-numerology line -- no new per-degree coincidence, only a joint lock. [E] E8 IS FIXED BY ITS DEGREE MULTISET: from deg(E8)={2,8,12,14,18,20,24,30} alone -- rank=#degrees=8 (=2nd degree","claim_id":"E8.DEGREE.JOINT.01","dependencies_as_recorded":"E8.REVERSE.AUDIT.01; E8.DEGREE.LADDER.01; v6; v66; v355; v431","external_data_as_recorded":"-","id":"claim:E8.DEGREE.JOINT.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":99,"scripts_as_recorded":"v437_e8_degree_joint.py","status_as_recorded":"E8 degree joint-lock [E] (the two structural integers g_car=5, N_fam=3 = unique roots of x^2-8x+15 with coeffs rank E8=8 and h/2=15; all E8 combinatorics fixed by its degrees; consolidation of v6/v66/v355/v431, no new mining)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the disjoint-pieces accounting (the '8' forced 4 ways + the foreign alpha) and the floor<->ceiling bridge inequality (floor ~1e-10 >> v100 conditional 1e-30.7); [C] the conservative floor value and the bounded scope (numerology only, not the physics bridge). The unconditional complement to v100; closes nothing.","checked_by_registry":false,"claim_excerpt":"THE UNCONDITIONAL IMPROBABILITY FLOOR + THE L1<->L2 BRIDGE (2026-06-27, v432): the defensible over-determination number that survives even if a skeptic REJECTS the declared formula grammar -- the complement of the conditional null model (v100) and the multiply-vs-compress framework (v427/v428). [E] DISJOINT MULTIPLICATIVE PIECES (per v428): compression removed (v427's seven readouts are ONE (2,3,5)/E8 object, not mul","claim_id":"OVERDET.FLOOR.01","dependencies_as_recorded":"OVERDET.WITNESS.MAP.01; OVERDET.WITNESS.RECLASS.01; v100; v305; ALPHA.QUILLEN.EXACT.01; v187","external_data_as_recorded":"-","id":"claim:OVERDET.FLOOR.01","location_as_recorded":"tfpt_safeguards","path":"verification/status_ledger.csv","row_number":100,"scripts_as_recorded":"v432_overdet_floor.py","status_as_recorded":"Unconditional over-determination floor [C] (disjoint pieces only, compression removed; floor ~1e-10 vs v100 conditional 10^-30.7; bounds numerology only, firewall)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the pure-counting census floor (4.40 sigma), the monotone concession ladder, and independence from v432's subjective pieces; [C] the honest 5-sigma gap (one further independent factor <=0.054) and the bounded scope (numerology only, not the physics bridge). Hardens OVERDET.FLOOR.01 (v432) -- replaces its contestable subjective assignments with an assumption-minimal counting floor; closes nothing.","checked_by_registry":false,"claim_excerpt":"HARDENING THE UNCONDITIONAL FLOOR -- THE ASSUMPTION-MINIMAL COUNTING FLOOR (2026-06-29, v436): OVERDET.FLOOR.01 (v432) multiplies the counting census by SUBJECTIVE chance assignments (input-'8' independence 0.1^3, seed 0.012, kaon 0.15) a skeptic can contest; this module shows the 'is it numerology?' verdict does NOT rest on them. [E] ASSUMPTION-MINIMAL FLOOR: the alpha cubic-class census (v100 layer D) is PURE COUNT","claim_id":"OVERDET.FLOOR.02","dependencies_as_recorded":"OVERDET.FLOOR.01; v100; v305; ALPHA.QUILLEN.EXACT.01; v187","external_data_as_recorded":"-","id":"claim:OVERDET.FLOOR.02","location_as_recorded":"tfpt_safeguards","path":"verification/status_ledger.csv","row_number":101,"scripts_as_recorded":"v436_overdet_floor2.py","status_as_recorded":"Assumption-minimal counting floor [E]/[C] (the alpha census 1/94500 = 4.40 sigma with no subjective probability; monotone concession ladder; independent of v432's subjective pieces; honest 5-sigma gap; hardens OVERDET.FLOOR.01)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the loop closure (outputs fix inputs), zero free dials, and pi-as-geometry are machine facts; [A] the refinement of v352's framing (loop, not framework+pi); [O] the continuum closure + the honest philosophical fork. A capstone synthesis; gives the deepest honest characterisation -- a unique self-consistent loop, no free numbers, one continuum residual.","checked_by_registry":false,"claim_excerpt":"THE BIRD'S-EYE RETHINK (2026-06-22, refining TFPT.IRREDUCIBLE.01/v352). Stepping all the way back: TFPT is not a LINEAR theory (axioms -> theorems) at all -- it is a CLOSED SELF-CONSISTENT LOOP whose outputs fix its own inputs, with ZERO free adjustable dimensionless parameters; pi (the only transcendental) is a fixed mathematical constant of the boundary geometry, not a dial. [E] IT IS A LOOP, NOT A LINEAR FOUNDATIO","claim_id":"TFPT.SELFLOOP.01","dependencies_as_recorded":"TFPT.IRREDUCIBLE.01; v6; v56; v54; v336; v351","external_data_as_recorded":"-","id":"claim:TFPT.SELFLOOP.01","location_as_recorded":"introduction","path":"verification/status_ledger.csv","row_number":102,"scripts_as_recorded":"v353_selfloop_capstone.py","status_as_recorded":"Capstone rethink [E]/[A]/[O] (a unique self-consistent loop with zero free dials; pi a fixed geometric constant; the one residual is the continuum closure; the fork is philosophical not numerical)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] both axioms forced (the over-determination counts: g_car three ways, the 8 four ways) + the irreducible inventory {framework, pi}; [O] the framework is the meta-axiom (tested by consequences, not proved). A synthesis confirming 'the inputs are not free axioms' at the deepest level and locating the single irreducible stance.","checked_by_registry":false,"claim_excerpt":"THE FRAMEWORK REDUCTION (2026-06-22) -- the deepest honest answer to 'the inputs are not axioms, they are back-determined by the theory'. BOTH P1 (c3=1/(8pi)) and P2 (g_car=5) are bootstrap-forced fixed points, not free postulates; the only genuine irreducibles are the FRAMEWORK (a discrete reflection-positive boundary with a finite carrier) and the transcendental pi. [E] P2 (g_car=5) IS FORCED three ways (v6): rank-","claim_id":"TFPT.IRREDUCIBLE.01","dependencies_as_recorded":"v6; v54; v83; v154; v216; v342; ANCHOR.VGEO.02","external_data_as_recorded":"-","id":"claim:TFPT.IRREDUCIBLE.01","location_as_recorded":"introduction","path":"verification/status_ledger.csv","row_number":103,"scripts_as_recorded":"v352_framework_irreducible.py","status_as_recorded":"Synthesis/inventory [E]/[O] (both axioms bootstrap-forced; irreducibles = framework + pi; the framework is the tested meta-axiom)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Correction [E]/[O] (inputs bootstrap-forced; g_car=5 icosahedral; golden emergent; residual = continuum realisation)","checked_by_registry":false,"claim_excerpt":"THE HONEST CORRECTION OF v349's FRAMING (prompted by the right objection 'the inputs are not axioms -- they are back-determined by the theory', 2026-06-22). v349 concluded 'the raw seam does not carry the golden ratio (D5 has h=8 -> sqrt2)' and reduced the keystone to 'is g_car=5 a pentagon or a count?'. That framing was WRONG on two counts; this corrects it while keeping v349's true computations. [E] THE INPUTS ARE ","claim_id":"SEAM.EQUIV.BOOTSTRAP.01","dependencies_as_recorded":"SEAM.EQUIV.GOLDEN.01; v6; v154; v56; v336; v274","external_data_as_recorded":"-","id":"claim:SEAM.EQUIV.BOOTSTRAP.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":104,"scripts_as_recorded":"v350_bootstrap_inputs_correction.py","status_as_recorded":"Correction [E]/[O] (inputs are bootstrap-forced fixed points; g_car=5 IS the icosahedral 5 of h(E8)=30; golden emergent from the mu4-glue; residual = the physical continuum realisation)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the computed negative (D5/A3 give sqrt2; dynamical data not golden; 5|h only on the output side; 2I != C5 x mu4); [O] the resolution that L2 = 'is g_car=5 a pentagon or a count?', an axiom-reading not a hidden derivation. A NEGATIVE/clarification module; closes nothing and prevents a false closure -- the golden ratio is the icosahedral input, not a hidden feature of the raw seam.","checked_by_registry":false,"claim_excerpt":"THE HONEST TEST OF 'DOES THE RAW SEAM CARRY THE GOLDEN RATIO?' (the v348 question, 2026-06-22) -- answer, computed and honest: NO. The bare carrier (D5, A3) and the dynamical seam data are NOT golden; the golden ratio genuinely enters WITH the icosahedral/E8 identification. A NEGATIVE result, but clarifying: it prevents a false closure and reduces the whole keystone to one almost childlike question. [E] RAW CARRIER N","claim_id":"SEAM.EQUIV.GOLDEN.01","dependencies_as_recorded":"SEAM.EQUIV.RIGID.01; SEAM.EQUIV.CLOSURE.01; v312; v313; v219; v246","external_data_as_recorded":"-","id":"claim:SEAM.EQUIV.GOLDEN.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":105,"scripts_as_recorded":"v349_raw_seam_golden_test.py","status_as_recorded":"Honest negative/clarification [E]/[O] (the raw seam does NOT carry phi; golden is the icosahedral input; L2 = 'is g_car=5 a pentagon or a count?')","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the rigidity reductions (Nielsen/Troyanov close the crystallographic mu4/pillowcase part), the icosian-ring lattice identity (E8 = icosians), the crystallographic role of phi (the 5-fold is non-crystallographic, phi bridges); [O] the single reduced arrow ('the raw seam carries the golden ratio'), with the honest flag that TFPT's phi is currently E8-side (potential circularity). Route B; closes nothing, reduces the keystone to one question.","checked_by_registry":false,"claim_excerpt":"ROUTE B (THE RIGIDITY ROUTE) FOR THE ONE OPEN ARROW L2, CARRIED OUT (2026-06-22) -- it lands on a strikingly SIMPLE statement: the whole keystone reduces to ONE question, does the raw seam carry the golden ratio? [E] RIGIDITY CLOSES THE CRYSTALLOGRAPHIC PART: the order-4 clock on a genus-0 surface has a UNIQUE conformal normal form z -> i z (Nielsen realisation theorem / Kerckhoff + uniformisation, v180); Troyanov's ","claim_id":"SEAM.EQUIV.RIGID.01","dependencies_as_recorded":"SEAM.EQUIV.CLOSURE.01; v180; v284; v219; v312; v313","external_data_as_recorded":"Nielsen realisation (Kerckhoff); Troyanov; Conway-Sloane (the icosian ring = E8)","id":"claim:SEAM.EQUIV.RIGID.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":106,"scripts_as_recorded":"v348_seam_rigidity_route.py","status_as_recorded":"Route B / reduction [E]/[O] (rigidity + the icosian-ring identity reduce L2 to one question: does the raw seam carry the golden ratio?; NOT closed)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the orbifold-Euler-characteristic locus (flat seam base vs spherical icosahedral base) + the closure-mode enumeration + the no-new-state blocking; [O] L2 itself. An analysis/roadmap; closes nothing, fabricates nothing -- it answers 'are there other ways to fully solve it' by enumerating all four modes and the honest verdict (only rigidity B as a theorem, else axiom P3).","checked_by_registry":false,"claim_excerpt":"THE CLOSURE-MODE CLASSIFICATION OF THE ONE OPEN ARROW L2 (the seam-orbifold realisation, v346) -- a direct honest answer to 'is there ANY other way to FULLY solve it?' (2026-06-22). [E] THE PRECISE LOCUS OF L2: the seam DIRECTLY gives (from the mu4 clock + four marks) the pillowcase base S^2(2,2,2,2), a EUCLIDEAN orbifold chi_orb = 2 - 4(1-1/2) = 0 (flat, v216/v325); but the 2I/E8 structure is the Seifert fibration o","claim_id":"SEAM.EQUIV.CLOSURE.01","dependencies_as_recorded":"SEAM.EQUIV.GEOM.01; v216; v284; v300; v331; v246; v336","external_data_as_recorded":"-","id":"claim:SEAM.EQUIV.CLOSURE.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":107,"scripts_as_recorded":"v347_seam_closure_modes.py","status_as_recorded":"Analysis/roadmap [E]/[O] (the flat->spherical base locus; four closure modes; no free theorem; only rigidity B or axiom P3; NOT closed)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the chain bookkeeping (5 of 6 links are theorems) + the (2,3,5)->2I axis selection among exceptional SU(2) subgroups; [O] the single orbifold-realisation arrow L2 (= SEAM.EQUIV.01). A capstone/roadmap; closes nothing, fabricates nothing -- it reduces the keystone to one geometric-realisation statement with the group pinned by the seam's own (2,3,5) atoms.","checked_by_registry":false,"claim_excerpt":"THE GEOMETRIC BRIDGE AS AN EXPLICIT SIX-LINK CHAIN, WITH THE ONE OPEN ARROW PINNED (2026-06-22) -- the honest capstone of the SEAM.EQUIV.01 investigation (v335/v336/v344/v345). The chain raw-seam => det K=1: L1 [E/C] raw seam -> mu4 clock + four marks (Gauss-Bonnet on the flat pillowcase S^2(2,2,2,2), v216); L2 [O] mu4 + the carrier (2,3,5) atoms -> the binary icosahedral 2I action C^2/Gamma -- THE ONE OPEN ARROW, th","claim_id":"SEAM.EQUIV.GEOM.01","dependencies_as_recorded":"SEAM.EQUIV.UNIFY.01; SEAM.DETK.02; v216; v219; v232; v345; v313","external_data_as_recorded":"McKay correspondence; Brieskorn/Slodowy du Val resolution","id":"claim:SEAM.EQUIV.GEOM.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":108,"scripts_as_recorded":"v346_seam_geometric_bridge.py","status_as_recorded":"Capstone/roadmap [E]/[O] (5 of 6 links theorems; the group forced by the icosahedral atoms; the keystone reduced to the single orbifold-realisation arrow L2 = SEAM.EQUIV.01)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the SNF/cokernel computation (= H_1 of the plumbing link), the ADE contrast, and the explicit perfectness of 2I=SL(2,5) (commutator subgroup = whole group); [O] the geometric realisation bridge (= SEAM.EQUIV.01). Executes R3's combinatorial core; closes nothing.","checked_by_registry":false,"claim_excerpt":"EXECUTING THE COMBINATORIAL CORE OF ROUTE R3 (the hypergraph-homotopy route to det K=1, v344) -- the most promising fresh angle, now carried out as far as it computably goes (2026-06-22). Computes explicitly the topology of the (2,3,5)-rewrite attractor graph's plumbing link: it is the POINCARE homology sphere (H_1=0, the det K=1 face), only E8 among ADE. R3's combinatorial half is thereby [E]-complete; the one remai","claim_id":"SEAM.DETK.02","dependencies_as_recorded":"SEAM.DETK.01; SEAM.EQUIV.UNIFY.01; v232; v312; v344; v55; v219","external_data_as_recorded":"Brieskorn/Hirzebruch plumbing topology (link H_1 = coker intersection form)","id":"claim:SEAM.DETK.02","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":109,"scripts_as_recorded":"v345_hypergraph_homotopy.py","status_as_recorded":"Execution of R3 [E]/[O] (combinatorial core complete: homology-sphere link via SNF + 2I perfect = Poincare sphere; geometric bridge stays SEAM.EQUIV.01)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the six-faces equivalence (|det Cartan|=|H_1| ADE arithmetic, computed) + the genus-1 obstruction + the three-route map; [C] the hypergraph route's alignment (attractor=E8 graph v312 + E8 link=Poincare sphere v232); [O] the unclosed combinatorial-to-geometric bridge (= SEAM.EQUIV.01). A synthesis/roadmap; closes nothing, fabricates nothing.","checked_by_registry":false,"claim_excerpt":"THE BIRD'S-EYE SYNTHESIS OF THE ONE OPEN KEYSTONE BIT det K=1 (2026-06-22): a full-spectrum map of SEAM.EQUIV.01's only open residual -- it is ONE statement with six equivalent faces; it is hard for ONE precise reason (the genus-1 obstruction); and there are exactly three genus-1 access routes, of which the hypergraph-homotopy route is the most promising fresh angle. [E] SIX FACES: det K=1 <=> holomorphy (1 primary) ","claim_id":"SEAM.DETK.01","dependencies_as_recorded":"SEAM.EQUIV.UNIFY.01; v232; v235; v219; v281; v282; v312; v336; v87","external_data_as_recorded":"-","id":"claim:SEAM.DETK.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":110,"scripts_as_recorded":"v344_detk_synthesis.py","status_as_recorded":"Synthesis/roadmap [E]/[C]/[O] (one bit/six faces; genus-1 obstruction; three access routes; hypergraph the fresh one; no closure)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the finiteness facts (A), the modular/attractor theorems (C/D), the convergence count; [C] the Cardy consistency (B); [O]/[P] the inherited residuals. An analysis module; closes nothing, fabricates nothing -- it shows all four BH-birth routes converge on the same single keystone + the decoupled QG contour (= v335).","checked_by_registry":false,"claim_excerpt":"THE FOUR BLACK-HOLE-BIRTH SOLUTION ROUTES INVESTIGATED (2026-06-22): direct answer to 'which closes ALL problems and is 100% provable' -- NONE individually; they CONVERGE on the same two irreducible residuals as v335 (SEAM.EQUIV.01 + the decoupled QG contour), reached now from the cosmological side. [E] ROUTE A (finite causal diamond) REFRAMES QG.AMB to a FINITE thermal trace: in a horizon-bounded static patch the ob","claim_id":"FOUR.ROUTES.01","dependencies_as_recorded":"SEAM.EQUIV.UNIFY.01; QG.AMB.01; v54; v190; v332; v334; v337; v239; v56","external_data_as_recorded":"Carlip (near-horizon Virasoro); Gibbons-Hawking (de Sitter entropy); Tomita-Takesaki","id":"claim:FOUR.ROUTES.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":111,"scripts_as_recorded":"v343_four_routes_analysis.py","status_as_recorded":"Analysis/roadmap [E]/[C]/[O] (none closes all or is 100% provable; all four converge on SEAM.EQUIV.01 + the decoupled QG contour)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the heat-kernel STRUCTURE (c3 = Gauss-Bonnet boundary coefficient; alpha^2 = Gilkey gauge-curvature a4 term; c3-ladder; multiplicities; pi-power); [C] the exact coefficient (seam F-normalisation); [O] the cubic Maxwell moment + the full determinant identification (= EM.WARD.01, tied to SEAM.EQUIV.01). Sharpens EM.WARD.01's origin from [P] toward [E]; no new gate.","checked_by_registry":false,"claim_excerpt":"HEAT-KERNEL SHARPENING OF EM.WARD.01 (2026-06-22): derives the ORIGIN and STRUCTURE of the F_U(1) determinant-line terms from textbook Seeley-DeWitt/Gilkey heat-kernel coefficients, advancing the EM-Ward origin from [P] (conjectured) to [E] for the term STRUCTURE; honestly fences the rest. NO new gate (sharpens EM.WARD.01). [E] c3 = 1/(8 pi) is the boundary GAUSS-BONNET heat-kernel coefficient: the seam is the flat p","claim_id":"EM.WARD.02","dependencies_as_recorded":"EM.WARD.01; v48; v216; v3; v159","external_data_as_recorded":"Gilkey, Invariance Theory and the Heat Equation, Thm 4.8.16","id":"claim:EM.WARD.02","location_as_recorded":"tfpt_1_architecture_e8","path":"verification/status_ledger.csv","row_number":112,"scripts_as_recorded":"v342_em_ward_heatkernel.py","status_as_recorded":"Heat-kernel origin [E]/[C]/[O] (term structure [E]; exact value [C]; cubic moment + identification [O]; no new gate)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]","checked_by_registry":false,"claim_excerpt":"Grand Mass Volume = the absolute mass-scaling normalisation [I] (NOT a [P] product rule): the individual c_q are a gauge, but the sector mass-matrix determinants are clean phi0-powers = K-row sums: det M_up~phi0^(4+2+0)=phi0^6=phi0^|R+(A3)|, det M_down~phi0^9=phi0^N_fam^2, det M_lep~phi0^10=phi0^A_Lambda; Grand Mass Volume det M_SM~phi0^(6+9+10)=phi0^25=phi0^g_car^2=phi0^Delta_Y. Q-row sums (4,5,6)=(|mu4|,g_car,|R+A3","claim_id":"FLAV.MASSVOL.01","dependencies_as_recorded":"FLAV.KQ.01; FLAV.QRATIO.01","external_data_as_recorded":"-","id":"claim:FLAV.MASSVOL.01","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":113,"scripts_as_recorded":"v46_grand_mass_volume.py","status_as_recorded":"Identity [I]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/Lattice [I]/[L]","checked_by_registry":false,"claim_excerpt":"the '11' is PASCAL (third, simplest origin; no special math): Pl(K) is the exterior algebra of the family fundamental 4=mu4 (A3=SU(4) fundamental). Lambda^k(4)=C(4,k)=Pascal row 4=(1,4,6,4,1), full sum 2^4=16=dim S+. |Pl(K)|=(1,4,6)={Lambda^0,Lambda^1,Lambda^2}(4) (distinct exterior powers). ||Pl(K)||_1=11=sum_{k<=2}C(4,k)=cumulative ext of mu4 up to degree 2=deg(u^c) (v44) = 2^4-C(4,3)-C(4,4)=16-g_car. family(x)carr","claim_id":"GATE.UWALL.18","dependencies_as_recorded":"GATE.UWALL.17; v37; v42; v44","external_data_as_recorded":"-","id":"claim:GATE.UWALL.18","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":114,"scripts_as_recorded":"v45_family_exterior.py","status_as_recorded":"Identity/Lattice [I]/[L]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Lattice/Lie [L] (typing) + [P] (normalisation)","checked_by_registry":false,"claim_excerpt":"LIE-LEVEL GROUNDING of the exterior leg (no special math): the carrier half-spinor is the even exterior algebra 16=Lambda^even(5)=C(5,0)+C(5,2)+C(5,4)=1+10+5 (already in CAR.SM.01). Under SU(5)<SO(10): u^c in 10=Lambda^2(5), d^c in 5bar=Lambda^4(5) => exterior degrees deg(u)=2, deg(d)=4; deg(u)+deg(d)=6=|R+(A3)| (hexagon), deg(d)-deg(u)=2=|Z2| (sheet); up Yukawa family-symmetric Sym^2 dim6, down general dim9=N_fam^2.","claim_id":"GATE.UWALL.17","dependencies_as_recorded":"GATE.UWALL.15; CAR.SM.01; SU(5)<SO(10)","external_data_as_recorded":"standard GUT rep theory","id":"claim:GATE.UWALL.17","location_as_recorded":"tfpt_research_contracts;tfpt_2","path":"verification/status_ledger.csv","row_number":115,"scripts_as_recorded":"v44_carrier_exterior.py","status_as_recorded":"Lattice/Lie [L] (typing) + [P] (normalisation)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical (typing confirmed + honest negative)","checked_by_registry":false,"claim_excerpt":"Lambda^2 F bridge test (honest): (1) POSITIVE - for SU(3) the exterior square is the conjugate rep, Lambda^2(M~)=conj(M~) exactly => the exterior leg IS the 3-bar (confirms the Exterior Leg typing); (2) anchor bivector 1^a=(0,1,1), Pl(K)=(-1,6,4) is its image under the 2nd compound of K^T (integer, combinatorial); (3) HONEST NEGATIVE - continuous Lambda^2(M~).(1^a) (moduli ~0.93,0.75,0.75) != integer Pl(K) nor its di","claim_id":"GATE.UWALL.16","dependencies_as_recorded":"GATE.UWALL.15; v39; v40","external_data_as_recorded":"-","id":"claim:GATE.UWALL.16","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":116,"scripts_as_recorded":"v43_exterior_bridge.py","status_as_recorded":"Numerical (typing confirmed + honest negative)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]","checked_by_registry":false,"claim_excerpt":"delta=1/2 glue-norm origin + (g_car,N_fam)/|mu4| unification: the two E8-glue discriminant norms ARE the carrier rank and family count over the glue index, q(D5)=g_car/|mu4|=5/4 (rank D5=g_car=5), q(A3)=N_fam/|mu4|=3/4 (rank A3=N_fam=3, n+1=4=|mu4|). Then all FOUR arithmetic ops are forced compiler atoms: sum=(g+n)/|mu4|=rank(E8)/|mu4|=2 (E8 root norm), diff=(g-n)/|mu4|=|Z2|/|mu4|=1/2=delta (lepton transport, used in","claim_id":"FLAV.DELTA.01","dependencies_as_recorded":"BND.GLUE.01; v20; v41","external_data_as_recorded":"-","id":"claim:FLAV.DELTA.01","location_as_recorded":"tfpt_1;tfpt_2","path":"verification/status_ledger.csv","row_number":117,"scripts_as_recorded":"v51_boundary_half_step.py","status_as_recorded":"Identity [I]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]","checked_by_registry":false,"claim_excerpt":"K+xQ pencil endpoints (audit ext. of v37): P(x)=det(K+xQ)=3x^3+7x^2+6x+4 anchored at four integer nodes by compiler atoms: P(-1)=2=|Z2| (K-Q sheet endpoint), P(0)=4=det K=|mu4|, P(1)=20=det L (transport), P(2)=68=2 p5(a) (twice anchor power sum p5=34). Also det(K-Q)=2=|Z2|, trace(K-Q)=3=N_fam. Audit-level detail of the mass->transport pencil, not a new gate [I]","claim_id":"FLAV.KQ.02","dependencies_as_recorded":"FLAV.KQ.01; v37","external_data_as_recorded":"-","id":"claim:FLAV.KQ.02","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":118,"scripts_as_recorded":"v52_pencil_endpoints.py","status_as_recorded":"Identity [I]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/Lie [I]/[L]","checked_by_registry":false,"claim_excerpt":"Integer-lift of Q - residual sharpened to ONE named lattice invariant det Q=N_fam (honest reduction, not closure) [I]/[L]. Continuing v69: (1) DERIVED - in the mu4-puncture homology basis {g1,g2,g3} (g4=-(g1+g2+g3)) the Z4=mu4 rotation is the integer matrix R=[[0,0,-1],[1,0,-1],[0,1,-1]], char (t+1)(t^2+1), eigenvalues {-1,i,-i}, R^4=I, R UNIMODULAR (det=-1, SNF=I). (2) the documented transport Q (rows (4,5,6)=(|mu4|","claim_id":"GATE.QGEOM.02","dependencies_as_recorded":"GATE.QGEOM.01; v69; v50","external_data_as_recorded":"-","id":"claim:GATE.QGEOM.02","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":119,"scripts_as_recorded":"v70_q_integer_lift.py","status_as_recorded":"Identity/Lie [I]/[L]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Lie/lattice [L]","checked_by_registry":false,"claim_excerpt":"D4-equivariant derivation of the Q-geometry (Alessandro residual gate #2) - advances Theorem Q from [P] (algebraically forced) to [L] (geometrically derived). The 4 punctures mu4={1,i,-1,-i} are square vertices with symmetry D4=Z4 semidirect Z2 (the 90-deg rotation z->iz IS mu4; the reflection is the sheet parity Sigma). (1) the Z4 4-cycle on the punctures acts on H_1(P^1\\\\mu4)=Z^4/(sum=0)=Z^3 (3 families) with eigen","claim_id":"GATE.QGEOM.01","dependencies_as_recorded":"QGEOM (was GATE); v50; v61; Theorem Q","external_data_as_recorded":"D4 representation theory; standard","id":"claim:GATE.QGEOM.01","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":120,"scripts_as_recorded":"v69_d4_q_geometry.py","status_as_recorded":"Lie/lattice [L]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/Lie [I]/[L] + anchor identification","checked_by_registry":false,"claim_excerpt":"Central-theorem RESIDUAL RESOLVED (honestly) as an anchor, not a gap [I-symbolic + L]. The Seeley-DeWitt coefficient for the carrier Dirac operator is a2 = (1/(4pi)^2)(1/6)(R d + 6E d) with E=-R/4 (Lichnerowicz) = -d/(192 pi^2) R, d=carrier dof (16=dim S+ or 32=2^g_car). The induced Einstein-Hilbert coefficient is 1/(16 pi G)=f2 Lambda^2 d/(192 pi^2) - UV-SENSITIVE (depends on the seam cutoff Lambda and the cutoff mo","claim_id":"SEAM.AREACOEFF.02","dependencies_as_recorded":"SEAM.AREACOEFF.01; v36; v67","external_data_as_recorded":"Sakharov 1967; Susskind-Uglum 1994; Chamseddine-Connes spectral action","id":"claim:SEAM.AREACOEFF.02","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":121,"scripts_as_recorded":"v68_seeley_dewitt_residual.py","status_as_recorded":"Identity/Lie [I]/[L] + anchor identification","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/Lie [I]/[L] (structure) + [A] (residual k=c3/2)","checked_by_registry":false,"claim_excerpt":"Central theorem (1/(8pi) area-law coefficient) - STRUCTURAL CLOSURE + reduction to ONE sharp coefficient (honest partial solution of Alessandro's central target). CLOSED [I]/[L]: by the Fursaev-Solodukhin (1995) conical/replica method, the curvature term W_R=k*Int(sqrt(g)R) gives horizon entropy S=4pi k A (conical defect: Int R ⊃ 4pi(1-n)A; S=-d/dn[W_n-n W_1]|_1). With the Einstein-Hilbert coefficient at the seam uni","claim_id":"SEAM.AREACOEFF.01","dependencies_as_recorded":"SEAM.THEOREM.01; SEAM.AREALAW.01; v36; v59","external_data_as_recorded":"Fursaev-Solodukhin 1995; Susskind-Uglum 1994; Callan-Wilczek 1994","id":"claim:SEAM.AREACOEFF.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":122,"scripts_as_recorded":"v67_area_law_coefficient.py","status_as_recorded":"Identity/Lie [I]/[L] (structure) + [A] (residual k=c3/2)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Lie/lattice [L] + identity [I]","checked_by_registry":false,"claim_excerpt":"Organizing simplification: the compiler atoms ARE the E8 fundamental Casimir invariant degrees deg(E8)={2,8,12,14,18,20,24,30} (exponents+1) [L]. CLEAN/non-trivial readings: 2=|Z2|, 8=rank E8, 14=dim G2 (the [K,Q] commutator G2, v37), 20=det L (v10), 24=|W(A3)|=4! (Weyl group A3=S4), 30=h(E8)=2*3*5. Weaker/fittable (flagged): 12=|R(A3)| (A3 roots), 18=p4(a)=2+2^4 (anchor power sum). EXACT sum identities: sum(degrees)","claim_id":"ARCH.E8DEG.01","dependencies_as_recorded":"v37; v10; v55; v56; h(E8)=30","external_data_as_recorded":"E8 invariant degrees (standard Lie theory)","id":"claim:ARCH.E8DEG.01","location_as_recorded":"tfpt_3","path":"verification/status_ledger.csv","row_number":123,"scripts_as_recorded":"v66_e8_casimir_degrees.py","status_as_recorded":"Lie/lattice [L] + identity [I]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical/data [N]","checked_by_registry":false,"claim_excerpt":"Prediction/falsification layer with EXPLICIT failure thresholds (Alessandro residual gate #6) [N], data-confrontation Python-only. Each prediction carries an explicit falsification threshold and a layer tag. CORE falsifiers (break [I]/[L]): v_GW=c (FAIL if robust v_GW!=c >5sigma; GW170817 gives |v_GW/c-1|<1e-15), no 4th chiral generation (FAIL on discovery; N_fam=3=rank A3=dim H1), seam denominator=8 (FAIL if c3!=1/(","claim_id":"PRED.LAYER.01","dependencies_as_recorded":"v62; v64; v3; v8; v60","external_data_as_recorded":"GW170817; ACT DR6; NuFIT 6.0; Planck-ACT-DESI","id":"claim:PRED.LAYER.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":124,"scripts_as_recorded":"v65_falsification_layer.py","status_as_recorded":"Numerical/data [N]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I] core + [P] argument","checked_by_registry":false,"claim_excerpt":"Causal Boundary Engineering - CONDITIONAL NO-GO for traversable seam shortcuts/CTCs (proof attempt that turned into a no-go). CORE [I] (machine-checked, v56-bound): a gapped positive transfer operator (spectrum {1,(2/3)^6,(1/3)^6}) has NO periodic orbit (T^n != I for all n>0; subdominant moduli <1 => T^n -> rank-1 projector) = discrete analog of no closed timelike curve. CHAIN [P] (cites standard theorems, not formal","claim_id":"CAUSAL.NOGO.01","dependencies_as_recorded":"GATE.GMETRIC.XI.01; v56; SEAM.CYCLE.01","external_data_as_recorded":"Friedman-Schleich-Witt 1993; Gao-Jafferis-Wall 2017; Faulkner et al. 2016","id":"claim:CAUSAL.NOGO.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":125,"scripts_as_recorded":"v64_causal_boundary_nogo.py","status_as_recorded":"Identity [I] core + [P] argument","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I] + taxonomy [A]","checked_by_registry":false,"claim_excerpt":"Seam-Engineering Index - an exact closed form for the IR-stability margin [I], plus the four-class possibility taxonomy [I]/[A]. Validates+sharpens the boundary-engineering synthesis: the documented G_metric bound ||V_metric||_rel <= 248 c3^2 = 31/(8 pi^2) (248=dim E8, 31=248/8=1+h^v(E8) = the WZW denominator c(E8)=248/31, v61) gives 2||V||=31/(4 pi^2)=0.78524 (NOT pi/4=0.78540, a 4th-digit coincidence). Hence Xi=2||","claim_id":"GATE.GMETRIC.XI.01","dependencies_as_recorded":"GATE.GMETRIC.*; v36; v54; v61","external_data_as_recorded":"-","id":"claim:GATE.GMETRIC.XI.01","location_as_recorded":"origin_theory;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":126,"scripts_as_recorded":"v63_seam_engineering_index.py","status_as_recorded":"Identity [I] + taxonomy [A]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical/data [N]","checked_by_registry":false,"claim_excerpt":"Confrontation of TFPT predictions with current research data (2024/25) - honest scorecard incl. tensions [N], data-confrontation (Python-only, external data). STRONG MATCHES: alpha^-1=137.0359992 vs CODATA 137.035999177 (~9 sig figs); sin^2 th12=0.30675 vs NuFIT 6.0 (2024) 0.307+-0.012 (0.02 sigma); beta_rad=0.2424 deg vs ACT DR6 (Diego-Palazuelos-Komatsu 2025) 0.215+-0.074 (0.37 sigma). MILD ~2 sigma TENSIONS: sin^2","claim_id":"DATA.SCORECARD.01","dependencies_as_recorded":"v3; v16; v21; v8; v60","external_data_as_recorded":"CODATA 2022; NuFIT 6.0 (2410.05380); ACT DR6 (2509.13654); Planck/ACT-DESI n_s","id":"claim:DATA.SCORECARD.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":127,"scripts_as_recorded":"v62_data_scorecard.py","status_as_recorded":"Numerical/data [N]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/Lie [I]/[L]","checked_by_registry":false,"claim_excerpt":"Boundary-CFT bridge (WZW central charges = compiler atoms) + SU(3)<->SU(4) reconciliation [I]/[L]; NOT a closure. (A) level-1 WZW central charges c=dim(g)/(1+h^v) are the atoms: c(E8)_1=248/31=8=rank E8, c(D5=SO10)_1=45/9=5=g_car, c(A3=SU4)_1=15/5=3=N_fam; coset c=8-5-3=0 = conformal-embedding criterion => (D5)_1x(A3)_1 ⊂ (E8)_1 is a conformal embedding (CFT mirror of the lattice glue (D5(+)A3)+mu4->E8); (5,3) split ","claim_id":"ARCH.CFT.01","dependencies_as_recorded":"BND.GLUE.01; v6; v15; v19; SEAM.THEOREM.01","external_data_as_recorded":"WZW/conformal embedding standard CFT; Strominger 1997","id":"claim:ARCH.CFT.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":128,"scripts_as_recorded":"v61_cft_bridge.py","status_as_recorded":"Identity/Lie [I]/[L]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I] + observational [N] + [P] consequence","checked_by_registry":false,"claim_excerpt":"Lambda-metrology branch selection => G_N as horizon-metrology OUTPUT, the 123-orders double overlap, and the ACT DR6 birefringence comparison. (1) The form rho_Lambda/Mbar^4=(3/(4pi^2))e^(-2 alpha^-1) is in Paper 1; NEW: with delta_top=48 c3^4=3/(256 pi^4) the physical branch prefactor is (8pi)^2 delta_top=3/(4pi^2) [I], and the alternative branch 2c3 e^(-2a) is mis-scaled by 2c3/delta_top=1/(24 c3^3)=64 pi^3/3=661.4","claim_id":"LAMBDA.BRANCH.01","dependencies_as_recorded":"EM.FP.01; v3; v8; v55","external_data_as_recorded":"ACT DR6 Diego-Palazuelos-Komatsu 2025 arXiv:2509.13654","id":"claim:LAMBDA.BRANCH.01","location_as_recorded":"origin_theory;tfpt_1","path":"verification/status_ledger.csv","row_number":129,"scripts_as_recorded":"v60_lambda_metrology_branch.py","status_as_recorded":"Identity [I] + observational [N] + [P] consequence","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical + Identity [I] (necessary condition)","checked_by_registry":false,"claim_excerpt":"Area-law evidence for the open Seam-Horizon step (necessary condition met, NOT a closure): (1) NUMERICAL [Python-only] - the simplest reflection-positive Gaussian system (harmonic chain) has ground-state block entanglement entropy that SATURATES to a constant when gapped (area law: 1D boundary=O(1) points) and grows ~(c/3)log L when gapless (CFT c-coefficient, c~1); demonstrated S(8)=S(16)=S(32)=0.271 gapped vs 2.197","claim_id":"SEAM.AREALAW.01","dependencies_as_recorded":"SEAM.THEOREM.01; v56; v58","external_data_as_recorded":"Srednicki 1993; Bombelli-Sorkin 1986","id":"claim:SEAM.AREALAW.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":130,"scripts_as_recorded":"v59_area_law_evidence.py","status_as_recorded":"Numerical + Identity [I] (necessary condition)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I] + open theorem [A]","checked_by_registry":false,"claim_excerpt":"Seam-Horizon chain (precise framing) + the OPEN Seam-Horizon Theorem. PRECISE: the seam is NOT identical to an event horizon - it is the abstract boundary normaliser whose LOCAL gravitational realisation is a horizon (black hole = local instance of seam grammar; de Sitter = global). EXACT arithmetic [I]: (geom origin) one-sided S^2 Gauss-Bonnet oint K dA=2pi chi(S^2)=4pi, Z2/Mobius => c3=1/(|Z2|*4pi)=1/(2*4pi)=1/(8pi","claim_id":"SEAM.THEOREM.01","dependencies_as_recorded":"SEAM.HORIZON.01; SEAM.CROSSLINK.01; v8; v57","external_data_as_recorded":"Jacobson 1995; Ryu-Takayanagi 2006","id":"claim:SEAM.THEOREM.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":131,"scripts_as_recorded":"v58_seam_horizon_chain.py","status_as_recorded":"Identity [I] + open theorem [A]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I] + [P] cross-links","checked_by_registry":false,"claim_excerpt":"Horizon cross-links - published black-hole results meeting compiler atoms (exact arithmetic [I]; physical seam=horizon identification is [P]): (1) JACOBSON/EINSTEIN: c3=1/(8pi) is exactly the Einstein-eq coefficient G_uv=8pi T_uv and EH action 1/(16piG)=c3/(2G); Jacobson 1995 derives Einstein eq from dQ=T dS on local Rindler horizons with entropy density 1/(4G), entropy coeff 1/4=1/|mu4| => if seam=horizon, gravity i","claim_id":"SEAM.CROSSLINK.01","dependencies_as_recorded":"SEAM.HORIZON.01; v8; v3; v55","external_data_as_recorded":"Jacobson 1995; Hod 1998; Motl 2003","id":"claim:SEAM.CROSSLINK.01","location_as_recorded":"origin_theory;tfpt_horizon_readouts","path":"verification/status_ledger.csv","row_number":132,"scripts_as_recorded":"v57_horizon_crosslinks.py","status_as_recorded":"Identity [I] + [P] cross-links","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/Lie [I]/[L]","checked_by_registry":false,"claim_excerpt":"Unique attractor: a gapped boundary transport selects ONE fixed point [I]/[L]. The boundary transport spectrum {1,(2/3)^6,(1/3)^6} has spectral gap Delta=-log(2/3)^6=6 log(3/2)=2.4328>0. By Perron-Frobenius a primitive gapped operator has a UNIQUE dominant eigenvector and iteration converges to it geometrically at rate lambda2/lambda1=(2/3)^6, independent of initial state (demonstrated: two different starts -> same f","claim_id":"SEAM.ATTRACTOR.01","dependencies_as_recorded":"SEAM.HORIZON.01; SEAM.CYCLE.01; v54; v55","external_data_as_recorded":"-","id":"claim:SEAM.ATTRACTOR.01","location_as_recorded":"origin_theory;tfpt_3","path":"verification/status_ledger.csv","row_number":133,"scripts_as_recorded":"v56_unique_attractor.py","status_as_recorded":"Identity/Lie [I]/[L]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/Lie [I]/[L]","checked_by_registry":false,"claim_excerpt":"A cyclic element INSIDE the compiler hull (computed, not asserted): built from the E8 Cartan matrix, the Coxeter element c=s1...s8 has order EXACTLY h(E8)=30=|Z2|*N_fam*g_car=2*3*5 (verified by matrix powers, v55), and its eigenvalues are primitive 30th roots exp(2pi i m/30) with m the E8 exponents {1,7,11,13,17,19,23,29} = EXACTLY the phi(30)=8 totatives of 30. 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Both pi-","claim_id":"SEAM.HORIZON.01","dependencies_as_recorded":"BND.GLUE.01; v6; v8; v10; tfpt_2 transport spec","external_data_as_recorded":"-","id":"claim:SEAM.HORIZON.01","location_as_recorded":"tfpt_3;tfpt_horizon_readouts","path":"verification/status_ledger.csv","row_number":135,"scripts_as_recorded":"v54_seam_horizon_keystones.py","status_as_recorded":"Identity [I]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]","checked_by_registry":false,"claim_excerpt":"Compiler core - the whole integer skeleton from one pair (g_car,N_fam)=(5,3): rank E8=g+n=8 (D5(+)A3 rank split), |Z2|=g-n=2 (carrier-family), |mu4|=(g+n)/2=4; (N_fam,|mu4|,g_car)=(3,4,5) is THE Pythagorean triple. NOT decorative: grand-mass-volume exponent Delta_Y=g_car^2=25 (det M_SM~phi0^25) splits as a DIFFERENCE OF SQUARES Delta_Y=g^2=N_fam^2 + (g-n)(g+n)=N_fam^2+|Z2|*rank(E8)=9+16=dim S+, i.e. down sector=N_fam","claim_id":"ARCH.CORE.01","dependencies_as_recorded":"FLAV.MASSVOL.01; v23; v47; BND.GLUE.01","external_data_as_recorded":"-","id":"claim:ARCH.CORE.01","location_as_recorded":"tfpt_1","path":"verification/status_ledger.csv","row_number":136,"scripts_as_recorded":"v53_compiler_core.py","status_as_recorded":"Identity [I]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I] (ratios) + [A] (U_point=anchor)","checked_by_registry":false,"claim_excerpt":"SIMPLE R-bridge closure (the much-simpler solution, no transcendental machinery): the selector stratum S_{8,Q}={det R=8, SNF(R)=(1,1,8), Spec(Q+)={1,2,3}} is now FULLY DERIVED - det R=8=rank E8 and SNF from the lattice (cf det Q=3=N_fam, v70), Spec(Q+)={1,2,3} from D4-equivariant geometry (v69). The four flavor operators are integer lattice maps with compiler-atom determinants (det Q,det K,det R,det L)=(3,4,8,20), pr","claim_id":"FLAV.RIGID.02","dependencies_as_recorded":"FLAV.RIGID.01; v49; v69; v70","external_data_as_recorded":"-","id":"claim:FLAV.RIGID.02","location_as_recorded":"tfpt_research_contracts;tfpt_2","path":"verification/status_ledger.csv","row_number":137,"scripts_as_recorded":"v71_simple_r_bridge.py","status_as_recorded":"Identity [I] (ratios) + [A] (U_point=anchor)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I] chain + [L] non-abelian Hodge","checked_by_registry":false,"claim_excerpt":"det Q = N_fam DERIVED from the cusp class (Alessandro Q-residual closed to the same geometry): the integer-lift datum det Q=|coker Q|=3 is the ORDER of the cusp monodromy class (eigenvalues {1,omega,omega^2}, omega^3=1) = the common DENOMINATOR of the cusp weights {0,1/3,2/3} that fix Spec(Q_+)=diag(1,2,3) (v69). 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(b) c3=1/(|Z2|*2pi*chi(S2))=1/(2*4pi)=1/(8pi) = one-sided Gauss-Bonnet of th","claim_id":"SEAM.KHALF.01","dependencies_as_recorded":"v67; v68; AX.P1.01; SEAM.HORIZON.01","external_data_as_recorded":"-","id":"claim:SEAM.KHALF.01","location_as_recorded":"origin_theory;tfpt_4","path":"verification/status_ledger.csv","row_number":139,"scripts_as_recorded":"v73_k_c3_half.py","status_as_recorded":"Identity [I] + Lattice/topology [L] (coefficient) + [A] (absolute scale only)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]","checked_by_registry":false,"claim_excerpt":"Compiler micro-lemmas (review synthesis, all exact identities compressing scattered factors): (1) SPINE QUOTIENT LADDER - the recurring O(1) factors 2/3,3/4,4/5,5/4,4/3 are adjacent quotients of the spine (|Z2|,N_fam,|mu4|,g_car)=(2,3,4,5); feed lambda2=(2/3)^6 (gap=Page rate=Koide target 2/3), eps=3/4 phi0=q(A3)phi0 (solar), phi0 lead (4/3)c3=1/(6pi), q(D5)+q(A3)=5/4+3/4=2. (2) PENCIL DIFFERENCES - P(x)=det(K+xQ)=3x","claim_id":"ARCH.MICRO.01","dependencies_as_recorded":"ANCHOR.GEN.01; FLAV.KQ.01; FLAV.PENCIL.01; FLAV.SOLAR.01; BND.GLUE.01","external_data_as_recorded":"-","id":"claim:ARCH.MICRO.01","location_as_recorded":"tfpt_1;tfpt_2","path":"verification/status_ledger.csv","row_number":140,"scripts_as_recorded":"v74_compiler_micro_lemmas.py","status_as_recorded":"Identity [I]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I] + [A] (v_geo, shared with 1/G)","checked_by_registry":false,"claim_excerpt":"Gate 1 COMPLETE - U_point reduces to v_geo (the absolute flavor amplitude is not an independent gate): quark ratios closed (Plucker, v49/v71) + lepton c exact (16/7,4/3,7/6, v20) + each sector c-product a clean phi0-power (Grand Mass Volume v46: det M ~ phi0^{6,9,10}; lepton product 16/7*4/3*7/6=32/9=2^gcar/Nfam^2). 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TIER A (physics, CLOSED under RP+gap): Decoupling Theorem - Delta_eff=Delta-2||V||=6log(3/2)-31/(4pi^2)=1.648>0 with ||V_metric||_rel<=248 c3^2=dim(E8) c3^2=31/(8pi^2) (31=2^gcar-1); strictly positive effective gap protects the admissible IR sector => every testable low-energy readout (masses, mixings, alpha^-1, R+R^2) is independent of G6. 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WAVE-5 (2026-08-29): unit choice closed; dimensionless hierarchies (M_Pl/v_EW, M_R/M_scal, Lambda_QCD/v_EW, T_reh/M_scal) remain predictive obligations.","checked_by_registry":false,"claim_excerpt":"v_geo = CLOSED METROLOGY STRUCTURE (R_+ unit torsor; one dimensionful calibration necessary by dimensional analysis -- the No-Unit theorem v153/v725; honest reframe, not a derived mass and not an open physics gap): no pure number can be dimensionful => one calibration is forced by LOGIC (every theory carries >=1 dimensionful input). ALL TFPT scales are dimensionless ratios times ONE M_bar: rho_Lambda/M_bar^4=(3/4pi^2","claim_id":"ANCHOR.VGEO.01","dependencies_as_recorded":"FLAV.UPOINT.01; v60; v55; v68","external_data_as_recorded":"-","id":"claim:ANCHOR.VGEO.01","location_as_recorded":"origin_theory;introduction;tfpt_4","path":"verification/status_ledger.csv","row_number":144,"scripts_as_recorded":"v78_vgeo_floor.py","status_as_recorded":"Identity [I] (ratios) + [A]/[O] (closed metrology: R_+ unit torsor; one calibration by dimensional analysis)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Formal [F]","checked_by_registry":false,"claim_excerpt":"Theorem A (carrier rank uniqueness g_car=5) machine-formalised in Lean 4: the Pascal carrier condition 2^(g-1)=C(g,0)+C(g,1)+C(g,2), division-free 2^g=g^2+g+2, has the UNIQUE solution g=5 (theorem carrier_rank_pascal_unique: forall g, 2^g=g^2+g+2 <-> g=5; growth lemma pascal_growth for g>=6; g_car_unique ExistsUnique; carrier_closure_integers N_fam=(2^4-1)/5=3, g+N_fam=8=rank E8). AUDIT: PASS (no sorry/admit, no doma","claim_id":"FORM.CAR.01","dependencies_as_recorded":"AX.P2.01; CAR.UNIQ.01; v6; v14","external_data_as_recorded":"-","id":"claim:FORM.CAR.01","location_as_recorded":"tfpt_1;tfpt_3","path":"verification/status_ledger.csv","row_number":145,"scripts_as_recorded":"lean4-carrier-rigidity","status_as_recorded":"Formal","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/Lattice [I]/[L] (4 accepted; m_p/m_e + eta_B firewalled)","checked_by_registry":false,"claim_excerpt":"Four validated review identities (passed arithmetic AND the anti-numerology/admissible-invariant discipline) + one disciplined rejection: (1) HYPERCHARGE LUCAS-BINET: carrier charges (q+,q-)=(3,-2) [X^2-X-6=(X-3)(X+2), Lean unique_carrier_pair] generate D_n=(3^n-(-2)^n)/5=1,1,7,13,55,133 = (N_Phi, -, scalaron exp 7, Delta_Q 13, quark numerator 55, dim E7 133) in order; c_u/c_d=D_5/(N_fam^2 D_4)=55/117 (cleaner than P","claim_id":"ARCH.REVIEW.01","dependencies_as_recorded":"CAR.UNIQ.01; FLAV.KQ.01; FLAV.SOLAR.01; v44; FR.MPME.01; FR.ETAB.01","external_data_as_recorded":"PDG (m_p/m_e firewall)","id":"claim:ARCH.REVIEW.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_4","path":"verification/status_ledger.csv","row_number":146,"scripts_as_recorded":"v79_review_identities.py","status_as_recorded":"Identity/Lattice [I]/[L]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/Lattice [I]/[L] (anchor singularity, type checker) + [P] (atlas/F4xG2 shadow audit)","checked_by_registry":false,"claim_excerpt":"Operator-pencil geometry of (K,Q,R,L) - the anchor plane as a small area in operator space (validated review block; all in admissible classes). STRONG: [2] ANCHOR SINGULARITY THEOREM det B(K+xQ)=9x^2+21x+10=(N_fam x+|Z2|)(N_fam x+g_car)=(3x+2)(3x+5), oriented anchor area degenerates at x=-|Z2|/N_fam=-2/3 (Koide target/gap base (2/3)^6) and x=-g_car/N_fam=-5/3 (D5/A3 glue asymmetry) => 2/3 is the FIRST SINGULAR POINT ","claim_id":"FLAV.PENCIL.02","dependencies_as_recorded":"FLAV.PENCIL.01; FLAV.KQ.01; v37; v52; v74","external_data_as_recorded":"-","id":"claim:FLAV.PENCIL.02","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":147,"scripts_as_recorded":"v80_operator_pencil_geometry.py","status_as_recorded":"Identity/Lattice [I]/[L] + audit [P]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/Lattice [I]/[L] (double cover / branch locus, clearing matrices, mixed-disc scalaron) + [P] (per-entry atlas reading of clearing matrices)","checked_by_registry":false,"claim_excerpt":"The mass-transport pencil P(x)=K+xQ as a projective line with two anchor-block singularities, and the DOUBLE COVER branched over them (validated review block; all in admissible classes). CENTRAL [I/L]: det B(K+xQ)=(3x+2)(3x+5) is quadratic => y^2=det B(K+xQ) is a 2:1 cover ramified exactly over its zeros, so the Koide/gap point x=-|Z2|/N_fam=-2/3 and the carrier point x=-g_car/N_fam=-5/3 are THE TWO BRANCH POINTS of ","claim_id":"FLAV.PENCIL.03","dependencies_as_recorded":"FLAV.PENCIL.01; FLAV.PENCIL.02; v37; v52; v74; v80","external_data_as_recorded":"-","id":"claim:FLAV.PENCIL.03","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":148,"scripts_as_recorded":"v81_singular_pencil_matrices.py","status_as_recorded":"Identity/Lattice [I]/[L] + audit [P]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I] (map uniqueness + multiplier = the established transfer gap) + Physical [P] (the one source->pole identification; no closure)","checked_by_registry":false,"claim_excerpt":"Koide RG attractor is FORCED, not postulated [I] + ONE [P] identification (sharpens FR.KOIDE.01/02/03 via the v81 double cover): a branch-divisor-preserving Moebius map of the pencil line that fixes BOTH branch points q=2 (Koide) and q=5 (carrier) is, in the cross-ratio coordinate rho=(q-2)/(5-q), EXACTLY rho->mu*rho, hence UNIQUE once mu is fixed [I]. The multiplier is NOT a new input: mu=(2/3)^6 is the subleading e","claim_id":"FR.KOIDE.04","dependencies_as_recorded":"FR.KOIDE.01; FR.KOIDE.03; FLAV.PENCIL.03; v54; v56; v81","external_data_as_recorded":"PDG lepton masses","id":"claim:FR.KOIDE.04","location_as_recorded":"tfpt_4","path":"verification/status_ledger.csv","row_number":149,"scripts_as_recorded":"v82_koide_attractor_splitting.py","status_as_recorded":"Physical (conjecture sharpened) + Identity [I]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I] (discriminant trichotomy, non-genericity, negative control) + [P] (physical sector identification of the placements)","checked_by_registry":false,"claim_excerpt":"Anchor-placement splitting trichotomy - the clean rational double cover is NON-GENERIC (anchor-first hardening) [I] + [P] (sector id). The splitting-type exponents (2,1,1) (= the anchor (1,1,2); v32 splitting O(-2)+O(-1)^2) placed across the three family slots give three DIFFERENT covers: (1,1,2) heavy-in-fam3 (lepton) det B(K+xQ)=(3x+2)(3x+5) disc=81=N_fam^4 -> SPLIT (individually rational branch labels {2,5}); (2,1","claim_id":"FLAV.PENCIL.04","dependencies_as_recorded":"FLAV.PENCIL.02; FLAV.PENCIL.03; v32; v80; v81","external_data_as_recorded":"-","id":"claim:FLAV.PENCIL.04","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":150,"scripts_as_recorded":"v82_koide_attractor_splitting.py","status_as_recorded":"Identity [I] + Physical [P] (sector id)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Red-team verdict: reduced, not closed [P]","checked_by_registry":false,"claim_excerpt":"Red Team / Stress Test Target A - adversarial attack on the (E8)_1 boundary-net identification (GATE.METRIC.03). CONFIRMS the conservative wording: central charge is NECESSARY not sufficient - (D8)_1=SO(16)_1 also has c=120/15=8 but is non-holomorphic (4 primaries 1,v,s,c), and the c=8 Narain family is positive-dimensional; (E8)_1 is the UNIQUE holomorphic c=8 net (even unimodular rank-8 lattice = E8), so HOLOMORPHY ","claim_id":"REDTEAM.A.01","dependencies_as_recorded":"GATE.METRIC.03; v77; v76; v61","external_data_as_recorded":"-","id":"claim:REDTEAM.A.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":151,"scripts_as_recorded":"redteam/rt_A_e8net.py","status_as_recorded":"Red-team [P] (reduced, not closed)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Red-team verdict: survives; Pascal selection now typed [A]/[P]","checked_by_registry":false,"claim_excerpt":"Red Team Target B - attack on the UPSTREAM physical premise of Theorem A (the Lean arithmetic 2^g=g^2+g+2 <=> g=5 is NOT attacked; it is verified [F]). Finding: the carrier rank is selected by the Pascal RULE, not the arithmetic. Perturbing the constant 2^g=g^2+g+c gives {5} only at c=2; the truncation degree K in 2^(g-1)=sum_{k<=K} C(g,k) sets g=2K+1 (K=0->1, 1->3, 2->5, 3->7), so choosing K=2 is the physical input.","claim_id":"REDTEAM.B.01","dependencies_as_recorded":"FORM.CAR.01; CAR.UNIQ.01; v2; v14","external_data_as_recorded":"-","id":"claim:REDTEAM.B.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":152,"scripts_as_recorded":"redteam/rt_B_pascal.py","status_as_recorded":"Red-team [F]+[A] (survives, narrowed)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Red-team verdict: survives as worded (reduced coefficient)","checked_by_registry":false,"claim_excerpt":"Red Team Target C - dimensional firewall on k=c3/2. The reduced coefficient k_red=c3/2=1/(16pi) is dimensionless; the only legal chain is k_phys=k_red/G, S=4pi k_phys A_phys=A_phys/(4G). The forbidden form k_phys=c3/2 is dimensionally false (legal only at G=1 / Planck units). Firewall scan of v67/v68/v73: 28 'c3/2' mentions, ZERO naked dimensionful identities, each file establishes the reduced/seam-unit/G=1 context; ","claim_id":"REDTEAM.C.01","dependencies_as_recorded":"SEAM.AREACOEFF.01; SEAM.AREACOEFF.02; v67; v68; v73","external_data_as_recorded":"-","id":"claim:REDTEAM.C.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":153,"scripts_as_recorded":"redteam/rt_C_kc3.py","status_as_recorded":"Red-team [I]+[A] (survives)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Red-team verdict: survives; four hypotheses now explicit; CP-phase residual, narrowed to a FIBER datum: arg(prod c)=0 exactly on both sectors, branch blindness = order divides N_fam=3 (T177/v561)","checked_by_registry":false,"claim_excerpt":"Red Team Target D - stress test of the U_point->v_geo bijection (FLAV.UPOINT.01). For positive reals (ratios,product) <=> (individuals) is a bijection and the TFPT sectors satisfy it (positive rational c, odd size 3=N_fam). Counterexamples off-assumption: even sector size leaves a SIGN ambiguity ({2,3} vs {-2,-3} share ratio 3/2 and product 6); complex amplitudes leave an n-th-root BRANCH ambiguity ({1,1,1},{w,w,w},{","claim_id":"REDTEAM.D.01","dependencies_as_recorded":"FLAV.UPOINT.01; v75; v20; v24","external_data_as_recorded":"-","id":"claim:REDTEAM.D.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":154,"scripts_as_recorded":"redteam/rt_D_upoint.py; v561_cp_channel_identities.py","status_as_recorded":"Red-team [I]+[A] (survives, narrowed)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Red-team verdict: floor of certified tiers; frontier scales must stay typed","checked_by_registry":false,"claim_excerpt":"Red Team Target E - single-scale audit of v_geo (ANCHOR.VGEO.01). The closed compiler + protected IR readouts all reduce to (pure number) x v_geo: M_scal=c3^(7/2) Mbar, f_a=(c3/|mu4|)^(7/2) Mbar, masses=(pi/sqrt2) c_f phi0^k v_geo, and 1/G shares the same anchor (v68/v75). The audit SURFACES non-pure-reduction candidates: the seam cutoff Lambda (only an identification seam=Planck collapses it to v_geo), the electrowe","claim_id":"REDTEAM.E.01","dependencies_as_recorded":"ANCHOR.VGEO.01; FLAV.UPOINT.01; v78; v68; v60","external_data_as_recorded":"-","id":"claim:REDTEAM.E.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":155,"scripts_as_recorded":"redteam/rt_E_vgeo.py","status_as_recorded":"Red-team [I]+[A] (survives, narrowed)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Lattice [L]: holomorphy => (E8)_1 unique (residual 1 closed); residuals 2 (constructive map) + 3 (bulk uniqueness) remain [P]/[A]","checked_by_registry":false,"claim_excerpt":"Red-team Target A residual 1 CLOSED [L] (holomorphy is necessary AND sufficient to pin (E8)_1): at level 1 the number of primaries = det(Cartan) = |fundamental group|, giving A3=4, D5=4, D8=4, E8=1. So holomorphy (single vacuum sector = mu-index 1 = det 1) excludes the SAME-c rival (D8)_1=SO(16)_1 (c=120/15=8 but 4 primaries 1,v,s,c) - equal central charge is necessary not sufficient - AND is sufficient: a holomorphi","claim_id":"GATE.METRIC.04","dependencies_as_recorded":"REDTEAM.A.01; GATE.METRIC.03; v77; v66; v1","external_data_as_recorded":"E8 lattice / level-1 RCFT (standard)","id":"claim:GATE.METRIC.04","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":156,"scripts_as_recorded":"v83_e8net_holomorphic_uniqueness.py","status_as_recorded":"Lattice [L] (residual 1 closed) + [P]/[A] (residuals 2-3 open)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/Lattice [I]/[L]: K=(g-1)/2 is the half-spinor midpoint, not a free truncation; B residual reduced to the standard half-spinor carrier","checked_by_registry":false,"claim_excerpt":"Red-team Target B residual REDUCED [I]/[L]: the carrier 'K=2 Pascal truncation' flagged by the red team as a free postulate is NOT free. K=(g-1)/2 is the Pascal-row MIDPOINT: sum_{k<=(g-1)/2} C(g,k) = 2^(g-1) for every odd g (verified g=3,5,7,9), i.e. the half-spinor split of the 2^g Dirac spinor. Equivalently the carrier is the even Clifford half-spinor Lambda^even(C^g_car): C(5,0)+C(5,2)+C(5,4)=1+10+5=16=2^(g_car-1","claim_id":"CAR.PASCAL.01","dependencies_as_recorded":"REDTEAM.B.01; FORM.CAR.01; CAR.UNIQ.01; v2; v44","external_data_as_recorded":"-","id":"claim:CAR.PASCAL.01","location_as_recorded":"tfpt_5_redteam;tfpt_1","path":"verification/status_ledger.csv","row_number":157,"scripts_as_recorded":"v83_e8net_holomorphic_uniqueness.py","status_as_recorded":"Identity/Lattice [I]/[L] (B residual reduced to the half-spinor input)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical [N] (registry lock)","checked_by_registry":false,"claim_excerpt":"Blind-prediction registry FROZEN 2026-06-09, machine-enforced (review point: pre-registration before JUNO/CMB-S4/LiteBIRD/DESI). predictions_frozen.json freezes every dimensionless prediction of record at 25 significant digits; v84 re-derives each decimal from the two axioms {c3,g_car} on every run, so formula and frozen value are locked together (changing either alone FAILS the suite; the file is covered by manifest","claim_id":"REG.FREEZE.01","dependencies_as_recorded":"EM.FP.01; FLAV.TH12.01; PRED.LAYER.01; freeze_file.csv","external_data_as_recorded":"JUNO, CMB-S4/LiteBIRD, DESI (future); NuFIT 6.0 / CODATA 2022 / ACT DR6 (current)","id":"claim:REG.FREEZE.01","location_as_recorded":"verification;tfpt_2;introduction","path":"verification/status_ledger.csv","row_number":158,"scripts_as_recorded":"v84_frozen_registry.py","status_as_recorded":"Numerical [N] (registry lock) + typing discipline","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/Lattice [I]/[L]: one master cover; family = GL(2) orbit; mu4 not a 4:1 cover; tilt stays [P]","checked_by_registry":false,"claim_excerpt":"MASTER-COVER THEOREM (answers next.txt P3; resolves P6 negatively; types P4) [I]/[L]: the anchor-block determinant is GL(2)-COVARIANT on the pencil plane span{K,Q} - det B((aK+bQ)+x(cK+dQ)) = (gamma x+alpha)^2 * p_KQ(moebius_G(x)) exactly (symbolic identity), with disc = 81*det(G)^2 = N_fam^4 x square. CONSEQUENCE: there is exactly ONE anchor-block double cover up to Moebius reparametrisation of the line, the master ","claim_id":"FLAV.PENCIL.05","dependencies_as_recorded":"FLAV.PENCIL.04; v80; v81; v82","external_data_as_recorded":"-","id":"claim:FLAV.PENCIL.05","location_as_recorded":"verification;next.txt","path":"verification/status_ledger.csv","row_number":159,"scripts_as_recorded":"v85_master_cover.py","status_as_recorded":"Identity/Lattice [I]/[L] (GL(2) covariance + family classification) + [P] physical readings","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Physical [P]: N_star=51.4 point inside the frozen band; demotion as compiler output stands","checked_by_registry":false,"claim_excerpt":"N_star band -> POINT [P] (the announced 'future derivation from a reheating model' executed; demotion of N_star as a compiler output STANDS): the only compiler input is M_scal=c3^{7/2}Mbar=3.0600e13 GeV [I] (v28/v36/v80); everything downstream is imported standard physics - scalaron width Gamma=N_eff M^3/(48pi Mbar^2) with N_eff=4 (SM Higgs doublet; Starobinsky/Vilenkin/Gorbunov-Panin), reheating at H=Gamma => T_reh=","claim_id":"COSMO.NSTAR.01","dependencies_as_recorded":"GRAV.SCAL.01 (M_scal); PRED.LAYER.01; REG.FREEZE.01","external_data_as_recorded":"Planck 2018 (n_s=0.9649+-0.0042), DESI-combined, CMB-S4/LiteBIRD (r, future); SM g*=106.75","id":"claim:COSMO.NSTAR.01","location_as_recorded":"origin_theory;tfpt_2;introduction","path":"verification/status_ledger.csv","row_number":160,"scripts_as_recorded":"v86_nstar_reheating.py","status_as_recorded":"Physical [P] (conditional on M_Star=M_scal + standard reheating)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Lattice [L]: bulk uniqueness rides on holomorphy; Target A = ONE residual","checked_by_registry":false,"claim_excerpt":"Red-team Target A residual (ii) CONDITIONALLY CLOSED [L] -> Target A = ONE residual: bulk-reconstruction uniqueness is NOT independent of residual (i). By the AQFT classification of full 2D CFTs over a chiral net (Longo-Rehren 1995; Kawahigashi-Longo-Mueger 2001; Bischoff-Kawahigashi-Longo-Rehren arXiv:1405.7863) the possible bulks = haploid commutative Q-systems = physical modular invariants of Rep(A); for a HOLOMOR","claim_id":"GATE.METRIC.05","dependencies_as_recorded":"GATE.METRIC.04; REDTEAM.A.01; v83; v77","external_data_as_recorded":"AQFT literature (LR/KLM/BKLR; standard)","id":"claim:GATE.METRIC.05","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":161,"scripts_as_recorded":"v87_bulk_uniqueness_reduction.py","status_as_recorded":"Lattice [L] (classification + machine contrast) + [P]/[A] (the one remaining hypothesis)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical [N]: leading reading survives at +0.98 sigma; residual = -1.02 lam^2 recorded; decision at sigma_gamma<1 deg","checked_by_registry":false,"claim_excerpt":"Red-team Target D follow-up: CP-phase residual QUANTIFIED [N] (not closed; freeze respected): frozen leading reading delta_CKM=pi/3+3 lam^2=1.198232 rad=68.654 deg (registry DELTA_CKM_RAD untouched) gives J=3.327e-5 [I]. Clean phase probe gamma_PDG=65.7+-3.0 deg: pull +0.98 sigma => leading reading SURVIVES. AUDIT (recorded, explicitly NOT promoted): the data central value sits 0.07 deg from the ALTERNATIVE coefficie","claim_id":"FLAV.CP.01","dependencies_as_recorded":"REDTEAM.D.01; REG.FREEZE.01; FLAV.CKM.01","external_data_as_recorded":"PDG 2024 / CKMfitter (gamma=65.7+-3.0 deg, J=3.08+-0.14e-5)","id":"claim:FLAV.CP.01","location_as_recorded":"tfpt_5_redteam;tfpt_2","path":"verification/status_ledger.csv","row_number":162,"scripts_as_recorded":"v88_cp_phase_audit.py","status_as_recorded":"Numerical [N] (audit + thresholds) + [P] (phase mechanism open)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Lattice [L]: Gate A <=> index-4 mu_4 simple-current extension of the carrier net","checked_by_registry":false,"claim_excerpt":"CARRIER INDEX LEMMA [L] - the Gate-A theorem gets an equivalent index-theoretic form (sharper as a target): by Kawahigashi-Longo-Mueger (mu_A=[B:A]^2 mu_B; lattice nets mu=|discriminant|=det Cartan) the carrier inclusion has Jones index [(E8)_1:(D5)_1x(A3)_1]=sqrt(16/1)=4=|mu_4|=|Z2|^2 - the glue-group order IS the inclusion index. The extension is the mu_4 simple-current extension at level 1: adjoint branching 248=(","claim_id":"GATE.METRIC.06","dependencies_as_recorded":"GATE.METRIC.05; GATE.METRIC.04; E8.GLU.01; v77","external_data_as_recorded":"KLM 2001 (mu-index relation; standard)","id":"claim:GATE.METRIC.06","location_as_recorded":"tfpt_5_redteam;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":163,"scripts_as_recorded":"v89_carrier_index_lemma.py","status_as_recorded":"Lattice [L] (index arithmetic + reframing) + [P]/[A] (seam-side identification)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: S=4pi k A derived; S=A/4 <=> c3=1/(8pi); residual = seam determinant => EH form","checked_by_registry":false,"claim_excerpt":"Seam-Horizon programme: the Fursaev-Solodukhin factor 4pi is now DERIVED, not imported [I] (removes the literature import of v67): (1) smoothed-cone Gauss-Bonnet - regularising the 2D cone (opening alpha) by a tangent spherical cap (tangency alpha=cos theta0) gives Int K dA = 2pi(1-cos theta0) = 2pi(1-alpha) EXACTLY, independent of the smoothing radius (topological; GB closure Int k_g=2pi alpha, chi(disk)=1; limits: ","claim_id":"SEAM.AREACOEFF.03","dependencies_as_recorded":"SEAM.AREACOEFF.01; SEAM.AREACOEFF.02; SEAM.KHALF.01; SEAM.THEOREM.01","external_data_as_recorded":"-","id":"claim:SEAM.AREACOEFF.03","location_as_recorded":"origin_theory;tfpt_horizon_readouts","path":"verification/status_ledger.csv","row_number":164,"scripts_as_recorded":"v90_conical_defect_chain.py","status_as_recorded":"Identity [I] (chain derived) + [A] (the one isolated residual)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: spine tetrahedron closures; dual cuts tautological; sub-grammar honestly typed","checked_by_registry":false,"claim_excerpt":"SPINE TETRAHEDRON - the compiler microkernel as ONE finite object (review proposal 2026-06-10, validated and typed): the spine T={2,3,4,5}={|Z2|,N_fam,|mu4|,g_car} equals {e3(a),p0(a),e1(a),e2(a)} for the anchor a=(1,1,2), so the tetrahedron is the anchor plus its zeroth moment, not a second structure [I]. Edge products {6,8,10,12,15,20} = {|R+(A3)|/C6, rank E8=h(D5)=det R, A_Lambda=|E(K5)|, |R(A3)|=dim SM gauge, dim","claim_id":"ARCH.SPINE.01","dependencies_as_recorded":"ANCHOR.GEN.01; FLAV.PENCIL.05; GATE.METRIC.06 (60=dim(10,6))","external_data_as_recorded":"-","id":"claim:ARCH.SPINE.01","location_as_recorded":"tfpt_1;tfpt_3","path":"verification/status_ledger.csv","row_number":165,"scripts_as_recorded":"v91_spine_tetrahedron.py","status_as_recorded":"Identity [I] (closures + negative control) + Audit (chi_T fingerprint; dual cuts = presentation)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/Lattice [I]/[L]: extension tower = carrier -> SO(16)_1 -> E8 (sheet pair); no freedom left in WHICH extension","checked_by_registry":false,"claim_excerpt":"GLUE UNIQUENESS [I]/[L] - the carrier extension tower completely classified (Gate A loses its last structural freedom): extensions of the carrier net/lattice correspond to isotropic subgroups of the discriminant form (Z4xZ4, q=(5x^2+3y^2)/8; q reproduces the level-1 sector weights of v87/v89). Exhaustive enumeration of all 15 subgroups: isotropic = {1, Z2, Z4, Z4}. 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base file untouched","checked_by_registry":false,"claim_excerpt":"Second [C] path EXTENSION VERIFIED RUNNING: verification/wolfram/tfpt_readouts_extension.wl mirrors the v84-v110 round (frozen registry, master cover, reheating arithmetic, SO(16)_1 modular data, carrier index, conical defect chain, spine tetrahedron, glue uniqueness, Koide relaxation toy, sheet diamond v94, centered diamond v95, branch-kernel selection v96, sheet-conjugation bridge v97, discriminant dictionary v98, ","claim_id":"GATE.WOLFRAM.02","dependencies_as_recorded":"GATE.WOLFRAM.01; REG.FREEZE.01","external_data_as_recorded":"Wolfram Engine 14.3 (local)","id":"claim:GATE.WOLFRAM.02","location_as_recorded":"verification/wolfram","path":"verification/status_ledger.csv","row_number":168,"scripts_as_recorded":"wolfram/tfpt_readouts_extension.wl","status_as_recorded":"Numerical (second path, extension verified 623/623)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Formal [F]: glue uniqueness + carrier index arithmetic kernel-verified","checked_by_registry":false,"claim_excerpt":"Lean 4 formalisation of the v89/v92 arithmetic cores - AUDIT: PASS (machine-formalised [F]): new module TfptCarrier/GlueUniqueness.lean proves by kernel decide (NO native_decide, no new axioms; #print axioms = propext, Classical.choice, Quot.sound only): (1) the isotropic elements of the carrier discriminant form (Z4xZ4, qZ=(5x^2+3y^2) mod 8) are exactly {(0,0),(1,1),(1,3),(2,2),(3,1),(3,3)}; (2) the order-4 isotropi","claim_id":"FORM.GLUE.01","dependencies_as_recorded":"GATE.METRIC.06; GATE.METRIC.07; FORM.P2.02","external_data_as_recorded":"-","id":"claim:FORM.GLUE.01","location_as_recorded":"experiments/lean4-carrier-rigidity","path":"verification/status_ledger.csv","row_number":169,"scripts_as_recorded":"lean4-carrier-rigidity/TfptCarrier/GlueUniqueness.lean","status_as_recorded":"Formal [F] (Lean kernel; no extra axioms)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"External reproduction PASS; one stale manifest row -> --check mode + release rule","checked_by_registry":false,"claim_excerpt":"EXTERNAL REPRODUCTION of the v83 package (Alessandro, 2026-06): TeX build.sh notes = 9 ok 0 failed; Python run_all v1-v83 = ALL CHECKS PASSED; Wolfram tfpt_readouts.wl = 116/116 ALL WOLFRAM CHECKS PASSED; redteam run_redteam.py reproduces the status matrix (A reduced not closed, B/D/E survive narrowed, C survives); lean_manifest.sha256 verifies literally (36 files, missing 0, bad 0; byte-identical to the v78 archive,","claim_id":"REVIEW.REPRO.02","dependencies_as_recorded":"GATE.METRIC.04; CAR.PASCAL.01; REDTEAM.A.01-E.01; FR.KOIDE.04","external_data_as_recorded":"external reviewer run (TeX/Python/Wolfram/redteam/Lean manifests)","id":"claim:REVIEW.REPRO.02","location_as_recorded":"verification;tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":170,"scripts_as_recorded":"verification/make_manifest.py (--check)","status_as_recorded":"External reproduction (substantive: PASS) + process fix","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: one surface carries R/K/L/F; winding synchronised; reality threshold corrected; firewall rejected","checked_by_registry":false,"claim_excerpt":"SHEET DIAMOND & WINDING LINE (second review round 2026-06-11; arithmetic fully validated, interpretations corrected where needed) [I]: (1) all four flavor operators are distinguished points of ONE two-parameter surface M(s,t)=R+Q diag(s,t,t): R=M(0,0), K=M(1,-1), L=M(2,0), F=M(1,1), with the global invariants det M(s,t)=3st^2+9st+6s+t^2+5t+8 and det B_M(s,t)=6st+12s+3t^2+15t+16; the mass-transport pencil K+xQ is the ","claim_id":"FLAV.DIAMOND.01","dependencies_as_recorded":"FLAV.KQ.01; FLAV.PENCIL.05; v74; v80; v81; v85","external_data_as_recorded":"-","id":"claim:FLAV.DIAMOND.01","location_as_recorded":"tfpt_2;verification","path":"verification/status_ledger.csv","row_number":171,"scripts_as_recorded":"v94_sheet_diamond.py","status_as_recorded":"Identity [I] (surface/winding/normal closures + negative controls) + Audit (F corner) + honest corrections","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: 11 = left and 26 = right Pluecker norm of K; older 26-readings corollaries","checked_by_registry":false,"claim_excerpt":"RIGHT-PLUECKER CANONICALISATION of the quark-ratio integers (load-bearing improvement; supersedes the loose-26 readings as the canonical source): with Pi_R(M) = 2x2 minors of (M1 | Ma): Pi_R(Q)=(0,4,5), Pi_R(K)=(12,12,-2), Pi_R(R)=(8,12,4), Pi_R(L)=(20,30,10)=10*(2,3,1) with sum 60 = E8 cascade start (v91 loop closed). CANONICAL READINGS: ||Pi_L(K)||_1=11 and ||Pi_R(K)||_1=26 put BOTH quark-ratio integers in the SAME","claim_id":"FLAV.PLUCKER.02","dependencies_as_recorded":"FLAV.PLUCKER.01; FLAV.QRATIO.01; FLAV.RIGID.01; v37; v42","external_data_as_recorded":"-","id":"claim:FLAV.PLUCKER.02","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":172,"scripts_as_recorded":"v94_sheet_diamond.py","status_as_recorded":"Identity [I] (canonical readings; old readings = corollaries)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: one center + two axes; cusp class on the sheet axis; G2 reading audit-typed","checked_by_registry":false,"claim_excerpt":"CENTERED FLAVOR DIAMOND (third review round 2026-06-11; all arithmetic validated incl. SNF) [I]: the v94 sheet diamond is a CENTERED CROSS - with the center C:=M(1,0)=(R+L)/2=(K+F)/2=[[4,3,0],[4,5,2],[5,5,3]] and the two axes U:=Q diag(1,0,0)=N_fam*1e1^T (WINDING axis: rank 1, Spec {3,0,0} = pure family charge) and V:=Q diag(0,1,1) (SHEET axis: rank 2), one has exactly Q=U+V and R=C-U, L=C+U, K=C-V, F=C+V: the five o","claim_id":"FLAV.DIAMOND.02","dependencies_as_recorded":"FLAV.DIAMOND.01; FLAV.PLUCKER.02; FLAV.QGEO.01 (cusp class); GATE.GMETRIC.XI.01 (31)","external_data_as_recorded":"-","id":"claim:FLAV.DIAMOND.02","location_as_recorded":"tfpt_2;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":173,"scripts_as_recorded":"v95_centered_diamond.py","status_as_recorded":"Identity [I] (normal form + invariants + cross-links) + Audit (G2 reading)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/Lattice: the cover defines the sector map; physics [P]","checked_by_registry":false,"claim_excerpt":"BRANCH-KERNEL SELECTION (next.txt P1 unblocked): at each branch point of the anchor-block cover the 2x2 anchor block is RANK 1 with canonical INTEGER kernels (Koide -2/3: right w=11*1-9a=(2,2,-7), left v=7*1-5a=(2,2,-3); carrier -5/3: right kernel = the democratic vector 1, left v=8*1-7a=(1,1,-6)). COLLAPSE LEMMA [L]: rank-1 forces P(x0).w perp span{1,a} => proportional to the antisymmetric direction (-1,1,0) of the ","claim_id":"FLAV.SHEET.01","dependencies_as_recorded":"FLAV.PENCIL.03; FLAV.PENCIL.05; FLAV.DIAMOND.02; FLAV.MASSVOL.01 (sector rows)","external_data_as_recorded":"-","id":"claim:FLAV.SHEET.01","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":174,"scripts_as_recorded":"v96_branch_kernel_selection.py","status_as_recorded":"Identity/Lattice [I]/[L] (kernels, collapse, ladder, controls) + [P] (sector-sheet physics)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/Lattice: one deck involution; one [P] dictionary left","checked_by_registry":false,"claim_excerpt":"SHEET-CONJUGATION BRIDGE (P1 -> ONE [P] residual): the family-side conjugation (cusp negation 0 fixed, 1/3<->2/3 on the Q_+ eigenspaces e1=(0,0,1), e2=(0,1,2), e3=(1,0,0)) has a UNIQUE anchor-compatible generation-space realisation - T.1=1 and T.a=a BOTH force scale 1 => integer involution T_A=[[0,1,0],[1,0,0],[2,-2,1]], det=-1; the two alternative pairings are REJECTED (T.a=a unsolvable). ANCHOR = CONJUGATION-SYMMET","claim_id":"FLAV.SHEET.02","dependencies_as_recorded":"FLAV.SHEET.01; FLAV.QGEO.01; GATE.QGEOM.02 (v70); GATE.METRIC.07 (v92 glues)","external_data_as_recorded":"-","id":"claim:FLAV.SHEET.02","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":175,"scripts_as_recorded":"v97_sheet_conjugation_bridge.py","status_as_recorded":"Identity/Lattice [I]/[L] (uniqueness, D4, index 2) + [P] (the one lattice dictionary)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/Lattice: P1 dissolved into the one existing Q-geometry gate","checked_by_registry":false,"claim_excerpt":"DISCRIMINANT DICTIONARY DERIVED (P1 closed modulo GATE.QGEO): the generation space carries an INTEGER mu4 - G = T_A*Sigma acts on the cusp basis as G e1=-e1, G e3=e2, G e2=-e3 (the v69 B1+E decomposition realised integrally; G^4=I, char (t+1)(t^2+1)); the cusp-0 eigenvector IS the unique self-conjugate Z4-class-2 line and the swapped cusp pair {1/3,2/3} IS the conjugate class pair {1,3} => the v97 dictionary 'Q_+ gra","claim_id":"FLAV.SHEET.03","dependencies_as_recorded":"FLAV.SHEET.01; FLAV.SHEET.02; FLAV.QGEO.01; GATE.QGEO.01; GATE.METRIC.07 (v92)","external_data_as_recorded":"-","id":"claim:FLAV.SHEET.03","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":176,"scripts_as_recorded":"v98_discriminant_dictionary.py","status_as_recorded":"Identity/Lattice [I]/[L] (dictionary derived) - residual folded into GATE.QGEO","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"P2 sharpened: canonical generator [I]; discrete-vs-continuous = experimental question","checked_by_registry":false,"claim_excerpt":"KOIDE FLOW TIME (P2 sharpened on both ends; corrects the ROBUSTNESS of v93 negative (i), not its arithmetic): [I] CANONICAL GENERATOR - the v82 flow is generated by dq/dt = (Delta/N_fam)(q-2)(q-5) = (Delta/N_fam) det B(q), Delta = 6 log(3/2) = the gap; the time-1 map IS the v82 Moebius F (machine-checked; e^-Delta = (2/3)^6 exact) => the missing P2 object is precisely a QFT mechanism producing 'gap x anchor-block qua","claim_id":"FR.KOIDE.06","dependencies_as_recorded":"FR.KOIDE.04; FR.KOIDE.05 (robustness of negative (i) corrected); COSMO.NSTAR.01 (M_scal)","external_data_as_recorded":"PDG 2024 m_tau = 1776.93 +- 0.09 MeV","id":"claim:FR.KOIDE.06","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":177,"scripts_as_recorded":"v99_koide_flow_time.py","status_as_recorded":"Identity [I] (generator) + Numerical [N] (fragility) + Physical [P] (conditional steps)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: 53/54 = a^T(R+Q)1/(2*1^T R a) sourced from the missing Sheet-Diamond corner F (det B_F=52); mechanism stays [C]","checked_by_registry":false,"claim_excerpt":"OPERATOR ORIGIN OF THE KOIDE SOURCE->POLE FACTOR 53/54 (external-review proposal 2026-06-14, validated; upgrades the FR.KOIDE.03 conjecture from a bare arithmetic guess 1-1/(2 N_fam^3) to an exact operator identity on the carrier): u_pole/u_source = a^T (R+Q) 1 / (2 * 1^T R a) = 53/(2*27) = 53/54. (1) THE CUBIC FAMILY BLOCK [I]: 1^T R a = 27, the E6xA2 flavor-shadow split 248 = dim E6 + det R + 2(1^T R a)N_fam = 78 +","claim_id":"FR.KOIDE.07","dependencies_as_recorded":"FR.KOIDE.03; FLAV.PENCIL.02; FLAV.PLUCKER.02; v80_operator_pencil_geometry.py","external_data_as_recorded":"-","id":"claim:FR.KOIDE.07","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":178,"scripts_as_recorded":"v183_koide_f_corner_transfer.py","status_as_recorded":"Identity [I] (exact operator factor + negative control) + Physical [C] (the transfer mechanism)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Physical [C]: m~1=m_3/A_Lambda anchors the washout; M_1=M_R phi0^4 does NOT pin M_1 (M_R = seesaw scale, not a compiler output); eta_B stays a sharper scenario","checked_by_registry":false,"claim_excerpt":"HONEST TEST OF THE ANCHORED-BOLTZMANN eta_B PROPOSAL (external review 2026-06-14; firewall verdict: SHARPER SCENARIO, not a closure): the proposal M_1 = M_R phi0^4 and m~1 = m_3/A_Lambda was tested exactly. (1) WASHOUT ANCHOR [C]: m~1 = m_3/A_Lambda = m_3/10 ~ 5e-3 eV (m_3 ~ sqrt(dm^2_atm) ~ 0.05 eV; A_Lambda=10 = |E(K5)| the action-grammar atom) lands in the strong-washout window [m_*, m_atm] -- a TFPT-flavoured val","claim_id":"FR.ETAB.03","dependencies_as_recorded":"FR.ETAB.02; FR.ETAB.01; FLAV.RGSTAB.01; v9_neutrino_texture.py; v169_etaB_boltzmann_interface.py","external_data_as_recorded":"NuFIT (dm^2_atm); Planck (eta_B)","id":"claim:FR.ETAB.03","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":179,"scripts_as_recorded":"v184_etaB_anchored_boltzmann.py","status_as_recorded":"Physical [C] (sharper scenario; washout anchored; M_1 unpinned)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Physical [C]: f_a=M_scal/128 axion can be all DM only near the theta_i~170 hilltop (exponentially sensitive) -> scenario, branch kill test not theory","checked_by_registry":false,"claim_excerpt":"AXION RELIC HONEST MISALIGNMENT ESTIMATE (external-review proposal 2026-06-14; the determinant-line axion can be all DM but stays a [C] scenario): (1) SCALES [I]: f_a = M_scal/(2 dim S+ |mu4|) = M_scal/128 ~ 2.39e11 GeV (M_scal = c3^{7/2} Mbar ~ 3.06e13 GeV), QCD axion m_a ~ 5.7 ueV (1e12/f_a) ~ 23.8 ueV (FR.DM.02). (2) HARMONIC MISALIGNMENT UNDER-PRODUCES [N]: Omega_a h^2 ~ 0.12 (f_a/9e11)^{7/6} <theta^2> gives pref","claim_id":"FR.DM.03","dependencies_as_recorded":"FR.DM.01; FR.DM.02; v25_frontier_conjectures.py","external_data_as_recorded":"Planck Omega_DM h^2 = 0.12","id":"claim:FR.DM.03","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":180,"scripts_as_recorded":"v185_axion_relic_solver.py","status_as_recorded":"Physical [C] (hilltop scenario SUPERSEDED by post-inflationary reframing FR.DM.02; angle not observable)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/guard [I]: the four F_transfer frontier observables are ledger-enforced to stay [C]/[A]/[O], never primitive [E]/[N]","checked_by_registry":false,"claim_excerpt":"THE F_TRANSFER DISCIPLINE GUARD (a CI-style firewall check, the machine-readable form of the Frontier rule; external-review proposal 2026-06-14): the four continuous-transfer frontier observables -- Koide (FR.KOIDE.*), eta_B (FR.ETAB.*), the axion relic (FR.DM.*), and m_p/m_e + Lambda_QCD (FR.MPME.*, QCD.LAMBDA.*) -- must NEVER be typed as primitive [E]/[N] compiler predictions; each must carry a conditional [C] / an","claim_id":"FR.TRANSFER.01","dependencies_as_recorded":"FR.KOIDE.07; FR.ETAB.03; FR.DM.03; QCD.LAMBDA.01; REG.FREEZE.01; AUDIT.NULLMC.01","external_data_as_recorded":"-","id":"claim:FR.TRANSFER.01","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":181,"scripts_as_recorded":"v187_ftransfer_laws.py","status_as_recorded":"Identity/guard [I] (ledger-enforced typing discipline)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/guard [I]: stale frontier prose (superseded wording) is forbidden from the active documents","checked_by_registry":false,"claim_excerpt":"THE FRONTIER-WORDING GUARD (a prose sentinel, no new physics; external-review proposal 2026-06-14): v187 protects the ledger TYPING, this guard protects the PROSE. It forbids stale sentences whose semantics an earlier round superseded, so a frozen Zenodo release can never re-introduce wording that was true yesterday and is half-true today. Forbidden patterns (each recording what superseded it): (1) 'leptogenesis inte","claim_id":"AUDIT.WORDING.01","dependencies_as_recorded":"FR.ETAB.03; FR.DM.03; FR.KOIDE.07; FR.TRANSFER.01","external_data_as_recorded":"-","id":"claim:AUDIT.WORDING.01","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":182,"scripts_as_recorded":"v188_frontier_wording_guard.py","status_as_recorded":"Identity/guard [I] (prose sentinel against semantic drift)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical [N]: joint null probability <= 1e-30.7 conditional on the declared grammar","checked_by_registry":false,"claim_excerpt":"NUMEROLOGY NULL TEST (look-elsewhere corrected; executes the legacy 'numerology grammar test' TODO from the CMB paper): (A) EXACT CENSUS - for each of the 13 scored frozen-registry observables the FULL declared grammar class (one-term (p/q) phi0^a lamC^c (1+lamC)^d pi^b e^(u/w) with p,q<=130, |a|<=2, |c|<=3, |d|,|b|<=1, |u|<=6, w<=6; two-term sums with coefficients<=12; machine-checked fairness: the class contains ev","claim_id":"AUDIT.NULLMC.01","dependencies_as_recorded":"REG.FREEZE.01 (scored predictions = frozen registry); DATA.SCORECARD.01 (documented data centrals)","external_data_as_recorded":"CODATA 2022 alpha^-1; NuFIT 6.0; ACT DR6; PDG/FLAG centrals (all as already documented in-repo)","id":"claim:AUDIT.NULLMC.01","location_as_recorded":"introduction;tfpt_3;tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":183,"scripts_as_recorded":"v100_numerology_null_mc.py","status_as_recorded":"Numerical [N] (statistical null-model rejection; Python-only)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: six atom landings in SdS mechanics; bulk reading [P]","checked_by_registry":false,"claim_excerpt":"THE MAXIMAL BLACK HOLE IS THE ANCHOR (carrier-in-the-bulk surface; Schwarzschild-de Sitter in seam units): (1) NARIAI = ANCHOR - at M_N = 1/(N_fam sqrt(L)) the horizon cubic is t^3-3t+2 = (t-1)^2(t+2), roots (1,1,-2) = the traceless projection of the anchor a=(1,1,2) (coefficients (-3,2) = (-N_fam,|Z2|); cf chi_a = (t-1)^2(t-2), ARCH.CORE.01). (2) the Koide 2/3 IS the Nariai entropy bound: S/horizon = S_dS/N_fam, tot","claim_id":"HOR.NARIAI.01","dependencies_as_recorded":"AX.P1.01; ARCH.CORE.01 (anchor); FLAV.PENCIL.03 (cover); FR.KOIDE.04 (orientation); HOR.01; GATE.METRIC.07 (SU(4)_1 weights)","external_data_as_recorded":"standard GR (SdS metric); photon/geometric-optics Hawking conventions","id":"claim:HOR.NARIAI.01","location_as_recorded":"tfpt_horizon_readouts;origin_theory;tfpt_2","path":"verification/status_ledger.csv","row_number":184,"scripts_as_recorded":"v101_horizon_anchor.py","status_as_recorded":"Identity [I] (exact GR arithmetic on compiler atoms) + Physical [P] (bulk reading)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: anchor = stationary repeller both sectors; principle reading [P]","checked_by_registry":false,"claim_excerpt":"ONE ORIENTATION - the anchor is the stationary repeller in BOTH sectors (variational upgrade of the v101 temperature lemma + the v82/v99 flavor flow): FLAVOR [I] - the canonical flow dq/dt = (Delta/N_fam)(q-2)(q-5) is the GRADIENT flow of the cubic V(q) = -(Delta/N_fam)(q^3/3 - 7q^2/2 + 10q); critical points = exactly the two branch points; stationary curvatures = +-the transfer gap (V''(Koide) = +Delta attractor, V'","claim_id":"HOR.ORIENT.01","dependencies_as_recorded":"HOR.NARIAI.01; FR.KOIDE.04; FR.KOIDE.06 (generator); FLAV.PENCIL.03","external_data_as_recorded":"standard GR (SdS); second law under net evaporation","id":"claim:HOR.ORIENT.01","location_as_recorded":"tfpt_horizon_readouts;origin_theory","path":"verification/status_ledger.csv","row_number":185,"scripts_as_recorded":"v102_seam_orientation.py","status_as_recorded":"Identity [I] (variational structure both sides) + Physical [P] (common-principle reading)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: one cosine of glue atoms; canonical curvature (2/3)^N_fam; clock [P]","checked_by_registry":false,"claim_excerpt":"TRISECTION NORMAL FORM (the canonical coordinate of the SdS moduli line; answers the HOR.ORIENT.01 curvature-matching question at the geometric level): the horizon cubic is uniformized by ANGLE TRISECTION - r = 2cos(theta) gives r^3-3r = 2cos(3theta) exactly, cubic <=> cos(3theta) = -3m; centered angle psi: m = cos(psi)/N_fam, Nariai psi=0, pure dS psi=pi/2; deck involution psi->-psi (= the x->1/x deck of HOR.NARIAI.","claim_id":"HOR.TRISECT.01","dependencies_as_recorded":"HOR.NARIAI.01; HOR.ORIENT.01; FR.KOIDE.04 (rate); GATE.QGEOM.02 (triality)","external_data_as_recorded":"standard GR (SdS)","id":"claim:HOR.TRISECT.01","location_as_recorded":"tfpt_horizon_readouts","path":"verification/status_ledger.csv","row_number":186,"scripts_as_recorded":"v103_trisection_normal_form.py","status_as_recorded":"Identity [I] (uniformization, normal form, curvature, slope) + Physical [P] (clock bridge)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: clock spectrum = anchor roots; quantum clock = the one [P]","checked_by_registry":false,"claim_excerpt":"THE CLASSICAL NARIAI CLOCK IS THE ANCHOR (third appearance) + honest (2/3)-test (executes the HOR.TRISECT.01 clock question at the classical level): STATIC PIN [I] - phi(rho) = rho solves d/drho[(1-L rho^2)phi'] = -2L phi EXACTLY on the dS2 static patch, so the exact SdS family itself pins the S^2-radius modulus mass m^2 = -2L = -|Z2|L (the Laplace-type form of the Nariai linearization is standard GR - Ginsparg-Perry","claim_id":"HOR.CLOCK.01","dependencies_as_recorded":"HOR.TRISECT.01; HOR.ORIENT.01; HOR.NARIAI.01; ARCH.CORE.01 (anchor)","external_data_as_recorded":"standard GR (Nariai linearization Laplace-type: Ginsparg-Perry 1983; Bousso-Hawking 1997)","id":"claim:HOR.CLOCK.01","location_as_recorded":"tfpt_horizon_readouts","path":"verification/status_ledger.csv","row_number":187,"scripts_as_recorded":"v104_nariai_clock.py","status_as_recorded":"Identity [I] (static pin, tower, clock spectrum, rate) + Physical [P] (quantum clock)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Residual inventory: 5 named structural objects + 1 scale + pi; completeness machine-pinned","checked_by_registry":false,"claim_excerpt":"THE RESIDUAL INVENTORY (one constant, one anchor, one clock to find; the COMPLETE machine-pinned gap list): (A) ONE-CONSTANT INVENTORY [I] - 2/3 = |Z2|/N_fam appears exactly in seven independent places across both sectors (flavor: Koide branch point, transfer-gap base (2/3)^6, attractor inside the physical basin; gravity: Nariai entropy bound, SdS branch separation, canonical amplitude+frequency, canonical curvature ","claim_id":"SYNTH.INVENTORY.01","dependencies_as_recorded":"HOR.CLOCK.01; HOR.TRISECT.01; HOR.NARIAI.01; HOR.ORIENT.01; FR.KOIDE.04/05/06; GATE.METRIC.05-07; GATE.RU.01; GATE.QGEO.01; ANCHOR.VGEO.01; REG.FREEZE.01","external_data_as_recorded":"frozen rho_Lambda (v84); 2D trace anomaly <T> = cR/(24pi) (standard)","id":"claim:SYNTH.INVENTORY.01","location_as_recorded":"origin_theory;introduction","path":"verification/status_ledger.csv","row_number":188,"scripts_as_recorded":"v105_residual_inventory.py","status_as_recorded":"Identity [I] (inventory + relocation arithmetic) + typing contract (gap completeness)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: seed NF + factorial spine + degree-2 inventory; locality hypothesis [P] named","checked_by_registry":false,"claim_excerpt":"EXTERNAL-REVIEW VALIDATION + the DEGREE-2 pattern named: (1) SEED NORMAL FORM [I] - phi0 = (|mu4|/N_fam) c3 + Omega_adm c3^|mu4| exactly: the seed is a linear seam term plus a topological fourth-order correction over all admissible fermion states (4/3 = |mu4|/N_fam, 48 = Omega_adm = N_fam dim S+, exponent 4 = |mu4|) - a structured anchor readout, not a fitted formula. (2) HYPERCHARGE SECOND MOMENT [I] computed from t","claim_id":"ARCH.QUAD.01","dependencies_as_recorded":"ARCH.CORE.01 (anchor); CAR.PASCAL.01 / REDTEAM.B.01 (the residual it names); FLAV.MASSVOL.01; HOR.01 (1920); REG.FREEZE.01; v100","external_data_as_recorded":"-","id":"claim:ARCH.QUAD.01","location_as_recorded":"tfpt_1;introduction","path":"verification/status_ledger.csv","row_number":189,"scripts_as_recorded":"v106_review_validation.py","status_as_recorded":"Identity [I] (seed NF, moment, spine, inventory) + [P] (named locality hypothesis) + audit","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: clock lives on the cusp ladder; exact bend target; [P] identification open","checked_by_registry":false,"claim_excerpt":"QUANTUM-CLOCK TARGET (R1 made quantitative; nothing fitted): the Ginsparg-Perry multi-mode clock has per-l equations lambda^2+lambda+(l(l+1)-2)=0 - l=0 anchor pair {1,-2}, l=1 zero modes {0,-1}, l>=2 complex with Re=-1/2=-delta (audit). NEW CROSS-LINK [I]: the classical decay set (l=0,1) = {0,-1,-2} = -Spec(V) = -N_fam x cusp weights - the classical seam clock decays exactly on the grading that carries the transfer o","claim_id":"HOR.CLOCK.02","dependencies_as_recorded":"HOR.CLOCK.01; SYNTH.INVENTORY.01 (R1); FLAV.QGEO.01; FLAV.DIAMOND.02 (Spec V); FR.KOIDE.04","external_data_as_recorded":"standard GR (Ginsparg-Perry tower); 2D trace anomaly normalisation","id":"claim:HOR.CLOCK.02","location_as_recorded":"tfpt_horizon_readouts","path":"verification/status_ledger.csv","row_number":190,"scripts_as_recorded":"v107_quantum_clock_target.py","status_as_recorded":"Identity [I] (tower, cross-link, target arithmetic, coupling) + Physical [P] (identification)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: g=5 <=> K=2 exactly; Target B residual = one hypothesis (QBL)","checked_by_registry":false,"claim_excerpt":"PASCAL LADDER THEOREM (Target B residual sharpened to zero slack): the closure 2^{g-1} = sum_{k<=K} C(g,k) has for every K exactly one solution g = 2K+1 (K=1..6 scanned over g=1..60; structurally: odd-g midpoint identity by binomial symmetry, even-g strict straddle around 2^{g-1} excludes all even g). EXACT EQUIVALENCE [I]: the carrier selection g=5 <=> the truncation degree K=2 - the Pascal-selection residual (CAR.P","claim_id":"CAR.LADDER.01","dependencies_as_recorded":"CAR.PASCAL.01; REDTEAM.B.01; ARCH.QUAD.01 (QBL named); CAR.UNIQ.01 (v14)","external_data_as_recorded":"-","id":"claim:CAR.LADDER.01","location_as_recorded":"tfpt_3_e8_audit_bootstrap;tfpt_1","path":"verification/status_ledger.csv","row_number":191,"scripts_as_recorded":"v108_pascal_ladder.py","status_as_recorded":"Identity/Lattice [I]/[L] (ladder, equivalence, controls, overdetermination) + [P] (QBL)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Formal: anchor ladder general; Pascal ladder solves-side general + K=2 bounded uniqueness","checked_by_registry":false,"claim_excerpt":"LEAN FORMALISATION of the anchor ladder and the Pascal ladder (hardening round, 2026-06-11): new modules TfptCarrier/AnchorLadder.lean and TfptCarrier/PascalLadder.lean, built and audited with the existing project (lake build 3353 jobs; scripts/audit.sh AUDIT: PASS - no sorry/axiom/unsafe, only the three standard kernel axioms). AnchorLadder: p_n(a) = 2 + 2^n for ALL n (general theorem, not a finite check); ladder at","claim_id":"FORM.LADDER.01","dependencies_as_recorded":"ARCH.CORE.01; CAR.LADDER.01; FORM.P2.02","external_data_as_recorded":"-","id":"claim:FORM.LADDER.01","location_as_recorded":"tfpt_1;tfpt_3_e8_audit_bootstrap","path":"verification/status_ledger.csv","row_number":192,"scripts_as_recorded":"lean4-carrier-rigidity (AnchorLadder.lean, PascalLadder.lean)","status_as_recorded":"Formal [F] (Lean kernel; no extra axioms)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: scalar pairing only across sheets; even tower tops at 2K; QBL anchored","checked_by_registry":false,"claim_excerpt":"SHEET-PAIRING LEMMA (the first exact representation-theoretic anchor of the QBL programme; connects red-team Target B to the sheet Z2): character-exact weight-multiset results from the D5 spinor weights (+-1/2)^5 alone - (1) NO SCALAR WITHIN A SHEET: zero-weight multiplicity of S+xS+ (and S-xS-) is 0, because the odd slot count g=5 flips the sign parity of -w (a parity theorem of the five-slot code): there is no inva","claim_id":"CAR.PAIR.01","dependencies_as_recorded":"CAR.LADDER.01; ARCH.QUAD.01 (QBL); GATE.METRIC.07 (sheet Z2); FLAV.SHEET.01-03; CAR.PASCAL.01","external_data_as_recorded":"-","id":"claim:CAR.PAIR.01","location_as_recorded":"tfpt_1","path":"verification/status_ledger.csv","row_number":193,"scripts_as_recorded":"v109_sheet_pairing.py","status_as_recorded":"Identity [I] (character-exact multiset identities) + Physical [P] (QBL reading)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: scalar kernel exists iff involution is sheet-odd; 2 = |Z2| kernels = glue ambiguity; QBL residue split into interface + analytic core","checked_by_registry":false,"claim_excerpt":"CALDERON-SHEET SELECTION THEOREM (which Calderon involutions certify a scalar kernel; the v109 follow-up): on the carrier H = S+ (+) S- the certified bilinear data of an involution eps (eps^2 = 1) are the matrix elements <f, eps g>; the v109 singlet counts per sheet block (0, 0, 1, 1) give the exact selection statement - (1) SELECTION THEOREM [I] (finite model): a sheet-ODD involution (swapping S+ <-> S-) certifies E","claim_id":"CAR.PAIR.02","dependencies_as_recorded":"CAR.PAIR.01; CAR.LADDER.01; ARCH.QUAD.01 (QBL); GLUE.LAGR.01 (two glues); GATE.METRIC.07 (sheet Z2)","external_data_as_recorded":"-","id":"claim:CAR.PAIR.02","location_as_recorded":"tfpt_1","path":"verification/status_ledger.csv","row_number":194,"scripts_as_recorded":"v110_calderon_sheet.py","status_as_recorded":"Identity [I] (finite-model selection theorem + ladder control) + Physical [P] (residue typing)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Theorem: transport degree exactly 2 (minimal complete grade); QBL residue reduced to two interface statements","checked_by_registry":false,"claim_excerpt":"QUADRATIC-TRANSPORT THEOREM (the transport half of the QBL analytic core becomes a theorem): grade seam transport by Clifford degree in the 10 field operators on the 5-slot Fock space (S = Lambda^*(C^5), 32-dim, S+ = 16 code states; integer Jordan-Wigner model, spanning claims via full-rank certificates mod p = 1000003, valid over Q) - (1) PARITY [exact block-zero]: all 10 linear words are sheet-ODD (map S+ -> S-), a","claim_id":"CAR.QTRANS.01","dependencies_as_recorded":"CAR.PAIR.01; CAR.PAIR.02; CAR.LADDER.01; ARCH.QUAD.01 (QBL); CAR.RANK","external_data_as_recorded":"-","id":"claim:CAR.QTRANS.01","location_as_recorded":"tfpt_1","path":"verification/status_ledger.csv","row_number":195,"scripts_as_recorded":"v111_quadratic_transport.py","status_as_recorded":"Identity [I] (exact finite theorem; mod-p certificates valid over Q) + Physical [P] (residue typing)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: Pascal closure = two countings of the channel's neutral set; one kernel per code state; QBL residue = single 2-point-kernel input","checked_by_registry":false,"claim_excerpt":"SELF-COUNTING CHANNEL (the Pascal closure is an IDENTITY of the certified channel, not an extra requirement; closes the state half of the QBL analytic core at the structural level): (1) CANONICAL BIJECTION [I] - for odd g negation w -> -w maps the S+ weights bijectively into the opposite sheet (the CAR.PAIR.01 parity stated as a bijection), so the Cartan-neutral kernels of the certified channel S+xS- are exactly the ","claim_id":"CAR.COUNT.01","dependencies_as_recorded":"CAR.PAIR.01; CAR.PAIR.02; CAR.QTRANS.01; CAR.LADDER.01; CAR.RANK; ARCH.QUAD.01 (QBL)","external_data_as_recorded":"-","id":"claim:CAR.COUNT.01","location_as_recorded":"tfpt_1","path":"verification/status_ledger.csv","row_number":196,"scripts_as_recorded":"v112_selfcounting_channel.py","status_as_recorded":"Identity [I] (bijection + exact multiset gradings + symbolic binomial identity) + Physical [P] (residue re-type)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: one quasi-free kernel determines the whole net (rank = c); QBL input = R2 premise; upgrade contract R2 => carrier [L]","checked_by_registry":false,"claim_excerpt":"ONE KERNEL IS THE WHOLE NET (the QBL input merges with the R2/holomorphy premise; anchors the carrier choice to the Gate-A objects): (1) MAJORANA BOOKKEEPING [I] - level-1 central charges c(D5)_1 = 45/9 = 5 = g_car, c(A3)_1 = 15/5 = 3 = N_fam, c(SO16)_1 = 120/15 = 8, c(E8)_1 = 248/31 = 8; the carrier net (D5)_1 x (A3)_1 = SO(10)_1 x SO(6)_1 = 10 + 6 = 16 FREE MAJORANA FERMIONS with c = 16/2 = 8; the whole extension t","claim_id":"CAR.QFREE.01","dependencies_as_recorded":"CAR.PAIR.02; CAR.COUNT.01; CAR.QTRANS.01; ARCH.QUAD.01 (QBL); GATE.METRIC.03-07 (Gate A); CAR.LADDER.01","external_data_as_recorded":"-","id":"claim:CAR.QFREE.01","location_as_recorded":"tfpt_1; tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":197,"scripts_as_recorded":"v113_quasifree_kernel.py","status_as_recorded":"Identity [I] (exact Pfaffian/Wick + polarization theorems + bookkeeping) + Physical [P] (premise merge)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Theorem: delta = 1/2 is a mu4-torsion identity on the involutive branch; flatness = (MU)^4 = 1 normal form; residue = bundle-side branch selection","checked_by_registry":false,"claim_excerpt":"TORSION NORMAL FORM + THE DELTA = 1/2 THEOREM (executes the GATE.UWALL.05 'genericity future work'; the distinguished lepton transport value delta = 1/2 stops being a point observation): (1) FLATNESS = mu4 TORSION [I, symbolic generic M] - prod_k U^k M U^{-k} = (MU)^4 exactly, so the Z4-family flatness constraint of the (U_wall) bundle IS the torsion statement 'T = MU is a fourth root of unity': the mu_4 atom appears","claim_id":"GATE.UWALL.06","dependencies_as_recorded":"GATE.UWALL.04; GATE.UWALL.05; FLAV.DELTA.01; v20; v30; v33","external_data_as_recorded":"-","id":"claim:GATE.UWALL.06","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":198,"scripts_as_recorded":"v114_torsion_delta.py","status_as_recorded":"Identity [I] (symbolic theorems) + Numerical [N] (branch census) + Physical [P] (residue)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Exact residue normal form A0* (diag = anchor/mu4 spectrum = cusp weights off-weights = (8 0 5)/144); anchor forces d1 = 0; residue = Groebner promotion","checked_by_registry":false,"claim_excerpt":"THE ANCHOR PINS THE RESIDUE (exact normal form for the U_wall flat-bundle residue; answers the GATE.UWALL.06 branch question): (1) MU4-AVERAGE LEMMA [I, symbolic generic X] - sum_k U^k X U^{-k} = 4 diag(X): mu_4 conjugation-averaging is the diagonal projection, so the exponents at infinity are 4 diag(A0) and the anchor splitting O(-2)+O(-1)^2 holds IFF diag A0 = (2,1,1)/4 = a/|mu_4| - the residue diagonal IS the anch","claim_id":"GATE.UWALL.07","dependencies_as_recorded":"GATE.UWALL.06; GATE.UWALL.04; v33; v40; CONTRACT.U.01","external_data_as_recorded":"-","id":"claim:GATE.UWALL.07","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":199,"scripts_as_recorded":"v115_anchor_residue.py","status_as_recorded":"Identity [I] (mu4-average + (8 0 5)/144 + exact normal form) + Numerical [N] (RH verification + uniqueness scan) + Physical [P] (residue)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Theorem: M_inf = 1 <=> a13 = 0 (resonance obstruction); flat anchor locus = one gauge orbit = exact A0*; U_wall bundle datum algebraically unique","checked_by_registry":false,"claim_excerpt":"RESONANCE THEOREM (the GATE.UWALL.07 [N] findings promoted to [I] by a LINEAR computation - the anticipated Groebner step turned out unnecessary): (1) TWISTED-AVERAGE LEMMA [I, symbolic generic A0]: at infinity the equivariant Fuchsian system reads dY/dw = -(1/w)(B0 + B1 w + ...)Y with B_m = sum_k i^{km} U^k A0 U^{-k}; the twisted mu_4 averages collapse to B0 = 4 diag(A0) and B1 = 4 a12 E_12 + 4 conj(a13) E_31 - only","claim_id":"GATE.UWALL.08","dependencies_as_recorded":"GATE.UWALL.07; GATE.UWALL.06; v19; v30; CONTRACT.U.01","external_data_as_recorded":"-","id":"claim:GATE.UWALL.08","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":200,"scripts_as_recorded":"v116_resonance_uniqueness.py","status_as_recorded":"Identity [I] (twisted average + resonance theorem + uniqueness) + Numerical [N] (sharpness control) + Physical [P] (scope)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Theorem: U_wall monodromy group = W(A3) = S4 (order 24 exact); diag M0 = (0 -i/2 i/2) exact - delta = 1/2 and d1 = 0 are matrix entries; only ODE identification stays [N]","checked_by_registry":false,"claim_excerpt":"THE MONODROMY IS THE WEYL GROUP OF A3 (the U_wall holonomy is an EXACT 24-element representation; the harmonic diagonal becomes a theorem): (1) THE EXACT MONODROMY [I]: M0 = [[0, -(1+i)/2, (1-i)/2], [-(1+i)/2, -i/2, -1/2], [(1-i)/2, -1/2, i/2]] (entries in (1/2)Z[i]) is unitary with det 1, tr 0, char poly lam^3 - 1 (the cusp class {1,w,w^2} EXACT), M0^3 = 1, and diag M0 = (0, -i/2, +i/2) - d1 = 0 AND delta = 1/2 are ","claim_id":"GATE.UWALL.09","dependencies_as_recorded":"GATE.UWALL.08; GATE.UWALL.07; GATE.UWALL.06; E8.GLU.01 (A3 factor); CONTRACT.U.01","external_data_as_recorded":"-","id":"claim:GATE.UWALL.09","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":201,"scripts_as_recorded":"v117_monodromy_weyl_a3.py","status_as_recorded":"Identity [I] (exact matrix + exact group enumeration) + Numerical [N] (ODE identification) + Physical [P] (status)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: hexagon = spec(M0) u spec(-M0); lepton 7 and 9 = det(1 -+ M0/2) x 8; product rule = mu4/det+; H2 values exact - address table open","checked_by_registry":false,"claim_excerpt":"THE HEXAGON IS THE SIGN-TWISTED FAMILY SPECTRUM (first exact piece of the H2 dictionary; the v20 lepton coefficients are resolvent determinants of the exact W(A3) monodromy GATE.UWALL.09): (1) SIGN-TWIST LEMMA [I]: -M0 has order 6 ((-M0)^3 = -1) and spec(M0) u spec(-M0) = mu_6 - the 6-site hypercharge hexagon spectrum IS the family monodromy spectrum together with its sheet twist, Z6 = Z2 x Z3 realised as (-1) x <M0>","claim_id":"FLAV.H2.02","dependencies_as_recorded":"GATE.UWALL.09; FLAV.H2.01; v20 (leg assignment); ARCH.QUAD.01 (Omega_adm); E8.GLU.01","external_data_as_recorded":"-","id":"claim:FLAV.H2.02","location_as_recorded":"tfpt_research_contracts; tfpt_2","path":"verification/status_ledger.csv","row_number":202,"scripts_as_recorded":"v118_hexagon_family_dictionary.py","status_as_recorded":"Identity [I] (exact spectral + determinant identities + group enumeration) + Physical [P] (address table)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: anchor ratio triad (2/3 4/3 5/3) = e/p0; 121 = anchor norm of R (audit); micro-identities exact","checked_by_registry":false,"claim_excerpt":"SECOND EXTERNAL-REVIEW VALIDATION (2026-06-11b): the anchor ratio triad, the 121 audit lemma and the normal-form micro-identities, all exact: (1) MICRO-IDENTITIES [I]: Omega_adm = 2 p1 p2 = 48; 10 b1 = 1 + p1 p3 = 41; Delta_Y = e2^2 = p0^2 + 2 rank E8 = 25; h(E8) = e3 p0 e2 = 30; rank E8 = p0 + e2 = 8; |R(E8)| = p1 p2 p3 = 240; dim E8 = 240 + (p4 - p3) = 248. (2) ANCHOR RATIO TRIAD [I] (named lemma): the three elemen","claim_id":"ARCH.TRIAD.01","dependencies_as_recorded":"ARCH.QUAD.01; FLAV.KQ.01; FLAV.DIAMOND.01-02; FR.KOIDE.06; SYNTH.INVENTORY.01","external_data_as_recorded":"-","id":"claim:ARCH.TRIAD.01","location_as_recorded":"introduction; tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":203,"scripts_as_recorded":"v119_review_validation_2.py","status_as_recorded":"Identity [I] (exact arithmetic/matrix identities; audit typing for the 121 lemma)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: lepton words = (rank g N); addresses = divmod hexagon; quark sums = (p3 p1+p3 |W(A3)| p1p3); assignment derivation open","checked_by_registry":false,"claim_excerpt":"THE ADDRESS TABLE (the open FLAV.H2.02 item structured; exact arithmetic on FROZEN v18/v20 integers): (1) THE LEPTON WORDS ARE THE COMPILER ATOMS [I]: (L_e, L_mu, L_tau) = (8, 5, 3) = (rank E8, g_car, N_fam) = (p0+e2, e2, p0), in mass order (longest word = lightest lepton). (2) ADDRESSES = EUCLIDEAN DIVISION BY THE HEXAGON [I]: (r, w) = L divmod p2 with p2 = 6 = |R+(A3)| itself an atom: e -> (2,1), mu -> (5,0), tau -","claim_id":"FLAV.H2.03","dependencies_as_recorded":"FLAV.H2.02; GATE.UWALL.09; ARCH.TRIAD.01; v18 (quark words); v20 (lepton words)","external_data_as_recorded":"-","id":"claim:FLAV.H2.03","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":204,"scripts_as_recorded":"v120_address_table.py","status_as_recorded":"Identity [I] (exact arithmetic on frozen integers) + Physical [P] (per-fermion derivation)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Theorem: R = unique hexagon matrix with atom margins + det 8; address table = R + first-generation winding; H2 residue = the margins","checked_by_registry":false,"claim_excerpt":"THE ADDRESS TABLE IS PINNED (the FLAV.H2.03 per-fermion item closed at the information level; exact census theorem): (1) THE WORD TABLE IS THE RESIDUE OPERATOR [I]: the established identity L = R + 2U (FLAV.DIAMOND.02, U = winding axis N_fam 1 e_1^T) says the word-length table IS L[sector][generation] with rows (up; down; lepton) = ((7,3,0); (7,5,2); (8,5,3)) = the v18/v20 word lengths verbatim; the addresses are R's","claim_id":"FLAV.H2.04","dependencies_as_recorded":"FLAV.H2.03; FLAV.DIAMOND.02 (L = R + 2U); FLAV.H2.01; ARCH.TRIAD.01; v18; v20; v71","external_data_as_recorded":"-","id":"claim:FLAV.H2.04","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":205,"scripts_as_recorded":"v121_address_pinning.py","status_as_recorded":"Identity [I] (exact census/uniqueness theorem on frozen operators) + Physical [P] (margins)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Theorem: established selectors (n-annihilator + det R = 8 + det K = 4) pin R uniquely; margins + anchor column + sum rules = consequences; det L = 20 automatic","checked_by_registry":false,"claim_excerpt":"THE MARGINS ARE THEOREMS (the FLAV.H2.04 residue closed: the established frozen selectors pin R uniquely - the atom margins lose their input status): THREE ESTABLISHED SELECTORS, all frozen pre-v120 - (S1) the D4 annihilator n = (5,-9,6) with n^T R = (8,0,0) (FLAV.DIAMOND.01/tfpt_2: n kills the unchanged (c2,c3) plane; n.a = 8); (S2) det R = 8 = rank E8 (v71 determinant quartet (3,4,8,20), product 1920 = |W(D5)|); (S","claim_id":"FLAV.H2.05","dependencies_as_recorded":"FLAV.H2.04; FLAV.DIAMOND.01-02; v71 (quartet); v94 (annihilator); CONTRACT.U.01","external_data_as_recorded":"-","id":"claim:FLAV.H2.05","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":206,"scripts_as_recorded":"v122_margin_theorem.py","status_as_recorded":"Identity [I] (exact census on frozen selectors) + Physical [P] (selector establishment)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Inventory: five classes re-pinned (R1 clock; R2 index-4 net with 3 loads; R3 EH; R4' selectors; R5 Q); flavor side discharged; sixth class fails the script","checked_by_registry":false,"claim_excerpt":"RESIDUAL INVENTORY UPDATED (post v110-v122; supersedes the CONTENTS of SYNTH.INVENTORY.01 while keeping its cardinality): (1) thirteen new ledger rows machine-pinned (CAR.PAIR.02, CAR.QTRANS.01, CAR.COUNT.01, CAR.QFREE.01, GATE.UWALL.06-09, FLAV.H2.02-05, ARCH.TRIAD.01). (2) R2 CARRIES THREE LOADS: the single index-4 boundary-net statement closes, when proven, the metric gate (GATE.METRIC.06), the carrier choice (CAR","claim_id":"SYNTH.INVENTORY.02","dependencies_as_recorded":"SYNTH.INVENTORY.01; GATE.METRIC.06; CAR.QFREE.01; ARCH.QUAD.01; FLAV.H2.05; HOR.CLOCK.02; GATE.QGEO","external_data_as_recorded":"-","id":"claim:SYNTH.INVENTORY.02","location_as_recorded":"origin_theory; introduction","path":"verification/status_ledger.csv","row_number":207,"scripts_as_recorded":"v123_inventory_update.py","status_as_recorded":"Identity [I] (machine bookkeeping + typing contract)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Terminal inventory: (A) no longer a class; ONE hinge (A2+GATE.QGEO) + F_transfer + irreducible {pi,v_geo}; Tier 2 folded; sixth class fails the script","checked_by_registry":false,"claim_excerpt":"TERMINAL RESIDUAL INVENTORY (post premise-(A) closure; supersedes the CONTENTS of SYNTH.INVENTORY.02): after the (A)-chain (v160-v165) premise (A) is NO LONGER an independent structural class. (1) (A) CLOSED AS A CLASS - the four (A)-closure rows exist (GATE.METRIC.16 fixed-point theorem; .17 cone eliminated, cone gap = one-particle gap; .18 numbers forced by mu4-equivariance; .19 factors into A2 + GATE.QGEO + irredu","claim_id":"SYNTH.INVENTORY.03","dependencies_as_recorded":"SYNTH.INVENTORY.02; GATE.METRIC.16; GATE.METRIC.17; GATE.METRIC.18; GATE.METRIC.19; ANCHOR.VGEO.02; FR.ETAB.01","external_data_as_recorded":"-","id":"claim:SYNTH.INVENTORY.03","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":208,"scripts_as_recorded":"v167_inventory_post_closure.py","status_as_recorded":"Identity [I] (machine bookkeeping + typing contract; ledger-row membership)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: transfer spectrum = (1 - n/N)^6; rate = -6 ln(1 - n/3); linearisation slope |Z2|; pole at N_fam forces three levels; R1 target now closed-form","checked_by_registry":false,"claim_excerpt":"THE RESUMMED CLOCK (R1's bend acquires a closed form; the HOR.CLOCK.02 job description transforms): (1) THE SPECTRUM READS (1 - n/N)^{p2} [I]: the frozen transfer eigenvalues {1, (2/3)^6, (1/3)^6} (v54/v69/v95) are EXACTLY lambda_n = (1 - n/N_fam)^{p2} for n = 0, 1, 2, with p2 = 6 = |R+(A3)| the hexagon size. (2) CLOSED-FORM CLOCK [I]: rate(n) = -p2 ln(1 - n/N_fam) reproduces {0, Delta, 6 ln 3} exactly; the HOR.CLOCK","claim_id":"HOR.CLOCK.03","dependencies_as_recorded":"HOR.CLOCK.02; HOR.CLOCK.01; FR.KOIDE.06 (transfer spectrum); SYNTH.INVENTORY.02 (R1)","external_data_as_recorded":"-","id":"claim:HOR.CLOCK.03","location_as_recorded":"tfpt_horizon_readouts","path":"verification/status_ledger.csv","row_number":209,"scripts_as_recorded":"v124_resummed_clock.py","status_as_recorded":"Identity [I] (exact spectral reading + series) + Physical [P] (semiclassical derivation)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: C[Z4] is a special Frobenius algebra (Longo Q-system) of index 4 = |mu4|; locality = isotropy; halfway C[Z2] = SO(16)_1; R2 = identification of constructed objects","checked_by_registry":false,"claim_excerpt":"THE GLUE Q-SYSTEM (the index-4 mu4 extension exists as an explicit Longo Q-system; the R2 gate sharpens from 'find a Q-system' to 'match the constructed one'): (1) Q-SYSTEM AXIOMS [I] on A = C[Z4] (the glue group algebra; multiplication delta_a x delta_b -> delta_{a+b}, unit delta_0): associativity, unit law, FROBENIUS (m x 1)(1 x m*) = m* m = (1 x m)(m* x 1), and SPECIALNESS m m* = |Z4| id all hold exactly => a spec","claim_id":"GATE.METRIC.08","dependencies_as_recorded":"GATE.METRIC.06; GATE.METRIC.07; CAR.QFREE.01; SYNTH.INVENTORY.02 (R2)","external_data_as_recorded":"-","id":"claim:GATE.METRIC.08","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":210,"scripts_as_recorded":"v125_glue_qsystem.py","status_as_recorded":"Identity [I] (exact finite Frobenius/Q-system axioms + isotropy) + Physical [P] (identification)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: clock weights = parabolic weights (spec A0*); lambda = (1-alpha)^6; linear term = classical entropy rate |Z2|H; det(1-A0*) = entropy curvature 2/9; quantum content = geometric tail","checked_by_registry":false,"claim_excerpt":"THE CLOCK AND THE WALL SHARE A SPECTRUM (the v124 resummed-clock weights ARE the Mehta-Seshadri parabolic weights; R1's first checkpoint passes classically): (1) THE WEIGHTS ARE THE PARABOLIC WEIGHTS [I]: the arguments n/N_fam = {0, 1/3, 2/3} of the resummed logarithm are EXACTLY spec A0* (the exact U_wall residue, GATE.UWALL.07); the spectral bridge lambda_n = (1 - alpha_n)^{p2} over alpha in spec A0* reproduces the","claim_id":"HOR.CLOCK.04","dependencies_as_recorded":"HOR.CLOCK.03; HOR.CLOCK.01; HOR.ORIENT.01; GATE.UWALL.07 (A0*); SYNTH.INVENTORY.02 (R1)","external_data_as_recorded":"-","id":"claim:HOR.CLOCK.04","location_as_recorded":"tfpt_horizon_readouts","path":"verification/status_ledger.csv","row_number":211,"scripts_as_recorded":"v126_clock_wall_bridge.py","status_as_recorded":"Identity [I] (exact spectral bridge + coefficient identities) + Physical [P] (re-target)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: clock = -p2 Tr ln(1 - alpha P) (ring/RPA determinant; one tower per hexagon site); k=1 ring = classical entropy rate; wall = RPA instability; kappa = alpha_1/pi","checked_by_registry":false,"claim_excerpt":"THE CLOCK IS A LOG-DETERMINANT (the geometric tail of HOR.CLOCK.03/04 is the standard ring/RPA resummation; the 'O(1) resummation' demanded by HOR.CLOCK.02 is now TYPED): (1) LOG-DET IDENTITY [I]: for a rank-1 insertion P (tr P^k = 1), -ln det(1 - alpha P) = -ln(1 - alpha) = sum_k alpha^k/k - so the resummed clock is EXACTLY rate = -p2 Tr ln(1 - alpha P): p2 = 6 identical one-loop ring towers, ONE PER HEXAGON SITE (=","claim_id":"HOR.CLOCK.05","dependencies_as_recorded":"HOR.CLOCK.04; HOR.CLOCK.03; HOR.CLOCK.02; FLAV.H2.02 (hexagon); SYNTH.INVENTORY.02 (R1)","external_data_as_recorded":"-","id":"claim:HOR.CLOCK.05","location_as_recorded":"tfpt_horizon_readouts","path":"verification/status_ledger.csv","row_number":212,"scripts_as_recorded":"v127_ring_resummation.py","status_as_recorded":"Identity [I] (log-det + ring ladder + coupling arithmetic) + Physical [P] (derivation)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: E8 = Z4-graded Lie algebra over the carrier (grading = glue Q-system; 6720 pair checks); ring multiplicity 6 = sheet-doubled GP zero modes","checked_by_registry":false,"claim_excerpt":"THE GRADED HULL + THE ZERO-MODE MULTIPLICITY (both named computations gain their structural anchors): R2 HALF - (1) EXPLICIT COSET CONSTRUCTION [I]: the 240 E8 roots, built as explicit norm-2 vectors in D5 (+) A3 + glue coordinates, decompose over the glue group Z4 as 240 = 52 + 64 + 60 + 64 (C0 = carrier roots 40+12; C1 = (16, 4bar) from norm 5/4 + 3/4; C2 = (10, 6) from 1 + 1; C3 = (16bar, 4)) - exactly the GATE.ME","claim_id":"E8.GRADE.01","dependencies_as_recorded":"GATE.METRIC.08; GATE.METRIC.06; HOR.CLOCK.05; HOR.CLOCK.01; E8.GLU.01","external_data_as_recorded":"-","id":"claim:E8.GRADE.01","location_as_recorded":"tfpt_research_contracts; tfpt_horizon_readouts","path":"verification/status_ledger.csv","row_number":213,"scripts_as_recorded":"v128_graded_hull.py","status_as_recorded":"Identity [I] (explicit construction + exact grading + arithmetic) + Physical [P] (anchors)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: lambda = (S/S_dS)^p2; rate = p2 ln(S_dS/S); alpha = entropy-deficit fraction = parabolic weight; orientation consistent; R1 = Gibbons-Hawking power law","checked_by_registry":false,"claim_excerpt":"THE CLOCK IS AN ENTROPY POWER LAW (the transfer eigenvalues are the Nariai entropy fractions to the hexagon power; the ring coupling is the fractional entropy deficit): (1) THE THREE ENTROPY LEVELS [I]: the established Nariai bookkeeping (HOR.NARIAI.01) has S/S_dS in {1, 2/3, 1/3} (pure dS; two-horizon total; single horizon - deficit S_dS/3 per step) - EXACTLY the complementary cusp weights 1 - n/N_fam. (2) THE CLOCK","claim_id":"HOR.CLOCK.06","dependencies_as_recorded":"HOR.CLOCK.05; HOR.CLOCK.04; HOR.NARIAI.01; HOR.ORIENT.01; GATE.UWALL.07","external_data_as_recorded":"-","id":"claim:HOR.CLOCK.06","location_as_recorded":"tfpt_horizon_readouts","path":"verification/status_ledger.csv","row_number":214,"scripts_as_recorded":"v129_entropy_power_law.py","status_as_recorded":"Identity [I] (entropy-level + power-law + triple-coupling identities) + Physical [P] (derivation)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: h = n_zero/2 = N_fam; p2 = 2h (Born rule); 3 = proper CKVs of S^2; x2 = horizon pair; R1 residue = standard zero-mode measure","checked_by_registry":false,"claim_excerpt":"THE BORN SQUARE (the amplitude weight is h = N_fam = half the zero-mode count; the clock exponent p2 = 2h is its Born square - the HOR.CLOCK.05 multiplicity and the HOR.CLOCK.06 weight are ONE object): (1) EXPONENT BOOKKEEPING [I]: in the standard collective-coordinate treatment each zero mode trades a Gaussian integral for a moduli factor ~ S^{1/2}; with n_zero = 6 the transition AMPLITUDE scales as A ~ (S/S_dS)^{n_","claim_id":"HOR.CLOCK.07","dependencies_as_recorded":"HOR.CLOCK.06; HOR.CLOCK.05; E8.GRADE.01; HOR.NARIAI.01","external_data_as_recorded":"-","id":"claim:HOR.CLOCK.07","location_as_recorded":"tfpt_horizon_readouts","path":"verification/status_ledger.csv","row_number":215,"scripts_as_recorded":"v130_born_square.py","status_as_recorded":"Identity [I] (exponent bookkeeping + mode-count identities) + Physical [P] (measure normalisation)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: ||Y_1m||^2 = A/(4pi) exactly (all three modes); Jacobian = S^(1/2) per mode; 4pi cancels in ratios; R1 residue = det-ratio cancellation only","checked_by_registry":false,"claim_excerpt":"THE MEASURE IS THE AREA (the per-mode S^{1/2} of the Born square is the zero-mode NORM, computed exactly; the R1 residue narrows to one determinant-ratio cancellation): (1) ZERO-MODE NORM = AREA [I]: on the sphere S^2(r) the L^2 norm^2 of each of the three normalised l = 1 harmonics is EXACTLY r^2 = A/(4pi) (all three modes integrated exactly) - the norm of every zero mode IS the horizon area, hence the entropy, up t","claim_id":"HOR.CLOCK.08","dependencies_as_recorded":"HOR.CLOCK.07; HOR.CLOCK.06; HOR.NARIAI.01; ARCH.QUAD.01 (c3 primitive)","external_data_as_recorded":"-","id":"claim:HOR.CLOCK.08","location_as_recorded":"tfpt_horizon_readouts","path":"verification/status_ledger.csv","row_number":216,"scripts_as_recorded":"v131_measure_is_area.py","status_as_recorded":"Identity [I] (exact sphere integrals + bookkeeping) + Physical [P] (det-ratio)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: zeta(0) of the det'-operator = -2/3 = -|Z2|/N_fam (a1 = 1/N_fam + |Z2| = 7/3); det-ratio question = one zeta-budget statement; S^2 share pinned","checked_by_registry":false,"claim_excerpt":"THE DET-RATIO ANOMALY IS THE KOIDE CONSTANT (the HOR.CLOCK.08 'last step' acquires its first exact invariant): (1) SPECTRAL SETUP (re-pinned): the Ginsparg-Perry sphere operator on the unit S^2 is L = -Delta - 2 (the -2 = -|Z2| = the HOR.CLOCK.01 modulus mass); eigenvalues mu_l = l(l+1) - 2 = (l+2)(l-1), degeneracy 2l+1; kernel = the 3 zero modes (l = 1); one negative mode (l = 0). (2) THE HEAT COEFFICIENT IS MADE OF","claim_id":"HOR.CLOCK.09","dependencies_as_recorded":"HOR.CLOCK.08; HOR.CLOCK.01; SYNTH.INVENTORY.01 (2/3 inventory); HOR.NARIAI.01","external_data_as_recorded":"-","id":"claim:HOR.CLOCK.09","location_as_recorded":"tfpt_horizon_readouts","path":"verification/status_ledger.csv","row_number":217,"scripts_as_recorded":"v132_detratio_anomaly.py","status_as_recorded":"Identity [I] (heat-kernel arithmetic + numerical continuation) + Physical [P] (full budget)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: reduced budget = -4/3 = -seed gain (per sector -2/3); 4d route = -109/45 no atom; zero modes 3+3 = horizon pair; route selection -> reduced seam reading","checked_by_registry":false,"claim_excerpt":"THE ZETA BUDGET, BOTH ROUTES COMPUTED EXACTLY (the reduced seam route carries pure anchor-ratio anomalies; the naive 4d route does not - the budget computation structurally selects the reduced seam reading): Euclidean Nariai = S^2 x S^2, so the temporal dS2 sector continues to the SAME unit sphere and both candidate routes are exactly computable. (1) THE REDUCED ROUTE [I]: each 2d sector carries the HOR.CLOCK.09 oper","claim_id":"HOR.CLOCK.10","dependencies_as_recorded":"HOR.CLOCK.09; ARCH.TRIAD.01 (triad); E8.GRADE.01; HOR.NARIAI.01","external_data_as_recorded":"-","id":"claim:HOR.CLOCK.10","location_as_recorded":"tfpt_horizon_readouts","path":"verification/status_ledger.csv","row_number":218,"scripts_as_recorded":"v133_zeta_budget.py","status_as_recorded":"Identity [I] (exact heat-kernel arithmetic both routes + numerics) + Physical [P] (route reading + remaining shares)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: a^T R^-1 = a^T L^-1 = Nariai root/(-2); invariance <=> orthogonality to R^-1 1; dual normal pair (d n); R4' target = the pair","checked_by_registry":false,"claim_excerpt":"THE DUAL ANCHOR LEMMA (the inverse flavor response of the anchor IS the Nariai root; the third purely algebraic leg of the flavor-horizon bridge; external review 2026-06-12, validated): (1) THE DUAL ANCHOR [I]: d := a^T R^-1 = a^T L^-1 = (-1/2, -1/2, 1) with d.1 = 0, d.a = 1 and d = (3/2)(a - (4/3)1)^T - the normalised TRACELESS anchor - and (1,1,-2) = -2d: the inverse flavor response stores EXACTLY the Nariai double","claim_id":"FLAV.DUAL.01","dependencies_as_recorded":"HOR.NARIAI.01; FLAV.DIAMOND.02; FLAV.H2.05 (selectors); HOR.CLOCK.04; HOR.CLOCK.06","external_data_as_recorded":"-","id":"claim:FLAV.DUAL.01","location_as_recorded":"tfpt_2; tfpt_horizon_readouts","path":"verification/status_ledger.csv","row_number":219,"scripts_as_recorded":"v134_dual_anchor.py","status_as_recorded":"Identity [I] (exact dual-vector + Sherman-Morrison + controls) + Physical [P] (bridge reading)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: det M = 3s(t+1)(t+2)+t^2+5t+8; walls 2 and 4 (s-independent); winding line (8 14 20); det F = 32; det B = 2 det M on t = 0; V-rowsum = Spec(Q+); 41 and 52 micro-identities","checked_by_registry":false,"claim_excerpt":"THE DETERMINANT SURFACE (the sheet diamond is a 2d surface with iso-volume walls at the discrete atoms; external review 2026-06-12, validated): (1) SURFACE + WALLS [I]: on the established diamond M(s,t) = R + Q diag(s,t,t) (FLAV.DIAMOND.01/02), det M(s,t) = 3s(t+1)(t+2) + t^2 + 5t + 8; two iso-volume WALLS independent of s: t = -2 => det = 2 = |Z2| (the Z2 wall), t = -1 => det = 4 = |mu_4| (the mu_4 wall; K = M(1,-1)","claim_id":"FLAV.SURF.01","dependencies_as_recorded":"FLAV.DIAMOND.01-02; FLAV.H2.04; ARCH.TRIAD.01; E8.GRADE.01 (52); FLAV.KQ.01 (11 13)","external_data_as_recorded":"-","id":"claim:FLAV.SURF.01","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":220,"scripts_as_recorded":"v135_det_surface.py","status_as_recorded":"Identity [I] (exact surface/wall/budget identities) + Physical [P] (reading)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: (d n) => R columnwise (each column 1-of-216); A0* zero mode = -(2 -9 5) signed squares; n.sigma = 121; W(A3) orbit excludes the naive lift","checked_by_registry":false,"claim_excerpt":"THE DUAL-NORMAL SELECTOR ((d,n) pins R columnwise; the R4' residue is bounded; external review 2026-06-12, validated and sharpened): (1) COLUMN NORMAL FORM [I]: d.c_j = a_j and n.c_j = 8 delta_1j for the columns of R; the common kernel of (d,n) is the primitive vector (6,8,7) (audit: p_2, rank E8, scalaron-7), so within the address box {0..5}^3 each line contains at most one lattice point; brute-force census (216 per","claim_id":"GATE.UWALL.10","dependencies_as_recorded":"FLAV.DUAL.01; GATE.UWALL.07; GATE.UWALL.09; FLAV.H2.04 (superseded census); FLAV.SURF.01; HOR.NARIAI.01","external_data_as_recorded":"-","id":"claim:GATE.UWALL.10","location_as_recorded":"tfpt_research_contracts; tfpt_2","path":"verification/status_ledger.csv","row_number":221,"scripts_as_recorded":"v136_dual_normal_selector.py","status_as_recorded":"Identity [I] (column census + spectral normal + orbit control) + Physical [P] (restated programme)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: H^1 = chi_1+chi_2+chi_3 with degrees (1 2 3) = Spec(Q+) = A3 exponents; cusp weights = spec(A0*); residue = naturality of the canonical map","checked_by_registry":false,"claim_excerpt":"THE Q+ GRADING IS COHOMOLOGY (the R5/GATE.QGEO dictionary at the spectrum level; external review 2026-06-12, validated and sharpened): (1) BASIS + CHARACTERS [I]: b_1(P^1 minus mu_4) = 3 = N_fam with holomorphic basis omega_k = z^(k-1)dz/(z^4-1), k = 1,2,3 (regular at infinity; the trivial character is absent - k = 4 would be the dlog form); the mu_4 character of omega_k is i^k, so H^1 = chi_1 + chi_2 + chi_3 with ea","claim_id":"FLAV.QGEO.04","dependencies_as_recorded":"GATE.QGEO.01; FLAV.QGEO.01-03; GATE.UWALL.07; GATE.UWALL.09; FLAV.SURF.01","external_data_as_recorded":"-","id":"claim:FLAV.QGEO.04","location_as_recorded":"tfpt_2; tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":222,"scripts_as_recorded":"v137_qplus_cohomology.py","status_as_recorded":"Identity [I] (cohomology basis + characters + residues + spectrum match) + Physical [P] (naturality residue)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: -98/45 = 22/45 - 8/3 external; edge = 2 x reduced budget (-4/3); diff -38/45 no atom; typing: seam clock = edge object full 4d determinant = firewall","checked_by_registry":false,"claim_excerpt":"THE VOLKOV-WIPF FIREWALL (R1 typed closure: the external full-4d graviton/ghost value is pinned and the edge part is exactly two copies of the reduced seam budget; external values verified against arXiv:2506.02142 Table 4.1 which states agreement with Volkov-Wipf Nucl. Phys. B582 (2000) 313 = hep-th/0003081): (1) EXTERNAL DATUM [I typed external]: alpha_bulk = 22/45, alpha_edge = -8/3, alpha_PI = -98/45 for d = 3 (S^","claim_id":"HOR.CLOCK.11","dependencies_as_recorded":"HOR.CLOCK.10; HOR.NARIAI.01; HOR.CLOCK.03-09 (the clock chain)","external_data_as_recorded":"Volkov-Wipf Nucl.Phys. B582 (2000) 313 hep-th/0003081; arXiv:2506.02142 Table 4.1","id":"claim:HOR.CLOCK.11","location_as_recorded":"tfpt_horizon_readouts","path":"verification/status_ledger.csv","row_number":223,"scripts_as_recorded":"v138_vw_firewall.py","status_as_recorded":"Identity [I] (exact arithmetic vs external values) + Physical [P] (typing decision) + External (VW hep-th/0003081; arXiv:2506.02142)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: d = (3/2)a - 2*1 (no R); det(1 a sigma) = 11; n unique from pairings (2 8 121); square selects t = 0; review lift exact","checked_by_registry":false,"claim_excerpt":"THE SELECTOR TRIANGLE (anchor + A0* zero mode + three atoms => R; the R4' residue shrinks to three pairings): (1) d IS ANCHOR DATA [I]: d = (3/2)a - 2*1 exactly - the dual anchor (FLAV.DUAL.01) has a closed form that never mentions R; the first selector of the pair (d,n) is DERIVED, not residual. (2) THE FRAME [I]: (1, a, sigma) is a basis of Z^3 with det(1|a|sigma) = 11 = ||Pl(K)||_1 - the quark constant as the fram","claim_id":"GATE.UWALL.11","dependencies_as_recorded":"FLAV.DUAL.01; GATE.UWALL.10; FLAV.DIAMOND.02; FLAV.KQ.01 (the 11)","external_data_as_recorded":"-","id":"claim:GATE.UWALL.11","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":224,"scripts_as_recorded":"v139_selector_triangle.py","status_as_recorded":"Identity [I] (closed form for d + frame volume + uniqueness + square selection) + Physical [P] (three-pairing residue)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity: only sign-twisted actions match H^1; equivariant iso Schur-rigid; i^Q+ assignment = Q+ and -U = Q+ o rho; residue = one Z_3 choice","checked_by_registry":false,"claim_excerpt":"THE CANONICAL MAP EXISTS AND IS RIGID (the GATE.QGEO naturality residue collapses to ONE Z_3 choice): (1) THREE mu_4 ACTIONS ONE MATCH [I]: the deck U = diag(1,i,-i) has characters (0,1,3) (invariant line, misses 2 - cannot match H^1); the sheet-twisted deck -U has (2,3,1) and the cusp exponential i^{Q+} has (1,2,3) - both with character SET {1,2,3} = the H^1 set (FLAV.QGEO.04): only the SIGN-TWISTED actions match, t","claim_id":"FLAV.QGEO.05","dependencies_as_recorded":"FLAV.QGEO.04; FLAV.H2.02 (sheet twist); GATE.UWALL.09 (U); GATE.QGEO.01","external_data_as_recorded":"-","id":"claim:FLAV.QGEO.05","location_as_recorded":"tfpt_2; tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":225,"scripts_as_recorded":"v140_canonical_map.py","status_as_recorded":"Identity [I] (character algebra + Schur rigidity + grading transport) + Physical [P] (one Z_3 choice)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Lattice [L]: Z_3 choice derived - geometric deck = sheet-twisted class; residual = realisation premise only","checked_by_registry":false,"claim_excerpt":"DECK SELECTION THEOREM (R5's Z_3 choice DERIVED, executing the v140 residue): the established integer deck G=T_A*Sigma (v97 anchor-forced conjugation; v98 integer mu4 on generation space) pairs the Q_+=1 cusp line with the SELF-CONJUGATE character 2 (G e1=-e1 exact eigenline; E-plane carries {1,3}); of the three Z_3 rotations only the sheet-twisted assignment (2,3,1)=chars(-U) is compatible - the cusp exponential i^{","claim_id":"FLAV.QGEO.06","dependencies_as_recorded":"FLAV.QGEO.05; FLAV.QGEO.04; v97; v98; v72","external_data_as_recorded":"-","id":"claim:FLAV.QGEO.06","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":226,"scripts_as_recorded":"v141_deck_selection.py","status_as_recorded":"Lattice/Lie [L] (derived selection + explicit conjugacy/obstruction) + [P] (realisation premise unchanged)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: third pairing integrality-forced mod 11; R4' = two line pairings","checked_by_registry":false,"claim_excerpt":"FRAME INTEGRALITY (R4' narrowed: three pairings -> two): the pairing triples (m.1, m.a, m.sigma) of INTEGER covectors against the frame (1,a,sigma) form an index-11 sublattice of Z^3, cut out by the single congruence x-3y+z = 0 (mod 11) - the index IS 11 = ||Pl(K)||_1 = det(1|a|sigma) (full 11^3 scan, exact). With the two line pairings at their established atoms (x,y)=(|Z2|,rank E8)=(2,8), integrality FORCES the sigm","claim_id":"GATE.UWALL.12","dependencies_as_recorded":"GATE.UWALL.11; GATE.UWALL.10; FLAV.H2.05; v134; v139","external_data_as_recorded":"-","id":"claim:GATE.UWALL.12","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":227,"scripts_as_recorded":"v142_frame_integrality.py","status_as_recorded":"Identity [I] (index-11 congruence + parity + reductions) + [P]/[A] (establishment of the two line pairings)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/Lattice [I]/[L]: Q-system realised at the finite Lie level; residual = the net statement","checked_by_registry":false,"claim_excerpt":"GRADED FROBENIUS (R2 identification at the finite Lie level): the Z4-graded hull (E8.GRADE.01/v128) carries (1) EXACT COSET DUALITY coset(-r) = -coset(r) mod 4 for all 240 roots (-C1=C3 bijectively, C0/C2 self-dual; sizes 52,64,60,64) => the Killing form restricts to a NONDEGENERATE pairing g_k x g_{-k} - a Frobenius grading; (2) the glue character average (1/4)sum_k i^{k deg} is EXACTLY the carrier projector (1 on C","claim_id":"GATE.METRIC.09","dependencies_as_recorded":"E8.GRADE.01; GATE.METRIC.08; GATE.METRIC.07; CAR.QFREE.01; v125; v128","external_data_as_recorded":"-","id":"claim:GATE.METRIC.09","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":228,"scripts_as_recorded":"v143_graded_frobenius.py","status_as_recorded":"Identity/Lattice [I]/[L] (duality, projector, orbits, fusion) + [P] (the one conformal-net step)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: within-family det-ratio cancellation derived; absorption obstruction stated sharply","checked_by_registry":false,"claim_excerpt":"DET-RATIO CANCELLATION EXACT WITHIN THE SdS FAMILY (the v131 step closed in the within-family sense): e2-RIGIDITY - the traceless SdS cubic (t^3-3t+2c) forces r_b r_c = 1 - Delta^2/3 EXACTLY (Delta = horizon split; no higher corrections); with the v132 anomaly zeta(0)|det' = -2/3 per sphere, det'(L_r) = r^{4/3} det'(L_1), so the two-sphere non-zero-mode determinant ratio against Nariai is det'_n/det'_N = (1 - Delta^2","claim_id":"HOR.CLOCK.12","dependencies_as_recorded":"HOR.CLOCK.07; HOR.CLOCK.08; HOR.CLOCK.09; HOR.CLOCK.10; v101; v103","external_data_as_recorded":"-","id":"claim:HOR.CLOCK.12","location_as_recorded":"tfpt_horizon_readouts","path":"verification/status_ledger.csv","row_number":229,"scripts_as_recorded":"v144_detratio_family.py","status_as_recorded":"Identity [I] (exact rigidity + closed-form ratio + audit coefficient) + [P] (finite-weight absorption)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: pairing values = atom identities; R4' = one lift map","checked_by_registry":false,"claim_excerpt":"PAIRING VALUES ARE ATOM IDENTITIES (R4' collapses from two values to ONE map): given the lift n = w0(sigma) + |mu4| e3 (the v139 audit identity read structurally: w0 = the A3 EXPONENT DUALITY m <-> h-m = 4-m, an established Lie involution; lift slot = the top-exponent line, lift size = the glue order), ALL THREE pairings are atom arithmetic: (1) n.1 = sigma.1 + |mu4| = -|Z2|+|mu4| = |Z2| (<=> |mu4| = 2|Z2|); (2) NEW ","claim_id":"GATE.UWALL.13","dependencies_as_recorded":"GATE.UWALL.12; GATE.UWALL.11; v136; v139; v142","external_data_as_recorded":"-","id":"claim:GATE.UWALL.13","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":230,"scripts_as_recorded":"v145_pairing_atoms.py","status_as_recorded":"Identity [I] (atom identities + new closure) + [P] (the one lift map)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: Moebius D4 = integer D4, parity by parity; premise at its floor","checked_by_registry":false,"claim_excerpt":"MOEBIUS D4 REALISATION (R5 at its floor): the FULL dihedral symmetry group of the seam curve <delta: z->iz, iota: z->1/z> = D4 (order 8) acts on H^1(P^1 minus mu4) EXACTLY as the integer model <G, T_A, Sigma>: (1) delta* omega_k = i^k omega_k (v137); (2) iota* swaps omega_1 <-> omega_3 and FIXES omega_2 with +1, det -1, no extra phases - the exponent duality with parity; (3) dihedral relations exact; (4) in the cusp ","claim_id":"FLAV.QGEO.07","dependencies_as_recorded":"FLAV.QGEO.06; FLAV.QGEO.05; FLAV.QGEO.04; v97; v98; v137; v141","external_data_as_recorded":"-","id":"claim:FLAV.QGEO.07","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":231,"scripts_as_recorded":"v146_moebius_d4.py","status_as_recorded":"Identity/Lattice [I]/[L] (exact cohomology action + parity match) + [P] (module identification)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: ring sum = Gaussian zero-mode integral; bend det'-clean; residue = measure + reference","checked_by_registry":false,"claim_excerpt":"THE CLOCK IS A GAUSSIAN ZERO-MODE INTEGRAL AND THE BEND IS DET'-CLEAN (R1's derivation structured to its floor): (1) GAUSSIAN MODEL THEOREM - for p2 modes with per-mode variance ratio (1-alpha) (FORCED by norm = area, v131), the Born-squared partition ratio is (1-alpha)^{p2}, i.e. rate = -p2 ln(1-alpha) EXACTLY = the v124 closed form, and the ln series IS the v127 ring sum term by term: the 'one-loop = ring sum' job ","claim_id":"HOR.CLOCK.13","dependencies_as_recorded":"HOR.CLOCK.12; HOR.CLOCK.07; HOR.CLOCK.08; v101; v126; v127; v131","external_data_as_recorded":"-","id":"claim:HOR.CLOCK.13","location_as_recorded":"tfpt_horizon_readouts","path":"verification/status_ledger.csv","row_number":232,"scripts_as_recorded":"v147_clock_gaussian.py","status_as_recorded":"Identity [I] (model theorem + det'-clean bend + localisation) + [P] (measure identification)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: odd glue sectors are Ramond modules; glue choice = R-projection; R2 = a twisted-sector net statement","checked_by_registry":false,"claim_excerpt":"NS/R SECTOR CENSUS (R2 scoped honestly; corrected same day - the first version graded the Ramond labels by the sum q_D+q_A, which is not the glue label): (1) NS CENSUS [I] - every Neveu-Schwarz state of the 16 carrier Majoranas has INTEGER (D5, SO(6)) weights, and integer weights lie in discriminant classes 2x(sum parity): the NS module supports ONLY the even pairs {(0,0),(2,0),(0,2),(2,2)} - the odd glue elements (1","claim_id":"GATE.METRIC.10","dependencies_as_recorded":"GATE.METRIC.09; GATE.METRIC.08; CAR.QFREE.01; v113; v125; v143","external_data_as_recorded":"-","id":"claim:GATE.METRIC.10","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":233,"scripts_as_recorded":"v148_fock_census.py","status_as_recorded":"Identity [I] (exact census) + [P] (scoping conclusion)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: n = (p2,p0,e2)(a) in the cusp frame; R4' = one assignment","checked_by_registry":false,"claim_excerpt":"BOTH DUAL NORMALS ARE ANCHOR DATA (R4' at one discrete assignment): the pairings of the torsion normal n = (5,-9,6) with the cusp eigenbasis (v98) are EXACTLY (n.e1, n.e2, n.e3) = (6,3,5) = (p_2(a), p_0(a), e_2(a)) - the anchor's second power sum, zeroth power sum and second elementary symmetric function, one per Q_+ degree; the cusp matrix is unimodular so the three pairings determine n uniquely. With d = (3/2)a - 2","claim_id":"GATE.UWALL.14","dependencies_as_recorded":"GATE.UWALL.13; GATE.UWALL.12; FLAV.DUAL.01; v98; v139; v145","external_data_as_recorded":"-","id":"claim:GATE.UWALL.14","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":234,"scripts_as_recorded":"v149_cusp_normal.py","status_as_recorded":"Identity [I] (cusp-frame anchor reading + equivalences) + [P] (the one assignment)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: EH mechanism exact at gapped-model level; gate narrowed, open [A]","checked_by_registry":false,"claim_excerpt":"THE EH FORM FROM THE REPLICA VARIATION, GAPPED-MODEL LEVEL (the first movement on R3/SEAM.THEOREM.01; the gate narrows, does NOT close): (1) CONICAL DEFICIT EXACT [I] - on C/Z_N the heat-trace deficit is the classical image sum (1/4N) sum csc^2(pi k/N) = (N^2-1)/(12N) = C(2pi/N), C(gamma) = (1/12)(2pi/gamma - gamma/2pi), t-INDEPENDENT (exact N=2..6, 40-digit N=2..40); (2) GAP => CUTOFF-INDEPENDENT [I]: for -Delta + m","claim_id":"SEAM.EHMODEL.01","dependencies_as_recorded":"SEAM.THEOREM.01; SEAM.AREACOEFF.03; SEAM.KHALF.01; v59; v73; v90","external_data_as_recorded":"Cheeger 1983 / Sommerfeld (conical heat kernel; classical)","id":"claim:SEAM.EHMODEL.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":235,"scripts_as_recorded":"v150_replica_eh_model.py","status_as_recorded":"Identity [I] (model mechanism exact) + [A] (the theorem proper stays open)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: Calderon kernel conically clean; EH content = local half determinants; residue = q(A3) normalisation + premise","checked_by_registry":false,"claim_excerpt":"THE BFK SPLIT (the Calderon-transfer step of SEAM.EHMODEL.01/v150 ANSWERED; SEAM.THEOREM.01 narrows again, stays open): (1) DOUBLING => C_N = C_D [I] - reflecting a wedge across its edges gives the cone of doubled angle with exact odd/even (D/N) spectral split, so C_N(theta) = C_cone(2 theta) - C_D(theta) = (pi^2 - theta^2)/(24 pi theta) = C_D(theta): the Kac corner constant is boundary-condition INDEPENDENT (the D/N","claim_id":"SEAM.EHMODEL.02","dependencies_as_recorded":"SEAM.EHMODEL.01; SEAM.THEOREM.01; v59; v150","external_data_as_recorded":"Kac 1966 (corner constant); Burghelea-Friedlander-Kappeler 1992 (gluing); Cheeger 1983","id":"claim:SEAM.EHMODEL.02","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":236,"scripts_as_recorded":"v151_bfk_split.py","status_as_recorded":"Identity [I] (BFK/Kac algebra exact) + [A] (the theorem proper stays open)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: R3 normalisation = the v68 anchor in dimensionless form; residual = kernel premise alone","checked_by_registry":false,"claim_excerpt":"THE R3 NORMALISATION IS THE DIMENSIONFUL ANCHOR (not a separate open item; SEAM.THEOREM.01's residual list shrinks to the kernel premise alone): (1) THE COEFFICIENT IS A LOG-RATIO [I] - the conical part of the massive 2d determinant is zeta_corner(s) = C(gamma) (m/mu)^{-2s} (the zeta-scale mu enters with the dimensionful mass m), so Delta log det' = 2 C(gamma) ln(m/mu) and k = ln(m/mu)/(12 pi); the bare ln m is scale","claim_id":"SEAM.EHMODEL.03","dependencies_as_recorded":"SEAM.EHMODEL.02; SEAM.EHMODEL.01; SEAM.KHALF.01; v68; v78; v150","external_data_as_recorded":"Sakharov 1967 (induced gravity; standard)","id":"claim:SEAM.EHMODEL.03","location_as_recorded":"origin_theory;tfpt_horizon_readouts","path":"verification/status_ledger.csv","row_number":237,"scripts_as_recorded":"v152_norm_is_anchor.py","status_as_recorded":"Identity [I] (dimensional bookkeeping exact) + [A] (the anchor stays declared)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: No-Unit Theorem; v_geo = irreducible metrology primitive, three residuals collapse to one unit  | 2026-08-29 wave-4 display retype: CLOSED METROLOGY STRUCTURE (R_+ unit torsor; one dimensionful calibration necessary by dimensional analysis).  No [E] upgrade of physics.  WAVE-5 (2026-08-29): unit choice closed; dimensionless hierarchies (M_Pl/v_EW, M_R/M_scal, Lambda_QCD/v_EW, T_reh/M_scal) remain predictive obligations.","checked_by_registry":false,"claim_excerpt":"NO-UNIT THEOREM (v_geo re-typed from open gap to CLOSED METROLOGY STRUCTURE -- R_+ unit torsor; one dimensionful calibration necessary by dimensional analysis, v153/v725; external review 2026-06-13 formalised, wave-4 display wording 2026-08-29): (1) every load-bearing compiler datum (g_car, |mu4|, N_fam, rank E8, alpha^-1, det(Q,K,R,L)=(3,4,8,20) product 1920, c3=1/(8pi), 2pi c3=1/4, phi0) is mass-dimension 0 and INV","claim_id":"ANCHOR.VGEO.02","dependencies_as_recorded":"ANCHOR.VGEO.01; FLAV.UPOINT.01; SEAM.EHMODEL.03; v68; v78; v152","external_data_as_recorded":"-","id":"claim:ANCHOR.VGEO.02","location_as_recorded":"origin_theory;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":238,"scripts_as_recorded":"v153_no_unit_theorem.py","status_as_recorded":"Identity [I] (scaling bookkeeping) + [A]/[O] (closed metrology: R_+ unit torsor; one calibration)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/Lattice [I]/[L]: (D5)1(x)(A3)1|x<(1,1)> = (E8)1; residue = seam-side identification","checked_by_registry":false,"claim_excerpt":"SIMPLE-CURRENT EXTENSION THEOREM (the central G_net closing theorem, assembled and stated as Definition+Theorem; external review 2026-06-13): the carrier net A = (D5)_1 (x) (A3)_1 extended by the isotropic mu_4 glue line L = <(1,1)> in Disc(D5)(+)Disc(A3) = Z4(+)Z4 is the local simple-current extension B = A |x L with (1) Jones index [B:A] = |L| = 4 = |mu4| (L isotropic: q(k(1,1)) = k^2 in Z, v92/v125; KLM/v89) [I]; ","claim_id":"GATE.METRIC.11","dependencies_as_recorded":"GATE.METRIC.10; GATE.METRIC.09; GATE.METRIC.07; GATE.METRIC.06; v89; v92; v125; v143; v148","external_data_as_recorded":"-","id":"claim:GATE.METRIC.11","location_as_recorded":"tfpt_5_redteam;tfpt_research_contracts;origin_theory","path":"verification/status_ledger.csv","row_number":239,"scripts_as_recorded":"v154_simple_current_theorem.py","status_as_recorded":"Identity/Lattice [I]/[L] (the extension theorem exact) + [P] (the seam-side identification)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: quasi-free boundary from Gaussian bulk; G_net premise = the one free-field premise (shared with area law, R3)","checked_by_registry":false,"claim_excerpt":"QUASI-FREE BOUNDARY (Python-only; the seam-side identification of GATE.METRIC.11/v154 reduced to ONE shared physical premise): (1) RESTRICTION OF A QUASI-FREE STATE IS QUASI-FREE [I] - a fermionic Gaussian state has real antisymmetric covariance Gamma with i*Gamma a contraction (eigenvalues in [-1,1]; pure: Gamma^2=-I); the boundary marginal (partial trace over the bulk) is the compression P Gamma P = principal subma","claim_id":"GATE.METRIC.12","dependencies_as_recorded":"GATE.METRIC.11; GATE.METRIC.10; CAR.QFREE.01; SEAM.EHMODEL.02; v59; v110; v113; v150","external_data_as_recorded":"-","id":"claim:GATE.METRIC.12","location_as_recorded":"tfpt_research_contracts;origin_theory","path":"verification/status_ledger.csv","row_number":240,"scripts_as_recorded":"v155_quasifree_boundary.py","status_as_recorded":"Identity [I] (compression contraction + Wick) + [P] (the one shared free-field premise)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/Lattice [I]/[L]: seam net constructed, (E8)1 character verified; residual = free-bulk premise + net existence","checked_by_registry":false,"claim_excerpt":"THE SEAM-NET CONSTRUCTION (Route 3 carried to its exact verifiable endpoint; B=(E8)1 turned from assertion into checked computation): (1) DtN = FREE CHIRAL DISPERSION [I] - the Dirichlet-to-Neumann (Calderon) operator of the 2d Laplacian on the half-space acts on a boundary mode e^{ikx} via the harmonic extension e^{ikx-|k|y} by -d_n u|_0 = |k| u, so the seam-Calderon operator for a free bulk is omega_k = |k|, the ma","claim_id":"GATE.METRIC.13","dependencies_as_recorded":"GATE.METRIC.12; GATE.METRIC.11; GATE.METRIC.03; v77; v83; v148; v154; v155","external_data_as_recorded":"Frenkel-Kac-Segal (E8 vertex/fermion construction); Kawahigashi-Longo (conformal nets)","id":"claim:GATE.METRIC.13","location_as_recorded":"tfpt_5_redteam;tfpt_research_contracts;origin_theory","path":"verification/status_ledger.csv","row_number":241,"scripts_as_recorded":"v156_seam_net_construction.py","status_as_recorded":"Identity/Lattice [I]/[L] (DtN + character identity exact) + [P]/[A] (free-bulk premise + net existence)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/Lattice [I]/[L]: freeness = the rigid holomorphic c=8 fixed point; premise (A) reduced to reaching it","checked_by_registry":false,"claim_excerpt":"FREENESS AS THE RIGID BOUNDARY FIXED POINT (simplicity-first reframing of premise A; the free-bulk postulate becomes a fixed-point property): (1) UNIVERSAL DtN SYMBOL [I]/[L] - the Dirichlet-to-Neumann (Calderon) operator of ANY 2nd-order elliptic bulk is an order-1 pseudodifferential operator with principal symbol |xi|_g (Lee-Uhlmann 1989) = |k| on a flat boundary mode, homogeneous degree 1; any bulk interaction shi","claim_id":"GATE.METRIC.14","dependencies_as_recorded":"GATE.METRIC.13; GATE.METRIC.12; SEAM.EHMODEL.02; v59; v83; v148; v155; v156","external_data_as_recorded":"Lee-Uhlmann 1989 (DtN principal symbol); holomorphic-VOA rigidity (standard)","id":"claim:GATE.METRIC.14","location_as_recorded":"tfpt_5_redteam;tfpt_research_contracts;origin_theory","path":"verification/status_ledger.csv","row_number":242,"scripts_as_recorded":"v157_rigid_fixed_point.py","status_as_recorded":"Identity/Lattice [I]/[L] (symbol homogeneity + rigidity count + |Z2| arithmetic) + [P] (the gapped flow reaching the fixed point)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: free chiral c=8 fixed point provably stable; (A) reduced to basin-of-attraction","checked_by_registry":false,"claim_excerpt":"THE FREE CHIRAL c=8 FIXED POINT IS STABLE (exact operator-dimension count; the finite core of premise (A)'s reaches-the-fixed-point residual): (1) DIMENSIONS [I] - in the 16-Majorana chiral theory psi has weight h=1/2, the fermion-bilinear current :psi_i psi_j: has h=1, the quartic :psi psi psi psi: has h=2, the 2k-fermi operator h=k; a 1d boundary perturbation is relevant/marginal/irrelevant as h </=/> 1; (2) NO REL","claim_id":"GATE.METRIC.15","dependencies_as_recorded":"GATE.METRIC.14; GATE.METRIC.13; v56; v59; v148; v157","external_data_as_recorded":"-","id":"claim:GATE.METRIC.15","location_as_recorded":"tfpt_research_contracts;origin_theory","path":"verification/status_ledger.csv","row_number":243,"scripts_as_recorded":"v158_fixed_point_stable.py","status_as_recorded":"Identity [I] (operator-dimension count) + [P] (basin/convergence of the gapped flow)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: quasi-free => kappa_{2n}=0 + PF dichotomy; (A) reduced to ONE scope premise (v56 on the full Schwinger cone)","checked_by_registry":false,"claim_excerpt":"SEAM GAUSSIANITY AS A CONDITIONAL FIXED-POINT THEOREM (the proposed closure of premise (A), formalised and honestly typed; the load relocates to ONE internal statement): (1) QUASI-FREE => kappa_{2n}=0 [I] - with the 2n-point moment = Pf(Gamma submatrix), the SIGNED set-partition moment<->cumulant inversion gives kappa(|S|=2)=Gamma_ij and kappa(|S|=4)=kappa(|S|=6)=0 exactly (verified on a concrete pure Majorana covari","claim_id":"GATE.METRIC.16","dependencies_as_recorded":"GATE.METRIC.12; GATE.METRIC.15; v56; v113; v155; v158","external_data_as_recorded":"-","id":"claim:GATE.METRIC.16","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":244,"scripts_as_recorded":"v160_seam_gaussianity_from_pf.py","status_as_recorded":"Identity [I] (signed cumulant inversion + Wick functoriality + PF dichotomy) + [P] (the scope premise: v56 acts on the full cone)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: cone gap = one-particle gap (Bogoliubov); (A) reduced from the infinite cone to ONE 16-dim one-particle identification","checked_by_registry":false,"claim_excerpt":"THE CONE REDUCES TO ONE PARTICLE (discharges the v160/GATE.METRIC.16 scope premise via Bogoliubov second quantisation; the infinite-dimensional Schwinger cone is eliminated, a finite one-particle statement remains): a quasi-free (Gaussianity-preserving) transport on the CAR algebra is T = Gamma(t), the second quantisation of a one-particle contraction t on the 16-dim Majorana space H_Sigma; the Fock space grades by c","claim_id":"GATE.METRIC.17","dependencies_as_recorded":"GATE.METRIC.16; v56; v113; v158; v160_seam_gaussianity_from_pf.py","external_data_as_recorded":"-","id":"claim:GATE.METRIC.17","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":245,"scripts_as_recorded":"v161_one_particle_reduction.py","status_as_recorded":"Identity [I] (Bogoliubov second-quantisation functoriality + cone gap = one-particle gap + fixed sector = Wick powers) + [P] (the one-particle symbol identification) + [C] (quasi-freeness forced by v158)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: gap (2/3)^6 forced + fixed = rank-8 K_Sigma; (A) factors into the already-open A2 + R1 (no new open content)","checked_by_registry":false,"claim_excerpt":"THE FINAL IDENTIFICATION, FORCED AS FAR AS IT GOES (the v161/GATE.METRIC.17 one-particle statement carries NO new open content; premise (A) factors into the two already-open items A2 + R1): the residual was 'the seam transport one-particle symbol is the gapped Calderon Bogoliubov map - (alpha) fixed = rank-8 K_Sigma, (beta) gap = (2/3)^6'. (1) THE GAP VALUE IS FORCED [I] - the cusp weights = spec(A0*) = {0,1/3,2/3} (","claim_id":"GATE.METRIC.18","dependencies_as_recorded":"GATE.METRIC.16; GATE.METRIC.17; v56; v113; v115; v137; v156; v157","external_data_as_recorded":"-","id":"claim:GATE.METRIC.18","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":246,"scripts_as_recorded":"v162_seam_transport_identification.py","status_as_recorded":"Identity [I] (gap forced by mu4-equivariance + spec(A0*); fixed = rank-8 Calderon) + [P]/[A] (A) factors into the already-open A2 (net existence) + R1 (seam clock)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Closure [C]: A2 = net-construction assembly, R1 = GATE.QGEO; (A) has zero independent open gates, irreducible core {pi,v_geo} a theorem","checked_by_registry":false,"claim_excerpt":"PREMISE (A) MAXIMAL HONEST CLOSURE (the two residual gates A2 + R1 pinned to their floor; (A) carries ZERO independent open content): (1) A2 (NET EXISTENCE) CLOSES BY ASSEMBLY [C] - every ingredient is a constructed object: 16 free Majoranas => free-fermion conformal net (Buchholz-Mack-Todorov / Boeckenhauer-Evans), holomorphic c=8 lattice net = (E8)1 (Frenkel-Kac-Segal VOA / Dong-Xu net / Kawahigashi-Longo machinery","claim_id":"GATE.METRIC.19","dependencies_as_recorded":"GATE.METRIC.16; GATE.METRIC.17; GATE.METRIC.18; v115; v116; v125; v137; v153; v156","external_data_as_recorded":"-","id":"claim:GATE.METRIC.19","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":247,"scripts_as_recorded":"v165_premise_a_closure.py","status_as_recorded":"Identity/assembly [C] (A2 net existence by established AQFT; R1 reduced to GATE.QGEO via A0* uniqueness) + [O] (the irreducible {pi,v_geo} geometric core, a theorem by v153)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: carrier content -> (41/10,-19/6,-7); PyR@TE 3 (external) reproduces them verbatim; F_transfer gauge inputs confirmed","checked_by_registry":false,"claim_excerpt":"PYRATE GAUGE CROSS-CHECK (independent third-party confirmation of EM.BUDGET.01/CAR.SM.01 and an F_transfer gauge-input check): the carrier/SM field content gives, by the textbook one-loop formula in GUT normalisation, (b1,b2,b3)=(41/10,-19/6,-7) [I]; (1) THREE INDEPENDENT PATHS to b1=41/10 - carrier algebra 10 b1 = g_car 2^{g_car-2}+1 = 41 (CAR.SM.01), the SM U(1) hypercharge index sum (3/5)Y^2 over the content, and ","claim_id":"EM.BUDGET.02","dependencies_as_recorded":"EM.BUDGET.01; CAR.SM.01; v2_carrier_pascal.py; v13_open_gates.py","external_data_as_recorded":"PyR@TE 3 (arXiv:2007.12700; github.com/LSartore/pyrate) SM 1+2-loop gauge betas","id":"claim:EM.BUDGET.02","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":248,"scripts_as_recorded":"v159_pyrate_gauge_crosscheck.py","status_as_recorded":"Identity [I] (one-loop coefficients exact) + [P] (F_transfer gauge inputs)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: lepton angles RG-stable (y_tau^2-suppressed), quark ratios scale-tagged; F_transfer lepton sector trivial","checked_by_registry":false,"claim_excerpt":"F_TRANSFER SCALE-TAGGING (the lepton-mixing predictions are RG-STABLE outputs; the quark mass-ratio readouts carry a scale tag): (1) the PMNS angles run only through the charged-lepton Y_e Y_e^+ eigenvalue gap y_tau^2 ~ 1.0e-4 [I] (the only mixing-ROTATING Yukawa term is (3/2) Y Y^+ Y, PyR@TE SM RGEs), so the one-loop running from the seam/scalaron scale (M_scal = c3^{7/2} Mbar ~ 3e13 GeV) down to M_Z is kappa_tau = ","claim_id":"FLAV.RGSTAB.01","dependencies_as_recorded":"EM.BUDGET.02; CAR.SM.01; v16_solar_dual_anchor.py; v21_solar_product_quark.py","external_data_as_recorded":"PyR@TE 3 (arXiv:2007.12700) SM Yukawa betas","id":"claim:FLAV.RGSTAB.01","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":249,"scripts_as_recorded":"v163_rg_stability_flavor.py","status_as_recorded":"Identity [I] (y^2-suppression bound) + [P] (F_transfer typing)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: Lambda_QCD parameter-free from b3=-7; m_p/m_e numerator sourced, ratio stays 'Open / not forced'","checked_by_registry":false,"claim_excerpt":"QCD CONFINEMENT SCALE PARAMETER-FREE FROM THE CARRIER b3 = -7 (the m_p/m_e numerator is independently sourced; the ratio itself stays an honest non-claim): (1) running alpha_s(M_Z) = 0.1179 down with the two-loop QCD RGE and b0(n_f) = 11 - 2 n_f/3 (b3 = -7 at n_f = 6; v159) + thresholds at m_b, m_c reproduces alpha_s(m_b) ~ 0.22 and alpha_s(m_c) ~ 0.38 = the measured values [I]; (2) continuing down, alpha_s reaches O","claim_id":"QCD.LAMBDA.01","dependencies_as_recorded":"EM.BUDGET.02; CAR.SM.01; FR.MPME.01","external_data_as_recorded":"PyR@TE 3 (arXiv:2007.12700) confirmed b3 = -7","id":"claim:QCD.LAMBDA.01","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":250,"scripts_as_recorded":"v164_qcd_scale.py","status_as_recorded":"Identity [I] (parameter-free confinement scale) + [P] (lattice O(1)) + [A] (ratio stays non-claim)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: free seam => lambda(Mbar)~0=beta_lambda (SM near-criticality explained); [P] m_H ~ 129-134 predicted; seam BC at the Planck scale","checked_by_registry":false,"claim_excerpt":"HIGGS QUARTIC FROM THE FREE SEAM (a derived boundary condition tying m_H to premise (A); validated at two loops): the seam UV is the free chiral c=8 fixed point (v157/v158, Gaussian, no relevant/marginal interactions), so the one marginal SM scalar coupling vanishes at the seam -- lambda(M_seam)=0 AND beta_lambda(M_seam)=0, the Shaposhnikov-Wetterich double-criticality, here MOTIVATED by the free seam rather than ass","claim_id":"HIGGS.FREESEAM.01","dependencies_as_recorded":"EM.BUDGET.02; GATE.METRIC.15; v158_fixed_point_stable.py; v159_pyrate_gauge_crosscheck.py","external_data_as_recorded":"PyR@TE 3 (arXiv:2007.12700) SM 2-loop beta_lambda/beta_yt","id":"claim:HIGGS.FREESEAM.01","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":251,"scripts_as_recorded":"v166_higgs_free_seam.py","status_as_recorded":"Identity [I] (freeness signature + scale selection) + [P] (the m_H prediction band)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/Lattice [I]/[L]: QGEO finite rigidity closed (cross-ratio 2, D4 order 8, b1=3, chi_k=A3 exps); the math half of GATE.QGEO","checked_by_registry":false,"claim_excerpt":"THE QGEO RIGIDITY THEOREM (the FINITE half of the Tier-1 hinge GATE.QGEO, hardened to [E]; v167 Tier 1): a genus-0 boundary with a faithful D4 action, one orbit of four parabolic marks, H^1 of rank 3 and the nontrivial mu4-character decomposition chi_1+chi_2+chi_3 is Moebius-equivalent to P^1 minus mu4 with the (1,2,3) grading. EXACT CHECKS: (1) mu4={1,i,-1,-i} has cross-ratio 2 and Moebius stabiliser <z->iz, z->1/z>","claim_id":"QGEO.RIGID.01","dependencies_as_recorded":"GATE.QGEO.01; FLAV.QGEO.02; FLAV.QGEO.01; v137_qplus_cohomology.py","external_data_as_recorded":"-","id":"claim:QGEO.RIGID.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":252,"scripts_as_recorded":"v168_qgeo_rigidity.py","status_as_recorded":"Identity/Lattice [I]/[L] (the finite rigidity theorem exact)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Physical [C]/[O]: seam-collar = P1-mu4 stays the one realisation premise (RIGID [E], REALIZE [C]); rest PRECISED by v503 and REDUCED by v506: marks + square derived, the order-4 clock reduced to ONE alignment bit ('the collar deck is the central involution of the mark-D4' -- order/uniqueness/orbit/tau = i follow, the fermionic Z4 order is forced, U^2 = (-1)^F); QGEO-R1 == P2-R1 = this single bit -- marker unchanged; v507 derives the CLASS of the deck (half-period translation) and characterises the bit as a tetrad with the non-split NS Fock extension class as its physical face -- only the position stays the input; v510 halves the bit: the position half is topology (covering-deck freeness excludes the edge class), the rest is the square-modulus datum tau = i alone; v512 restates the rest as the flag-transitivity postulate (V4 -> D4 symmetry-lift bit) and narrows the [E]-closure search space to the RP positivity of the odd sector","checked_by_registry":false,"claim_excerpt":"THE SEAM-COLLAR REALISATION (the physical half of GATE.QGEO; the one Tier-1 realisation premise, stays [C]/[O]): the QGEO Rigidity Theorem (QGEO.RIGID.01/v168) closes the PHYSICS only if its hypotheses -- genus-0 seam collar, faithful D4 action, one orbit of four parabolic marks -- follow from the seam construction (P1) itself. The cohomological half is established (b1=N_fam=3, cusp grading = A3 exponents), but the i","claim_id":"QGEO.REALIZE.01","dependencies_as_recorded":"QGEO.RIGID.01; GATE.QGEO.01; GATE.METRIC.19; QGEO.EMERGE.LIGHT.01; P2.TYPING.01; v503; SEAM.CLOCK.RIGIDITY.01; v506; SEAM.BIT.ORIGIN.01; v507; SEAM.BIT.FREEDOM.01; v510; SEAM.TAU.FLAG.01; v512","external_data_as_recorded":"-","id":"claim:QGEO.REALIZE.01","location_as_recorded":"tfpt_research_contracts;origin_theory","path":"verification/status_ledger.csv","row_number":253,"scripts_as_recorded":"v168_qgeo_rigidity.py","status_as_recorded":"Physical [C] (seam-side identification) + [O] (open realisation)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Reduction certificate [E]/[O]: the central theorem reduces to ONE open realisation premise (QGEO.REALIZE.01); five of six steps are [E]","checked_by_registry":false,"claim_excerpt":"THE SEAM COLLAR REALISATION THEOREM, ASSEMBLED AS ONE CENTRAL STATEMENT + REDUCTION CERTIFICATE (the single structural proof obligation of the whole theory, formulated cleanly; NOT a fabricated proof): THEOREM -- given (1) an oriented one-sided RP seam collar, (2) a sheet-odd Calderon involution, (3) quasi-free one-particle seam data with gap (2/3)^6, (4) a faithful D4 action on the boundary marks, (5) four parabolic","claim_id":"QGEO.REALIZE.02","dependencies_as_recorded":"QGEO.REALIZE.01; QGEO.RIGID.01; GATE.METRIC.13; GATE.METRIC.18; QFT.NETRP.01; v137_qplus_cohomology.py; v156_seam_net_construction.py; v162_seam_transport_identification.py; v168_qgeo_rigidity.py; v175_net_existence_full_cone.py","external_data_as_recorded":"-","id":"claim:QGEO.REALIZE.02","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":254,"scripts_as_recorded":"v176_seam_collar_realisation.py","status_as_recorded":"Reduction certificate [E] (five steps established) + [O] (the one realisation premise)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Proof tree [E]/[O]: UNIFORM/COHOM/MODULE/NET closed [E]; the residual is exactly the two obligations MARKS + KERNEL","checked_by_registry":false,"claim_excerpt":"THE QGEO PROOF TREE (the v176 'one realisation premise' split into its honest constituents; the open residual sharpened from one diffuse premise into exactly TWO named obligations; external residual-class audit 2026-06-14): REALIZE = MARKS . UNIFORM . COHOM . MODULE . KERNEL . NET, with FOUR nodes now closed CONSTRUCTIVELY. [E] QGEO.UNIFORM.01 (Lemma 2, constructive -- strengthens v168's cross-ratio check to the full","claim_id":"QGEO.TREE.01","dependencies_as_recorded":"QGEO.REALIZE.02; QGEO.RIGID.01; QGEO.MARKS.01; QGEO.KERNEL.01; v137_qplus_cohomology.py; v141_deck_selection.py; v168_qgeo_rigidity.py; v176_seam_collar_realisation.py","external_data_as_recorded":"-","id":"claim:QGEO.TREE.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":255,"scripts_as_recorded":"v177_seam_marking_kernel.py","status_as_recorded":"Proof tree [E] (four nodes closed constructively) + [O] (two named obligations)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open [O]: raw RP seam collar -> genus-0 four-marked D4 boundary (one of the two genuine obligations)","checked_by_registry":false,"claim_excerpt":"THE SEAM MARKING OBLIGATION (genuine open obligation 1 of 2; the structural residual of the theory, NOT a finite computation): the RAW RP seam collar must canonically produce a genus-0, four-parabolic-marked boundary with a faithful D4 action -- the four marks coming from the anchor atom e1(a)=4=|mu4| (NOT an arbitrary marking), with mark collisions excluded (else b1=N_fam=3, the D4 faithfulness or the H^1 character ","claim_id":"QGEO.MARKS.01","dependencies_as_recorded":"QGEO.TREE.01; QGEO.UNIFORM.01; ARCH.SPINE.01; v177_seam_marking_kernel.py","external_data_as_recorded":"-","id":"claim:QGEO.MARKS.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":256,"scripts_as_recorded":"v177_seam_marking_kernel.py","status_as_recorded":"Physical/geometric [O] (open constructive obligation)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open [O]: raw RP seam Calderon kernel = the mu4-equivariant free gapped contraction as an operator (one of the two genuine obligations)","checked_by_registry":false,"claim_excerpt":"THE SEAM CALDERON-KERNEL OBLIGATION (genuine open obligation 2 of 2; the structural residual of the theory, NOT a finite computation): the RAW RP seam Calderon operator must equal the mu4-equivariant free c=8 gapped one-particle contraction on that boundary AS AN OPERATOR (C_Sigma = U^{-1} C_mu4 U), not merely as the same spectral list. Rails already laid: the DtN/Calderon symbol is universally |k| (free chiral dispe","claim_id":"QGEO.KERNEL.01","dependencies_as_recorded":"QGEO.TREE.01; QGEO.NET.01; GATE.METRIC.13; GATE.METRIC.18; v110; v113; v156_seam_net_construction.py; v158_fixed_point_stable.py; v162_seam_transport_identification.py","external_data_as_recorded":"-","id":"claim:QGEO.KERNEL.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":257,"scripts_as_recorded":"v177_seam_marking_kernel.py","status_as_recorded":"Physical/operator [O] (open constructive obligation)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Deeper reduction [E]/[O]: MARKS + KERNEL finite cores closed; each reduced to one sharper premise (topological clock / full-operator reduction); neither obligation closed","checked_by_registry":false,"claim_excerpt":"DEEPER REDUCTION OF THE TWO OBLIGATIONS (an honest attempt at QGEO.MARKS.01 + QGEO.KERNEL.01; NEITHER is closed -- they are genuine constructive-geometry/AQFT statements, not finite computations -- but each finite/algebraic CORE is now closed [E] and each obligation is reduced to ONE sharper irreducible premise [O]): (1) MARKS FINITE CORE [E] -- given a genus-0 double with an order-4 clock rho (conjugate to z->iz, fi","claim_id":"QGEO.REDUCE.01","dependencies_as_recorded":"QGEO.MARKS.01; QGEO.KERNEL.01; QGEO.TREE.01; v156_seam_net_construction.py; v158_fixed_point_stable.py; v162_seam_transport_identification.py; v177_seam_marking_kernel.py","external_data_as_recorded":"Lee-Uhlmann 1989 (DtN principal symbol)","id":"claim:QGEO.REDUCE.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":258,"scripts_as_recorded":"v178_marks_kernel_attempt.py","status_as_recorded":"Deeper reduction [E] (finite cores) + [O] (the two sharper irreducible premises)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Geometric [O]: the SINGLE residual is the seam conformal realisation (P^1,mu4) with the carrier clock as the order-4 Moebius map; MARKS+KERNEL both reduce to it","checked_by_registry":false,"claim_excerpt":"THE SEAM CONFORMAL-REALISATION PREMISE -- the SINGLE structural residual of the whole theory (the two obligations QGEO.MARKS.01 + QGEO.KERNEL.01 collapse onto it; honest unification, the premise itself stays OPEN). The two residual premises left by v178 are NOT independent: (A) MARKS's residual decomposes into three pieces, two of which are already-established TFPT facts and the third forced -- (1) GENUS-0 IS P1: the","claim_id":"QGEO.CONF.01","dependencies_as_recorded":"QGEO.MARKS.01; QGEO.KERNEL.01; QGEO.REDUCE.01; AX.P1.01; SEAM.KHALF.01; v58_seam_horizon_chain.py; v73_k_c3_half.py; v117_monodromy_weyl_a3.py; v156_seam_net_construction.py; v158_fixed_point_stable.py","external_data_as_recorded":"Lee-Uhlmann 1989; Selberg/Eisenstein spectral theory (cusped surfaces)","id":"claim:QGEO.CONF.01","location_as_recorded":"tfpt_research_contracts;origin_theory","path":"verification/status_ledger.csv","row_number":259,"scripts_as_recorded":"v179_conformal_realisation.py","status_as_recorded":"Geometric realisation premise [O] (the single residual; component reductions [I] established)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Geometric [O]: QGEO.CONF.01 replaced by the milder seam-ISOMETRY premise (the clock is an order-4 isometry); conformal realisation now implied via uniformisation + Kerekjarto + finite-order Moebius","checked_by_registry":false,"claim_excerpt":"THE SEAM-ISOMETRY PREMISE -- the milder, non-circular form of the single structural residual (QGEO.CONF.01 is REPLACED by it via three classical theorems; honest reduction, still OPEN): 'the carrier clock is an order-4 orientation-preserving ISOMETRY of the RP seam metric'. The chain: (1) UNIFORMISATION (Poincare-Koebe) -- a genus-0 Riemann surface is conformally P^1, and the RP seam metric induces a conformal struct","claim_id":"QGEO.ISO.01","dependencies_as_recorded":"QGEO.CONF.01; QGEO.MARKS.01; AX.P1.01; v117_monodromy_weyl_a3.py; v179_conformal_realisation.py","external_data_as_recorded":"Poincare-Koebe uniformisation; Kerekjarto 1919 / Constantin-Kolev 2003; Aut(P^1)=PSL(2,C)","id":"claim:QGEO.ISO.01","location_as_recorded":"tfpt_research_contracts;origin_theory","path":"verification/status_ledger.csv","row_number":260,"scripts_as_recorded":"v180_clock_is_mobius.py","status_as_recorded":"Geometric isometry premise [O] (milder residual; the conformal-class identification is now implied) + [E] (the three cited reductions)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Face of keystone [O]: QGEO.SYM.01 = the definitional conformal-deck face of SEAM.EQUIV.01; per v323/QGEO.BW.01 downstream of SEAM.EQUIV.01 + rotation-invariant vacuum, not an independent residual","checked_by_registry":false,"claim_excerpt":"A COROLLARY OF SEAM.EQUIV.01 (no independent open premise; reclassified 2026-06-22, v335): per v323/QGEO.BW.01 it is downstream of SEAM.EQUIV.01 + a rotation-invariant vacuum, and the rotation-invariant vacuum is a conformal-NET AXIOM (a chiral net's Moebius-covariant vacuum is the unique invariant positive-energy vector; rotations U(1) < Moebius), so SEAM.EQUIV.01 => QGEO.SYM.01 with NO extra premise -- machine-pinn","claim_id":"QGEO.SYM.01","dependencies_as_recorded":"SEAM.EQUIV.01; QGEO.BW.01; QGEO.ISO.01; QGEO.CONF.01; AX.P2.01; v117_monodromy_weyl_a3.py; v180_clock_is_mobius.py","external_data_as_recorded":"Nielsen realisation (finite cyclic on genus-0); Kerekjarto / Constantin-Kolev; Poincare-Koebe; Bisognano-Wichmann","id":"claim:QGEO.SYM.01","location_as_recorded":"tfpt_research_contracts;origin_theory","path":"verification/status_ledger.csv","row_number":261,"scripts_as_recorded":"v181_clock_is_conformal_symmetry.py","status_as_recorded":"Conformal-symmetry/deck face of SEAM.EQUIV.01 [O] (downstream per v323) + [E] (equivariant uniformisation + the weakening)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [E] for h^0=5=rank(D5)=g_car and rankH1=3=N_fam from one mu4 divisor; [C] for the carrier=mode-space identification (does not replace the over-determined g_car=5)","checked_by_registry":false,"claim_excerpt":"THE RIEMANN-ROCH CARRIER READING (external-review proposal 2026-06-14): (g_car, N_fam)=(5,3) are the two canonical invariants of ONE object, the four-point seam divisor D=mu4 on P^1. [E]: h^0(P^1,O(mu4))=deg+1=5 (function side) and rank H_1(P^1\\\\mu4)=deg-1=3 (cycle side, already QGEO.COHOM.01/v177); g_car=5=rank(D5) (carrier=so(10) half-spinor, rank D5+rank A3=5+3=8=rank E8, v1), N_fam=3=(dim S+ -1)/g_car. [C]: the i","claim_id":"ARCH.RRCAR.01","dependencies_as_recorded":"ARCH.CORE.01; AX.P2.01; QGEO.COHOM.01; E8.GLU.01; v177_seam_marking_kernel.py; v1_e8_glue.py","external_data_as_recorded":"-","id":"claim:ARCH.RRCAR.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":262,"scripts_as_recorded":"v189_riemann_roch_carrier.py","status_as_recorded":"Identity [E] (RR arithmetic) + Physical [C] (carrier identification)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: Lambda^even(C_car=5-dim)=S^+=16=2^{g_car-1}=the D5 half-spinor, closing mu4->g_car->D5; [C] for the carrier=Clifford-spinor-of-the-mode-space identification (hardens v189, does not change over-determined g_car=5)","checked_by_registry":false,"claim_excerpt":"RIEMANN-ROCH CARRIER HARDENED FROM g_car TO D5 ITSELF (external-review point 7, 2026-06-14): v189 read g_car=5=h^0(P^1,O(mu4)) and matched rank(D5); this goes one step further -- the 5-dim carrier mode space C_car:=H^0(P^1,O(mu4)) generates the so(10)=D5 half-spinor by its EVEN CLIFFORD ALGEBRA. (1) [I] dim Lambda^even(C^5) = C(5,0)+C(5,2)+C(5,4) = 1+10+5 = 16 = 2^{g_car-1} = dim S^+ (the repo's dim_Splus). (2) [I] s","claim_id":"ARCH.RRCAR.02","dependencies_as_recorded":"ARCH.RRCAR.01; AX.P2.01; E8.GLU.01; v189_riemann_roch_carrier.py; v1_e8_glue.py","external_data_as_recorded":"-","id":"claim:ARCH.RRCAR.02","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":263,"scripts_as_recorded":"v197_rr_carrier_clifford_d5.py","status_as_recorded":"Identity [I] (Clifford dim chain) + Physical [C] (carrier = mode-space spinor)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [E]: S_tot/S_dS >= 2/3 via (x-1)^2 >= 0, equality at the Nariai merge","checked_by_registry":false,"claim_excerpt":"THE ONE-LINE NARIAI ENTROPY BOUND (external-review proposal 2026-06-14): the SdS entropy ratio S_tot/S_dS = (x^2+1)/Phi3(x) (x=r_b/r_c; Phi3=x^2+x+1 the N_fam=3 cyclotomic; HOR.NARIAI.01) satisfies S_tot >= (2/3) S_dS with equality exactly at the Nariai merge x=1, via the perfect square 3(x^2+1)-2*Phi3(x)=(x-1)^2 >= 0 -- a variation-free proof of the entropy floor (the global minimum on x>0 is 2/3=|Z2|/N_fam). Consis","claim_id":"HOR.NARIAI.02","dependencies_as_recorded":"HOR.NARIAI.01; v101_horizon_anchor.py; v8_horizon.py","external_data_as_recorded":"-","id":"claim:HOR.NARIAI.02","location_as_recorded":"tfpt_horizon_readouts","path":"verification/status_ledger.csv","row_number":264,"scripts_as_recorded":"v190_nariai_entropy_bound.py","status_as_recorded":"Identity [E] (exact variation-free entropy bound)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Structural [C]: an affine relabeling exhibiting the known 2/3 ramification; NOT an independent theorem (decoy pairs admit equally exact maps)","checked_by_registry":false,"claim_excerpt":"THE UNIVERSAL BRANCH LINE (external-review proposal 2026-06-14; HONESTLY typed [C], an exact affine RELABELING, NOT a theorem): the map q=7/2+(N_fam^2/2)m carries the SdS branch points m=+-1/N_fam onto the flavor branch points {2,5}={|Z2|,g_car} (m=0 -> 7/2, the branch-divisor sum 7 over 2 / scalaron half-exponent). [E] arithmetic, but the map exists for ANY two pairs of points (two intervals are always affinely equi","claim_id":"HOR.BRANCHLINE.01","dependencies_as_recorded":"HOR.NARIAI.01; HOR.NARIAI.02; FLAV.PENCIL.01; v101_horizon_anchor.py","external_data_as_recorded":"-","id":"claim:HOR.BRANCHLINE.01","location_as_recorded":"tfpt_horizon_readouts","path":"verification/status_ledger.csv","row_number":265,"scripts_as_recorded":"v191_universal_branch_line.py","status_as_recorded":"Physical/structural [C] (exact affine relabeling, not a theorem)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Geometric [O]: QGEO.ENERGY.01 (rho preserves the DtN energy form) is a sharper operator-identity restatement of QGEO.SYM.01 -- relocates the bedrock, does not eliminate it","checked_by_registry":false,"claim_excerpt":"THE ENERGY-CONSERVING-CLOCK REFORMULATION (external-review proposal 2026-06-14; HONESTLY typed: RELOCATES the bedrock, does NOT eliminate it): the proposed premise QGEO.ENERGY.01 (rho^* Lambda_Sigma rho = Lambda_Sigma -- the carrier clock preserves the Calderon/DtN energy form of the RP seam double) feeds the existing downstream chain (conformality -> Moebius -> z|->iz -> mu4 -> QGEO.SYM.01, the v180/v181 reduction).","claim_id":"QGEO.ENERGY.01","dependencies_as_recorded":"QGEO.SYM.01; QGEO.ISO.01; v181_clock_is_conformal_symmetry.py; v180_clock_is_mobius.py","external_data_as_recorded":"-","id":"claim:QGEO.ENERGY.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":266,"scripts_as_recorded":"v192_qgeo_energy_clock.py","status_as_recorded":"Geometric premise [O] (operator-identity restatement of QGEO.SYM.01; relocates, not eliminates)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Geometric [O]: QGEO.ENERGY.02 = [rho,Lambda_Sigma]=0 (energy commutator); non-circular proof target for QGEO.SYM.01 IFF the raw-seam DtN (sub-claim 2) is RP-definable; exact rider: the EH coefficient selects q(A3)=3/4 (family), not q(D5)=5/4 (carrier)","checked_by_registry":false,"claim_excerpt":"THE ENERGY-COMMUTATOR CONTRACT (external-review proposal 2026-06-14; the NON-CIRCULAR sharpening of QGEO.ENERGY.01): the proposed premise is the operator identity [rho, Lambda_Sigma]=0 on the rank-8 Calderon polarisation -- rho the carrier clock, Lambda_Sigma the Dirichlet-to-Neumann (Calderon) energy form of the RAW RP seam double. Three sub-claims make it non-circular: (1) [E] rho is defined from the CARRIER algebr","claim_id":"QGEO.ENERGY.02","dependencies_as_recorded":"QGEO.ENERGY.01; QGEO.SYM.01; QGEO.COHOM.01; HOR.CLOCK.01; v150_replica_eh_model.py; v192_qgeo_energy_clock.py","external_data_as_recorded":"-","id":"claim:QGEO.ENERGY.02","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":267,"scripts_as_recorded":"v193_qgeo_energy_commutator.py","status_as_recorded":"Geometric premise [O] (energy-commutator proof target; sharper, non-circular IFF sub-claim 2)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Geometric [O]: subclaim 2 (raw-seam DtN RP-definability) met at the canonical OS level + finite core [E]; QGEO.SYM.01 reduces to intrinsic Bisognano-Wichmann modular covariance of the quasi-free seam state -- sharper, still [O], not closed","checked_by_registry":false,"claim_excerpt":"SUBCLAIM 2 OF QGEO.ENERGY.02 TACKLED -- 'the raw RP-seam DtN is RP-definable' (external-review next-lever 2026-06-14): a REDUCTION, not a closure. (1) FINITE CORE [E]: rho:z|->iz on H^1(P^1\\\\mu4)=<w1,w2,w3>, wk=z^{k-1}dz/(z^4-1), acts as rho* wk = i^k wk (characters i,-1,-i DISTINCT; (iz)^4-1=z^4-1 invariant) -- verified symbolically; distinct eigenvalues => any operator commuting with rho is DIAGONAL on H^1, and the","claim_id":"QGEO.DTN.01","dependencies_as_recorded":"QGEO.ENERGY.02; QGEO.SYM.01; QGEO.TREE.01; SEAM.HORIZON.01; v177_seam_marking_kernel.py; v155_quasifree_boundary.py; v54_seam_horizon_keystones.py","external_data_as_recorded":"-","id":"claim:QGEO.DTN.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":268,"scripts_as_recorded":"v194_raw_seam_dtn_rp.py","status_as_recorded":"Geometric premise [O] (reduction: subclaim-2 hinge met, finite core [E], bedrock -> BW modular)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [E]: orbit-counting (order-4 rho fixes {0,inf}; no trivial H^1 char; rank 3 => 4 punctures) forces the marks to a free mu4 orbit; residual [O] relocates from 'seam is P^1\\\\mu4' to 'H^1 carries the A3-exponent rep' -- less circular","checked_by_registry":false,"claim_excerpt":"LEFSCHETZ/CHARACTER DERIVATION OF THE FOUR SEAM MARKS (external-review path 2/priority 2, 2026-06-14): instead of POSITING D4 boundary marks (the old QGEO.MARKS.01 finite core), the marks are FORCED to be a free mu4 orbit by orbit-counting plus the H^1 character. (1) [E] rho:z|->iz has order 4 and fixes EXACTLY {0,infinity}; rho^2:z|->-z also fixes only {0,infinity}; so any point off the fixed locus has a FREE order-","claim_id":"QGEO.MARKS.02","dependencies_as_recorded":"QGEO.MARKS.01; QGEO.TREE.01; QGEO.SYM.01; v177_seam_marking_kernel.py; v178_marks_kernel_attempt.py","external_data_as_recorded":"-","id":"claim:QGEO.MARKS.02","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":269,"scripts_as_recorded":"v195_marks_lefschetz_character.py","status_as_recorded":"Identity [E] (orbit/character core) + premise [O] (H^1-rep)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical/identity [N]/[I]: E_fail=0 exactly at the mu4 config and >0 for perturbations (mu4 minimiser); full-operator minimisation = the v194 Bisognano-Wichmann residual [O] -- a concrete discretisable handle on the bedrock","checked_by_registry":false,"claim_excerpt":"THE E_fail VARIATIONAL FUNCTIONAL (external-review path 1, 2026-06-14): a concrete, numerically-testable sharpening of the v194/QGEO.ENERGY.02 target. E_fail(Sigma,rho) = ||[rho,Lambda_Sigma]||^2_HS + ||rho^4-1||^2 + ||Theta rho Theta - rho^{-1}||^2, with E_fail=0 <=> the QGEO.SYM.01 conditions hold (energy commutator + order-4 clock + RP-reflection twist). (1) [E] on the finite H^1 block (rho=diag(i,-1,-i), Lambda d","claim_id":"QGEO.VARI.01","dependencies_as_recorded":"QGEO.ENERGY.02; QGEO.DTN.01; QGEO.SYM.01; v193_qgeo_energy_commutator.py; v194_raw_seam_dtn_rp.py","external_data_as_recorded":"-","id":"claim:QGEO.VARI.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":270,"scripts_as_recorded":"v196_seam_energy_functional.py","status_as_recorded":"Numerical/identity [N]/[I] (finite vanishing exact) + target [O] (full-operator min = BW)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Geometric [O]: bedrock cracked to omega o rho = omega (raw seam state mu4-invariant) -- principal symbol |k| commutes exactly (Fourier diag), Tomita-Takesaki removes the BW circularity, finite block holds; the irreducible residual is the mu4-symmetry of the raw seam measure (operational QGEO.SYM.01), still [O]","checked_by_registry":false,"claim_excerpt":"CRACKING THE BEDROCK TO A STATE-INVARIANCE (2026-06-14): the v194 residual -- the full-L^2 commutator [rho,Lambda_Sigma]=0, framed as Bisognano-Wichmann geometric modular flow with a circularity worry -- is (a) made EXACT at the principal-symbol level and (b) reduced via Tomita-Takesaki to a clean state-invariance, removing the circularity. (1) PRINCIPAL SYMBOL [E]: the DtN principal symbol |k|=sqrt(-d^2/dtheta^2) (L","claim_id":"QGEO.MODULAR.01","dependencies_as_recorded":"QGEO.DTN.01; QGEO.ENERGY.02; QGEO.SYM.01; QGEO.VARI.01; v194_raw_seam_dtn_rp.py; v177_seam_marking_kernel.py","external_data_as_recorded":"-","id":"claim:QGEO.MODULAR.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":271,"scripts_as_recorded":"v198_modular_commutator_reduction.py","status_as_recorded":"Geometric premise [O] (bedrock reduced to a non-circular state-invariance; principal symbol exact)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/premise [E]/[O]: omega o rho=omega is non-circular (rho a carrier automorphism, raw CAR algebra) and reduces to [rho,H_1]=0 <=> H_1 is mu4-character-block-diagonal; residual = the bounded sub-principal symbol has no off-character matrix elements; not a closure","checked_by_registry":false,"claim_excerpt":"ATTACKING omega o rho = omega DIRECTLY ON THE RAW SEAM (work package A, external-review priority 1, 2026-06-14): a further localising reduction, not a closure. (1) SETUP NON-CIRCULAR [E]: rho is the carrier clock = the Coxeter element of W(A3)=S4 (order 4, rho^4=1, v117), an automorphism of the RAW CAR algebra (16 Majoranas = the carrier net, v156/v175); both rho and the algebra are defined from the CARRIER side with","claim_id":"QGEO.STATE.01","dependencies_as_recorded":"QGEO.MODULAR.01; QGEO.SYM.01; QGEO.DTN.01; v198_modular_commutator_reduction.py; v177_seam_marking_kernel.py","external_data_as_recorded":"-","id":"claim:QGEO.STATE.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":272,"scripts_as_recorded":"v199_seam_state_invariance.py","status_as_recorded":"Identity [E] (non-circular setup + reduction) + premise [O] (bounded sub-principal residual)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/premise [E]/[O]: the v199 sub-principal block-diagonality is FORCED by the v195 mu4-mark orbit under a mark-local DtN (a mark-sum over mu4 points is Z4-invariant => Fourier support on modes ≡0 mod 4 => block-diagonal); residual reduces to DtN mark-locality (conformal-deck flatness), the narrowest form of QGEO.SYM.01; not a closure","checked_by_registry":false,"claim_excerpt":"THE v199 BEDROCK RESIDUAL REDUCED ONE GENUINE STEP FURTHER (2026-06-15): block-diagonality of the sub-principal symbol is NOT an independent postulate. (1) [E] the seam DtN is Lambda=|k|+M_f, M_f = multiplication by a curvature function f(theta) on the seam circle (standard Steklov sub-principal structure), so <n|M_f|n'>=f_{n-n'}. (2) [E] M_f is mu4-character-block-diagonal <=> f has Fourier support only on modes ≡0 ","claim_id":"QGEO.SUBPRIN.01","dependencies_as_recorded":"QGEO.STATE.01; QGEO.MARKS.02; QGEO.SYM.01; v199_seam_state_invariance.py; v195_marks_lefschetz_character.py; v198_modular_commutator_reduction.py","external_data_as_recorded":"-","id":"claim:QGEO.SUBPRIN.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":273,"scripts_as_recorded":"v201_seam_subprincipal_marks.py","status_as_recorded":"Identity [E] (block-diagonality = image of the mu4 marks) + premise [O] (mark-local DtN residual)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/Lattice [E]/[L] + premise [O]: cross-ratio 2 (v168) => j=1728 => square modulus => order-4 CM clock (DERIVED, not assumed); unifies the two open QGEO residuals (v180 ISO + v201 SUBPRIN) into ONE canonical flat-pillowcase-metric statement; does NOT close QGEO.SYM.01 (the constant-curvature representative choice stays open, milder/more canonical than the bare isometry premise)","checked_by_registry":false,"claim_excerpt":"PILLOWCASE REDUCTION OF QGEO.SYM.01 (2026-06-15): the two separately-tracked open QGEO residuals -- QGEO.ISO.01 (v180; the carrier clock is an order-4 ISOMETRY of the seam metric) and QGEO.SUBPRIN.01 (v201; the DtN sub-principal symbol is MARK-LOCAL, the seam flat away from the mu4 marks) -- are ONE statement: 'the seam carries the uniformising flat orbifold (pillowcase) metric'; and the order-4 clock is DERIVED from","claim_id":"QGEO.PILLOW.01","dependencies_as_recorded":"QGEO.ISO.01; QGEO.SUBPRIN.01; QGEO.RIGID.01; v168_qgeo_rigidity.py; v180_clock_is_mobius.py; v201_seam_subprincipal_marks.py","external_data_as_recorded":"Troyanov 1991 (cone-metric uniformisation); standard elliptic-curve Aut classification (j=1728 -> Z/4, j=0 -> Z/6)","id":"claim:QGEO.PILLOW.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":274,"scripts_as_recorded":"v214_seam_pillowcase.py","status_as_recorded":"Identity/Lattice [E]/[L] (cross-ratio 2 => j=1728 => order-4 CM clock) + premise [O] (canonical constant-curvature metric)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open / falsifiable: bedrock omega o rho=omega recast as four levers (exactly 4 square marks, mod-4 sub-principal support, transfer gap (2/3)^6), freeze-bound via seam_deck_symmetry; carrier-side [E] regression guards, decisive emergence test deferred to QGEO.REALIZE.01; not a closure and not a Bisognano-Wichmann proof","checked_by_registry":false,"claim_excerpt":"BEDROCK AS A FALSIFIABLE KILL-TEST (2026-06-15): QGEO.SYM.01 (omega o rho = omega) is recast as four independently-falsifiable predictions about the raw seam DtN, NOT a proof (a foundational symmetry cannot be derived from nothing, v181/v153; Bisognano-Wichmann would presuppose the very covariance it should produce). Non-circular reduction (v198/v199/v201): omega o rho=omega <=> [rho,C]=0 for the quasi-free covarianc","claim_id":"QGEO.KILL.01","dependencies_as_recorded":"QGEO.SYM.01; QGEO.PILLOW.01; QGEO.SUBPRIN.01; v168_qgeo_rigidity.py; v201_seam_subprincipal_marks.py; v214_seam_pillowcase.py","external_data_as_recorded":"-","id":"claim:QGEO.KILL.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":275,"scripts_as_recorded":"v215_seam_deck_killtest.py","status_as_recorded":"Open (falsifiable kill-test; carrier-side K1-K4 [E], seam-side emergence deferred [O])","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/Lattice [E] + premise [O]: the mark COUNT (4 = 2 chi) and EQUALITY (all order-2) are DERIVED from Gauss-Bonnet + Z2 branch + flatness (three independent selectors: all-order-2, N_fam=3, free order-4); only the square modulus (cross-ratio 2, the order-4 clock) stays the carrier input; executes K1 of QGEO.KILL.01, does NOT close QGEO.REALIZE.01","checked_by_registry":false,"claim_excerpt":"THE FOUR MARKS EMERGE FROM GAUSS-BONNET (2026-06-15; executes the K1 lever of QGEO.KILL.01): an independent Euclidean-orbifold derivation of the seam-mark structure. (1) [E] MARK COUNT = 2 chi: Z2 branch points (cone angle pi, deficit pi) on a flat sphere (chi=2) give n*pi = 2pi*chi(S^2) = 4pi => n = 2 chi = 4 = |mu4| = e1(a) = N_fam+1; the SAME chi=2 that supplies the 8 in c3 = 1/(|Z2| 2pi chi) = 1/(8pi). (2) [E] th","claim_id":"QGEO.MARKS.03","dependencies_as_recorded":"QGEO.MARKS.02; QGEO.PILLOW.01; QGEO.KILL.01; AX.P1.01; v195_marks_lefschetz_character.py; v214_seam_pillowcase.py","external_data_as_recorded":"Gauss-Bonnet; Thurston/Conway classification of closed Euclidean 2-orbifolds","id":"claim:QGEO.MARKS.03","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":276,"scripts_as_recorded":"v216_marks_gauss_bonnet.py","status_as_recorded":"Identity/Lattice [E] (Gauss-Bonnet count + Euclidean-orbifold uniqueness) + premise [O] (square modulus)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical [N] + premise [O]: free-n + free-positions scan on the actual DtN/state confirms 4-square is the unique joint minimiser of {clock-invariance, 3 families, gap (2/3)^6}; executes K1 of QGEO.KILL.01 numerically, does NOT close QGEO.REALIZE.01; Python-only","checked_by_registry":false,"claim_excerpt":"NUMERICAL EMERGENCE SCAN (2026-06-15; the numerical sibling of QGEO.MARKS.03, as v210 is to v201): with the NUMBER of marks n AND their POSITIONS free, the 4-equally-spaced (square) configuration is the joint minimiser of {clock-invariance + 3-family cohomology + transfer gap (2/3)^6} on the actual seam DtN/state. (1) [N] n=4 equally-spaced marks give a clock-invariant quasi-free state ||rho_4 C rho_4^dag - C|| ~ 1e-","claim_id":"QGEO.EMERGE.01","dependencies_as_recorded":"QGEO.MARKS.03; QGEO.KILL.01; v200_seam_variational_scan.py; v210_mark_local_dtn.py; v216_marks_gauss_bonnet.py","external_data_as_recorded":"-","id":"claim:QGEO.EMERGE.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":277,"scripts_as_recorded":"v217_marks_emergence_scan.py","status_as_recorded":"Numerical [N] (emergence confirmation on the real DtN/state) + premise [O] (selector is carrier input)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Physical bridge [C]: the TFPT CKM point (no flavor fit) + standard short-distance input give BR(K+)=9.45e-11 and BR(K_L)=3.33e-11; consistent with NA62 at ~1.2 sigma; dated kill test = stable NA62 outside [7,12]e-11 or KOTO-II off the GN point; not a compiler power","checked_by_registry":false,"claim_excerpt":"RARE KAON SECTOR K -> pi nu nubar FROM THE TFPT CKM POINT (2026-06-15, archive integration): the kernel fixes the full CKM matrix (s12=lambda_C, s23=phi0/(1+lambda_C)=|V_cb|, s13=lambda_C^3/3, delta=pi/3+3 lambda_C^2=1.19823 rad; v18/v88) with NO flavor fit; feeding the exact point into the standard Brod-Gorbahn-Stamou short-distance formulas gives BR(K+ -> pi+ nu nubar)=9.45e-11 and BR(K_L -> pi0 nu nubar)=3.33e-11.","claim_id":"FR.RAREKAON.01","dependencies_as_recorded":"v18_quark_yukawa.py; v88_cp_phase_audit.py","external_data_as_recorded":"NA62 (13.0 +3.3/-3.0)e-11; KOTO; Brod-Gorbahn-Stamou SD input","id":"claim:FR.RAREKAON.01","location_as_recorded":"tfpt_2_standard_model","path":"verification/status_ledger.csv","row_number":278,"scripts_as_recorded":"v202_rare_kaon.py","status_as_recorded":"Physical bridge [C] (CKM point [I], branching ratios external-SD [C], dated kill test [X])","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [E]: the EHT polarization coupling 16 c3^4 = 1/(256 pi^4) = delta_top/3 is the SAME compiler number as the alpha-kernel correction; the 1/r^2 shape + achromaticity + sign-flip are TFPT-fixed [C], the amplitude an MHD/GR weight; dated [X] kill test = three nulls after honest GRMHD subtraction; NOT the UFE metric (Nariai/seam=horizon supersedes it)","checked_by_registry":false,"claim_excerpt":"EHT ACHROMATIC POLARIZATION-ROTATION INTERCEPT (2026-06-15, archive integration): beta_BH(r) = Q_e^eff Q_m^eff/(256 pi^4 r^2) = 16 c3^4 (Q_e Q_m / r^2) around a horizon-scale black hole. (1) [E] the coupling 16 c3^4 = 1/(256 pi^4) EXACTLY (c3=1/8pi) -- no free coupling. (2) [E] alpha-kernel cross-link: 16 c3^4 = delta_top/3 with delta_top = 48 c3^4 = 3/(256 pi^4), the SAME top-form coefficient that fixes the alpha-ke","claim_id":"HOR.EHT.01","dependencies_as_recorded":"AX.P1.01; HOR.01; EM.FP.01","external_data_as_recorded":"EHT/ngEHT polarimetry (forward GRMHD subtraction)","id":"claim:HOR.EHT.01","location_as_recorded":"tfpt_horizon_readouts","path":"verification/status_ledger.csv","row_number":279,"scripts_as_recorded":"v203_eht_achromatic.py","status_as_recorded":"Identity [E] (coupling 16 c3^4=1/(256 pi^4)=delta_top/3) + physical bridge [C] (1/r^2 shape, achromaticity, sign-flip) + dated kill test [X] (three nulls)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical [N]: argmin E_fail over the clock angle = theta=pi/2 (the mu4 clock z|->iz), decoys lose; a numerical sign that the variational principle selects mu4; full operator-valued minimisation stays the v199 residual [O]","checked_by_registry":false,"claim_excerpt":"THE DISCRETISED VARIATIONAL TEST (work package B, external-review, 2026-06-14): v196 showed E_fail=0 at the mu4 config on the fixed H^1 block; here the clock angle is a FREE parameter and E_fail is MINIMISED over it. (1) [N] taking rho(theta)=diag(e^{i m theta}) on the H^1 generators m=(1,2,3) and E_fail(theta)=||rho(theta)^4-1||^2 + faithfulness penalty (penalising coincident characters), a scan over theta in (0,pi)","claim_id":"QGEO.VARI.02","dependencies_as_recorded":"QGEO.VARI.01; QGEO.STATE.01; v196_seam_energy_functional.py; v199_seam_state_invariance.py","external_data_as_recorded":"-","id":"claim:QGEO.VARI.02","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":280,"scripts_as_recorded":"v200_seam_variational_scan.py","status_as_recorded":"Numerical sign [N] (argmin = mu4 clock) + open full minimisation [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Reduction [I]/[C]: external-review concerns A/B/D reduce to {QGEO.SYM.01; F_transfer}; C is data-only (JUNO/CMB-S4)","checked_by_registry":false,"claim_excerpt":"THE FOUR EXTERNAL-REVIEW CONCERNS REDUCE TO THE TWO ALREADY-NAMED RESIDUALS + ONE DATA-ONLY ITEM (a careful 2026-06-14 review raised A mapping 2D->4D, B UV-gravity abstractness, C grammar-tuning/meta-look-elsewhere, D Koide Mobius flow; this maps them honestly): three reduce by the same discipline as v175-v181 onto {QGEO.SYM.01 (the seam realisation), F_transfer (the continuous transfer functor / missing dynamical pr","claim_id":"REVIEW.MAP.01","dependencies_as_recorded":"QGEO.SYM.01; FR.KOIDE.06; FR.ETAB.02; AUDIT.NULLMC.01; REG.FREEZE.01; QFT.FOCK.01; HOR.NARIAI.01; SEAM.CYCLE.01","external_data_as_recorded":"-","id":"claim:REVIEW.MAP.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":281,"scripts_as_recorded":"v182_reviewer_residual_map.py","status_as_recorded":"Reduction map [I]/[C] (A/B/D reduce to the two named residuals; C is experiment-only)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Physical [C]: thermal-leptogenesis route viable (band brackets observed 6.1e-10); M1/washout scenario inputs, eta_B stays [C]","checked_by_registry":false,"claim_excerpt":"ETA_B LEPTOGENESIS TRANSFER OPERATIONALISED (the Tier-3 F_transfer Boltzmann path made falsifiable; NOT a new structural class, NOT a compiler theorem): type-I thermal leptogenesis eta_B ~ 0.96e-2 eps_1 kappa_f (sphaleron a_sph=28/79) fed by TFPT's neutrino sector -- normal ordering (m2,m3 from dm2_sol,dm2_atm) and the predicted phase delta_CP=4pi/3=240deg (|sin|=0.866). (1) Davidson-Ibarra eps_1=(3/16pi)M1 m3/v^2 ~ ","claim_id":"FR.ETAB.02","dependencies_as_recorded":"FR.ETAB.01; FLAV.RGSTAB.01; v9_neutrino_texture.py","external_data_as_recorded":"NuFIT (dm2_sol, dm2_atm); Planck (eta_B = 6.1e-10)","id":"claim:FR.ETAB.02","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":282,"scripts_as_recorded":"v169_etaB_boltzmann_interface.py","status_as_recorded":"Physical [C] (viable falsifiable scenario; M1/washout scenario inputs)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/Lattice [I]/[L]: E8 atlas = projection of power-sum + determinant alphabets; audit bridge, anti-numerology","checked_by_registry":false,"claim_excerpt":"E8 SLICE COMPRESSION LEMMA (the seven E8 audit slices are ONE projection of two small alphabets; anti-numerology compression, NOT new physics): (1) the anchor power sums p_n(a)=2+2^n give P=(3,4,6,10) whose K4 edge products are all carrier blocks (12=|R(A3)|, 18=N_fam|R+(A3)|, 30=h(E8), 24=|W(A3)|, 40=|R(D5)|, 60=D_start; triples 120,240,720) [I]; (2) the six Sheet-Diamond operators Q,K,R,C,L,F have determinants (3,4","claim_id":"E8.SLICE.01","dependencies_as_recorded":"ARCH.SPINE.01; FLAV.KQ.01; CAR.SM.01","external_data_as_recorded":"-","id":"claim:E8.SLICE.01","location_as_recorded":"tfpt_3","path":"verification/status_ledger.csv","row_number":283,"scripts_as_recorded":"v170_diamond_slice_compression.py","status_as_recorded":"Identity/Lattice [I]/[L] (exact integer/lattice identities)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: OS positivity = positive moment problem; Sugawara gap safety 31=1+h^v(E8); cluster 729/665, xi=0.411","checked_by_registry":false,"claim_excerpt":"ATOMIC OS MOMENT LEMMA + SUGAWARA GAP SAFETY (the admissible transfer sector's OS positivity as a positive moment problem, and its gap as an E8 Sugawara inequality): (1) spec(T)={1,(2/3)^6,(1/3)^6}={1,64/729,1/729} makes every scalar two-point correlator C(n)=A+B r^n+C s^n the moment sequence of the positive atomic measure A d1+B dr+C ds, so every OS Hankel matrix factorises as a Vandermonde Gram H=W diag(A,B,C) W^T ","claim_id":"QFT.OSMOMENT.01","dependencies_as_recorded":"GATE.METRIC.XI.01; SEAM.CYCLE.01; GATE.METRIC.07","external_data_as_recorded":"-","id":"claim:QFT.OSMOMENT.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":284,"scripts_as_recorded":"v171_os_moment_cluster.py","status_as_recorded":"Identity [I] (moment/spectral/Sugawara exact) + [C] (declared V_metric norm)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [I]: seed 4/3 = halved (E8)1 Weyl anomaly on S^2; b3=7=scalaron exponent (confinement<->inflation)","checked_by_registry":false,"claim_excerpt":"TRACE-ANOMALY ORIGIN OF THE SEED PREFACTOR 4/3 + the shared integer 7 (b3 = scalaron exponent): (1) the retained seed phi0=(4/3)c3+48 c3^4 has base (4/3)c3=1/(6pi); the prefactor 4/3 is the conformal Weyl anomaly of the seam CFT -- over S^2 (chi=2) the (E8)1 (c=8) trace anomaly is c*chi/6=8/3, halved by the one-sided |Z2| Moebius identification to 4/3 = dim S+/dim g_SM = 16/12; the Cabibbo seed prefactor IS the halve","claim_id":"SEED.ANOMALY.01","dependencies_as_recorded":"CAR.SM.01; FR.MPME.01; ANCHOR.GEN.01; v138_vw_firewall.py","external_data_as_recorded":"Volkov-Wipf Nucl.Phys.B582(2000)313","id":"claim:SEED.ANOMALY.01","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":285,"scripts_as_recorded":"v172_trace_anomaly_seed.py","status_as_recorded":"Identity [I] (trace anomaly + b3 + VW factorisation exact)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Formalised [F]: theta_eff=0 via Pfaffian reality (sheet pairing + gamma5-Hermiticity + RP positive branch)","checked_by_registry":false,"claim_excerpt":"STRONG CP AS PFAFFIAN REALITY (theta_eff=0 as a model-level CAR/Pfaffian theorem; formalises the tfpt_2 structural chain): in the self-dual CAR (16-Majorana) seam model, (1) the sheet-odd Calderon involution {D_Sigma, Sigma}=0 forces the spectrum into +-lambda pairs [I] (verified: eigenvalues symmetric about 0 to 1e-15); (2) gamma5-Hermiticity D^dag=gamma5 D gamma5 makes conj(det D)=det D, so the fermion-measure Pfaf","claim_id":"FLAV.STRONGCP.02","dependencies_as_recorded":"FLAV.QGEO.02; CAR.QFREE.01; GATE.METRIC.13","external_data_as_recorded":"-","id":"claim:FLAV.STRONGCP.02","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":286,"scripts_as_recorded":"v173_pfaffian_cp_car.py","status_as_recorded":"Formalised [F] (machine-checked model demonstration)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/Lattice [I]/[L]: CAR cone 2^15->2^11; Witten index 11=Plucker norm=dim S+ - g_car; g-theorem Delta c=0 rigidity","checked_by_registry":false,"claim_excerpt":"SEAM FOCK-SPACE READINGS (three exact audit bridges that sharpen the QFT/topological reading of already-used objects): (1) CAR CONE COMPRESSION [I] -- the even CAR algebra of the 16 seam Majoranas has dim Lambda^even(R^16)=2^15=32768 directions (cumulant blocks C(16,4)=1820, C(16,6)=8008, C(16,8)=12870), but a quasi-free Bogoliubov transport is the second quantisation Gamma(t)|_Lambda^m=Lambda^m(t), so the whole cone","claim_id":"QFT.FOCK.01","dependencies_as_recorded":"GATE.UWALL.06; CAR.QFREE.01; GATE.METRIC.14; v42_exterior_leg.py; v161_one_particle_reduction.py","external_data_as_recorded":"-","id":"claim:QFT.FOCK.01","location_as_recorded":"tfpt_2;tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":287,"scripts_as_recorded":"v174_seam_fock_readings.py","status_as_recorded":"Identity/Lattice [I]/[L] (cone count + Witten index + central-charge conservation)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Formalised [F]: full-cone RP (all m, CAR functor) + (E8)1 net existence (assembled+verified); the one [O] is the seam realisation QGEO.REALIZE.01","checked_by_registry":false,"claim_excerpt":"NET EXISTENCE + FULL-CONE RP DISCHARGED TO [F] (the heavy artillery; the 'three open QFT theorems' are two [F] + one irreducible [O], nothing fabricated): (1) FULL-CONE REFLECTION POSITIVITY FOR ALL m [F] -- the CAR second-quantisation functor Gamma(t)=(+)_m Lambda^m(t) of the one-particle seam contraction t acts on the COMPLETE Fock space Lambda^*(R^16) (dim 2^16=65536); by the exterior-power spectrum theorem every ","claim_id":"QFT.NETRP.01","dependencies_as_recorded":"GATE.METRIC.11; GATE.METRIC.13; GATE.METRIC.16; GATE.METRIC.17; QGEO.RIGID.01; QGEO.REALIZE.01; v83_e8net_holomorphic_uniqueness.py; v125_glue_qsystem.py; v161_one_particle_reduction.py","external_data_as_recorded":"Buchholz-Mack-Todorov; Boeckenhauer-Evans-Kawahigashi; Frenkel-Kac-Segal; Dong-Xu; Kawahigashi-Longo","id":"claim:QFT.NETRP.01","location_as_recorded":"tfpt_research_contracts;tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":288,"scripts_as_recorded":"v175_net_existence_full_cone.py","status_as_recorded":"Formalised/Identity [F]/[I] (all-m functoriality + verified net data) + [O] (the seam realisation)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Physical bridge KILLED [X] fired 2026-08-04: a_mu^seam = delta_2/(2 pi) = 45/(524288 pi^9) = 2.879e-9 stays an exact value [E], but the WP25+BMW lattice-HVP consensus (Experiment - SM = 0.5 sigma) puts the converged Delta a_mu outside 2.879e-9 +- 0.5e-9 -- the [C] vertex identification is excluded in its present form; bridge dissolved, compiler core untouched; not a compiler power","checked_by_registry":false,"claim_excerpt":"MUON g-2 SEAM VERTEX (2026-06-15, archive integration of the old muon-g2 note, re-typed for the current kernel): the carrier fixes a second-order topological defect delta_2 = B*gamma*delta_top^2 = (5/4)delta_top^2 (delta_top=Omega_adm c3^4=48 c3^4=3/256pi^4, v2/v23; B*gamma=(3/2)(5/6)=5/4 the carrier compression quotient, v51); the seam-loop projection a_mu^seam = delta_2/(2 pi) = 45/(524288 pi^9) = 2.879e-9. (1) [E]","claim_id":"FR.MUONG2.01","dependencies_as_recorded":"v2_carrier_pascal.py; v23_anchor_generator.py; v51_boundary_half_step.py","external_data_as_recorded":"Fermilab+BNL world average; Aoyama et al. WP2020 dispersive SM; lattice/CMD-3 HVP","id":"claim:FR.MUONG2.01","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":289,"scripts_as_recorded":"v204_muon_seam_g2.py","status_as_recorded":"Physical bridge KILLED: dated kill test [X] fired 2026-08-04 (exact value stays [E]; the [C] vertex identification is excluded in its present form -- bridge dissolved, compiler core untouched)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [E]: xi = c3/phi_tree = 3/4 = q(A3) = ln(m/mu) -- an independent route to the gravitational 3/4; the kappa^2=xi phi0/c3^2 ansatz is the [C] bridge, G is a metrology output, 1/G the one anchor","checked_by_registry":false,"claim_excerpt":"GRAVITATIONAL 3/4 OVER-DETERMINATION (2026-06-15, archive integration of the old Eliminating-K note): the torsion-compression ansatz kappa^2 = xi phi0/c3^2 with the Einstein limit kappa^2=8 pi G fixes xi = 8 pi c3^2/phi0 = c3/phi0 (since 8 pi c3^2 = c3), and at tree level phi_tree=1/(6 pi) this is EXACTLY 3/4. (1) [E] tree identity xi = c3/phi_tree = (1/8pi)/(1/6pi) = 3/4. (2) [E] Einstein-limit reduction 8 pi c3^2 =","claim_id":"GRAV.XI.01","dependencies_as_recorded":"v152_norm_is_anchor.py; v68_seeley_dewitt_residual.py; v60_lambda_metrology_branch.py","external_data_as_recorded":"-","id":"claim:GRAV.XI.01","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":290,"scripts_as_recorded":"v205_xi_threequarter.py","status_as_recorded":"Identity [E] (tree 3/4 + over-determination) + physical bridge [C] (the kappa^2 ansatz)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical/bridge [N]/[C]: delta_Sigma=48 e^{-2pi alpha^-1/3}~1.085e-123, (8pi)^2 convention split, |log10|~122.96 (v60 consistent); H0=66.5..67.1 below Planck, does NOT relieve the Hubble tension; [C] readout (imported Omega_b, omega_DM)","checked_by_registry":false,"claim_excerpt":"COSMOLOGICAL-CONSTANT BRANCH H0 = 66.5..67.1 (2026-06-15, archive integration of the tfpt-31 CC note; sharpens the qualitative H0-vs-Lambda row): the seam number delta_Sigma = m_1 e^{-2 pi alpha^-1/3} with the lowest-block m_1=Omega_adm=48. (1) [N] delta_Sigma^lead = 48 e^{-2 pi*137.036/3} ~ 1.085e-123. (2) [E] convention split M_Pl^4/Mbar^4 = (8 pi)^2 = 631.65 (unreduced vs reduced Planck density -- must be displaye","claim_id":"GRAV.H0.01","dependencies_as_recorded":"v60_lambda_metrology_branch.py; v55_coxeter_cycle.py","external_data_as_recorded":"Planck 2018 (H0=67.36+-0.54); SH0ES (73.0+-1.0)","id":"claim:GRAV.H0.01","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":291,"scripts_as_recorded":"v206_h0_lambda_branch.py","status_as_recorded":"Numerical [N] (delta_Sigma, 123-orders) + physical bridge [C] (H0 flatness readout)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open/plausibility [O]: a complementary continuum-FRG argument (non-Gaussian UV fixed point exists from {c3,phi0}); y^2=16 c3^2 exact; NOT load-bearing, the seam-net (v175) stays primary, G_metric open","checked_by_registry":false,"claim_excerpt":"ASYMPTOTIC SAFETY -- A SECOND [P] ROUTE TO THE METRIC SECTOR (2026-06-15, archive integration of the old Five-Problems note; NOT load-bearing, does NOT close G_metric): the current theory closes QG via the discrete seam-net/AQFT programme (v175; open premise QGEO.REALIZE.01); this records a COMPLEMENTARY continuum-FRG argument that a non-Gaussian UV fixed point exists from the same axioms. Setup d_t g = (2 + eta_R(g)","claim_id":"GRAV.ASYMP.01","dependencies_as_recorded":"v175_net_existence_full_cone.py; v28_gravity_fR.py","external_data_as_recorded":"Reuter Asymptotic-Safety programme (external)","id":"claim:GRAV.ASYMP.01","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":292,"scripts_as_recorded":"v207_asymptotic_safety.py","status_as_recorded":"Open/plausibility [O] (a [P]-typed second QG route; not load-bearing) + [E] (y^2=16 c3^2)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity/bridge [E]/[C]: T_H=kappa/2pi from modular flow (2pi=1/4c3); scalaron Wald entropy S_W=(A/4G)(1+R_h/3M_s^2) exact from v28; area law S_BH=A/4G; the BH/modular identification is [C]","checked_by_registry":false,"claim_excerpt":"BLACK-HOLE THERMODYNAMICS FROM THE SEAM: modular Hawking temperature + scalaron-corrected Wald entropy (2026-06-15, archive integration of the dropped tfpt-42 stationary-horizons/compact-objects section, re-typed through the Tomita-Takesaki seam work v198/v199). (1) [E] MODULAR T_H: the modular flow Delta^{it}=e^{-2 pi t K_H} (Bisognano-Wichmann/Tomita-Takesaki) gives KMS at beta=2 pi and T_H = kappa/(2 pi); the 2 pi","claim_id":"HOR.BHTHERMO.01","dependencies_as_recorded":"AX.P1.01; HOR.01; v57_horizon_crosslinks.py; v28_gravity_fR.py; v198_modular_commutator_reduction.py","external_data_as_recorded":"Bisognano-Wichmann; Wald entropy","id":"claim:HOR.BHTHERMO.01","location_as_recorded":"tfpt_horizon_readouts","path":"verification/status_ledger.csv","row_number":293,"scripts_as_recorded":"v208_bh_thermodynamics.py","status_as_recorded":"Identity [E] (modular 2pi=1/4c3, scalaron Wald factor, area law) + physical bridge [C] (the BH/modular identification)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open/synthesis [O]: BH = seam fixed point (no singularity, phi->phi_*), maximal BH = anchor (Nariai roots (1,1,-2)=traceless a), info via Page recovery (2/3)^6, Planck-scale floor; [P] reading, NOT load-bearing, RN metric not resurrected","checked_by_registry":false,"claim_excerpt":"BLACK HOLE AS A SEAM FIXED POINT (topological defect), NOT a singularity (2026-06-15, archive integration of the old Five-Problems BH picture; the SUPERSEDED torsion/RN-vortex metric is DROPPED -- RN-type metric superseded by Nariai/seam=horizon v101-v104/v190, cf. v203). Built from established suite atoms. (1) [E] NO SINGULARITY = SEAM FIXED POINT: the gapped attractor multiplier lambda_2=(2/3)^6=64/729 with gap Del","claim_id":"HOR.BHCORE.01","dependencies_as_recorded":"v54_seam_horizon_keystones.py; v56_unique_attractor.py; v57_horizon_crosslinks.py; v101_horizon_anchor.py; v190_nariai_entropy_bound.py","external_data_as_recorded":"-","id":"claim:HOR.BHCORE.01","location_as_recorded":"tfpt_horizon_readouts","path":"verification/status_ledger.csv","row_number":294,"scripts_as_recorded":"v209_bh_regular_core.py","status_as_recorded":"Open/synthesis [O] (a [P]-typed structural reading; not load-bearing) + [E] (the underlying anchor/attractor atoms)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical/premise [N]/[O]: mark-local DtN => omega o rho = omega certified for realistic von-Mises Steklov profiles AND at the quasi-free state level (rho C rho^dag = C to 1e-13); negative controls (off-centre, Z3, generic) break by O(1); the seam being mark-local stays [O], the narrowest form of QGEO.SYM.01, not a closure","checked_by_registry":false,"claim_excerpt":"MARK-LOCAL DtN CERTIFIED ON REALISTIC STEKLOV PROFILES + AT THE STATE LEVEL (2026-06-15): a numerical SHARPENING of QGEO.SUBPRIN.01/v201, carried to the quasi-free STATE (the actual omega o rho = omega, not just [rho,Lambda]=0); NOT a closure of QGEO.SYM.01. v201 argued at the abstract mode level; here a real von-Mises curvature bump g(theta) localised at a puncture, summed over the four mu4 marks f(theta)=sum_{j=0}^","claim_id":"QGEO.MARKLOCAL.01","dependencies_as_recorded":"QGEO.SUBPRIN.01; QGEO.STATE.01; QGEO.MODULAR.01; v201_seam_subprincipal_marks.py; v198_modular_commutator_reduction.py","external_data_as_recorded":"-","id":"claim:QGEO.MARKLOCAL.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":295,"scripts_as_recorded":"v210_mark_local_dtn.py","status_as_recorded":"Numerical certification [N] (implication on realistic profiles + state level) + premise [O] (the physical seam being mark-local)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Formal [F]/[O]: the QGEO.SYM.01 conditional theorem (mark-local DtN => omega o rho = omega, via 4th-root orthogonality + character block-diagonality) is Lean-proved (AUDIT: PASS, clean axioms); the seam-deck premise stays [O], a typed target like CalderonProjector -- not a closure of QGEO.SYM.01","checked_by_registry":false,"claim_excerpt":"LEAN 4 FORMALISATION of the QGEO.SYM.01 CONDITIONAL THEOREM (2026-06-15; the algebraic core of v201/v210, machine-proved) -- AUDIT: PASS, no sorry/admit, no domain axioms (#print axioms = propext, Classical.choice, Quot.sound only; the two block-diagonality theorems even use only propext+Quot.sound). New module TfptCarrier/SeamDeckClosure.lean proves: (1) [F] geom_sum_fourth_root: for ζ:ℂ with ζ^4=1, Σ_{j<4} ζ^j = (i","claim_id":"FORM.QGEO.01","dependencies_as_recorded":"QGEO.MARKLOCAL.01; QGEO.SUBPRIN.01; QGEO.MARKS.01; FORM.GLUE.01","external_data_as_recorded":"-","id":"claim:FORM.QGEO.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":296,"scripts_as_recorded":"lean4-carrier-rigidity","status_as_recorded":"Formal [F] (conditional theorem) + [O] (the seam-deck premise)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Formal [F]/[O]: QGEO.UNIFORM.01 (order-4 Moebius normal form z->iz, D4 relation sigma.rho.sigma=rho^{-1}, orbit->mu4, multiplier classification zeta=+-i) Lean-proved (AUDIT: PASS, clean axioms, signature-locked); the raw-seam marking obligation QGEO.MARKS.01 stays [O]","checked_by_registry":false,"claim_excerpt":"LEAN 4 FORMALISATION of QGEO.UNIFORM.01 (the geometric normal form of v177; the UNIFORM node of the QGEO proof tree) -- AUDIT: PASS, no sorry/admit, no domain axioms (only propext, Classical.choice, Quot.sound). New module TfptCarrier/MobiusUniformisation.lean machine-proves the constructive uniformisation content: (1) [F] rho_pow_four: the clock rho:z->iz has rho^4=id; (2) [F] rho_order_exactly_four: rho^2 != id (rh","claim_id":"FORM.QGEO.02","dependencies_as_recorded":"QGEO.TREE.01; QGEO.MARKS.01; FORM.QGEO.01; FORM.GLUE.01","external_data_as_recorded":"-","id":"claim:FORM.QGEO.02","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":297,"scripts_as_recorded":"lean4-carrier-rigidity","status_as_recorded":"Formal [F] (uniformisation normal form) + [O] (the raw-seam marking obligation QGEO.MARKS.01)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Formal [F]/[O]: QGEO.COHOM.01 (pullback character rho* omega_k = i^k omega_k, grading (1,2,3)=A3 exponents) + MODULE reflection parity (sigma swaps omega1<->omega3, fixes omega2) Lean-proved (AUDIT: PASS, clean axioms, signature-locked); the MARKS/KERNEL obligations and MODULE uniqueness stay [O]","checked_by_registry":false,"claim_excerpt":"LEAN 4 FORMALISATION of QGEO.COHOM.01 (the character node of v177) + the MODULE reflection parity -- AUDIT: PASS, no sorry/admit, no domain axioms (only propext, Classical.choice, Quot.sound). New module TfptCarrier/CohomologyGrading.lean machine-proves: (1) [F] the three H^1(P^1 minus mu4) eigenforms omega_k = z^{k-1}/(z^4-1) (k=1,2,3) have pullback character rho* omega_k = i^k omega_k under the clock rho:z->iz -- o","claim_id":"FORM.QGEO.03","dependencies_as_recorded":"QGEO.TREE.01; QGEO.MARKS.01; FORM.QGEO.01; FORM.QGEO.02","external_data_as_recorded":"-","id":"claim:FORM.QGEO.03","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":298,"scripts_as_recorded":"lean4-carrier-rigidity","status_as_recorded":"Formal [F] (COHOM character grading + MODULE reflection parity) + [O] (the raw-seam obligations)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Physical [C]: theta_i = pi N_fam/g_car = 3 pi/5 = 108 deg (spine quotient) lands on Omega_DM ~106 deg ROBUSTLY (mild-anharmonic, far below the 170 deg hilltop) -- a more robust DM branch than v185; an alternative ansatz, the full solver decides; kill test outside ~[0.08,0.16] demotes the branch","checked_by_registry":false,"claim_excerpt":"AXION DM SPINE-ANGLE BRANCH theta_i = pi N_fam/g_car = 3 pi/5 = 108 deg (2026-06-15): an ALTERNATIVE, more ROBUST misalignment angle than the determinant-line hilltop theta_i ~ 170 deg (FR.DM.03/v185, which over-produces Omega_a h^2 ~ 0.66 ~ 5.5x). (1) [I] RATIONAL MOTIVE: theta_i = pi N_fam/g_car = 3 pi/5 = 108 deg EXACTLY (the central spine quotient 3/5 = N_fam/g_car, a rational multiple of pi, NOT tuned to the rel","claim_id":"DM.AXION.SPINE.01","dependencies_as_recorded":"FR.DM.01; FR.DM.02; FR.DM.03; v185_axion_relic_solver.py","external_data_as_recorded":"Planck Omega_DM h^2 = 0.12","id":"claim:DM.AXION.SPINE.01","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":299,"scripts_as_recorded":"v211_axion_spine_angle.py","status_as_recorded":"Physical [C] (spine angle = structural rational / NOT observable post-inflationary; relic from f_a + N_DW=1; reframed by FR.DM.02)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity [E]: theta_i = 3 pi/5 is the regular g_car-gon (pentagon) interior angle, cos theta_i = -1/(2 phi), and the golden character is unique to g_car=5 -- so the 'unmapped' golden/icosahedral E8 structure (v354/v313) is the geometry of the one external cosmological input theta_i (v211); [C] a re-reading that refines v354 and gives a geometric motive for the spine branch, but does NOT upgrade DM.AXION.SPINE.01 (stays [C]) or close any gate","checked_by_registry":false,"claim_excerpt":"THE 'UNMAPPED' ICOSAHEDRAL/GOLDEN E8 STRUCTURE SURFACES IN THE ONE EXTERNAL COSMOLOGICAL INPUT theta_i (2026-06-26, v429): a geometric re-reading answering the parsimony question 'why does so much idle E8 structure exist?' for the one case where the idle structure has a job. [E] THETA_I = g_car-GON INTERIOR ANGLE: because N_fam = g_car-2, the spine quotient theta_i = pi N_fam/g_car = (g_car-2)pi/g_car is EXACTLY the ","claim_id":"DM.AXION.PENTAGON.01","dependencies_as_recorded":"DM.AXION.SPINE.01; E8.REVERSE.AUDIT.01; GOLD.ATOMS.01","external_data_as_recorded":"-","id":"claim:DM.AXION.PENTAGON.01","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":300,"scripts_as_recorded":"v429_axion_pentagon_phi.py","status_as_recorded":"Identity [E] (theta_i = regular g_car-gon interior angle; cos = -1/(2 phi); golden character unique to g_car=5) + [C] bridge re-reading (no status change)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Physical [C]: M_1 = M_scal phi0^2/A_Lambda ~ 8.65e9 GeV and m~1 = m_3/A_Lambda ~ 5 meV both use the decuple A_Lambda=10 (no hidden seesaw scale) -- cleaner than v184's M_R phi0^4; eta_B brackets 6.1e-10 but stays [C] (coupling mechanism posited, not derived)","checked_by_registry":false,"claim_excerpt":"LEPTOGENESIS SCALARON-DECUPLE BRANCH (2026-06-15): BOTH Boltzmann inputs share the decuple A_Lambda = 10 = |E(K5)| -- M_1 = M_scal phi0^2/A_Lambda ~ 8.65e9 GeV and m~1 = m_3/A_Lambda ~ 5 meV. A cleaner [C] route than FR.ETAB.03/v184's M_1 = M_R phi0^4, which only RELOCATED the free input to the un-pinned seesaw scale M_R. (1) [I] SHARED DECUPLE: A_Lambda = 10 = |E(K5)| (action-grammar atom) divides BOTH inputs -- M_1","claim_id":"FR.ETAB.04","dependencies_as_recorded":"FR.ETAB.01; FR.ETAB.02; FR.ETAB.03; v169_etaB_boltzmann_interface.py","external_data_as_recorded":"NuFIT (dm2_atm); Planck (eta_B = 6.1e-10)","id":"claim:FR.ETAB.04","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":301,"scripts_as_recorded":"v212_leptogenesis_decuple.py","status_as_recorded":"Physical [C] (sharper scenario; both Boltzmann inputs share A_Lambda=10, no hidden seesaw scale) + [X] kill test","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Contract [C]/[O]: F_transfer = F_observable o F_threshold o F_RG, four axioms (mu4-deck equivariant, Plucker-preserving, positive/stochastic, external-module-explicit), four instances v183/v212/v211/v164; discrete kernels [E], external solvers [C]; the third research contract alongside U_wall/G_metric, guarded by v187, NOT a closure; 2026-08-05 (v777): the jet route is closed by the executed K1 kill of FTRANSFER.CLOCKS.01 -- the surviving form is the FIBERED functor (discrete PGL2 base, constant seam obstruction cocycle {0, +-Delta^2/2}, thermal-vs-RG coset split, relic degenerate); next named step: coset assignment from KMS/modular clock typing","checked_by_registry":false,"claim_excerpt":"THE F_transfer FUNCTOR CONTRACT (2026-06-15): the four frontier transfers are ONE typed functor F_transfer = F_observable o F_threshold o F_RG satisfying four structural axioms, each instance a DISCRETE compiler kernel [E/I] composed with an EXTERNAL continuous solver [C/O]. This is the third research contract (alongside U_wall and G_metric), the structural complement of the v187 typing GUARD: v187 enforces the [C]/[","claim_id":"CONTRACT.F.01","dependencies_as_recorded":"FR.KOIDE.04; FR.ETAB.04; DM.AXION.SPINE.01; FR.MPME.01; v187_ftransfer_laws.py","external_data_as_recorded":"-","id":"claim:CONTRACT.F.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":302,"scripts_as_recorded":"v213_ftransfer_functor.py","status_as_recorded":"Contract [C]/[O] (typed functor: discrete kernels [E], external solvers [C]; not a closure)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] det(C+xU)=14+6x linear, det(C+yV)=14+14y+4y^2 quadratic; curvatures (8,6)=(rank E_8, |R^+(A_3)|)","checked_by_registry":false,"claim_excerpt":"DIAMOND AXIS CURVATURE LEMMA (2026-06-15): along the two canonical axes of the centered cross (C center, U winding, V sheet, v95) the Sheet-Diamond determinant is LINEAR on the winding axis and QUADRATIC on the sheet axis: det(C+xU)=14+6x (flat, slope 6=|R^+(A_3)|), det(C+yV)=14+14y+4y^2 (2nd difference 8=rank E_8); the anchor block satisfies det B(C+xU)=28+12x=2 det(C+xU) and det B(C+yV)=28+21y+3y^2 (2nd difference ","claim_id":"DIAMOND.AXIS.01","dependencies_as_recorded":"v94_sheet_diamond.py; v95_centered_diamond.py","external_data_as_recorded":"-","id":"claim:DIAMOND.AXIS.01","location_as_recorded":"tfpt_2_standard_model","path":"verification/status_ledger.csv","row_number":303,"scripts_as_recorded":"v218_diamond_axis_geometry.py","status_as_recorded":"Identity (exact)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] Pl ladder K->C->F: steps (1,8,10) and (1,8,16) = decuple then full generation; transfer reading [C]","checked_by_registry":false,"claim_excerpt":"PLUCKER TRANSFER LADDER (2026-06-15): the anchor-Plucker coordinates lift K->C->F in two exact steps: Pl(K)=(-1,6,4), Pl(C)=(0,14,14), Pl(F)=(1,22,30); Pl(C)-Pl(K)=(1,8,10)=(N_Phi, rank E_8, A_Lambda) and Pl(F)-Pl(C)=(1,8,16)=(N_Phi, rank E_8, dim S^+). Each step adds (1,8) in the first two coordinates; the third adds first the decuple A_Lambda=10 then the full spinor generation dim S^+=16. The Plucker identity is [E","claim_id":"DIAMOND.PLUCKER.01","dependencies_as_recorded":"v94_sheet_diamond.py; v213_ftransfer_functor.py","external_data_as_recorded":"-","id":"claim:DIAMOND.PLUCKER.01","location_as_recorded":"tfpt_2_standard_model","path":"verification/status_ledger.csv","row_number":304,"scripts_as_recorded":"v218_diamond_axis_geometry.py","status_as_recorded":"Identity (exact)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] Disc(chi)=q(r)^2 Disc(q) for Q,K,C,F: squares (1,3,4,6), kernels (13,48,65,105); audit/heuristic blocks honestly typed","checked_by_registry":false,"claim_excerpt":"SPECTRAL RAMIFICATION LADDER (2026-06-15): for Q,K,C,F the characteristic polynomial splits as (t-r)(t^2-bt+c) with r rational, and the full cubic discriminant factors as Disc(chi)=q(r)^2 Disc(q): squares |q(r)| in {1,3,4,6}=(N_Phi,N_fam,|mu4|,|R^+(A_3)|), kernels Disc(q) in {13,48,65,105}=(Delta_Q, Omega_adm, g_car Delta_Q, N_fam g_car 7), with Delta_Q=13=b^2+s^2=|R(A_3)|+1 the carrier-split norm (v14). The missing ","claim_id":"DIAMOND.SPECTRAL.01","dependencies_as_recorded":"v14_carrier_uniqueness.py; v94_sheet_diamond.py","external_data_as_recorded":"-","id":"claim:DIAMOND.SPECTRAL.01","location_as_recorded":"tfpt_2_standard_model","path":"verification/status_ledger.csv","row_number":305,"scripts_as_recorded":"v218_diamond_axis_geometry.py","status_as_recorded":"Identity (exact)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] 2I (order 120) irrep degrees {1,2,2,3,3,4,4,5,6} = affine E8 Kac marks, sum 30=h(E8), sum^2 120=|R^+(E8)|; the McKay graph built from the group; E8 = the (2,3,5) icosahedral top. Backward certificate [E], 'explains (2,3,5)' [C], raw-seam origin [O]","checked_by_registry":false,"claim_excerpt":"McKAY BEDROCK (2026-06-16): WHY the three atoms are {2,3,5}. E8 is the exceptional TOP of the McKay tower of finite SU(2) subgroups (2T->affine E6 h=12, 2O->affine E7 h=18, 2I binary icosahedral order 120 -> affine E8 h=30=2*3*5). Built FROM the group, not asserted: (1) the 120 unit-quaternion icosians close to 2I with element orders {1,2,3,4,5,6,10} (it CONTAINS the 2,3,5 rotation-axis orders), 9 conjugacy classes; ","claim_id":"MCKAY.E8.01","dependencies_as_recorded":"AX.P2.01; E8.GLU.01; ARCH.CORE.01","external_data_as_recorded":"McKay correspondence (Du Val/Slodowy)","id":"claim:MCKAY.E8.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":306,"scripts_as_recorded":"v219_icosahedral_mckay.py","status_as_recorded":"Lattice (McKay correspondence, exact)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] 41=N_Zi(5,4)=10 b1, 13=N_Zi(3,2)=Delta_Q, 7=N_Zomega(3,2)=scalaron; (3,2)->(5,6,7,13); the square<->EM, hex<->scalaron architecture bridge [C]","checked_by_registry":false,"claim_excerpt":"CM-NORM DUALITY (2026-06-16): the two exceptional CM moduli give two central TFPT integers as ideal NORMS. SQUARE seam (Gaussian Z[i], j=1728): N(g_car+i|mu4|)=5^2+4^2=41=10 b1 -- the EM index IS the Gaussian norm of the carrier-glue vector; N(3+2i)=13=Delta_Q. HEX partner (Eisenstein Z[omega], j=0): N(3+2 omega)=3^2-3*2+2^2=7=scalaron exponent. The (3,2)=(colour,weak) split generates (5,6,7,13)=(g_car,|R^+(A3)|,scal","claim_id":"CMNORM.DUAL.01","dependencies_as_recorded":"ANCHOR.GEN.01; EM.B1.01; SEAM.KHALF.01","external_data_as_recorded":"-","id":"claim:CMNORM.DUAL.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":307,"scripts_as_recorded":"v222_cm_norm_duality.py","status_as_recorded":"Identity (exact ring arithmetic)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] (Z/30)^x = E8 exponents, order-4 element 7 = mu4 clock on the exponents, 4 invariant planes; seam-clock identification [C]","checked_by_registry":false,"claim_excerpt":"COXETER TOTATIVE CLOCK (2026-06-16): the mu4 clock is the order-4 character of the E8 Coxeter cycle. (Z/30)^x={1,7,11,13,17,19,23,29}=the E8 exponents=live Coxeter phases; phi(30)=8=rank E8, 30=|Z2|*N_fam*g_car=2*3*5. (Z/30)^x ~ Z/4 x Z/2, order-4 generator 7 (7^2=19,7^4=1 mod 30): a literal mu4 clock <7>={1,7,13,19} on the exponents; conjugate pairs m+(30-m)=30 give |mu4|=4 invariant 2-planes the clock permutes. Onl","claim_id":"COX.CLOCK.01","dependencies_as_recorded":"SEAM.COX.01; AX.P2.01","external_data_as_recorded":"-","id":"claim:COX.CLOCK.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":308,"scripts_as_recorded":"v223_coxeter_totative_clock.py","status_as_recorded":"Identity (exact)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] 248=120+128, exponents sum 120=|R^+(E8)|, degrees sum 128=rank*dim S^+; magnitude channel 120 / phase channel 128 [C]; dark-sector reading [O]; exact hexagonal realisation sum rho^{d_k}=4rho (arg pi/3, sheet-even) vs sum rho^{m_k}=4 (arg 0, sheet-odd) [E] -- the phase-channel angle is sheet-blind (T177/v561)","checked_by_registry":false,"claim_excerpt":"DEGREE/EXPONENT CHANNEL SPLIT (2026-06-16): 248=120+128 as a magnitude/phase channel typing (replaces the over-strong 'S^- is dark matter'). E8 exponents {1,7,11,13,17,19,23,29} sum=120=|R^+(E8)| (MAGNITUDE channel: positive roots/root transitions); E8 degrees {2,8,12,14,18,20,24,30} sum=128=2^(rank-1)=rank*dim S^+ (PHASE/GLUE channel); 248=120+128=adj(D8)+spinor(D8); sum(deg)-sum(exp)=rank=8. The (ratios,product) ma","claim_id":"E8.CHAN.01","dependencies_as_recorded":"E8.CAS.01; FLAV.CP.01","external_data_as_recorded":"-","id":"claim:E8.CHAN.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":309,"scripts_as_recorded":"v227_degree_exponent_channel_split.py; v561_cp_channel_identities.py","status_as_recorded":"Identity (exact)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] deg-4 divisor => (h0,rankH1)=(5,3)=(g_car,N_fam), sum 8=rank E8, even Clifford 16=dim S^+; mode-space reading [C], the seam->divisor step [O] (=QGEO.SYM.01)","checked_by_registry":false,"claim_excerpt":"RIEMANN-ROCH INDEX GATE (2026-06-16): P2 as the mode space of a degree-4 seam divisor (bedrock LANGUAGE for P2, NOT a proof from nothing). deg D=4=|mu4| on P^1 => h0(O(D))=deg+1=5=g_car (Riemann-Roch, genus 0); rank H1(P^1 minus 4 marks)=4-1=3=N_fam; h0+rank H1=8=rank E8, h0-rank H1=2=|Z2|, (h0+rank H1)/2=4=|mu4|; Lambda^even(C^5)=1+10+5=16=dim S^+ (the D5 half-spinor, ARCH.RRCAR.02). Negative controls: deg 3->(4,2),","claim_id":"QGEO.RR.01","dependencies_as_recorded":"ARCH.RR.01; ARCH.RRCAR.02; QGEO.SYM.01","external_data_as_recorded":"-","id":"claim:QGEO.RR.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":310,"scripts_as_recorded":"v228_rr_index_gate.py","status_as_recorded":"Identity (exact index) [E]/[C]/[O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] code dim 16, transport spectrum {1,(2/3)^6,(1/3)^6}, recovery bound ||T^n delta||<=(2/3)^{6n}||delta||; holographic/Petz reading [C] gated on the Seam-Horizon theorem","checked_by_registry":false,"claim_excerpt":"SEAM FINITE RECOVERABILITY CODE (2026-06-16): the seam as a finite quantum-error-correction-style code with recovery rate (2/3)^6=64/729. Code dimension = dim S^+ = 16 = 2^(g_car-1); the gapped boundary transport T on the cusp-weight 3-space (deviation directions (1,-1,0) and the Nariai anchor (1,1,-2)) is symmetric, doubly stochastic (CPTP), with spectrum {1,(2/3)^6,(1/3)^6}; on the trace-zero deviation subspace ||T","claim_id":"QEC.SEAM.01","dependencies_as_recorded":"SEAM.ATTRACT.01; SEAM.TRANSFER.01; HOR.PAGE.01","external_data_as_recorded":"-","id":"claim:QEC.SEAM.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":311,"scripts_as_recorded":"v221_seam_qecc.py","status_as_recorded":"Numerical (contraction bound) [E]/[C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] j(i)=1728 (Z/4) vs j(rho)=0 (Z/6, arg=pi/3); delta=pi/3+3 lam^2 leading term = the hex CM phase; deck stays Z/4, CP is the Z/6 fiber [C]. NOT a CP derivation; scope narrowed: the invariant part is the leading term pi/3, the full delta is branch/frame-relative (T177/v561)","checked_by_registry":false,"claim_excerpt":"CP HEXAGONAL MODULUS (2026-06-16): CP lives in the HEXAGONAL phase fiber, not the square seam deck (a geometric sharpening of red-team Target D, the magnitude bijection misses the CP phases). The seam deck is the SQUARE modulus j(i)=1728, automorphism Z/4 (the mu4 clock); its exceptional partner is the HEX modulus j(rho)=0, rho=e^{i pi/3}, automorphism Z/6, CM by Z[omega], arg(rho)=pi/3. The frozen leading CKM readin","claim_id":"CP.MOD.01","dependencies_as_recorded":"FLAV.CP.01; QGEO.PILLOW.01; QGEO.KILL.01","external_data_as_recorded":"PDG gamma (look-elsewhere comparison)","id":"claim:CP.MOD.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":312,"scripts_as_recorded":"v220_cp_hexagonal_modulus.py; v561_cp_channel_identities.py","status_as_recorded":"Identity/Numerical (modular) [E]/[C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] d=(-1/2,-1/2,1)=-1/2 Nariai, n=(5,-9,6) reads det on the first-gen column, det(1,d,n)=21=3*7; CP orientation READING Im det(1,d,rho n)=21 sin(pi/3) [C], narrowed: degree +1 in the frame normalisation (21 sin(pi/3) is frame data), invariant core = the fiber datum Im rho = sin(pi/3), sign a declared orientation (T177/v561)","checked_by_registry":false,"claim_excerpt":"DUAL NORMAL FRAME (2026-06-16): the pair (d,n) is one canonical boundary compass for flavor and horizon, with CP as orientation. d=a^T R^{-1}=a^T L^{-1}=(-1/2,-1/2,1)=-1/2 (1,1,-2) (frame-independent; the Nariai/horizon normal; d.1=0, d.a=1); n=(5,-9,6) with n^T R=(det R,0,0)=(8,0,0), n^T L=(det L,0,0)=(20,0,0) (n annihilates the stable columns 2,3 -- the first-generation/torsion selector). Oriented volume det(1,d,n)","claim_id":"DUAL.FRAME.01","dependencies_as_recorded":"HOR.DUALANCHOR.01; FLAV.SELECTOR.01; CP.MOD.01","external_data_as_recorded":"-","id":"claim:DUAL.FRAME.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":313,"scripts_as_recorded":"v225_dual_normal_frame.py; v561_cp_channel_identities.py","status_as_recorded":"Identity (exact) [E]/[C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] M(s,t)=R+Q diag(s,t,t), K/C/F on the sheet axis, curved (2nd diff 8) vs flat winding (slope 6), Plucker steps (1,8,10),(1,8,16); F_transfer = the sheet geodesic, Koide its 1-D projection [C]","checked_by_registry":false,"claim_excerpt":"DIAMOND F_TRANSFER PATH (2026-06-16): F_transfer is ONE path on the Sheet Diamond, not four external interfaces. Family M(s,t)=R+Q diag(s,t,t): the transfer corners K=M(1,-1), C=M(1,0), F=M(1,1) lie on the SHEET axis (s=1). The sheet axis is CURVED det M(1,t)=4t^2+14t+14 (dets (K,C,F)=(4,14,32), 2nd diff 8=rank E8), the winding axis det M(s,0)=6s+8 is FLAT (slope 6=|R^+(A3)|); the Plucker ladder Pl(C)-Pl(K)=(1,8,10)=","claim_id":"FTR.PATH.01","dependencies_as_recorded":"DIAMOND.PLUCKER.01; DIAMOND.AXIS.01; CONTRACT.F.01","external_data_as_recorded":"-","id":"claim:FTR.PATH.01","location_as_recorded":"tfpt_2_standard_model","path":"verification/status_ledger.csv","row_number":314,"scripts_as_recorded":"v224_diamond_ftransfer_path.py","status_as_recorded":"Identity (exact) [E]/[C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] (16/7,4/3,7/6), ring closure c_e c_tau=8/3=|Z2|c_mu, product 32/9; etale Frobenius algebra (det Gram=disc(m)!=0); mu6=mu3 x mu2 spectrum; PMNS extension [C]","checked_by_registry":false,"claim_excerpt":"LEPTON ETALE FROBENIUS ALGEBRA (2026-06-16): the three charged-lepton coefficients form a genuine commutative Frobenius algebra over the mu6 resolvent. Exact coefficients (c_e,c_mu,c_tau)=(16/7,4/3,7/6), ring closure c_e c_tau=8/3=|Z2| c_mu, product c_e c_mu c_tau=32/9=2^g_car/N_fam^2. A=Q[t]/(m), m=(t-c_e)(t-c_mu)(t-c_tau): the trace-form Gram G_ij=Tr(t^i t^j) is nondegenerate, det G=discriminant(m)!=0 (A etale/sepa","claim_id":"LEP.FROB.01","dependencies_as_recorded":"FLAV.LEPTON.01; ARCH.HEXRES.01; CP.MOD.01","external_data_as_recorded":"charged-lepton masses (reference)","id":"claim:LEP.FROB.01","location_as_recorded":"tfpt_2_standard_model","path":"verification/status_ledger.csv","row_number":315,"scripts_as_recorded":"v229_lepton_frobenius_algebra.py","status_as_recorded":"Identity (exact algebra) [E]/[C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] C row sums (7,11,13)=(hex norm, QBL Fock count, square norm)=(N_omega(3,2), 1+4+6, N_i(3,2)); the center collects the three local norms [C]","checked_by_registry":false,"claim_excerpt":"CENTER BUDGET NORMS (2026-06-16): the Sheet-Diamond center budget (7,11,13) is the three LOCAL NORMS of the theory. C=R+Q diag(1,0,0), row sums (7,11,13): 7=N_Z[omega](3+2 omega) (Eisenstein/hexagonal CM norm = scalaron exponent), 13=N_Z[i](3+2 i) (Gaussian/square CM norm = Delta_Q), 11=C(4,0)+C(4,1)+C(4,2)=1+4+6 (QBL boundary Fock count on the |mu4|=4 corners = dim S^+ - g_car = 16-5). So C = (hex norm, boundary Foc","claim_id":"CENTER.NORM.01","dependencies_as_recorded":"CMNORM.DUAL.01; DIAMOND.AXIS.01; ARCH.QBL.01","external_data_as_recorded":"-","id":"claim:CENTER.NORM.01","location_as_recorded":"tfpt_2_standard_model","path":"verification/status_ledger.csv","row_number":316,"scripts_as_recorded":"v230_center_budget_norms.py","status_as_recorded":"Identity (exact) [E]/[C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] delta_CKM,lead=arg(rho)=pi/3, delta_PMNS=arg(rho^4)=4pi/3, rho^4=-rho so the two CP phases = one hexagonal unit x the Z2 sheet; sheet-flipped Jarlskog orientations; reduces Target D's CP inputs from 2 to 1, physical derivation [C]","checked_by_registry":false,"claim_excerpt":"CP PHASES AS MU6 POWERS (2026-06-17): both CP phases are mu6 powers of ONE hexagonal CM unit, split by the sheet -- a structural reduction of red-team Target D, sharper than v220/v225 (which only located the residual). With rho=e^{i pi/3} the primitive 6th root (j=0 Eisenstein CM, CP.MOD.01): (1) rho^6=1, rho^3=-1 (the Z2 sheet half-turn); (2) delta_CKM leading = arg(rho^1)=pi/3 (quark, FLAV.CP.01), delta_PMNS = arg(","claim_id":"CP.MU6.01","dependencies_as_recorded":"CP.MOD.01; DUAL.FRAME.01; FLAV.CP.01","external_data_as_recorded":"delta_PMNS=4pi/3 (tfpt_2 phase lattice)","id":"claim:CP.MU6.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":317,"scripts_as_recorded":"v231_cp_mu6_phases.py","status_as_recorded":"Identity (exact) [E]/[C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] McKay(2I)=affine E8; finite E8 = 8 exceptional P^1's intersection graph (det 1 Cartan); 2I perfect => link is the Poincare homology sphere pi1=2I order 120; [C] the seam is a du Val exceptional curve (model for QGEO.REALIZE.01, presupposes E8, bedrock [O])","checked_by_registry":false,"claim_excerpt":"THE SEAM AS THE E8 KLEINIAN SINGULARITY (2026-06-17): a canonical algebraic-geometric MODEL for the open seam-realisation premise QGEO.REALIZE.01, the du Val side of the McKay correspondence (MCKAY.E8.01/v219). (1) the McKay graph of 2I is affine E8 (9 nodes); dropping the unique trivial-rep node (the single Kac mark=1) leaves the FINITE E8 Dynkin on 8 nodes = the dual intersection graph of the 8 exceptional P^1's of","claim_id":"TOPO.E8.01","dependencies_as_recorded":"MCKAY.E8.01; QGEO.SYM.01; E8.GLU.01","external_data_as_recorded":"du Val/Kleinian correspondence; Poincare homology sphere","id":"claim:TOPO.E8.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":318,"scripts_as_recorded":"v232_e8_kleinian_seam.py","status_as_recorded":"Lattice/Topology (exact) [E]/[C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] mu6=mu3 x mu2; quark rho^1 and lepton rho^4 share the family triality class omega^2 (the 2/3 cusp centre), opposite sheet; CP = universal triality phase + sheet, power choice removed; physical derivation [C]","checked_by_registry":false,"claim_excerpt":"CP = THE UNIVERSAL TRIALITY PHASE, SHEET-SPLIT (2026-06-17): one step past CP.MU6.01/v231 in the canonical mu6 = mu3 (family/triality) x mu2 (sheet) factorisation. (1) mu6=mu3 x mu2 (gcd(3,2)=1): the Z3 triality centre {1,omega,omega^2} = the cusp weights {0,1/3,2/3} x 2pi, the sheet is mu2={1,-1}; the hexagonal CM unit factors as rho = omega^2 * (-1). (2) SAME FAMILY CLASS: rho^4 = rho^1 * rho^3 with rho^3 in mu2, s","claim_id":"CP.TRIALITY.01","dependencies_as_recorded":"CP.MU6.01; FLAV.CP.01; TOPO.E8.01","external_data_as_recorded":"delta_PMNS=4pi/3 (tfpt_2 phase lattice)","id":"claim:CP.TRIALITY.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":319,"scripts_as_recorded":"v233_cp_triality_phase.py","status_as_recorded":"Identity (exact) [E]/[C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] #mark-1 = |Gamma^ab| = |H1(link)|; only E8->1 (2I unique perfect, Poincare unique homology sphere); holomorphic c=8 unique E8; the three faces (holomorphy/homology-sphere/one-1dim-irrep) are one E8-selector => Target A/G_net/P2/QGEO are ONE gate; closing theorem 'free bulk => holomorphic boundary' stated [O]","checked_by_registry":false,"claim_excerpt":"SEAM-HOLOMORPHY SELECTION CERTIFICATE (2026-06-17): the entire structural residual of TFPT is ONE condition with THREE provably-equivalent faces, all forcing E8 -- so P2/G_net/Target A/QGEO are ONE gate, not four. THE CONDITION: 'the seam carries no nontrivial abelian sector.' Faces: (i) AQFT -- the boundary chiral net is HOLOMORPHIC (mu-index 1, single vacuum sector; Target A, v83/v154); (ii) geometry -- the seam li","claim_id":"GATE.HOLO.01","dependencies_as_recorded":"E8.GLU.01; MCKAY.E8.01; TOPO.E8.01; GATE.METRIC.06","external_data_as_recorded":"Minkowski-Siegel (unique even unimodular rank-8); holomorphic c in 8Z","id":"claim:GATE.HOLO.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":320,"scripts_as_recorded":"v234_seam_holomorphy_selection.py","status_as_recorded":"Lattice/AQFT selection (exact) [E]/[O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] free gapped bosonic bulk = K-matrix; #anyons=|det K|, c=signature, holomorphic<=>det 1; the v92 tower D5(+)A3(16)->D8(4)->E8(1) is the condensation tower; holomorphic=E8=Kitaev E8 state; residual = 'condense the |mu4| Lagrangian glue' = the sheet/QGEO selection [O]","checked_by_registry":false,"claim_excerpt":"SEAM CHERN-SIMONS REALISATION (2026-06-17): the closing step of GATE.HOLO.01 realised in standard abelian Chern-Simons / quantum-Hall language, where 'holomorphic <=> det K = 1' is a THEOREM -- a genuine reduction of the analytic step into anyon condensation, NOT a closure. A free gapped BOSONIC 2+1d bulk = an even integer K-matrix; #anyons (torus degeneracy) = |det K|, edge chiral central charge c = signature(K), an","claim_id":"GATE.HOLO.02","dependencies_as_recorded":"GATE.HOLO.01; GATE.METRIC.07; TOPO.E8.01; QGEO.SYM.01","external_data_as_recorded":"Kitaev E8 phase; abelian CS bulk-boundary (#anyons=|det K|)","id":"claim:GATE.HOLO.02","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":321,"scripts_as_recorded":"v235_seam_chern_simons.py","status_as_recorded":"Lattice/CS realisation (exact) [E]/[O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] mu=(2-1)(3-1)(5-1)=8=rank E8 (5th origin of the '8'); Milnor monodromy eigenvalues = E8 exponents/30 = the order-30 Coxeter cycle (charpoly Phi_30); both clocks = mu3 in <h>=Z/30 (CP) + mu4 in Galois (Z/30)^x; one singularity generates the skeleton [I]","checked_by_registry":false,"claim_excerpt":"BRIESKORN CAPSTONE (2026-06-17): the (2,3,5) Brieskorn singularity x^2+y^3+z^5 is the ONE generator of the discrete skeleton -- the capstone of the icosahedral round (v55/v219/v223/v232/v233). Its three exponents ARE the atoms (|Z2|,N_fam,g_car)=(2,3,5). (1) MILNOR NUMBER = the '8': mu=(2-1)(3-1)(5-1)=(|Z2|-1)(N_fam-1)(g_car-1)=1*2*4=8=rank E8=#exceptional P^1 = the '8' in c3=1/(8 pi), a FIFTH independent origin (aft","claim_id":"TOPO.BRIESKORN.01","dependencies_as_recorded":"MCKAY.E8.01; COX.CLOCK.01; CP.TRIALITY.01; TOPO.E8.01; SEAM.COX.01","external_data_as_recorded":"Brieskorn/Milnor fibration; Pham monodromy theorem","id":"claim:TOPO.BRIESKORN.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":322,"scripts_as_recorded":"v236_brieskorn_capstone.py","status_as_recorded":"Lattice/Topology (exact) [E]/[I]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] genus-g GSD=|det K|^g, no topological degeneracy <=> det K=1 <=> SRE; only E8 (det 1) is the bosonic SRE c=8 phase (Kitaev E8); plane unique-vacuum is necessary not sufficient (torus sees det K); residual = 'the seam is SRE' [O], a physical yes/no statement","checked_by_registry":false,"claim_excerpt":"SEAM SRE CLOSURE (2026-06-17): the closing step of GATE.HOLO.01/02 recast as a PHYSICAL, falsifiable condition -- no topological ground-state degeneracy <=> det K=1 <=> the seam bulk is short-range-entangled (SRE/invertible). Sharpens the residual from definitional ('condense the Lagrangian glue', v235) to a yes/no statement about topological order. (1) the abelian K-matrix ground-state degeneracy on a genus-g surfac","claim_id":"GATE.HOLO.03","dependencies_as_recorded":"GATE.HOLO.02; GATE.HOLO.01; QGEO.SYM.01","external_data_as_recorded":"gapped 2+1d topological order (GSD=|det K|^g); Kitaev E8 SRE phase","id":"claim:GATE.HOLO.03","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":323,"scripts_as_recorded":"v237_seam_sre_closure.py","status_as_recorded":"Lattice/topological-order (exact) [E]/[O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] finite block: modular flow = reversible unitary group with mu4 conserved <=> [rho,Lambda]=0; L = log T a doubly-stochastic generator with e^{L}=T; dissipative gap = -log((2/3)^6) = 6 log(3/2) = OS mass gap (v64); GKSL split. [O] geometric modular flow on the full seam algebra (= QGEO.SYM.01) and the continuum embedding -- a target, not a closure","checked_by_registry":false,"claim_excerpt":"STATIC->DYNAMIC FLIP (2026-06-17): the seam's modular flow (reversible) and its recovery channel read as a Markov/Lindblad generator (irreversible), with the dissipative gap EQUAL to the OS mass gap -- the point where the static compiler becomes a dynamics. Companion to v196/v198 (modular) and v221/v64 (recovery), which state the structure STATICALLY (a commutator, a contraction bound, a mass-gap number); this reads ","claim_id":"DYN.SEMIGROUP.01","dependencies_as_recorded":"QGEO.MODULAR.01; QEC.SEAM.01","external_data_as_recorded":"-","id":"claim:DYN.SEMIGROUP.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":324,"scripts_as_recorded":"v238_modular_lindblad_dynamics.py","status_as_recorded":"Numerical (finite-block) [E]/[O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] KMS at beta=1 (modular flow is thermal); seam unit 2 pi = 1/(4 c3) = horizon temperature T_H = c3/M; one object with v238. [O] the geometric-boost identification = QGEO.SYM.01 -- a target, not a closure","checked_by_registry":false,"claim_excerpt":"KMS / THERMAL TIME (2026-06-17): the modular flow of v238 makes the seam state a KMS (thermal) state at the canonical inverse temperature beta = 1, and the geometric (Unruh/Bisognano-Wichmann) normalisation fixes the physical seam temperature via the seam unit 2 pi = 1/(4 c3). Tomita-Takesaki: a cyclic-separating state is automatically KMS at beta = 1 for its own modular flow. (1) [E] KMS at beta=1: omega(A sigma_i(B","claim_id":"DYN.KMS.01","dependencies_as_recorded":"DYN.SEMIGROUP.01; HOR.BHTHERMO.01","external_data_as_recorded":"-","id":"claim:DYN.KMS.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":325,"scripts_as_recorded":"v239_kms_thermal_time.py","status_as_recorded":"Numerical (finite-block) [E]/[O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] GNS Hilbert space + cyclic/separating vector from (M,omega); modular flow = v238; OS Hamiltonian H_OS = -log T >= 0 with gap = v64 mass gap, and H_OS = -L. [O] the geometric/operator-level OS step = QGEO.SYM.01 + Layer-2 RP/gap -- a target, not a closure","checked_by_registry":false,"claim_excerpt":"GNS / OS RECONSTRUCTION (2026-06-17, finite toy): from the discrete seam data (a *-algebra M + the state omega) one reconstructs a Hilbert space, a cyclic vector, the modular flow (v238/v239) AND a POSITIVE Hamiltonian -- so two QFT primitives (the Hilbert space and a positive Hamiltonian) are OUTPUTS of the seam data, not extra inputs. (1) [E] GNS: <A,B>=Tr(rho A^dag B) is Hermitian and positive-definite (rho>0), di","claim_id":"DYN.GNS.01","dependencies_as_recorded":"DYN.SEMIGROUP.01; QEC.SEAM.01; QG.GAPDEC.01","external_data_as_recorded":"-","id":"claim:DYN.GNS.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":326,"scripts_as_recorded":"v240_gns_os_reconstruction.py","status_as_recorded":"Numerical (finite-block) [E]/[O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] 16-sector abelian MTC from the glue form, fusion = group law, condensation tower 16->4->1 = v235/v237 (Lagrangian -> E8, order-2 -> D8); [C] sector<->SM-multiplet identification -- particles = stable defect sectors of the seam code, made precise","checked_by_registry":false,"claim_excerpt":"PARTICLES = DHR SUPERSELECTION SECTORS (2026-06-17): the discriminant/anyon content of the carrier and the condensation tower (v235/v237) made explicit as an abelian modular tensor category (MTC) -- the particle-spectrum layer of the emergent QFT. The carrier discriminant form is the Lean-verified glue form (FORM.GLUE.01): on Z4 x Z4, q(x,y)=(5x^2+3y^2)/8 mod 1, bilinear B((x,y),(x',y'))=(5xx'+3yy')/4 mod 1, topologi","claim_id":"DHR.SECTORS.01","dependencies_as_recorded":"GATE.HOLO.02; GATE.HOLO.03; FORM.GLUE.01","external_data_as_recorded":"-","id":"claim:DHR.SECTORS.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":327,"scripts_as_recorded":"v241_dhr_sectors.py","status_as_recorded":"Numerical (finite MTC) [E]/[C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] T=diag(theta) spin-statistics (6 bosons, 2 fermions, 8 anyons); modular S unitary/symmetric, S^2=C, S^4=I; Verlinde reproduces the group-law fusion; Gauss-Milgram gives c=8=g_car+N_fam. [C] the boson/fermion-to-field map is the interpretation","checked_by_registry":false,"claim_excerpt":"SPIN-STATISTICS + MODULAR (S,T) DATA (2026-06-17): the exchange statistics, modular S/T matrices, Verlinde fusion and Gauss-Milgram central charge of the carrier MTC -- the statistics+kinematics layer on top of v241. Same abelian MTC: Z4 x Z4, q(x,y)=(5x^2+3y^2)/8 mod 1 (the Lean glue form FORM.GLUE.01), B(a,b)=q(a+b)-q(a)-q(b), theta(a)=e^{2 pi i q(a)}. (1) [E] spin-statistics: T=diag(theta_a) splits the 16 anyons i","claim_id":"DHR.MODULAR.01","dependencies_as_recorded":"DHR.SECTORS.01; GATE.HOLO.02","external_data_as_recorded":"-","id":"claim:DHR.MODULAR.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":328,"scripts_as_recorded":"v242_spin_statistics_modular.py","status_as_recorded":"Numerical (finite MTC) [E]/[C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] mass gap -> HR asymptotic states; 2-particle S = monodromy (unitary, diagonal, factorised); Yang-Baxter bicharacter; crossing; trivial S on condensed E8. [O] the 4d S-matrix / cross-sections = the open holographic uplift","checked_by_registry":false,"claim_excerpt":"SCATTERING: HAAG-RUELLE SKELETON + BRAIDING S-MATRIX (2026-06-17): the S-matrix layer of the emergent QFT. The seam net has a mass gap (v64/v238), so Haag-Ruelle scattering theory constructs asymptotic in/out states; and for the abelian anyon MTC (v241/v242) the 2-particle S-matrix is the monodromy (double braiding), a pure phase. Same MTC: Z4 x Z4, q=(5x^2+3y^2)/8, theta=e^{2 pi i q}, M(a,b)=theta(a+b)/(theta(a)thet","claim_id":"DHR.SMATRIX.01","dependencies_as_recorded":"DHR.MODULAR.01; DYN.SEMIGROUP.01; v64","external_data_as_recorded":"-","id":"claim:DHR.SMATRIX.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":329,"scripts_as_recorded":"v243_haag_ruelle_braiding.py","status_as_recorded":"Numerical (finite MTC + cited HR) [E]/[O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] carrier half-spinor = one SM generation (16), SM gauge group embeds in the carrier, one Dirac operator gives gravity (v36) + matter (Gilkey); [X] unification + Higgs hooks; [O] CONTRACT.QFT4D.01: the spectral action of the seam Dirac operator = 4d SM+gravity Lagrangian -- the Phase-3 target, not closed","checked_by_registry":false,"claim_excerpt":"4D LAGRANGIAN VIA THE SPECTRAL ACTION (2026-06-17): the honest CONTRACT for the Phase-3 structural gap (the 2d chiral seam net v156/v175 + its dynamics v238-v243 -> the physical 4d theory). The natural TFPT bridge is NOT a holographic guess but Connes' spectral action: a SINGLE Dirac operator whose spectral action Tr f(D/Lambda) yields gravity AND the matter (gauge+Higgs) Lagrangian. The gravity half is verified (v36","claim_id":"CONTRACT.QFT4D.01","dependencies_as_recorded":"FORM.P2.02; QG.G2.01; DHR.SECTORS.01","external_data_as_recorded":"-","id":"claim:CONTRACT.QFT4D.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":330,"scripts_as_recorded":"v244_spectral_action_contract.py","status_as_recorded":"Contract [O] (with [E] arithmetic + [X] hooks)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] SO(10) 16 = one anomaly-free SM generation with correct hypercharges/charges; sin^2 th_W = 3/8 (g3=g2=sqrt(5/3)g1); Higgs = (1,2)_{1/2} inner fluctuation. [O] the seam->Dirac realisation + measured-coupling reproduction stay the open contract","checked_by_registry":false,"claim_excerpt":"SPECTRAL-ACTION MATTER CONTENT (2026-06-17): the computable core of CONTRACT.QFT4D.01 (v244) -- the NCG matter representation, discharging the representation-theory + tree-relation core to [E] and leaving only the seam->Dirac realisation and the measured-coupling reproduction as the open residual. The carrier half-spinor is the SO(10) 16 (dim S^+ = 2^(g_car-1) = 16). One generation = SO(10) 16 = SU(5)(10+5bar+1) = SM","claim_id":"QFT4D.MATTER.01","dependencies_as_recorded":"CONTRACT.QFT4D.01; FORM.P2.02","external_data_as_recorded":"-","id":"claim:QFT4D.MATTER.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":331,"scripts_as_recorded":"v245_spectral_matter_content.py","status_as_recorded":"Numerical (exact rep theory) [E]/[O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[X] plain-SM run misses unification at 1- and 2-loop (1-loop spread ~9; 2-loop min spread ~3.2 at 1.7e14) and sin^2 th_W 3/8 vs 0.231; [O] no admissible threshold source (SM content, no new state; the E8 spine is arithmetic, not a tower) -- spectral-action 4d-GUT route in tension like NCG-SM, likely falsified unless extended; not a confirmation","checked_by_registry":false,"claim_excerpt":"UNIFICATION DATA CROSS-CHECK (2026-06-17): the honest data-confrontation kill-test for the spectral-action prediction (CONTRACT.QFT4D.01, v244/v245). Does the boundary condition g1=g2=g3, sin^2 th_W=3/8 at the unification scale survive contact with the MEASURED Standard-Model couplings? Answer: NOT in the plain SM. Inputs (PDG, GUT-normalised, at M_Z; consistent with the PyR@TE cross-check v159): alpha_i^-1 = (59.01,","claim_id":"QFT4D.RGTEST.01","dependencies_as_recorded":"QFT4D.MATTER.01; CONTRACT.QFT4D.01","external_data_as_recorded":"PDG gauge couplings + sin^2 thetaW(M_Z)","id":"claim:QFT4D.RGTEST.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":332,"scripts_as_recorded":"v246_unification_data_crosscheck.py","status_as_recorded":"Data confrontation (kill-test) [X]/[O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] E8->SO(10)xSU(4) branching: SO(10) content {1,10,16,45}, 126 absent (126_H forbidden), only one 45/15 (proton-marginal); [O] the field-content principle","checked_by_registry":false,"claim_excerpt":"E8 HULL FORBIDS THE 126 (2026-06-17): the E8 audit hull supplies exactly {1,10,16,45} for SO(10) -- turning the scalaron-match '16-Higgs over 126-Higgs' selection into an algebraic statement. The carrier D5(+)A3 = SO(10)xSU(4) is a rank-8 subalgebra of E8 via SO(16); the adjoint 248 branches as (45,1)+(1,15)+(10,6)+(16,4)+(16bar,4bar) = 45+15+60+64+64 = 248 (SO(16) split: 120 adjoint + 128 spinor = spinor_SO10 (x) sp","claim_id":"PS.E8BRANCH.01","dependencies_as_recorded":"E8.GLU.01; QFT4D.MATTER.01","external_data_as_recorded":"-","id":"claim:PS.E8BRANCH.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":333,"scripts_as_recorded":"v247_e8_branching_no126.py","status_as_recorded":"Lattice/rep theory [E]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] A_F -> SU(2)xSU(2)xSU(4) PS group, 16=(4,2,1)+(4bar,1,2), exact hypercharges/charges, matching a1^-1=(3/5)a2R^-1+(2/5)a4^-1, sin^2=3/8; [O] seam-reconstruction + the colour/family distinction","checked_by_registry":false,"claim_excerpt":"PATI-SALAM NCG ALGEBRA + EXACT SM MATCHING (2026-06-17): the finite algebra A_F = H_L (+) H_R (+) M_4(C) and its consequences (Reviewer-A Theorem 2). (1) [E] unimodular gauge group SU(2)_L x SU(2)_R x SU(4)_c (ranks 1+1+3=5=rank SO(10), dims 3+3+15=21). (2) [E] one generation 16 = (4,2,1)+(4bar,1,2) = 8+8. (3) [E] Y = T_3R + (B-L)/2 reproduces the EXACT SM hypercharges for all six multiplets (Q,u^c,d^c,L,e^c,nu^c), a","claim_id":"PS.ALGEBRA.01","dependencies_as_recorded":"QFT4D.MATTER.01; PS.E8BRANCH.01","external_data_as_recorded":"-","id":"claim:PS.ALGEBRA.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":334,"scripts_as_recorded":"v248_ps_algebra.py","status_as_recorded":"Numerical (exact rep theory) [E]/[O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] matching+unification-exists; [X] SM-only fails, 126 breaks the match, proton decay selects content; [C] M_PS=scalaron coincidence; [O] gauging fork + exact kappa + one-45 marginality","checked_by_registry":false,"claim_excerpt":"CARRIER-NATIVE PATI-SALAM/SO(10) UNIFICATION KILL-TEST + NEGATIVE CONTROLS (2026-06-17): the suite claim-check of experiments/gauge-unification. Two-step M_Z->(SM)->M_PS->(PS)->M_GUT (SO(10): a4=a2L=a2R), matching a4=a3, a2L=a2, a2R^-1=(5/3)a1^-1-(2/3)a3^-1. (1) [E] matching holds and a valid 1-loop unification solution exists (M_PS < M_GUT < M_Pl). (2) [X] NEG: pure SM running does NOT unify (residual spread ~8.8 at","claim_id":"PS.RGTEST.01","dependencies_as_recorded":"PS.ALGEBRA.01; QFT4D.RGTEST.01","external_data_as_recorded":"PDG gauge couplings","id":"claim:PS.RGTEST.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":335,"scripts_as_recorded":"v249_ps_unification.py","status_as_recorded":"Data confrontation (kill-test) [X]/[O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] H_F=3x16=48, Yukawas already fixed (test is NCG consistency); [O] the 7 NCG axioms (first-order condition the hard one), sigma=scalaron, inner-fluctuation Higgs content -- reduces 4d QFT to one spectral triple","checked_by_registry":false,"claim_excerpt":"THE SPECTRAL-TRIPLE CONTRACT (2026-06-17): the object that would turn 'carrier is gauged' from a fork into a theorem (Reviewer-A Theorem 3 + the sigma=scalaron identification). Target: a real even almost-commutative triple (A,H,D,J,gamma) with A_F = PS algebra (v248), H_F = 3x16, D_F = D_M (x) 1 + gamma_5 (x) D_F(R,L,phi0,Majorana). (1) [E] H_F = N_fam x dim S^+ = 3x16 = 48 (three generations of the SO(10) spinor); A","claim_id":"CONTRACT.QFT4D.DIRAC.01","dependencies_as_recorded":"PS.ALGEBRA.01; CONTRACT.QFT4D.01","external_data_as_recorded":"-","id":"claim:CONTRACT.QFT4D.DIRAC.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":336,"scripts_as_recorded":"v250_dirac_triple_contract.py","status_as_recorded":"Contract [O] (with [E] finite facts)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] order-zero + real-even (J^2=1,KO-6 signs,D odd) + first order holds(Yukawa)/violated(Majorana, localized to sigma); the CCvS beyond-first-order Pati-Salam mechanism exhibited; [C] sigma=scalaron; [O] full 96-dim triple + spectral action","checked_by_registry":false,"claim_excerpt":"FIRST-ORDER CONDITION VIOLATED BY THE MAJORANA/sigma (2026-06-17): the Chamseddine-Connes-van Suijlekom 'beyond first order' mechanism exhibited on a faithful minimal model -- advances CONTRACT.QFT4D.DIRAC.01 (v250) from a contract to an exhibited mechanism. HONEST CORRECTION to the external review: the sigma field does NOT 'rescue' the first-order condition; the opposite is true (CCvS 2013) -- one DROPS the first-or","claim_id":"PS.DIRAC.01","dependencies_as_recorded":"CONTRACT.QFT4D.DIRAC.01; PS.ALGEBRA.01","external_data_as_recorded":"-","id":"claim:PS.DIRAC.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":337,"scripts_as_recorded":"v251_first_order_sigma.py","status_as_recorded":"Numerical (NCG mechanism) [E]/[C]/[O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] dim 96 + Hermitian/odd + reality J + grading + KO-6 + order-zero + first-order holds(SM)/violated(PS, localized to nu_R,e_R) + spectrum=masses+seesaw; [C] Poincare duality; [O] orientability + no-junk + spectral action; discharges 5 of the 7 v250 obligations to [E]","checked_by_registry":false,"claim_excerpt":"FULL 96-DIM FINITE SPECTRAL TRIPLE BUILT + NCG AXIOMS VERIFIED (2026-06-17): advances CONTRACT.QFT4D.DIRAC.01 (v250) from a contract listing 7 open obligations to a concrete object on which 5 are discharged to [E]. H_F = H_particle (+) H_antiparticle = particle/antiparticle doubling of three SO(10) 16-plets, dim 96 = 2 x Omega_adm. One generation = nu_L,nu_R,e_L,e_R (colour singlets) + (u,d)x(L,R)x3 colours = 16. D_F","claim_id":"PS.DIRAC.02","dependencies_as_recorded":"CONTRACT.QFT4D.DIRAC.01; PS.DIRAC.01; PS.ALGEBRA.01","external_data_as_recorded":"-","id":"claim:PS.DIRAC.02","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":338,"scripts_as_recorded":"v252_full_finite_triple.py","status_as_recorded":"Numerical (NCG axioms) [E]/[C]/[O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] M_s exact + kappa pinned to O(1)~1.3 by RG interval scan; [C] heat-kernel origin kappa=sqrt((f2/f0)c_PS/c_grav) scale-free; [X] 126 neg control; [O] exact decimal needs cutoff moments fixed","checked_by_registry":false,"claim_excerpt":"kappa IN M_PS = kappa M_s PINNED TO O(1) ~ 1 (2026-06-17): discharges the open residual 6(b) of v249 ('exact kappa, now ~1.0-1.2, not pinned') as far as is honest. The scalaron scale M_s = c3^{7/2} Mbar ~ 3.06e13 GeV is exact from {c3=1/(8pi), Mbar}. kappa := M_PS/M_s with M_PS the RG output of the carrier-native PS two-step (v249). HEAT-KERNEL ORIGIN: in the spectral action S = Tr f(D/Lambda) the gauge kinetic terms","claim_id":"PS.KAPPA.01","dependencies_as_recorded":"PS.RGTEST.01; PS.DIRAC.02","external_data_as_recorded":"-","id":"claim:PS.KAPPA.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":339,"scripts_as_recorded":"v253_kappa_scalaron_ps.py","status_as_recorded":"Numerical (RG interval + heat-kernel) [E]/[C]/[X]/[O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] finite fluctuations = SM Higgs doublet (no junk/no 126) + sigma beyond first order + sigma B-L=2 singlet; [C] sigma=scalaron; closes v250 #5 + no-junk obligation + sigma QN","checked_by_registry":false,"claim_excerpt":"INNER FLUCTUATIONS Omega^1_D -> SM HIGGS DOUBLET (no 126, no junk) + sigma (2026-06-17): closes the open obligation v250 #5 (Higgs content, NOT 126), the NO-JUNK obligation, and fixes the sigma quantum numbers (v250 #4 rep-theory half). Inner fluctuation D -> D + A + eps' J A J^-1 with A = sum pi(a)[D_F,pi(b)] in Omega^1_D = span{pi(a)[D_F,pi(b)]}. Because D_F is purely chirality-odd (Yukawa L<->R + Majorana), every ","claim_id":"PS.NCG.FLUCT.01","dependencies_as_recorded":"PS.DIRAC.02; PS.DIRAC.01","external_data_as_recorded":"-","id":"claim:PS.NCG.FLUCT.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":340,"scripts_as_recorded":"v254_inner_fluctuations.py","status_as_recorded":"Numerical (NCG inner fluctuations) [E]/[C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] Seeley-DeWitt expansion structure + trace inputs (b/a^2=1/3) + sin^2 thetaW=3/8 + scalaron from R^2; [C] Higgs quartic ~125 GeV + explicit kappa(f2/f0); [O] cutoff moments; closes v252 spectral-action obligation","checked_by_registry":false,"claim_excerpt":"SPECTRAL-ACTION HEAT-KERNEL EXPANSION (a0,a2,a4) + EXPLICIT kappa(f2/f0) (2026-06-17): closes the open obligation v252 #11 (spectral-action expansion) and makes the kappa-dependence on the cutoff moments explicit (v253 #5). The bosonic spectral action S = Tr f(D/Lambda) has the Seeley-DeWitt expansion S ~ 2 f4 Lambda^4 a0 + 2 f2 Lambda^2 a2 + f0 a4 (f4,f2 moments, f0=f(0)). (1) [E] expansion structure: a0=cosmologica","claim_id":"PS.SPECACT.01","dependencies_as_recorded":"PS.DIRAC.02; PS.KAPPA.01; CONTRACT.QFT4D.01","external_data_as_recorded":"-","id":"claim:PS.SPECACT.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":341,"scripts_as_recorded":"v255_spectral_action_expansion.py","status_as_recorded":"Numerical (spectral action) [E]/[C]/[O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] KO-6 skew intersection form + rank2/corank1/null(1,1,-1) + orientability local condition; [C] canonical triple satisfies both (literature); [O] self-contained machine proof needs full canonical bimodule -- no faked closure","checked_by_registry":false,"claim_excerpt":"ORIENTABILITY + POINCARE DUALITY -- HONEST STRUCTURAL TREATMENT (2026-06-17): the two NCG obligations of v250 that do NOT close to a clean [E] on the simplified v252 representation. NO faked proof. KO-dimension 6 forces the intersection form cap(p,q)=Tr(gamma pi(p) J pi(q) J^-1) to be ANTISYMMETRIC (from J gamma=-gamma J + order-zero + reality), so a skew form on the SM K-theory K_0(C(+)H(+)M_3)=Z^3 (odd rank) is nec","claim_id":"PS.NCG.ORIENT.01","dependencies_as_recorded":"PS.DIRAC.02","external_data_as_recorded":"-","id":"claim:PS.NCG.ORIENT.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":342,"scripts_as_recorded":"v256_orientability_poincare.py","status_as_recorded":"Numerical (NCG; honest status) [E]/[C]/[O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] strict orientability + strict Poincare duality FAIL (KO-6, 3 nu_R -- known model-class feature) + quasi-orientability HOLDS (boxes disjoint by chirality); [C] modified Poincare duality / Stephan PD-restoring triple; corrects v256 over-claim -- no faked closure","checked_by_registry":false,"claim_excerpt":"ORIENTABILITY + POINCARE DUALITY -- HONEST LITERATURE-CONFIRMED RESOLUTION (2026-06-17): corrects the slightly-too-generous typing of v256. The published result (Cacic-Stephan 'Moduli Spaces of Dirac Operators for Finite Spectral Triples' arXiv:0902.2068; Chamseddine-Connes-Marcolli CCM07; Standard-Model-vacuum arXiv:hep-th/0601192) is that the CCM Standard-Model finite triple (KO-dimension 6, with three right-handed","claim_id":"PS.NCG.ORIENT.02","dependencies_as_recorded":"PS.NCG.ORIENT.01; PS.DIRAC.02","external_data_as_recorded":"arXiv:0902.2068 (Cacic-Stephan); arXiv:hep-th/0601192 (SM vacuum); CCM07","id":"claim:PS.NCG.ORIENT.02","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":343,"scripts_as_recorded":"v257_quasiorient_modpd.py","status_as_recorded":"Numerical (NCG; honest status) [E]/[C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] inversion identity log((1-C)C^-1)=H exactly + C_F a positive contraction + chirality-odd (Dirac-type) + unitary-equivalent to v252 (same mass spectrum) + Majorana=off-diagonal covariance (seesaw m_D^2/M_R); [C] C_F=P_F C_Sigma P_F so D_F is the KK shadow of the boundary geometry (rests on the open seam realisation).","checked_by_registry":false,"claim_excerpt":"DIRAC AS MODULAR/COVARIANCE INDUCTION (2026-06-17): the finite Dirac operator D_F (v252) is the modular/covariance induction of the boundary seam quasi-free (KMS, beta=1) state restricted to the carrier, not an independent posit -- closes the 'posited Yukawa vs derived operator' gap of v250/v252 (proposal Q2: D_F as Kasparov product, covariance formula as the finite implementation). Quasi-free/modular dictionary: one","claim_id":"PS.DIRAC.03","dependencies_as_recorded":"PS.DIRAC.02; DYN.KMS.01; CONTRACT.QFT4D.DIRAC.01","external_data_as_recorded":"Araki quasi-free states; Casini-Huerta modular Hamiltonian","id":"claim:PS.DIRAC.03","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":344,"scripts_as_recorded":"v258_dirac_covariance_induction.py","status_as_recorded":"Numerical (NCG/modular) [E]/[C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] KMS cutoff moments f_0=f_2=f_4=1 so f_2/f_0=f_4/f_2=1 (sympy) + seam-fixed beta=1 + non-vacuous neg control (Gaussian cutoff gives sqrt(pi)/2 != 1) + kappa=sqrt(c_PS/c_grav) (no cutoff function left); [C] RG kappa~1.3 pins c_PS/c_grav~1.7 (O(1) band [0.3,3]) and lambda(Lambda) likewise a finite-triple number -- the [O] free scheme becomes a finite computation over the built triple.","checked_by_registry":false,"claim_excerpt":"MODULAR/KMS SPECTRAL-ACTION CUTOFF (2026-06-17): the spectral-action cutoff f is the seam's own modular/KMS weight (beta=1 by Tomita-Takesaki/BW, v239; 2pi=1/(4c3), v58), so the heat-kernel cutoff f(u)=e^{-u} is derived not chosen and the moment ratio f_2/f_0=1 exactly -- reducing the last open scheme freedom of PS.KAPPA.01/PS.SPECACT.01 from a free function to a finite-triple trace ratio kappa=sqrt(c_PS/c_grav) (pro","claim_id":"PS.SPECACT.02","dependencies_as_recorded":"PS.SPECACT.01; PS.KAPPA.01; DYN.KMS.01","external_data_as_recorded":"-","id":"claim:PS.SPECACT.02","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":345,"scripts_as_recorded":"v259_modular_cutoff_kappa.py","status_as_recorded":"Numerical (spectral action) [E]/[C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] E8 Cartan even/det1/pos-def + K3 lattice rank22/det-1/even/signature(3,19) with E8(-1)^2 a summand + seam=T^2/(z->-z) 4 fixed points (pillowcase, orbifold Euler char 0) + carrier-16=Kummer nodes |A[2]|=2^4=16=dim S+=4x4 + honesty (the rank-16 Kummer lattice is NOT literally E8(-1)^2, distinct sublattices of H^2(K3)); [C] two faces of E8 in K3 (local du Val C^2/2I v232/v236; global H^2 summand) + the carrier<->node geometric unification.","checked_by_registry":false,"claim_excerpt":"KUMMER/K3 UNIFICATION OF SEAM + CARRIER-16 + E8 (2026-06-17): one smooth Kummer/K3 surface carries the seam (pillowcase = the elliptic-involution quotient of the square torus tau=i, j=1728, v214), the carrier-16 (the 16 Kummer nodes = dim S+, v197) and the E8 lattice (the H^2(K3) intersection form U^3(+)E8(-1)^2), so the v1 glue D5(+)A3 + mu4 => E8 is the lattice shadow of a single geometric object (the K3/Kummer pro","claim_id":"ARCH.K3.01","dependencies_as_recorded":"E8.GLU.01; QGEO.PILLOW.01; ARCH.RRCAR.02","external_data_as_recorded":"standard K3 lattice theory (U^3(+)E8(-1)^2)","id":"claim:ARCH.K3.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":346,"scripts_as_recorded":"v260_k3_kummer_unification.py","status_as_recorded":"Lattice (K3/Kummer) [E]/[C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] one index=marks=fixed points=glue order=4 + one carrier-16 (spinor/lattice/triple) + one gap 6log(3/2) (OS/recovery/Lindblad) + the three closures re-derived (Kasparov/KMS cutoff/K3) + the 10-component relative-object manifest; [O] the whole QFT layer reduces to one premise QGEO.SYM.01 (seam realisation), ambient QG QG.AMB.01 separate; [C] the Modular Spectral Universality master statement holds modulo QGEO.SYM.01.","checked_by_registry":false,"claim_excerpt":"MODULAR SPECTRAL CLOSURE (2026-06-17): the assembly/reduction certificate turning the whole QFT layer (v238-v260) into ONE relative object TFPT_QFT=(A_Sigma,omega_Sigma,Delta_Sigma,rho,A_F,H_F,D_F,J,gamma,S_rel) reduced to ONE open premise. Cross-validates the invariants that must agree across the round (index=marks=fixed points=glue order=4; carrier-16 across spinor/lattice/triple; one gap 6log(3/2) static+dynamic),","claim_id":"QFT.MSC.01","dependencies_as_recorded":"PS.DIRAC.03; PS.SPECACT.02; ARCH.K3.01; PS.DIRAC.02; GATE.METRIC.06; GATE.METRIC.07; QGEO.MARKS.03; DYN.KMS.01; DYN.GNS.01","external_data_as_recorded":"-","id":"claim:QFT.MSC.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":347,"scripts_as_recorded":"v261_modular_spectral_closure.py","status_as_recorded":"Numerical (assembly certificate) [E]/[C]/[O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] b3=-7 carrier output; [N] 2-loop alpha_s running reproduces PDG alpha_s(2 GeV)~0.30; [C] m_p/m_e~1824 reproduced within ~7% external budget (lattice C_p + alpha_s); [X] firewall -- m_p/m_e not an admissible compiler integer, stays [C].","checked_by_registry":false,"claim_excerpt":"F_QCD TRANSFER REPRODUCTION OF m_p/m_e (2026-06-18): the contract-only F_transfer/qcd_matching_mp_me pipeline implemented as a real solver. 2-loop alpha_s(M_Z)=0.1179 run with n_f thresholds (carrier b3=-7) gives alpha_s(2 GeV)~0.30 and Lambda^(3)_MSbar~0.33 GeV; with the lattice bridge C_p=m_p/Lambda (external O(1)) and the closed m_e, m_p/m_e~1824 vs measured 1836.15 within ~7% external budget. NOT a compiler power","claim_id":"FR.MPME.02","dependencies_as_recorded":"FR.MPME.01; QCD.LAMBDA.01; CONTRACT.F.01","external_data_as_recorded":"alpha_s(M_Z) PDG; lattice m_p/Lambda_MSbar O(1)","id":"claim:FR.MPME.02","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":348,"scripts_as_recorded":"v262_fqcd_mp_me.py","status_as_recorded":"Numerical (transfer reproduction) [C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] M_nu=-m_D M_R^{-1} m_D^T symmetric + seesaw-suppressed (output of D_F) + mu-tau-symmetric image; [C] reproduces v9 angles (theta23=45, sin^2 th12=1/3-phi0/2) under the seam lemma; [O] theta13=0 in the leading texture, CP magnitude from mu6/triality (v231/v233), absolute nu-mass scale (M_R) open. Operator advance, not a closure.","checked_by_registry":false,"claim_excerpt":"M_nu AS THE TYPE-I SEESAW OF D_F (2026-06-18): the light neutrino matrix is the seesaw of the finite Dirac operator's own blocks, M_nu=-m_D M_R^{-1} m_D^T, advancing the v9 solar-angle texture from a posited matrix to a seesaw object. A mu-tau-symmetric (m_D,M_R) gives a mu-tau-symmetric M_nu reproducing theta23=45deg and sin^2 theta12=1/3-phi0/2 under the seam misalignment. theta13=0 in the leading texture, the CP m","claim_id":"FLAV.PMNS.02","dependencies_as_recorded":"FLAV.TH12.01; PS.DIRAC.02; FLAV.SOLAR.01; CP.TRIALITY.01","external_data_as_recorded":"-","id":"claim:FLAV.PMNS.02","location_as_recorded":"tfpt_2_standard_model","path":"verification/status_ledger.csv","row_number":349,"scripts_as_recorded":"v263_mnu_from_df.py","status_as_recorded":"Numerical (seesaw operator) [E]/[C]/[O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] Gauss-Bonnet 4 marks + block-diagonal/state-invariance chain on the pillowcase; [N] Z4-Fourier support (4Z) of the pillowcase curvature; [O] the metric-realisation premise (QGEO.SYM.01) stays open -- a reduction to one metric statement, NOT a closure (NEG control: curvature off the mu4 orbit breaks the chain).","checked_by_registry":false,"claim_excerpt":"RAW-SEAM => MARK-LOCALITY REDUCTION (2026-06-18): composes v216+v201+v198 on the canonical pillowcase metric to make the converse implication explicit and isolate the bedrock. The flat pillowcase has curvature only at the 4 marks (Gauss-Bonnet), so the DtN sub-principal symbol is a mu4-orbit sum, Z4-invariant (Fourier on 4Z), block-diagonal, [rho,M_f]=0; with |k| commuting (v198) [rho,Lambda]=0 => omega o rho=omega O","claim_id":"QGEO.ENERGY.03","dependencies_as_recorded":"QGEO.SYM.01; QGEO.SUBPRIN.01; QGEO.MODULAR.01; QGEO.MARKS.03; QGEO.PILLOW.01","external_data_as_recorded":"-","id":"claim:QGEO.ENERGY.03","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":350,"scripts_as_recorded":"v264_raw_seam_marklocal.py","status_as_recorded":"Geometric premise [O] (reduction, not closure)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[C] A canonical (boundary only) + B conditional PS UV branch; [X] SM-only GUT killed; [E] wording guard + decision JSON written. The fork is a frozen decision tree, not an ambiguity.","checked_by_registry":false,"claim_excerpt":"4D-QFT FORK FROZEN AS A BRANCH POLICY (2026-06-18): boundary-only is the canonical 4D reading; carrier-native Pati-Salam is a falsifiable UV branch; SM-only 4D-GUT unification is killed. A frozen decision tree (qft4d_fork_freeze.json) with explicit promotion/demotion rules, not an open ambiguity.","claim_id":"QFT4D.FORK.01","dependencies_as_recorded":"QFT4D.RGTEST.01; PS.RGTEST.01; PS.E8BRANCH.01; QFT.MSC.01","external_data_as_recorded":"-","id":"claim:QFT4D.FORK.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":351,"scripts_as_recorded":"v265_qft4d_fork_freeze.py","status_as_recorded":"Branch policy (frozen) [C]/[X]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[C] boundary-only is the default 4D reading; the MSC closes the relative boundary object modulo QGEO.SYM.01, ambient QG separate.","checked_by_registry":false,"claim_excerpt":"CANONICAL 4D READING = BOUNDARY ONLY (2026-06-18): TFPT delivers the boundary QFT, the relative spectral action and the SM readout; a 4D-GUT is not claimed by default (E8 is the audit hull, not an unbroken 4D gauge group).","claim_id":"QFT4D.BOUNDARY.DEFAULT.01","dependencies_as_recorded":"QFT.MSC.01; QFT4D.FORK.01","external_data_as_recorded":"-","id":"claim:QFT4D.BOUNDARY.DEFAULT.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":352,"scripts_as_recorded":"v265_qft4d_fork_freeze.py","status_as_recorded":"Branch policy (canonical) [C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[X] the plain SM couplings do not meet (recomputed); E8 is the audit hull, not a 4D gauge group, so non-unification is expected.","checked_by_registry":false,"claim_excerpt":"SM-ONLY 4D-GUT UNIFICATION KILLED (2026-06-18): 1-loop SM running with b=(41/10,-19/6,-7) does not unify -- at the alpha1=alpha2 scale alpha3^-1 is off by ~5.6, spread ~8.8 at 2e16 GeV. The canonical expectation, not a failure (re-derives v246).","claim_id":"QFT4D.SMONLYGUT.01","dependencies_as_recorded":"QFT4D.RGTEST.01","external_data_as_recorded":"-","id":"claim:QFT4D.SMONLYGUT.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":353,"scripts_as_recorded":"v265_qft4d_fork_freeze.py","status_as_recorded":"Kill-test [X]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[C] PS is a conditional UV candidate (E8 content + sin^2 thetaW=3/8 + kappa band); not promoted to default; carrier gauging stays [O].","checked_by_registry":false,"claim_excerpt":"PATI-SALAM AS A CONDITIONAL UV BRANCH (2026-06-18): carrier-native Pati-Salam is permitted as a falsifiable UV completion, NOT the default -- E8-allowed content {1,10,16,45} (no 126), sin^2 thetaW=3/8, kappa O(1) band; carrier gauging stays the contract CONTRACT.QFT4D.DIRAC.01.","claim_id":"PS.UVBRANCH.01","dependencies_as_recorded":"PS.E8BRANCH.01; PS.ALGEBRA.01; PS.RGTEST.01; QFT4D.FORK.01","external_data_as_recorded":"-","id":"claim:PS.UVBRANCH.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":354,"scripts_as_recorded":"v265_qft4d_fork_freeze.py","status_as_recorded":"Branch policy (conditional) [C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[C] kappa band met; [O] the explicit reps-at-scales threshold model is the open part (deferred to v266).","checked_by_registry":false,"claim_excerpt":"PATI-SALAM THRESHOLD MODEL EXPLICIT (2026-06-18): the PS UV branch is admissible only with an explicit two-step threshold model meeting the scalaron scale (M_PS=kappa M_s, kappa in [1.0,1.7]); the detailed reps-at-scales model is the open part (v266 target).","claim_id":"PS.THRESHOLD.01","dependencies_as_recorded":"PS.RGTEST.01; PS.KAPPA.01; QFT4D.FORK.01","external_data_as_recorded":"-","id":"claim:PS.THRESHOLD.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":355,"scripts_as_recorded":"v265_qft4d_fork_freeze.py","status_as_recorded":"Branch policy (threshold) [C]/[O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[X] proton-decay is a frozen safety constraint/kill rule for the PS branch, not a discovery prediction (no fake tau_p window).","checked_by_registry":false,"claim_excerpt":"PROTON-DECAY SAFETY RULE (2026-06-18): no discovery tau_p is predicted; PS is killed if its thresholds need forbidden reps, leave the kappa band, or predict tau_p below the current bound; until a sharp window is published proton decay is a safety constraint, not a discovery.","claim_id":"PS.PROTON.KILL.01","dependencies_as_recorded":"PS.RGTEST.01; QFT4D.FORK.01","external_data_as_recorded":"-","id":"claim:PS.PROTON.KILL.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":356,"scripts_as_recorded":"v265_qft4d_fork_freeze.py","status_as_recorded":"Kill-test rule [X]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] prose sentinel over the active .tex: forbidden bare over-claims absent (6/6) + required scoped policy phrases present (3/3).","checked_by_registry":false,"claim_excerpt":"4D OVER-CLAIM WORDING GUARD (2026-06-18): bare 4D over-claims ('TFPT solves 4D QFT', 'SM couplings unify', '4D GUT prediction', 'unbroken E8 gauge') are absent from the active docs, and the scoped fork-policy phrases ('boundary only is canonical', 'SM-only ... killed', 'not claimed by default') are present.","claim_id":"QFT4D.NO_OVERCLAIM.01","dependencies_as_recorded":"QFT4D.FORK.01","external_data_as_recorded":"-","id":"claim:QFT4D.NO_OVERCLAIM.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":357,"scripts_as_recorded":"v265_qft4d_fork_freeze.py","status_as_recorded":"Formal/prose guard [E]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] explicit two-step solutions (M_PS,M_GUT,alpha_GUT) for both E8-allowed contents, M_PS on the scalaron scale; [C] realises the threshold policy; selects the content via proton decay (PS.PROTON.02).","checked_by_registry":false,"claim_excerpt":"EXPLICIT PATI-SALAM THRESHOLD MODEL (2026-06-18): the two-step carrier-native PS chain made explicit for the two E8-allowed contents -- minimal 16-Higgs (M_PS~4.2e13=scalaron, M_GUT~2.4e15) and +(15,1,1) (M_GUT~5.9e15) -- realising the PS.THRESHOLD.01 policy with concrete reps-at-scales and M_PS on the scalaron scale. Decides branch B together with PS.PROTON.02.","claim_id":"PS.THRESHOLD.02","dependencies_as_recorded":"PS.THRESHOLD.01; PS.RGTEST.01; PS.KAPPA.01","external_data_as_recorded":"-","id":"claim:PS.THRESHOLD.02","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":358,"scripts_as_recorded":"v266_ps_threshold_proton.py","status_as_recorded":"Numerical (two-step RG) [E]/[C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[X] minimal content killed by Super-K + Hyper-K decisive for the survivor; [C] +(15,1,1) survives now and is the only E8-allowed proton-safe content; [O] marginal (one 45) + O(3) hadronic uncertainty. Promotes branch B to a content-selected, dated-kill-test UV branch (still not the default).","checked_by_registry":false,"claim_excerpt":"PROTON-DECAY WINDOW DECIDES BRANCH B (2026-06-18): d=6 tau_p(p->e+pi0) over the explicit thresholds -- minimal 16-Higgs tau_p~4.4e33 yr < Super-K (2.4e34) => KILLED even at the high hadronic band; +(15,1,1) [E8-allowed single 45] tau_p~1.6e35 yr > Super-K => survives now, but sits AT the Hyper-K reach (~1.4e35) => decisively falsifiable within the decade. Branch B is content-selected (must be +(15,1,1)) and Hyper-K-d","claim_id":"PS.PROTON.02","dependencies_as_recorded":"PS.THRESHOLD.02; PS.PROTON.KILL.01; PS.E8BRANCH.01; QFT4D.FORK.01","external_data_as_recorded":"-","id":"claim:PS.PROTON.02","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":359,"scripts_as_recorded":"v266_ps_threshold_proton.py","status_as_recorded":"Kill-test (proton decay) [X]/[C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] order-4 symmetry forces cross-ratio 2 / j=1728 / the pillowcase / mark-local DtN / omega o rho=omega (the whole chain) + neg controls (generic Z2, hex Z6); [C] arithmetic/Galois rigidity (j=1728 CM, {1,i,-1,-i} over Q); [O] the bare order-4 symmetry (QGEO.SYM.01) stays the one foundational postulate -- the reduction is closed, the axiom is not.","checked_by_registry":false,"claim_excerpt":"QGEO RIGIDITY / MINIMAL-AXIOM FORM (2026-06-18): the bedrock QGEO.SYM.01 is sharpened to its minimal form -- the single bare statement 'the raw RP seam admits the carrier mu4 clock as a conformal symmetry permuting its 4 marks' (= omega o rho = omega) FORCES everything: square config (cross-ratio 2 <=> j=1728 <=> order-4 CM auto), the unique flat pillowcase metric (Troyanov, v214), mark-local Z4-Fourier DtN (v201/v26","claim_id":"QGEO.SYM.02","dependencies_as_recorded":"QGEO.SYM.01; QGEO.PILLOW.01; QGEO.ENERGY.03; QGEO.RIGID.01; QGEO.MODULAR.01","external_data_as_recorded":"Troyanov uniformisation; Belyi/Grothendieck dessins d'enfants","id":"claim:QGEO.SYM.02","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":360,"scripts_as_recorded":"v267_qgeo_rigidity_minimal_axiom.py","status_as_recorded":"Geometric premise [E]/[C]/[O] (rigidity; minimal axiom)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] gamma=5/6=tr_E Y^2 (exponent origin) + own-channel separation (eps^2 ~ 1.6e-3 != 0.023); [C] value 0.0231 vs ~0.0222; [O] CP magnitude + absolute scale open. Closes the theta_13 exponent origin, not full PMNS dynamics.","checked_by_registry":false,"claim_excerpt":"REACTOR ANGLE EXPONENT = CARRIER HYPERCHARGE TRACE (2026-06-18): the theta_13 value sin^2 theta_13 = phi0 e^{-5/6} = 0.0231 (v16) has its EXPONENT origin closed exactly -- gamma = tr_E Y^2 = 5/6 over the 5-slot carrier hypercharge Y=diag(-1/3,-1/3,-1/3,1/2,1/2) (anomaly-free roots of 6Y^2-Y-1=0), complement 1/6 the neutrino ratio. theta_13 is confirmed a SEPARATE carrier-trace channel: the mu-tau-breaking eps=3phi0/4","claim_id":"FLAV.TH13.01","dependencies_as_recorded":"FLAV.TH12.01; FLAV.SOLAR.01; FLAV.PMNS.02; CAR.SM.01","external_data_as_recorded":"NuFIT 6.0 / PDG sin^2 theta_13 ~ 0.0222","id":"claim:FLAV.TH13.01","location_as_recorded":"tfpt_2_standard_model","path":"verification/status_ledger.csv","row_number":361,"scripts_as_recorded":"v268_theta13_carrier_trace.py","status_as_recorded":"Numerical/identity (flavor readout) [E]/[C]/[O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] three-layer typing + power-counting renormalizable (dim<=4) + finite counterterm basis (7+3); [C] Epstein-Glaser order-by-order existence (cited theorem applied) + adiabatic/gap link to S_phys; [O] perturbative only -- ambient measure QG.AMB.01 stays open. A contract/skeleton, not a nonperturbative closure.","checked_by_registry":false,"claim_excerpt":"PERTURBATIVE 4D S-MATRIX (S_pert) AS AN EPSTEIN-GLASER / pAQFT SKELETON (2026-06-18): the honest middle layer of the three-layer S-matrix -- S_top (2d DHR braiding monodromy |M|=1, statistics, v243), S_pert (4d EG/BV S-matrix of the Connes spectral action), S_phys (LSZ on the OS-reconstructed admissible Wightman functions, v240). The spectral-action a_4 interaction is power-counting renormalizable (all operators mass","claim_id":"QFT4D.SPERT.01","dependencies_as_recorded":"CONTRACT.QFT4D.01; DHR.SMATRIX.01; DYN.GNS.01; PS.SPECACT.01; QFT4D.FORK.01","external_data_as_recorded":"Epstein-Glaser causal perturbation theory; Brunetti-Fredenhagen pAQFT","id":"claim:QFT4D.SPERT.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":362,"scripts_as_recorded":"v269_spert_paqft_skeleton.py","status_as_recorded":"Contract [C]/[O] (perturbative skeleton)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the three angle channels + the exact unitary assembly; [C] the derived Jarlskog CP strength + its NuFIT confrontation; [O] the phase's operator origin (delta = mu6/triality, not M_nu) + the absolute scale. A PMNS assembly + CP-strength readout, not a full operator closure.","checked_by_registry":false,"claim_excerpt":"COMPLETE COMPLEX PMNS MATRIX + LEPTONIC JARLSKOG J_PMNS (CP STRENGTH) (2026-06-18): the four TFPT channels (sin^2 th12 = 1/3 - phi0/2 v9/v263, sin^2 th23 = 1/2 v9/v263, sin^2 th13 = phi0 e^{-5/6} v16/v268, delta = 4 pi/3 = 240 deg v231/v233) assemble into one exactly-unitary complex PMNS matrix U = R23 U13(delta) R12, from which the Jarlskog CP strength J_PMNS = Im(U_e1 U_mu2 U*_e2 U*_mu1) = s12 c12 s23 c23 s13 c13^2","claim_id":"FLAV.PMNS.03","dependencies_as_recorded":"FLAV.TH12.01; FLAV.PMNS.02; FLAV.TH13.01; CP.MU6.01; CP.TRIALITY.01","external_data_as_recorded":"NuFIT 5.2 (2022) PMNS global fit; PDG 2024","id":"claim:FLAV.PMNS.03","location_as_recorded":"tfpt_2_standard_model","path":"verification/status_ledger.csv","row_number":363,"scripts_as_recorded":"v270_pmns_jarlskog_assembly.py","status_as_recorded":"Readout [C] (CP strength); [O] phase origin + absolute scale","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] order structure + scaling degree (sd=4=d) + one log counterterm (omega=0) + loop factor 1/(16 pi^2) (exact, Wolfram-mirrored); [C] the phi^4 one-loop beta + the spectral-action initial condition; [O] order-2/one-loop only, all-order + nonperturbative stay open. Turns the v269 skeleton into a concrete one-loop number.","checked_by_registry":false,"claim_excerpt":"CONCRETE EPSTEIN-GLASER ONE-LOOP QUARTIC RENORMALIZATION (2026-06-18): takes the v269 S_pert pAQFT skeleton from 'exists' to an actual EG number (no path integral). [E] T_1=:L_int: needs no extension; the first EG renormalization is the order-2 product T_2. [E] the massless Feynman propagator has Steinmann scaling degree sd=2 in d=4; the one-loop bubble (two propagators) has sd=4=d, so the UV singular order omega=sd-","claim_id":"QFT4D.SPERT.02","dependencies_as_recorded":"QFT4D.SPERT.01; CONTRACT.QFT4D.01; PS.SPECACT.01; HIGGS.FREESEAM.01","external_data_as_recorded":"Epstein-Glaser causal perturbation theory; Steinmann scaling degree","id":"claim:QFT4D.SPERT.02","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":364,"scripts_as_recorded":"v271_eg_oneloop_quartic.py","status_as_recorded":"Numerical/Identity [E] (one-loop EG core) + [C] (beta + IC) + [O] (all-order)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the absolute nu-scale = one seesaw ratio (parallels v_geo); [N]/[C] the TFPT PS->GUT window is consistent with the observed spectrum at O(1) Dirac Yukawa + the cosmological floor; [O] the absolute value stays one open UV input (M_R not a clean Mbar power, v184); [X] the NO floor is the kill test. Closes the PMNS bookkeeping, not the absolute number.","checked_by_registry":false,"claim_excerpt":"ABSOLUTE NEUTRINO-MASS SCALE TYPED HONESTLY (2026-06-18): does NOT fabricate a Sigma m_nu number (would contradict the v184 firewall); closes the PMNS bookkeeping instead. [E] the absolute scale reduces to ONE seesaw ratio m_3 = (y_nu v_EW)^2/M_R -- one irreducible UV input like v_geo (No-Unit, v153); the ratios (m2/m3, ordering, PMNS angles v270) are pinned. [N] the observed m_3 = sqrt(dm2_atm) = 0.050 eV with the T","claim_id":"FLAV.NUSCALE.01","dependencies_as_recorded":"FLAV.PMNS.02; FLAV.PMNS.03; PS.RGTEST.01; FR.MPME.02; ANCHOR.VGEO.02","external_data_as_recorded":"NuFIT 5.2 dm2; Planck 2018 + DESI 2024 Sigma m_nu bound","id":"claim:FLAV.NUSCALE.01","location_as_recorded":"tfpt_2_standard_model","path":"verification/status_ledger.csv","row_number":365,"scripts_as_recorded":"v272_nu_mass_scale.py","status_as_recorded":"Bookkeeping [E] + window [N]/[C] + [O] absolute scale + [X] kill","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the EG gauge self-energy scaling-degree mechanism + the exact one-loop b_i=(41/10,-19/6,-7) from the content (Wolfram-mirrored); [C] the physical RG directions; [O] two-loop + all-order. The gauge analogue of v271's quartic.","checked_by_registry":false,"claim_excerpt":"EG ONE-LOOP GAUGE SELF-ENERGY -> (b1,b2,b3) = (41/10,-19/6,-7) (2026-06-18): takes v271's quartic mechanism to the gauge sector. [E] the one-loop gauge 2-point function is the order-2 EG product of two currents, scaling degree sd=4=d so omega=sd-d=0 -> exactly one local counterterm per gauge coupling (wavefunction/coupling renormalization), the SAME marginal mechanism and loop factor 1/(16 pi^2) as the quartic. [E] t","claim_id":"QFT4D.SPERT.03","dependencies_as_recorded":"QFT4D.SPERT.02; QFT4D.SPERT.01; EM.BUDGET.02; CAR.SM.01","external_data_as_recorded":"Epstein-Glaser causal perturbation theory; standard one-loop gauge beta","id":"claim:QFT4D.SPERT.03","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":366,"scripts_as_recorded":"v273_eg_gauge_running.py","status_as_recorded":"Identity [E] (EG one-loop b_i, exact) + [C] (RG directions) + [O] (all-order)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] one anchor + the conformal-seam reason; [N] the two-route over-determination (gravity vs dark energy, 0.11%); [A] the re-typing of v_geo to an over-determined anchor = the Planck mass. Sharpens v153/v78.","checked_by_registry":false,"claim_excerpt":"THE SINGLE MASS ANCHOR IS OVER-DETERMINED; NO DERIVABLE ABSOLUTE SCALE IS A THEOREM (2026-06-18): sharpens the No-Unit theorem (v153). [E] one anchor: every dimensionful output is a pure number x M_bar^d (rho_Lambda/M_bar^4 = (3/4 pi^2) e^{-2 alpha^-1} = 7.13e-121 v60/v7, M_scal/M_bar = c3^{7/2} v7, the whole mass spectrum); the absolute neutrino scale (v272) and v_geo are the SAME anchor. [N] OVER-DETERMINATION: two","claim_id":"SCALE.OVERDET.01","dependencies_as_recorded":"ANCHOR.VGEO.02; COSMO.LAM.01; QG.AMB.01; FLAV.NUSCALE.01","external_data_as_recorded":"Planck 2018 dark-energy density; CODATA G / reduced Planck mass","id":"claim:SCALE.OVERDET.01","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":367,"scripts_as_recorded":"v274_scale_overdetermination.py","status_as_recorded":"Identity [E] + over-determination [N] + re-typing [A]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] Tier A decoupling + the c=8 boundary-net facts; [C] the perturbative layer; [O] the nonperturbative ambient measure stays open; [X] the promotion/kill condition. A consolidation/roadmap that gives the QG.AMB.01 gate a module -- it does not close it.","checked_by_registry":false,"claim_excerpt":"OBLIGATION ROADMAP FOR QG.AMB.01 (the ambient nonperturbative QG measure), CONSOLIDATED INTO ONE MODULE (2026-06-18; QG.AMB.01 since reclassified as a DECOUPLED general QG problem, NOT a TFPT gate, v335): the (now decoupled, non-TFPT) general QG problem had no module of its own; this gives it one without claiming closure. [E] Tier A gap decoupling: Delta_eff = 6 log(3/2) - 2*248 c3^2 = 2.433 - 0.785 = 1.648 > 0 (v36/","claim_id":"QGAMB.ROADMAP.01","dependencies_as_recorded":"QG.AMB.01; QG.GAPDEC.01; GATE.METRIC.03; QFT4D.SPERT.01","external_data_as_recorded":"-","id":"claim:QGAMB.ROADMAP.01","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":368,"scripts_as_recorded":"v275_qgamb_roadmap.py","status_as_recorded":"Roadmap [E]/[C] + [O] open core + [X] promotion/kill","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Red-team verdict: the v269-v275 round survives as typed; two narrowings folded into v269 (gravity-sector Stelle ghost -> S_pert unitary for matter+gauge only) and v274 (over-determination conditional on the Lambda-branch). The perturbative gravity ghost IS the QG.AMB.01 frontier.","checked_by_registry":false,"claim_excerpt":"RED TEAM Target F -- adversarial audit of the perturbative 4D-QFT + scale round (v269-v275), published in release 5.2. TWO attacks land and force a narrowing (now folded into v269/v274); the rest survive as typed. (1) GRAVITY S_pert NON-UNITARY: power-counting renormalizability is not unitarity -- the spectral-action R^2/Weyl^2 sector gives a 4-derivative propagator 1/(p^2(p^2+M^2)) whose massive spin-2 mode has a NE","claim_id":"REDTEAM.F.01","dependencies_as_recorded":"QFT4D.SPERT.01; QFT4D.SPERT.02; QFT4D.SPERT.03; FLAV.PMNS.03; FLAV.NUSCALE.01; SCALE.OVERDET.01; QGAMB.ROADMAP.01","external_data_as_recorded":"Stelle 1977 (higher-derivative gravity ghost)","id":"claim:REDTEAM.F.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":369,"scripts_as_recorded":"redteam/rt_F_qft4d.py","status_as_recorded":"Red-team [P] (survives, narrowed)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the isometry=>commutator closure (numerically verified, all orders) + the all-orders upgrade of v198/v201; [C] tau=i forced by order-4; [O] the one geometric postulate (raw seam = flat tau=i pillowcase) stays open. Narrows QGEO.SYM.01 to a single flat-geometry statement; does NOT close it.","checked_by_registry":false,"claim_excerpt":"FLAT PILLOWCASE CLOSES THE MODULAR COMMUTATOR TO ALL ORDERS (2026-06-18): collapses the bedrock QGEO.SYM.01 to ONE geometric postulate (does NOT prove the premise). For a quasi-free seam state QGEO.SYM.01 = (omega o rho = omega) <=> [rho,C]=0 <=> [rho,H]=0 (C=(1+e^H)^-1, v258). [E] ISOMETRY=>COMMUTATOR: if H=f(Delta_flat) (the DtN of a flat metric, no curvature corrections) and the order-4 deck rho (z->iz) is a flat-","claim_id":"QGEO.SYM.03","dependencies_as_recorded":"QGEO.SYM.01; QGEO.SYM.02; QGEO.MODULAR.01; QGEO.SUBPRIN.01; QGEO.PILLOW.01; PS.DIRAC.03","external_data_as_recorded":"Stone/spectral theorem (isometry commutes with functions of the Laplacian)","id":"claim:QGEO.SYM.03","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":370,"scripts_as_recorded":"v276_qgeo_flat_closes_commutator.py","status_as_recorded":"Reduction [E] (flat => commutator all orders) + [C] (tau=i forced) + [O] (one geometric postulate)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the full (E8)_1 matching target (c=8, det 1, 248 currents, single primary) + the explicit D8 counterexample isolating holomorphy as THE discriminator; [C] the seam-side match via v276/v260; [O] the single holomorphy bit stays open. Reduces QG.AMB.01 Tier-B to one checkable condition; does NOT close it.","checked_by_registry":false,"claim_excerpt":"SEAM-CALDERON -> (E8)_1 MATCHING CERTIFICATE (2026-06-18): the concrete Tier-B step of QG.AMB.01 (v275) -- computes the full (E8)_1 matching target and pins the residual to ONE bit (does NOT close it; the rt_A 'reduced, not closed' verdict stands). [E] c=8 (Sugawara, c((E8)_1)=248/31=8=g_car+N_fam), matching the seam (v77), but c=8 alone does not pin the net. [E] THE DISCRIMINATOR IS HOLOMORPHY: det Cartan(E8)=1 (one","claim_id":"QGAMB.TIERB.01","dependencies_as_recorded":"QGAMB.ROADMAP.01; GATE.METRIC.03; REDTEAM.A.01; QGEO.SYM.03; ARCH.K3.01; GATE.HOLO.02","external_data_as_recorded":"E8/D8 lattice theta functions; Frenkel-Kac-Segal lattice VOA","id":"claim:QGAMB.TIERB.01","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":371,"scripts_as_recorded":"v277_seam_calderon_e8_match.py","status_as_recorded":"Reduction [E] (full (E8)_1 match + discriminator) + [C] (seam-side) + [O] (one holomorphy bit)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the LSZ bridge structure + the one-loop optical theorem (exact: cut = two-body phase space) + the threshold analyticity; [C] the gap->asymptotic-states link + finite Z; [O] the gravity ghost (-> QG.AMB.01). Connects S_pert to S_phys and verifies one-loop unitarity for matter+gauge.","checked_by_registry":false,"claim_excerpt":"S_pert -> S_phys LSZ BRIDGE + ONE-LOOP UNITARITY (2026-06-18): connects the EG perturbative S-matrix (v269/v271/v273) to the physical asymptotic S-matrix (S_phys = LSZ on the OS-reconstructed Wightman functions, v240); the three-layer S-matrix is now S_top (v243) | S_pert (v269) --LSZ--> S_phys (v240). [E] LSZ BRIDGE: S_phys matrix elements = (amputate external legs)(on-shell residue sqrt(Z)) of the connected time-or","claim_id":"QFT4D.SPERT.04","dependencies_as_recorded":"QFT4D.SPERT.01; QFT4D.SPERT.02; DYN.GNS.01; DHR.SMATRIX.01; REDTEAM.F.01","external_data_as_recorded":"Lehmann-Symanzik-Zimmermann reduction; Haag-Ruelle scattering theory","id":"claim:QFT4D.SPERT.04","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":372,"scripts_as_recorded":"v278_lsz_bridge_unitarity.py","status_as_recorded":"Bridge [E] (LSZ structure + one-loop optical theorem) + [C] (gap/Z) + [O] (gravity ghost)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the precise lemma + proof-tree completeness (exactly one open leaf) + the fixed geometric side; [C] the two proof routes; [F] the all-orders step in Lean; [O] the one constructive-QFT residual. The formal obligation write-up; does NOT close QGEO.SYM.01.","checked_by_registry":false,"claim_excerpt":"QGEO.SYM.01 AS ONE PRECISE CONSTRUCTIVE-QFT LEMMA + PROOF-TREE COMPLETENESS (2026-06-18): the formal write-up of the one human math obligation (does NOT close it). LEMMA (constructive-QFT form): let Sigma = P^1 minus mu_4 carry the free c=8 RP/OS quasi-free state omega_Sigma with DtN Lambda_Sigma; PREMISE (the one open input, QGEO.SYM.01): the raw seam carries the FLAT tau=i pillowcase metric g_flat (the Troyanov-uni","claim_id":"QGEO.OBLIG.01","dependencies_as_recorded":"QGEO.SYM.01; QGEO.SYM.02; QGEO.SYM.03; FORM.QGEO.04; QGEO.MARKLOCAL.01; QGEO.PILLOW.01","external_data_as_recorded":"Troyanov (prescribed-curvature cone metrics); Osterwalder-Schrader reconstruction","id":"claim:QGEO.OBLIG.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":373,"scripts_as_recorded":"v279_qgeo_obligation_lemma.py","status_as_recorded":"Obligation lemma [E] (proof-tree complete) + [C] (routes) + [O] (one residual)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Formal [F]: the v276 flat-metric all-orders commutator closure is a Lean theorem (SeamDeckClosure.flat_all_orders_clock), standard axioms only, no sorry, full build green.","checked_by_registry":false,"claim_excerpt":"FLAT-METRIC ALL-ORDERS CLOSURE FORMALISED IN LEAN (2026-06-18): TfptCarrier/SeamDeckClosure.lean (theorems diagonal_commutesClock, flat_all_orders_clock) machine-proves the v276 all-orders step -- any SPECTRAL FUNCTION g of the Fourier-diagonal flat Laplacian (specFun g d) commutes with the carrier clock rho=diag(i^n) (CommutesClock), i.e. given the flat tau=i metric the DtN modular Hamiltonian H=g(Delta_flat) is clo","claim_id":"FORM.QGEO.04","dependencies_as_recorded":"FORM.QGEO.01; FORM.QGEO.02; QGEO.SYM.03","external_data_as_recorded":"Lean 4 (leanprover/lean4 v4.29.1) + Mathlib","id":"claim:FORM.QGEO.04","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":374,"scripts_as_recorded":"lean4-carrier-rigidity","status_as_recorded":"Formal [F] (Lean theorem, all-orders closure)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the pillowcase orbifold + order-4 orbit + the exact geometric chain omega o rho = omega numerically realised; [C] the RP-state is metric-determined (route-(i) evidence); [O] the premise stays open. A self-investigable numerical experiment on the real flat tau=i pillowcase.","checked_by_registry":false,"claim_excerpt":"FLAT tau=i PILLOWCASE DtN EXPERIMENT (2026-06-18): a direct numerical experiment on the actual seam orbifold, realising the QGEO chain on the geometric side (does NOT prove the premise). [E] the pillowcase = the Z2-even sector of the flat torus T^2=C/(Z+iZ) modulo z->-z; the 4 cone points are the 2-torsion fixed points (deficit pi each, sum 4pi=2pi*2 Gauss-Bonnet). [E] the order-4 deck rho (z->iz) descends to the pil","claim_id":"QGEO.STEKLOV.01","dependencies_as_recorded":"QGEO.SYM.01; QGEO.SYM.03; QGEO.OBLIG.01; QGEO.PILLOW.01; QGEO.MARKS.03","external_data_as_recorded":"-","id":"claim:QGEO.STEKLOV.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":375,"scripts_as_recorded":"v280_pillowcase_steklov.py","status_as_recorded":"Numerical experiment [E] (geometric chain) + [C] (RP-state) + [O] (premise)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] #anyons=|det Gram| + the condensation tower 16->4->1 + Gauss-Milgram c=8 + E8 the unique holomorphic point; [O] the single holomorphy bit. The modular-data view of QG.AMB.01 Tier-B; complements v277. Exact core mirrored in Wolfram.","checked_by_registry":false,"claim_excerpt":"MODULAR-DATA / ANYON-CONDENSATION LAYER OF THE Tier-B HOLOMORPHY BIT (2026-06-18): complements v277 (det+character) with the anyon/modular-data view. [E] #anyons = |det Gram|: E8 -> 1 (holomorphic, single sector), D8=SO(16)_1 -> 4 (anyons 1,v,s,c), carrier D5(+)A3 -> det(D5)*det(A3)=4*4=16. [E] the anyon-condensation tower D5(+)A3 (det 16) -> D8 (det 4) -> E8 (det 1), each step condensing a Lagrangian Z2 boson (|det|","claim_id":"QGAMB.MODULAR.01","dependencies_as_recorded":"QGAMB.TIERB.01; GATE.HOLO.02; QGAMB.ROADMAP.01; E8.GLU.01","external_data_as_recorded":"Frenkel-Kac-Segal lattice VOA; Gauss-Milgram / anyon condensation","id":"claim:QGAMB.MODULAR.01","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":376,"scripts_as_recorded":"v281_holomorphy_modular_data.py","status_as_recorded":"Reduction [E] (modular data + condensation tower + Gauss-Milgram) + [O] (one bit)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] tau=i the order-4 CM point + chi_E8=j^{1/3} (chi_E8(i)=12) + the one-object identification; [C] the obligation count drops 2->1; [O] the single unified premise stays open. The candidate simplification of the two math obligations. Exact core mirrored in Wolfram.","checked_by_registry":false,"claim_excerpt":"THE E8-AT-tau=i UNIFICATION: TWO OBLIGATIONS -> ONE OBJECT (2026-06-18): the candidate simplification. The (E8)_1 character as a modular function of the seam torus modulus tau is chi_E8(tau)=Theta_E8/eta^8=E4/eta^8=j(tau)^{1/3} (since j=E4^3/eta^24=(E4/eta^8)^3=chi_E8^3). [E] tau=i is the order-4 CM point (cross-ratio 2 <=> j=1728 <=> tau=i, unique order-4 CM by Z[i], v214/v267) -- the flat tau=i pillowcase geometry ","claim_id":"QGAMB.UNIFY.01","dependencies_as_recorded":"QGEO.SYM.03; QGEO.OBLIG.01; QGAMB.TIERB.01; QGAMB.MODULAR.01; QGEO.PILLOW.01","external_data_as_recorded":"E8 theta / Klein j-function CM values (j(i)=1728)","id":"claim:QGAMB.UNIFY.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":377,"scripts_as_recorded":"v282_e8_tau_i_unification.py","status_as_recorded":"Unification [E] (chi_E8=j^{1/3}, tau=i shared) + [C] (count 2->1) + [O] (one premise)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[N]/[C] data confrontation (pulls vs current bounds) + [X] the two sharp near-term kill tests. A consolidation/scorecard, not new physics.","checked_by_registry":false,"claim_excerpt":"LIVE KILL-TEST SCORECARD OF THE RECENT ROUND'S COMPUTABLE PREDICTIONS (2026-06-18): a data-confrontation consolidation (confronts, does not add physics), each row tagged with the decisive near-term experiment. [N] PMNS angles: sin^2 th12=1/3-phi0/2=0.30675 vs NuFIT 0.303(12) [+0.31 sigma]; sin^2 th13=phi0 e^{-5/6}=0.02311 vs 0.02225(59) [+1.45 sigma]; sin^2 th23=0.5 maximal (octant-ambiguous) -- decisive JUNO/Daya-Ba","claim_id":"PRED.LIVE.01","dependencies_as_recorded":"FLAV.TH13.01; FLAV.PMNS.03; FLAV.NUSCALE.01; PS.PROTON.02; EM.FP.01","external_data_as_recorded":"NuFIT 5.2/6.0; PDG 2024; Planck 2018 + DESI 2024; Super-K","id":"claim:PRED.LIVE.01","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":378,"scripts_as_recorded":"v283_live_killtest_scorecard.py","status_as_recorded":"Data confrontation [N]/[C] + [X] (two near-term kill tests)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] 5/6 Route-(i) lemmas discharged + the L3 flat-DtN verification; [C] the Troyanov reduction (constant curvature -> flat tau=i); [O] the one constant-curvature/geometric-state lemma. Decomposes Route (i) and isolates its single open lemma; does NOT close it.","checked_by_registry":false,"claim_excerpt":"ROUTE (i) (RP-STATE UNIQUENESS) LEMMA DECOMPOSITION (2026-06-18): turns Route (i) from one hard target into a 6-lemma chain with 5 lemmas discharged [E]/[F] and exactly one open lemma isolated (does NOT prove the open premise). L1 [E] RP data define the raw DtN intrinsically (v194 QGEO.DTN.01, OS on the quasi-free state). L2 [E] the four branch marks force the pillowcase conformal class (v195 QGEO.MARKS.02 Lefschetz/","claim_id":"QGEO.ROUTEI.01","dependencies_as_recorded":"QGEO.SYM.01; QGEO.OBLIG.01; QGEO.DTN.01; QGEO.MARKS.03; PS.DIRAC.03; QGEO.SYM.03; QGEO.STEKLOV.01","external_data_as_recorded":"Troyanov (constant-curvature cone metrics); Lee-Uhlmann (DtN symbol)","id":"claim:QGEO.ROUTEI.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":379,"scripts_as_recorded":"v284_route_i_rp_uniqueness.py","status_as_recorded":"Lemma decomposition [E] (5/6 discharged) + [C] (Troyanov) + [O] (one open lemma)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] 3/4 Route-(ii) lemmas discharged + the discriminator + the route-(i)/(ii) coincidence; [O] the unified open lemma (canonical seam<->(E8)_1 equivalence). Decomposes Route (ii), isolates its single open lemma, and shows it coincides with Route (i)'s -- confirming v282 at the lemma level. Does NOT close it.","checked_by_registry":false,"claim_excerpt":"ROUTE (ii) (SEAM-NET CONDENSATION) LEMMA DECOMPOSITION + ROUTE-COINCIDENCE (2026-06-18): a 4-lemma chain with 3 discharged and the open lemma shown to COINCIDE with Route (i)'s (the v282 unification at the lemma level; does NOT prove the open premise). M1 [E] no nontrivial abelian sector <=> |det K|=1 <=> holomorphic (mu-index 1) (v234 GATE.HOLO.01: #(1-dim irreps)=|Gamma^ab|=|H1|=1 <=> E8; v235 GATE.HOLO.02 Chern-Si","claim_id":"QGAMB.ROUTEII.01","dependencies_as_recorded":"QGEO.SYM.01; GATE.HOLO.01; GATE.HOLO.02; QGAMB.TIERB.01; QGAMB.MODULAR.01; QGAMB.UNIFY.01; QGEO.ROUTEI.01","external_data_as_recorded":"Frenkel-Kac-Segal lattice VOA; anyon condensation","id":"claim:QGAMB.ROUTEII.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":380,"scripts_as_recorded":"v285_route_ii_seam_condensation.py","status_as_recorded":"Lemma decomposition [E] (3/4 discharged + route coincidence) + [O] (unified lemma)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the four-object/six-arrow typing + the import firewall (routes non-circular) + the exact-label taxonomy + the single-open-arrow certificate; [O] the named Seam Equivalence Theorem stays open. A contract concentrating the open structure on one arrow; does NOT prove it. Route split 2026-07-22: closed if SEAM.EQUIV.MMST.01 OR SEAM.EQUIV.TWISTOR.01 closes; currently MMST conditional-closed modulo cited theorems, TWISTOR open => parent stays [O] as an unconditional claim.","checked_by_registry":false,"claim_excerpt":"THE SEAM EQUIVALENCE CONTRACT (2026-06-18): concentrates the whole open structure on ONE named arrow (does NOT prove it). THE NAMED THEOREM: the raw reflection-positive seam state (gap, chirality, carrier clock) reconstructs canonically the SAME state as the holomorphic (E8)_1 boundary net at the tau=i pillowcase, respecting the DtN, KMS modular flow, mu4 deck, Q-system extension, det K=1 and the (E8)_1 character (sh","claim_id":"SEAM.EQUIV.01","dependencies_as_recorded":"QGEO.SYM.01; QGEO.OBLIG.01; QGAMB.UNIFY.01; QGEO.ROUTEI.01; QGAMB.ROUTEII.01; SEAM.EQUIV.MMST.01; SEAM.EQUIV.TWISTOR.01","external_data_as_recorded":"-","id":"claim:SEAM.EQUIV.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":381,"scripts_as_recorded":"v286_seam_equivalence_contract.py","status_as_recorded":"Contract [E] (typing + firewall + taxonomy) + [O] (the named theorem)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the AQFT chain typing + the four discharged steps (L1/L2/L4/L5) + the single-missing-theorem isolation (L3); [O] the one external theorem 'invertible Gaussian bulk => single-sector boundary'. A dependency checker, not a proof.","checked_by_registry":false,"claim_excerpt":"ROUTE A (AQFT) DEPENDENCY CHECKER (2026-06-18): for the open Gral arrow 'free Gaussian RP bulk => holomorphic single-sector boundary net', types the 5-lemma AQFT chain and isolates the ONE missing standard theorem (does NOT prove the arrow). L1 [E] RawRPSeam --OS--> CAR/quasi-free boundary system (v155 quasi-free boundary, v160 Gaussianity from the Pfaffian, v240 GNS/OS, v175 net existence + full-cone RP). L2 [E] gap","claim_id":"SEAM.EQUIV.A01","dependencies_as_recorded":"SEAM.EQUIV.01; QFT.NETRP.01; GATE.HOLO.01; QGAMB.TIERB.01; QGAMB.ROUTEII.01","external_data_as_recorded":"Doplicher-Haag-Roberts / invertible-phase (SRE) boundary theory","id":"claim:SEAM.EQUIV.A01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":382,"scripts_as_recorded":"v287_free_rp_bulk_to_holomorphic_boundary.py","status_as_recorded":"Dependency checker [E] (4/5 discharged) + [O] (the one external theorem)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] character orthogonality + the full-L^2 Z4 block-diagonality (lifts v201/v284 to the full operator) + the negative control + Lean consistency; [O] the one sharper residual (raw sub-principal mark-locality). Real progress on Route B; does NOT close the premise.","checked_by_registry":false,"claim_excerpt":"ROUTE B (DtN) FULL-L^2 SUB-PRINCIPAL Z4 BLOCK-DIAGONALITY (2026-06-18): proves (numerically, on the full Toeplitz operator) the advisor's 'probably provable' step, lifting v201/v284 from the finite H^1 block to the full L^2 operator. Setup: the seam DtN Lambda = |D_theta| + M_f with <n|M_f|n'> = f_{n-n'} (boundary curvature f), rho = diag(i^n). [E] CHARACTER ORTHOGONALITY: a mark-sourced curvature f(theta)=sum_{j<4} ","claim_id":"SEAM.EQUIV.B01","dependencies_as_recorded":"SEAM.EQUIV.01; QGEO.SUBPRIN.01; QGEO.ROUTEI.01; FORM.QGEO.04; QGEO.MODULAR.01","external_data_as_recorded":"-","id":"claim:SEAM.EQUIV.B01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":383,"scripts_as_recorded":"v288_full_l2_subprincipal_z4.py","status_as_recorded":"Reduction [E] (full-L^2 lift, lifts v201/v284) + [O] (mark-locality residual)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the chain typing + L3 (orbit) + L4 (Fourier support) + L5 (full operator); [C] L1 (conic parametrix, literature); [O] L2 (Flat-Away), the single open analytic lemma. A finer decomposition of the v288 residual, NOT a closure.","checked_by_registry":false,"claim_excerpt":"RAW MARK-LOCALITY DECOMPOSITION (2026-06-18): decompose the ONE remaining Route-B residual after v288 ('why is the raw seam sub-principal term mark-local?') into an explicit 5-lemma chain, discharge the four standard/established lemmas and isolate the single open analytic lemma (Flat-Away). The best closing lever for Route B; does NOT close mark-locality. CHAIN (raw RP seam => mark-local sub-principal term): L1 [C] C","claim_id":"MARKLOCAL.RAW.01","dependencies_as_recorded":"SEAM.EQUIV.B01; SEAM.EQUIV.01; QGEO.ENERGY.03; QGEO.SUBPRIN.01; FORM.QGEO.04","external_data_as_recorded":"conic parametrix / b-calculus (Melrose)","id":"claim:MARKLOCAL.RAW.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":384,"scripts_as_recorded":"v289_marklocal_raw.py","status_as_recorded":"Decomposition [E] (chain + L3/L4/L5) + [C] (L1 literature) + [O] (L2 Flat-Away)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the adversary construction + the commutator pass + the spectrum/heat shift (the discriminators); [O] the consequence that Flat-Away must use spectral input. An honest red-team test; it does NOT manufacture a pass and sharpens (not closes) the open lemma.","checked_by_registry":false,"claim_excerpt":"ROUTE-B RED-TEAM: Z4 BLOCK-DIAGONALITY != MARK-LOCALITY (2026-06-18). Constructs the strongest adversary against Route B -- a SMOOTH Z4-symmetric off-mark curvature f(theta)=eps*cos(4 theta) -- and shows HONESTLY (no manufactured pass): [E] the adversary is Z4-symmetric (Fourier support only on {+-4} subset 4Z) but NOT mark-local (f(pi/4)=-eps != 0), a smooth off-mark curvature rather than a sum of mu4-orbit sources;","claim_id":"SEAM.ADVERSARY.01","dependencies_as_recorded":"SEAM.EQUIV.B01; MARKLOCAL.RAW.01; FLATAWAY.RP.01; QGEO.SUBPRIN.01","external_data_as_recorded":"-","id":"claim:SEAM.ADVERSARY.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":385,"scripts_as_recorded":"v290_z4_smooth_curvature_adversary.py","status_as_recorded":"Red-team [E] (adversary passes commutator, shifts spectrum/heat) + [O] (consequence)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[O] the lemma + the verdict (three open handles); [E] the spectral-rigidity + heat-kernel uniqueness demonstrations (flat is the unique match in the smooth Z4 family); [C] the RP-energy/Troyanov route. A contract turning Flat-Away into a precise, attackable mini-theorem; does NOT prove it.","checked_by_registry":false,"claim_excerpt":"THE FLAT-AWAY LEMMA AS A NAMED MINI-THEOREM (2026-06-18). States the one open link of v289 precisely and types its three proof routes (opened by the v290 red-team). LEMMA: given RawRPSeam with the mass gap, chirality and the four mu4 branch marks, the SMOOTH curvature density in the DtN sub-principal symbol VANISHES away from the branch divisor (the seam is flat away from the four marks). It is the bottleneck because","claim_id":"FLATAWAY.RP.01","dependencies_as_recorded":"SEAM.ADVERSARY.01; MARKLOCAL.RAW.01; SEAM.EQUIV.B01; SEAM.EQUIV.01; QGEO.ROUTEI.01","external_data_as_recorded":"Troyanov (prescribed-curvature uniqueness)","id":"claim:FLATAWAY.RP.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":386,"scripts_as_recorded":"v291_flataway_contract.py","status_as_recorded":"Contract [O] (lemma + verdict) + [E] (spectral/heat uniqueness) + [C] (Troyanov route)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the quadratic, positive-definite structure of the heat-trace deviation over the full smooth-Z4 space + the L^2 identification; [O] the one external fact (the seam fixes a_2). A genuine reduction of Flat-Away to one spectral invariant; NOT a proof.","checked_by_registry":false,"claim_excerpt":"HEAT-KERNEL ROUTE FOR FLAT-AWAY (2026-06-18): reduces the open Flat-Away lemma to ONE named spectral invariant by showing the heat-trace deviation is a positive-definite quadratic form in the off-mark curvature. Setup Lambda=|D_theta|+M_f, f=sum_k g_{4k} cos(4k theta). [E] QUADRATIC LEADING ORDER: Delta Tr(e^{-t Lambda}) = c(t) eps^2 + O(eps^4) (Delta Tr/eps^2 constant ~0.208 at t=0.5), no first-order term (average c","claim_id":"FLATAWAY.HEAT.01","dependencies_as_recorded":"FLATAWAY.RP.01; SEAM.ADVERSARY.01; SEAM.EQUIV.B01; MARKLOCAL.RAW.01","external_data_as_recorded":"-","id":"claim:FLATAWAY.HEAT.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":387,"scripts_as_recorded":"v292_flataway_heat_reduction.py","status_as_recorded":"Reduction [E] (positive-definite heat form) + [O] (one external invariant a_2)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the splitting mechanism + the quadratic form + the positive-definite Hessian over the full Z4 space + the clock-filter contrast; [O] the one external fact (pin the seam's Steklov spectrum). A strengthening of v291 to the full deformation space; NOT a proof.","checked_by_registry":false,"claim_excerpt":"SPECTRAL-RIGIDITY ROUTE FOR FLAT-AWAY (2026-06-18): upgrades the v291 one-direction scan to the FULL smooth-Z4 deformation space, showing the flat seam is a STRICT isolated minimum of the spectral-mismatch functional S(f)=sum_n (lambda_n(f)-lambda_n(0))^2. [E] SPLITTING MECHANISM: the flat Steklov spectrum |n| is doubly degenerate (+-n); a Z4 mode 4k connects n<->-n exactly at |n|=2k and splits that level at first or","claim_id":"FLATAWAY.SPEC.01","dependencies_as_recorded":"FLATAWAY.RP.01; FLATAWAY.HEAT.01; SEAM.ADVERSARY.01; SEAM.EQUIV.B01","external_data_as_recorded":"-","id":"claim:FLATAWAY.SPEC.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":388,"scripts_as_recorded":"v293_flataway_spectral_hessian.py","status_as_recorded":"Strengthening [E] (Hessian PD over full Z4 space) + [O] (pin the spectrum)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the Gauss-Bonnet divisor + the strictly-convex energy with its unique minimiser + no zero-cost direction; [C] Troyanov/Euclidean-cone uniqueness (literature); [O] the variational premise (RP+gap selects the minimiser). A third independent reduction of Flat-Away; NOT a proof.","checked_by_registry":false,"claim_excerpt":"RP-ENERGY / TROYANOV ROUTE FOR FLAT-AWAY (2026-06-18): the third independent reduction -- the flat pillowcase is the UNIQUE constant-curvature (energy-minimising) metric in the conformal class with the prescribed mark divisor. [E] PRESCRIBED DIVISOR + GAUSS-BONNET: the pillowcase = S^2 with 4 cone points of angle pi; the cone Gauss-Bonnet sum (2pi-theta_i)=4pi=2pi chi(S^2) holds for the flat (K=0 off marks) metric, t","claim_id":"FLATAWAY.ENERGY.01","dependencies_as_recorded":"FLATAWAY.RP.01; FLATAWAY.HEAT.01; FLATAWAY.SPEC.01; QGEO.ROUTEI.01","external_data_as_recorded":"Troyanov (prescribed-curvature uniqueness)","id":"claim:FLATAWAY.ENERGY.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":389,"scripts_as_recorded":"v294_flataway_rp_energy.py","status_as_recorded":"Reduction [E] (convex energy, unique minimiser) + [C] (Troyanov) + [O] (variational premise)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the vanishing first variation + the convexity positive-definiteness (all orders) + the exact divided-difference a_2 kernel (validated to 1e-7) + the degenerate-split closed form; [O] the one external fact (the seam fixes a_2). Upgrades v292 from numerical to analytic; NOT a closure of Flat-Away.","checked_by_registry":false,"claim_excerpt":"EXACT ANALYTIC a_2 COEFFICIENT FOR FLAT-AWAY (2026-06-18): upgrades the v292 positive-definiteness of the heat-trace deviation from a numerical scan to a proof, and derives the exact second-order coefficient in closed form. Setup Lambda(eps)=|D_theta|+eps M_f, f=sum_k g_k cos(4k theta) (zero-mean, support 4Z). [E] FIRST VARIATION VANISHES: d/d eps Tr e^{-t Lambda(eps)}|_0 = -t Tr(M_f e^{-t|D_theta|}) = -t f_hat(0) su","claim_id":"FLATAWAY.A2.01","dependencies_as_recorded":"FLATAWAY.HEAT.01; FLATAWAY.RP.01; FORM.FLATAWAY.01; SEAM.ADVERSARY.01","external_data_as_recorded":"Klein inequality / Peierls-Bogoliubov (trace convexity)","id":"claim:FLATAWAY.A2.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":390,"scripts_as_recorded":"v295_flataway_a2_exact.py","status_as_recorded":"Proof [E] (convexity positive-definiteness + exact kernel) + [O] (one external invariant)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] Lean-proven: positive-weighted sum of squares is positive-definite (heatDeviation_eq_zero_iff), the formal Delta=0 <=> flat core of the Flat-Away heat route. Built + axiom-clean. Does NOT close the open input (positivity of the weights is consumed from v295).","checked_by_registry":false,"claim_excerpt":"LEAN: FLAT-AWAY HEAT POSITIVE-DEFINITENESS (2026-06-18). Lean 4 formalisation (TfptCarrier/SeamDeckClosure.lean Part 5) of the algebraic core of the v292/v295 heat route: the heat-trace deviation as a quadratic form heatDeviation s W g = sum_{k in s} W k * (g k)^2 in the smooth Z4 curvature modes. THEOREMS: heatDeviation_nonneg (non-negative for non-negative weights) and heatDeviation_eq_zero_iff (with STRICTLY POSIT","claim_id":"FORM.FLATAWAY.01","dependencies_as_recorded":"FLATAWAY.A2.01; FLATAWAY.HEAT.01; FORM.QGEO.04","external_data_as_recorded":"Lean 4 + Mathlib (AxiomCheck: propext/Classical.choice/Quot.sound)","id":"claim:FORM.FLATAWAY.01","location_as_recorded":"lean4-carrier-rigidity/TfptCarrier/SeamDeckClosure.lean","path":"verification/status_ledger.csv","row_number":391,"scripts_as_recorded":"v295_flataway_a2_exact.py","status_as_recorded":"Formal","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the closed-form evaluation of the exact a_2 coefficient (geometric tail + finite middle) + manifest positivity + the small-t law with the t^2 cancellation; reproduces v295 to machine precision. An exact analytic upgrade; does NOT close Flat-Away.","checked_by_registry":false,"claim_excerpt":"EXACT a_2 COEFFICIENT IN CLOSED FORM (2026-06-18): evaluates the v295 infinite mode sum analytically. W_k(t)=(1/2) sum_{n in Z} Phi(|n|,|n+4k|) with the divided-difference kernel of e^{-tx}. [E] TAILS TELESCOPE: for n>=0, Phi(n,n+4k)=e^{-nt} C_k/(16k^2) with FIXED C_k=4kt+e^{-4kt}-1 (geometric in n); likewise n<=-4k with D_k=e^{4kt}-4kt-1; using C_k + D_k e^{-4kt}=4kt(1-e^{-4kt}) the two tails close to W_k^tail=t(1-e","claim_id":"FLATAWAY.A2.CLOSED.01","dependencies_as_recorded":"FLATAWAY.A2.01; FLATAWAY.HEAT.01; FORM.FLATAWAY.01","external_data_as_recorded":"-","id":"claim:FLATAWAY.A2.CLOSED.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":392,"scripts_as_recorded":"v296_flataway_a2_closed.py","status_as_recorded":"Closed form [E] (geometric tail + finite middle)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the flat fingerprint + exact degenerate split + the hard degeneracy obstruction (soft->discrete sharpening of v291/v293) + the two-metric isolation; [C] the (E8)_1 derivation of the pin (conditional on Route A) via 2d Steklov rigidity; [O] the verdict. Strictly sharpens Flat-Away and closes the pin onto one established input; does NOT make SEAM.EQUIV.01 unconditional.","checked_by_registry":false,"claim_excerpt":"THE FLAT-AWAY ATTACK -- HARDEN + DERIVE (2026-06-19): two moves on the single external fact the v291/v293/v295 routes left open ('pin the seam's Steklov spectrum / fix the a_2 heat coefficient to the flat value'). (I) HARDEN: v291/v293 show the flat seam is a SOFT minimum (spectral mismatch 'grows with eps'); here the obstruction becomes a DISCRETE on/off invariant. [E] FLAT FINGERPRINT: spec(|D_theta|) is the intege","claim_id":"FLATAWAY.RIGID.01","dependencies_as_recorded":"FLATAWAY.SPEC.01; FLATAWAY.A2.01; FORM.FLATAWAY.01; SEAM.EQUIV.A.LIT.01","external_data_as_recorded":"-","id":"claim:FLATAWAY.RIGID.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":393,"scripts_as_recorded":"v300_flataway_rigid.py","status_as_recorded":"Spectral rigidity [E] + (E8)_1 pin [C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the carrier/c=8/embedding/det invariants; [C] the free-fermion invertibility import (Kitaev); [O] the reduced residual (gapped + quasi-free). Discharges the TOPOLOGICAL-ORDER part of Route A's last hypothesis, reducing it to a spectral input; does NOT manufacture the gap, does NOT close SEAM.EQUIV.01.","checked_by_registry":false,"claim_excerpt":"DISCHARGE ROUTE A'S 'INVERTIBLE BULK' VIA THE FREE-FERMION CLASSIFICATION (2026-06-19): the single open hypothesis of Route A (v297 LIT-A, 'the raw quasi-free seam bulk is invertible/SRE'); since v300 collapsed Route B into Route A's rationality, this is the LAST unconditional gap of SEAM.EQUIV.01. THE MOVE: a GAPPED free-fermion (Gaussian/quasi-free) 2+1D bulk cannot carry intrinsic topological order -- free fermion","claim_id":"SEAM.EQUIV.A.INV.01","dependencies_as_recorded":"SEAM.EQUIV.A.LIT.01; FLATAWAY.RIGID.01; QGAMB.TIERB.01; SEAM.EQUIV.01","external_data_as_recorded":"Kitaev periodic table (free-fermion class D); SO(16)_1 conformal embedding","id":"claim:SEAM.EQUIV.A.INV.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":394,"scripts_as_recorded":"v301_route_a_invertible.py","status_as_recorded":"Free-fermion invertibility [E/C] (topological-order discharge)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the frozen transfer spectrum + the derived Recovery gap 6 ln(3/2) + the positivity margin; [C] the OS/quasi-free 'transfer gap = mass gap' identification; [O] the verdict. Identifies the last input with an established carrier-forced quantity; reduces SEAM.EQUIV.01 to a composition of cited theorems over established TFPT facts; does NOT claim SEAM.EQUIV.01 is machine-proved.","checked_by_registry":false,"claim_excerpt":"THE LAST LEVER -- THE SEAM GAP IS THE DERIVED RECOVERY GAP (2026-06-19): after v300 (Route B = Route A's rationality) and v301 (Route A's invertibility discharged), the WHOLE open content of SEAM.EQUIV.01 was the single spectral statement 'the quasi-free seam bulk is gapped'. This shows that gap is NOT a free input but the already-established RECOVERY GAP of the seam transfer operator, derived from the carrier {c3,g_","claim_id":"SEAM.EQUIV.GAP.01","dependencies_as_recorded":"SEAM.EQUIV.A.INV.01; GATE.UWALL.07; SYNTH.INVENTORY.02; SEAM.EQUIV.01","external_data_as_recorded":"Osterwalder-Schrader reconstruction; quasi-free exponential clustering","id":"claim:SEAM.EQUIV.GAP.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":395,"scripts_as_recorded":"v302_seam_gap.py","status_as_recorded":"Derived spectral gap [E] + OS/clustering [C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the F_pole seam-rate identity (Koide multiplier = (2/3)^6 = seam eigenvalue); [C] the Boltzmann/relic relaxations (shared shape, external rate); [I] the QCD RG UV-attractor (carrier coefficient b3=-7); [O] the unifying verdict. Demonstrates the SHARED discrete->dynamic shape across F_transfer; does NOT reduce the three external rates to the seam, does NOT upgrade any frontier number to [E].","checked_by_registry":false,"claim_excerpt":"THE DISCRETE->DYNAMIC LENS ON F_transfer (2026-06-19): asks whether the main-branch mechanism -- a gapped, positivity-preserving relaxation to a UNIQUE attractor (the local-averaging update m<-(A+2I)/4 m -> the E8 marks, gap 6 log(3/2)) -- is also the shape of the four F_transfer instances, or an unrelated bolt-on. Answer: ALL FOUR share the SAME shape (a gapped contraction/flow to a unique attractor: Perron-Frobeniu","claim_id":"FR.DYNAMICS.01","dependencies_as_recorded":"CONTRACT.F.01; FR.KOIDE.04; SEAM.ATTRACTOR.01; SEAM.EQUIV.GAP.01","external_data_as_recorded":"Boltzmann H-theorem; cosmological misalignment; QCD 1-loop RG (standard physics)","id":"claim:FR.DYNAMICS.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":396,"scripts_as_recorded":"v303_ftransfer_dynamics.py","status_as_recorded":"Dynamical-systems unification [E/C] (one shape / one seam-rate)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the typed citable stack (LIT-A/B/C with statements + references) + the composition + the shared-hypothesis isolation + non-circularity; [O] the one open hypothesis (seam-bulk invertibility = Route B's Flat-Away). A documentation/typing module; it does NOT prove the hypothesis.","checked_by_registry":false,"claim_excerpt":"ROUTE A LITERATURE THEOREM STACK (2026-06-18): writes Route A's single import (v287 L3) as a precise, citable composition of three established theorems, isolating the one open hypothesis. [E] LIT-A: invertible/SRE gapped phase => trivial bulk topological order (no nontrivial anyons, trivial Drinfeld center). Refs: Kitaev, Ann. Phys. 321 (2006); Freed-Hopkins, Geom. Topol. 25 (2021). [E] LIT-B: the bulk modular catego","claim_id":"SEAM.EQUIV.A.LIT.01","dependencies_as_recorded":"SEAM.EQUIV.A01; SEAM.EQUIV.01; FLATAWAY.RP.01; SEAM.EQUIV.B01","external_data_as_recorded":"Kitaev; Freed-Hopkins; Mueger; Kawahigashi-Longo-Mueger; Conway-Sloane; Dong-Xu","id":"claim:SEAM.EQUIV.A.LIT.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":397,"scripts_as_recorded":"v297_route_a_literature_stack.py","status_as_recorded":"Theorem stack [E] (citable composition) + [O] (one shared hypothesis)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the E8 marks as the unique attractor of a minimal graph update (on v219's McKay hull), the spherical tower terminus, the cascade coarse-graining; [C] the Wolfram computational-substrate reading; [O] the deep rewrite-to-full-structure question + honest negatives (phi0 is the analytic seed not an edge fraction). An honest audit of the hypergraph connection; NOT a derivation of TFPT from a rewrite system.","checked_by_registry":false,"claim_excerpt":"E8 AS A NETWORK ATTRACTOR / WOLFRAM-PROGRAM READING (2026-06-18): an HONEST experimental audit of whether TFPT's structure is naturally a hypergraph/rewrite system, built on the McKay bedrock v219. It does NOT force TFPT into a hypergraph nor fabricate a rewrite. [E] E8 MARKS ARE A GRAPH ATTRACTOR: on the affine-E8 / McKay-(2,3,5) 9-node graph (adjacency A, chain n1..n8 + n9 on n6) the minimal lazy local-averaging up","claim_id":"E8.NETWORK.01","dependencies_as_recorded":"MCKAY.E8.01; COX.TOTATIVE.01; CASCADE.BRIDGE.01","external_data_as_recorded":"-","id":"claim:E8.NETWORK.01","location_as_recorded":"introduction","path":"verification/status_ledger.csv","row_number":398,"scripts_as_recorded":"v298_e8_network_attractor.py","status_as_recorded":"Reading [E] (marks attractor + tower + cascade) + [C] (Wolfram substrate) + [O] (rewrite-to-full-structure)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the hypergraph facts (icosahedron 3-uniform, |Aut|=120; equivariant subdivision; 2I fusion tensor with E8 slice), the spectral selection (Smith rho<=2 -> ADE; Collatz-Wielandt locality), and the two negative controls (A_n, D_n never reach E8); [E*] the autonomous local rule (self-generated witness + local gate) running E6->E7->E8->Ê8, exact under the (2,3,*) seed and growth policy; [O] the seed itself = P2 (NOT 'P2 derived'). A second network-theoretic reading of the (2,3,5)/E8 core; does NOT close P2 and adds no physics.","checked_by_registry":false,"claim_excerpt":"HYPERGRAPH/WOLFRAM BRIDGE, HARDENED (2026-06-19): the 3-arm (2,3,r) branch type is the IRREDUCIBLE seed on which a LOCAL witness-based spectral growth dynamics REACHES E8 = T(2,3,5) as the LAST FINITE point: it runs E6 -> E7 -> E8 and stops at the affine boundary E8-hat (Ê8) -- E8 the maximal FINITE point, Ê8 the critical rho=2 edge. EXPLICITLY NOT 'P2 derived': the seed itself is the irreducible input (= P2). A seco","claim_id":"HYP.0D.01","dependencies_as_recorded":"MCKAY.E8.01; E8.NETWORK.01; QBL.GATE.01","external_data_as_recorded":"Smith 1970 (rho<=2 <=> affine ADE); Collatz-Wielandt; Kawahigashi-Longo-Mueger (fusion)","id":"claim:HYP.0D.01","location_as_recorded":"introduction","path":"verification/status_ledger.csv","row_number":399,"scripts_as_recorded":"v299_hypergraph_0d_autonomous.py","status_as_recorded":"Bridge [E] (hypergraph facts, Smith, Collatz-Wielandt, controls) + [E*] (autonomous rule under seed+policy) + [O] (the seed = P2)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the truncation-artefact algebra (Stelle ghost from the local R+R^2 propagator; entire form factor has no extra pole; polynomial truncation re-introduces the ghost); [C] the KMS-cutoff link (v259) and the conditional ghost-freedom under entire analyticity; [O] the entire-analyticity assumption of the resummation + the nonperturbative gap. A conditional perturbative narrowing of rt_F, consistent with the SEAM.EQUIV.01 firewall; QG.AMB.01 stays [O].","checked_by_registry":false,"claim_excerpt":"INFINITE-DERIVATIVE / NONLOCAL READING OF THE GRAVITY SECTOR (2026-06-19): a CONDITIONAL narrowing of the red-team rt_F / v278 Stelle-ghost attack -- NOT a closure of QG.AMB.01 and NO new parameter (the cutoff is the v259 seam KMS weight). [E] STELLE GHOST = TRUNCATION ARTEFACT: the local R+R^2/Weyl^2 four-derivative propagator 1/(p^2(p^2+M^2)) = (1/M^2)[1/p^2 - 1/(p^2+M^2)] partial-fractions to a healthy massless gr","claim_id":"QGAMB.IDG.01","dependencies_as_recorded":"QG.AMB.01; v259; v278; rt_F","external_data_as_recorded":"Tomboulis 1997; Biswas-Mazumdar-Siegel 2006; Biswas-Gerwick-Koivisto-Mazumdar 2012","id":"claim:QGAMB.IDG.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":400,"scripts_as_recorded":"v304_idg_nonlocal_ghost.py","status_as_recorded":"Open (conditional narrowing of the perturbative Stelle-ghost attack; NOT a QG.AMB.01 closure)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[I]/[N] the generator-economy images + the 6.5x compression ratio + the witness-multiplicity bookkeeping + the shared-seed correlation map + the foreign-integer negative control. Makes the compression and correlation explicit; does NOT add physics and does NOT upgrade any status.","checked_by_registry":false,"claim_excerpt":"WITNESS-INDEPENDENCE / GENERATOR-ECONOMY AUDIT (2026-06-21): the STRUCTURAL anti-numerology firewall complementing the v100 phenomenological null test. [E] GENERATOR ECONOMY: 13 headline integers (|mu4|=4, g_car=5, |Z2|=2, N_fam=3, dim S+=16, rank E8=8, |R(E8)|=240, dim E8=248, |2I|=120, h(E8)=30, |W(D5)|=1920, Omega_adm=48, gap exponent 6) are all documented images of the single anchor a=(1,1,2) (e=(4,5,2), p_n=2+2^","claim_id":"WITNESS.ECON.01","dependencies_as_recorded":"ANCHOR.GEN.01; REG.FREEZE.01; DATA.SCORECARD.01","external_data_as_recorded":"-","id":"claim:WITNESS.ECON.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":401,"scripts_as_recorded":"v305_witness_independence.py","status_as_recorded":"Identity/Numerical [I]/[N] (structural firewall)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[N] the per-observable back-solve + error-weighted mean = axiom seed (0.04%) + the precise-cluster spread + the leave-one-out out-of-sample residuals + the shuffle power control. A cross-validation statistic; does NOT upgrade any prediction's status.","checked_by_registry":false,"claim_excerpt":"LEAVE-ONE-OUT SEED CROSS-VALIDATION (2026-06-21): turns the 'many observables, one seed phi0' liability into a falsifiable out-of-sample test [N] (Python-only, external data). [N] back-solving phi0 independently from the 5 seed-grammar observables (sin^2 theta12, sin^2 theta13, beta, Omega_b, lambda_C; NuFIT 6.0 / ACT DR6 / Planck / PDG centrals) and error-weighted-averaging reproduces the AXIOM seed phi0=1/(6pi)+48 ","claim_id":"SEED.CROSSVAL.01","dependencies_as_recorded":"ANCHOR.GEN.01; REG.FREEZE.01; DATA.SCORECARD.01","external_data_as_recorded":"NuFIT 6.0; ACT DR6; Planck 2018; PDG 2024","id":"claim:SEED.CROSSVAL.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":402,"scripts_as_recorded":"v306_seed_crossval.py","status_as_recorded":"Numerical [N] (out-of-sample cross-validation)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[N] the cross-sector beta<->lambda_C back-solve to the same seed (0.01 sigma) + the 3-observable one-parameter chi^2/dof<1 + the declared theta13 exclusion + the shuffle power control. A consistency statistic; does NOT upgrade any prediction or close any gate.","checked_by_registry":false,"claim_excerpt":"CROSS-SECTOR ONE-PARAMETER SEED TEST (2026-07-01, v465): the theta13-independent, externally-runnable SUBSET of SEED.CROSSVAL.01/v306 -- the sharpest shared-origin signature is a correlation no non-shared-origin model predicts: a CMB EB/TB birefringence angle beta and a quark Cabibbo angle lambda_C=|Vus| (unrelated in the SM) are two readouts of the ONE axiom seed phi0=1/(6pi)+48 c3^4. [E] plumbing: axiom phi0 reprod","claim_id":"SEED.CROSSSECTOR.01","dependencies_as_recorded":"SEED.CROSSVAL.01; ANCHOR.GEN.01; REG.FREEZE.01","external_data_as_recorded":"NuFIT 6.0; ACT DR6; Planck PR4; PDG 2024","id":"claim:SEED.CROSSSECTOR.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":403,"scripts_as_recorded":"v465_seed_crosssector_joint.py","status_as_recorded":"Numerical [N] (cross-sector consistency statistic)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[N] the charged-lepton m_e/m_mu back-solve to the axiom seed (-0.11%) + the 6/7-channel chi^2/dof<1 five-sector cluster + the shuffle power control; [C] the source->pole transport band and the one-seed honesty. A consistency statistic; does NOT upgrade any prediction or close any gate.","checked_by_registry":false,"claim_excerpt":"SIXTH SEED CHANNEL, NEW MEASUREMENT SECTOR (2026-07-01, v466): the charged-lepton mass ratio m_e/m_mu=(12/7)phi0^2 is a sixth independent readout of the ONE axiom seed phi0=1/(6pi)+48 c3^4, extending the empirical over-determination (SEED.CROSSVAL.01/v306, SEED.CROSSSECTOR.01/v465) from three measurement sectors to five. [E] plumbing: axiom phi0 reproduces the frozen m_e/m_mu=(12/7)phi0^2=0.00484673 to 1e-9. [N] NEW ","claim_id":"SEED.LEPTONMASS.01","dependencies_as_recorded":"SEED.CROSSVAL.01; SEED.CROSSSECTOR.01; REG.FREEZE.01; CORRECTIONS.NUMERIC.01","external_data_as_recorded":"PDG 2024 (charged-lepton + heavy-quark masses); FLAG (m_c/m_s)","id":"claim:SEED.LEPTONMASS.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":404,"scripts_as_recorded":"v466_seed_leptonmass_channel.py","status_as_recorded":"Numerical [N]/[C] (new-sector seed consistency statistic; source->pole transport-conditional)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[N] the registry-wide classification + theory-alive (no KILL) + the watch/pressure-point identification (sin^2 theta13 ~2 sigma) + the JUNO kill test + the r/n_s/w fronts. An operational decision layer over REG.FREEZE.01; does NOT change any prediction's status.","checked_by_registry":false,"claim_excerpt":"DATA WATCHDOG / DECISION PIPELINE (2026-06-21): the operational decision layer over the frozen registry (REG.FREEZE.01/v84) [N] (Python-only, external data). [N] reads predictions_frozen.json and classifies all 21 entries (16 predictions + 2 assigned textures + 2 conditional bands + 1 F_transfer bridge: rare kaon) PASS/WATCH/TENSION/KILL by live n_sigma vs repo-documented current bests (CODATA 2022, NuFIT 6.0, ACT DR","claim_id":"DATA.WATCHDOG.01","dependencies_as_recorded":"REG.FREEZE.01; DATA.SCORECARD.01","external_data_as_recorded":"CODATA 2022; NuFIT 6.0; ACT DR6; Planck 2018; PDG 2024; BK18","id":"claim:DATA.WATCHDOG.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":405,"scripts_as_recorded":"v307_data_watchdog.py","status_as_recorded":"Numerical/data [N] (decision pipeline)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the exact Cartan-det discriminators + the well-typed four-link composition + the derived-gap input; [O] the cited OS step + the end-to-end machine proof (Lean target). Pins the keystone's open content to one named step; NOT a closure of SEAM.EQUIV.01.","checked_by_registry":false,"claim_excerpt":"SEAM.EQUIV.01 COMPOSITION CERTIFICATE (2026-06-21, TOE attack point 1): assembles the v297 literature stack into ONE well-typed logical chain gap>0 -> invertible/SRE (Kitaev) -> holomorphic c=8 (Mueger/KLM) -> (E8)_1 (Conway-Sloane), out(i)=in(i+1). [E] arithmetic discriminators exact (sympy): |det Cartan(E8)|=1 (one anyon/primary/invertible/holomorphic) vs |det Cartan(D8=SO(16))|=4 (the same-c rival, NON-holomorphic","claim_id":"SEAM.EQUIV.CHAIN.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.EQUIV.GAP.01; v297; v301; v302","external_data_as_recorded":"-","id":"claim:SEAM.EQUIV.CHAIN.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":406,"scripts_as_recorded":"v308_seam_equiv_chain.py","status_as_recorded":"Reduction/certificate [E]/[O] (composition)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the non-circular marks+clock assembly + the explicit modular-Hamiltonian round-trip + [rho,K]=0 state invariance + the Z2 negative control; [O] the Bisognano-Wichmann intrinsicality of the raw collar. The sharpest single open theorem made explicit; NOT a closure.","checked_by_registry":false,"claim_excerpt":"BEDROCK omega o rho = omega VIA AN EXPLICIT MODULAR HAMILTONIAN (2026-06-21, TOE attack point 2): the next concrete step on the open bedrock QGEO.SYM.01. [E] NON-CIRCULAR upstream: marks=2 chi(S^2)=4 (Gauss-Bonnet, v216) and the order-4 clock z->iz from cross-ratio 2 / j=1728 (v214/v267), so mu4 is DERIVED, not assumed (rho^4=I). [E] for the thermal quasi-free covariance C=1/(1+e^{H1}) the one-particle modular Hamilt","claim_id":"QGEO.MODHAM.01","dependencies_as_recorded":"QGEO.SYM.01; v198; v210; v214; v216","external_data_as_recorded":"-","id":"claim:QGEO.MODHAM.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":407,"scripts_as_recorded":"v309_modular_bedrock.py","status_as_recorded":"Reduction [E]/[O] (modular bedrock)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the 16=1+10+5 decomposition + the four exact anomaly cancellations + the one-loop (b1,b2,b3)=(41/10,-19/6,-7) + the N_fam=3 RG-pinning negative controls; [C]/[O] the full EG interacting S-matrix + Yukawa. A genuine closure of the carrier->anomaly-free-SM+RG sub-question; does NOT close the interacting theory.","checked_by_registry":false,"claim_excerpt":"THE CARRIER HALF-SPINOR IS ONE ANOMALY-FREE SM GENERATION + THE SM RG (2026-06-21, TOE attack point 3): connects the discrete compiler to constructive 4D QFT, closing the spectrum+anomaly+beta sub-question exactly. [E] 16=Lambda^even(C^5)=1+10+5; SU(5) c SO(10): 10+5bar+1 = one SM generation (Q,u^c,d^c,L,e^c,nu^c), 16 Weyl states. [E] ANOMALY-FREE: sum Y=0, sum Y^3=0, [SU2]^2U1=0, [SU3]^2U1=0 (exact Fraction arithmet","claim_id":"CAR.SM.ANOM.01","dependencies_as_recorded":"CAR.SM.01; QFT4D.SPERT.03; v273; v159","external_data_as_recorded":"standard GUT representation theory","id":"claim:CAR.SM.ANOM.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":408,"scripts_as_recorded":"v310_carrier_sm_anomaly.py","status_as_recorded":"Identity [E] (spectrum+anomaly+RG) + [C]/[O] (S-matrix)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the geometric clustering at rate (2/3)^6 + finite correlation length/susceptibility + the v76 decoupling margin + the ungapped negative control; [C] the spectral-action low-energy dictionary; [O] the full ambient measure (gap-decoupled, inert). Shows the physical sector is a convergent object; does NOT construct QG.AMB.01.","checked_by_registry":false,"claim_excerpt":"THE PHYSICAL QG MEASURE AS A GAP-DECOUPLED, CLUSTERING OBJECT (2026-06-21, TOE attack point 4): the honest statement in place of an over-claimed 4D measure for QG.AMB.01/G_metric. [E] the seam transfer spectrum {1,(2/3)^6,(1/3)^6} gives geometric clustering of the connected correlator at rate (2/3)^6, correlation length xi=1/Delta=1/(6 ln(3/2)). [E] finite susceptibility sum (2/3)^{6n}=1/(1-(2/3)^6)=729/665<inf => a ","claim_id":"QGAMB.CLUSTER.01","dependencies_as_recorded":"QG.AMB.01; GATE.METRIC.01; QG.GAPDEC.01; v36; v76; v259","external_data_as_recorded":"Osterwalder-Schrader / Chamseddine-Connes","id":"claim:QGAMB.CLUSTER.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":409,"scripts_as_recorded":"v311_gap_decoupled_measure.py","status_as_recorded":"Reduction [E]/[C]/[O] (gap-decoupled measure)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the marks-as-Perron + the golden-ratio subleading eigenvalue + the two honest negatives (recovery rate not graph-spectral; seed not an edge fraction); [O] the rewrite-to-full-structure question (now delimited to two injectables). Sharpens v298/v299; does NOT derive P1/P2 from a rewrite.","checked_by_registry":false,"claim_excerpt":"THE HYPERGRAPH SUBSTRATE SHARPENED -- WHAT A REWRITE MUST INJECT (2026-06-21, TOE attack point 5): turns the open rewrite-to-full-structure question into a precise list. [E] the affine-E8 Kac marks (1,2,3,4,5,6,4,2,3) are the Perron eigenvector (A.marks=2 marks, top eigenvalue 2) -- the Coxeter skeleton is graph-spectral (v298/v299). [E] the subleading eigenvalue is exactly 2cos(pi/5)=golden ratio phi (the icosahedra","claim_id":"HYP.INJECT.01","dependencies_as_recorded":"E8.NETWORK.01; HYP.0D.01; v219; v298; v299","external_data_as_recorded":"-","id":"claim:HYP.INJECT.01","location_as_recorded":"introduction","path":"verification/status_ledger.csv","row_number":410,"scripts_as_recorded":"v312_hypergraph_substrate.py","status_as_recorded":"Reduction [E]/[O] (substrate sharpening)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the exact golden-min-poly factorisation + the (2,3,5)=2cos(pi/k) spectral-angle identification + the new g_car spectral witness + the 31/30 icosahedral-selection identity (with the honest anti-numerology framing) + the phi-not-a-readout null; [C] the E8-quasicrystal substrate direction. A new structural reading; does NOT add a physical readout and does NOT close the substrate question.","checked_by_registry":false,"claim_excerpt":"THE GOLDEN RATIO IS THE g_car=5 SIGNATURE -- THE (2,3,5) ATOMS ARE THE NETWORK SPECTRAL ANGLES (2026-06-21, v312 follow-up made exact). [E] EXACT: the affine-E8 adjacency charpoly factors x(x^2-4)(x^2-1)(x^2-x-1)(x^2+x-1); the golden minimal polynomial x^2-x-1 divides it, so phi=2cos(pi/5)=(1+sqrt5)/2 is an EXACT algebraic eigenvalue (not a numerical near-value). [E] ATOMS = SPECTRAL ANGLES: the non-trivial eigenvalu","claim_id":"GOLD.ATOMS.01","dependencies_as_recorded":"MCKAY.E8.01; HYP.INJECT.01; v219; v312; v63","external_data_as_recorded":"-","id":"claim:GOLD.ATOMS.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":411,"scripts_as_recorded":"v313_golden_atoms_spectral.py","status_as_recorded":"Identity/Lattice [E] (spectral) + [C] (quasicrystal direction)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the CRT direct-product factorisation + the exponent/totative factorisation + the Q(zeta30) compositum + the Galois=mu4 x Z2 identification (seam clock = carrier-field Galois) + the Gauss-sum carrier generator; [C] the couple-vs-factorize verdict. Answers the v314 coupling question exactly (Galois compositum, not a dynamical map); does NOT add a physical readout.","checked_by_registry":false,"claim_excerpt":"COUPLE OR FACTORIZE? THE ORDER-30 COXETER SECTORS COUPLE AS A CYCLOTOMIC FIELD (2026-06-21, v314 follow-up). The v314 question -- does 30=g_car*(2 N_fam)=5*6 couple the carrier (5-fold, golden, Q(sqrt5)) and family (6=2*3, rational) sectors, or just factorize? [E] GROUP FACTORIZES: gcd(5,6)=1 => Z/30 = Z/5 x Z/6 (CRT, direct product); order-5 subgroup <c^6>, order-6 <c^5> -- group-level decoupled (consistent with the","claim_id":"COX.COUPLE.01","dependencies_as_recorded":"RATE.TRANSLATE.01; COX.TOTATIVE.01; v314; v223; v55","external_data_as_recorded":"-","id":"claim:COX.COUPLE.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":412,"scripts_as_recorded":"v315_coxeter_coupling.py","status_as_recorded":"Identity/Lattice [E] (cyclotomic Galois) + [C] (verdict)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the family-factor placement of the CP unit zeta_6=zeta_30^5 + the sheet flip + the Galois-Z2 = CP-conjugation identification + the carrier-static fact + the magnitude/seed separation; [C] the identification with the physical delta_CKM/delta_PMNS (inherits v231/v233). Bridges the v315 Galois coupling to SM phenomenology (the phase sector); does NOT upgrade the CP-phase typing.","checked_by_registry":false,"claim_excerpt":"DOES THE GALOIS mu4 x Z2 (v315) ORGANIZE THE PHYSICAL READOUTS? YES -- THE CP PHASES (2026-06-21, v315 follow-up to phenomenology). [E] FAMILY FACTOR: the hexagonal CP unit rho=zeta_6=zeta_30^5 is the order-6=2 N_fam factor c^5 of v315 (5=30/6); the carrier is zeta_5=zeta_30^6 (order 5=g_car, c^6) -- the CP phase lives in the FAMILY factor, not the carrier. [C] CP PHASES (inherits v231/v233): delta_CKM,lead=pi/3=arg(","claim_id":"GALOIS.READOUT.01","dependencies_as_recorded":"COX.COUPLE.01; CP.TRIALITY.01; v315; v231; v233","external_data_as_recorded":"-","id":"claim:GALOIS.READOUT.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":413,"scripts_as_recorded":"v316_galois_readout.py","status_as_recorded":"Identity/Lattice [E] (cyclotomic CP) + [C] (physical identification)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the cusp-weights = cube-roots identification + the transitive mu3 orbit + the recovery-eigenvalue attachment + the Galois 1+2 refinement (fixed=attractor, pair=hierarchy) + the same-Z2-as-CP-conjugation + the counts; [C] the verdict. Shows the family STRUCTURE is the same arithmetic (mu3 orbit, Galois-refined) as the CP phase; does NOT derive the mass magnitudes (analytic seed).","checked_by_registry":false,"claim_excerpt":"ARE THE 3 GENERATIONS A mu3/GALOIS ORBIT? YES (mu3), REFINED 1+2 BY GALOIS (2026-06-21, v316 follow-up to the generation structure). [E] GENERATIONS = CUBE ROOTS: the 3 cusp weights {0,1/3,2/3} (Spec(Q+)=3a+1={1,2,3}=A3 exponents) map under w->e^{2 pi i w} to the 3rd roots of unity {1,zeta_3,zeta_3^2}. [E] mu3 ORBIT (transitive): the cyclic family symmetry w->w+1/3 mod 1 permutes them cyclically -- ONE transitive Z/3","claim_id":"GALOIS.FAMILY.01","dependencies_as_recorded":"GALOIS.READOUT.01; COX.COUPLE.01; v316; v315; v56","external_data_as_recorded":"-","id":"claim:GALOIS.FAMILY.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":414,"scripts_as_recorded":"v317_galois_family.py","status_as_recorded":"Identity/Lattice [E] (mu3+Galois orbit) + [C] (verdict)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the Q(zeta30)/Galois=mu4 x Z2 skeleton (degree=rank E8) + the anchor-rigidity + the phi0={a,pi} reduction (pure pi, anchor-derived coefficients) + the 0-dimensionless-free-parameter inventory ({a,pi,v_geo}); [O] the seam realisation. A synthesis/inventory capstone of the v313-v317 arc; does NOT close the open bedrock and does NOT add a physical readout.","checked_by_registry":false,"claim_excerpt":"THE CAPSTONE: THE SM STRUCTURAL SECTOR IS Q(zeta30) + GALOIS mu4 x Z2, COMPLETE INPUT {a, pi, v_geo} (2026-06-21, synthesis of the v313-v317 arc). [E] ARITHMETIC SKELETON: the SM STRUCTURAL sector (3 generations, 2 CP phases, the orbit/hierarchy ordering) lives in the cyclotomic field Q(zeta30): [Q(zeta30):Q]=phi(30)=8=rank E8, 30=|Z2|*N_fam*g_car=h(E8), Galois (Z/30)^x=mu4 x Z2 (order 8) -- carrier mu4=(Z/5)^x (gold","claim_id":"ARITH.CAPSTONE.01","dependencies_as_recorded":"GALOIS.FAMILY.01; GALOIS.READOUT.01; COX.COUPLE.01; ARCH.CORE.01; NOUNIT.01; v313; v314; v315; v316; v317","external_data_as_recorded":"-","id":"claim:ARITH.CAPSTONE.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":415,"scripts_as_recorded":"v318_arithmetic_capstone.py","status_as_recorded":"Synthesis/inventory [E] (arithmetic + {a;pi} reduction) + [O] (seam realisation)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the Q vs Q(sqrt5) field split of the discrete spectrum + the dynamic-in-Q fact + the (2,3)-sector translation + the 5-fold field obstruction (heat-kernel + eigenvalue negatives) + the order-30 shared clock + the quasicrystal counts; [C]/[O] the translation-functor verdict. Answers the discrete<->dynamic translation question exactly (a field split); does NOT close the substrate question.","checked_by_registry":false,"claim_excerpt":"DO THE DISCRETE-KERNEL AND DYNAMIC RATES TRANSLATE? AN EXACT NUMBER-FIELD SPLIT (2026-06-21, v312/v313 follow-up). [E] FIELD SPLIT: the affine-E8 adjacency spectrum is the rational part {0,+-1,+-2} in Q plus the golden part {+-phi,+-1/phi} in Q(sqrt5) (min poly x^2-x-1, discriminant 5); the dynamic transfer spectrum {1,(2/3)^6,(1/3)^6} is ENTIRELY rational (in Q). [E] TRANSLATION (the (2,3)-fold/family sector): the r","claim_id":"RATE.TRANSLATE.01","dependencies_as_recorded":"GOLD.ATOMS.01; SEAM.EQUIV.GAP.01; v313; v54; v56","external_data_as_recorded":"-","id":"claim:RATE.TRANSLATE.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":416,"scripts_as_recorded":"v314_rate_translation.py","status_as_recorded":"Identity/Lattice [E] (number-field split) + [C]/[O] (functor verdict)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the order-30 = 5x6 coprime-hand factorization + the dynamic-hand arithmetic (Z/6=2 N_fam, exponent 6, rate (2/3)^6, zeta_6=zeta_30^5) + the law-vs-live (0 vs 1) reading (rate(0)=0 the attractor, totatives start at 1) + the static-hand golden field-obstruction (Z/5=g_car, no rate) + the one-full-turn=30 Coxeter period; [C] the 'the bridge IS one clock' interpretation. A synthesis of the v313-v318 arc + v124/v55 into the clock picture; does NOT add a physical readout and does NOT close the open bedrock.","checked_by_registry":false,"claim_excerpt":"THE TRANSLATION CLOCK: THE DISCRETE<->DYNAMIC BRIDGE IS THE ORDER-30 COXETER ELEMENT, A CLOCK WITH TWO COPRIME HANDS 5 x 6 (2026-06-22, synthesis of the v313-v318 arc + v124/v55, answering 'is the static<->dynamic translation a clock running 0,1,2,3,4,5 or 1,2,3,4,5?'). [E] TRANSLATION IS A CLOCK: the only object holding both the static carrier (Q(sqrt5)) and the dynamic family (rational) data is the order-30 Coxeter","claim_id":"TRANSLATE.CLOCK.01","dependencies_as_recorded":"RATE.TRANSLATE.01; COX.COUPLE.01; ARITH.CAPSTONE.01; v314; v315; v124; v55","external_data_as_recorded":"-","id":"claim:TRANSLATE.CLOCK.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":417,"scripts_as_recorded":"v319_translation_clock.py","status_as_recorded":"Synthesis/Identity [E] (clock factorization + hand arithmetic) + [C] (one-clock reading)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the exact Galois relation delta_PMNS=delta_CKM,lead+pi (rho^4=-rho, both powers of zeta_6) + the non-triviality; [C] the leading-order prediction delta_PMNS,lead=240 deg; [N] current compatibility; [X] the pre-registered kill test (DUNE/Hyper-K/JUNO). A NEW falsifiable cross-prediction from the Galois arc; does NOT derive magnitudes and does NOT upgrade the CP-phase typing beyond the relation.","checked_by_registry":false,"claim_excerpt":"A NEW FALSIFIABLE PREDICTION FROM THE GALOIS STRUCTURE: THE TWO CP PHASES ARE LOCKED, delta_PMNS = delta_CKM,lead + pi (2026-06-22, the v316 follow-up turned testable). [E] ONE UNIT TWO POWERS: both CP phases are powers of one hexagonal unit rho=zeta_6 in the family Galois factor (v316): delta_CKM,lead=arg(rho)=pi/3 (60 deg), delta_PMNS=arg(rho^4)=4pi/3 (240 deg), rho^4=-rho. [E] FORCED RELATION: delta_PMNS-delta_CKM","claim_id":"GALOIS.CP.PREDICT.01","dependencies_as_recorded":"GALOIS.READOUT.01; ARITH.CAPSTONE.01; v316; v231; v233","external_data_as_recorded":"NuFIT 6.0 (PMNS delta_CP)","id":"claim:GALOIS.CP.PREDICT.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":418,"scripts_as_recorded":"v320_galois_cp_relation.py","status_as_recorded":"Identity [E] (Galois relation) + [C] (prediction) + [X] (kill test)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[N] the ranked forward board (each kill test locked to a freeze_file row) + the v320 CP-relation entry + the JUNO-rank-1 ordering + the power check. A forward decision ledger complementing v307; does NOT add a physical readout.","checked_by_registry":false,"claim_excerpt":"THE FORWARD KILL-TEST BOARD: THE DECISIVE UPCOMING MEASUREMENTS, RANKED (2026-06-22, forward companion to v307's current-data board). [N] assembles the decisive NEXT measurements, each LOCKED to a freeze_file.csv kill row (so the test and the frozen signal cannot drift apart): #1 JUNO sin^2 theta12=0.306747 (fastest, sub-percent), #2 CMB-S4/LiteBIRD r in [0.0033,0.0048] (kill robust r>0.01), #3 DESI/Euclid w=-1 (kill","claim_id":"KILL.BOARD.01","dependencies_as_recorded":"DATA.WATCHDOG.01; GALOIS.CP.PREDICT.01; REG.FREEZE.01","external_data_as_recorded":"JUNO; CMB-S4; LiteBIRD; DESI; Euclid; DUNE; Hyper-K; LEGEND; nEXO; PSI n2EDM","id":"claim:KILL.BOARD.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":419,"scripts_as_recorded":"v321_killtest_board.py","status_as_recorded":"Numerical/data [N] (forward decision ledger)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the discrete hexagonal node + the |mu4| multiplier + the discrimination geometry; [C] the sub-leading budget (the lepton holonomy term is only bounded by the quark analog, not closed); [N] the +1.08 sigma current tension; [X] the sharpened pre-registered kill test (node discrimination). Sharpens v320; does NOT derive magnitudes or upgrade the CP typing.","checked_by_registry":false,"claim_excerpt":"THE v320 CP-LOCK PREDICTION SHARPENED INTO A QUANTITATIVE PRE-REGISTERED KILL TEST (2026-06-22). [E] DISCRETE LADDER: the leading CP phase sits on the six hexagonal nodes arg(rho^k)=k*60 deg; delta_CKM,lead=60 (node 1), delta_PMNS,lead=240 (node 4). [E] MULTIPLIER = DECK ORDER: delta_PMNS,lead=|mu4|*delta_CKM,lead=4*(pi/3)=4pi/3=delta_CKM,lead+pi (rho^4=-rho) -- the node selector IS the seam clock order |mu4|=4. [C] ","claim_id":"GALOIS.CP.SHARPEN.01","dependencies_as_recorded":"GALOIS.CP.PREDICT.01; GALOIS.READOUT.01; v320; v316","external_data_as_recorded":"NuFIT 6.0 (PMNS delta_CP)","id":"claim:GALOIS.CP.SHARPEN.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":420,"scripts_as_recorded":"v322_cp_lock_sharpened.py","status_as_recorded":"Identity [E] (node+multiplier) + [C] (budget) + [N] (tension) + [X] (kill test)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the finite-model BW construction (rotation-covariant C => geometric modular flow + a free clock symmetry) + the v309 discriminator (period-4 preserves the clock but is not geometric); [C] the linkage to v308 via the cited BW/Hislop-Longo theorem (QGEO.SYM.01 downstream of SEAM.EQUIV.01); [O] rotation-invariance of the raw seam. Sharpens v309; does NOT close the bedrock.","checked_by_registry":false,"claim_excerpt":"THE KEYSTONE PUSHED ONE STEP -- BISOGNANO-WICHMANN MAKES THE SEAM MODULAR FLOW GEOMETRIC (2026-06-22): the mu4 deck invariance is NOT an independent axiom. [E] CLOCK = GEOMETRIC ROTATION: rho=diag(i^n)=exp(i(pi/2)L), L=diag(n) the seam rotation generator; rho^4=exp(i2pi L)=I -- mu4 in U(1)_rot (quarter turns). [E] BW: a rotation-covariant covariance C=f(L) gives K=log((1-C)/C)=g(L), so [K,L]=0 (the modular flow commu","claim_id":"QGEO.BW.01","dependencies_as_recorded":"QGEO.SYM.01; QGEO.MODHAM.01; SEAM.EQUIV.CHAIN.01; v308; v309; v198","external_data_as_recorded":"Bisognano-Wichmann / Hislop-Longo (cited)","id":"claim:QGEO.BW.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":421,"scripts_as_recorded":"v323_bw_geometric_modular.py","status_as_recorded":"Reduction [E]/[C]/[O] (BW geometric modular flow)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the fibration construction (T_net (x) T_cusp carries the skeleton + the gap) + the v312 negative (no gap without the fiber); [C] the 'minimal substrate = carrier x family' reading matching the v315 5x6 split; [O] deriving the cusp weight from a pure rewrite stays open. Sharpens v312; not a closure.","checked_by_registry":false,"claim_excerpt":"THE MINIMAL HYPERGRAPH SUBSTRATE THAT WORKS -- A (2,3,5)-NETWORK FIBERED BY A 3-FOLD CUSP CHANNEL (2026-06-22, the constructive v312 follow-up): reproduces BOTH the E8 skeleton AND the recovery gap. [E] NETWORK FACTOR (carrier/5-fold): T_net=(A+2I)/4 fixes the Kac marks (eigenvalue 1 = E8 skeleton), subleading (phi+2)/4 (golden); (2/3)^6 NOT in its spectrum (the v312 negative). [E] CUSP FIBER (family/3-fold): T_cusp=","claim_id":"HYP.FIBER.01","dependencies_as_recorded":"HYP.INJECT.01; COX.COUPLE.01; GALOIS.FAMILY.01; v312; v315; v317; v319; v221; v76","external_data_as_recorded":"-","id":"claim:HYP.FIBER.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":422,"scripts_as_recorded":"v324_hypergraph_fiber.py","status_as_recorded":"Construction [E]/[C] (fibered substrate)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] Lean-built: the well-typed composition seamEquivChain + the axiom audit (residual = the named cited theorems + the one OS input) + the decide-proven discriminator (1 != 4). A formal audit-contract skeleton of the v308 keystone chain; the three literature steps are named axioms (cited, not re-proved), so it MACHINE-PINS the residual but does NOT close SEAM.EQUIV.01.","checked_by_registry":false,"claim_excerpt":"LEAN: SEAM.EQUIV.01 COMPOSITION CHAIN (2026-06-22). Lean 4 formalisation (TfptCarrier/SeamEquivChain.lean) of the v308 closing chain: the four nodes GapPositive -> InvertibleSRE -> HolomorphicC8 -> SeamIsE8 assembled as a well-typed composition theorem seamEquivChain, with the three cited literature steps (Kitaev free-fermion invertibility; Mueger / Kawahigashi-Longo-Mueger holomorphy; Conway-Sloane E8 uniqueness) de","claim_id":"FORM.SEAMEQUIV.01","dependencies_as_recorded":"SEAM.EQUIV.CHAIN.01; SEAM.EQUIV.01; SEAM.EQUIV.GAP.01","external_data_as_recorded":"Lean 4 + Mathlib (v4.29.1; #print axioms = named cited steps + OS gap)","id":"claim:FORM.SEAMEQUIV.01","location_as_recorded":"lean4-carrier-rigidity/TfptCarrier/SeamEquivChain.lean","path":"verification/status_ledger.csv","row_number":423,"scripts_as_recorded":"v308_seam_equiv_chain.py","status_as_recorded":"Formal","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the assembled keystone theorem with all exact pieces machine-checked (marks=4, j=1728, chi_orb=0, det Cartan E8=1, gap>0, mod-4 fingerprint); [O] the single open lemma (raw seam = flat tau=i pillowcase / rotation-invariant state) shared by both bedrock IDs and Lean-pinned. An assembly certificate (like v176/v261), does NOT close the bedrock.","checked_by_registry":false,"claim_excerpt":"THE SEAM KEYSTONE AS ONE CITABLE THEOREM (2026-06-22): the raw seam state is the flat tau=i pillowcase state, with EXACTLY ONE open lemma. Assembles the keystone pieces into one statement -- IF (raw RP-collar seam state = flat tau=i pillowcase / rotation-invariant state) THEN 4 square marks + mu4 deck + omega o rho=omega + holomorphic c=8 => (E8)_1, with the carrier recovery gap as input. [E] FOUR SQUARE MARKS: n=2ch","claim_id":"QGEO.KEYSTONE.01","dependencies_as_recorded":"QGEO.SYM.01; SEAM.EQUIV.01; QGEO.BW.01; v214; v216; v280; v308; v323; v76","external_data_as_recorded":"Troyanov uniformisation (cited)","id":"claim:QGEO.KEYSTONE.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":424,"scripts_as_recorded":"v325_pillowcase_keystone.py","status_as_recorded":"Synthesis/reduction [E]/[O] (keystone-as-one-theorem)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the F_pole seam-rate contraction; [C] the Boltzmann/relic relaxations (shape, external rates); [I] the QCD RG flow; [N] the rare-kaon bridge. A productisation/solver harness of v303, NOT a new claim; the external rates stay honestly fenced.","checked_by_registry":false,"claim_excerpt":"THE F_transfer SOLVER SUITE (2026-06-22): the four transfer readouts as ONE runnable harness, each a gapped relaxation to a unique attractor, with values + uncertainties + honest typing (productises FR.DYNAMICS.01/v303). [E] F_pole (Koide): Moebius contraction to Q*=2/3 with multiplier (2/3)^6 = the seam-clock subleading eigenvalue, unique attractor at the SEAM rate. [C] F_Boltzmann (eta_B): washout contraction to th","claim_id":"FR.SUITE.01","dependencies_as_recorded":"FR.DYNAMICS.01; v303; v82; v184; v185; v202","external_data_as_recorded":"NuFIT/PDG/NA62 (data targets)","id":"claim:FR.SUITE.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":425,"scripts_as_recorded":"v326_ftransfer_suite.py","status_as_recorded":"Numerical/synthesis [E]/[C]/[I] (F_transfer solver suite)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the rule spectrum {1,2/3,0} + the recovery-rate derivation (2/3)^6 + the non-graph-spectral PROOF p(2/3)!=0; [O] the arity {2,3} is still the anchor input. Sharpens v324/v312 (the injected datum reduced to the anchor arity); not a derivation of the atoms.","checked_by_registry":false,"claim_excerpt":"DERIVING THE CUSP WEIGHT 2/3 FROM A MINIMAL REWRITE (2026-06-22, sharpening HYP.FIBER.01/v324 + HYP.INJECT.01/v312). A minimal local rule -- a family channel with N_fam=3 slots, one absorbing attractor (w=0) and |Z2|=2 surviving (the Z2 pair) -- supplies the cusp fiber. [E] MINIMAL REWRITE: M=[[1,0,0],[0,1/3,1/3],[0,1/3,1/3]] has spectrum {1,2/3,0}; the recovery survival 2/3=(N_fam-1)/N_fam=|Z2|/N_fam EMERGES from th","claim_id":"HYP.REWRITE.01","dependencies_as_recorded":"HYP.FIBER.01; HYP.INJECT.01; v312; v324; v317; v76","external_data_as_recorded":"-","id":"claim:HYP.REWRITE.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":426,"scripts_as_recorded":"v327_hypergraph_rewrite.py","status_as_recorded":"Construction/proof [E]/[O] (cusp weight from a minimal rewrite)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[N] the precise +2.0 sigma tension + the no-relief audit; [E] the separate-channel structure (v268) + the seed-hyperplane consistency; [X] the pre-registered kill. Names and quantifies the honest weak point; no new claim, no freeze change.","checked_by_registry":false,"claim_excerpt":"THE theta13 PRESSURE POINT -- THE HONEST WEAK SPOT, QUANTIFIED AND PRE-REGISTERED (2026-06-22). [N] TENSION: sin^2 theta13 = phi0 e^{-5/6} = 0.023108 vs NuFIT 6.0 NO (0.02195 +- 0.00058) is +2.0 sigma -- the most-tensioned CORE prediction (v62/v307). [E] SEPARATE CHANNEL: theta13 is the carrier hypercharge trace (exponent gamma=tr_E Y^2=5/6 EXACT, v268), NOT the seesaw mu-tau breaking that sets theta12 (eps=3 phi0/4 ","claim_id":"FLAV.TH13.PRESSURE.01","dependencies_as_recorded":"FLAV.TH13.01; DATA.SCORECARD.01; SEED.CROSSVAL.01; v268; v62; v306; v307","external_data_as_recorded":"NuFIT 6.0 (sin^2 theta13 NO)","id":"claim:FLAV.TH13.PRESSURE.01","location_as_recorded":"tfpt_2_standard_model","path":"verification/status_ledger.csv","row_number":427,"scripts_as_recorded":"v328_theta13_pressure.py","status_as_recorded":"Numerical/data [N]/[X] (theta13 pressure point)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] Lean-built: the composition bedrockReducesToRotationInvariance + the axiom audit (residual = chain steps + recovery_gap + named BW steps + the ONE shared premise) + the decide-proven geometric-vs-clock discriminator. Machine-pins the v323 collapse (two bedrock items -> one shared premise RotationInvariantVacuum); plus qgeoSymIsCorollary (2026-06-22): with the cited conformal-net vacuum axiom (conformal_net_vacuum_rotation_invariant), StateInvariance (=QGEO.SYM.01) follows from SeamIsE8 ALONE, so QGEO.SYM.01 is a COROLLARY of SEAM.EQUIV.01 with no independent open premise. Does NOT close SEAM.EQUIV.01.","checked_by_registry":false,"claim_excerpt":"LEAN: QGEO.SYM.01 FROM SEAM.EQUIV.01 VIA BISOGNANO-WICHMANN (2026-06-22). Lean 4 formalisation (TfptCarrier/BWKeystone.lean) of the v323 linkage: the nodes RotationInvariantVacuum -> GeometricModularFlow -> Mu4ModularSymmetry -> StateInvariance (=QGEO.SYM.01) assembled with the cited Bisognano-Wichmann/Hislop-Longo steps as named axioms, composed over the v308 chain (seamEquivChain discharges SeamIsE8). The theorem b","claim_id":"FORM.QGEO.BW.01","dependencies_as_recorded":"QGEO.BW.01; QGEO.SYM.01; SEAM.EQUIV.CHAIN.01; FORM.SEAMEQUIV.01; v323; v308","external_data_as_recorded":"Lean 4 + Mathlib (v4.29.1; #print axioms = chain steps + BW steps + RotationInvariantVacuum)","id":"claim:FORM.QGEO.BW.01","location_as_recorded":"lean4-carrier-rigidity/TfptCarrier/BWKeystone.lean","path":"verification/status_ledger.csv","row_number":428,"scripts_as_recorded":"v323_bw_geometric_modular.py","status_as_recorded":"Formal","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the many-body OS-gap=transfer-gap identity (second quantization, size-independent) + the sufficiency chain (rotation-invariance => QGEO.SYM.01 + SRE => (E8)_1); [O] the necessity of H on the raw collar. Discharges the v308 OS input at the finite level and assembles H as the single sufficient premise; does NOT close the bedrock.","checked_by_registry":false,"claim_excerpt":"CLOSING THE OS STEP: THE BULK GAP IS THE TRANSFER GAP (2026-06-22, second quantization) + the single sufficient premise. The v308 chain left ONE analytic input -- the OS identification 'OS-reconstructed bulk gap = transfer gap'. [E] OS GAP = TRANSFER GAP: the OS/Euclidean many-body Hamiltonian is dGamma(-log T) (T the v221/v302 recovery transfer); its spectrum is the set of sums of single-mode energies, so the many-b","claim_id":"QGEO.OSGAP.01","dependencies_as_recorded":"SEAM.EQUIV.CHAIN.01; QGEO.BW.01; QGEO.KEYSTONE.01; v240; v308; v323; v325; v237","external_data_as_recorded":"-","id":"claim:QGEO.OSGAP.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":429,"scripts_as_recorded":"v329_os_gap_reduction.py","status_as_recorded":"Reduction [E]/[O] (OS gap = transfer gap + single premise)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the admissible-sector measure is CONSTRUCTED (RP + clustering + tightness => projective limit + OS reconstruction); [O] the full ambient (metric-sector) measure stays open, gap-decoupled. A genuine PARTIAL construction of QG.AMB.01 on the decoupled sector, NOT a closure.","checked_by_registry":false,"claim_excerpt":"CONSTRUCTING THE AMBIENT MEASURE ON THE GAP-DECOUPLED ADMISSIBLE SECTOR (2026-06-22) as a bona fide Osterwalder-Schrader object, with the honest fence (the constructive step v275's roadmap calls for). [E] REFLECTION POSITIVITY: the seam transfer T (v221/v311; spectrum {1,(2/3)^6,(1/3)^6}) is symmetric PSD, so the finite-volume transfer-matrix measures are RP (OS-0). [E] EXPONENTIAL CLUSTERING: the connected 2-pt C(n)","claim_id":"QGAMB.MEASURE.01","dependencies_as_recorded":"QGAMB.ROADMAP.01; v275; v311; v240; v221; v76","external_data_as_recorded":"-","id":"claim:QGAMB.MEASURE.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":430,"scripts_as_recorded":"v330_qgamb_admissible_measure.py","status_as_recorded":"Construction [E]/[O] (admissible-sector OS measure)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] Lean-built: the carrier Cartan determinants |det A3|=4, |det D5|=4 => carrier index 16 as real Matrix.det computations (kernel decide, no native_decide axiom). Grounds the v281/v308 carrier anyon count AND the rank-8 holomorphy discriminator (|det Cartan(E8)|=1 = one anyon, via the integer inverse, kernel decide) in real determinants/matrix algebra; Mathlib leaves E8_det=1 (the sign) as proof_wanted, which positive-definiteness supplies.","checked_by_registry":false,"claim_excerpt":"LEAN: THE CARRIER CARTAN DETERMINANTS AS REAL Matrix.det COMPUTATIONS (2026-06-22). Lean 4 (TfptCarrier/CartanDeterminants.lean) grounds the carrier piece of the holomorphy/anyon discriminator in ACTUAL determinants of the integer Cartan matrices, proved (kernel decide, no extra axiom) rather than asserted: |det Cartan(A3)|=4=|mu4| (3x3, via Matrix.det_fin_three) and |det Cartan(D5)|=4 (5x5, via decide at maxRecDepth","claim_id":"FORM.CARTAN.DET.01","dependencies_as_recorded":"SEAM.EQUIV.CHAIN.01; QGEO.KEYSTONE.01; v281; v325","external_data_as_recorded":"Lean 4 + Mathlib (kernel decide; Mathlib leaves E8_det as proof_wanted)","id":"claim:FORM.CARTAN.DET.01","location_as_recorded":"lean4-carrier-rigidity/TfptCarrier/CartanDeterminants.lean","path":"verification/status_ledger.csv","row_number":431,"scripts_as_recorded":"v325_pillowcase_keystone.py","status_as_recorded":"Formal","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the DtN equivalence (rotation-invariance <=> square marks, both directions) + the order-4 CM identification (cross-ratio 2 => j=1728); [O] the dynamical selection of the square (the residual of H). Reduces the necessity direction to one named configuration; does NOT close the bedrock.","checked_by_registry":false,"claim_excerpt":"THE NECESSITY OF H REDUCED (2026-06-22): rotation-invariance of the seam DtN is EQUIVALENT to the four marks sitting at the square (tau=i), so the one open lemma is exactly the order-4 CM selection (the necessity companion to v329's sufficiency). [E] SQUARE => [rho,Lambda]=0: with marks at {0,pi/2,pi,3pi/2} the curvature is Z4-symmetric (Fourier support 0 mod 4), M_f couples only modes differing by 4Z, [rho,Lambda]=0","claim_id":"QGEO.NECESS.01","dependencies_as_recorded":"QGEO.OSGAP.01; QGEO.KEYSTONE.01; QGEO.SUBPRIN.01; v329; v201; v210; v214; v216; v267","external_data_as_recorded":"-","id":"claim:QGEO.NECESS.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":432,"scripts_as_recorded":"v331_necessity_of_H.py","status_as_recorded":"Reduction [E]/[O] (necessity of H = the order-4 CM selection)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the conformal-mode obstruction (wrong-sign kinetic, divergent Gaussian) + the gap insulation + the polynomial-ghost control; [C] the IDG taming (conditional on entire analyticity, v304); [O] the metric-sector measure stays open. Characterizes the QG.AMB metric-sector residual precisely; does NOT close it.","checked_by_registry":false,"claim_excerpt":"THE METRIC SECTOR OF QG.AMB.01 CHARACTERIZED (2026-06-22): the obstruction is exactly the conformal-mode (Gibbons-Hawking-Perry) problem, the physical sector is gap-insulated, and the only route is the conditional IDG taming (makes v330's metric-sector fence precise). [E] CONFORMAL-MODE WRONG SIGN: c_conf(D)=-(D-1)(D-2)/4 is NEGATIVE for D>=3 (c_conf(4)=-3/2) while the transverse-traceless coefficient is positive -- ","claim_id":"QGAMB.METRIC.01","dependencies_as_recorded":"QGAMB.MEASURE.01; QGAMB.ROADMAP.01; QGAMB.IDG.01; v330; v275; v304; v76","external_data_as_recorded":"-","id":"claim:QGAMB.METRIC.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":433,"scripts_as_recorded":"v332_qgamb_metric_sector.py","status_as_recorded":"Characterization [E]/[C]/[O] (metric-sector = the conformal-mode obstruction)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] Lean-built: i^4=1, i^2=-1, and the mu4 commutation (offset-4 commutes, offset-2 does not) on concrete 6x6 matrices over Z[i], all kernel decide (no native_decide). Grounds the v201/v323 mark-locality criterion in exact linear algebra.","checked_by_registry":false,"claim_excerpt":"LEAN: THE mu4 MARK-LOCALITY COMMUTATION AS REAL LINEAR ALGEBRA (2026-06-22). Lean 4 (TfptCarrier/Mu4Commutation.lean) turns the v201/v309/v323 finite-model fact (the mu4 clock rho=diag(i^n) commutes with a DtN sub-principal coupling IFF that coupling is mark-local, i.e. couples only Fourier modes differing by a multiple of 4) into an EXACT, kernel-checked statement over the Gaussian integers Z[i]: [E] i^4=1 (an offse","claim_id":"FORM.MU4COMM.01","dependencies_as_recorded":"QGEO.SUBPRIN.01; QGEO.BW.01; QGEO.NECESS.01; v201; v309; v323; v331","external_data_as_recorded":"Lean 4 + Mathlib (GaussianInt; kernel decide)","id":"claim:FORM.MU4COMM.01","location_as_recorded":"lean4-carrier-rigidity/TfptCarrier/Mu4Commutation.lean","path":"verification/status_ledger.csv","row_number":434,"scripts_as_recorded":"v331_necessity_of_H.py","status_as_recorded":"Formal","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the modular order-4 uniqueness (S fixes i) + the deck-order->CM map (order-4 => j=1728 => tau=i) + the mark-equilibration (Fekete) attractor; [O] the deck acting geometrically (= QGEO.SYM.01). Sharpens the v331 residual from 'why the square' to 'the deck acts geometrically'; does NOT close the bedrock.","checked_by_registry":false,"claim_excerpt":"THE CM-SELECTION MECHANISM (2026-06-22): tau=i (the square) is the UNIQUE order-4 modulus and the attractor of mark-equilibration, so the last keystone residual is 'the deck acts geometrically', not 'why the square' (the v331 follow-up). [E] ORDER-4 MODULAR ELEMENT: S=[[0,-1],[1,0]] in SL(2,Z) has S^2=-I, S^4=I (order 4) and fixes tau=i (S.i=-1/i=i); i is the unique order-4 elliptic point of PSL(2,Z) (the only other ","claim_id":"QGEO.CMSELECT.01","dependencies_as_recorded":"QGEO.NECESS.01; QGEO.SYM.01; v331; v214; v216; v267; v56","external_data_as_recorded":"-","id":"claim:QGEO.CMSELECT.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":435,"scripts_as_recorded":"v333_cm_selection.py","status_as_recorded":"Reduction [E]/[O] (CM selection = unique order-4 modulus + equilibration attractor)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the obstruction + the GHP sign flip + the IDG pole-freeness + the polynomial-ghost control; [C] the conditional GHP+IDG construction; [O] the contour's nonperturbative validity. Advances v332 to a conditional construction; does NOT close QG.AMB.01.","checked_by_registry":false,"claim_excerpt":"THE CONFORMAL-MODE RESOLUTION (2026-06-22): the Gibbons-Hawking-Perry contour rotation (IR sign) + the infinite-derivative (IDG) dressing (UV pole) give a CONDITIONALLY convergent metric-sector measure; the residual is the nonperturbative validity of the contour (the v332 follow-up). [E] THE OBSTRUCTION: c_conf(4)=-(D-1)(D-2)/4=-3/2<0, so the unrotated conformal Gaussian integral(exp(+|c|phi^2)) DIVERGES. [E] GHP CON","claim_id":"QGAMB.CONFORMAL.01","dependencies_as_recorded":"QGAMB.METRIC.01; QGAMB.IDG.01; QGAMB.MEASURE.01; v332; v304; v330; v76","external_data_as_recorded":"-","id":"claim:QGAMB.CONFORMAL.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":436,"scripts_as_recorded":"v334_conformal_resolution.py","status_as_recorded":"Construction [E]/[C]/[O] (conformal-mode GHP+IDG conditional resolution)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the corollary reduction (QGEO.SYM.01 via the cited net-vacuum axiom) + the one-theorem framing + the QG.AMB decoupling/reclassification; [O] SEAM.EQUIV.01's one continuum lemma. A synthesis collapsing the status to one solvable theorem + one decoupled foreign problem; does NOT close SEAM.EQUIV.01.","checked_by_registry":false,"claim_excerpt":"THE KEYSTONE UNIFICATION (2026-06-22): there is ONE open theorem (SEAM.EQUIV.01), QGEO.SYM.01 is its COROLLARY (a conformal-net axiom), and QG.AMB.01 is a decoupled general QG problem, NOT a TFPT gate -- collapsing the 'two open structural items' narrative to 'one solvable theorem + one decoupled foreign problem'. [E] QGEO.SYM.01 = COROLLARY: a chiral conformal net has a Moebius-covariant vacuum (the unique invariant","claim_id":"SEAM.EQUIV.UNIFY.01","dependencies_as_recorded":"SEAM.EQUIV.CHAIN.01; QGEO.BW.01; QGEO.SYM.01; QG.AMB.01; v308; v323; v329; v333; v76","external_data_as_recorded":"-","id":"claim:SEAM.EQUIV.UNIFY.01","location_as_recorded":"introduction","path":"verification/status_ledger.csv","row_number":437,"scripts_as_recorded":"v335_seam_equiv_unify.py","status_as_recorded":"Synthesis/reduction [E]/[O] (one keystone theorem; QGEO.SYM corollary; QG.AMB decoupled)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[C] the two legs are citable as general theorems (not yet specialised to the raw collar in print); [E] the arithmetic target pins; [O] the narrowed residual. Does NOT close SEAM.EQUIV.01.","checked_by_registry":false,"claim_excerpt":"THE ONE OPEN LEMMA OF SEAM.EQUIV.01, stated precisely and mapped to the recent rigorous literature (2026-06-22): the continuum-limit and OS-reconstruction legs are now CITABLE, the genuinely-open residual narrows to 'the raw collar is a gapped quasi-free state whose massless scaling limit is the c=8 (E8)_1 net'. [C] CONTINUUM LEG: Osborne-Stottmeister (CFT from Lattice Fermions, doi:10.1007/s00220-022-04521-8, CMP 39","claim_id":"SEAM.EQUIV.CONTINUUM.01","dependencies_as_recorded":"SEAM.EQUIV.CHAIN.01; SEAM.EQUIV.UNIFY.01; v308; v277; v335","external_data_as_recorded":"Osborne-Stottmeister (CFT from Lattice Fermions, CMP 398 (2023) 219, doi:10.1007/s00220-022-04521-8; builds on the MMST OAR framework, Morinelli-Morsella-Stottmeister-Tanimoto, arXiv:2010.11121); Adamo-Moriwaki-Tanimoto (arXiv:2407.18222); Adamo-Giorgetti-Tanimoto (arXiv:2506.01008, 2d conformal nets from even lattices; arXiv:2508.07109, automatic diffeomorphism covariance of conformal-net reps)","id":"claim:SEAM.EQUIV.CONTINUUM.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":438,"scripts_as_recorded":"v336_continuum_limit.py","status_as_recorded":"Reduction [C]/[O] (continuum lemma narrowed + literature-anchored)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the margin, the factorization through the gapped sector, and the gap-suppression are exact/machine-checked; the decoupling is rigorous GIVEN the factorization. Does NOT construct the ambient measure -- proves TFPT does not need it.","checked_by_registry":false,"claim_excerpt":"THE DECOUPLING THEOREM (consolidated, citable, 2026-06-22): every TFPT dimensionless readout factors through the gapped admissible sector and is INDEPENDENT of the ambient QG measure -- the theorem that makes the QG.AMB.01 reclassification (v335) honest. [E] GAP MARGIN: Delta - 2*dim(E8)*c3^2 = 6 ln(3/2) - 496/(64 pi^2) = 6 ln(3/2) - 31/(4 pi^2) ~ 1.648 > 0 (the ambient back-reaction scale 2*248*c3^2 = 31/(4 pi^2) ex","claim_id":"DECOUPLING.THEOREM.01","dependencies_as_recorded":"QG.AMB.01; v76; v311; v330; v332; v335","external_data_as_recorded":"-","id":"claim:DECOUPLING.THEOREM.01","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":439,"scripts_as_recorded":"v337_decoupling_theorem.py","status_as_recorded":"Theorem [E] (factorization through the gap => ambient-measure independence)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[N] the data-confrontation (repo-documented NuFIT 6.0 centrals, both variants) + the budget arithmetic; [E] the within-3-sigma check; [X] the JUNO kill. Does not change the frozen prediction.","checked_by_registry":false,"claim_excerpt":"THE THETA13 SUB-LEADING BUDGET vs the current global fit (2026-06-22): the +2 sigma pressure point (v328) quantified against BOTH NuFIT 6.0 normal-ordering variants and JUNO; neither defuses nor excludes -- fences correctly. [N] SK-DEPENDENT TENSION: sin^2 theta13 = phi0 e^{-5/6} = 0.023108 is +2.0 sigma vs the no-SK central (0.02195 +- 0.00058) and +1.7 sigma vs the with-SK NO best fit (0.02215 +- 0.00057) -- a ~0.3","claim_id":"THETA13.BUDGET.01","dependencies_as_recorded":"THETA13.PRESSURE.01; v306; v328; REG.FREEZE.01","external_data_as_recorded":"NuFIT 6.0 (2024), nu-fit.org v60 parameters","id":"claim:THETA13.BUDGET.01","location_as_recorded":"tfpt_2_standard_model","path":"verification/status_ledger.csv","row_number":440,"scripts_as_recorded":"v338_theta13_budget.py","status_as_recorded":"Data-confrontation [N]/[E]/[X] (mild +1.7-2.0 sigma; within 3 sigma; JUNO decides)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the No-Unit dimensional argument + b3; [X] the non-unification spread; [N] the lattice O(1); [C] the cosmological scenarios; [A] the four-way classification. A boundary audit (like v35/v167/v275); does NOT close anything, fabricates nothing.","checked_by_registry":false,"claim_excerpt":"THE HONEST FIRST-PRINCIPLES BOUNDARY, mapped precisely (2026-06-22): answers (a) can M_Planck/v_geo be computed from first principles? and (b) can F_transfer (Koide, m_p/m_e, eta_B, axion) be made a first-principles compiler output? BOTH NO -- with the exact reason for each residual, classified into FOUR honest kinds. [E] v_geo/M_Planck FORBIDDEN BY THEOREM (No-Unit, v153): a mass is dimension 1 while every TFPT datu","claim_id":"FIRSTPRINCIPLES.BOUNDARY.01","dependencies_as_recorded":"v153; v274; v262; v246; v35; ANCHOR.VGEO.01; FR.MPME.02","external_data_as_recorded":"PDG alpha_s(M_Z); lattice m_p/Lambda3","id":"claim:FIRSTPRINCIPLES.BOUNDARY.01","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":441,"scripts_as_recorded":"v339_firstprinciples_boundary.py","status_as_recorded":"Boundary audit [E]/[X]/[C] (what is derived / external / tensioned / forbidden)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the dimensionless A_s formula + the no-mass-definition consequence; [N] the reheating-channel quantification; [P] the archive comparison (the old N_star=3/phi0-1 is a posited algebraic count, NOT re-promoted to [E]); [X] the test. Does NOT change the frozen band.","checked_by_registry":false,"claim_excerpt":"A_s is predicted (not missing), is DIMENSIONLESS (so it does NOT define an absolute mass), and the apparent -11 sigma tension is a reheating-channel question -- reconciled with the archived old derivation (TFPT v4.5/v4.6, 2026-06-22). [E] A_s = N_star^2 (M_scal/Mbar)^2/(24 pi^2) = N_star^2 c3^7/(24 pi^2) (v86); M_scal/Mbar = c3^{7/2} = 1.2565e-5 is a PURE RATIO, so A_s carries NO absolute scale -- it pins N_star (the","claim_id":"AS.RECONCILE.01","dependencies_as_recorded":"v86; v153; v84; SCALE.OVERDET.01","external_data_as_recorded":"Planck 2018 A_s; archive _archive/tfpt-45/07_cmb_operational_closure_planck_pipeline.tex","id":"claim:AS.RECONCILE.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":442,"scripts_as_recorded":"v340_As_reconcile.py","status_as_recorded":"Reconciliation [E]/[N]/[P]/[X] (A_s predicted+dimensionless; tension = reheating channel; archive comparison)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the coefficient identifications (8 b1 = (4/5)M; c3 Gauss-Bonnet; -5/4=-q(D5); c3/phi_base=q(A3)) + the Quillen-form split at the root + the 'no new gate' clarification (machine-checked); [O] the still-open part = EM.WARD.01's residual (the first-principles AQFT derivation of the functional). Sharpens v3/v48/EM.WARD.01 from fixed point to stationarity; does NOT open a new gate and does NOT prove the variational principle.","checked_by_registry":false,"claim_excerpt":"THE ALPHA FIXED POINT AS THE STATIONARITY OF A U(1) DETERMINANT LINE (2026-06-22): reformulates the EM closure from 'a very cleverly built fixed point' into 'the stationarity of a named functional', identifying every ingredient as an index / heat-kernel coefficient / discriminant form -- the 'derive the FORM' step (external review). F_{U(1)} = a^3 - 2 c3^3 a^2 - (4/5) c3^6 M ln(1/phi_seam) = 0 written in Quillen form","claim_id":"ALPHA.QUILLEN.01","dependencies_as_recorded":"EM.WARD.01; v3; v48; v159; v216; v1","external_data_as_recorded":"-","id":"claim:ALPHA.QUILLEN.01","location_as_recorded":"tfpt_1_architecture_e8","path":"verification/status_ledger.csv","row_number":443,"scripts_as_recorded":"v341_alpha_quillen.py","status_as_recorded":"Reformulation [E]/[O] (alpha = stationarity of a named U(1) determinant line; sharpens the existing [P] EM.WARD.01; no new gate)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the three TFPT prerequisites (dim-4 power-counting -> finite counterterm space; BRST nilpotency via Jacobi for su(2)/su(3); the seam gap -> adiabatic limit); [C] the two imported heavy legs (all-order T_n existence by causal factorisation; all-order BRST invariance / Slavnov-Taylor); NOT [E] (no in-repo formal induction), matter+gauge only (gravity fenced to v304/v370/v380; ambient QG.AMB.01 a [C] redundancy). A typed all-order contract, not a path integral.","checked_by_registry":false,"claim_excerpt":"The all-order Epstein-Glaser/BRST contract for the perturbative 4D S-matrix S_pert (2026-06-23, review Point 3): the 'all-order closing statement' for the 4D perturbative QFT leg, typing the standard causal-perturbation-theory closure for the TFPT finite interaction class -- NOT a 4D path integral and NOT a new mechanism. [E] POWER-COUNTING: every gauge+matter vertex (Yang-Mills + Dirac-Yukawa + Higgs + ghost) is a m","claim_id":"QFT4D.EG.ALLORDER.01","dependencies_as_recorded":"v269; v271; v273; v278; v302; v304; v370; v380; v369","external_data_as_recorded":"Epstein-Glaser 1973; Brunetti-Fredenhagen 2000; Piguet-Sorella 1995; Kugo-Ojima 1979","id":"claim:QFT4D.EG.ALLORDER.01","location_as_recorded":"tfpt_5_redteam; tfpt_2","path":"verification/status_ledger.csv","row_number":444,"scripts_as_recorded":"v381_qft4d_eg_allorder.py","status_as_recorded":"All-order EG/BRST contract [C] (imported EG causal factorisation + BRST renormalisation on the TFPT finite dim-4 gauge+matter class + the seam gap); prerequisites power-counting/BRST-nilpotency/gap [E]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the Quillen split at the root + named-atom coefficients + the value alpha^-1=137.0359992 (reused from v3/v48/v341, machine-checked); [O] the from-first-principles exactness proof (the named target); [C] it is a face of SEAM.EQUIV.01, not a second independent gate. A typing/registration of the pre-existing EM.WARD.01 residual, reusing v341's (Wolfram-mirrored) identities; introduces no new number. UPDATE (2026-08-28, external master-object review wave 2, v985): the channel-swap face is resolved at the FINITE level -- the deck swap r -> r+2 maps the jump |spectrum| [0,2,4,2] onto the mark pattern |[4,-2,0,-2]| exactly (odd swap fails), the graded det' difference is c3-free = log(ln2/4), and the channelwise unit ratio is uniform 4/ln2; finite KMS rigidity-premise executed [E] (v995: 33 directions killed; 196608 -> 0); ln-2-rate detline shadow [E-measured] (v996, numerical not theorem); continuum Bismut-Freed, type-III KMS uniqueness and the from-first-principles exactness of F_U(1) stay [O] (BFK 2^{-4} needs no physical compensation: relative det, 2026-08-29).  | 2026-08-29: relative det Q(A)=log[det'Delta_A/det'Delta_{A0}]+8 b1 c3^6 log phi(A); BFK 2^{-4} A/tau/alpha-independent at fixed cut number (delta log 2^{-4}=0, no physical compensation).  Stays [O].  WAVE-5 (2026-08-29): rigidity premise of SEAM.MMST.TYPEIII.CHARGED.01; no marker move. | LATE EVENING (2026-08-30 v1014): finite restriction isomorphism verified; orientation fixes the conjugate branch; the residual constant phase is fixed by the A0 reference normalization -- recorded.  Stays [O].","checked_by_registry":false,"claim_excerpt":"Names the Quillen determinant-line VARIATION as a tracked [O] target (2026-06-23, review Point 10): delta_tau(log det_zeta Delta_U(1) + 8 b1 c3^6 log phi_seam)=0 on the determinant line over the mu4 seam moduli -- i.e. F_U(1) IS the exact zeta-regularised Quillen functional of the seam U(1), not merely an assembled fixed point. Elevates EM.WARD.01's residual (v341/v342) to its own citable target so the one remaining ","claim_id":"ALPHA.QUILLEN.EXACT.01","dependencies_as_recorded":"EM.WARD.01; SEAM.EQUIV.01; v341; v342; v3; v48; v216; v336","external_data_as_recorded":"-","id":"claim:ALPHA.QUILLEN.EXACT.01","location_as_recorded":"tfpt_1_architecture_e8","path":"verification/status_ledger.csv","row_number":445,"scripts_as_recorded":"v382_alpha_quillen_exact.py; v985_quillen_channel_swap.py; v995_kms_subnet_rigidity.py; v996_gauge_grammar_kill.py; v1014_bridge_refinements.py","status_as_recorded":"Named target [E]/[O] (the Quillen determinant-line variation-exactness; a face of SEAM.EQUIV.01, elevates EM.WARD.01's residual to a citable target; no new gate; 2026-08-28: the v974 CHANNEL-SWAP face resolved at the finite level by mu4-character grading, v985; completeness wave: finite KMS rigidity-premise [E] v995, ln-2-rate detline shadow v996 -- continuum Bismut-Freed stays [O])","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the three computed gaps (flavor 6 ln(3/2); discrete 2-phi=1/phi^2; decoupling 1.648) + the two number-field facets (v314); [C] the cross-sector identification (gravity/QG/QFT/recovery/F_transfer) + the meta-theorem 'parameter-freeness = spectral gap, theory-wide'. A synthesis (like v303/v337/v353), reuses established gaps, introduces no new number.","checked_by_registry":false,"claim_excerpt":"The UNIVERSAL spectral-gap / Perron-Frobenius principle (2026-06-23, bird's-eye synthesis): every TFPT sector is the SAME structural object -- a gapped operator with a UNIQUE leading attractor (the physics) and a spectral gap (the reason there is no free parameter). Extends v303 (which named this only for F_transfer) to the sectors made parameter-free AFTER it. [E] FLAVOR (computed): cusp transfer spectrum {1,(2/3)^6","claim_id":"DYNAMICS.UNIVERSAL.01","dependencies_as_recorded":"v56; v82; v303; v312; v313; v314; v337; v358; v359; v365; v381; v221; v157; v158","external_data_as_recorded":"-","id":"claim:DYNAMICS.UNIVERSAL.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":446,"scripts_as_recorded":"v383_dynamics_universal.py","status_as_recorded":"Universal synthesis [E]/[C] (every sector = a gapped operator with a unique attractor + spectral gap => parameter-free; extends v303 theory-wide; 3 gaps computed, the cross-sector identification [C])","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] ledger CI, No-Unit dimensionlessness, checked gap-decoupling margin and three-way classification within the historical compiler residual only. [O] no statement about T1-T8 closure; the audit closes nothing and introduces no number.","checked_by_registry":false,"claim_excerpt":"Historical compiler-residual audit (2026-06-23; scope corrected 2026-09-05): v384 classifies the then-listed compiler residual into three external kinds, (A) external math proof, (B) theorem-forbidden, and (C) external physics. It does not classify the physical completeness gates T1-T8 and does not imply zero open internal TFPT mechanisms. [E] LEDGER CI: every claim in that historical residual list is present in stat","claim_id":"RESIDUAL.CERTIFICATION.01","dependencies_as_recorded":"SEAM.EQUIV.01; ALPHA.QUILLEN.EXACT.01; QG.AMB.01; ANCHOR.VGEO.01; FR.POLE.SOLVE.01; TFPT.TOE.COMPLETE.01; v153; v336; v369; v337; v187","external_data_as_recorded":"-","id":"claim:RESIDUAL.CERTIFICATION.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":447,"scripts_as_recorded":"v384_residual_certification.py","status_as_recorded":"Historical compiler-residual audit [E]; explicitly not a TOE-completeness audit. TFPT.TOE.COMPLETE.01 and all T1-T8 remain Open [O].","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the all-order-robustness link (v381) + the proton-safety scale hierarchy (M_PS/M_bound~1e7); [X] the plain-SM-GUT kill + the frozen kill-test surface; [C] the optional PS branch. A consolidation (like v265/v337/v384); does NOT re-run the RGE or claim a tau_p discovery; no new number.","checked_by_registry":false,"claim_excerpt":"The optional carrier-Pati-Salam UV branch on the ALL-ORDER footing -- a single citable kill-test surface with the proton-decay SAFETY hierarchy computed (2026-06-24). A consolidation: does NOT re-run the RGE (v246 did 1+2-loop) nor re-derive the PS scale (v249/v253); it ADDS the all-order connection (v381) and the computed proton-safety margin (turning v265's 'no fake tau_p window' policy into a number). [E] CARRIER ","claim_id":"UVBRANCH.KILLTEST.01","dependencies_as_recorded":"v159; v246; v247; v248; v249; v253; v265; v381","external_data_as_recorded":"PDG K_L->mu e bound; Super-K proton decay","id":"claim:UVBRANCH.KILLTEST.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":448,"scripts_as_recorded":"v385_uvbranch_killtest.py","status_as_recorded":"UV-branch kill-test surface [E]/[X]/[C] (carrier-PS on the all-order footing; proton-SAFE hierarchy computed; plain-SM GUT killed; no fake tau_p)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the single positive-residue pole + the UV softening (e^{-u} faster than any power) + the GR limit and first correction; [C] the tree unitarity and the amplitude structure (perturbative-only). Extends v304/v370/v380 from propagator to amplitude; does NOT touch the non-perturbative measure (QG.AMB.01); the scale M=M_scal (v253) and the form factor = the seam KMS cutoff (v259), no new number.","checked_by_registry":false,"claim_excerpt":"The entire-form-factor graviton-exchange AMPLITUDE is finite, UV-softened and tree-unitary (2026-06-24) -- perturbative gravity as an explicit scattering problem, extending v304/v370/v380 from the propagator to the amplitude. The dressed spin-2 propagator P(p^2)=e^{-p^2/M^2}/p^2=1/(p^2 a) with a(u)=e^u (u=p^2/M^2), M=M_scal. [E] ONE POLE, GHOST-FREE: a=e^u entire and nowhere zero (v380) => the only pole is p^2=0 with","claim_id":"GRAV.AMPLITUDE.01","dependencies_as_recorded":"v259; v304; v370; v380; v253; v369","external_data_as_recorded":"-","id":"claim:GRAV.AMPLITUDE.01","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":449,"scripts_as_recorded":"v386_grav_amplitude.py","status_as_recorded":"Perturbative graviton amplitude [E]/[C] (entire-form-factor exchange: finite, ghost-free, UV-softened, tree-unitary; perturbative-only)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the four computed correction rates + the unified (lambda_2/lambda_1)^n form + the two-facet split (Q vs Q(sqrt5)); [C] the correction-calculus reading. A harvest/application of v383 (as v303/v337 are of v56); reuses established eigenvalues, introduces no new number.","checked_by_registry":false,"claim_excerpt":"The practical harvest of v383 (2026-06-24): the same spectral gap that makes each sector parameter-free ALSO sets the SIZE of its first correction -- for a gapped operator the deviation from the attractor decays at the ratio lambda_2/lambda_1 per step, so that ratio IS the leading-correction size. [E] FLAVOR: lambda_1=1, lambda_2=(2/3)^6=64/729 => first Koide correction ~0.0878 (v56/v82). [E] RECOVERY: the seam QECC ","claim_id":"CORRECTIONS.GAP.01","dependencies_as_recorded":"v56; v82; v221; v303; v312; v314; v337; v383","external_data_as_recorded":"-","id":"claim:CORRECTIONS.GAP.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":450,"scripts_as_recorded":"v387_corrections_gap.py","status_as_recorded":"Correction calculus [E]/[C] (each sector's gap sets its first-correction size; (2/3)^6 family vs golden family; the harvest of v383)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the four-class classification + the seam (2/3)^6 and golden (phi+2)/4 rates + the exact-identity zero-correction facts (det R=8, N_Phi=1, theta_eff=0) + the explicit theta12 texture (eps=c3+36 c3^4); [C] the typed-correction-budget reading. A typing of v387 (as v384 is of v383); reuses established eigenvalues and closed forms, introduces no new number.","checked_by_registry":false,"claim_excerpt":"The gap correction (v387) is a TYPED budget, NOT a uniform band on every prediction (2026-06-24): the (lambda_2/lambda_1)^n size is a property of the distance from a gapped operator's leading eigenvector, so it is only defined where a subleading lambda_2 exists. The prediction surface splits into FOUR correction classes (the verdict already implied by v303: of the four F_transfer instances only F_pole carries the sea","claim_id":"CORRECTIONS.BUDGET.01","dependencies_as_recorded":"v303; v371; v383; v387; v314; v337; v221; v312; v187","external_data_as_recorded":"-","id":"claim:CORRECTIONS.BUDGET.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":451,"scripts_as_recorded":"v388_corrections_budget.py","status_as_recorded":"Typed correction budget [E]/[C] (the gap correction is keyed to the mechanism class, not a uniform band; seam-gapped=(2/3)^6/golden, exact-identity=0, external-rate=external, fixed-point=explicit texture)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the Euclidean power-counting UV-finiteness at every loop order (super-polynomial falloff; one dressed line turns a quadratic divergence into a finite integral; the superficial degree -> -infinity), regulated by the derived seam scale M_scal (v253/v259); [C]/[O] full loop UNITARITY of the nonlocal form factor (the Lorentzian continuation / macro-causality, the genuinely open point), NOT claimed solved. Extends v386 from tree to loop FINITENESS only; introduces no new number.","checked_by_registry":false,"claim_excerpt":"The entire-form-factor graviton is UV-finite at the LOOP level by power counting (2026-06-24) -- the honest next step past v386 (which established the tree amplitude), extending v304/v370/v380/v386 from the propagator to the superficial degree of divergence of loop graphs. HONEST SCOPE: this is the standard infinite-derivative/nonlocal-gravity finiteness statement (Tomboulis; Biswas-Mazumdar-Siegel; Modesto); it is N","claim_id":"GRAV.LOOP.FINITE.01","dependencies_as_recorded":"v253; v259; v304; v370; v380; v386","external_data_as_recorded":"-","id":"claim:GRAV.LOOP.FINITE.01","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":452,"scripts_as_recorded":"v389_grav_loop_finiteness.py","status_as_recorded":"Perturbative graviton loop UV-finiteness [E] (power counting; super-polynomial falloff, degree -> -infinity at every loop order, seam-regulated) + loop unitarity [C]/[O] (the honest open point, not claimed solved)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the exact arithmetic (h(E8)=30=2*3*5; discriminants -4,-3,5; ramified-prime set {2,3,5} with product 30; j(i)=1728=12^3; 2cos(pi/5)=phi); [C] the completion/identification reading. A synthesis (like v383); reuses the three smallest CM/real-quadratic fields, tau=i (v282) and the Z/4 deck (v288), introduces no new number.","checked_by_registry":false,"claim_excerpt":"The prime-2 facet of the order-30 Coxeter clock, completing v383 (2026-06-24). The clock 30=2*3*5=h(E8) had two named number-field facets (the golden phi in Q(sqrt5), prime-5/carrier; (2/3)^6 in Q, prime-3/family); this names the prime-2 facet and identifies it with structure ALREADY in the theory: the Gaussian field Q(i), i.e. the CM point tau=i and the order-4 mu4=Z/4 square seam deck (v282/v288/v333). [E] THE CLOC","claim_id":"COXETER.PRIME2.01","dependencies_as_recorded":"v220; v282; v288; v314; v333; v383; v387","external_data_as_recorded":"-","id":"claim:COXETER.PRIME2.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":453,"scripts_as_recorded":"v390_prime2_facet.py","status_as_recorded":"Prime-2 facet of the Coxeter clock [E]/[C] (h(E8)=30=2*3*5; one quadratic facet field per prime, ramified at it; the prime-2/Gaussian/Z4-seam facet completes v383's golden and family facets)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Formal: iter_sub (closed form r^n), iter_tendsto (gap => attractor), starts_agree (parameter-freeness), no_gap_no_forget (gap is essential), seam/golden rates in [0,1); PLUS the finite-dim case (component_tendsto, deviation_tendsto = convergence to the dominant eigendirection, deviation_unique = parameter-free, flavor_deviation_tendsto on {1,(2/3)^6,(1/3)^6}); the general non-diagonalisable / infinite-dim PF stays cited","checked_by_registry":false,"claim_excerpt":"LEAN 4 FORMALISATION of the SCALAR CORE of the universal spectral-gap principle (door #4, 2026-06-24) -- new module TfptCarrier/SpectralGapAttractor.lean, lake build OK (target TfptCarrier.SpectralGapAttractor; aggregator TfptCarrier rebuilt, 3364 jobs), no sorry, only the three standard kernel axioms. It formalises the meta-theorem of v303/v383/v387 at the one-dimensional reduction: the affine gap contraction iter(r","claim_id":"FORM.SPECTRALGAP.01","dependencies_as_recorded":"DYNAMICS.UNIVERSAL.01; CORRECTIONS.GAP.01; FR.DYNAMICS.01","external_data_as_recorded":"-","id":"claim:FORM.SPECTRALGAP.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":454,"scripts_as_recorded":"lean4-carrier-rigidity (SpectralGapAttractor.lean)","status_as_recorded":"Formal [F] (Lean kernel; no extra axioms) -- the scalar core + the finite-dimensional diagonalisable case of the spectral-gap meta-theorem (v383): gap => unique attractor + geometric decay => parameter-free","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the solvable model (det_zeta(-d^2+m^2) on a circle and its closed-form heat-kernel variation), the heat-kernel-data mechanism (so 8 b1 c3^6 is the right kind of object), the re-verified v382 split, and the reduction to a named sub-target; [O] the headline ALPHA.QUILLEN.EXACT.01 stays open (NOT closed here) and SEAM.EQUIV.01 continuum existence stays the other external [O]. An honest attempt that reduces, does not close; no new number, alpha^-1 stays [E].","checked_by_registry":false,"claim_excerpt":"An HONEST attempt at the external target ALPHA.QUILLEN.EXACT.01 (door #5, 2026-06-24): it REDUCES the open step to a sharper named sub-target via a solvable model, but does NOT close it -- the status of ALPHA.QUILLEN.EXACT.01 stays [O] (external math, type A, v384). [E] SOLVABLE MODEL: det_zeta(-d^2/dtau^2 + m^2) on a circle of circumference beta = (2 sinh(beta m/2))^2 (textbook); its m-variation is the closed form b","claim_id":"ALPHA.QUILLEN.PROGRESS.01","dependencies_as_recorded":"ALPHA.QUILLEN.EXACT.01; SEAM.EQUIV.01; EM.WARD.01; v336; v341; v382","external_data_as_recorded":"-","id":"claim:ALPHA.QUILLEN.PROGRESS.01","location_as_recorded":"tfpt_1_architecture_e8","path":"verification/status_ledger.csv","row_number":455,"scripts_as_recorded":"v391_alpha_quillen_progress.py","status_as_recorded":"Honest attempt / reduction [E]/[O] (a solvable-model zeta-det mechanism + the reduction of ALPHA.QUILLEN.EXACT.01 to the named sub-target 'seam a_2 = 8 b1 c3^6'; the headline target stays OPEN, not closed)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the solvable 4D model reaching the nonzero a_4 (t^0) conformal-anomaly order (the order v391's 1D circle could not reach and the very order v342 grounds via Gilkey 30/360=1/12), the v391<->v342 unification (a zeta-det variation IS heat-kernel data AT the a_4 order), the measure identity (4 pi)^-2=4 c3^2, and the re-verified v382 split; [O] the headline ALPHA.QUILLEN.EXACT.01 stays open (the actual seam a_4=8 b1 c3^6 and the cubic a^3 Chern term, v384), and the exact seam F-normalisation fixing the coefficient value stays [C] (v342). A second honest step that grounds/connects, does not close; no new number, alpha^-1 stays [E].","checked_by_registry":false,"claim_excerpt":"A SECOND HONEST step on the external target ALPHA.QUILLEN.EXACT.01 (2026-06-27, v433): it GROUNDS and CONNECTS, it does NOT close it -- ALPHA.QUILLEN.EXACT.01 stays [O] (external math, type A, v384), alpha^-1 stays [E]. [E] SOLVABLE 4D MODEL REACHES a_4: the flat Delta=-d^2+m^2 on T^4 (vol V) has Tr e^{-tD}=V/(4 pi)^2 t^-2 e^{-t m^2}, Gilkey coeffs a_0=V/(4 pi)^2, a_2=-V m^2/(4 pi)^2, a_4=V m^4/(2(4 pi)^2); the t^0/a","claim_id":"ALPHA.QUILLEN.PROGRESS.02","dependencies_as_recorded":"ALPHA.QUILLEN.EXACT.01; ALPHA.QUILLEN.PROGRESS.01; SEAM.EQUIV.01; EM.WARD.01; v336; v341; v342; v382; v391","external_data_as_recorded":"-","id":"claim:ALPHA.QUILLEN.PROGRESS.02","location_as_recorded":"tfpt_1_architecture_e8","path":"verification/status_ledger.csv","row_number":456,"scripts_as_recorded":"v433_alpha_quillen_heatkernel.py","status_as_recorded":"Second honest step / grounding [E]/[O] (a solvable 4D model exhibiting the nonzero a_4 conformal-anomaly order + the v391<->v342 connection; the headline target stays OPEN, not closed)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] b1 = 41/6 (SM) = 41/10 (GUT) is the U(1)_Y a_4 heat-kernel coefficient of the carrier content (beta=a_4 theorem), grounding the counterterm's matter factor; the geometry factors as 8 b1 c3^6 = b1*(rank E8)*c3^6; the cubic factors as a^2(a-2c3^3) (a^3 = the first moment of the Chern density, a level). [C] residual (1) 'exact a_4 = 8 b1 c3^6' == residual (3) 'seam F-normalisation' (ONE obligation). [O] residual (2) the alpha^3 Chern level + ALPHA.QUILLEN.EXACT.01 stay open. A third honest step that grounds, reduces (3 residuals -> 1[C]+1[O]) and locates, it does not close; no new number, alpha^-1 stays [E].","checked_by_registry":false,"claim_excerpt":"A THIRD HONEST step on the external target ALPHA.QUILLEN.EXACT.01 (2026-06-28, v434): it settles the status of the three residuals named after v433 and shows they are NOT three independent open problems -- the target stays [O], alpha^-1 stays [E]. [E] b1 IS THE U(1) a_4 HEAT-KERNEL COEFFICIENT (the beta-function = a_4 theorem, Vassilevich): computed from the carrier hypercharge content with the standard spin weights ","claim_id":"ALPHA.QUILLEN.PROGRESS.03","dependencies_as_recorded":"ALPHA.QUILLEN.EXACT.01; ALPHA.QUILLEN.PROGRESS.01; ALPHA.QUILLEN.PROGRESS.02; EM.WARD.01; EM.WARD.02; v159; v216; v246; v341; v342; v382; v433","external_data_as_recorded":"-","id":"claim:ALPHA.QUILLEN.PROGRESS.03","location_as_recorded":"tfpt_1_architecture_e8","path":"verification/status_ledger.csv","row_number":457,"scripts_as_recorded":"v434_alpha_quillen_betafunction.py","status_as_recorded":"Third honest step / grounding+reduction [E]/[C]/[O] (b1 = the U(1) a_4 heat-kernel coefficient via beta=a_4; residuals 1&3 collapse to one seam F-normalisation [C]; residual 2 the alpha^3 Chern level located but [O]; the headline target stays OPEN)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the pi-power/metric-independence test isolates a^3 as the UNIQUE pi^0/c3^0 (metric-independent) term -- the signature of a topological level, NOT a Seeley-DeWitt curvature integral (the other two carry pi^3, pi^6); plus the dual ladder (coupling 3-n at c3-order 3n). [C] conditional on the CS/eta reading (EM1, v48) the a^3 coefficient is an integer level, =1 the unit level, not a free real. [O] the EM1 CS-boundary derivation + ALPHA.QUILLEN.EXACT.01 stay open; seam F-norm stays the one [C] (v434); alpha^-1 stays [E]. A fourth honest step that sharpens the only remaining [O]; no new number, Python-only.","checked_by_registry":false,"claim_excerpt":"A FOURTH HONEST step on the external target ALPHA.QUILLEN.EXACT.01 (2026-06-29, v435): it attacks the SINGLE remaining [O] left after v434 -- residual (2), the cubic alpha^3 Chern/Maxwell moment -- and SHARPENS it with a verifiable test plus a conditional typing, it does NOT close it; the target stays [O], alpha^-1 stays [E]. [E] pi-POWER / METRIC-INDEPENDENCE TEST: the three EM-closure coefficients carry pi-powers e","claim_id":"ALPHA.QUILLEN.PROGRESS.04","dependencies_as_recorded":"ALPHA.QUILLEN.EXACT.01; ALPHA.QUILLEN.PROGRESS.01; ALPHA.QUILLEN.PROGRESS.02; ALPHA.QUILLEN.PROGRESS.03; EM.WARD.01; EM.WARD.02; v48; v342; v382; v384; v433; v434","external_data_as_recorded":"-","id":"claim:ALPHA.QUILLEN.PROGRESS.04","location_as_recorded":"tfpt_1_architecture_e8","path":"verification/status_ledger.csv","row_number":458,"scripts_as_recorded":"v435_alpha_quillen_chernlevel.py","status_as_recorded":"Fourth honest step / metric-independence test + conditional level typing [E]/[C]/[O] (the pi-power test isolates a^3 as the unique pi^0/c3^0 metric-independent topological rung; conditional on the CS/eta reading the a^3 coefficient is an integer level, =1 the unit; the EM1 CS-boundary proof and the headline target stay OPEN)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the multi-size convergence (monotone Cauchy-like c1(L)->1) + the Richardson extrapolation to c=8 + the decreasing successive differences (numerical evidence the scaling limit exists and gives c=8); [O] the abstract continuum existence (cited MMST v336) and the (E8)_1-vs-SO(16)_1 holomorphy discriminator (v377/v378) stay open. Extends v376 from the value (two sizes) to the convergence (five sizes); strengthens v336's residual, does not close it.","checked_by_registry":false,"claim_excerpt":"An HONEST attack on the one open lemma of SEAM.EQUIV.01 -- the continuum scaling-limit existence (2026-06-24). It does NOT close v336 (the abstract existence is the cited MMST theorem); it STRENGTHENS the case with the existence-relevant observable v376 did not test: that the finite-size data CONVERGE (a divergent/drifting sequence would have no continuum limit). [E] MULTI-SIZE CONVERGENCE: the Calabrese-Cardy correl","claim_id":"SEAM.S3.SCALINGLIMIT.01","dependencies_as_recorded":"SEAM.EQUIV.CONTINUUM.01; v336; v367; v368; v376; v377; v378","external_data_as_recorded":"-","id":"claim:SEAM.S3.SCALINGLIMIT.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":459,"scripts_as_recorded":"v392_seam_s3_scalinglimit.py","status_as_recorded":"Scaling-limit convergence evidence [E] (the finite-size central charge converges to c=8 and Richardson-extrapolates there -- the existence-relevant observable) + the abstract existence stays [O] (cited MMST v336); an honest attack that strengthens, does not close","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the four computed bands (fixed-point 9/(128 pi^3)~0.227%, seam-gapped (2/3)^6~8.78%, QG cap 64/665~9.62%, exact-identity 0) + the external quoted bands; [C] the assembled numeric budget. A harvest of v388 into testable numbers (theoretical error bars); reuses the phi0 puncture, (2/3)^6 and the chi cap, introduces no new number.","checked_by_registry":false,"claim_excerpt":"The typed correction budget (v388) turned into ACTUAL first-correction magnitudes -- a computed theoretical-uncertainty surface (2026-06-24), the short-term testable harvest of v388: instead of merely TYPING each prediction's correction, this gives the NUMBER, so a parameter-free central value can be quoted as 'value +- computed first correction'. [E] FIXED-POINT band: the phi0-derived fixed points (theta12, theta13,","claim_id":"CORRECTIONS.NUMERIC.01","dependencies_as_recorded":"CORRECTIONS.BUDGET.01; v388; v337; v374; v212; v187","external_data_as_recorded":"-","id":"claim:CORRECTIONS.NUMERIC.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":460,"scripts_as_recorded":"v393_corrections_numeric.py","status_as_recorded":"Numeric correction budget [E]/[C] (the typed budget v388 as actual first-correction magnitudes: fixed-point 0.227%, seam-gapped 8.78%/QG-capped 9.62%, exact-identity 0, external quoted -- a computed theoretical-uncertainty surface)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the exact arithmetic (atoms=primes=fields; chi=3^6/(3^6-2^6); 2/3=|Z2|/N_fam; 4=|mu4|=2^2; 30=5x6); [C] the seam-as-universal-dynamic-engine reading. A re-reading of established atoms/eigenvalues (v390/v319), introduces no new number.","checked_by_registry":false,"claim_excerpt":"The clockwork coherence (2026-06-24, bird's-eye): the three Coxeter primes ARE the three anchor atoms ARE the three number-field facets, and the prime-2 seam is the common dynamical factor. A re-reading tying v390 (facets) to the anchor a=(1,1,2) and v319 (5x6 clock). [E] ANCHOR ATOMS = COXETER PRIMES: a=(1,1,2) has e3=2=|Z2|, p0=3=N_fam, e2=5=g_car, product 2*3*5=30=h(E8) -- the clock's three primes ARE the anchor's","claim_id":"COXETER.ATOMS.01","dependencies_as_recorded":"v314; v319; v383; v387; v390; v23; v53","external_data_as_recorded":"-","id":"claim:COXETER.ATOMS.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":461,"scripts_as_recorded":"v394_coxeter_atoms.py","status_as_recorded":"Clockwork coherence [E]/[C] (Coxeter primes = anchor atoms = facet fields; chi=3^6/(3^6-2^6); both dynamic rates carry prime-2; 30=5x6) -- a bird's-eye re-reading, no new number","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the coupled local rule + joint attractor + recovery hand + v324 spectral match + growth consistency; [O] the 3-arm seed (P2) and analytic phi0 remain irreducible. Unifies v299/v327/v324; not a derivation of phi0 or P2.","checked_by_registry":false,"claim_excerpt":"THE COUPLED HYPERGRAPH REWRITE -- ONE LOCAL RULE UNIFIES v299+v327+v324 (2026-06-24): carrier x family from a single coupled rewrite on a 9x3 labelled grid, not three hand-built pieces. [E] LOCAL COUPLED MICRO-RULE: one micro-step = network lazy diffusion on each cusp column + v327 M on each node's family vector; steps commute, T_micro = T_net (x) M (purely local on 27 cells). [E] JOINT ATTRACTOR: top eigenvalue 1 wi","claim_id":"HYP.COUPLED.01","dependencies_as_recorded":"v299; v312; v317; v324; v327","external_data_as_recorded":"-","id":"claim:HYP.COUPLED.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":462,"scripts_as_recorded":"v395_hypergraph_coupled.py","status_as_recorded":"Coupled hypergraph rewrite [E]/[O] (one local rule unifies carrier x family; joint attractor marks x e0; recovery (2/3)^6 after one hand; v324 fiber emerges as cusp readout; v299 growth unchanged) -- mechanism unified, phi0 + seed remain","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] exact combinatorial identities + Gauss-Bonnet + puncture negative; [C] tree-level seed reading; [O] puncture term. Sharpens v312/v395; does not close full phi0.","checked_by_registry":false,"claim_excerpt":"THE phi0 LEADING TERM FROM ICOSAHEDRAL COMBINATORICS (2026-06-24, sharpening v312/v395): the tree-level retained seed phibase = 1/(6 pi) has a forced combinatorial reading on the icosahedral hypergraph; the puncture 48 c3^4 stays analytic. [E] ICO COUNTS ANCHOR-FORCED: V=12, E=30=h(E8), F=20=g_car(g_car-1), |Aut|=120=4h=|2I| (all from {g_car,N_fam}={5,3}). [E] LEADING TERM EXACT: phibase = 1/(6 pi) = (4/3) c3 = F/(4 ","claim_id":"HYP.PHI0.01","dependencies_as_recorded":"v312; v216; v342; v327; v395","external_data_as_recorded":"-","id":"claim:HYP.PHI0.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":463,"scripts_as_recorded":"v396_phi0_icosahedral.py","status_as_recorded":"phi0 leading term [E]/[C]/[O] (phibase = F/(g_car N_fam) c3 = 1/(6 pi); F/h = |Z2|/N_fam; Gauss-Bonnet consistent; puncture 48 c3^4 still analytic) -- combinatorial reinterpretation, not full phi0 closure","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the exact split phi0 = 1/(6 pi) + 48 c3^4, the puncture count Omega_adm=N_fam dim S+=48, the closed form 3/(256 pi^4), the hypergraph negative (reused from v396/ARCH.QUAD.01, machine-checked); [O] the from-first-principles heat-kernel-contact-term proof (the named target); [C] a face of the seam boundary analysis, not a second independent gate. A typing/registration of v396's puncture residual; introduces no new number.","checked_by_registry":false,"claim_excerpt":"NAMES THE phi0 PUNCTURE TERM AS A TRACKED [O] HEAT-KERNEL TARGET (2026-06-24, v408): dtop = Omega_adm c3^4 = 48 c3^4 = 3/(256 pi^4) IS the order-4 (|mu4|) local boundary Seeley-DeWitt contact term of the mu4 puncture divisor, summed over Omega_adm = N_fam dim S+ = 48 admissible fermion states -- the analytic complement of the icosahedral tree term phibase (v396, HYP.PHI0.01). Elevates v396's flagged puncture residual","claim_id":"HYP.PHI0.PUNCTURE.01","dependencies_as_recorded":"HYP.PHI0.01; ARCH.QUAD.01; v396; v312; v216; v342; v391","external_data_as_recorded":"-","id":"claim:HYP.PHI0.PUNCTURE.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":464,"scripts_as_recorded":"v408_phi0_puncture_heatkernel.py","status_as_recorded":"Named target [E]/[O] (the phi0 puncture 48 c3^4 as the order-4 boundary Seeley-DeWitt contact term of the mu4 puncture, summed over Omega_adm=N_fam dim S+=48; a face of the seam boundary analysis, elevates v396's puncture residual to a citable target; no new gate)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the sheet involution/projector spectra carry no contraction rate in (0,1), so no prime-2-only attractor exists; [C] prime-2 is the universal dynamical parity factor (necessary, not autonomous), dynamics needs coupling to family-3 or carrier-5. Closes the v394 open question's falsifiable corollary; the full 'appears in every gap' universality stays the v383 reading. No new number.","checked_by_registry":false,"claim_excerpt":"CLOSED AS A STRUCTURAL LEMMA (2026-06-24, v409): prime-2 (the seam sheet involution) is NECESSARY but NOT autonomous, so no prime-2-only attractor exists -- resolving the v394 open question's falsifiable corollary. The facets are prime-2 (Q(i)/tau=i/Z4 seam deck, static) + prime-3 (Eisenstein zeta3 CP, static; (2/3)^6, dynamic) + prime-5 (golden, static; (phi+2)/4, dynamic). The prime-2 seam appears as the common FAC","claim_id":"RES.COXETER.SYMMETRY.01","dependencies_as_recorded":"COXETER.ATOMS.01; v314; v383; v390; v394","external_data_as_recorded":"-","id":"claim:RES.COXETER.SYMMETRY.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":465,"scripts_as_recorded":"v394_coxeter_atoms.py; v409_coxeter_prime2_lemma.py","status_as_recorded":"Structural lemma [E]/[C] (prime-2 necessary, not autonomous: the sheet involution has spectrum {+-1} and projector {0,1}, none in (0,1), so no prime-2-only attractor; reuses established atoms, no new number) -- closes the v394 open-question corollary","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the involution/projector eigenvalue lemmas + the no-contraction-rate corollary + the dynamical reading, machine-proved in TfptCarrier/CoxeterPrime2.lean (axiom-pure: only the three standard kernel axioms). Upgrades v409 to the Lean tier; no new number.","checked_by_registry":false,"claim_excerpt":"LEAN 4 FORMALISATION of the RES.COXETER.SYMMETRY.01 falsifiable corollary (2026-06-24): new module TfptCarrier/CoxeterPrime2.lean machine-proves 'no prime-2-only attractor exists', upgrading the v409 Python check to a Lean theorem. [E] involution_eigenvalue: r*r=1 -> r in {1,-1}; idempotent_eigenvalue: r*r=r -> r in {0,1}; involution_not_contraction / idempotent_not_contraction: neither set meets the open interval (0","claim_id":"FORM.COXETER.PRIME2.01","dependencies_as_recorded":"RES.COXETER.SYMMETRY.01; COXETER.ATOMS.01; v394; v409","external_data_as_recorded":"Lean 4 + Mathlib","id":"claim:FORM.COXETER.PRIME2.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":466,"scripts_as_recorded":"v409_coxeter_prime2_lemma.py","status_as_recorded":"Lean formalisation [E] (no prime-2-only attractor: involution eigenvalues +-1, projector {0,1}, none in (0,1), while 2/3 is a contraction rate; axiom-pure) -- machine-proves the v409 corollary","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the three exact clock matches (A_Lambda=2*5; Koide=(|Z2|/N_fam)^6; axion=pi*N_fam/g_car) + the proton C_p non-uniqueness (multiple simple values in its +-5.3% band => non-discriminating => external); [C] the verdict that the external residue shrinks to essentially C_p. A falsifiable probe (the answer could have been '0 on the clock'); refuses to assign C_p a clock value (anti-numerology); reuses established atoms/rates, introduces no new number.","checked_by_registry":false,"claim_excerpt":"A FALSIFIABLE probe of how external the 'external physics' really is (2026-06-24): do the frontier scheme-numbers land on the {2,3,5} clock (= the anchor atoms |Z2|,N_fam,g_car, v394) or not? Strict No-Free-Pattern discipline (v100): 'on the clock' means an EXACT match to a ratio/power of {2,3,5}/golden, NOT a wide-band fit. [E] eta_B DECUPLE: A_Lambda=10=|Z2|*g_car=2*5=p3(anchor) ON CLOCK (v212). [E] KOIDE RATE: the","claim_id":"FR.CLOCK.PROBE.01","dependencies_as_recorded":"v100; v187; v211; v212; v303; v374; v394","external_data_as_recorded":"PDG/lattice C_p, alpha_s","id":"claim:FR.CLOCK.PROBE.01","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":467,"scripts_as_recorded":"v397_external_clock_probe.py","status_as_recorded":"Clock probe of the frontier [E]/[C] (3 of 4 'external' scheme-numbers -- A_Lambda, Koide rate, axion spine -- land EXACTLY on the {2,3,5} clock; only the proton C_p is genuinely external; a falsifiable anti-numerology test)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the RP-definability hinge (OS canonical transfer + quasi-free) + the band-limited character-block-diagonal core swept N=4..64 (hardens v177/v199 beyond H^1) + the holomorphy=>(E8)_1 arithmetic (det Cartan 1 vs 4, c=8, index 4); [O] the full-L^2 / intrinsic-Bisognano-Wichmann step (G_net's irreducible analytic residual). A contract+evidence consolidation (genre of v275/v343/v384/v392); NOT a closure of SEAM.EQUIV.01 (continuum=cited MMST v336); no new number.","checked_by_registry":false,"claim_excerpt":"THE SEAM STATE RIGIDITY THEOREM AS ONE NAMED TARGET (2026-06-24, Paper A / the G_net closure contract): consolidates the scattered state-invariance reductions (v177/v198/v199/v308/v309/v335) into a single citable theorem and HARDENS the finite-block evidence to a multi-mode sweep. Does NOT close SEAM.EQUIV.01 (the continuum scaling-limit existence stays the cited MMST/Adamo step, v336/v392). [E] RP-DEFINABILITY HINGE","claim_id":"SEAM.RIGIDITY.01","dependencies_as_recorded":"SEAM.EQUIV.01; v54; v155; v177; v198; v199; v308; v309; v335; v83; v154; v336","external_data_as_recorded":"-","id":"claim:SEAM.RIGIDITY.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":468,"scripts_as_recorded":"v398_seam_state_rigidity.py","status_as_recorded":"Seam State Rigidity contract+evidence [E]/[O] (Paper A: the G_net keystone as one named theorem -- RP-definability hinge + band-limited mu4-character core swept N=4..64 + holomorphy=>(E8)_1; the one residual = full-L^2 / intrinsic BW). NOT a closure of SEAM.EQUIV.01","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the parameter-free local-equation coefficients (8pi=1/c3, Lambda prefactor 3/(4pi^2)) + the redundancy discriminators (det 1 vs 4, GSD=1, Petz (2/3)^6, margin 1.648) + the O_phys-subset-A_Sigma enumeration over 5 readout classes; [C] the completeness verdict; [O] SEAM.EQUIV.01 + intrinsic BW (no new gate). A completion-accounting module (genre of v384); no construction, no new number.","checked_by_registry":false,"claim_excerpt":"GRAVITY-COMPLETE = BOUNDARY-COMPLETE + AMBIENT-REDUNDANCY (2026-06-24, Paper B / the gravity closure accounting): the explicit verdict combining the parameter-free LOCAL field equation (v358/v359) and the ambient REDUNDANCY (v369). Does NOT construct the ambient measure and does NOT close SEAM.EQUIV.01. [E] LOCAL EQUATION PARAMETER-FREE: G_ab+Lambda g_ab=(1/c3)T_ab with 1/c3=8pi (the four c3-roles consistent: Unruh 1","claim_id":"GRAVITY.COMPLETE.01","dependencies_as_recorded":"GRAV.NONLINEAR.01; QGAMB.REDUNDANCY.01; QG.AMB.01; v358; v359; v369; v60; v36; v54","external_data_as_recorded":"-","id":"claim:GRAVITY.COMPLETE.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":469,"scripts_as_recorded":"v399_gravity_complete.py","status_as_recorded":"Gravity-completeness accounting [E]/[C]/[O] (Paper B: the explicit verdict = local parameter-free equation + ambient redundancy; O_phys subset A_Sigma over 5 readout classes; residual = SEAM.EQUIV.01 + intrinsic BW, no new gate)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the one-pole/ghost-free pole algebra + the monotone truncation-zero fact (v380) + the IR R+R^2 matching with the atom-fixed scale c3^7 + the carrier-atom scale exponent 7; [O] the entire-a analyticity assumption + perturbative-only (not the ambient measure). A contract + IR-matching module; consolidates v304/v370/v380/v386; no new number.","checked_by_registry":false,"claim_excerpt":"THE NONLOCAL SPECTRAL-GRAVITY ACTION; LOCAL R+R^2 IS ITS IR PROJECTION (2026-06-24, Paper C / the 4D gravity-action contract): consolidates v304/v370/v380/v386 and adds the IR-matching check. Does NOT prove the entire-analyticity of the resummed form factor (stays the cited heat-kernel resummation, the [O] of v304/v380); PERTURBATIVE only. [E] ENTIRE FORM FACTOR -> ONE POLE: the dressed spin-2 propagator 1/(p^2 a) wi","claim_id":"GRAV.NONLOCAL.01","dependencies_as_recorded":"GRAV.AMPLITUDE.01; GRAV.LOOP.FINITE.01; v304; v370; v380; v386; v36; v28; v253; v369","external_data_as_recorded":"-","id":"claim:GRAV.NONLOCAL.01","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":470,"scripts_as_recorded":"v400_grav_nonlocal_action.py","status_as_recorded":"Nonlocal-gravity action contract [E]/[O] (Paper C: the entire form factor gives a ghost-free one-pole propagator whose IR projection is exactly the atom-scaled R+R^2; the entire-a assumption + perturbative-only stay [O]). Consolidates v304/v370/v380/v386, adds the IR-matching check","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the input-set reduction to {a,pi,v_geo} + the dimensional bookkeeping (mass/1G/Lambda/U_point/(m/mu)=number x v_geo^{1,2,4,1,0}) + gravity-adds-no-unit; [N] the 0.11% G-vs-Lambda over-determination (conditional, v274); [O] the theorem-forbidden typing (TOE_strict = TOE_dimensionless + [v_geo]). A metrology end-cap (consolidates v153/v274/v364/v384); no new derivation, no new number.","checked_by_registry":false,"claim_excerpt":"THE FINAL INPUT SET {a, pi, v_geo} CERTIFIED (2026-06-24, Paper D / the scale-modulus closure): 0 dimensionless dials + 1 dimensionful unit, consolidating v153 (No-Unit), v274 (over-determined anchor), v364 (gravity adds no unit), v384 (v_geo is theorem-forbidden, type B). Does NOT 'solve' v_geo (a dimensionless compiler provably cannot output a scale); it CERTIFIES the single declared unit. [E] INPUT SET: a=(1,1,2) ","claim_id":"METROLOGY.CLOSURE.01","dependencies_as_recorded":"RESIDUAL.CERTIFICATION.01; ANCHOR.VGEO.01; v153; v274; v364; v384","external_data_as_recorded":"-","id":"claim:METROLOGY.CLOSURE.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":471,"scripts_as_recorded":"v401_metrology_closure.py","status_as_recorded":"Metrology closure [E]/[N]/[O] (Paper D: the final input set {a,pi,v_geo} -- 0 dimensionless dials + 1 unit; dimensional bookkeeping over all dimensionful observables; G-vs-Lambda over-determination 0.11%; v_geo theorem-forbidden). A metrology end-cap, no new derivation","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the functor composition law (each sector factors source->threshold->RG->observable) + the exact atom sources (Q_src; A_Lambda=10, delta=4pi/3; f_a=M_scal/128; b3=-7) + the kill-test coverage for all four; [C] the frontier firewall (physical predictions stay conditional, only the algebraic source is [E], never re-pressed into the compiler). A consolidation of the FR.*.SOLVE solvers; no new number.","checked_by_registry":false,"claim_excerpt":"THE F_transfer FUNCTOR CERTIFICATE (2026-06-24, Paper E / the physical-interface contract): the four frontier sectors are ONE functor F_transfer = F_observable o F_threshold o F_RG, consolidating the typed solvers (FR.POLE.SOLVE.01, FR.BOLTZMANN.SOLVE.01, FR.RELIC.SOLVE.01, FR.QCD.BUDGET.01). Does NOT re-press any frontier observable into the compiler (forbidden by the frontier firewall, v187); it certifies the compo","claim_id":"FTRANSFER.SUITE.01","dependencies_as_recorded":"FR.POLE.SOLVE.01; FR.BOLTZMANN.SOLVE.01; FR.RELIC.SOLVE.01; FR.QCD.BUDGET.01; v9; v93; v164; v185; v187; v211; v212; v262","external_data_as_recorded":"-","id":"claim:FTRANSFER.SUITE.01","location_as_recorded":"tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":472,"scripts_as_recorded":"v402_ftransfer_suite.py","status_as_recorded":"F_transfer functor certificate [E]/[C] (Paper E: the four frontier sectors as one F_observable o F_threshold o F_RG with exact atom sources + kill-test coverage + the firewall; physical predictions stay conditional). A consolidation, no new number","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the field arithmetic (independence => degree 8 = rank E8; Galois (Z/2)^3; the 7 subfields = 4 imaginary (|mu4|) + 3 real (N_fam); ramified only at {2,3,5}=the atoms; the E8-special 2^omega(h)=rank with the E7 negative control); [C] the arithmetic-hull reading and the 7-subfields<->7-slices candidate. A synthesis composing the established facet fields (v390/v394), introduces no new number; the prime set {2,3,5} forced by h(E8)=30.","checked_by_registry":false,"claim_excerpt":"The three number-field facets COMPOSE to a degree-8 = rank(E8) abelian field (2026-06-24): K=Q(i,sqrt-3,sqrt5), the arithmetic hull dual to the E8 lattice hull, composing the v390/v394 facets that were only ever used one at a time. [E] INDEPENDENCE: the squarefree parts -1,-3,5 are multiplicatively independent in Q*/(Q*)^2 (no nonempty subset product is a square), so the three quadratics are linearly disjoint and [K:","claim_id":"ARITH.HULL.01","dependencies_as_recorded":"COXETER.PRIME2.01; COXETER.ATOMS.01; v23; v390; v394; v222","external_data_as_recorded":"-","id":"claim:ARITH.HULL.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":473,"scripts_as_recorded":"v403_facet_compositum.py","status_as_recorded":"Arithmetic hull [E]/[C] (the three facet fields compose to K=Q(i,sqrt-3,sqrt5): degree 2^3=8=rank E8, Galois (Z/2)^3, 7 subfields = 4 imaginary (|mu4|) + 3 real (N_fam), ramified only at {2,3,5}; 2^omega(h)=rank is E8-special) -- a synthesis, no new number","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the modular arithmetic (chi^3=j; j(i)=1728, chi(i)=12; j(omega)=0, chi(omega)=0; the two-elliptic-point uniqueness); [C] the seam/flavor rigidity reading and the dual-keystone candidate. Extends v282 to the second CM point; core values j=1728/j=0 already mirrored (v214/v220/v267/v282), so Python-only by the synthesis convention; no new number.","checked_by_registry":false,"claim_excerpt":"The (E8)_1 vacuum character at the two CM points (2026-06-24): chi_E8 = E4/eta^8 = j^{1/3} equals 12 at the seam CM point tau=i and 0 at the family CM point tau=omega, extending v282 (chi_E8(i)=12) to the second elliptic point. [E] chi_E8^3=j (q-series). [E] SEAM tau=i (Q(i), order 4): cross-ratio 2 => j=1728 => chi_E8(i)=1728^{1/3}=12 (E8 present, v282/v214). [E] FAMILY tau=omega (Q(sqrt-3), order 6): the equianharm","claim_id":"E8.CMDUAL.01","dependencies_as_recorded":"QGAMB.UNIFY.01; v282; v214; v220; v267; v390","external_data_as_recorded":"-","id":"claim:E8.CMDUAL.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":474,"scripts_as_recorded":"v404_e8_char_cm_duality.py","status_as_recorded":"E8 character CM-duality [E]/[C] (chi_E8(i)=12 vs chi_E8(omega)=0: the (E8)_1 character maximal at the seam tau=i, zero at the family tau=omega; the two are the only elliptic points so the values are forced) -- the seam/flavor rigidity duality, extends v282","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the arithmetic (chi_E8(omega)=0; A2 Cartan det 3=N_fam, h=3; the E6xA2 slice with det R=8=dim A2; delta=the tau=omega CM phase; cusp weights=the order-3 deck); [C] the dual-keystone reading; [O] the canonical-map Z3 choice (v140) + the v_geo-class scale. A named contract (genre of v286/v398), reuses established facts; NOT a closure; no new number.","checked_by_registry":false,"claim_excerpt":"The dual keystone at tau=omega (2026-06-24): the family/flavor sector as the order-3 Eisenstein/A2 face of E8, dual to the seam=(E8)_1 at tau=i (SEAM.EQUIV.01/v404). A NAMED CONTRACT (genre of v286/v398), NOT a closure. [E] chi_E8(omega)=j(omega)^{1/3}=0 (E4 vanishes at tau=omega, v404) vs chi_E8(i)=12 -- the family sits where the holomorphic (E8)_1 structure degenerates. [E] A2 is the tau=omega Eisenstein/hexagonal ","claim_id":"SEAM.EQUIV.02","dependencies_as_recorded":"E8.CMDUAL.01; SEAM.EQUIV.01; v404; v220; v233; v72; v69; v137; v140","external_data_as_recorded":"-","id":"claim:SEAM.EQUIV.02","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":475,"scripts_as_recorded":"v405_seam_equiv_omega.py","status_as_recorded":"Dual keystone at tau=omega [E]/[C]/[O] (the family/flavor sector as the order-3 Eisenstein/A2 face: chi_E8(omega)=0, A2 Cartan det 3=N_fam reads R in E6xA2 with det R=8=dim A2, delta=the tau=omega CM phase, cusp weights=the order-3 deck; dual to the seam=(E8)_1 at tau=i). A named contract, NOT a closure","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the three angles + the scale-reduction to one seesaw ratio; [C] the CP-phase origin via the tau=omega keystone (upgrades v270's [O] to a keystone consequence) + the derived J=-0.0297 + the net closure (zero free flavor dials beyond v_geo); [O] the seesaw operator realisation / v_geo-class scale (v272/v184) + the NO floor kill test. A closure-accounting building on v405; no new number.","checked_by_registry":false,"claim_excerpt":"The PMNS dynamics closed modulo the tau=omega keystone (2026-06-24): the CP-phase ORIGIN is the family CM point (v405) and the absolute scale is one v_geo-class unit, so PMNS has zero free flavor dials beyond v_geo. Resolves the two [O]'s v270 left open (the assembled phase + the open scale). [E] the three angles sin^2 th12=1/3-phi0/2 (v9), th23=45 (v9), sin^2 th13=phi0 e^{-5/6} (v268) assemble to one exactly-unitary","claim_id":"FLAV.PMNS.CLOSE.01","dependencies_as_recorded":"SEAM.EQUIV.02; FLAV.PMNS.03; FLAV.NUSCALE.01; v405; v270; v272; v9; v268; v153","external_data_as_recorded":"NuFIT 6.0 (delta_CP; angles)","id":"claim:FLAV.PMNS.CLOSE.01","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":476,"scripts_as_recorded":"v406_pmns_phase_origin.py","status_as_recorded":"PMNS closed modulo the keystone [E]/[C]/[O] (CP-phase origin = the tau=omega CM phase v405; angles [E]; J=-0.0297 derived; absolute scale = one seesaw ratio = v_geo; zero free flavor dials beyond v_geo). Resolves v270's open phase + scale","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the frame/pairings (v139) + the new identification n.a=8=dim A2=det R and {2,8,121}=the tau=omega family-slice atoms; [C] the reduction of R4' to SEAM.EQUIV.02; [O] the lone flagged residue why 11=||Pl(K)||_1. A reduction tying the selector residue to the dual keystone; reuses v139's exact data; no new number.","checked_by_registry":false,"claim_excerpt":"The R4' selector residue folds into the tau=omega keystone (2026-06-24): the three (d,n) selector pairings ARE the tau=omega family-slice atoms, so deriving the selector pair reduces to the family sector being the E6 x A2 (tau=omega) object (v405). [E] the frame (1,a,sigma) is a Z^3 basis with det(1|a|sigma)=11=||Pl(K)||_1, and n=(5,-9,6) is the unique covector with n.1=2, n.a=8, n.sigma=121=11^2 -> (d,n)=>R columnwi","claim_id":"FLAV.SELECTOR.CLOSE.01","dependencies_as_recorded":"SEAM.EQUIV.02; FLAV.RIGID.01; v405; v139; v136; v42","external_data_as_recorded":"-","id":"claim:FLAV.SELECTOR.CLOSE.01","location_as_recorded":"tfpt_1","path":"verification/status_ledger.csv","row_number":477,"scripts_as_recorded":"v407_dn_pairings_omega.py","status_as_recorded":"R4' selector folds into the keystone [E]/[C]/[O] (the (d,n) pairings {2,8,121}={|Z2|, rank E8=dim A2=det R, ||Pl(K)||_1^2} are the tau=omega family-slice atoms; n.a=8=dim A2 reads R in E6xA2; deriving (d,n) folds into SEAM.EQUIV.02; residue = why 11)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity","checked_by_registry":false,"claim_excerpt":"The sheet generator V is a binary internal compiler (2026-06-24): the rank-2 sheet axis V=Q diag(0,1,1) of the centered cross (v95/v218) has powers that print the binary carrier spine. [E] CLOSED FORM (induction F(n)*V=F(n+1)): V^n={{0,2^(n-1),0},{0,2^n,0},{0,2^(n+1)-2,1}}, so V^n.1=(2^(n-1),2^n,2^(n+1)-1)=(1,2,3),(2,4,7),(4,8,15),(8,16,31),... [E] BILINEAR FAMILIES (exact in n, 1=(1,1,1), a=(1,1,2)): 1.V^n.1=7*2^(n-","claim_id":"SHEET.GEN.BINARY.01","dependencies_as_recorded":"FLAV.KQ.01; v95; v218; v135","external_data_as_recorded":"-","id":"claim:SHEET.GEN.BINARY.01","location_as_recorded":"tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":478,"scripts_as_recorded":"v410_sheet_generator_binary.py","status_as_recorded":"Sheet generator V is a binary compiler [E]/[C]: V^n closed form + V^n.1 binary spine + four bilinear families (6,7,9,11; 13,27,55,56); spine FORCED by Spec(V)={0,1,2}, Lie/theta readings audit-typed [C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity","checked_by_registry":false,"claim_excerpt":"The quark u/d ratio is a pure V-power readout (2026-06-24): the established c_u/c_d=g_car*||Pl(K)||_1/(N_fam^2 Delta_Q)=55/117 (v94) re-expresses EXACTLY via the sheet generator V (v410). [E] c_u/c_d=(1.V^4.1)/((a.V.1)(1.V^2.1))=55/(9*13)=55/117, with 55=1.V^4.1, 9=a.V.1=N_fam^2, 13=1.V^2.1=Delta_Q. [E] IDENTITY: same number as 5*11/(9*13); the V-power numerator repackages g_car*11=55=1.V^4.1. [C] HONEST TYPING: an e","claim_id":"FLAV.UD.VPOWER.01","dependencies_as_recorded":"FLAV.QUARK.01; FLAV.RIGID.01; v94; v410","external_data_as_recorded":"-","id":"claim:FLAV.UD.VPOWER.01","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":479,"scripts_as_recorded":"v411_ud_ratio_vpower.py","status_as_recorded":"u/d ratio as a V-power readout [E]/[C]: c_u/c_d=(1.V^4.1)/((a.V.1)(1.V^2.1))=55/117, identical to 5*11/(9*13); exact re-encoding, value stays [C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity","checked_by_registry":false,"claim_excerpt":"The sheet source corner J (2026-06-24): the determinant surface has two s-independent iso-volume walls (v135) t=-1 (det=4=|mu4|, carries K) and t=-2 (det=2=|Z2|); the operator on the Z2 wall, J:=M(1,-2)=C-2V=((4,1,0),(4,1,2),(5,1,1)), was unnamed and completes the sheet axis J,K,C,F=M(1,-2..1). [E] CLEAN CHAR POLY: chi_J=lam^3-6lam^2+3lam-2 => (tr,e2,det)=(6,3,2)=(|R^+(A3)|,N_fam,|Z2|). [E] RESOLVENT/ANCHOR: a.J.a=30","claim_id":"DIAMOND.SHEET.SOURCE.J.01","dependencies_as_recorded":"FLAV.KQ.01; v135; v95","external_data_as_recorded":"-","id":"claim:DIAMOND.SHEET.SOURCE.J.01","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":480,"scripts_as_recorded":"v412_sheet_source_corner_J.py","status_as_recorded":"Sheet source corner J=M(1,-2) on the Z2 wall [E]/[C]: chi_J=(6,3,2), a.J.a=30=h(E8), det(I+J)=12, det(2I+J)=40; readings audit-typed","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity","checked_by_registry":false,"claim_excerpt":"The sheet axis is a discrete characteristic-difference calculator (2026-06-24): on M_t=C+tV (v95/v218) the elementary-symmetric coefficients encode atoms as DIFFERENCE ORDERS. [E] e1(t)=3t+12, e2(t)=2t^2+15t+25, e3(t)=det M_t=4t^2+14t+14 => Delta e1=3=N_fam, Delta^2 e2=4=|mu4|, Delta^2 e3=8=rank E8 (the e3 curvature cross-cited to v218/v224; the full (e1,e2,e3) ladder is new). [E] ANCHOR-ENERGY LADDER: a.M_t.a=52+11t","claim_id":"DIAMOND.SHEET.CALCULUS.01","dependencies_as_recorded":"FLAV.KQ.01; v218; v224; v410","external_data_as_recorded":"-","id":"claim:DIAMOND.SHEET.CALCULUS.01","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":481,"scripts_as_recorded":"v413_sheet_characteristic_calculus.py","status_as_recorded":"Sheet axis = characteristic-difference calculator [E]/[C]: Delta e1=3, Delta^2 e2=4, Delta^2 e3=8; anchor energy 52+11t (30->41->52->63); readings audit-typed","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity","checked_by_registry":false,"claim_excerpt":"The center C is a resolvent portal G2 -> F4 -> E8 (2026-06-24): the center C=M(1,0) (v95) is the t=0 evaluation of V; its shifted determinants climb the exceptional ladder. [E] CENTER INVARIANTS (v95): tr C=12=dim g_SM=chi_E8(i), det C=14=dim G2, sum C=31=2^g_car-1=248/8. [E] RESOLVENT LADDER: det(C)=14=dim G2, det(I+C)=52=dim F4, det(2I+C)=120=|R^+(E8)| -- the exceptional shell ladder G2->F4->E8^+ as det(C+kI), k=0,","claim_id":"DIAMOND.CENTER.RESOLVENT.01","dependencies_as_recorded":"FLAV.KQ.01; v95; v230","external_data_as_recorded":"-","id":"claim:DIAMOND.CENTER.RESOLVENT.01","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":482,"scripts_as_recorded":"v414_center_resolvent_portal.py","status_as_recorded":"Center C resolvent portal [E]/[C]: det C=14=dim G2, det(I+C)=52=dim F4, det(2I+C)=120=|R^+(E8)| (G2->F4->E8^+); reading audit-typed","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity","checked_by_registry":false,"claim_excerpt":"The square CM-norm dictionary is operator-realised and the mu4 deck is intrinsic (2026-06-25): the Gaussian arithmetic of v222/v230 lifted from numbers to OPERATORS via J=[U,V]/3, the complex structure born from the commutator of the binary V and ternary U compilers (v410/v95). [E] J=((-1,1,0),(-2,1,0),(-3,1,0)) integer, Spec(J)={i,-i,0}, J^2=-I on the rank-2 image, J^3+J=0 (a mu4 quarter-turn). [E] 3I+2J has spectru","claim_id":"DIAMOND.GAUSS.01","dependencies_as_recorded":"CMNORM.DUAL.01; CENTER.NORM.01; SHEET.GEN.BINARY.01; FORM.QGEO.02; v222; v230; v410; v95; v146; v140","external_data_as_recorded":"-","id":"claim:DIAMOND.GAUSS.01","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":483,"scripts_as_recorded":"v415_gaussian_operator.py","status_as_recorded":"Gaussian operator [E]/[C]: J=[U,V]/3 is the mu4 quarter-turn (J^2=-I), 3+2i/5+4i are eigenvalues of 3I+2J/5I+4J (norms 13=Delta_Q/41=10 b1), the norms become operator identities, intrinsic order-4 deck D=-I+J-J^2 with chi2=ker[U,V]=a-1; geometric-deck match sharpens (not closes) the v140 Z3 residue [C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity","checked_by_registry":false,"claim_excerpt":"The atom trichotomy (2026-06-25): {2,3,5} are ramified/inert/split in the two exceptional CM rings, and each atom is the unique ramified prime of one quadratic facet of K=Q(i,sqrt-3,sqrt5) (v403). Sharpens v222/v230 (atoms read only as CM norms) and v390/v394/v403 (the three facets) into one prime-splitting table. [E] Z[i] (square/seam, tau=i): 2=|Z2| RAMIFIES (2=-i(1+i)^2), 3=N_fam INERT (3 mod 4, norm 9=N_fam^2), 5","claim_id":"ARITH.TRICHOTOMY.01","dependencies_as_recorded":"ARITH.HULL.01; CMNORM.DUAL.01; COXETER.ATOMS.01; COXETER.PRIME2.01; v403; v222; v390; v394; v313","external_data_as_recorded":"-","id":"claim:ARITH.TRICHOTOMY.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":484,"scripts_as_recorded":"v416_atom_trichotomy.py","status_as_recorded":"Atom trichotomy [E]/[C]: {2,3,5} ram/inert/split in Z[i] (2 ram, 3 inert, 5 split) vs Z[omega] (3 ram, 2,5 inert); the ramified prime of each ring = its atom; each atom is the unique ramified prime of one facet of Q(i,sqrt-3,sqrt5), product 30=h(E8); seam/flavor/golden reading [C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity","checked_by_registry":false,"claim_excerpt":"The Eisenstein/CP operator -- the hexagonal dual of the Gaussian seam operator v415 (2026-06-25): where v415 put the SQUARE seam (tau=i, mu4) on operators via J=[U,V]/3, this puts the HEX/flavor side (tau=omega, mu3/mu6) on operators and unifies both with the seam into ONE order-30 Coxeter clock. [E] EISENSTEIN DECK: the family rotation P=(1 2 3) has P^3=I, chi_P=x^3-1, P^2+P+I=ONES, so on the plane perp to (1,1,1) i","claim_id":"DIAMOND.EISEN.01","dependencies_as_recorded":"DIAMOND.GAUSS.01; CMNORM.DUAL.01; CENTER.NORM.01; FLAV.CP.01; v415; v222; v230; v233; v316; v320; v404; v95","external_data_as_recorded":"-","id":"claim:DIAMOND.EISEN.01","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":485,"scripts_as_recorded":"v417_eisenstein_cp_operator.py","status_as_recorded":"Eisenstein/CP operator [E]/[C]: the family rotation P realises the hex norm 7=N_omega(3+2omega) via (3I+2P)(3I+2P^2)={7,7,25} (dual of v415's {13,13,9}); the CP clock W=-P^2 (W^2=P, W^3=-I, Spec {-1,zeta6,zeta6^-1}) gives delta_CKM=pi/3, delta_PMNS=4pi/3; all flavor clocks are zeta30-powers, the seam mu4 the Galois side phi(30)=8=rank E8; the carrier mu5 has no 3x3 operator [C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity","checked_by_registry":false,"claim_excerpt":"The cyclotomic norm triple (2026-06-25): the carrier split (3,2) read in the three atom-rings gives (7,13,55)=(scalaron, Delta_Q, quark numerator), and the missing CARRIER-5 clock of v417 is found as the 4x4 Phi5-companion C5 (Z[zeta5], rank phi(5)=4). [E] CARRIER-5 CLOCK: C5 has chi=x^4+x^3+x^2+x+1, C5^5=I, tr=-1 (the four primitive 5th roots); the GOLDEN ratio is its real-part data zeta5+zeta5^4=2cos(72)=(sqrt5-1)/","claim_id":"ARITH.NORMTRIPLE.01","dependencies_as_recorded":"ARITH.TRICHOTOMY.01; CMNORM.DUAL.01; DIAMOND.GAUSS.01; DIAMOND.EISEN.01; FLAV.QUARK.01; v416; v222; v415; v417; v411; v410; v14; v313","external_data_as_recorded":"-","id":"claim:ARITH.NORMTRIPLE.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":486,"scripts_as_recorded":"v418_cyclotomic_norm_triple.py","status_as_recorded":"Cyclotomic norm triple [E]/[C]: the carrier split (3,2) over the three atom-rings Z[omega],Z[i],Z[zeta5] gives det(3I+2 Comp(Phi_{3,4,5}))=(7,13,55)=(scalaron,Delta_Q,quark numerator); the carrier-5 clock is the 4x4 Phi5-companion C5 (golden in its 2cos values, N(3+2 zeta5)=55=quark numerator); NEG control anchor (5,4)->(21,41,461) fails in the carrier ring; (3,2) FORCED (v14) not unique, but the UNIQUE CROSS-SECTOR seed -- only (3,2)->(7,13,55) spans gravity/flavor/masses while (2,1)->(3,5,11) is all-core [C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity","checked_by_registry":false,"claim_excerpt":"The seam mu4 IS the carrier's Galois group (2026-06-25): a positive resolution of the v409/RES.COXETER.SYMMETRY.01 cyclic/Galois asymmetry. In the cyclotomic picture the flavor clocks (sheet/family/carrier/CP) are powers of zeta30 (cyclic side, order h(E8)=30), but the seam mu4 (i) sits on the Galois side (Z/30)^x (order rank E8=8); v409 flagged this as 'prime-2 is the Galois bridge'. [E] 30=2*3*5 SQUAREFREE => Z/30 ","claim_id":"SEAM.GALOIS.01","dependencies_as_recorded":"RES.COXETER.SYMMETRY.01; ARITH.NORMTRIPLE.01; ARITH.HULL.01; CMNORM.DUAL.01; v409; v418; v403; v316; v223; v415","external_data_as_recorded":"-","id":"claim:SEAM.GALOIS.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":487,"scripts_as_recorded":"v419_seam_galois_carrier.py","status_as_recorded":"Seam mu4 = carrier's Galois group [E]/[C]: 30 squarefree => no order-4 cyclic, so the seam mu4 is the Galois side (Z/30)^x=mu4 x Z2; the mu4 factor IS (Z/5)^x=Gal(Q(zeta5)) (carrier), the Z2 IS (Z/3)^x (family/CP); the Frobenius zeta5->zeta5^2 is the explicit order-4 operator G with G C5 G^-1=C5^2, G^4=I; resolves the v409 asymmetry (seam = automorphism, not a hand) [C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Physical","checked_by_registry":false,"claim_excerpt":"F_pole, the external side (2026-06-25): the Koide source->pole transfer is a ONE-LOOP ELECTROMAGNETIC effect, not an algebraic step -- the honest 'do the external physics' follow-up to v93 (which left the source->pole flow time t~2.84 as an undetermined [P] generator) and to the clock No-Go (the unitary/algebraic lens cannot reach a contraction rate). [E] KOIDE RESCALING INVARIANCE: Q(m)=sum m/(sum sqrt m)^2 is degre","claim_id":"FR.POLE.QED.01","dependencies_as_recorded":"FR.KOIDE.04; FR.KOIDE.05; CONTRACT.F.01; FR.POLE.SOLVE; v93; v82; v327; v371; v187","external_data_as_recorded":"PDG 2024 lepton pole masses; alpha (v3)","id":"claim:FR.POLE.QED.01","location_as_recorded":"tfpt_4","path":"verification/status_ledger.csv","row_number":488,"scripts_as_recorded":"v420_fpole_qed_running.py","status_as_recorded":"F_pole external [E]/[C]/[O]: the Koide source->pole transfer is a one-loop EM effect; Koide is rescaling-invariant (Q(c*m)=Q(m)) so the shift is flavor-split; the tree->pole gap 0.0022 is one-loop-EM-sized (=phi0/24 to 0.6%, =alpha/pi to ~5%), pole at 2/3 (IR attractor); a 1-loop QED per-lepton-log estimate shifts Koide by EM-loop order toward 2/3; the exact flow time t~2.84 is scheme-dependent external QED, only sized; F_pole stays [C], firewalled (v187) -- rate forced (v327/v82), flow external","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Lattice","checked_by_registry":false,"claim_excerpt":"The Galois<->Net bridge (2026-06-25): the seam mu4 = Gal(Q(zeta5)) is the SAME cyclic Z/4 as the (E8)_1 simple-current glue -- NOT a mere order-4 coincidence -- connecting the Galois gearbox of v419 to G_net/SEAM.EQUIV.01. [E] CARRIER GLUE CYCLIC Z/4: disc(A3)=coker(Cartan A3)=Z/4 and disc(D5)=Z/4 (one Smith invariant factor 4 = CYCLIC, not Klein), det=4 each; the D_n discriminant is Z/4 for n ODD and Z2xZ2 for n EVE","claim_id":"SEAM.GALOIS.NET.01","dependencies_as_recorded":"SEAM.GALOIS.01; SEAM.EQUIV.01; E8.GLU.01; GATE.METRIC.06; ARITH.HULL.01; v419; v1; v89; v154; v92; v281; v403; v428","external_data_as_recorded":"-","id":"claim:SEAM.GALOIS.NET.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":489,"scripts_as_recorded":"v422_galois_net_bridge.py","status_as_recorded":"Galois<->Net bridge / four-fold mu4 identity [E]/[C]: the seam mu4=Gal(Q(zeta5))=(Z/5)^x is the SAME cyclic Z/4 as the (E8)_1 glue <(1,1)> AND the discriminant disc(A3)=disc(D5)=Z/4 (D5 cyclic because rank 5 odd; D8 even=Klein control); only the carrier prime 5 gives (Z/p)^x=Z/4; glue order 4 => 16/4^2=1=E8 (vs Klein/order-2 => D8 det 4); cyclic Z/4 selects E8, Klein excluded -- the v419 Galois gearbox IS the holomorphic net's glue, a direct Galois->G_net bridge. Deck/divisor=Galois=discriminant=simple-current is a compression per v428 (one object read four ways), not four witnesses [C]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical","checked_by_registry":false,"claim_excerpt":"The No-Ambient-Dependency certificate (2026-06-25): no frozen TFPT readout is COMPUTED from the ambient QG measure QG.AMB.01 -- sharpening the v369/v384 prose redundancy ('QG.AMB.01 is a [C] redundancy, not dynamics') into a machine-checked DAG+script fact, told HONESTLY. [E] GAP-DECOUPLING MARGIN: 2 dim(E8) c3^2 = 31/(4 pi^2) (31=2^g_car-1) ~ 0.785, Delta = 6 ln(3/2) ~ 2.433, so Delta_eff ~ 1.648 > 0 (v76/v337); chi","claim_id":"QGAMB.NODEP.01","dependencies_as_recorded":"QG.AMB.01; DECOUPLING.THEOREM.01; SEAM.EQUIV.01; v337; v369; v384","external_data_as_recorded":"-","id":"claim:QGAMB.NODEP.01","location_as_recorded":"tfpt_4","path":"verification/status_ledger.csv","row_number":490,"scripts_as_recorded":"v423_no_ambient_dependency.py","status_as_recorded":"No-Ambient-Dependency [E]/[C]: no frozen readout is computed from QG.AMB.01 -- it is a certification SINK (every dependent is a gravity-gate/QG row, no prediction), not a value source (script '-'; predictions computed by v3/v7/v9/v268, never an ambient-measure script), and its only predictive link is theta13's architectural 4D-QFT contract edge (coherence, not numerical); the gap margin Delta_eff~1.648>0 decouples its back-reaction (v337). v369 prose -> machine-checked DAG/script fact [E]; verdict [C], does NOT prove SEAM.EQUIV.01","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical","checked_by_registry":false,"claim_excerpt":"The (LTO-RP) reduction of the keystone (2026-06-25): an HONEST MMST-style reduction of SEAM.EQUIV.01's one open lemma -- the raw collar's intrinsic Bisognano-Wichmann property (the residual of v308/v309) -- to the recent commuting-projector theorem of Naaijkens-Penneys-Wallick [NPW26, arXiv:2605.10693], with the central mapping CORRECTED and the two open sub-steps made explicit. Does NOT close SEAM.EQUIV.01. [E] CORR","claim_id":"SEAM.EQUIV.LTORP.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.EQUIV.CHAIN.01; QGEO.MODHAM.01; v308; v309; v302; v240; v214; v267; v199","external_data_as_recorded":"NPW26 (arXiv:2605.10693)","id":"claim:SEAM.EQUIV.LTORP.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":491,"scripts_as_recorded":"v424_seam_lto_rp_reduction.py","status_as_recorded":"(LTO-RP) keystone reduction [E]/[C]: SEAM.EQUIV.01's intrinsic-BW lemma reduced to the cited NPW26 commuting-projector theorem, mapping corrected -- (LTO-RP)=u_Theta=J=intrinsic BW (theta K theta=-K), NOT omega o rho=omega; the mu4 clock is a modular symmetry [rho,K]=0 (sigma^psi=rho type-wrong); A-and-NOT-B refutes clock-invariance => (LTO-RP). Make-or-break: NPW26 prove (LTO-RP) for topologically-ordered models (trace/anyonic), the seam is invertible (|det E8|=1) + beta=1 KMS (not a trace), in neither bucket. REDUCTION not closure; two open sub-steps (Z/2-reflection commuting-projector LTO realisation; invertible-KMS (LTO-RP)). SEAM.EQUIV.01 stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical","checked_by_registry":false,"claim_excerpt":"The single-flow reduction of F_transfer (2026-06-25): the four frontier transfers (F_pole, F_Boltzmann, F_relic, F_QCD) do NOT each need a separate external solver -- their DYNAMICS is the ONE native flow of the theory (the seam modular/recovery semigroup, v238/v240, gap 6 ln(3/2)) restricted to each sector. Native flow + EXTERNAL ANCHORS, firewall-clean (the observable stays [C] until the anchor is supplied). [E] TH","claim_id":"DYN.TRANSFER.UNIVERSAL.01","dependencies_as_recorded":"CONTRACT.F.01; DYN.SEMIGROUP.01; DYNAMICS.UNIVERSAL.01; QCD.LAMBDA.01; v238; v240; v99; v320; v159; v383","external_data_as_recorded":"-","id":"claim:DYN.TRANSFER.UNIVERSAL.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":492,"scripts_as_recorded":"v425_dyn_transfer_universal.py","status_as_recorded":"Single-flow reduction [E]/[C]: the four F_transfer flows are the ONE v238 recovery semigroup restricted to sectors (native gap 6 ln(3/2), native rates e^{-Delta}=(2/3)^6, b3=-7); F_pole=v99 generator at q=2, F_Boltzmann washout=that contraction (CP 4pi/3 native), F_QCD rate native -- only the ANCHORS (v_geo/C_p/M_R) external; F_relic's cosmological IC theta_i the one wall. Reduction not internalisation, firewall-clean; extends v383 static->dynamic","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical","checked_by_registry":false,"claim_excerpt":"The invertible beta=1-KMS variant of (LTO-RP) (2026-06-25): the one corner Naaijkens-Penneys-Wallick [NPW26, arXiv:2605.10693] leave open -- they prove (LTO-RP) only for TOPOLOGICALLY ORDERED commuting-projector models (Toric Code via a TRACE state; Levin-Wen anyonic), while the TFPT seam is the opposite corner (invertible, holomorphic (E8)_1, no anyons, AND a beta=1 KMS state, not a trace). A constructive finite-dim","claim_id":"SEAM.EQUIV.LTORP.KMS.01","dependencies_as_recorded":"SEAM.EQUIV.LTORP.01; SEAM.EQUIV.01; SEAM.EQUIV.CHAIN.01; QGEO.MODHAM.01; v424; v309; v302; v240; v214","external_data_as_recorded":"NPW26 (arXiv:2605.10693)","id":"claim:SEAM.EQUIV.LTORP.KMS.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":493,"scripts_as_recorded":"v426_seam_lto_rp_kms.py","status_as_recorded":"Invertible beta=1-KMS (LTO-RP) [E]/[C]: the corner NPW26 leave open (they do topologically-ordered; the seam is invertible + KMS, not a trace) is constructively satisfiable -- a gapped reflection-symmetric mu4-even collar has Theta K Theta=-K (u_Theta=J) and [rho,K]=0, so (LTO-RP) holds by direct Tomita-Takesaki; |det E8|=1 (no anyons), state not a trace; neg controls have teeth. Advances v424 sub-step (ii); SEAM.EQUIV.01 stays [O] (continuum sub-step (i) remains), finite-dim witness not continuum theorem","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical","checked_by_registry":false,"claim_excerpt":"The multiply-vs-compress FRAMEWORK for over-determination (2026-06-25; classification refined by v428/OVERDET.WITNESS.RECLASS.01): a reviewer's methodological correction made machine-explicit -- 'every independent restriction multiplies the implausibility of coincidence' is true ONLY for witnesses from genuinely DISJOINT grammars; witnesses that are projections of the SAME generator count as COMPRESSION, not Bayesian","claim_id":"OVERDET.WITNESS.MAP.01","dependencies_as_recorded":"E8.REVERSE.AUDIT.01; ARITH.HULL.01; SEAM.GALOIS.01; CAR.PASCAL.01; TOPO.BRIESKORN.01; ARCH.CORE.01; v415; v417; v418; v419; v422; v45; v53","external_data_as_recorded":"-","id":"claim:OVERDET.WITNESS.MAP.01","location_as_recorded":"tfpt_safeguards","path":"verification/status_ledger.csv","row_number":494,"scripts_as_recorded":"v427_overdet_witness_map.py","status_as_recorded":"Witness map [E]/[C]: disjoint grammars multiply, same-generator projections compress; the seven arithmetic witnesses are refined by v428 to COMPRESSION (facets of one (2,3,5)/E8 object, v236). The genuine multiplication is the multiply-forced inputs + foreign witnesses (alpha^-1~137); coincidence is expensive for the discrete core; does not by itself establish physics","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity","checked_by_registry":false,"claim_excerpt":"The honest correction of v427 (2026-06-25): applying v427's own multiply-vs-compress test to v427 itself. [E] THE ONE GENERATOR (v236/TOPO.BRIESKORN.01): the (2,3,5) Brieskorn singularity generates E8/Coxeter-30 -- Milnor mu=(2-1)(3-1)(5-1)=8=rank E8, 30=2*3*5=h(E8), phi(30)=8. [E] WITNESS RE-CLASSIFICATION: each of v427's seven witnesses maps to a facet of that SAME object (primes 2,3,5 of 30, the clock 30, or E8), ","claim_id":"OVERDET.WITNESS.RECLASS.01","dependencies_as_recorded":"OVERDET.WITNESS.MAP.01; TOPO.BRIESKORN.01; ARCH.CORE.01; v305; v313","external_data_as_recorded":"-","id":"claim:OVERDET.WITNESS.RECLASS.01","location_as_recorded":"tfpt_safeguards","path":"verification/status_ledger.csv","row_number":495,"scripts_as_recorded":"v428_overdet_reclass.py","status_as_recorded":"Witness re-classification [E]/[C]: v427's seven arithmetic witnesses are facets of ONE (2,3,5)/E8 object (v236) => compression, not seven multiplications. The genuine multiplication is the '8' forced four independent ways (rank E8, h(D5), phi(30), Milnor) + the foreign alpha^-1~137. Honest correction of v427 (consistent with v305/v236/v313)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical","checked_by_registry":false,"claim_excerpt":"The half-sided modular inclusion (Borchers/Wiesbrock) as an INTRINSIC Bisognano-Wichmann route (2026-06-30) for face (ii) of SEAM.EQUIV.01 -- geometric modular flow WITHOUT presupposing covariance. Complementary to v323/v426 (which assume a rotation-covariant covariance) and to the Adamo-Giorgetti-Tanimoto covariance theorem. The standard-pair criterion (Borchers/Wiesbrock/Longo): a pair (K,P) with K self-adjoint (De","claim_id":"SEAM.EQUIV.BW.HSMI.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.EQUIV.LTORP.01; SEAM.EQUIV.LTORP.KMS.01; QGEO.MODHAM.01; v323; v426; v309","external_data_as_recorded":"Borchers/Wiesbrock half-sided modular inclusion; Longo standard pairs; Adamo-Giorgetti-Tanimoto (arXiv:2508.07109)","id":"claim:SEAM.EQUIV.BW.HSMI.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":496,"scripts_as_recorded":"v438_seam_hsmi_borchers.py","status_as_recorded":"Half-sided modular inclusion [E]/[C]: a Longo standard pair (P>=0, [K,P]=P, J:JKJ=-K, JPJ=P_-) is a +half-sided modular inclusion, so by Borchers the seam modular flow is geometric INTRINSICALLY (no covariance presupposed); face (ii) becomes a structure consequence. Finite witnesses: ladder algebra exact, sl(2,R) positivity, BW reflection; neg control indefinite boost. SEAM.EQUIV.01 stays [O] (continuum standard pair = continuum existence, same wall as MMST/NPW26)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical","checked_by_registry":false,"claim_excerpt":"The Lieb-Robinson/Nachtergaele-Sims continuum-existence MOTOR for the gapped seam collar (2026-06-30) -- grounds the BULK half of the cited MMST existence (SEAM.MMST.INCLASS.01/v336) in the explicit v367 p+ip lattice model, narrowing the open analytic step to the chiral EDGE scaling limit. [E] UNIFORM GAP: the collar gap is independent of N (Delta(N)=const>0 across N=20..160), the lattice image of the OS transfer gap","claim_id":"SEAM.EQUIV.CONTINUUM.LR.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.MMST.INCLASS.01; SEAM.S3.RP.01; SEAM.EQUIV.CONTINUUM.03; v367; v336; v302; v329","external_data_as_recorded":"Lieb-Robinson/Nachtergaele-Sims bounds; MMST (scaling limit)","id":"claim:SEAM.EQUIV.CONTINUUM.LR.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":497,"scripts_as_recorded":"v439_seam_lieb_robinson.py","status_as_recorded":"Lieb-Robinson motor [E]/[C]: the gapped p+ip collar (v367) has a uniform-in-N gap, exponential clustering with N-independent xi, and a finite light cone, so by Nachtergaele-Sims its bulk thermodynamic limit EXISTS -- grounding the bulk half of the cited MMST existence in OUR model. SEAM.EQUIV.01 stays [O], the open step narrowed to the chiral massless edge scaling limit","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical","checked_by_registry":false,"claim_excerpt":"The beta-interpolation connecting the NPW26-PROVEN trace case (beta=0) to the seam's beta=1 KMS case along an obstruction-free homotopy (2026-06-30) -- upgrading the single-point v426 witness for v424 sub-step (ii) to a PATH argument. NPW26 prove (LTO-RP) for the TRACE state (beta=0, C=1/2); the TFPT seam is the beta=1 KMS state; v426 showed (LTO-RP) holds AT beta=1; this module shows it holds ALONG the whole interpo","claim_id":"SEAM.EQUIV.LTORP.BETA.01","dependencies_as_recorded":"SEAM.EQUIV.LTORP.01; SEAM.EQUIV.LTORP.KMS.01; SEAM.EQUIV.01; v424; v426","external_data_as_recorded":"NPW26 (arXiv:2605.10693)","id":"claim:SEAM.EQUIV.LTORP.BETA.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":498,"scripts_as_recorded":"v440_seam_lto_rp_beta.py","status_as_recorded":"beta-interpolation [E]/[C]: the (LTO-RP)/BW data (Theta K Theta=-K, [rho,K]=0) are beta-independent; along the whole path C_beta=1/(1+e^{beta K}) from the NPW26 trace (beta=0) to the seam KMS (beta=1) every covariance is reflection-related, mu4-invariant and valid, norm-continuous, no obstruction -- a PATH argument for v424 (ii), stronger than v426. SEAM.EQUIV.01 stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical","checked_by_registry":false,"claim_excerpt":"The applicability ledger (2026-06-30) -- a hypothesis-by-hypothesis audit of the THREE external theorems the seam keystone cites (MMST scaling limit, NPW26 (LTO-RP), Adamo-Giorgetti-Tanimoto covariance), isolating the SINGLE genuinely-imported analytic fact. Answers the reviewer worry that the cited theorems may carry hidden hypotheses, by classifying every hypothesis as either a TFPT-internal computed fact (with its","claim_id":"SEAM.EQUIV.APPLICABILITY.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.MMST.INCLASS.01; SEAM.EQUIV.LTORP.01; SEAM.EQUIV.LTORP.KMS.01; v424; v426; v440; v336; v154; v215","external_data_as_recorded":"MMST; NPW26 (arXiv:2605.10693); Adamo-Giorgetti-Tanimoto (arXiv:2508.07109)","id":"claim:SEAM.EQUIV.APPLICABILITY.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":499,"scripts_as_recorded":"v441_seam_applicability_ledger.py","status_as_recorded":"Applicability ledger [E]/[C]: a hypothesis-by-hypothesis audit of MMST/NPW26/Adamo finds 11 of 12 hypotheses are TFPT-internal computed facts and exactly 1 is external -- the continuum existence of the chiral massless scaling limit; covariance is an Adamo consequence (defuses v215), not an input. SEAM.EQUIV.01's external dependence is pinned to ONE analytic fact; stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical","checked_by_registry":false,"claim_excerpt":"The uniform-in-N hardening of the Seam State Rigidity Theorem (2026-06-30; hardens SEAM.RIGIDITY.01/v398) -- the band-limited mu4-character rigidity is NOT a small-N artifact. v398 verified [rho,K]=0 by a finite sweep N=4..64; this module makes it uniform in N and adds an N-independent rigidity bound. [E] EXACT UNIFORM 4-SECTOR COMMUTATION: rho=diag(i^n) has EXACTLY 4 distinct eigenvalues {1,i,-1,-i} for ALL N (an or","claim_id":"SEAM.RIGIDITY.UNIFORM.01","dependencies_as_recorded":"SEAM.RIGIDITY.01; SEAM.EQUIV.01; QGEO.MODHAM.01; v398; v439; v309; v199","external_data_as_recorded":"MMST (rigidity/scaling limit)","id":"claim:SEAM.RIGIDITY.UNIFORM.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":500,"scripts_as_recorded":"v442_seam_rigidity_uniform.py","status_as_recorded":"Uniform-in-N rigidity [E]/[C]: the band-limited mu4-character rigidity of v398 is uniform in N -- exact 4-sector commutation to N=256, a uniform gap, and an N-independent clock-breaking lower bound ||[rho,V]||=2; not a small-N artifact. SEAM.RIGIDITY.01/SEAM.EQUIV.01 stays [O] (the full-L^2 forcing is the cited rigidity/MMST step)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Lattice","checked_by_registry":false,"claim_excerpt":"The empirical/structural DISCRIMINATOR bundle (2026-06-30; mode D of the v347 closure-mode classification) -- concrete FALSIFIABLE kill tests separating the claimed seam=(E8)_1 from the nearest c=8 rival SO(16)_1=(D8)_1. v347 lists four closure modes; mode D is 'test the consequences', realised here as sharp discriminators. [E]/[X] PRIMARY/GSD DISCRIMINATOR: |det Cartan(E8)|=1 (ONE primary, holomorphic) vs |det Carta","claim_id":"SEAM.E8.DISCRIMINATOR.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.EQUIV.CLOSURE.01; SEAM.S3.MODULAR.01; v347; v90; v89; v281; v422","external_data_as_recorded":"-","id":"claim:SEAM.E8.DISCRIMINATOR.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":501,"scripts_as_recorded":"v443_seam_e8_discriminator.py","status_as_recorded":"E8 vs SO(16) kill tests [E]/[X]: mode D of v347 realised as discriminators -- torus GSD 1 vs 4, level-1 currents 248 vs 120, lattice theta 240 vs 112 norm-2 roots; c=8 alone does NOT decide (v277), only det K=1 (genus-1, v90) selects E8. Falsifiable: a seam with GSD>1 falsifies (E8)_1. SEAM.EQUIV.01 stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical","checked_by_registry":false,"claim_excerpt":"The CHIRAL EDGE scaling-limit MOTOR (2026-06-30) -- the edge half of the one SEAM.EQUIV.01 continuum residual, attacking exactly the step v439 left open. v439 grounded the BULK thermodynamic limit (uniform gap, exponential clustering, finite light cone) and explicitly narrowed the open analytic step to the chiral massless EDGE scaling limit; this module attacks THAT residual on the SAME explicit v367/v368 p+ip collar","claim_id":"SEAM.EQUIV.CONTINUUM.EDGE.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.MMST.INCLASS.01; SEAM.EQUIV.CONTINUUM.LR.01; SEAM.S3.SCALINGLIMIT.01; SEAM.EQUIV.CONTINUUM.02; v367; v368; v376; v392; v336; v439","external_data_as_recorded":"MMST (scaling limit); bulk-edge correspondence / anomaly inflow","id":"claim:SEAM.EQUIV.CONTINUUM.EDGE.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":502,"scripts_as_recorded":"v444_seam_edge_scaling.py","status_as_recorded":"Chiral edge scaling motor [E]/[C]: the v367/v368 lattice edge carries the conformal data of a chiral c=1/2 Majorana CFT (linear chiral dispersion v~0.98 with opposite per-edge velocities; algebraic edge correlator eta~1 vs exponential bulk; trivial-phase neg control; N-stable Cauchy scaling-collapse), so the 16-copy edge is a chiral c_-=8 (E8)_1 CFT -- grounding the EDGE half of the cited MMST scaling limit the way v439 grounds the bulk. SEAM.EQUIV.01 stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Formal","checked_by_registry":false,"claim_excerpt":"LEAN 4 FORMALISATION of the Borchers/Wiesbrock standard-pair algebra (2026-06-30; the kernel-hardening of v438/SEAM.EQUIV.BW.HSMI.01) -- new module TfptCarrier/SeamStandardPair.lean, lake build OK, #print axioms CLEAN. It kernel-checks the four standard-pair RELATIONS on the centred 5-mode ladder over Z: [F] boost-translation commutator [K,P]=P (boost_translation_comm), [F] reflection involution J^2=1 (reflection_inv","claim_id":"FORM.SEAM.BW.HSMI.01","dependencies_as_recorded":"SEAM.EQUIV.BW.HSMI.01; SEAM.EQUIV.01; FORM.SEAM.MMST.01; v438","external_data_as_recorded":"Borchers/Wiesbrock half-sided modular inclusion; Longo standard pairs","id":"claim:FORM.SEAM.BW.HSMI.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":503,"scripts_as_recorded":"lean4-carrier-rigidity/TfptCarrier/SeamStandardPair.lean","status_as_recorded":"Formal [F] (Lean kernel; the standard-pair relations kernel-proved axiom-free, the Borchers step + continuum input named axioms)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical","checked_by_registry":false,"claim_excerpt":"The rigidity FORCING theorem (2026-06-30; upgrades v442/SEAM.RIGIDITY.UNIFORM.01 from 'permit' to 'force') -- v442 (and v398) established that a mu4-block-diagonal K commutes with the order-4 clock rho=diag(i^n); this module proves the CONVERSE and exact structure, isolating the single remaining physical premise. [E] FORCING (commute <=> block-diagonal, EXACT): for rho=diag(i^n), [rho,K]=0 iff K_ij=0 whenever i!=j mo","claim_id":"SEAM.RIGIDITY.FORCING.01","dependencies_as_recorded":"SEAM.RIGIDITY.01; SEAM.RIGIDITY.UNIFORM.01; SEAM.EQUIV.01; QGEO.SYM.01; v442; v398; v54; v281; v154; v351; v323; v335","external_data_as_recorded":"-","id":"claim:SEAM.RIGIDITY.FORCING.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":504,"scripts_as_recorded":"v445_seam_rigidity_forcing.py","status_as_recorded":"Rigidity FORCING [E]/[C]: commuting with the order-4 mu4 clock is EXACTLY mu4-block-diagonality (entrywise iff swept N=4..128; exact commutant dim sum n_s^2 < N^2; off-block slack zero; the order-2 commutant is strictly larger; 4 distinct eigenvalues), upgrading v442's 'permit' to 'force'. The single residual is the physical transfer lying in the commutant (clock-invariance=QGEO.SYM.01); SEAM.RIGIDITY.01/SEAM.EQUIV.01 stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Formal","checked_by_registry":false,"claim_excerpt":"LEAN 4 FORMALISATION of the applicability ledger (2026-06-30; the kernel-hardening of v441/SEAM.EQUIV.APPLICABILITY.01) -- new module TfptCarrier/SeamApplicabilityLedger.lean, lake build OK, #print axioms CLEAN. It turns the audit COUNT into a kernel-checked combinatorial fact: of the 12 cited-theorem hypotheses (MMST/NPW26/Adamo, mirrored from the v441 LEDGER in order), exactly 11 are TFPT-internal and exactly 1 ext","claim_id":"FORM.SEAM.APPLICABILITY.01","dependencies_as_recorded":"SEAM.EQUIV.APPLICABILITY.01; SEAM.EQUIV.01; FORM.SEAM.MMST.01; v441","external_data_as_recorded":"MMST; NPW26 (arXiv:2605.10693); Adamo-Giorgetti-Tanimoto (arXiv:2508.07109)","id":"claim:FORM.SEAM.APPLICABILITY.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":505,"scripts_as_recorded":"lean4-carrier-rigidity/TfptCarrier/SeamApplicabilityLedger.lean","status_as_recorded":"Formal [F] (Lean kernel; the 11-internal/1-external audit count + MMST arithmetic kernel-proved axiom-free, the one external fact named)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical","checked_by_registry":false,"claim_excerpt":"DERIVING clock-invariance ('transfer in the commutant') from RP-symmetry (2026-06-30; closes the single residual of v445/SEAM.RIGIDITY.FORCING.01 one notch further) -- v445 reduced rigidity to the OPERATOR statement [rho,Lambda_Sigma]=0 (clock-invariance); this module shows that commutation is itself a CONSEQUENCE of a STRUCTURAL symmetry (mu4-invariance of the seam RP data, the four Gauss-Bonnet marks) via the OS ca","claim_id":"SEAM.RIGIDITY.CLOCKINV.01","dependencies_as_recorded":"SEAM.RIGIDITY.FORCING.01; SEAM.RIGIDITY.01; SEAM.EQUIV.01; QGEO.SYM.01; v445; v442; v54; v258; v216; v323","external_data_as_recorded":"-","id":"claim:SEAM.RIGIDITY.CLOCKINV.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":506,"scripts_as_recorded":"v446_seam_clock_invariance.py","status_as_recorded":"Clock-invariance derived [E]/[C]: [rho,Lambda]=0 is a CONSEQUENCE of mu4-symmetry of the RP data (the four marks) via OS reconstruction (v54) + the modular formula (v258) -- the OS canonical transfer of mu4-symmetric data inherits the clock (swept N, iff-sharp neg control), is a contraction, and its modular Hamiltonian commutes with the clock. With v445 this reduces the rigidity residual from an operator commutation to 'the RP data is mu4-symmetric' (QGEO.SYM.01); SEAM.EQUIV.01 stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical","checked_by_registry":false,"claim_excerpt":"An INDEPENDENT (topological) reading of the edge central charge c_-=8 (2026-06-30) -- corroborating v444/SEAM.EQUIV.CONTINUUM.EDGE.01 from a different observable. v444 read c_- from the CORRELATOR exponent (eta=1); this module reads the SAME c_-=8 from the bulk TOPOLOGY (Chern number) + the bulk-edge correspondence, a robust integer that does not depend on any fit, on the same v367/v368 p+ip collar. [E] INTEGER CHERN","claim_id":"SEAM.EQUIV.EDGE.CHERN.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.EQUIV.CONTINUUM.EDGE.01; v444; v367; v368; v376","external_data_as_recorded":"bulk-edge correspondence / anomaly inflow","id":"claim:SEAM.EQUIV.EDGE.CHERN.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":507,"scripts_as_recorded":"v447_seam_edge_chern.py","status_as_recorded":"Independent topological c_-=8 [E]/[C]: the M=1 collar has integer Chern C=+1 (FHS, no fit; C=0 trivial, C=-1 opposite chirality), the open strip carries |C|=1 chiral edge branch per boundary, and the Li-Haldane entanglement spectrum tracks the edge; bulk-edge gives c_-=16*(1/2)*1=8=g_car+N_fam, corroborating v444 from a different observable. SEAM.EQUIV.01 stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical","checked_by_registry":false,"claim_excerpt":"Pinning the ONE external MMST fact empirically (2026-06-30) -- the edge FOUR-point function is quasi-free and conformally convergent, extending v444's two-point scaling limit to the next order. v441 isolated the keystone's single EXTERNAL hypothesis (continuum existence of the chiral scaling limit, MMST); v444 grounded it at the TWO-point level; this module takes the FOUR-point step on the same v367/v368 collar. [E] ","claim_id":"SEAM.EQUIV.EDGE.FOURPOINT.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.EQUIV.CONTINUUM.EDGE.01; SEAM.EQUIV.APPLICABILITY.01; v444; v441; v336","external_data_as_recorded":"MMST (scaling limit)","id":"claim:SEAM.EQUIV.EDGE.FOURPOINT.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":508,"scripts_as_recorded":"v448_seam_edge_fourpoint.py","status_as_recorded":"External MMST fact pinned at 4-point [E]/[C]: the edge four-point is quasi-free (G^2=G) and Cauchy-convergent to the free-fermion conformal cross-ratio 2+sqrt(3) (vs an off-scale exponential bulk control), extending v444's two-point scaling limit to 4-point order. The one external MMST existence fact is empirically supported at both orders; SEAM.EQUIV.01 stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Formal","checked_by_registry":false,"claim_excerpt":"LEAN 4 FORMALISATION of the rigidity FORCING converse (2026-06-30; the kernel-hardening of v445/SEAM.RIGIDITY.FORCING.01, also hardening v442/SEAM.RIGIDITY.UNIFORM.01) -- new module TfptCarrier/SeamRigidityForcing.lean, lake build OK, #print axioms CLEAN. It kernel-checks the load-bearing forcing algebra over Fin 4 / Z: [F] commutator_zero_iff (the ENTRYWISE forcing clock4 a = clock4 b <=> a=b, i.e. i^a=i^b <=> a==b ","claim_id":"FORM.SEAM.RIGIDITY.FORCING.01","dependencies_as_recorded":"SEAM.RIGIDITY.FORCING.01; SEAM.RIGIDITY.UNIFORM.01; SEAM.EQUIV.01; v445; v442","external_data_as_recorded":"Lean 4 + Mathlib (v4.29.1; #print axioms = propext/Classical.choice/Quot.sound for the kernel facts + the named operator premise)","id":"claim:FORM.SEAM.RIGIDITY.FORCING.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":509,"scripts_as_recorded":"lean4-carrier-rigidity/TfptCarrier/SeamRigidityForcing.lean","status_as_recorded":"Formal [F] (Lean kernel; the entrywise forcing iff (uniform in N), the exact commutant dimension and the order discriminator kernel-proved axiom-free, the operator-level clock-invariance named)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical","checked_by_registry":false,"claim_excerpt":"UNIFORM-IN-N control of the edge scaling limit (2026-06-30) -- the empirical content of the cited MMST uniform-convergence theorem (the single residual of SEAM.EQUIV.01 after v444/v447/v448), strengthened on the same v367/v368 p+ip collar. v444 grounded the two-point, v448 the four-point, each at a SINGLE conformal cross-ratio; this module adds the UNIFORMITY the abstract theorem actually asserts. [E] CROSS-RATIO A C","claim_id":"SEAM.EQUIV.MMST.UNIFORM.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.EQUIV.CONTINUUM.EDGE.01; SEAM.EQUIV.EDGE.FOURPOINT.01; v444; v448; v336; v367; v368","external_data_as_recorded":"MMST (uniform convergence)","id":"claim:SEAM.EQUIV.MMST.UNIFORM.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":510,"scripts_as_recorded":"v449_seam_mmst_uniform.py","status_as_recorded":"Uniform-in-N edge convergence [E]/[C]: two independent edge four-point cross-ratios converge to distinct conformal values (2+sqrt(3) and 2) at one 1/N rate (|Q-Q_inf|*N bounded by a single constant), vs an off-scale bulk control -- the empirical content of the cited MMST uniform-convergence theorem; SEAM.EQUIV.01 stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical","checked_by_registry":false,"claim_excerpt":"A THIRD independent reading of the edge central charge c_-=8 (2026-06-30) -- the Calabrese-Cardy entanglement scaling, after v444 (correlator) and v447 (topology). For a critical 1D free-fermion chain the Calabrese-Cardy law S(ell)=(c/3)ln[(L/pi)sin(pi ell/L)]+const fixes the central charge. [E] CALABRESE-CARDY LAW: the block entanglement entropy of the critical XX (Dirac) chain has a flat log slope -> c_Dirac=1.000 ","claim_id":"SEAM.EQUIV.EDGE.ENTANGLEMENT.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.EQUIV.CONTINUUM.EDGE.01; SEAM.EQUIV.EDGE.CHERN.01; v444; v447","external_data_as_recorded":"-","id":"claim:SEAM.EQUIV.EDGE.ENTANGLEMENT.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":511,"scripts_as_recorded":"v450_seam_edge_entanglement.py","status_as_recorded":"Entanglement c_-=8 [E]/[C]: the Calabrese-Cardy law gives c_Dirac=1=2*(1/2) for the critical free-fermion chain (vs a saturating gapped control), so c_Majorana=1/2 and c_-=16*(1/2)=8=g_car+N_fam -- a third independent reading of the edge central charge after v444/v447; SEAM.EQUIV.01 stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical","checked_by_registry":false,"claim_excerpt":"The Cardy finite-size conformal TOWER (2026-06-30) -- the edge spectrum reproduces the EXACT Ising primary dimensions {1/16,1/2}, naming the edge CFT. v450 fixed the central charge c=1/2; this module reads the OPERATOR CONTENT from the finite-size spectrum (Cardy: E_n - E_0 = (2 pi v / L) x_n). On the critical uniform Majorana ring (the v367/v368 edge universality class). [E] SPIN DIMENSION h_sigma=1/16: the periodic","claim_id":"SEAM.EQUIV.EDGE.CARDY.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.EQUIV.CONTINUUM.EDGE.01; SEAM.EQUIV.EDGE.ENTANGLEMENT.01; SEAM.EQUIV.EDGE.CHERN.01; v444; v450; v447","external_data_as_recorded":"-","id":"claim:SEAM.EQUIV.EDGE.CARDY.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":512,"scripts_as_recorded":"v451_seam_edge_cardy_tower.py","status_as_recorded":"Cardy tower {1/16,1/2} [E]/[C]: the edge finite-size spectrum reproduces the exact Ising chiral primary dimensions h_sigma=1/16 (R-NS split) and h_epsilon=1/2 (NS pair gap), L-independent (conformal 1/L scaling); with c=1/2 (v450) the edge is the Ising/Majorana CFT, 16 copies => c_-=8=g_car+N_fam; SEAM.EQUIV.01 stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity","checked_by_registry":false,"claim_excerpt":"The (E8)_1 torus MODULAR DATA (2026-06-30) -- one primary, S-invariant, T-phase e^{-2pi i/3}, the holomorphic c=8 signature, extending v156's character q-expansion to the modular transformation data. A holomorphic (single-primary) RCFT must have its torus character transform as a weight-0 modular form: S-invariant and T-multiplied by e^{-2 pi i c/24}. [E] S-INVARIANCE: chi(-1/tau)=chi(tau) for chi=E4/eta^8 (weight 0)","claim_id":"SEAM.EQUIV.E8.MODULAR.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.EQUIV.EDGE.CHERN.01; v156; v444; v281; v336","external_data_as_recorded":"-","id":"claim:SEAM.EQUIV.E8.MODULAR.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":513,"scripts_as_recorded":"v452_seam_e8_modular.py","status_as_recorded":"(E8)_1 modular data [E]/[C]: the character chi=E4/eta^8 is S-invariant (one primary), T-multiplies by e^{-2pi i/3} (=e^{-2pi i c/24}, c=8) and has leading power q^{-1/3} (c=8=0 mod 8, holomorphic) -- the full torus modular signature of the seam (E8)_1 net; SEAM.EQUIV.01 stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity","checked_by_registry":false,"claim_excerpt":"DERIVING the mu4-symmetry of the seam RP data (QGEO.SYM.01) from the four marks (2026-06-30) -- the LAST structural premise of the rigidity chain folded into the existing realisation premise. After v446 the rigidity residual was 'the seam RP data is mu4-symmetric' (QGEO.SYM.01); this module shows it is NOT an independent premise. [E] THE MARKS ARE mu4: the four Gauss-Bonnet marks are exactly {1,i,-1,-i} = roots of z^","claim_id":"SEAM.RIGIDITY.MU4FROMMARKS.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.RIGIDITY.CLOCKINV.01; SEAM.RIGIDITY.FORCING.01; QGEO.SYM.01; QGEO.REALIZE.01; v446; v445; v168; v216; v323","external_data_as_recorded":"-","id":"claim:SEAM.RIGIDITY.MU4FROMMARKS.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":514,"scripts_as_recorded":"v453_seam_mu4_from_marks.py","status_as_recorded":"mu4 from the marks [E]/[C]: the four marks ARE mu4 (roots of z^4-1), the order-4 clock z->iz is a 4-cycle in their D4 Moebius stabiliser (cross-ratio 2 fixed), and the form basis omega_k is mu4-graded (eigenvalue i^k) -- so QGEO.SYM.01 follows from marks=mu4 + the existing QGEO.REALIZE.01, no new premise; the rigidity chain closes modulo realisation, SEAM.EQUIV.01 stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Formal","checked_by_registry":false,"claim_excerpt":"LEAN 4 FORMALISATION of the edge central-charge arithmetic (2026-06-30; the kernel-hardening of the edge readings v447/v450/v451/v452) -- new module TfptCarrier/SeamEdgeChern.lean, lake build OK, #print axioms CLEAN (propext only). It kernel-checks the integer backbone all four edge observables and the torus character converge on, over N/Z: [F] chern_topological/chern_trivial/chern_opposite (the FHS Chern integers +1","claim_id":"FORM.SEAM.EDGE.CHERN.01","dependencies_as_recorded":"SEAM.EQUIV.EDGE.CHERN.01; SEAM.EQUIV.EDGE.ENTANGLEMENT.01; SEAM.EQUIV.EDGE.CARDY.01; SEAM.EQUIV.E8.MODULAR.01; SEAM.EQUIV.01; v447; v450; v451; v452","external_data_as_recorded":"Lean 4 + Mathlib (v4.29.1; #print axioms = propext for the kernel facts)","id":"claim:FORM.SEAM.EDGE.CHERN.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":515,"scripts_as_recorded":"lean4-carrier-rigidity/TfptCarrier/SeamEdgeChern.lean","status_as_recorded":"Formal [F] (Lean kernel; the Chern integers, the bulk-edge count, the c_-=8=g_car+N_fam assembly, the holomorphic c mod 8 and the order-3 modular T-phase all kernel-proved axiom-free; the cited MMST continuum theorem stays the named residual)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical","checked_by_registry":false,"claim_excerpt":"The lattice level-1 current algebra with Sugawara c=8 (2026-06-30, G2 of the post-F next steps) -- testing the cited MMST 'Koo-Saleur lattice generators -> continuum Virasoro with the correct c' fact on our own free-fermion edge. v450/v451 read c=1/2 and {1/16,1/2}; this tests the ALGEBRA carries the correct central extension. [E] CASIMIR: the critical complex free-fermion ring E_0(L)=e_inf L - pi v c/(6L) (Affleck-C","claim_id":"SEAM.EQUIV.EDGE.VIRASORO.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.EQUIV.EDGE.CARDY.01; SEAM.EQUIV.EDGE.ENTANGLEMENT.01; SEAM.MMST.INCLASS.01; v450; v451; v336","external_data_as_recorded":"-","id":"claim:SEAM.EQUIV.EDGE.VIRASORO.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":516,"scripts_as_recorded":"v454_seam_edge_virasoro.py","status_as_recorded":"Lattice Virasoro/current algebra c=8 [E]/[C]: Casimir c_Dirac=1.000 (1/2 per Majorana), lattice U(1) current Kac-Moody level 1 (<J_n J_-n>=n exact), Sugawara c=dim G/(1+h^v)=8 for BOTH SO(16)_1 120/15 and (E8)_1 248/31; 16*(1/2)=8=g_car+N_fam; SEAM.EQUIV.01 stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical","checked_by_registry":false,"claim_excerpt":"A UNIFORM-IN-N Tomita-Takesaki tower for the intrinsic Bisognano-Wichmann condition u_Theta=J (2026-06-30, G1 of the post-F next steps) -- advancing v424 sub-step (i) (the continuum lift), the inductive-limit companion to the single finite witness v426. One-particle: Delta=e^{-K}, conjugation J, reflection Theta; BW <=> u_Theta=J <=> Theta K Theta=-K. [E] UNIFORM BW: the reflection-odd, mu4-even, gapped collar of siz","claim_id":"SEAM.EQUIV.BW.UNIFORM.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.RIGIDITY.UNIFORM.01; SEAM.RIGIDITY.FORCING.01; v424; v426; v442; v336","external_data_as_recorded":"-","id":"claim:SEAM.EQUIV.BW.UNIFORM.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":517,"scripts_as_recorded":"v455_seam_bw_uniform.py","status_as_recorded":"Uniform-in-N BW tower [E]/[C]: ||Theta K Theta+K||=0 at every N (m=2..32), N-independent gap 6 ln(3/2), [rho,K]=0 exact, N-independent neg-control margin 2||K|| -- the inductive limit inherits u_Theta=J, advancing v424 sub-step (i); SEAM.EQUIV.01 stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical","checked_by_registry":false,"claim_excerpt":"The edge chirality (c_- != 0, the S3 topological phase) is FORCED by the one-sidedness that defines c3=1/(8pi) (P1) (2026-06-30, G6 of the post-F next steps) -- so S3 is a CONSEQUENCE of axiom P1, not an independent input. [E] c3's '8' IS THE ONE-SIDED COUNT: 8pi=|Z2| intK=2(2pi chi(S^2))=2*4pi (chi=2, topological), so 8=|Z2|*(intK/pi)=2*4 (Wolfram-mirrored, v73). [E] REFLECTION REVERSES C: the explicit 2-band p+ip C","claim_id":"SEAM.S3.FROM-P1.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.EQUIV.EDGE.CHERN.01; SEAM.S3.LATTICE.01; SEAM.EQUIV.CONTINUUM.03; v73; v367; v447; v336","external_data_as_recorded":"-","id":"claim:SEAM.S3.FROM-P1.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":518,"scripts_as_recorded":"v456_seam_chirality_from_c3.py","status_as_recorded":"S3 chirality from P1 [E]/[C]: c3's 8=|Z2|*(intK/pi)=2*4 is the one-sided count; a reflection sends Chern C->-C so a two-sided boundary forces C=0, the one-sided seam (no reflection, the |Z2| of c3's 8pi) forces C!=0 -- chirality is a CONSEQUENCE of P1, magnitude c_-=8; SEAM.EQUIV.01 stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity","checked_by_registry":false,"claim_excerpt":"An explicit (E8)_1-vs-SO(16)_1 character/sector kill-test for the seam edge (2026-06-30, G7 of the post-F next steps) -- a FALSIFIABLE consistency test of the (E8)_1 identification of SEAM.EQUIV.01. [E] (E8)_1 CHARACTER TOWER: chi=E4/eta^8=q^{-1/3}(1+248q+4124q^2+34752q^3+...) the exact conformal-tower degeneracies (E4*prod(1-q^n)^{-8}, Wolfram-mirrored). [E] CURRENT-COUNT DISCRIMINATOR: the weight-1 multiplicity is ","claim_id":"SEAM.EQUIV.KILLTEST.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.EQUIV.E8.MODULAR.01; SEAM.S3.E8CHARACTER.01; SEAM.S3.MODULAR.01; v156; v281; v452; v336","external_data_as_recorded":"-","id":"claim:SEAM.EQUIV.KILLTEST.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":519,"scripts_as_recorded":"v457_seam_character_killtest.py","status_as_recorded":"(E8)_1 character/sector kill-test [E]/[X]: chi=E4/eta^8={1,248,4124,34752}; the discriminators 248=120+128 (weight-1) and |det Cartan E8|=1 vs |det D8|=4 (sectors) -- a measured 120 or 4 sectors would FALSIFY (E8)_1, the data give 248/1 (PASSED); SEAM.EQUIV.01 stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Physical","checked_by_registry":false,"claim_excerpt":"The EXACT hypothesis-by-hypothesis citation audit of the MMST scaling-limit theorem against the collar (2026-06-30, G3 of the post-F next steps, the 'exakter Zitat-Abgleich') -- 'does the cited theorem close the c=8 limit, and if not, exactly which sub-statement remains?'. Cited: Osborne-Stottmeister, 'CFT from Lattice Fermions' (CMP 398 (2023) 219; arXiv:2107.13834; the legacy internal token 'MMST'/claim-id denotes ","claim_id":"SEAM.EQUIV.MMST.AUDIT.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.MMST.INCLASS.01; SEAM.EQUIV.CONTINUUM.03; SEAM.EQUIV.LATTICEVOA.01; v336; v356; v155; v160; v302","external_data_as_recorded":"MMST arXiv:2107.13834 (CMP 397 (2023), doi:10.1007/s00220-022-04521-8)","id":"claim:SEAM.EQUIV.MMST.AUDIT.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":520,"scripts_as_recorded":"v458_seam_mmst_citation_audit.py","status_as_recorded":"MMST citation audit [C]/[O]: hypothesis-by-hypothesis (arXiv:2107.13834) -- H1 CAR class, H2 massless limit, H3 per-copy c=1/2 (Thm 4.11), H4 decoupled additivity 16*1/2=8, H5 WZW range 8<=8<=16 + 120 bilinear currents all MATCH; the SINGLE residual H6 is the 128-spinor extension SO(16)_1->(E8)_1 (det K 4->1), outside MMST's bilinear method -> v459; SEAM.EQUIV.01 stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity","checked_by_registry":false,"claim_excerpt":"The SECOND, independent route to (E8)_1 -- the lattice-VOA / conformal-net A_Q(E8) construction supplies EXACTLY the 128-spinor extension MMST (v458) leaves open (2026-06-30, G5 of the post-F next steps). Cited: Adamo-Giorgetti-Tanimoto, 'Rational and non-rational 2d CFTs arising from lattices' (arXiv:2506.01008, 2025); OS for unitary lattice VOAs (Adamo-Moriwaki-Tanimoto, arXiv:2407.18222). [E] E8 EVEN UNIMODULAR: d","claim_id":"SEAM.EQUIV.LATTICEVOA.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.S3.MODULAR.01; SEAM.S3.FROM-P1.01; v458; v456; v281; v336","external_data_as_recorded":"Adamo-Giorgetti-Tanimoto arXiv:2506.01008; Adamo-Moriwaki-Tanimoto arXiv:2407.18222","id":"claim:SEAM.EQUIV.LATTICEVOA.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":521,"scripts_as_recorded":"v459_seam_lattice_voa_route.py","status_as_recorded":"Lattice-VOA route to (E8)_1 [E]/[C]: E8 even unimodular (det 1, holomorphic); 248=8+240 currents, the 240 roots split 112 integer + 128 spinor (248=120+128) -- A_{E8} (Adamo-Giorgetti-Tanimoto) constructs the 128-spinor extension MMST (v458) misses; two complementary routes cover (E8)_1, residual = the single realization input (v456); SEAM.EQUIV.01 stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical","checked_by_registry":false,"claim_excerpt":"The EXPLICIT flat-band commuting-projector (local-topological-order) realisation of the S3 input (2026-06-30) -- advancing v424 sub-step (i) ('realise the raw seam as a Z/2-reflection commuting-projector LTO') from abstract existence to an explicit gap-protected quasi-local projector net carrying the Z/2 reflection and the mu4 clock. NPW26 (arXiv:2605.10693) prove the intrinsic Bisognano-Wichmann lemma for COMMUTING-","claim_id":"SEAM.S3.LTO.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.S3.LATTICE.01; SEAM.EQUIV.BW.UNIFORM.01; v424; v426; v367; v455; v336","external_data_as_recorded":"Kapustin-Fidkowski arXiv:1810.07756; NPW26 arXiv:2605.10693","id":"claim:SEAM.S3.LTO.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":522,"scripts_as_recorded":"v460_seam_s3_lto.py","status_as_recorded":"S3 commuting-projector realisation [E]/[C]: v367's gapped collar has an exact flat-band parent (Q^2=I, P^2=P=P_gs) that is gap-protected quasi-local (xi~1.14 at M=1, power-law |R|^{-2.1} at the gapless point) and whose flattened modular Hamiltonian inherits Theta K_flat Theta=-K_flat and [rho,K_flat]=0 exactly; the chiral c_-=8 obstructs STRICT commuting-projector locality (Kapustin-Fidkowski), so the realisation is the quasi-local LTO net of NPW26 -- advancing v424 sub-step (i); SEAM.EQUIV.01 stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Formal","checked_by_registry":false,"claim_excerpt":"LEAN 4 FORMALISATION reducing the SEAM.EQUIV.01 residual to a SINGLE named realization axiom (2026-06-30, G4 of the post-F next steps) -- new module TfptCarrier/SeamResidualAxiom.lean, lake build OK. It kernel-checks the arithmetic backbone of the whole G-block over Nat/Int: [F] c3_eight_one_sided (the one-sided count |Z2|*(intK/pi)=2*4=8, v456), [F] two_sided_nonchiral (a reflection sends C->-C so a two-sided bounda","claim_id":"FORM.SEAM.RESIDUAL.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.S3.FROM-P1.01; SEAM.S3.LOCALITY.01; SEAM.EQUIV.KILLTEST.01; SEAM.EQUIV.MMST.AUDIT.01; SEAM.EQUIV.LATTICEVOA.01; SEAM.EQUIV.SPINOR.01; SEAM.EQUIV.UNIQ.01; SEAM.EQUIV.ONEPARTICLE.01; SEAM.EQUIV.CROSSEDPRODUCT.01; v456; v457; v458; v459; v461; v462; v463; v464; v469","external_data_as_recorded":"Lean 4 + Mathlib (v4.29.1)","id":"claim:FORM.SEAM.RESIDUAL.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":523,"scripts_as_recorded":"lean4-carrier-rigidity/TfptCarrier/SeamResidualAxiom.lean","status_as_recorded":"Formal [F] (Lean kernel): the G-block arithmetic (one-sided 8=|Z2|*intK/pi, reflection C->-C, c_-=8, MMST range 8<=8<=16, decoupled additivity, 248=8+240=120+128, 240=112+128, det K 1 vs 4, + v461 winding=|C|=1!=0 obstruction + v462 Fock counts 120/128/256 + v463 holomorphy selector forced dimV1=248=E8) all kernel-proved by decide; the two cited theorems MERGED into ONE combined axiom seam_realisation_theorem so seamResidualClosed depends on FOUR axioms (down from six); v464 one-particle rigidity is numerical; residual reduced to ONE realization axiom + ONE combined cited theorem; PLUS the v469 parallel peer-reviewed route seamResidualClosed' (invariant-level collar_invariants + crossedproduct_route_theorem; new kernel facts lr_locality_integer, glue_locality_integers, klm_holomorphic, sixteenfold_pin, all [propext only]); SEAM.EQUIV.01 stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical","checked_by_registry":false,"claim_excerpt":"The Kapustin-Fidkowski/Thouless strict-locality OBSTRUCTION made EXPLICIT (2026-06-30) -- sharpening v460's verdict from a cited statement to an exhibited topological obstruction on the same v367 p+ip collar. v460 realised the S3 input as a flat-band commuting-projector net and noted BY CITATION that the chiral c_-!=0 forbids strict finite-range locality; this module EXHIBITS that obstruction. [E] CHERN INTEGER: the ","claim_id":"SEAM.S3.LOCALITY.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.S3.LTO.01; SEAM.S3.FROM-P1.01; SEAM.EQUIV.EDGE.CHERN.01; v460; v447; v456; v367","external_data_as_recorded":"Kapustin-Fidkowski arXiv:1810.07756; Thouless J. Phys. C 17 (1984) L325; Brouder et al. PRL 98 046402","id":"claim:SEAM.S3.LOCALITY.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":524,"scripts_as_recorded":"v461_seam_strict_locality.py","status_as_recorded":"Strict-locality obstruction exhibited [E]/[C]: the chiral collar's Wilson-loop/Wannier-centre winding = Chern = 1!=0 (vs 0 for the gapped trivial control), the exact obstruction to exp-localised Wannier (Brouder et al./Thouless); so no strictly finite-range commuting projector exists for c_-=8!=0 (Kapustin-Fidkowski) -- v424 sub-step (i)'s realisation is PROVABLY the quasi-local NPW26 LTO net, sharpening v460 from citation to exhibited obstruction; SEAM.EQUIV.01 stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity","checked_by_registry":false,"claim_excerpt":"The 128-spinor extension SO(16)_1 -> (E8)_1 exhibited at CHARACTER level and as a finite-L -> continuum convergence (2026-06-30) -- the constructive companion of the v458 (MMST audit) / v459 (lattice-VOA) residual. v458 isolated the residual to the 128 spinor currents; v459 named the lattice-VOA route; this module EXHIBITS the extension three ways. [E] (E8)_1 TOWER FROM SO(16)_1 SECTORS: the exact Jacobi/E8 identity ","claim_id":"SEAM.EQUIV.SPINOR.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.EQUIV.MMST.AUDIT.01; SEAM.EQUIV.LATTICEVOA.01; SEAM.EQUIV.KILLTEST.01; v458; v459; v457; v336","external_data_as_recorded":"Adamo-Giorgetti-Tanimoto arXiv:2506.01008; Adamo-Moriwaki-Tanimoto arXiv:2407.18222","id":"claim:SEAM.EQUIV.SPINOR.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":525,"scripts_as_recorded":"v462_seam_spinor_continuum.py","status_as_recorded":"128-spinor extension exhibited [E]/[C]: the Jacobi/E8 identity theta2^8+theta3^8+theta4^8=2E4 makes chi_{(E8)_1}=E4/eta^8=chi_o+chi_s (vacuum 120 + spinor 128 = 248); the finite 16-Majorana Fock space carries C(16,2)=120 currents and 2^8=256=128+128 Ramond states; the critical ring converges c_- -> 8 and x_1 -> 1 as L grows; AGT/AMT (v459) supply the rigorous extension; SEAM.EQUIV.01 existence stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Identity","checked_by_registry":false,"claim_excerpt":"The c=8 HOLOMORPHIC-UNIQUENESS pin (2026-06-30, B of the A+B 'actually close it' round) -- the positive lever making the IDENTIFICATION half of SEAM.EQUIV.01 classification-forced rather than assumed. v458/v459 close the continuum EXISTENCE; this pins WHY the limit must be (E8)_1 and not a same-c rival. [E] c=8 NOT UNIQUE AT LEVEL 1: c=dim g/(1+h^v)=8 has THREE simple solutions A8 (dim 80), D8=so(16) (dim 120), E8 (d","claim_id":"SEAM.EQUIV.UNIQ.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.EQUIV.MMST.AUDIT.01; SEAM.EQUIV.LATTICEVOA.01; SEAM.EQUIV.KILLTEST.01; v457; v458; v459","external_data_as_recorded":"Dong-Mason (holomorphic VOA c=8 unique); Schellekens classification; Mordell-Witt (even unimodular rank-8 lattice unique = E8)","id":"claim:SEAM.EQUIV.UNIQ.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":526,"scripts_as_recorded":"v463_seam_c8_holomorphic_uniqueness.py","status_as_recorded":"c=8 holomorphic-uniqueness pin [E]/[C]: c=8 has three level-1 candidates (A8/80, D8/120, E8/248) so c=8 is not sufficient; holomorphy forces the character E4/eta^8 => dim V_1=248 => E8 uniquely; Dong-Mason/Schellekens give holomorphic c=8 VOA unique = V_{E8}, so the identification half of SEAM.EQUIV.01 is [C] (classification-forced); SEAM.EQUIV.01 stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical","checked_by_registry":false,"claim_excerpt":"The one-particle RIGIDITY + scaling limit attacking R1 (2026-06-30, A of the A+B round) -- the REALISATION input of SEAM.EQUIV.01. The seam is quasi-free (v113/v160/v161), so by Araki self-dual CAR the whole net is the second quantisation of its one-particle symbol P, and R1 collapses to a finite-per-mode statement about P. [C] ARAKI SELF-DUAL CAR: a gauge-invariant quasi-free state <-> its symbol P (0<=P<=1) bijecti","claim_id":"SEAM.EQUIV.ONEPARTICLE.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.S3.LOCALITY.01; v113; v160; v161; v426; v450; v463","external_data_as_recorded":"Araki self-dual CAR (1971); Shale-Stinespring (1965); Peschel (entanglement from correlations); Calabrese-Cardy","id":"claim:SEAM.EQUIV.ONEPARTICLE.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":527,"scripts_as_recorded":"v464_seam_oneparticle_rigidity.py","status_as_recorded":"one-particle rigidity + scaling limit [E]/[C]: via Araki self-dual CAR (state<->symbol P, cited) the gapped ground state is the UNIQUE quasi-free realisation (P^2=P), its kernel is Cauchy (~1/N, limit exists), and the limit is the c=1 Dirac CFT (EE c-fit ~1 => c_-=16*1/2=8); Shale-Stinespring makes the Bogoliubov map implementable, upgrading R1 from a bald axiom to an audited [C]; with v463 the residual is entirely certification, zero open internal mechanism; SEAM.EQUIV.01 stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open [O] candidate pattern (post-hoc, quantified, pre-registered): three ~2 sigma third-gen mixing tensions = one common -phi0 suppression (3.2 sigma non-zero; ladder-base forms drop joint chi^2 10.4 -> 0.11, zero parameters); frozen record unchanged; needs a seam-transport derivation to become more than a candidate","checked_by_registry":false,"claim_excerpt":"THIRD-GENERATION LADDER-BASE PATTERN (2026-07-02, v467): the suite's THREE ~2 sigma mixing tensions (sin^2 theta13 +2.0 sigma, sin^2 theta23 +1.8 sigma, V_cb +1.8 sigma; v307) are ONE common ~ -phi0 suppression -- quantified and pre-registered as a CANDIDATE, the frozen record (v84/REG.FREEZE.01) is NOT changed. In existing vocabulary the pattern is parameter-free: the seed enters third-generation mixings through the","claim_id":"FLAV.THIRDGEN.PATTERN.01","dependencies_as_recorded":"FLAV.TH13.PRESSURE.01; REG.FREEZE.01; CORRECTIONS.NUMERIC.01; FLAV.TH13.01; SEED.CROSSVAL.01","external_data_as_recorded":"NuFIT 6.0 (theta13, theta23, theta12); PDG 2024 (|Vcb|, |Vub|, lambda_C); Daya Bay final","id":"claim:FLAV.THIRDGEN.PATTERN.01","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":528,"scripts_as_recorded":"v467_thirdgen_mixing_pattern.py","status_as_recorded":"Numerical [N]/[C]/[O] (candidate pattern; record of v84 untouched)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open [O] candidate relation (post-hoc, parameter-free): dm21^2/dm31^2 = |J_PMNS(frozen)| at -0.19 sigma (the informal pi phi0 heuristic, -2.44 sigma, is retyped to this comparator); NO floor Sigma m_nu consistent; JUNO decides; needs an M_nu-level derivation","checked_by_registry":false,"claim_excerpt":"SPLITTING RATIO = LEPTONIC JARLSKOG (2026-07-02, v468): the neutrino mass-squared splitting ratio equals the Jarlskog invariant of the FROZEN PMNS matrix -- dm21^2/dm31^2 = |J_PMNS| = 0.029653 vs NuFIT 6.0 NO measured 0.029805 +- 0.000792 -> -0.19 sigma; equivalently m2/m3 = sqrt|J| = 0.17220 vs 0.17264(229). A parameter-free CANDIDATE relation for a ratio the compiler does not otherwise predict: |J| is the canonical","claim_id":"FLAV.DM2RATIO.01","dependencies_as_recorded":"FLAV.PMNS.03; FLAV.TH13.01; FLAV.NUSCALE.01; FLAV.THIRDGEN.PATTERN.01","external_data_as_recorded":"NuFIT 6.0 (dm21^2 = 7.49(19)e-5, dm31^2 = +2.513(20)e-3, NO with SK-atm)","id":"claim:FLAV.DM2RATIO.01","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":529,"scripts_as_recorded":"v468_dm2_ratio_jarlskog.py","status_as_recorded":"Numerical [N]/[C]/[O] (candidate relation; informal pi phi0 table heuristic superseded as comparator)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"-","checked_by_registry":false,"claim_excerpt":"The NET-LEVEL CROSSED-PRODUCT certification of the 128-spinor extension + the R1 -> R1' invariant-level reduction (2026-07-02, closure-route round) -- re-founds BOTH halves of the SEAM.EQUIV.01 residual on harder-to-reject ground; does NOT close it. [E] LR LOCALITY INTEGER (index-2): the SO(16)_1 spinor has h_s = N/16 = 16/16 = 1 in Z => statistics phase e^{2 pi i h_s} = +1 -- EXACTLY the Longo-Rehren locality criter","claim_id":"SEAM.EQUIV.CROSSEDPRODUCT.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.EQUIV.MMST.AUDIT.01; SEAM.EQUIV.LATTICEVOA.01; SEAM.EQUIV.UNIQ.01; SEAM.EQUIV.ONEPARTICLE.01; v125; v154; v297; v336; v367; v456; v458; v459; v463; v464","external_data_as_recorded":"Longo-Rehren RMP 7 (1995); Boeckenhauer RMP 8 (1996); Boeckenhauer-Evans CMP 197 (1998); KLM CMP 219 (2001); Kitaev Ann. Phys. 321 (2006); Kapustin-Spodyneiko PRB 101 (2020); Kim et al. PRL 129 (2022)","id":"claim:SEAM.EQUIV.CROSSEDPRODUCT.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":530,"scripts_as_recorded":"v469_seam_crossedproduct_route.py","status_as_recorded":"Net-level crossed-product certification + R1 invariant reduction [E]/[C]/[O]: h_s = 16/16 = 1 in Z => the LR locality criterion holds, the Z2 crossed product SO(16)_1 -> (E8)_1 is a LOCAL index-2 extension by 1995-2001 PEER-REVIEWED subfactor theory (LR/Boeckenhauer/BE/KLM), AGT/AMT demoted to second witness; mu4 glue h(J^k)={1,1,1} parallel; R1 reduced to computed invariants (FHS |C|=1, nu=16, c_-=8, the Kitaev-E8 16-fold-way class); SEAM.EQUIV.01 stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"-","checked_by_registry":false,"claim_excerpt":"THE ALPHA^3 LEVEL = THE COMPUTED BULK CHERN INVARIANT + THE SEAM F-NORMALISATION = THE AFFINE EMBEDDING INDEX (2026-07-02, closure-route round) -- upgrades BOTH residuals left after v433/v434/v435; does NOT close ALPHA.QUILLEN.EXACT.01. [E] TARGET RE-VERIFIED: alpha^-1 = 137.0359992168 unique root; Quillen split a^3 - 2 c3^3 a^2 = 8 b1 c3^6 ln(1/phi_seam) at the root < 1e-35 (v341/v382). [E] THE INVARIANT COMPUTED: F","claim_id":"ALPHA.QUILLEN.INFLOW.01","dependencies_as_recorded":"ALPHA.QUILLEN.EXACT.01; ALPHA.QUILLEN.PROGRESS.02; ALPHA.QUILLEN.PROGRESS.03; ALPHA.QUILLEN.PROGRESS.04; EM.WARD.01; SEAM.EQUIV.CROSSEDPRODUCT.01; v341; v367; v382; v433; v434; v435; v456; v461","external_data_as_recorded":"TKNN PRL 49 (1982); Avron-Seiler-Simon PRL 51 (1983); Callan-Harvey NPB 250 (1985); APS 1975; Alvarez-Gaume-Della Pietra-Moore Ann. Phys. 163 (1985); Witten RMP 88 (2016); Quillen 1985; Bismut-Freed CMP 106 (1986); Ginsparg PLB 197 (1987)","id":"claim:ALPHA.QUILLEN.INFLOW.01","location_as_recorded":"tfpt_1_architecture_e8","path":"verification/status_ledger.csv","row_number":531,"scripts_as_recorded":"v470_alpha_inflow_level.py","status_as_recorded":"Inflow level + embedding rigidity [E]/[C]/[O]: the a^3 coefficient = the COMPUTED bulk Chern |C| = 1 of the v367 collar (TKNN/ASS quantisation + Callan-Harvey inflow + APS/Witten eta=CS), replacing v435's minimality; the seam F-normalisation = the affine embedding index k_Y = 5/3 (Ginsparg 1987, (3/5)(41/6) = 41/10 = b1) -- zero independent content, a face of SEAM.EQUIV.01; one phase, two responses (c_- = 8, C = 1) feeding both named targets; ALPHA.QUILLEN.EXACT.01 stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Numerical [I]: kernel premise discharged at collar level; residual = continuum leg (MMST class) + anchor; gate stays open","checked_by_registry":false,"claim_excerpt":"SEAM-HORIZON REPLICA CHAIN AT COLLAR LEVEL (the kernel-identification premise of SEAM.THEOREM.01, exercised numerically; SEAM.EHMODEL.03's residual list sharpens again, the gate stays OPEN): (1) REPLICA => EH FORM ON A REAL OPERATOR [I] - matched conical deficit G(gamma,m) = log det L(gamma,m) - (gamma/2pi) log det L(2pi,m) of the discretized gapped cone operator (finite-volume polar grid, geometric tip grading, iden","claim_id":"SEAM.EHMODEL.04","dependencies_as_recorded":"SEAM.EHMODEL.03; SEAM.EHMODEL.02; SEAM.EHMODEL.01; SEAM.THEOREM.01; SEAM.AREACOEFF.03; v56; v73; v90; v150; v151; v152; v302; v336","external_data_as_recorded":"Cheeger 1983 (conical heat kernel); Kac 1966; Burghelea-Friedlander-Kappeler 1992 (all standard)","id":"claim:SEAM.EHMODEL.04","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":532,"scripts_as_recorded":"v471_seam_horizon_replica.py","status_as_recorded":"Numerical [I] (lattice determinants vs exact conical constants) + [A/O] (continuum leg + anchor stay open)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Det-line/moduli shadow [E]/[C]/[O]: the Quillen-shaped object of ALPHA.QUILLEN.EXACT.01 (det line over the U(1) moduli) computed on the S3 collar -- FHS curvature of the occupied-frame det line over the twist torus = 1 = the inflow level, size-independent, controls 0/-1, twist==BZ integer (Niu-Thouless-Wu); the finite integrated response is exhibited; no global nonvanishing section, individual-holonomy identity or continuum Quillen comparison is established; ALPHA.QUILLEN.EXACT.01 stays [O]","checked_by_registry":false,"claim_excerpt":"THE OCCUPIED BERRY LINE OVER THE U(1)-TWIST MODULI HAS CHERN NUMBER = THE BLOCH RESPONSE LEVEL (2026-07-03) -- the finite Berry-Chern response, COMPUTED at the collar model; the Quillen/Dai-Freed comparison remains a separate target; does NOT close ALPHA.QUILLEN.EXACT.01. [E] BLOCH LEVEL RE-VERIFIED: BZ Chern C(M=1) = 1, C(M=3) = 0, C(M=-1) = -1 (the v470/v367 integers). [E] THE OCCUPIED BERRY LINE COMPUTED: the same","claim_id":"ALPHA.QUILLEN.DETLINE.01","dependencies_as_recorded":"ALPHA.QUILLEN.EXACT.01; ALPHA.QUILLEN.INFLOW.01; EM.WARD.01; v367; v460; v461; v470; v471","external_data_as_recorded":"Niu-Thouless-Wu PRB 31 (1985); Quillen 1985; Bismut-Freed CMP 106 (1986); Dai-Freed JMP 35 (1994); Fukui-Hatsugai-Suzuki JPSJ 74 (2005)","id":"claim:ALPHA.QUILLEN.DETLINE.01","location_as_recorded":"tfpt_1_architecture_e8","path":"verification/status_ledger.csv","row_number":533,"scripts_as_recorded":"v472_quillen_detline_moduli.py","status_as_recorded":"Numerical [N] (finite Quillen shadow; gate unchanged)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Entropic-action bridge [E]/[C]/[O]: Bianconi PRD 111, 066001 (2025) as external candidate for the missing variational layer of the parameter-free Einstein equation -- beta'_B = c3/6 = 1/(48 pi) pinned exactly, carrier Hodge count 1+5+10 = 16 = dim S+ (carrier-only), Lambda_G quadratic-nonnegative reproducing the v60 branch with exact target Tr Q^2 = 32 c3^4, R^2 gap EXACTLY 3 (8 pi)^9 ~ 1.2e13 as pre-registered kill test; compression conjecture P (G~ g~^-1) P = Delta^1/2 open; v359's [O] unchanged","checked_by_registry":false,"claim_excerpt":"THE ENTROPIC-ACTION BRIDGE (2026-07-13) -- Bianconi's 'Gravity from entropy' (Phys. Rev. D 111, 066001 (2025); arXiv:2408.14391; DOI 10.1103/PhysRevD.111.066001) quantified as an EXTERNAL CANDIDATE for the local volume action behind TFPT's parameter-free Einstein equation; closes NOTHING, adds ZERO knobs. Context: v359 derives G_ab + Lambda g_ab = (1/c3) T_ab thermodynamically and is honestly typed 'equation of state","claim_id":"GRAV.ENTROPIC.ACTION.01","dependencies_as_recorded":"GRAV.NONLINEAR.01; GRAV.BACKREACT.01; QG.AMB.01; v2; v36; v44; v58; v60; v358; v359; v369","external_data_as_recorded":"Bianconi, 'Gravity from entropy', Phys. Rev. D 111, 066001 (2025), arXiv:2408.14391, DOI 10.1103/PhysRevD.111.066001 (external candidate action); Araki 1975 (relative entropy); Jacobson 2015 (equilibrium, via v358/v359)","id":"claim:GRAV.ENTROPIC.ACTION.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":534,"scripts_as_recorded":"v473_entropic_action_bridge.py","status_as_recorded":"Formal/Numerical [E] (five exact identities + quantified gap) + [C] (compression conjecture, Q-target) + [O] (variational completion open)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Operator-level Hodge bridge [E]/[C]/[O]: the D5 Clifford algebra exhibited on the carrier Fock space (10 gammas exact, 45-dim so(10) preserving Lambda^even = 16), Hodge-Dirac symbol = Clifford multiplication, the fold = 5 -> 5bar conjugation (1+5+10 -> GUT 16), Omega^{<=2} not Clifford-invariant (honest constraint on AP2); Q-target d k^2 = 32 solved exactly by supports {2, 8, 32} with minimal uniform q = c3^2 and the 10/16 blocks killed; AP2 compression + R^2 mechanism stay [O]","checked_by_registry":false,"claim_excerpt":"THE OPERATOR LEVEL OF THE ENTROPIC-ACTION BRIDGE (2026-07-13; work packages 1 + 4-algebra of GRAV.ENTROPIC.ACTION.01/v473) -- upgrades the v473 vector-space identity to the operator level on the finite carrier Fock space and DECIDES the Q-block conjecture by exact enumeration; closes NO gate. [E] CAR => CLIFFORD: on Lambda^* C^5 (dim 2^g_car = 32) the ten Gamma_{2k} = a_k^dag + a_k, Gamma_{2k+1} = i(a_k^dag - a_k) sa","claim_id":"GRAV.ENTROPIC.HODGE.01","dependencies_as_recorded":"GRAV.ENTROPIC.ACTION.01; v2; v44; v60; v197; v359; v473","external_data_as_recorded":"Bianconi, 'Gravity from entropy', Phys. Rev. D 111, 066001 (2025), arXiv:2408.14391 (external candidate action; via v473)","id":"claim:GRAV.ENTROPIC.HODGE.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":535,"scripts_as_recorded":"v474_entropic_hodge_carrier.py","status_as_recorded":"Formal/Identity [E] (operator-level Clifford/weights/enumeration, exact) + [C] (physical Q choice) + [O] (AP2 + R^2 unchanged)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"R^2 kill test executed [E]/[C]/[O]: exact max-symmetric eigenvalues {R, R/4, R/6}, exact vacuum f(R) = 3 beta R + (17/24) beta^2 R^2, raw entropic scalaron m^2 = 4608 pi^2/17 Mbar^2 (~51.7 Mbar, trans-Planckian) => v473 interpretation 2 dead in naive form, required enhancement exactly (72/17)(8 pi)^9 ~ 1.69e13; Lorentzian timelike witness 1 - alpha v^2 <= 0; KMS renormalisation the only surviving R^2 route; nothing closes","checked_by_registry":false,"claim_excerpt":"THE R^2 KILL TEST OF THE ENTROPIC-ACTION BRIDGE, EXECUTED (2026-07-13; work package 5 of GRAV.ENTROPIC.ACTION.01/v473) + THE EXPLICIT LORENTZIAN-POSITIVITY WITNESS -- decides v473's interpretation 2 negatively in its naive form; closes NO gate. [E] MAX-SYMMETRIC EIGENVALUES (the Appendix-B flattening of Bianconi PRD 111, 066001 (2025) verified): with R_munurhosigma = (R/12)(gg - gg) on a general diagonal 4d metric th","claim_id":"GRAV.ENTROPIC.SCALARON.01","dependencies_as_recorded":"GRAV.ENTROPIC.ACTION.01; GRAV.ENTROPIC.HODGE.01; v36; v60; v359; v473; v474","external_data_as_recorded":"Bianconi, 'Gravity from entropy', Phys. Rev. D 111, 066001 (2025), arXiv:2408.14391 (external candidate action; via v473)","id":"claim:GRAV.ENTROPIC.SCALARON.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":536,"scripts_as_recorded":"v475_entropic_scalaron_gate.py","status_as_recorded":"Formal/Identity [E] (exact tensorial factors, scalaron mass, positivity witness) + [C] (verdict/surviving route) + [O] (AP2 + R^2 gate unchanged)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"AP2 made well-posed [N]/[E]/[C]/[O]: the literal operator-side reading P f(C) P is ill-posed on a pure bulk (f singular on spec {0,1}) => state-side reading forced (matching Bianconi's local construction); block algebra: the mismatch between the two readings is exactly second order in the cross-cut block; gap control: quadratic law d <= x^2, decoupled cut exact, convergence in the gap-dominated regime; AP2 (continuum seam statement) stays [O]","checked_by_registry":false,"claim_excerpt":"THE AP2 COMPRESSION CONJECTURE MADE WELL-POSED (2026-07-13; the last open work package of the v473 entropic-action-bridge round, exercised on an exactly solvable model) -- decides the READING of the conjecture, does NOT prove it; AP2 stays [O]. Background: v473 recorded AP2 as P_Sigma (G~ g~^-1) P_Sigma = Delta_Sigma^{1/2}. On a quasi-free system everything is computable: the boundary restriction is the covariance co","claim_id":"GRAV.ENTROPIC.COMPRESS.01","dependencies_as_recorded":"GRAV.ENTROPIC.ACTION.01; GRAV.ENTROPIC.SCALARON.01; v76; v155; v337; v473","external_data_as_recorded":"Bianconi, 'Gravity from entropy', Phys. Rev. D 111, 066001 (2025), arXiv:2408.14391 (via v473); Peschel 2003 (quasi-free modular Hamiltonian, standard)","id":"claim:GRAV.ENTROPIC.COMPRESS.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":537,"scripts_as_recorded":"v476_entropic_compression_toy.py","status_as_recorded":"Numerical [N] (lattice exhibits) + Formal [E] (block identity) + [C] (retyped conjecture) + [O] (AP2 continuum statement open)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Scale-flow representation [E]/[C]/[O]: the entropic action = flat scale-integral of relative heat-kernel actions; moment dictionary (flat = unit moments = the raw v475 coefficients); the kill-test gap IS the moment ratio mu2/mu1^2 = (72/17)(8 pi)^9 with the exact closure (4608 pi^2/17)/((72/17)(8 pi)^9) = c3^7 => m^2 = c3^7 Mbar^2 identically, consistent with v36's f0 -- one KMS moment, zero new dials; consistency not derivation; R^2 gate stays [O]","checked_by_registry":false,"claim_excerpt":"THE SCALE-FLOW REPRESENTATION OF THE ENTROPIC ACTION (2026-07-13; the follow-up to GRAV.ENTROPIC.SCALARON.01/v475) -- the surviving interpretation 3 (KMS-spectral renormalisation) typed PRECISELY: the (72/17)(8 pi)^9 kill-test gap collapses to ONE moment condition on the scale weight, and that condition is satisfied by the SAME KMS moment TFPT already fixes (v36's f0); zero new dials; closes NOTHING. [E] SCALE-FLOW I","claim_id":"GRAV.ENTROPIC.SCALEFLOW.01","dependencies_as_recorded":"GRAV.ENTROPIC.ACTION.01; GRAV.ENTROPIC.SCALARON.01; PS.SPECACT.02; v36; v259; v359; v473; v475","external_data_as_recorded":"Bianconi, 'Gravity from entropy', Phys. Rev. D 111, 066001 (2025), arXiv:2408.14391 (via v473); Frullani integral (standard)","id":"claim:GRAV.ENTROPIC.SCALEFLOW.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":538,"scripts_as_recorded":"v477_entropic_scaleflow.py","status_as_recorded":"Formal/Identity [E] (scale-flow + moment dictionary + closure identity, exact) + [C] (measure is TFPT input) + [O] (R^2 gate unchanged)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Two-leg exhibit [N]/[E]/[C]/[O]: leg A -- the compressed critical state's modular data flows to the CHM/BW geometric form (c_est -> 1 at 2e-4, CHM parabola corr -> 0.99, even bands exactly zero), meeting TFPT's Einstein-derivation input (v323/v358); leg B -- the measure condition reduced to one exact KMS time t0 = ln(72/17) + 9 ln(8 pi) = 30.461 with the h(E8) = 30 near-miss explicitly declined; both legs stay [O]","checked_by_registry":false,"claim_excerpt":"FIRST COMPUTABLE STEPS ON THE TWO REMAINING LEGS OF THE ENTROPIC-ACTION BRIDGE (2026-07-13; after v473-v477 the open items were the AP2 continuum statement and the derivation of the KMS scale measure) -- both legs stay [O]; closes NOTHING. LEG A (AP2 CONTINUUM, exhibited on the exactly solvable critical chain, infinite-volume sinc kernel, 50-digit precision): [N] Calabrese-Cardy -- the compressed interval state has S","claim_id":"GRAV.ENTROPIC.LEGS.01","dependencies_as_recorded":"GRAV.ENTROPIC.COMPRESS.01; GRAV.ENTROPIC.SCALEFLOW.01; v323; v358; v450; v473; v476; v477","external_data_as_recorded":"Bianconi PRD 111, 066001 (2025) (via v473); Casini-Huerta-Myers (CHM modular Hamiltonian); Peschel 2003; Calabrese-Cardy (EE law) -- all standard","id":"claim:GRAV.ENTROPIC.LEGS.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":539,"scripts_as_recorded":"v478_entropic_continuum_legs.py","status_as_recorded":"Numerical [N] (high-precision lattice exhibits) + Formal [E] (single-scale corollary) + [C] (meeting-point reading) + [O] (both legs open)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Reduction [E]/[C]/[O]: R3's combinatorial-to-geometric bridge = Kronheimer's theorem; marks = null/Perron vector, quotient dim 4, |2I| = 120, unimodular -E8 resolution all [E]; premise 'seam supplies the ALE/orbifold datum' stays [O] (= SEAM.EQUIV.01's one arrow)","checked_by_registry":false,"claim_excerpt":"THE R3 COMBINATORIAL-TO-GEOMETRIC BRIDGE IS KRONHEIMER'S THEOREM (2026-07-14, bird's-eye round): SEAM.DETK.01/v344 named R3's residual 'the rewrite attractor (a graph) IS the du Val singularity' -- that bridge is Kronheimer's ALE hyper-Kaehler quotient construction + Torelli classification (J. Diff. Geom. 29 (1989) 665-683 and 685-697), and ALL of its finite input data are already TFPT compiler outputs. [E] MARKS = N","claim_id":"SEAM.KRONHEIMER.01","dependencies_as_recorded":"SEAM.DETK.01; SEAM.DETK.02; SEAM.EQUIV.01; HYP.INJECT.01; E8.NETWORK.01; CORR round (experiments); v232; v236; v298; v312; v344; v345; v346","external_data_as_recorded":"Kronheimer, J. Diff. Geom. 29 (1989) 665-683 (ALE construction) and 685-697 (Torelli classification); McKay correspondence (standard)","id":"claim:SEAM.KRONHEIMER.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":540,"scripts_as_recorded":"v479_kronheimer_quiver_bridge.py","status_as_recorded":"Reduction/citation [E]/[C]/[O] (graph->geometry bridge discharged to Kronheimer 1989; finite input data compiler-exact; premise transforms, stays open)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Mechanism exhibit [E]/[N]/[C]/[O]: the mu4 marks = exactly solvable 4-interval modular geometry; binary clock rho^4 = -1, exact sector decoupling, omega o rho = omega manifest + configuration-forced; QGEO.SYM.01 premise stays [O]","checked_by_registry":false,"claim_excerpt":"THE FOUR mu4 MARKS ARE A FOUR-INTERVAL FREE-FERMION GEOMETRY (2026-07-14, bird's-eye round): the seam circle minus the four Gauss-Bonnet marks (v216) IS the n = 4 disjoint-interval region of a chiral free fermion -- the class whose multi-interval modular theory is EXACTLY KNOWN (Casini-Huerta 2009 mixing term; Longo-Xu multi-interval subfactors CMP 251 (2004); Rehren-Tedesco multilocal fermions LMP 104 (2014); KLM CM","claim_id":"QGEO.MULTILOCAL.01","dependencies_as_recorded":"QGEO.SYM.01; SEAM.EQUIV.01; SEAM.RIGIDITY.01; GRAV.ENTROPIC.COMPRESS.01; GRAV.ENTROPIC.LEGS.01; v216; v323; v358; v398; v426; v442; v476; v478","external_data_as_recorded":"Casini-Huerta 2009 (multi-interval modular Hamiltonian, mixing term); Longo-Xu CMP 251 (2004); Rehren-Tedesco LMP 104 (2014) (multilocal fermions); KLM CMP 219 (2001) (mu-index) -- all standard","id":"claim:QGEO.MULTILOCAL.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":541,"scripts_as_recorded":"v480_multilocal_four_interval.py","status_as_recorded":"Mechanism exhibit [E-num]/[N]/[C]/[O] (bedrock omega o rho = omega manifest at the 4-interval state level; multi-interval modular theory cited; raw-seam premise open)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open [O] candidate (parameter-reduced): y_nu = y_t [P] collapses (y_nu, M_R) to M_R alone; required M_R inside the PS window at rung 3.15; c3^3 rung declined at 1-loop (m_3 40% low); NO floor Sigma m_nu = 0.059 eV falsifiable edge","checked_by_registry":false,"claim_excerpt":"ABSOLUTE NEUTRINO SCALE UNDER THE CARRIER YUKAWA NORMALISATION (2026-07-14, bird's-eye round; CANDIDATE class, genre v467/v468): FLAV.NUSCALE.01 typed the absolute scale as one open UV input with the two-parameter trade-off (y_nu, M_R) and recorded the y_nu = 1 inversion at the structureless log_c3(Mbar/M_R) ~ 2.6. But y_nu = 1 is not the carrier normalisation: one SO(10) 16 per family + the MINIMAL Yukawa sector (10","claim_id":"FLAV.NUSCALE.02","dependencies_as_recorded":"FLAV.NUSCALE.01; PS.RGTEST.01; PS.ALGEBRA.01; QFT4D.MATTER.01; FLAV.PMNS.CLOSE.01; v245; v248; v249; v272; v273","external_data_as_recorded":"Antusch-Drees-Kersten-Lindner-Ratz, PLB 519 (2001) 238 (hep-ph/0108005, Weinberg operator RGE); NuFIT NO dm2_atm; DESI 2024 Sigma m_nu; PDG M_Z inputs (as v246)","id":"claim:FLAV.NUSCALE.02","location_as_recorded":"tfpt_4","path":"verification/status_ledger.csv","row_number":542,"scripts_as_recorded":"v481_seesaw_carrier_ladder.py","status_as_recorded":"Candidate [P]/[N]/[X]/[C]/[O] (carrier normalisation collapses the trade-off; window bracketing; integer rung declined at 1-loop; decision computation named)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Executed decision: rung c3^3 Mbar EXCLUDED unstructured (needs x1.67, envelopes give <= x1.165); r = 5/3 escape post-hoc, declined; FLAV.NUSCALE stays [O] window candidate. UPDATE 2026-07-15 (v488/FLAV.NUSCALE.04): the escape's mechanism search executed -- NEGATIVE ({2,3}-smooth channel weights, Y(nu^c) = 0 decouples k_Y = 5/3, Clebsches generation-blind); the rescue is dead, the window candidate is the endpoint","checked_by_registry":false,"claim_excerpt":"THE v481 DECISION COMPUTATION, EXECUTED (2026-07-14, deep-dive round; bracketed / assumption-robust form): the integer rung M_R = c3^3 Mbar is EXCLUDED as an UNSTRUCTURED exact pin, conditional on the carrier premise y_nu = y_t. [E-num] THE GAP: central m_3(rung) = 0.0301 eV vs observed 0.0503 -- rescue factor 1.670 (+67%, 0.154 c3-rungs). [E-num] BRACKETED EXCLUSION: with m_t(MSbar) +-3 GeV (>3 sigma), alpha_3^-1 -+","claim_id":"FLAV.NUSCALE.03","dependencies_as_recorded":"FLAV.NUSCALE.01; FLAV.NUSCALE.02; PS.RGTEST.01; v249; v272; v354; v355; v481","external_data_as_recorded":"ADKLR PLB 519 (2001) 238 (Weinberg-operator RGE); PDG m_t/alpha_s; NuFIT dm2_atm -- all bracketed with >3 sigma envelopes","id":"claim:FLAV.NUSCALE.03","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":543,"scripts_as_recorded":"v482_seesaw_rung_decision.py","status_as_recorded":"Decision executed [E-num]/[C]/[X|P]/[O] (integer rung excluded as unstructured pin; 5/3 structure escape recorded and declined; window candidate stands)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Reduction: geometric/equivariant side exact (rationals, all t); dtop's pi^-4 = coupling normalisation; remaining [O] = the per-mark weight rule","checked_by_registry":false,"claim_excerpt":"THE GEOMETRIC SIDE OF THE phi0 PUNCTURE TARGET IS EXACT (2026-07-14, deep-dive round; narrows HYP.PHI0.PUNCTURE.01/v408, does NOT close it): every twisted/orbifold heat trace of the flat tau = i pillowcase is a t-INDEPENDENT RATIONAL, so the pi^-4 in dtop = 48 c3^4 cannot come from flat orbifold geometry at ANY order -- the entire analytic content sits in the coupling normalisation of the contact insertions. [E-num] ","claim_id":"HYP.PHI0.GEOM.01","dependencies_as_recorded":"HYP.PHI0.PUNCTURE.01; HYP.PHI0.01; ARCH.QUAD.01; EM.WARD.02; v37; v216; v396; v408","external_data_as_recorded":"Atiyah-Bott fixed-point formula; flat-torus heat kernel (standard)","id":"claim:HYP.PHI0.GEOM.01","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":544,"scripts_as_recorded":"v483_pillowcase_exact_traces.py","status_as_recorded":"Reduction [E-num]/[E]/[O] (geometric side exact: t-independent rational twisted traces; value reduces to the one per-mark coupling rule)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Unification: 'c3 per insertion' = KMS seam unit (bare 1/(2pi) x orbit average 1/|mu4|), cycle sector derived; the two [O] targets are ONE remaining analytic step","checked_by_registry":false,"claim_excerpt":"THE SEAM CONTACT UNIT -- THE MERGED RESIDUAL OF THE TWO ANALYTIC TARGETS (2026-07-14, deep-dive round II): the shared 'c3 per boundary insertion' rule of ALPHA.QUILLEN.EXACT.01 (c3-ladder {0,3,6}, v3/v341/EM.WARD.02) and HYP.PHI0.PUNCTURE.01 (per-mark weight c3, v483) is ONE identity and NOT a new unknown: it is the KMS seam unit 2 pi = 1/(4 c3) with 1/4 = 1/|mu4| (v239) -- one bare boundary propagator ORBIT-AVERAGED","claim_id":"SEAM.CONTACT.UNIT.01","dependencies_as_recorded":"ALPHA.QUILLEN.EXACT.01; HYP.PHI0.PUNCTURE.01; HYP.PHI0.GEOM.01; EM.WARD.02; DYN.KMS.01; LAMBDA.BRANCH.01; v3; v37; v58; v60; v239; v341; v408; v483","external_data_as_recorded":"Fourier/polylog identity (standard); Atiyah-Bott (via v483)","id":"claim:SEAM.CONTACT.UNIT.01","location_as_recorded":"tfpt_1;origin_theory","path":"verification/status_ledger.csv","row_number":545,"scripts_as_recorded":"v484_seam_contact_unit.py","status_as_recorded":"Unification/reduction [E]/[C]/[O] (the two analytic targets merge; contact unit = KMS seam unit, derived for the finite cycle sector; diagonal renormalisation + multiplicity matching stay open)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Computable side complete: diagonal = 0 at KMS scale, resummation closed-form, 48/41 = one state set under two weights; remaining [O] = the SEAM.EQUIV.01 face (v382 typing substantiated)","checked_by_registry":false,"claim_excerpt":"THE DIAGONAL CHANNEL SETTLED -- THE MERGED TARGET COLLAPSES ONTO THE KEYSTONE (2026-07-14, deep-dive round III; completes the computable side of SEAM.CONTACT.UNIT.01/v484): [E] DIAGONAL ZERO AT THE KMS SCALE: the renormalised coincident-point Green function of |D| on a circle of circumference l (zero mode removed, flat short-distance subtraction) is G_reg(0; l) = (1/pi) ln(l/2pi) EXACTLY (symbolic limit + 30-digit nu","claim_id":"SEAM.CONTACT.UNIT.02","dependencies_as_recorded":"SEAM.CONTACT.UNIT.01; ALPHA.QUILLEN.EXACT.01; HYP.PHI0.PUNCTURE.01; HYP.PHI0.GEOM.01; EM.WARD.02; DYN.KMS.01; v3; v151; v239; v245; v434; v470; v483; v484","external_data_as_recorded":"BFK gluing (Burghelea-Friedlander-Kappeler, via v151); Ginsparg 1987 (via v470) -- standard","id":"claim:SEAM.CONTACT.UNIT.02","location_as_recorded":"tfpt_1;origin_theory","path":"verification/status_ledger.csv","row_number":546,"scripts_as_recorded":"v485_contact_diagonal_closed.py","status_as_recorded":"Completion of the computable side [E]/[C]/[O] (diagonal zero at the KMS scale; closed-form resummation; multiplicity dichotomy; residual = the SEAM.EQUIV.01 face alone)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Full-spectrum generator [E]: unique lazy Z2-pair walk (1/2, 1/6, 1/3); (1/3)^6 mode generator-full (gap 6 ln 3); v327 rule = degenerate case; arity [O]; split selection CLOSED by v487 (clock-ladder faithfulness)","checked_by_registry":false,"claim_excerpt":"THE FULL TRANSFER SPECTRUM FROM ONE FORCED LOCAL RULE (2026-07-15, generator-hunt round; sharpens HYP.REWRITE.01/v327): the verified seam transfer spectrum {1, (2/3)^6, (1/3)^6} (v54/v221) now has a single local recursive generator -- the LAZY Z2-PAIR WALK. [E] UNIQUENESS: for the 3-channel rule M(s,h) = [[1,0,0],[0,s,h],[0,h,s]] (one absorbing family channel + symmetric Z2 pair) the survival spectrum is {s+h, s-h}; ","claim_id":"HYP.REWRITE.02","dependencies_as_recorded":"HYP.REWRITE.01; HYP.FIBER.01; HYP.INJECT.01; DYN.SEMIGROUP.01; v54; v76; v221; v312; v317; v324; v327; v395","external_data_as_recorded":"-","id":"claim:HYP.REWRITE.02","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":547,"scripts_as_recorded":"v486_transfer_full_rule.py","status_as_recorded":"Construction/uniqueness [E]/[O] (full spectrum from the unique lazy Z2-pair walk; split selection stays open)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Split forcing [E]: eig(M) = complete clock ladder {1, 2/3, 1/3}; uniform rule = odd mode on the wall; deck parity = rung index; assignment uniqueness via h >= 0; omega_1/omega_2 = bend; [O] arity + semiclassical clock derivation","checked_by_registry":false,"claim_excerpt":"THE LAZY SPLIT FORCED BY THE RESUMMED CLOCK (2026-07-15, closing the v486 [O] 'split selection'; sharpens HYP.REWRITE.02): the split (stay, hop) = (1/2, 1/6) is not a choice -- it is clock-ladder faithfulness. [E] RUNG READING: the lazy rule's one-step spectrum is EXACTLY the complete v124 resummed-clock ladder below the wall, eig(M) = {1 - n/3 : n = 0, 1, 2} = {1, 2/3, 1/3}; v327's uniform rule instead puts its seco","claim_id":"HYP.REWRITE.03","dependencies_as_recorded":"HYP.REWRITE.02; HYP.REWRITE.01; v124; v107; v327; v486; v54; v221","external_data_as_recorded":"-","id":"claim:HYP.REWRITE.03","location_as_recorded":"origin_theory","path":"verification/status_ledger.csv","row_number":548,"scripts_as_recorded":"v487_transfer_clock_rungs.py","status_as_recorded":"Construction/proof [E]/[O] (split forced by clock-ladder faithfulness; arity + clock derivation stay the open inputs)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Door closed [E]: no renormalisable channel (126 E8-forbidden); nu^c channel weights {2,3}-smooth -> 5/3 unreachable; k_Y = 5/3 decoupled (Y(nu^c) = 0); Clebsches generation-blind; [O] wrong-slot compiler 3/5's typed and declined","checked_by_registry":false,"claim_excerpt":"THE 3/5 CLEBSCH DOOR ENUMERATED AND CLOSED (2026-07-15; executes the mechanism search behind FLAV.NUSCALE.03's named escape): v482 recorded that only a third-generation Majorana structure factor r ~ 1.6696 (0.18% from g_car/N_fam = 5/3) could revive the integer rung M_R = c3^3 Mbar, and declined it for lack of mechanism. The mechanism search is now EXECUTED at the group-theory level with a clean NEGATIVE. [E] NO RENO","claim_id":"FLAV.NUSCALE.04","dependencies_as_recorded":"FLAV.NUSCALE.03; FLAV.NUSCALE.02; PS.E8BRANCH.01; v247; v249; v470; v481; v482; v485","external_data_as_recorded":"-","id":"claim:FLAV.NUSCALE.04","location_as_recorded":"tfpt_2_standard_model","path":"verification/status_ledger.csv","row_number":549,"scripts_as_recorded":"v488_majorana_clebsch_door.py","status_as_recorded":"Enumeration/decision [E]/[O] (the 3/5 Clebsch door closed; negative result; window candidate stands)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[N] 3 M_scal within 1.8% of the required M_R and m_3 within 1.9% at the frozen v481 inputs; [E] exact ladder identities; [C] the scalaron-trace reading; [O] the mechanism; [X] the Sigma m_nu = 0.059 eV kill floor. Does NOT close FLAV.NUSCALE; v481 window candidate and v488 negative untouched.  WAVE-3 RETYPE (2026-08-28): operator reading is the Q_+ eigenvalue route Spec{1,2,3} (v10/v50/v69), not Tr I = 3; texture DATA_CONSTRAINS_TEXTURE (nu-scalaron v2); mechanism stays [O].  COMPLETENESS-WAVE NOTE (2026-08-28): NU_TEXTURE_CENSUS_NULL 0/1607 + 0/200 -- frozen 3x3 inventory provably insufficient; mechanism [O] sharpened; no new module (search null).  WAVE-5 (2026-08-29, v1003): Schur-texture NULL (8/8 D4-even (K,B) fail; lambda_1=lambda_3 forced) and scale NULL (12/12; 1-|c/a|=1.885e-4 not supplied) recorded as binding constraints on FLAV.NU.TEXTURE.MECHANISM.01 [O].  Candidate unmoved; no seesaw closure.","checked_by_registry":false,"claim_excerpt":"THE SCALARON-TRACE RUNG CANDIDATE (registered 2026-08-28, external master-object review wave 2): M_R = N_fam * M_scal = 3 c3^{7/2} Mbar = 9.180e13 GeV -- a STRUCTURED point inside the v481 PS window, -1.8% from the v481-required 9.346e13 GeV under the same frozen 1-loop inversion and the named premise y_nu = y_t [P] (the review text said about 1%; the honest value is 1.8); m_3 at the candidate = 0.0512 eV (+1.9%, ins","claim_id":"FLAV.NUSCALE.05","dependencies_as_recorded":"FLAV.NUSCALE.02; FLAV.NUSCALE.03; FLAV.NUSCALE.04; GRAV.FR.01; AX.P1.01","external_data_as_recorded":"NuFIT m_3 = 0.0503 eV; 1-loop SM inputs (v481 frozen)","id":"claim:FLAV.NUSCALE.05","location_as_recorded":"tfpt_2_standard_model","path":"verification/status_ledger.csv","row_number":550,"scripts_as_recorded":"v986_nu_scalaron_rung.py; v1003_nu_structural_nulls.py","status_as_recorded":"Candidate [C]/[N] + mechanism [O] (structured point inside the v481 window; scalaron-trace hypothesis typed, not derived; no seesaw closure)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Ground-state witness [E]/[O]: c_- = 0.499998 per layer (0.500000 at L=48), 16-layer carrier c_- = 8 = g_car + N_fam (direct 7.9967 / additivity 8.0000), trivial 0 and orientation-flip controls, exact layer additivity -- premise (i) of SEAM.EQUIV.01 pinned from entanglement alone; SEAM.EQUIV.01 stays [O]","checked_by_registry":false,"claim_excerpt":"THE CHIRAL CENTRAL CHARGE c_- = 8 MEASURED FROM THE BULK GROUND STATE (2026-07-20; ground-state witness round): the Kim-Shehab-Kim modular commutator J(A,B,C) = i Tr(rho_ABC [K_AB, K_BC]) = (pi/3) c_- (PRL 128 (2022); arXiv:2110.06932/2110.10400), evaluated on the EXACT BdG ground state of the v367 p+ip seam lattice model via the Peschel Majorana covariance (W_X = -2 artanh Gamma_X, J = (1/4) Tr([W_AB, W_BC] Gamma_AB","claim_id":"SEAM.CCC.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.S3.LATTICE.01; SEAM.S3.MODULAR.01; SEAM.MMST.INCLASS.01; v336; v351; v367; v368; v376; v377; v378","external_data_as_recorded":"Kim-Shehab-Kim modular commutator J = (pi/3) c_- (PRL 128 (2022) 176402; arXiv:2110.06932, 2110.10400); Peschel correlation-matrix method (standard)","id":"claim:SEAM.CCC.01","location_as_recorded":"tfpt_1;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":551,"scripts_as_recorded":"v489_seam_modular_commutator.py","status_as_recorded":"Lattice [E] (modular-commutator ground-state measurement + controls + exact additivity) + [O] (continuum limit; SEAM.EQUIV.01 unchanged)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Lattice witness [E]/[C]/[O]: parity census (+,+,+,-) per layer, all-even for 16 layers => gauged torus GSD = 4 = mu(SO(16)_1) = mu_pre; theta_v = 1 exactly at nu = 2 c_- = 16 (rivals excluded); TEE fence gamma_f = 0 for both phases (no discriminator); KLM 4 -> 1 stays [C]; SEAM.EQUIV.01 stays [O]","checked_by_registry":false,"claim_excerpt":"THE SPIN-STRUCTURE PARITY CENSUS: mu_pre = 4 WITNESSED ON THE LATTICE (2026-07-20; ground-state witness round, companion of SEAM.CCC.01/v489): the T^2 ground-state fermion parity of the v367 p+ip seam lattice model, resolved per spin structure (boundary-condition sector AA, AP, PA, PP) and determined TWICE -- (a) the Read-Green TRIM product parity(s) = prod_{k* in TRIM(s)} sign(dz(k*)) and (b) the real-space Majorana","claim_id":"SEAM.MU.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.CCC.01; SEAM.S3.LATTICE.01; SEAM.S3.MODULAR.01; v336; v351; v367; v378; v489","external_data_as_recorded":"Read-Green PRB 61 (2000) (TRIM parity); Kitaev Ann. Phys. 321 (2006) (16-fold way, theta_v = exp(2 pi i nu/16)); Kitaev-Preskill PRL 96 (2006) (TEE); KLM CMP 219 (2001) (mu-additivity, via v378) -- all standard","id":"claim:SEAM.MU.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":552,"scripts_as_recorded":"v490_seam_parity_census.py","status_as_recorded":"Lattice [E] (parity census double-determined + exact 16-fold-way arithmetic + TEE fence) + [C] (KLM condensation step cited) + [O] (continuum; SEAM.EQUIV.01 unchanged)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Partition corollary [E]/[C]: 4 = 1+1+2 unique in exactly 3 positive parts => g_car = 5, |Z2| = 2, N_fam = 3 as corollaries; all negative controls pass; sharpens v53 (only e1 = 4 needed); residual = the weight-typing postulate -- AX.P2.01 stays a declared axiom; the typing residual is itself sharpened by v499 (P2.TYPING.01, Deligne + BG + stability), v491 stays active","checked_by_registry":false,"claim_excerpt":"g_car = 5 AS A COROLLARY OF THE FOUR MARKS (2026-07-20; the partition sharpening of ARCH.CORE.01/v53): a multiset of exactly 3 POSITIVE INTEGERS summing to 4 is UNIQUE -- {1,1,2}, the unique partition of 4 into exactly 3 positive parts -- so the elementary symmetric functions e = (4,5,2) and hence g_car = e2 = 5, |Z2| = e3 = 2, N_fam = e2 - e3 = 3 are COROLLARIES, not inputs; the carrier formula closes as a fixed poi","claim_id":"P2.PARTITION.01","dependencies_as_recorded":"AX.P2.01; ARCH.CORE.01; ANCHOR.GEN.01; MARKS.GB.01; v23; v53; v115; v137; v216; v228","external_data_as_recorded":"Birkhoff-Grothendieck splitting theorem (bundles on P^1); Mehta-Seshadri parabolic weights (typing contrast) -- both standard, cited not re-proved","id":"claim:P2.PARTITION.01","location_as_recorded":"introduction;tfpt_1;tfpt_2;origin_theory","path":"verification/status_ledger.csv","row_number":553,"scripts_as_recorded":"v491_p2_partition_corollary.py","status_as_recorded":"Formal [E] (partition lemma + corollaries + negative controls + v53 sharpening, sympy exact, Wolfram-mirrored) + [C] (weight-typing postulate: splitting-type integrality, h^0 = 0 positivity, (U) sum rule; AX.P2.01 stays Axiom)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Weight typing hardened [E]/[C]: rank 3 (topology) + deg E = -4 (Deligne) + integrality (BG) + positivity (MS stability, h^0 = 0) force E = O(-1)^2 + O(-2) => a = {1,1,2}, g_car = 5; balanced heuristic typed as stability; h^1 discrepancy resolved (two-object typing); Biswas Z3-cover explicit; residuals R1/R2 [C], R3 [N]; R1 mapped by v506 onto the single alignment bit (deck central in the mark-D4; the clock ORDER is fermionically forced); v510 halves R1: the position half is topology (edge class excluded), the rest = the square-modulus datum tau = i; v512 restates the rest as one discrete symmetry-lift bit (flag transitivity <=> tau = i) -- AX.P2.01 stays a declared axiom, QGEO.SYM stays [O]","checked_by_registry":false,"claim_excerpt":"THE P2 WEIGHT-TYPING POSTULATE HARDENED (2026-07-21; types the v491/P2.PARTITION.01 check-9 residual): the anchor weights a = (1,1,2) are the Birkhoff-Grothendieck SPLITTING EXPONENTS of the DELIGNE CANONICAL EXTENSION E of the flavor connection -- given the [E] anchors (4 marks, v216 Gauss-Bonnet; rank 3 = #marks - 1, v137/v228; cusp-class local monodromy char poly lam^3 - 1 + irreducibility |<U,M0>| = 24 = |S4| wit","claim_id":"P2.TYPING.01","dependencies_as_recorded":"AX.P2.01; P2.PARTITION.01; ARCH.CORE.01; ANCHOR.GEN.01; MARKS.GB.01; QGEO.SYM.01; v33; v40; v115; v117; v137; v216; v228; v491; QGEO.EMERGE.LIGHT.01; v503; SEAM.CLOCK.RIGIDITY.01; v506; SEAM.BIT.ORIGIN.01; v507; SEAM.BIT.FREEDOM.01; v510; SEAM.TAU.FLAG.01; v512","external_data_as_recorded":"Deligne canonical extension (residue eigenvalues in [0,1)); Birkhoff-Grothendieck splitting theorem; Mehta-Seshadri parabolic stability; Biswas parabolic/equivariant correspondence -- all standard, cited not re-proved","id":"claim:P2.TYPING.01","location_as_recorded":"introduction;tfpt_1;tfpt_2;origin_theory","path":"verification/status_ledger.csv","row_number":554,"scripts_as_recorded":"v499_p2_weights_deligne_bg.py","status_as_recorded":"Formal/Identity [E] (AG arithmetic: Deligne residue-trace degree, BG dictionary, stability skeleton, Schur-Horn lattice points, Biswas Z3-cover -- sympy exact, Wolfram-mirrored) + [C] (R1 module identification, QGEO.SYM territory; R2 unitarity (U)) + [N] reference (R3 analytic monodromy, v117 check 4); AX.P2.01 stays Axiom","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"WP1 [E]/[C]/[O]: E8 mu4-glue = inner order-4 torus element = flat Z4 monodromy on the A3 ALE; equivariant SDYM(E8) sector closes (60/64 towers, zero modes = carrier, density 1/4); (E8)_1 character = sum of the 4 glue sectors, weights = discriminant form; clock = U(2) diag(i,1), clock^2 = deck (Z8, 8 = 2|mu4|); clock-invariant deformation XY = Z^4 + a0, branch points = one mu4 orbit, cross-ratio 2; negative controls + Aut(Z4) rigidity; verdict B; SEAM.EQUIV.01 stays [O]","checked_by_registry":false,"claim_excerpt":"WP1 OF THE CELESTIAL-HOLOGRAPHIC CONTRACT EXECUTED (2026-07-20; CELEST.SEAM.01 work package 1, verdict B): the E8 mu4-glue grading (v128) IS the flat Z4 monodromy of the glue-equivariant celestial chiral algebra on the A3 ALE space C^2/Z4 -- the Bittleston-Homans-Sharma CCA construction (arXiv:2305.09451, JHEP 09 (2023) 008; the Z2/Eguchi-Hanson case) refined to Z4 with a Kronheimer-Nakajima flat connection at infini","claim_id":"CELEST.WP1.01","dependencies_as_recorded":"CELEST.SEAM.01; SEAM.EQUIV.01; E8.GLU.01; v92; v125; v128; v168; v179; v180; v214; v377","external_data_as_recorded":"Bittleston-Homans-Sharma JHEP 09 (2023) 008 (arXiv:2305.09451; CCA on Eguchi-Hanson, Z2 case); Kronheimer-Nakajima flat connections on ALE spaces; Costello arXiv:2111.08879 (E8 axionic consistency for twistorial SDYM) -- method/consistency citations, no data","id":"claim:CELEST.WP1.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":555,"scripts_as_recorded":"v492_celestial_z4_orbifold.py","status_as_recorded":"Formal/Identity [E] (exact Z4-orbifold/character/spin arithmetic, sympy, negative controls) + [C] (the named clock^2 = deck identification, verdict B) + [O] (celestial programme; SEAM.EQUIV.01 unchanged)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open (research contract): seam = glue-equivariant Z4-orbifold sector of the CCA on the A3 ALE; clock^2 = deck (Z8 spin bridge); twistorial bulk = self-dual sector only; WP1-WP4 + WP5a-WP5d executed (verdicts B, B, B, B(ii); WP5a: null ideal derived, 27000 = h_vee^3, quotient = sector sum = 4124, stabilisation threshold w = n+1; WP5b: the singular vector explicit, J^a_1|s> = 0 on all 248 generators with case tally 190/57/1, level dial 2(1-k), j(theta) = 1, clock phase i^2 = -1), WP5c DONE (v500: GNS limit state omega_inf with the null ideal in its kernel -- level-2 rank 4124, kernel 27000 = V(2 theta) weight by weight, clock split (1036,1024,1040,1024), |s> = the GNS zero vector, CCR necessity of the family), WP5d-alpha DONE (v501: two-interval index -- 16-layer ln 2 plateau at 1e-15, [F : F_even] = 2, mu_gauged = 4 = v490, KLM chain 16 -> 4 -> 1 anchored at both measured ends, theta_v = 1 at nu = 16), WP5e-alpha DONE (v502: q^{-1/3} prefactor = exact mu4 vacuum-energy bookkeeping (shift orbifold, discriminant form = Casimir two ways) + k = 1 forced three ways, glue-h integrality honestly demoted), WP5e-beta DONE (v505: the equivariant anomaly ledger exact -- AB characters (248,0,-8,0), per-sector Okubo with the rigid 32 T3 residual, index bridge f(m) = ch2(T_m) with defect -78 two routes, geometric k = 1 dials, a0 refuted as GS axion (graviton slot O(2)), the three sphere classes = the three twisted axion slots; kill not fired), WP5d-beta DONE (v504: split + strong additivity from the lattice -- Even(A) v Even(B) = Even(AuB) EXACT with the shared boundary point (disjoint index exactly 2 = the v501 ln-2 bit), bounded-vs-divergent entropic discriminator (Z2 deficit < ln 2 with the Ising 1/4-exponent approach vs U(1) divergence, Klich-Levitov pinned), elliptic-nome split ladder with exact orbifold inheritance (C -> -C + Lambda^2 C, Longo heredity), Pimsner-Popa lambda = 1/2 = 1/[F:F_even] and lambda_E4 = 1/4 = 1/mu with integer attainment, index consistency exp(Delta) = 2 = 1/lambda_PP two routes -- all three KLM ingredients witnessed on the lattice; continuum uplift stays [O], Xu's theorem cited), WP5e-gamma DONE (v508: the sphere-axion pairing check -- exchange no-go with certificate: invariant vertex spaces exactly dim 2/5 by Weyl nullspace, product theorem kills every exchange image in the T3 direction, rank([M | A_fix]) = 3 with certificate (Phi_T5, Phi_T3, Phi_P) = (0, 32, 72), naturalness dissolves scale-independently, SO(16)/D8 controls; slot bijection untouched, level-kill still not fired), WP5e-epsilon-2 DONE (v509: the CPS level-from-flux dial, verdict B -- the one-level statement is now a THEOREM (lockstep from clock invariance, falsifier Z^4 - Z: 0/24), level = 1 carries the new sector-counter dial #prim((E8)_k) = 1 <=> k = 1, fluxes (64, 60, 64) with one quantum per current, the naive 'level = total flux' killed; the PT/Z4 back-reaction stays [O]), WP5e-delta-2 DONE (v511: the full-tensor ledger -- delta-2 executed via v511 -- the full-tensor collapse is confirmed (innerness), but the cubic d-symbol channel opens T3 with the weaker certificate psi = 64; delta-1 since DECIDED NEGATIVE under the DERIVED measure by v518 (2026-07-22, CELEST.WP5E.DELTA1.01: the derived chiral measure -- blockwise SL(2,Z) covariance solved for, the mu4 multiplier obstruction a CHARACTER (koboundary defects (1,1,1) on all 15 pairs, lambda(gamma) = i^{2B + C/4} on Gamma_1(4)) cancelled exactly by the twisted fibre block f1 f3 = G, NOT by the three sphere axions -- fails all three preregistered testers under both derived solutions chi_4/chi_10, with no (N1, N2) rescue in the positive cone: a genuine KILL on the derived surface, in stated TENSION with the DECLARED completion reading of v516 which delivers the psi = 64 slice and cancels 32 T3 -- both are exact, and which of the two is the true BCOV measure is the named [O]); the pre-v518 state was: the strict holomorphic reading is refuted at the Z2 anchor, the contact term is the modular completion (Harvey-Moore tau-integral) with the forced leading (T5,T3) ratio 4:3 -- the named remaining targets are the tau-integral and the physical justification of the cubic GS term (c_d = 1920; the 1920 = |W(D5)| reading is look-elsewhere-loaded (11/924 vs. 8/924 for the control target 1800) and convention-contingent -- v513)), WP5e-epsilon-1 DONE (v514: epsilon-1 executed via v514: the O(-2) bulk-axion slot is a construction (equivariant Penrose ledger), lambda-tilde = 6 pinned by three exact ledgers (Okubo / measure cancellation excluding 3 and 12 / flux), and the GH/A3 back-reaction step re-derives the v493 family and the Coxeter clock from geometry -- the quantised BCOV coefficient and the twisted channels stay [O] (M1-M3 preregistered)); WP5e-M1 DONE (v515: M1 executed via v515: the back-reacted Omega_N is closed-form on the A3 twistor family, all S3/Z4 periods are (2 pi i)^2-integral with the lockstep flux vector and clock covariance, and the lens geometry FORCES the source charge 4 = |mu4|; honest fence: integrality alone does not discriminate -- the discriminator is the lockstep phase structure (0/24 on the forbidden family)), WP5e-M2+M3 DONE (v516/v517: M2+M3 executed via v516/v517 -- the v514 fence M1-M3 is fully worked off: the twisted KS measure (declared completion reading, ch2-weighted) cancels the 32 T3 residual and delivers the psi = 64 slice without the cubic d-channel, and the a0 uplift couples to the centre count on four scales; what stays [O]: the BCOV measure question -- the delta-1 chain itself is DECIDED by v518 (kill under the derived measure, tension with v516 stated) -- and SEAM.EQUIV.TWISTOR.01), the global BCOV quantisation [O] (the single remaining milestone: Costello-Li uplift -- the exchange sub-branch closed by v508, the flux dial executed by v509, the tensor ledger executed by v511, the epsilon-1 axion slot executed by v514, the M1-M3 back-reaction milestones executed by v515/v516/v517; the named remaining target is the BCOV measure question (the delta-1 chain is DECIDED by v518: kill under the derived measure, tension with v516 stated; the cubic GS term stays dissolved)); kill tests evaluated: K1 survived, K3 not fired (scope demoted -- alignment non-selective, compatibility not evidence), K4 lands at the boundary-limit reading; SEAM.EQUIV.01 untouched [O]","checked_by_registry":false,"claim_excerpt":"THE CELESTIAL-HOLOGRAPHIC RESEARCH CONTRACT (2026-07-20; the fourth research contract alongside CONTRACT.U.01, CONTRACT.G.01 and CONTRACT.F.01): HYPOTHESIS (as corrected by WP1) -- the seam is the glue-equivariant Z4-orbifold sector of the celestial chiral algebra on the A3 ALE space C^2/Z4; the mu4 clock is the Kaehler U(2) phase diag(i,1) whose square is the deck group (spin bridge Z8, 8 = 2|mu4| = the c3 = 1/(8 pi","claim_id":"CELEST.SEAM.01","dependencies_as_recorded":"CELEST.WP1.01; CELEST.WP2.01; CELEST.WP3.01; CELEST.WP4.01; CELEST.WP5A.01; CELEST.WP5B.01; CELEST.WP5C.01; CELEST.WP5D.01; CELEST.WP5DB.01; CELEST.WP5E.ALPHA.01; CELEST.WP5E.BETA.01; CELEST.WP5E.GAMMA.01; CELEST.WP5E.EPS2.01; CELEST.WP5E.DELTA2.01; CELEST.WP5E.EPS1.01; CELEST.WP5E.M1.01; CELEST.WP5E.M2.01; CELEST.WP5E.M3.01; CELEST.WP5E.DELTA1.01; SEAM.EQUIV.01; CONTRACT.G.01; GATE.METRIC.01; v92; v125; v128; v168; v180; v214; v492; v493; v495; v496; v497; v498; v500; v501; v502; v504; v505; v508; v509; v511; v514; v515; v516; v517; v518","external_data_as_recorded":"Bittleston-Homans-Sharma JHEP 09 (2023) 008; Costello arXiv:2111.08879; Costello-Paquette-Sharma PRL 130, 061602 (Burns holography); Bittleston-Sharma-Skinner CMP 403 (2023); Strominger PRL 127, 221601 (w(1+infinity)) -- literature framing, no data","id":"claim:CELEST.SEAM.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":556,"scripts_as_recorded":"v492_celestial_z4_orbifold.py","status_as_recorded":"Open (research contract; WP1-WP5d executed [E]/[C]/[L] via v492/v493/v495/v496/v497/v498/v500/v501/v504 -- WP5d: alpha (mu-index) + beta (split + strong additivity) executed via v501/v504, all three KLM ingredients witnessed on the lattice, continuum uplift stays [O] (Xu's theorem cited); WP5e alpha stage [E] via v502 + beta stage [E] via v505 (equivariant twistor skeleton; kill not fired) + gamma stage [E] via v508 (exchange no-go with certificate (0, 32, 72); negative result, kill not fired) + epsilon-2 stage [E] via v509 (level-from-flux: the one-level statement is now a THEOREM of clock invariance, the sector-counter dial #prim((E8)_k) = 1 <=> k = 1 pins the level; the PT/Z4 back-reaction stays [O]); + delta-2 stage [E] via v511 (the full-tensor ledger: collapse confirmed by innerness, the cubic d-symbol channel opens T3 with the weaker certificate psi = 64, relaxed solution c_d = 1920 = |W(D5)|); + epsilon-1 stage [E] via v514 (epsilon-1 executed via v514: the O(-2) bulk-axion slot is a construction (equivariant Penrose ledger), lambda-tilde = 6 pinned by three exact ledgers (Okubo / measure cancellation excluding 3 and 12 / flux), and the GH/A3 back-reaction step re-derives the v493 family and the Coxeter clock from geometry -- the quantised BCOV coefficient and the twisted channels stay [O] (M1-M3 preregistered)); WP5e-M1 DONE (v515: M1 executed via v515: the back-reacted Omega_N is closed-form on the A3 twistor family, all S3/Z4 periods are (2 pi i)^2-integral with the lockstep flux vector and clock covariance, and the lens geometry FORCES the source charge 4 = |mu4|; honest fence: integrality alone does not discriminate -- the discriminator is the lockstep phase structure (0/24 on the forbidden family)); WP5e-M2+M3 DONE (v516/v517: M2+M3 executed via v516/v517 -- the v514 fence M1-M3 is fully worked off: the twisted KS measure (declared completion reading, ch2-weighted) cancels the 32 T3 residual and delivers the psi = 64 slice without the cubic d-channel, and the a0 uplift couples to the centre count on four scales; what stays [O]: the BCOV measure question -- the delta-1 chain itself is DECIDED by v518 (kill under the derived measure, tension with v516 stated) -- and SEAM.EQUIV.TWISTOR.01); the global BCOV quantisation [O] (single remaining milestone -- the exchange sub-branch closed by v508, the epsilon-2 flux dial executed by v509, the delta-2 tensor ledger executed by v511, the epsilon-1 axion slot executed by v514, the M1-M3 back-reaction milestones executed by v515/v516/v517 (the v514 fence fully worked off); named remaining target: the BCOV MEASURE QUESTION -- the delta-1 chain is DECIDED by v518 (CELEST.WP5E.DELTA1.01: kill under the derived measure, all three testers fail; tension with v516 stated), so what remains is which of the two exact measures (the declared v516 completion reading vs the v518 derived chiral measure) is the true BCOV measure; the cubic GS term stays dissolved (psi = 64 delivered by v516, no branch fires under the derived measure, v518)))","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"WP2 [E]/[C]/[O]: clock-invariance selects XY = Z^4 + a0 sharply; a0 = pure seam scale, tau = i pillowcase frozen (j = 1728 for all a0); clock on H2 = Coxeter element of W(A3) = Picard-Lefschetz monodromy; surviving direction = chi_1-Fourier diagonal, spheres in lockstep; BHS Z2 -> Z4: -4*Nambu bracket anchored at the orbifold, corrections linear in a0, grade-conserving (no sector leak), a0 <-> c^2 slot; negative controls j = 0 / j != 1728 / grading leak; verdict B; SEAM.EQUIV.01 and v216 [O] untouched","checked_by_registry":false,"claim_excerpt":"WP2 OF THE CELESTIAL-HOLOGRAPHIC CONTRACT EXECUTED (2026-07-20; CELEST.SEAM.01 work package 2, verdict B; companion of CELEST.WP1.01/v492): the clock-invariant deformation XY = Z^4 + a0 of the A3 seam orbifold -- geometry, period/monodromy household, and the Bittleston-Homans-Sharma deformed-algebra pattern (arXiv:2305.09451, JHEP 09 (2023) 008; the Z2/Eguchi-Hanson case, fibre XY - Z^2 = -c^2) transferred to k = 4. ","claim_id":"CELEST.WP2.01","dependencies_as_recorded":"CELEST.SEAM.01; CELEST.WP1.01; SEAM.EQUIV.01; v92; v125; v128; v168; v179; v180; v214; v216; v492","external_data_as_recorded":"Bittleston-Homans-Sharma JHEP 09 (2023) 008 (arXiv:2305.09451; deformed CCA on Eguchi-Hanson, Z2 case, c^2 corrections) -- method citation, no data","id":"claim:CELEST.WP2.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":557,"scripts_as_recorded":"v493_celestial_wp2_clock_deformation.py","status_as_recorded":"Formal/Identity [E] (exact deformation geometry/period/algebra arithmetic, sympy, negative controls) + [C] (three named identifications, verdict B; v216 precision typed) + [O] (algebra/contract programme; SEAM.EQUIV.01 and v216 unchanged)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"WP3 [E]/[C]/[O]: Okubo coefficient 5/(2(dim+2)) derived for all 8 algebras (sl4 control); lambda~^2 = h_vee + 6 closed form; lambda_e8 = 6 resp. 1/10 exact; (kappa/c3)^2 = 12 = |mu4| N_fam resp. 1/300 exact, kappa/c3 irrational; so8 slip flagged; look-elsewhere: alignment 8/8 (zero selectivity), g_car | h_vee 1/8 (e8 only), joint test post hoc; K3 not fired, scope demoted -- compatibility, not e8-selective evidence; verdict B; SEAM.EQUIV.01 stays [O]","checked_by_registry":false,"claim_excerpt":"WP3 OF THE CELESTIAL-HOLOGRAPHIC CONTRACT EXECUTED (2026-07-21; CELEST.SEAM.01 work package 3, verdict B; the pre-registered 'alignment test only'): the Green-Schwarz axion coefficient lambda_g of celestial/twistorial SDYM (Costello, arXiv:2111.08879, eq. 1.2.4: kappa = lambda_g/(8 pi sqrt 3)) against the TFPT seam constant c3 = 1/(8 pi). Exact arithmetic throughout (Fraction/sympy, 25 checks). [E] OKUBO IDENTITY DER","claim_id":"CELEST.WP3.01","dependencies_as_recorded":"CELEST.SEAM.01; CELEST.WP1.01; SEAM.EQUIV.01; v92; v125; v128; v492; v493","external_data_as_recorded":"Costello arXiv:2111.08879 (twistorial SDYM axionic consistency, GS coupling eq. 1.2.4, appendix A samples); Costello-Paquette JHEP 10 (2022) 193 (arXiv:2201.02595, eq. 1.5) -- method/normalisation citations, no data","id":"claim:CELEST.WP3.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":558,"scripts_as_recorded":"v495_celestial_wp3_gs_alignment.py","status_as_recorded":"Formal/Identity [E] (exact Okubo/Killing/lambda arithmetic for all 8 algebras, Fraction/sympy, sl4 negative control, look-elsewhere battery) + [C] (the convention typing of the 8 pi and sqrt 3; the alignment reading with the look-elsewhere caveat, verdict B) + [O] (celestial programme WP5; SEAM.EQUIV.01 unchanged)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"WP4 [E]/[C]/[O]: the (E8)_1 character is NOT a conformal block of the E8[C^2] S-algebra in its own jet grading -- mismatch localised three ways (spin unbounded; growth n^{2/3} vs n^{1/2}; level-2 null ideal 27000 = h_vee^3 absent from the jets); BUT the boundary/period reading holds exactly at the current stratum (zero modes 60, jet slice (60,64,60,64), mu4 period sum 248, glue weights (0,1,1,1) integer) -- the MMST scaling-limit shape of SEAM.EQUIV.01; K4 fires only against the exact reading; verdict B(ii); constructive limit -> WP5; SEAM.EQUIV.01 stays [O]","checked_by_registry":false,"claim_excerpt":"WP4 OF THE CELESTIAL-HOLOGRAPHIC CONTRACT EXECUTED (2026-07-21; CELEST.SEAM.01 work package 4, verdict B(ii); the 'type mismatch, head-on'): the (E8)_1 character E4/eta^8 against the glue-equivariant E8[C^2] S-algebra. Exact integer/Fraction/sympy arithmetic (25 checks). [E] BASE: v492 replication (240 = 52+64+60+64, dims with Cartan (60,64,60,64)); equivariant tower D[d] = 60(d+1) even / 64(d+1) odd; cumulative gene","claim_id":"CELEST.WP4.01","dependencies_as_recorded":"CELEST.SEAM.01; CELEST.WP1.01; SEAM.EQUIV.01; v125; v128; v336; v377; v449; v492","external_data_as_recorded":"Costello-Paquette JHEP 10 (2022) 193 (arXiv:2201.02595, Table 1: the celestial S-algebra grading); Bittleston-Homans-Sharma JHEP 09 (2023) 008 (arXiv:2305.09451, equivariant sector); Sym^2(248) = 1 + 3875 + 27000 (standard E8 representation theory) -- method/grading citations, no data","id":"claim:CELEST.WP4.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":559,"scripts_as_recorded":"v496_celestial_wp4_character_shadow.py","status_as_recorded":"Formal/Identity [E] (exact counting/character/theta arithmetic, integer/Fraction/sympy; mismatch localisation with exact cross-multiplication) + [C] (literature gradings CP Table 1 + Sym^2(248) decomposition; the boundary-limit reading, verdict B(ii)) + [O] (the constructive limit -> WP5; SEAM.EQUIV.01 unchanged)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] LO identities + exact-SR values; [C] pulls +0.57 sigma (Planck) / -1.33 sigma (P-ACT-LB record leg); kill = robust positive running; band [50,60] stays the record","checked_by_registry":false,"claim_excerpt":"Spectral-index running of the Starobinsky branch, PROMOTED from the 2026-07-20 scorecard prediction-of-record row (same N_star_reheating group as n_s/r/A_s; never an independent hit). [E] LO identities (sympy exact): alpha_s = dn_s/dln k = -2/N_star^2 = -r/6, beta_s = -4/N_star^3 (NOT -8/N^3); LO band N_star in [50,60]: [-8.0e-4, -5.6e-4]. [E] exact slow roll on the Einstein-frame Starobinsky potential (third-order L","claim_id":"COSMO.RUNNING.01","dependencies_as_recorded":"COSMO.INF.01; COSMO.NSTAR.01; GATE.NSTAR.01","external_data_as_recorded":"Planck 2018 X; ACT DR6 P-ACT-LB (Calabrese+ 2025 JCAP); LiteBIRD/CMB-S4 forecasts","id":"claim:COSMO.RUNNING.01","location_as_recorded":"tfpt_1","path":"verification/status_ledger.csv","row_number":560,"scripts_as_recorded":"v494_cosmo_running_mu_record.py","status_as_recorded":"Identity [E] (LO relations + exact slow roll) + Physical [C] (data confrontation; N_star input)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[C] mu band 1.5-2.3e-8; branch split 3.0e-9 = 3 sigma at Voyage-2050; PIXIE baseline does not reach; [E] frozen comb structurally blind (0.007 sigma); kill = robust mu outside [0.9, 4]e-8","checked_by_registry":false,"claim_excerpt":"CMB mu-distortion as the A_s/N_star BRANCH DISCRIMINATOR, PROMOTED from the 2026-07-20 scorecard prediction-of-record row (data-limited; shares the Nstar_branch alternative group with the two A_s readings -- one branch question, several readings). [C] Chluba-Erickcek-Ben-Dayan k-space window calibrated +21% on the LCDM Planck-2018 anchor to the literature mu_LCDM ~ 2.0e-8: sharp branch N_star = 51.4 (A_s = 1.76e-9) m","claim_id":"COSMO.MUDIST.01","dependencies_as_recorded":"COSMO.INF.01; COSMO.NSTAR.01; GATE.NSTAR.01","external_data_as_recorded":"COBE/FIRAS |mu| < 9e-5; PIXIE baseline forecast 9e-8; Voyage-2050 sigma(mu) ~ 1e-9; Chluba-Erickcek-Ben-Dayan 2012 window","id":"claim:COSMO.MUDIST.01","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":561,"scripts_as_recorded":"v494_cosmo_running_mu_record.py","status_as_recorded":"Physical [C] (Chluba-window bridge, data-limited) + Identity [E] (comb-blindness attenuation)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"WP5a [E]/[C]/[O]: the boundary limit is a precise coefficientwise limit -- chi_w family (E_w = m + w r, quarter units) contains the chiral jet grading at w = 2 and stabilises to the quarter-moded loop Fock at threshold w = n+1 (exact, n <= 8, w <= 10); the limit does NOT produce the truncation (897266 >> 248) -- but the ideal SIZE is DERIVED from root data (Sym^2(248) = 27000 + 3875 + 1, 27000 = h_vee^3, Freudenthal + Weyl + peeling) and the quotient 31124 - 27000 = 4124 = the independent mu4 theta-split sector sum; SO(16)_1 negative control (four blocks, 5304 != 14^3, h = 1/2 breaks fusion); only P = |mu4| = 4 gives 248; open: singular vector as operator (WP5b), GNS limit state (WP5c), local normality/Haag duality (WP5d), Costello-Li uplift (WP5e); SEAM.EQUIV.01 stays [O]","checked_by_registry":false,"claim_excerpt":"WP5a OF THE CELESTIAL-HOLOGRAPHIC CONTRACT EXECUTED (2026-07-21; CELEST.SEAM.01 work package 5a, the first constructive milestone of WP5 -- 'the null ideal from the limit'; the v496 boundary-limit shadow made precise): exact integer/Fraction arithmetic throughout (34 checks), no floats. [E] STABILISATION THEOREM: a one-parameter family chi_w of graded Fock characters on the CHIRAL jet generators (loop energy m = p-q ","claim_id":"CELEST.WP5A.01","dependencies_as_recorded":"CELEST.SEAM.01; CELEST.WP1.01; CELEST.WP4.01; SEAM.EQUIV.01; v125; v128; v336; v377; v449; v492; v496","external_data_as_recorded":"Kac, Infinite dimensional Lie algebras (level-1 integrability + singular-vector generation of the maximal submodule -- used only through counting consequences); Costello-Paquette JHEP 10 (2022) 193 (arXiv:2201.02595, S-algebra grading); Bittleston-Homans-Sharma JHEP 09 (2023) 008 (arXiv:2305.09451, equivariant sector) -- method citations, no data","id":"claim:CELEST.WP5A.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":562,"scripts_as_recorded":"v497_celestial_wp5a_null_ideal.py","status_as_recorded":"Formal/Identity [E] (exact stabilisation/derivation/control arithmetic, integer/Fraction; Freudenthal + Weyl + peeling machinery unit-tested) + [C] (the named identifications: radial decoupling = collar limit; Kac singular vector via counting consequence) + [O] (the operator question WP5b-e; SEAM.EQUIV.01 unchanged)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"WP5b [E]/[C]/[O]: the deletion operator EXISTS and is explicit -- |s> = (E^theta_{-1})^2|0> in a machine-built Chevalley/Frenkel-Kac basis, J^a_1|s> = 0 on all 248 generators (case tally 190/57/1, exactly one case sees k), level dial 2(1-k): only k = 1 deletes, no deletion object in the centerless loop algebra; mu4-compatible: j(theta) = 1, clock phase i^2 = -1, class(2 theta) = 2 sheet-even, 8 quarters = q^2, expressible in the sector-C_1 equivariant variables (KILL branch not triggered); U(g)|s> = V(2 theta) = 27000 = h_vee^3 (orbit BFS = Freudenthal through depth 4), quotient 4124 = sector sum; controls: the 248-current state and generic states not singular, cube at k = 2 (generic Kac mechanics), D8 contrast (5304 != 14^3, h = 1/2 breaks fusion) -- one-block closure E8/mu4-specific; open: the twisted-slot moding carries |s> only via the per-period dictionary -- the precise WP5c GNS/limit-state question; WP5c-e stay [O]; SEAM.EQUIV.01 stays [O]","checked_by_registry":false,"claim_excerpt":"WP5b OF THE CELESTIAL-HOLOGRAPHIC CONTRACT EXECUTED (2026-07-21; CELEST.SEAM.01 work package 5b, the second constructive milestone of WP5 -- 'the singular vector as an operator'; WP5a/v497 fixed the ideal's size and location, WP5b constructs the deleting object): exact integer/Fraction arithmetic throughout (53 checks), no floats, deterministic. [E] CONSTRUCTION: |s> = (E^theta_{-1})^2|0>, theta the highest root, wei","claim_id":"CELEST.WP5B.01","dependencies_as_recorded":"CELEST.SEAM.01; CELEST.WP5A.01; CELEST.WP4.01; SEAM.EQUIV.01; v128; v492; v496; v497","external_data_as_recorded":"Kac, Infinite dimensional Lie algebras (the level-1 singular vector (E^theta_{-1})^{k+1}|0> -- reproduced by machine here at k = 1 and k = 2, cited only beyond level 2); Frenkel-Kac cocycle construction (machine-rebuilt and verified, not cited); Costello-Paquette JHEP 10 (2022) 193 + Bittleston-Homans-Sharma JHEP 09 (2023) 008 (equivariant-sector framing) -- method citations, no data","id":"claim:CELEST.WP5B.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":563,"scripts_as_recorded":"v498_celestial_wp5b_singular_vector.py","status_as_recorded":"Formal/Identity [E] (exact construction/singularity/control arithmetic, integer/Fraction, deterministic; Chevalley basis + affine PBW engine unit-tested on all 61504 pairs) + [C] (the named identifications: Weyl complete reducibility beyond BFS depth 4; Kac mechanics beyond level 2; per-period quarter dictionary) + [O] (the GNS/limit-state question WP5c-e -- the twisted-slot moding tension is the precise WP5c question; SEAM.EQUIV.01 unchanged)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"WP5c [E]/[C]/[O]: the GNS limit state EXISTS and is explicit -- the quasi-free family omega_w (affine k=1 vacuum + x^{wr}-contracted radial oscillators; compact adjoint machine-determined on all 61504 pairs) is positive for every finite w, stabilises exactly at the WP5a threshold w = N+1, and its limit has GNS levels (1, 248, 4124): full 9361-block exact Gram, level-2 rank 4124 = chi_2, kernel 27000 = V(2 theta) weight by weight, every block PSD, rank table (0,0,1,8,44); the 248 layer survives (level-1 rank 248 PD); the clock descends to GNS with rank split (1036,1024,1040,1024) = the per-period theta-split; |s> is the GNS zero vector (WP5b S4.10 resolved at the state level); CCR obstruction: no w-uniform damping state -- the family is necessary AND exists (KILL not triggered); controls: k = 2 keeps everything, k = 0 has no current layer, D8 = one block of four, wrong family/no damping caught (710955/897266 != 248); open: local normality, net/Haag duality (WP5d), Costello-Li (WP5e); SEAM.EQUIV.01 stays [O]","checked_by_registry":false,"claim_excerpt":"WP5c OF THE CELESTIAL-HOLOGRAPHIC CONTRACT EXECUTED (2026-07-21; CELEST.SEAM.01 work package 5c, the third constructive milestone of WP5 -- 'the GNS limit state'; WP5a/v497 made the boundary limit precise, WP5b/v498 built the deleting operator, WP5c constructs the STATE whose GNS kernel contains the null ideal): exact integer/Fraction arithmetic throughout (35 checks), no floats, deterministic. [E] CONSTRUCTION: the ","claim_id":"CELEST.WP5C.01","dependencies_as_recorded":"CELEST.SEAM.01; CELEST.WP5A.01; CELEST.WP5B.01; SEAM.EQUIV.01; v128; v492; v496; v497; v498","external_data_as_recorded":"Kac, Infinite dimensional Lie algebras (positivity of the contravariant form beyond level 2 -- levels <= 2 machine-checked here); Bratteli-Robinson (quasi-free states, standard extension); Costello-Paquette JHEP 10 (2022) 193 + Bittleston-Homans-Sharma JHEP 09 (2023) 008 (equivariant-sector framing) -- method citations, no data","id":"claim:CELEST.WP5C.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":564,"scripts_as_recorded":"v500_celestial_wp5c_gns_limit_state.py","status_as_recorded":"Formal/Identity [E] (exact construction/Gram/control arithmetic, integer/Fraction, deterministic; the compact anti-involution machine-determined; the full 9361-block level-2 Gram exact) + [C] (the named identifications: quasi-free extension; Kac positivity beyond level 2; module identification in the component route) + [O] (local normality, net structure/Haag duality, Costello-Li -- WP5d/e; SEAM.EQUIV.01 unchanged)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"WP5d-alpha [E]/[L]/[N]/[C]/[O]: the two-interval mu-index measured entropically on the seam lattice edge -- fermionic MI extensive (mu = 1 reference, c fit 0.5000, |F| -> 0), the sector-summed orbifold pays exactly one classical bit (16-layer carrier ln 2 plateau to 1.1e-15 at N = 512), [F : F_even] = 2, mu_gauged = 4 = the v490 census (two independent lattice witnesses); complementary-pair budget <= ln 4 (double-limit statement) + the orbifold duality-failure witness; condensation arithmetic anchored at both measured ends: 16 -> 4 -> 1 (KLM/Longo-Rehren, Sigma d^2, theta_v = 1 exactly at nu = 16, rivals != 1) => mu = 1 after condensation, preregistered KILL not triggered; controls: nu = 1 non-removable, trivial phase zero, wrong sector sum loses the full ln 2; open: WP5d-beta (continuum Haag duality / local normality / split, exploration running) + WP5e (Costello-Li); SEAM.EQUIV.01 stays [O]","checked_by_registry":false,"claim_excerpt":"WP5d-ALPHA OF THE CELESTIAL-HOLOGRAPHIC CONTRACT EXECUTED (2026-07-21; CELEST.SEAM.01 work package 5d, alpha stage -- 'the two-interval index from the lattice'; the local-net question): numpy/scipy Gaussian machinery + exact Fractions (39 checks). Roadmap discriminator: (E8)_1 => mu = 1 (Haag-dual two-interval net, ONE sector); SO(16)_1 => mu = 4; preregistered KILL = 'the two-interval mu-offset does NOT vanish after","claim_id":"CELEST.WP5D.01","dependencies_as_recorded":"CELEST.SEAM.01; CELEST.WP5C.01; SEAM.CCC.01; SEAM.MU.01; SEAM.EQUIV.01; v367; v378; v450; v489; v490","external_data_as_recorded":"Kawahigashi-Longo-Mueger CMP 219 (2001) (two-interval subfactor index mu = Sigma d_i^2); Longo-Xu (multi-interval subfactors); Casini-Huerta-Magan-Pontello (entropic order parameters, the (1/2) ln mu defect); Peschel J. Phys. A 36 (2003) (Gaussian covariance); Calabrese-Cardy (interval entropy) -- method citations, no data","id":"claim:CELEST.WP5D.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":565,"scripts_as_recorded":"v501_celestial_wp5d_two_interval_index.py","status_as_recorded":"Formal [E] (the exact arithmetic: Cartan dets, KLM/Longo-Rehren quotients, Sigma d^2, theta_v at nu = 16, machine identities) + Lattice/Numerical [L]/[N] (the Gaussian lattice witnesses, ED-validated to 1e-15: extensivity, the ln 2 plateau, the duality-asymmetry witness) + [C] (the continuum dictionary offset = ln index -- KLM/Longo-Xu/CHMP -- and the interacting condensation step) + [O] (continuum Haag duality / local normality / split of the quotient net = WP5d-beta; Costello-Li = WP5e; SEAM.EQUIV.01 unchanged)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"WP5e-alpha [E]/[C]/[O]: the q^{-1/3} prefactor of E4/eta^8 derived as exact mu4 vacuum-energy bookkeeping (inner clock => shift orbifold theta = 0^8, common -c/24 = -1/3 at c = 8; discriminant form = Casimir via spectral flow AND 16-Majorana free fermions; rotation reading fails 3/16 != 3/8) and k = 1 forced three independent ways (current condition h(J) = k = 1; conformal embedding 47(k-1)(k+266/47) = 0 resp. 128(k-1) = 0; c = 8 <=> 240(k-1) = 0; plus the WP5b singular-vector dial 31124 - 27000 = 4124) with the honest sharpening that glue-h integrality holds for ALL k and fixes nothing; controls: D8 same prefactor (discriminator = h-integrality), rotation twists break the common prefactor, wrong k fails all five dials; the BCOV/twistor inflow itself stays [O] -- WP5e not closed, SEAM.EQUIV.01 untouched","checked_by_registry":false,"claim_excerpt":"WP5e-ALPHA OF THE CELESTIAL-HOLOGRAPHIC CONTRACT EXECUTED (2026-07-21; CELEST.SEAM.01 work package 5e, alpha stage -- 'prefactor and level bookkeeping', the CFT-side anchor of the BCOV/Costello-Li twistor uplift): exact sympy/Fraction arithmetic, no floats (33 checks). Roadmap target: boundary partition function = E4/eta^8 INCLUDING the q^{-1/3} prefactor; preregistered KILL = 'the anomaly inflow demands a level != 1","claim_id":"CELEST.WP5E.ALPHA.01","dependencies_as_recorded":"CELEST.SEAM.01; CELEST.WP1.01; CELEST.WP4.01; CELEST.WP5A.01; CELEST.WP5B.01; CELEST.WP5C.01; CELEST.WP5D.01; SEAM.EQUIV.01; v492; v496; v497; v498; v500; v501","external_data_as_recorded":"Costello arXiv:2111.08879 (one-loop axion coefficient); Costello-Paquette-Sharma PRL 130, 061602 (level-from-flux); BCOV / Costello-Li (framing of the open twistor target) -- literature framing, no data","id":"claim:CELEST.WP5E.ALPHA.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":566,"scripts_as_recorded":"v502_celestial_wp5e_prefactor_level.py","status_as_recorded":"Formal/Identity [E] (exact prefactor/level arithmetic: Hurwitz-zeta vacuum energies, inner/shift twist distribution, discriminant-form = Casimir two-route identity, current/embedding/central-charge k-fixing, singular-vector dial -- sympy/Fraction exact, Wolfram-mirrored) + [C] (Kac generation for k >= 3) + [O] (the BCOV/Costello-Li twistor inflow = WP5e proper; SEAM.EQUIV.01 unchanged)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Emergence test light [E]/[N]/[C]/[O]: no dynamical selection of the square (global det' winner = hexagonal, tau = i a saddle, criticality = Palais symmetry); the square is pinned by rigidity alone (DtN mod-4 indicator = isolated zero at tau = i; j = 1728 iff t = 1; Z2 chain modulus-blind); residual convergence: QGEO-R1 == P2-R1 = ONE common rest, the order-4 clock (Coxeter of W(A3) = the v499 cusp-class carrier datum); v215 lever 7 lifted from deferred to light-executed -- marker unchanged, QGEO.REALIZE.01 stays [C]/[O]","checked_by_registry":false,"claim_excerpt":"THE v215 DEFERRED EMERGENCE TEST (LEVER 7) EXECUTED LIGHT + RESIDUAL CONVERGENCE QGEO-R1 == P2-R1 (2026-07-21; analysis/kill-test class, v347/v264 style; NO marker moves -- QGEO.REALIZE.01 stays [C]/[O], AX.P2.01 stays an axiom): v215 lever 7 said the decisive (deferred) kill of the bedrock is to compute the raw P1 seam-collar DtN WITHOUT inputting the marks and check whether four SQUARE marks EMERGE; v216 already de","claim_id":"QGEO.EMERGE.LIGHT.01","dependencies_as_recorded":"QGEO.KILL.01; QGEO.REALIZE.01; QGEO.RIGID.01; P2.TYPING.01; CELEST.WP1.01; CELEST.WP2.01; v215; v216; v264; v280; v347; v492; v493; v499","external_data_as_recorded":"Osgood-Phillips-Sarnak J. Funct. Anal. 80 (1988) 148 (extremals of determinants of Laplacians; hexagonal maximiser) -- literature anchor, no data","id":"claim:QGEO.EMERGE.LIGHT.01","location_as_recorded":"tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":567,"scripts_as_recorded":"v503_qgeo_emergence_light.py","status_as_recorded":"Formal [E] (exact structure: pillowcase = half torus pair structure, permutation identities R^2 = Z2, clock-forcing a3 = a2 = a1 = 0 with j = 1728 identically, Coxeter charpoly) + Numerical [N] (eta/E2*/j at 40 digits; v280-style lattice DtN curves) + [C] (clock = carrier input) + [O] (the dynamical realisation of the clock); NO marker moves -- QGEO.REALIZE.01 stays [C]/[O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"WP5d-beta [E]/[L]/[N]/[C]/[O]: split + strong additivity witnessed on the seam lattice edge for the orbifold prescription -- strong additivity EXACT with the shared boundary Majorana (GF2 spans full, rank 32/32; disjoint index exactly 2 = the v501 ln-2 bit), the entropic touching defect BOUNDED < ln 2 with the Ising 1/4-exponent approach (p = 0.2444) while the preregistered U(1) control diverges ((1/2) ln Var Q, Klich-Levitov pinned): bounded-vs-divergent is the lattice discriminator; split via the elliptic-nome sigma_k ladder (1.3-2.0%, sigma_1 ~ x^{1/2}, trace norm summable) with EXACT orbifold inheritance (C -> -C + Lambda^2 C compound, Longo heredity); Pimsner-Popa E(a) - a/2 = PaP/2 identically (lambda = 1/2 = 1/[F:F_even], integer attainment 16384 + 2048 with 0 violations), lambda_E4 = 1/4 = 1/mu, index consistency exp(Delta) = 2 = 1/lambda_PP two routes; controls: dimerised trivial, wrong prescription exactly 0, finite-size honesty documented; with v501 all THREE KLM ingredients of complete rationality witnessed on the lattice; continuum uplift stays [O] (Xu's theorem cited, not claimed; WP5e/Costello-Li); SEAM.EQUIV.01 stays [O]","checked_by_registry":false,"claim_excerpt":"WP5d-BETA OF THE CELESTIAL-HOLOGRAPHIC CONTRACT EXECUTED (2026-07-21; CELEST.SEAM.01 work package 5d, beta stage -- 'split + strong additivity from the lattice'; the two remaining Kawahigashi-Longo-Mueger legs of complete rationality = split property + strong additivity + finite two-interval mu-index, the index being WP5d-alpha/v501): numpy/scipy Gaussian machinery + exact GF2/integer algebra (37 checks, deterministi","claim_id":"CELEST.WP5DB.01","dependencies_as_recorded":"CELEST.SEAM.01; CELEST.WP5D.01; SEAM.CCC.01; SEAM.MU.01; SEAM.EQUIV.01; v367; v450; v489; v490; v501","external_data_as_recorded":"Kawahigashi-Longo-Mueger CMP 219 (2001) (complete rationality = split + strong additivity + finite mu-index); Xu (algebraic orbifold CFTs: finite-group orbifolds of completely rational nets are completely rational -- cited, not claimed); Longo-Xu (multi-interval subfactors; bounded-vs-divergent dichotomy); Longo (split heredity under finite index); Pimsner-Popa (the conditional-expectation index bound); Casini-Huerta-Magan-Pontello (entropic order parameters); Buchholz-Schulz-Mirbach (strong-additivity failure of the U(1) current net); Klich-Levitov (charge-variance log law); Buchholz-Wichmann (nuclearity); Peschel J. Phys. A 36 (2003) (Gaussian covariance) -- method citations, no data","id":"claim:CELEST.WP5DB.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":568,"scripts_as_recorded":"v504_celestial_wp5d_klm_completeness.py","status_as_recorded":"Formal [E] (the exact algebra spans/indices, the PP identities with integer attainment, the Lambda^2-compound and parity machine identities, the index consistency) + Lattice/Numerical [L]/[N] (the deficit tables, the nome ladder, the power laws, the Klich-Levitov slope; Gaussian-exact, ED-validated) + [C] (the KLM dictionary: Longo-Xu bounded-deficit dichotomy, Longo split heredity, CHMP order parameters) + [O] (the continuum proof for the seam quotient net and the condensed (E8)_1 net -- Xu's orbifold theorem cited, not claimed; WP5e/Costello-Li; SEAM.EQUIV.01 unchanged)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"WP5e-beta [E]/[C]/[O]: the Atiyah-Bott/Lefschetz skeleton of the twistor inflow exact -- denominators (2,4,2) with Dedekind sum 5/4, characters (248,0,-8,0) two routes, invariant Okubo 36<x,x>^2 with the twisted sectors NOT reducing and the AB sum leaving the rigid 32 T3 residual; index bridge f(m) = ch2(T_m) exact with glue defect -78 both routes; level dials k = 1 geometric (current count 240/0/0/0, residual 0/360/814/1362, one scale => one level -- since v509 (WP5e-epsilon-2) a THEOREM of clock invariance, no longer a heuristic); E3 refuted: a0 = graviton modulus O(2), not the axion O(-2) (mismatch 4 = |mu4|), the three sphere classes = the three twisted axion slots; controls diag(i,i)/SO(16)/k = 2 quantified; kill branch does not fire on the equivariant skeleton; the global BCOV quantisation stays [O] -- with the rigid 32 T3 twisted residual and the sphere-axion pairing as the named remaining targets; SEAM.EQUIV.01 untouched","checked_by_registry":false,"claim_excerpt":"WP5e-BETA OF THE CELESTIAL-HOLOGRAPHIC CONTRACT EXECUTED (2026-07-21; CELEST.SEAM.01 work package 5e, beta stage -- 'the equivariant anomaly ledger on twistor space', the twistor-side milestone of the BCOV/Costello-Li uplift; WP5e-alpha = v502 anchored the CFT side): exact sympy/Fraction arithmetic, no floats (47 checks). Roadmap target: the anomaly-inflow side of the boundary partition function; preregistered KILL =","claim_id":"CELEST.WP5E.BETA.01","dependencies_as_recorded":"CELEST.SEAM.01; CELEST.WP1.01; CELEST.WP2.01; CELEST.WP3.01; CELEST.WP4.01; CELEST.WP5E.ALPHA.01; SEAM.EQUIV.01; v492; v493; v495; v496; v502","external_data_as_recorded":"Costello arXiv:2111.08879 (one-loop box anomaly, GS axion coupling); Bittleston-Sharma-Skinner CMP 403 (Poisson-CS tower, O(-2)-valued Poisson structure); Costello-Paquette-Sharma PRL 130, 061602 (level-from-flux); Kronheimer/McKay ALE intersection data -- literature framing, no data","id":"claim:CELEST.WP5E.BETA.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":569,"scripts_as_recorded":"v505_celestial_wp5e_beta_equivariant_ledger.py","status_as_recorded":"Formal/Identity [E] (exact equivariant arithmetic: Atiyah-Bott denominators/characters, per-sector Okubo decomposition with the rigid 32 T3 residual, index bridge f(m) = ch2(T_m) with the -78 defect, geometric level dials, axion-slot weight arithmetic -- sympy/Fraction exact, Wolfram-mirrored) + [C] (the dictionaries above) + [O] (the global BCOV quantisation = WP5e proper; SEAM.EQUIV.01 unchanged)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Clock rigidity [E]/[C]: the deck has exactly two Moebius square roots, both automatically order 4; marks-preserving root <=> deck = central involution of the mark-D4 (counterexample shows harmonicity alone insufficient); the NS Fock implementation is FORCED to order 4 (U^2 = (-1)^F exact in Cl(16), nonsplit; Z8 tower V^2 prop U, V^4 prop (-1)^F; R sector splits) -- the order-4 clock input reduces to ONE alignment bit ('deck central in the mark-D4'); the fermionic Z4 forces the order, not the alignment; QGEO-R1 == P2-R1 now = this single bit; no marker moves; v507 characterises the bit as a tetrad with a physical face (non-split NS Fock extension class) and derives the deck CLASS (half-period translation) -- only the position stays the input; v510 excludes the edge class topologically (covering-deck freeness = P1's closed seam circle): the bit reduces to the square-modulus datum tau = i alone","checked_by_registry":false,"claim_excerpt":"SEAM CLOCK RIGIDITY -- ROUTE B OF THE v503 CLASSIFICATION EXECUTED (2026-07-21; two exact theorems in one module, Part A Moebius + Part B Fock, 34 checks; NO marker moves -- QGEO.REALIZE.01 stays [C]/[O], AX.P2.01 stays an axiom): v503 localised the one remaining identification input as 'why does the raw seam carry the order-4 clock' (QGEO-R1 == P2-R1). v506 reduces that input to ONE alignment bit. [E] THEOREM A (Moe","claim_id":"SEAM.CLOCK.RIGIDITY.01","dependencies_as_recorded":"QGEO.REALIZE.01; QGEO.RIGID.01; QGEO.EMERGE.LIGHT.01; P2.TYPING.01; SEAM.BIT.ORIGIN.01; v117; v168; v214; v215; v216; v490; v492; v493; v499; v503; v507; SEAM.BIT.FREEDOM.01; v510","external_data_as_recorded":"Fidkowski-Kitaev Z8 classification of interacting Majorana chains (PRB 81, 134509) -- literature anchor, no data","id":"claim:SEAM.CLOCK.RIGIDITY.01","location_as_recorded":"tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":570,"scripts_as_recorded":"v506_seam_clock_rigidity.py","status_as_recorded":"Formal/Identity [E] (Theorem A: complete PGL2(C) square-root classification, D4 centrality criterion, counterexample, n-arithmetic, stabiliser trichotomy -- sympy exact; Theorem B: U^2 = (-1)^F in exact Cl(16) Fractions, nonsplit Z4 extension, Z8 tower, R-sector split control, 16-fold-way arithmetic -- Wolfram-mirrored) + [C] (the one alignment bit: deck central in the mark-D4); QGEO.REALIZE.01 stays [C]/[O], P2.TYPING.01 R1 mapped onto the same bit","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Bit origin [E]/[C]: marks = half-periods of the seam double, every mark-free collar deck IS a half-period translation (class forced); a marks-preserving root exists iff lambda in {-1, 2, 1/2} <=> deck pairs harmonic <=> tau = i AND deck = the CM-fixed half-period (tetrad closed by the fermionic face: central <=> non-split NS Fock extension U^2 = (-1)^F, edge <=> split U^2 = +1, 0 roots); silver = in-family misalignment witness -- TAUTOLOGY REFUTED, the one alignment bit stays the [C] carrier input (position, not class); no marker moves; v510 types the position half as topology (covering-deck freeness excludes the edge class): the rest is the square-modulus datum tau = i alone","checked_by_registry":false,"claim_excerpt":"THE TAUTOLOGY ATTACK ON THE v506 ALIGNMENT BIT, EXECUTED AND REFUTED (2026-07-21; one module, Part A torus origin + Part B fermion dichotomy, 26 checks; NO marker moves -- the bit stays [C], SEAM.CLOCK.RIGIDITY.01 and QGEO.REALIZE.01 text-precised only): v506 reduced the last identification input to ONE bit ('the collar deck is the central involution of the mark-D4'). Conjecture under attack: marks and deck both desc","claim_id":"SEAM.BIT.ORIGIN.01","dependencies_as_recorded":"SEAM.CLOCK.RIGIDITY.01; QGEO.REALIZE.01; QGEO.RIGID.01; QGEO.EMERGE.LIGHT.01; P2.TYPING.01; v117; v168; v214; v215; v216; v260; v490; v492; v493; v499; v503; v506; SEAM.BIT.FREEDOM.01; v510","external_data_as_recorded":"Fidkowski-Kitaev Z8 classification of interacting Majorana chains (PRB 81, 134509) -- literature anchor, no data","id":"claim:SEAM.BIT.ORIGIN.01","location_as_recorded":"tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":571,"scripts_as_recorded":"v507_seam_bit_origin.py","status_as_recorded":"Formal/Identity [E] (origin theorem: half-period fixed points, rational descent identity, free-involution census in all three stabiliser types; core solve lambda in {-1, 2, 1/2}; CM dictionary; equivalence tetrad + circularity audit; fermion dichotomy: Utilde^2 = 256 gamma-monomial vs +2^7 scalar in exact Cl(16) Fractions, root counts 2 vs 0, arrangement census 28/21 -- sympy exact, Wolfram-mirrored) + [C] (the one alignment bit: which half-period, i.e. the deck position); SEAM.CLOCK.RIGIDITY.01 and QGEO.REALIZE.01 stay as they are, P2.TYPING.01 R1 unchanged","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Bit freedom [E]/[C]: the collar deck is a covering deck, hence FREE on the seam circle; the unique free involution is the antipode (Aut(C_16) = D_16, complete census) and NONSPLIT <=> FREE over all 17 involutions -- the edge/silver class is topologically EXCLUDED (its real structure's fix circle passes through the deck poles; the edge class is the branched pillowcase involution's restriction); harmonic + free => mu4 exactly, but freeness does not give harmonicity (honest counterwitnesses) -- the alignment bit reduces from 'harmonic AND central' to the square-modulus datum tau = i alone: the position half is topology, the modulus half stays the one [C] carrier input; v512 restates the modulus half as the flag-transitivity bit; no marker moves","checked_by_registry":false,"claim_excerpt":"THE FREEDOM ATTACK ON THE v506/v507 ALIGNMENT BIT -- THE POSITION HALF OF THE BIT IS TOPOLOGY (2026-07-21; one module, Part A dihedral/fermionic + Part B Moebius/RP-geometry, 30 checks; NO marker moves -- the modulus datum stays [C], SEAM.CLOCK.RIGIDITY.01, SEAM.BIT.ORIGIN.01 and QGEO.REALIZE.01 text-precised only, P2.TYPING.01 R1 halved): v507 left the last identification input as ONE bit with four equivalent faces;","claim_id":"SEAM.BIT.FREEDOM.01","dependencies_as_recorded":"SEAM.BIT.ORIGIN.01; SEAM.CLOCK.RIGIDITY.01; QGEO.REALIZE.01; QGEO.REALIZE.02; QGEO.RIGID.01; QGEO.EMERGE.LIGHT.01; P2.TYPING.01; v216; v264; v456; v490; v492; v503; v506; v507","external_data_as_recorded":"-","id":"claim:SEAM.BIT.FREEDOM.01","location_as_recorded":"tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":572,"scripts_as_recorded":"v510_seam_bit_freedom.py","status_as_recorded":"Formal/Identity [E] (dihedral theorem: unique free involution = antipode, Aut(C_16) = D_16 complete census, quotient topology chi 0 vs 1; complete Cl(16) Fock census NONSPLIT <=> FREE over all 17 involutions; real-structure classification: two deck-commuting families, per-configuration uniqueness table; harmonic + free => b = +-i exactly; counterwitnesses -- sympy exact / exact Cl(16) Fractions, Wolfram-mirrored) + [C] (the square-modulus datum tau = i); SEAM.CLOCK.RIGIDITY.01, SEAM.BIT.ORIGIN.01 and QGEO.REALIZE.01 stay as they are (text precised only), P2.TYPING.01 R1 halved","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"WP5e-gamma [E]/[C]/[O]: the exchange route for the sphere-axion pairing is KILLED with a three-functional certificate -- invariant quadratics on the glue Cartan exactly span{s5, s3} (dim 2), quartics exactly span{P1, P2, P3, T5, T3} (dim 5), the product of any two invariant quadratics has zero T5/T3 content (master kill: Phi_T3 annihilates every exchange image, Phi_T3(A_fix) = 32 != 0); strict two-index rule collapses the sphere couplings entirely (m = 0 only), twist-insertion channels give a rank-2 exchange matrix with rank([M | A_fix]) = 3 and certificate (Phi_T5, Phi_T3, Phi_P) = (0, 32, 72); K^(0) = -15 K^(2) side discovery; ch2-natural and AB-weight couplings miss scale-independently (naturalness dissolves); SO(16) has no sphere partners AND uncancelled T5, D8 has no T3 structure; the 32 T3 burden moves to the twisted BCOV contact terms (delta-1, binary: coefficient exactly (9, -30, -15, 0, 32) computed not fitted) and the full-tensor ledger (delta-2); slot bijection untouched, level-kill still not fired, SEAM.EQUIV.01 stays [O], no marker moves","checked_by_registry":false,"claim_excerpt":"WP5e-GAMMA OF THE CELESTIAL-HOLOGRAPHIC CONTRACT EXECUTED (2026-07-21; CELEST.SEAM.01 work package 5e, gamma stage -- 'the sphere-axion pairing check', an honest rigid NEGATIVE result in the v505 style; exact sympy/Fraction arithmetic, no floats, 27 checks, ~4 s): can the three twisted sphere axions eta_m (m = 1, 2, 3; Coxeter eigencharacters {i, -1, -i} on H^2(ALE), v505 S5.8) cancel the rigid 32 T3 residual of the ","claim_id":"CELEST.WP5E.GAMMA.01","dependencies_as_recorded":"CELEST.SEAM.01; CELEST.WP5E.ALPHA.01; CELEST.WP5E.BETA.01; SEAM.EQUIV.01; v492; v493; v495; v502; v505","external_data_as_recorded":"Costello arXiv:2111.08879 (one-loop box anomaly, GS axion coupling); Bittleston-Sharma-Skinner CMP 403 (Poisson-CS tower, O(-2)-valued Poisson structure); Costello-Paquette-Sharma PRL 130, 061602 (level-from-flux) -- literature framing, no data","id":"claim:CELEST.WP5E.GAMMA.01","location_as_recorded":"tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":573,"scripts_as_recorded":"v508_celestial_wp5e_gamma_pairing.py","status_as_recorded":"Formal/Identity [E] (exact vertex-space/selection/certificate arithmetic: invariant quadratics dim 2 and quartics dim 5 by Weyl nullspace, product theorem, rank-3 certificate (0, 32, 72), naturalness resolution, SO(16)/D8 controls -- sympy/Fraction exact, Wolfram-mirrored) + [C] (the number fences 32 = 20 + 12, 72 = 2 lambda~^2_e8) + [O] (the twisted BCOV contact terms delta-1 (binary) + the full-tensor ledger delta-2; SEAM.EQUIV.01 unchanged; CELEST.SEAM.01 stays Open)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"WP5e-epsilon-2 [E]/[C]/[O] (verdict B): k = 1 from flux quantisation -- partially derived. DERIVED exact: one level is a THEOREM (lockstep from clock invariance: one mu4 orbit, |Pi_j| = sqrt(2) t equal, monodromy = pure phase i, det(A-1) = -4 no invariant flux vector; falsifier Z^4 - Z: 0/24 orderings lockstep), flux-per-current = 1 uniformly (pairing matrix = identity up to diagram flip, pinned by complete enumeration from the v505 ch2 ledger; fluxes (64, 60, 64) = flavour multiplicity, NOT the level -- the naive reading killed by the lockstep test itself), the sector-counter dial pins the value (16 = ord^2 fractional sectors condense through the Lagrangian mu4 glue to 1; #primaries((E8)_k) = 1 iff k = 1), and the CPS skeleton is exact (level linear in the flux quantum, minimal quantum N = 1 <-> k = 1). ANALOGY [C]: the CPS dictionary on PT/Z4. OPEN [O]: the type-I B-model backreaction on PT/Z4. The v505 'one scale => one level' sentence is lifted to theorem status (text move, no gate move); WP5e stays [O]; SEAM.EQUIV.01 untouched; no marker moves","checked_by_registry":false,"claim_excerpt":"WP5e-EPSILON-2 OF THE CELESTIAL-HOLOGRAPHIC CONTRACT EXECUTED (2026-07-21; CELEST.SEAM.01 work package 5e, epsilon-2 stage -- 'the CPS level-from-flux dial', verdict B; exact sympy/Fraction arithmetic, no floats, 28 checks, <1 s): derive the boundary level k = 1 from flux quantisation on the lockstep spheres, following the Costello-Paquette-Sharma (CPS) Burns-holography mechanism (PRL 130, 061602; arXiv:2306.00940). ","claim_id":"CELEST.WP5E.EPS2.01","dependencies_as_recorded":"CELEST.SEAM.01; CELEST.WP5E.ALPHA.01; CELEST.WP5E.BETA.01; CELEST.WP5E.GAMMA.01; SEAM.EQUIV.01; v492; v493; v502; v505; v508","external_data_as_recorded":"Costello-Paquette-Sharma PRL 130, 061602 + arXiv:2306.00940 (Burns holography, level-from-flux mechanism); Costello arXiv:2111.08879 (one-loop box anomaly) -- literature framing, no data","id":"claim:CELEST.WP5E.EPS2.01","location_as_recorded":"tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":574,"scripts_as_recorded":"v509_celestial_wp5e_eps2_level_from_flux.py","status_as_recorded":"Formal/Identity [E] (exact CPS-skeleton/pairing/lockstep/sector arithmetic: S^3 period (2 pi i)^2 N, exceptional flux 2 pi N, contraction 2N, pairing enumeration 48 -> 2, fluxes (64, 60, 64), current count (240, 0, 0, 0), #primaries (1, 3, 5, 10, 15, 27), lockstep theorem det(A-1) = -4 with the 0/24 negative probe, k = 2 / SO(16) / A2 controls -- sympy/Fraction exact, Wolfram-mirrored) + [C] (the CPS dictionary itself on PT/Z4: their geometry is the C^2 blow-up with one (-1)-sphere and so(8) at negative level, not the A3 ALE -- typed as an analogy until the backreaction is computed) + [O] (the type-I B-model backreaction on PT/Z4 -- twisted Kodaira-Spencer measure, the A3 Omega_N; the same fence as v502 S5.7/v505)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"WP5e-delta-2 [E]/[C]/[O] (intermediate verdict): the full-tensor ledger -- the v508 collapse is CONFIRMED full-tensorially and arity-crossing (innerness theorem: h in the g0 Cartan, every invariant tensor charge-0 mod 4; all 15 non-neutral trilinear triples Hom = 0), and the charge-0 ledger contains exactly ONE structure invisible to the quadratic ansatz: the su(4) d-symbol (unique symmetric trilinear on e8, so(10) has no cubic Casimir), whose exchange quartic Q_dd = (1/60)(T3 - P3/4) breaks the Phi_T3 master kill (1/60 != 0) -- the T3 channel OPENS; the pairing stays obstructed in the charge reading with the weaker certificate {Phi_T5, psi = Phi_P - Phi_T3/4}, psi(A_fix) = 64 = dim g1 [C], and becomes exactly solvable relaxed: A_fix = -u + 8v + 2w + 1920 Q_dd with c_d = 1920 = |W(D5)| [C] (the |W(D5)| reading look-elsewhere-loaded and convention-contingent -- v513); SO(16)/D8 has no symmetric cubic and no odd sectors (E8/mu4 doubly special), false g0/sector controls separate; the burden on delta-1 is sharpened to the psi = 64 slice or the selection-rule relaxation (delta-1 itself UNDECIDED at exploration level at promotion time, since DECIDED by v518 (CELEST.WP5E.DELTA1.01: kill under the derived measure, tension with v516 stated; the pre-v518 state: strict holomorphic reading refuted at the Z2 anchor, contact term = modular completion / Harvey-Moore tau-integral, forced (T5,T3) ratio 4:3, massive coset levels n >= 2 mandatory); SEAM.EQUIV.01 stays [O], no marker moves","checked_by_registry":false,"claim_excerpt":"WP5e-DELTA-2 OF THE CELESTIAL-HOLOGRAPHIC CONTRACT EXECUTED (2026-07-21; CELEST.SEAM.01 work package 5e, delta-2 stage -- 'the full-tensor ledger', the named escape route of the v508 exchange no-go, intermediate verdict, exact; integer-scaled weight multisets + Kostant/Weyl alternating sums + sympy/Fraction, no floats, 41 checks, ~4 s): does the FULL adjoint tensor structure of e8 (non-Cartan external legs, higher-ar","claim_id":"CELEST.WP5E.DELTA2.01","dependencies_as_recorded":"CELEST.SEAM.01; CELEST.WP5E.ALPHA.01; CELEST.WP5E.BETA.01; CELEST.WP5E.GAMMA.01; CELEST.WP5E.EPS2.01; SEAM.EQUIV.01; v492; v493; v502; v505; v508; v509","external_data_as_recorded":"Costello arXiv:2111.08879 (one-loop box anomaly, GS axion coupling); Bittleston-Sharma-Skinner CMP 403 (twistor uplift on ALE); Harvey-Moore hep-th/9510182 (tau-integral / modular completion, framing for the delta-1 fence) -- literature framing, no data","id":"claim:CELEST.WP5E.DELTA2.01","location_as_recorded":"tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":575,"scripts_as_recorded":"v511_celestial_wp5e_delta2_tensor_ledger.py","status_as_recorded":"Formal/Identity [E] (exact Hom-table/certificate arithmetic: g0 = d5 (+) a3 without u(1), sector factorisation into minuscule orbits, innerness theorem at arities 2 and 3, bilinear table (2, 1, 1, 1), trilinear neutral dims (3, 2, 2, 1, 1), unique symmetric survivor = su(4) d-symbol, Q_dd = (1/60)(T3 - P3/4) two routes, rank-3/4 certificate psi(A_fix) = 64, relaxed solution (-1, 8, 2; 1920), SO(16)/false-g0/false-sector controls -- sympy/Fraction exact, Wolfram-mirrored) + [C] (the number fences 64 = dim g1 = 2^6, 1920 = |W(D5)| = 8 x 240; the |W(D5)| reading typed look-elsewhere-loaded and convention-contingent by v513) + [O] (the arity >= 4 ledger, the physical justification of the cubic GS term, ch2-naturalness for cubic vertices UNDECIDED; delta-1 UNDECIDED at exploration level at promotion time; since DECIDED by v518 (CELEST.WP5E.DELTA1.01: kill under the derived measure, tension with v516 stated); SEAM.EQUIV.01 unchanged; CELEST.SEAM.01 stays Open)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Flag transitivity [E]/[C]: bare mark-transitivity is FALSIFIED as a selector (pair-exchanging V4 simply transitive for every delta, no local jet sees the bit); the sharp selector is FLAG transitivity (marks AND sides) <=> delta = pi/2 <=> tau = i <=> the clock, welded into a 12-fold exact equivalence web (D4 enhancement, mark mirror, odd-split (2/pi) ln cot(delta/2), arc-Laplacian 4/pi, K3 indicator closed form, rho-twist existence, cusp-4-cycle implementability, harmonic, j = 1728) -- the last input reduces from a continuous modulus to ONE discrete symmetry-lift bit (V4 -> D4), concretely measurable in its negation; the bit stays the one [C] carrier input; the free RP/Theta battery (v521) is the eighth and the twist-state class (v525) the ninth side-blind test (the free-plus-twist class is exhausted); face #13 extends the web to 13; no marker moves","checked_by_registry":false,"claim_excerpt":"THE FLAG-TRANSITIVITY EQUIVALENCE WEB -- THE tau = i ATTACK EXECUTED ON THE FREE RP SEAM CIRCLE (2026-07-22; one module, 29 checks; NO marker moves -- the bit stays [C], QGEO.REALIZE.01 and P2.TYPING.01/AX.P2.01 text-precised only, SEAM.BIT.FREEDOM.01 cross-referenced): after v510 the last identification input is the square-modulus datum tau = i; which ESTABLISHED seam datum excludes the free-but-non-harmonic configu","claim_id":"SEAM.TAU.FLAG.01","dependencies_as_recorded":"SEAM.BIT.FREEDOM.01; SEAM.BIT.ORIGIN.01; SEAM.CLOCK.RIGIDITY.01; QGEO.REALIZE.01; QGEO.EMERGE.LIGHT.01; P2.TYPING.01; AX.P2.01; v117; v215; v216; v483; v503; v506; v507; v510","external_data_as_recorded":"-","id":"claim:SEAM.TAU.FLAG.01","location_as_recorded":"introduction;tfpt_1;tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":576,"scripts_as_recorded":"v512_seam_tau_flag.py","status_as_recorded":"Formal/Identity [E] (complete V4/D4 symmetry census, flag/arc orbit arithmetic, odd-split and K3-indicator closed forms, twist mode identity, H4 Schur rigidity, negative controls -- sympy exact + mpmath 30 digits, Wolfram-mirrored) + [C] (the symmetry-lift bit itself: flag transitivity stays a postulate; the gain is the FORM, not a derivation)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"c_d non-derivation [E]/[O]: the fingerprint c_d = 1920 = |W(D5)| does NOT survive the honest battery -- convention table {1920, 120, 256, 32, 69120} (only 1 of 5 normalisations hits), charge-legal flux products 2048/1800 bracket and miss (the 64*60/2 hit is charge-forbidden), look-elsewhere 11/924 vs control 1800 -> 8/924, quantisation gives only lattices (60 Z, 32nd multiple; ch3 units exclude), and the twisted cubic index 32i clashes in provenance with the true quartic 32 (classes 1/3 vs 0/2) -- NUMEROLOGY as a derivation claim; the convention-stable [E] core is c_d = Phi_T3(A_fix) x 2 h_vee(E8) = 32 x 60; the v511 [C] fence text-sharpened only, the physical generation of the 32 stays [O]; no marker moves","checked_by_registry":false,"claim_excerpt":"THE c_d NEGATIVE CERTIFICATE -- CAN GEOMETRY DERIVE c_d = 1920? (2026-07-22; anti-numerology certificate in the v508 style, honest rigid NEGATIVE result; 24 checks, ~2 s; NO marker moves -- the v511 [C] fence stays [C] and is text-sharpened only, the physical generation of the 32 stays [O], CELEST.SEAM.01 stays Open): the v511 full-tensor ledger found exactly ONE legal cubic channel (the su(4) d-symbol, Q_dd = (1/60)","claim_id":"CELEST.DTERM.NONDERIV.01","dependencies_as_recorded":"CELEST.SEAM.01; CELEST.WP5E.GAMMA.01; CELEST.WP5E.EPS2.01; CELEST.WP5E.DELTA2.01; v505; v508; v509; v511","external_data_as_recorded":"-","id":"claim:CELEST.DTERM.NONDERIV.01","location_as_recorded":"tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":577,"scripts_as_recorded":"v513_celestial_dterm_nonderivation.py","status_as_recorded":"Formal/Identity [E] (exact convention/enumeration/lattice/index arithmetic -- sympy/Fraction, no floats, Wolfram-mirrored); the v511 [C] fence '1920 = |W(D5)|' TEXT-SHARPENED to look-elsewhere-loaded and convention-contingent (fence stays [C]); [O] the physical justification of the cubic GS term and the generation of the 32","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"WP5e-epsilon-1 [E]/[C]/[O] (verdict B): the O(-2) bulk-axion slot -- executed. CONSTRUCTED exact: the slot is an explicit equivariant mode ledger (Penrose accounting closes block by block, d <= 6, all 4 characters; d = 0 multiplicity (1, 0, 0, 0): the bulk axion survives the projection; Molien = the v492 hypersurface XY = Z^4 with relation degree 8 = the a0 weight; twisted minimal content (2t, 6t^2, 2t) = the Coxeter eigenvalues -- the E3 bijection per character; graviton control O(+2) separates a0); lambda~ = 6 is pinned by three exact ledgers (Okubo (6<x,x>)^2; measure chain mu-exact with the wrong bookings 3 and 12 excluded; flux single-channel iff k = 1); the GH/A3 back-reaction step re-derives the v493 family and the Coxeter clock from centre geometry (2 branches, period lockstep, source charge 4 = |mu4|, EH asymptotic log exactly 0 -- the CPS log is an exceptional-locus statement, multipole rule m = 0 mod 4 with (4, +-4) carrying -a0). CONDITIONAL [C]: Costello's flat-PT matching. OPEN [O]: the quantised BCOV one-loop coefficient on PT/Z4 and the twisted channels (32 T3) -- M1 (A3 Omega_N), M2 (twisted KS measure), M3 (a0 uplift) preregistered with success + kill criteria; WP5e stays [O]; SEAM.EQUIV.01 untouched; no marker moves","checked_by_registry":false,"claim_excerpt":"WP5e-EPSILON-1 OF THE CELESTIAL-HOLOGRAPHIC CONTRACT EXECUTED (2026-07-22; CELEST.SEAM.01 work package 5e, epsilon-1 stage -- 'the O(-2) bulk-axion slot', verdict B; exact sympy/Fraction arithmetic, no floats, 34 checks, ~4 s): build the s = 0 tower field explicitly (v505 E3: the BSS axion is, via Omega-contraction, the O(-2) slot; a0 does NOT fill it), pin lambda~ = 6 (v495: lambda~^2 = 36 = h_vee + 6) as a residue ","claim_id":"CELEST.WP5E.EPS1.01","dependencies_as_recorded":"CELEST.SEAM.01; CELEST.WP5E.BETA.01; CELEST.WP5E.GAMMA.01; CELEST.WP5E.EPS2.01; CELEST.WP5E.DELTA2.01; SEAM.EQUIV.01; v492; v493; v495; v505; v508; v509; v511","external_data_as_recorded":"Costello arXiv:2111.08879 (box anomaly, GS axion coupling); Bittleston-Sharma-Skinner arXiv:2208.12701 (Poisson-CS tower); Costello-Paquette-Sharma arXiv:2306.00940 (Omega_N backreaction, level = flux quantum); Gibbons-Hawking Phys. Lett. 78B (1978) -- literature framing, no data","id":"claim:CELEST.WP5E.EPS1.01","location_as_recorded":"tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":578,"scripts_as_recorded":"v514_celestial_wp5e_eps1_axion_slot.py","status_as_recorded":"Formal/Identity [E] (exact slot/residue/GH arithmetic: equivariant Penrose ledger block by block d <= 6, character series P_m, Molien hypersurface relation degree 8, Okubo perfect square (6<x,x>)^2, measure chain mu-exact excluding 3 and 12, flux single-channel iff k = 1, GH centre dichotomy, period lockstep 4 pi t0 (i-1)(1, i, i^2), Coxeter clock from geometry, EH log ledger with asymptotic coefficient exactly 0, multipole selection rule m = 0 mod 4 -- sympy/Fraction exact, Wolfram-mirrored) + [C] (Costello's flat-PT matching lambda_g^2 E = A: the measure chain is CLASSICAL bookkeeping) + [O] (the quantised BCOV one-loop coefficient on PT/Z4; the twisted channels 32 T3 not covered by the bulk axion -- M1-M3 preregistered with success + kill criteria)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"M1 [E]/[C]/[O] (SUCCESS on the preregistered criterion): M1 executed via v515 -- the back-reacted Omega_N is closed-form on the A3 twistor family (Omega_N = Omega_0 + sum N_p K_p, BM kernels on the centre twistor lines), all S3/Z4 periods are (2 pi i)^2-integral with the lockstep flux vector N(1,1,1,1) and clock covariance Pi -> i Pi, and the lens geometry FORCES the source charge 4 = |mu4| (quotient large-gauge quantisation: only N = 0 mod 4 passes); honest fence: integrality alone does not discriminate -- the discriminator is the lockstep phase structure (0/24 on the forbidden Z^4 - Z family vs 8/24) + the clock forcing of equal fluxes; neither preregistered KILL fires. CONDITIONAL [C]: global kernel patching, Hitchin small resolution, CPS brane dictionary. OPEN [O]: M2 (twisted KS measure), M3 (a0 uplift), the quantised BCOV coefficient on PT/Z4; SEAM.EQUIV.TWISTOR.01 untouched (v515 is preparation, not the Costello-Li construction); no marker moves","checked_by_registry":false,"claim_excerpt":"MILESTONE M1 OF THE CELESTIAL-HOLOGRAPHIC CONTRACT EXECUTED (2026-07-22; CELEST.SEAM.01 WP5e back-reaction programme, milestone M1 -- 'the A3 Omega_N', SUCCESS on the preregistered v514 S8.1 criterion; exact sympy arithmetic, no floats, 30 checks, ~1 s): compute the A3 analogue of CPS eq. 3.5 on PT/Z4 -- the back-reacted holomorphic 3-form Omega_N sourced by the glue currents wrapping the three lockstep spheres -- an","claim_id":"CELEST.WP5E.M1.01","dependencies_as_recorded":"CELEST.SEAM.01; CELEST.WP5E.EPS1.01; CELEST.WP5E.EPS2.01; CELEST.WP5E.BETA.01; SEAM.EQUIV.TWISTOR.01; v492; v493; v505; v509; v514","external_data_as_recorded":"Costello-Paquette-Sharma arXiv:2306.00940 (Omega_N brane backreaction, eq. 3.5/3.33; large-gauge quantisation); Hitchin 'Polygons and gravitons' (A-series twistor family, small resolution); Gibbons-Hawking Phys. Lett. 78B (1978) -- literature framing, no data","id":"claim:CELEST.WP5E.M1.01","location_as_recorded":"tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":579,"scripts_as_recorded":"v515_celestial_wp5e_m1_omega_n.py","status_as_recorded":"Formal/Identity [E] (exact residue/family/period/kernel arithmetic: Poincare residue three routes, cover factor 4 = |mu4|, closed twistor family XY = Z^4 + 4 t0^2 la^2 Z^2 - t0^4(1 - la^4)^2, CY-compatible clock lift Omega -> +Omega, period lockstep 2 pi i t0 (i-1)(1, i, i^2) with covariance Pi -> i Pi, BM kernel (2 pi i)^2 anchor + dK = 0 + scale degree 0, lens forcing N in 4Z, 12 conifold nodes on Z8 -- sympy exact, no floats, Wolfram-mirrored) + [C] (global patching of the local BM kernels on the resolved 3-fold; Hitchin small resolution; the CPS 'exceptional-curve branes = glue currents' dictionary) + [O] (M2: the twisted KS measure per sector; M3: the a0 uplift; the quantised BCOV coefficient on PT/Z4)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"M2 [E]/[C]/[O] (SUCCESS on the preregistered criterion, on the DECLARED completion measure): M2 executed via v516 -- the completion contact contact_j = (Q^(0) - Q^(j))/det_j carries the exact weight identity w_m = sum_j (1 - i^{jm})/det_j = 4 h_m = |mu4| h_m = -4 ch2(T_m) (the sphere axions pair through their own McKay ch2 charges, no free scale); parameter-free locks (T5 = 0 for any scale, ratio 4:3 reproduced, T3 budget forces c = 4 = |mu4|); every twisted channel becomes the perfect Okubo square 36<x,x>^2/det_j, total 45<x,x>^2 = (5/4) x 36 = Dedekind x Okubo (the v505 S3.8 unique quartic-free weighting); both v508 certificates killed and the v511 psi = 64 slice supplied exactly -- the cubic d-channel is NOT needed (c_d free = 0); controls: wrong scale/shuffle/so16 (KILL fires there)/diag(i,i)/Z2-EH anchor (scale 2 = |Z2|). FENCE [C]: the completion reading (loop = unphased sector trace with the same zero-mode normalisation) is DECLARED within this module, supported by the delta-1 modular-completion finding, NOT derived from the BCOV integral here -- the completion reading is since DERIVED at probe level from two independent constructive sources (F-independence + Quillen pairing) under the typed premises TP-1..TP-4 (v520); the w_m normalisation is now DERIVED at probe level -- 1/det_j is the Atiyah-Bott/zeta-determinant fixed-point factor, computed from three independent sources (v523); the residual [O] narrows to the global BCOV integral beyond the fibre zero-mode factor; no marker moves","checked_by_registry":false,"claim_excerpt":"MILESTONE M2 OF THE CELESTIAL-HOLOGRAPHIC CONTRACT EXECUTED (2026-07-22; CELEST.SEAM.01 WP5e back-reaction programme, milestone M2 -- 'the twisted Kodaira-Spencer measure', SUCCESS on the preregistered v514 S8.2 criterion ON THE DECLARED COMPLETION MEASURE, verdict B; exact sympy/Fraction arithmetic, no floats, 23 checks, ~1 s): quantise the O(-2) tower on PT/Z4 using the eps1 mode ledger and compute the one-loop box","claim_id":"CELEST.WP5E.M2.01","dependencies_as_recorded":"CELEST.SEAM.01; CELEST.WP5E.BETA.01; CELEST.WP5E.GAMMA.01; CELEST.WP5E.DELTA2.01; CELEST.WP5E.EPS1.01; CELEST.WP5E.M1.01; SEAM.EQUIV.TWISTOR.01; v495; v502; v505; v508; v511; v513; v514; v515","external_data_as_recorded":"Costello arXiv:2111.08879 (one-loop box anomaly, GS axion coupling); Bittleston-Sharma-Skinner CMP 403 (Poisson-CS tower); Harvey-Moore hep-th/9510182 (tau-integral / modular completion, framing) -- literature framing, no data","id":"claim:CELEST.WP5E.M2.01","location_as_recorded":"tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":580,"scripts_as_recorded":"v516_celestial_wp5e_m2_twisted_ks_measure.py","status_as_recorded":"Formal/Identity [E] (exact weight/contact/table/control arithmetic: completion-weight identity w = 4h = -4 ch2 with no free scale, parameter-free locks (T5 = 0 any scale, 4:3 ratio, T3 budget => c = |mu4|), contact term two bases, per-sector Okubo squares 36<x,x>^2/det_j, total (5/4) x 36, certificate kills 32 -> 0 / 72 -> 0 / psi 64 -> 0, exchange-span remainder, mu-blind chain, all five controls -- sympy/Fraction exact, Wolfram-mirrored) + [C] (the DECLARED completion reading: loop = unphased sector trace with the same zero-mode measure -- supported by the delta-1 modular-completion finding, not derived) + [O] (the BCOV-integral derivation of the completion reading, delta-1b/1c/1d; SEAM.EQUIV.TWISTOR.01 unchanged)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"M3 [E]/[C]/[O] (SUCCESS on the preregistered criterion): M3 executed via v517 -- the (4, +-4) multipole uplifted to the GLT kernel chi = log P4 (the log of the v515 family polynomial; harmonic for any kernel, residue identity matches the V-ledger with flux -4 pi per centre); the log-type correction is delivered on FOUR COUPLED CENTRE-COUNT SCALES: asymptotic kernel log 4 = |mu4| (first seam-fibre correction exactly a0/eta^4, exact m-grading, no log x power terms -- the v514 honest zero preserved), GLT tower p_{4k} = 4(-a0)^k with the n = 0 mod 4 selection rule, exceptional-locus log chi(0) = log a0 = 4 log t0 + i(4 phi0 + pi), and period response d log Pi/d log a0 = 1/4 = 1/|mu4| integrating to the clock monodromy i (v493 reproduced) with a0-rigid node support and topological (2 pi i)^2 fluxes; controls: (4,0) clock-invariant, EH/Z2 reads 2 = |Z2| on every dial, k = 3/5 orbits move the coefficient with the centre count, the forbidden family fails both dials (p3 = 3, e4 = 0) -- the KILL (decoupling from the centre count) does NOT fire. FENCE [C]: the GLT dictionary; [O]: the full nonlinear Kahler potential of the resolved A3 ALE; no marker moves","checked_by_registry":false,"claim_excerpt":"MILESTONE M3 OF THE CELESTIAL-HOLOGRAPHIC CONTRACT EXECUTED (2026-07-22; CELEST.SEAM.01 WP5e back-reaction programme, milestone M3 -- 'the a0 uplift', SUCCESS on the preregistered v514 S8.3 criterion; exact sympy arithmetic, no floats, 23 checks, ~7 s): uplift the (l, m) = (4, +-4) GH multipole (= the a0 direction) to the Beltrami differential on PT/Z4 and compute the induced Kahler-potential correction (preregistere","claim_id":"CELEST.WP5E.M3.01","dependencies_as_recorded":"CELEST.SEAM.01; CELEST.WP5E.EPS1.01; CELEST.WP5E.M1.01; CELEST.WP5E.M2.01; SEAM.EQUIV.TWISTOR.01; v493; v505; v509; v514; v515; v516","external_data_as_recorded":"Lindstrom-Rocek CMP 115 (1988) (generalized Legendre transform); Ivanov-Rocek CMP 182 (1996) (O(2) multiplet kernels); Costello-Paquette-Sharma arXiv:2306.00940 ('N log' Kahler flux); Gibbons-Hawking Phys. Lett. 78B (1978) -- literature framing, no data","id":"claim:CELEST.WP5E.M3.01","location_as_recorded":"tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":581,"scripts_as_recorded":"v517_celestial_wp5e_m3_a0_uplift.py","status_as_recorded":"Formal/Identity [E] (exact kernel/expansion/period/monodromy arithmetic: null-coordinate harmonicity for arbitrary kernels, residue V-ledger identity 1/(2r), kernel log coefficient 4 = |mu4| with first correction a0/eta^4 and exact m-grading, GLT tower p_{4k} = 4(-a0)^k with the n = 0 mod 4 selection rule, exceptional-locus log 4 log t0 + clock phase 4i, period response 1/4 integrating to monodromy i, a0-rigid node support and (2 pi i)^2 fluxes, all four controls -- sympy exact, Wolfram-mirrored) + [C] (the GLT dictionary eta_p log eta_p = the GH Kahler-potential kernel; Lindstrom-Rocek / Ivanov-Rocek) + [O] (the full nonlinear Kahler potential of the resolved A3 ALE; SEAM.EQUIV.TWISTOR.01 unchanged)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"DECIDED (negative under the derived measure): the delta-1 chain is closed -- the derived chiral measure kills the route, the v516 declared-measure tension is the named [O]; since decided at probe level by v520 in favour of the declared reading (kill sharpened; residual [O]: the constructive w_m derivation)","checked_by_registry":false,"claim_excerpt":"THE DELTA-1 CHAIN OF THE CELESTIAL-HOLOGRAPHIC CONTRACT DECIDED (2026-07-22; CELEST.SEAM.01 WP5e, delta-1b + delta-1c + delta-1d consolidated -- 'the derived chiral measure kills the delta-1 route', an honest, decided NEGATIVE result in the v508 style; 30 checks, ~20 s): does the Harvey-Moore/BCOV fundamental-domain integral on PT/Z4, evaluated under a measure DERIVED from blockwise SL(2,Z) covariance of the dressed ","claim_id":"CELEST.WP5E.DELTA1.01","dependencies_as_recorded":"CELEST.SEAM.01; CELEST.WP5E.M2.01; CELEST.WP5E.M3.01; CELEST.WP5E.EPS1.01; CELEST.WP5E.GAMMA.01; CELEST.WP5E.DELTA2.01; CELEST.DTERM.NONDERIV.01; SEAM.EQUIV.TWISTOR.01; v502; v505; v508; v511; v513; v514; v515; v516; v517","external_data_as_recorded":"Harvey-Moore Nucl.Phys. B463 (1996) 315 (fundamental-domain unfolding); Costello-Li BCOV arXiv:1201.4501; Bittleston-Homans-Sharma JHEP 09 (2023) 008 -- literature framing, no data","id":"claim:CELEST.WP5E.DELTA1.01","location_as_recorded":"tfpt_research_contracts;tfpt_3","path":"verification/status_ledger.csv","row_number":582,"scripts_as_recorded":"v518_celestial_wp5e_delta1_derived_kill.py","status_as_recorded":"DECIDED: kill under the derived measure, tension with v516 stated ([E] exact Weil/Q(zeta_8) algebra, loop words + koboundary defects + 1/960 phase arithmetic, ledgers, G = f1 f3, the decision table; [C] the f1f3/KS-weight identification + kernel-family convention + chi_k choice; [O] the BCOV-integral derivation that decides between the declared (v516) and derived (v518) measures -- since decided at probe level by v520 for the declared reading, residual [O] = the constructive w_m derivation; NO marker moves)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[C] closed modulo cited theorems (the MMST route of SEAM.EQUIV.01; route split 2026-07-22, no status change in substance); residual [O] = the cited continuum existence (v336)  EXECUTED UPDATE (2026-08-28, v994): 5/7 identification criteria [E-measured]; C6 written-out [C] (psi_lambda_convergence_theorem_en.tex; 2/pi^2=0.20264 vs 0.203); C7 cited [O]; status UNCHANGED [C].  | 2026-08-29 v998: C7 arithmetic shadow exact (HS bound 2.11, Theta_E8=E4 through q^8, character four orders, 60-digit S); net-level C7 stays cited.  Display unmoved.","checked_by_registry":false,"claim_excerpt":"THE MMST ROUTE OF THE SEAM EQUIVALENCE TARGET (2026-07-22 route split, carved out of SEAM.EQUIV.01 -- an ID restructuring, NO status change in substance; this row carries exactly the statement previously attached to 'SEAM.EQUIV.01 closed modulo a cited theorem'): the conditional scaling-limit route. The explicit lattice model (v367/v368) and the S3 closure stack -- central charge c = 8 (v376), the (E8)_1 character wi","claim_id":"SEAM.EQUIV.MMST.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.MMST.INCLASS.01; SEAM.EQUIV.CONTINUUM.03; SEAM.S3.LATTICE.01; SEAM.S3.INFLOW.01; SEAM.S3.CENTRALCHARGE.01; SEAM.S3.E8CHARACTER.01; SEAM.S3.MODULAR.01; SEAM.S3.RP.01; SEAM.CCC.01; SEAM.MU.01; FORM.SEAM.MMST.01","external_data_as_recorded":"Osborne-Stottmeister arXiv:2107.13834, CMP 398 (2023) 219; MMST OAR arXiv:2010.11121; AGT arXiv:2506.01008 -- cited theorems, no data","id":"claim:SEAM.EQUIV.MMST.01","location_as_recorded":"tfpt_research_contracts;introduction;tfpt_1;tfpt_3;tfpt_4","path":"verification/status_ledger.csv","row_number":583,"scripts_as_recorded":"v366_mmst_seam_collar.py; v994_mmst_criteria_battery.py; v998_seam_modular_closure.py","status_as_recorded":"Conditional [C] (closed modulo cited theorems: the MMST/OS continuum existence, v336; every computable level pinned [E]; Lean FORM.SEAM.MMST.01)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open [O]: the twistor/Costello-Li route of SEAM.EQUIV.01; the CELEST.SEAM.01 work packages are preparation; closes only with the global BCOV quantisation + the WOIT.OS.TWISTOR.01 bridge","checked_by_registry":false,"claim_excerpt":"THE TWISTOR ROUTE OF THE SEAM EQUIVALENCE TARGET (2026-07-22 route split, the second continuum route named in its own right -- an ID restructuring, NO status change in substance): the open Costello-Li-grade construction -- the interacting holomorphic open+closed twistorial algebra on PT/Gamma (the global BCOV+SDYM quantisation, WP5e proper of CELEST.SEAM.01) whose boundary partition function is E4/eta^8 INCLUDING the","claim_id":"SEAM.EQUIV.TWISTOR.01","dependencies_as_recorded":"SEAM.EQUIV.01; CELEST.SEAM.01; WOIT.OS.TWISTOR.01; CELEST.WP1.01; CELEST.WP4.01; CELEST.WP5A.01; CELEST.WP5B.01; CELEST.WP5C.01; CELEST.WP5D.01; CELEST.WP5DB.01; CELEST.WP5E.ALPHA.01; CELEST.WP5E.BETA.01; CELEST.WP5E.GAMMA.01; CELEST.WP5E.DELTA2.01; CELEST.WP5E.EPS2.01; CELEST.WP5E.EPS1.01; CELEST.WP5E.M1.01; CELEST.WP5E.M2.01; CELEST.WP5E.M3.01; CELEST.WP5E.DELTA1.01","external_data_as_recorded":"Costello-Li BCOV arXiv:1201.4501; Bittleston-Homans-Sharma JHEP 09 (2023) 008; Costello arXiv:2111.08879 -- literature framing, no data","id":"claim:SEAM.EQUIV.TWISTOR.01","location_as_recorded":"tfpt_research_contracts;tfpt_3","path":"verification/status_ledger.csv","row_number":584,"scripts_as_recorded":"v492_celestial_z4_orbifold.py","status_as_recorded":"Open (research route [O]: the Costello-Li construction; preparation [E]/[C] via the CELEST.SEAM.01 work packages v492-v518)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open (research contract): the OS twistor bridge -- Theta real structure + interacting RP + OS reconstruction to (H, Omega, U(P^up_+), A_Mink) with one chiral generation, the TFPT charge lattice and the (E8)_1 net as an actual boundary net; seven preregistered kill tests; the actual bridge from compiler to physics; alpha stage executed via v519 (Theta + free RP, kill test 1 discharged on the free level only -- stays live on the interacting algebra); beta-1 executed via v522 (UNDECIDED: the clock reading was the wrong operationalisation, the clock is time-like, GSO-fixed RP holds, kill test 2 does not fire; contract precision (iii) added); beta-2 executed via v524 (SUCCESS, [C]-typed per precision (iii): H_phys explicit and PD at both levels, the clock a positive transfer step with spectral calculus -- N = 8 spectrum exactly {1, sqrt(2)-1} -- and a reconstructed unitary rotation group; the pre-declared KMS deviation carries exactly the silver witnesses; no kill fires); beta-3/gamma milestones next","checked_by_registry":false,"claim_excerpt":"THE OSTERWALDER-SCHRADER TWISTOR BRIDGE (2026-07-22; the new central research contract after the external review of the celestial/twistor branch -- THIS IS THE ACTUAL BRIDGE FROM COMPILER TO PHYSICS; everything in CELEST.SEAM.01 is preparation for it). INPUT: X_+ = (PT/Gamma)_+ (Gamma = Gamma_ALE = <Deck> ~ Z4 in SU(2), normalised by the clock rho = diag(i,1) with rho^2 = Deck); A_hol = the INTERACTING open+closed tw","claim_id":"WOIT.OS.TWISTOR.01","dependencies_as_recorded":"CELEST.SEAM.01; SEAM.EQUIV.TWISTOR.01; SEAM.EQUIV.01; SEAM.BIT.FREEDOM.01; SEAM.CLOCK.RIGIDITY.01","external_data_as_recorded":"Woit arXiv:2104.05099 (Euclidean Twistor Unification) -- literature framing, no data","id":"claim:WOIT.OS.TWISTOR.01","location_as_recorded":"tfpt_research_contracts;tfpt_3","path":"verification/status_ledger.csv","row_number":585,"scripts_as_recorded":"v519_woit_theta_rp_free.py","status_as_recorded":"Open (research contract)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the free/equivariant alpha stage (Theta classification, exact relations, kill test 1 discharged at the free level, free RP on the bond cut selecting the same family); [C]/[O] everything interacting -- kill test 1 stays live on A_hol; no marker moves","checked_by_registry":false,"claim_excerpt":"THE WOIT-ALPHA MILESTONE (2026-07-22): the real structure exists, and free reflection positivity picks the SAME family -- the alpha stage of WOIT.OS.TWISTOR.01 executed as one module (Part W = Theta, Part R = free RP). [E] THETA CLASSIFICATION COMPLETE: exactly TWO families of anti-linear structures on C^2 normalise the clock rho = diag(i,1) -- family D (z -> mu conj(z), |mu| = 1): Theta rho Theta = rho^-1 EXACTLY, T","claim_id":"WOIT.THETA.FREE.01","dependencies_as_recorded":"WOIT.OS.TWISTOR.01; SEAM.BIT.FREEDOM.01; SEAM.CLOCK.RIGIDITY.01; SEAM.BIT.ORIGIN.01; CELEST.SEAM.01","external_data_as_recorded":"Woit arXiv:2104.05099 (Euclidean Twistor Unification) -- literature framing, no data","id":"claim:WOIT.THETA.FREE.01","location_as_recorded":"tfpt_research_contracts;tfpt_3","path":"verification/status_ledger.csv","row_number":586,"scripts_as_recorded":"v519_woit_theta_rp_free.py","status_as_recorded":"Identity/Lattice (exact sympy + exact Cl(16); 40-digit gap-certified RP inertia certificates)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"DECIDED (ERFOLG-A at probe level): single-valuedness is derived from two independent constructive sources (F-independence + Quillen pairing) under the typed premises TP-1..TP-4; the v516 completion reading wins, the v518 kill is sharpened; residual [O]: the w_m normalisation is since DERIVED at probe level by v523 (1/det_j = the Atiyah-Bott/zeta-determinant fixed-point factor, three independent sources); what remains open is the global BCOV integral beyond the fibre zero-mode factor","checked_by_registry":false,"claim_excerpt":"THE WP5E BCOV MEASURE QUESTION DECIDED AT PROBE LEVEL (2026-07-22; delta-1e + delta-1f consolidated in the v518 style, one module, 39 checks, ~20 s; ERFOLG-A on the preregistered decision layer): which of the two exact, mutually contradictory measures on PT/Z4 is the true BCOV measure -- (A) the DECLARED completion reading (v516: unphased sector trace, w_m = 4 h_m, supplies psi = 64) or (B) the DERIVED chiral measure","claim_id":"CELEST.WP5E.MEASURE.01","dependencies_as_recorded":"CELEST.SEAM.01; CELEST.WP5E.M2.01; CELEST.WP5E.DELTA1.01; SEAM.EQUIV.TWISTOR.01; v502; v505; v508; v511; v514; v515; v516; v517; v518","external_data_as_recorded":"Harvey-Moore Nucl.Phys. B463 (1996) 315 (fundamental-domain unfolding); Costello-Li BCOV arXiv:1201.4501; Quillen Funct. Anal. Appl. 19 (1985) (determinant metric) -- literature framing, no data","id":"claim:CELEST.WP5E.MEASURE.01","location_as_recorded":"tfpt_research_contracts;tfpt_3","path":"verification/status_ledger.csv","row_number":587,"scripts_as_recorded":"v520_celestial_wp5e_measure_decision.py","status_as_recorded":"DECIDED at probe level for the declared reading ([E] exact Weil/Q(zeta_8) algebra, exact invariant subspace, characters + 1/960 grid, ledgers, levelwise 4-design, Z2 anchor arithmetic, change-of-variables corollary, controls; numeric documented: transports 28+ digits, SVD memberships 1e-8/1e-3, certificates fresh tau, HM kernels 30+ digits; [C] the typed premises TP-1..TP-4; [O] the constructive BCOV derivation of w_m -- since DERIVED at probe level by v523, narrowing the [O] to the global BCOV integral beyond the fibre zero-mode factor; NO marker moves)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"KILL (honest negative, preregistered): free RP and Theta existence are side-blind on the whole M(delta) family -- the eighth side-blind test on the v512 scoreboard (7 -> 8), face #13 added [C] (12 -> 13; since 13 -> 15 by v528); the alignment bit is NOT derivable from OS positivity and remains genuine discrete input; [O] gap: mark-decorated/interacting states -- the mark-decorated (free-plus-twist) half since decided side-blind by v525 (the ninth side-blind test, 8 -> 9); what remains is the genuinely interacting A_hol","checked_by_registry":false,"claim_excerpt":"THE RP/THETA ATTACK ON THE ALIGNMENT BIT DECIDED (2026-07-22; one module, 25 checks, ~25 s; an honest, decided NEGATIVE result in the v508 style): does free reflection positivity (v519 RP) or anti-linear Theta existence (with the v519 side conditions) BREAK for delta != pi/2 on the deformed mark family M(delta) = {+-1, +-e^(i delta)} -- which would DERIVE the v512 alignment bit from OS positivity? NO: the entire free","claim_id":"SEAM.BIT.RPBLIND.01","dependencies_as_recorded":"SEAM.TAU.FLAG.01; SEAM.BIT.FREEDOM.01; SEAM.BIT.ORIGIN.01; SEAM.CLOCK.RIGIDITY.01; WOIT.THETA.FREE.01; v506; v507; v510; v512; v519","external_data_as_recorded":"-","id":"claim:SEAM.BIT.RPBLIND.01","location_as_recorded":"tfpt_research_contracts;tfpt_3","path":"verification/status_ledger.csv","row_number":588,"scripts_as_recorded":"v521_seam_bit_rp_blind.py","status_as_recorded":"Formal/Identity [E] (exact solveset censuses, exact Gram entries, exact Cl(16) implementers, 40-digit gap-certified inertia spectra, continuum axis elimination, precondition controls) + [C] (face #13 = a reformulation of the bit) + [O] (mark-decorated states / interacting A_hol); the bit stays the one [C] carrier input; NO marker moves","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"UNDECIDED (typed, per the frozen preregistration): the [C-1] clock-tower reading of 'gauge' fails Hermiticity structurally (the mu4 clock is euclidean-time-like); the gaugeable part is exactly the GSO/fermion-parity Z2, under which gauge-fixed RP HOLDS ((29,0,0)/(8,0,0) PD); kill tests (1) and (2) do NOT fire at the free level; contract precision (iii) added (prose); beta1 proper re-routed via beta2; WOIT.OS.TWISTOR.01 stays Open","checked_by_registry":false,"claim_excerpt":"THE WOIT-BETA1 MILESTONE EXECUTED (2026-07-22; one module, 16 checks, ~5 s; typed result, verdict UNDECIDED per the frozen preregistration -- 'the clock is time-like, GSO is the gauge datum'): contract clause beta_1 ('Theta on the gauge-invariant subalgebra + gauge-fixed RP on the equivariant SDYM(E8) sector'; kill test (2): 'RP fails after gauge fixing') executed on the free/equivariant seam skeleton. FINDING: the p","claim_id":"WOIT.BETA1.GSO.01","dependencies_as_recorded":"WOIT.OS.TWISTOR.01; WOIT.THETA.FREE.01; SEAM.BIT.RPBLIND.01; SEAM.CLOCK.RIGIDITY.01; v510; v519","external_data_as_recorded":"Woit arXiv:2104.05099 (Euclidean Twistor Unification) -- literature framing, no data","id":"claim:WOIT.BETA1.GSO.01","location_as_recorded":"tfpt_research_contracts;tfpt_3","path":"verification/status_ledger.csv","row_number":589,"scripts_as_recorded":"v522_woit_beta1_gso_gauge.py","status_as_recorded":"UNDECIDED per the frozen preregistration ([E] exact Hermiticity witness + censuses, time-like reflection census, GSO 2-torsion identification, 40-digit gap-certified GSO-fixed RP certificates, exact Cl(16) Kramers restriction, Ramond/wrong-projection/site-cut/family-A controls; [C] contract precision (iii) -- prose only; [O] beta1 proper via beta2, kill tests live on A_hol); NO marker moves","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"ERFOLG (the w_m normalisation DERIVED at probe level): 1/det_j is the Atiyah-Bott/zeta-determinant fixed-point factor, computed from three independent sources (the equivariant mode ledger with Abel value (1/2, 1/4, 1/2); the zeta/reflection determinant 4 sin^2(pi j/4) with the unique real Quillen section; the delta-1f block constant term 1/det_b) and the v516 chain closes number by number (w = 4h, c = 4 = |mu4|, squares (18, 9, 18), total 45<x,x>^2, psi +-64); all negative controls behave (Z2/EH anchor passes at c = 2 = |Z2|, so16 kill fires, diag(i,i) breaks the zeta = AB identity, k = 3/5 weights wander correctly); typed premises TP-REG/TP-Q/TP-NUM/TP-CH; the residual [O] narrows to the global BCOV integral beyond the fibre zero-mode factor; no marker moves","checked_by_registry":false,"claim_excerpt":"THE CONSTRUCTIVE w_m DERIVATION EXECUTED (2026-07-23; the residual [O] of v516/v520, one module, 26 checks, ~1 s; verdict ERFOLG per the frozen preregistration): is the completion normalisation 1/det_j the standard Atiyah-Bott/holomorphic-Lefschetz fixed-point weight AND the Quillen-factorised zeta determinant of the twisted fibre Laplacian -- i.e. COMPUTED rather than declared? YES, from three independent sources. (","claim_id":"CELEST.WP5E.WM.01","dependencies_as_recorded":"CELEST.SEAM.01; CELEST.WP5E.M2.01; CELEST.WP5E.MEASURE.01; CELEST.WP5E.DELTA1.01; SEAM.EQUIV.TWISTOR.01; v505; v514; v516; v517; v518; v520","external_data_as_recorded":"Atiyah-Bott Ann. Math. 86/88 (holomorphic Lefschetz); Quillen Funct. Anal. Appl. 19 (1985) (determinant metric); Costello-Li BCOV arXiv:1201.4501 -- literature framing, no data","id":"claim:CELEST.WP5E.WM.01","location_as_recorded":"tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":590,"scripts_as_recorded":"v523_celestial_wp5e_wm_derived.py","status_as_recorded":"Formal/Identity [E] (exact Q(i)/Q(sqrt2)/cyclotomic mode ledgers, Abel values, tensor-trace splitting, reflection-formula zeta determinants, Quillen arithmetic, delta-1f block constant terms, the full v516 chain, all controls -- sympy/Fraction exact, Wolfram-mirrored; numeric documented: Hurwitz/Lerch and stripped block limits at 40 digits) + [C] (the typed premises TP-REG/TP-Q/TP-NUM/TP-CH) + [O] (the global BCOV integral beyond the fibre zero-mode factor)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"SUCCESS ([C]-typed per precision (iii)): the OS quotient of the free system is explicit -- H_phys PD and nondegenerate at both levels (37 = 29+8; 16 = 4^2 thermal/KMS), the Klein-Landau transfer semigroup exactly Hermitian with the site/bond dichotomy as its positivity pattern, the mu4 clock = T^{N/4} positive with spectral calculus (N = 8 spectrum exactly {1, sqrt(2)-1}) and a reconstructed unitary rotation group; the v522 non-Hermiticity is exactly the wrap artifact; the pre-declared KMS deviation carries exactly the silver witnesses; Theta_phys^2 = +1 Kramers-free; no kill fires, all seven stay live on A_hol; beta3 next; WOIT.OS.TWISTOR.01 stays Open","checked_by_registry":false,"claim_excerpt":"THE WOIT-BETA2 MILESTONE EXECUTED (2026-07-23; one module, 20 checks, ~5 s; verdict SUCCESS per the frozen preregistration, [C]-typed per contract precision (iii)): contract clause beta_2 ('the OS quotient of the free system made explicit -- success: (H, Omega) constructed from the v519 bond-cut form with the clock acting unitarily; kill: the quotient degenerates (zero or indefinite completion)') executed. (1) H_phys","claim_id":"WOIT.BETA2.OS.01","dependencies_as_recorded":"WOIT.OS.TWISTOR.01; WOIT.THETA.FREE.01; WOIT.BETA1.GSO.01; SEAM.BIT.RPBLIND.01; v510; v519; v522","external_data_as_recorded":"Woit arXiv:2104.05099 (Euclidean Twistor Unification); Klein-Landau Comm. Math. Phys. 87 (1983) (local symmetric semigroups) -- literature framing, no data","id":"claim:WOIT.BETA2.OS.01","location_as_recorded":"tfpt_research_contracts;tfpt_3","path":"verification/status_ledger.csv","row_number":591,"scripts_as_recorded":"v524_woit_beta2_os_quotient.py","status_as_recorded":"SUCCESS per the frozen preregistration, [C]-typed per contract precision (iii) ([E] exact Hermiticity/semigroup/square identities, exact clock spectrum {1, sqrt(2)-1}, exact wrap-artifact resolution and censuses, 40-digit gap-certified inertia/spectral certificates; [C] the precision-(iii) operationalisation of 'the clock acting unitarily'; [O] beta3 next, all seven kill tests live on A_hol); NO marker moves","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"KILL (honest negative, preregistered): every well-defined mark-decorated state functional in the free-plus-twist class keeps RP positive on the always-existing cuts along the whole M(delta) ladder -- the NINTH side-blind test on the v512 scoreboard (8 -> 9); quasi-free decorations are RP-spectrally invisible (exact congruence mechanism), insertion spectra and the 4-twist Casimir measure delta but never reach the positivity verdict, the only pi/2-exclusive structures presuppose the bit; the free-plus-twist class is EXHAUSTED -- the interacting half is since decided by v529 (SEAM.INT.FKTOY.01): the TENTH side-blind test (9 -> 10) on genuinely non-Wick dynamics, while Kill-Test-2 fires at toy level (RP breaks for every g > 0; straddle law); the alignment bit remains genuine discrete input","checked_by_registry":false,"claim_excerpt":"THE TWIST-STATE ATTACK ON THE ALIGNMENT BIT DECIDED (2026-07-23; one module, 20 checks, ~80 s; an honest, decided NEGATIVE result in the v508 style -- the NINTH side-blind test on the v512 scoreboard, 8 -> 9): do mark-decorated STATES (Kadanoff-Ceva twist/defect insertions, sigma-gauge arc decorations, mu4/Bogoliubov bond defects -- the v521 [O] gap, everything Pfaffian/Wick-computable) make RP side-sensitive on M(de","claim_id":"SEAM.BIT.TWISTBLIND.01","dependencies_as_recorded":"SEAM.BIT.RPBLIND.01; SEAM.TAU.FLAG.01; SEAM.BIT.FREEDOM.01; WOIT.THETA.FREE.01; v510; v512; v519; v521","external_data_as_recorded":"-","id":"claim:SEAM.BIT.TWISTBLIND.01","location_as_recorded":"tfpt_research_contracts;tfpt_3","path":"verification/status_ledger.csv","row_number":592,"scripts_as_recorded":"v525_seam_bit_twist_blind.py","status_as_recorded":"Formal/Identity [E] (Pfaffian-exact insertion machinery cross-validated three ways, exact integer incidence frame, exact congruence mechanisms, 40-digit gap-certified inertia/spectrum/energy/parity certificates) + [C] (each lifting is a construction choice, all tested) + [O] (the genuinely interacting A_hol with non-Pfaffian-reducible OS data); the bit stays the one [C] carrier input; NO marker moves","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"SUCCESS: beta MEASURED = N at both levels; T_seam = 4 c3 = Bisognano-Wichmann/Hawking normalisation; modular Hamiltonian closed; c3 third leg class-1 selected; entropy log-law confirms, horizon fractions do NOT transfer; non-compact => T=0; no marker moves","checked_by_registry":false,"claim_excerpt":"THE THERMAL SEAM: KMS -> NARIAI/BH BRIDGE (2026-07-23; one module, 22 checks, ~8.4 s; verdict SUCCESS): the reconstructed free OS quotient of the 16-Majorana NS seam circle is KMS, and its temperature normalisation CLOSES onto the Nariai/BH chain as the THIRD LEG of c3. (1) beta MEASURED, NOT ASSUMED: the circle kernel C(d)=(2/N)/sin(pi d/N) has exactly one finite thermal-mode representation with detailed balance; N=","claim_id":"SEAM.THERMAL.KMS.01","dependencies_as_recorded":"WOIT.BETA2.OS.01; WOIT.OS.TWISTOR.01; v58; v104; v208; v519; v524","external_data_as_recorded":"Bisognano-Wichmann Commun. Math. Phys. 42 (1975); Hawking 1975 -- literature framing, no data","id":"claim:SEAM.THERMAL.KMS.01","location_as_recorded":"tfpt_3;tfpt_research_contracts;tfpt_horizon_readouts;origin_theory;tfpt_1","path":"verification/status_ledger.csv","row_number":593,"scripts_as_recorded":"v526_seam_thermal_kms_nariai_bridge.py","status_as_recorded":"SUCCESS ([E] exact sympy/cyclotomic + 40-digit Tomita certificates; [C] bridge reading typed; [C-5] non-gating clock-vs-modular findings); NO marker moves","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"STRUCTURE SUCCESS (closed-form origin of {1,sqrt2-1} via Hankel pencil / tan(pi/8) / second quantisation / silver-midpoint carrier / arcsinh(1) gap) + CONNECTION KILL (11466-candidate census: 0 hits above null; placebos comparable); lattice datum not continuum; no marker moves","checked_by_registry":false,"claim_excerpt":"THE SILVER CLOCK EIGENVALUE EXPLAINED AND DEMYSTIFIED (2026-07-23; one module, 22 checks, ~10 s; double verdict, anti-numerology style): STRUCTURE = SUCCESS (closed-form origin of {1, sqrt2-1}); CONNECTION = KILL (frozen-registry readout census, 0 hits). (1) STRUCTURE SUCCESS: {1, sqrt2-1} closed -- diagonal Hankel pencil at N=8, tan(pi/8)=C(3)/C(1), doubling = exact second quantisation, carrier = silver-midpoint axe","claim_id":"SEAM.CLOCK.SILVER.01","dependencies_as_recorded":"WOIT.BETA2.OS.01; SEAM.THERMAL.KMS.01; SEAM.TAU.FLAG.01; v519; v524; v526","external_data_as_recorded":"-","id":"claim:SEAM.CLOCK.SILVER.01","location_as_recorded":"tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":594,"scripts_as_recorded":"v527_seam_clock_silver_spectrum.py","status_as_recorded":"STRUCTURE SUCCESS + CONNECTION KILL ([E] exact sympy Hankel/trig + 40-digit census); NO marker moves","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"SUCCESS: the bit is PHYSICALLY DEFINED as the twist-class choice (facets #14/#15 both directions; O=1/2 at m=4; unification with flag-transitivity; Kramers typed as POSITION half); [C] interferometric measurement sketch; bit remains formal input; v512 web 13->15; no marker moves","checked_by_registry":false,"claim_excerpt":"THE ALIGNMENT BIT AS AN EXACT MEASURABLE TWIST-CLASS CHOICE (2026-07-23; one module, 18 checks, ~46 s; verdict SUCCESS -- the physical definition): the alignment bit is the choice of which twist class nature realizes, read out by the order parameter O. (1) FACET #14 (eta-flip <=> delta=pi/2): both directions exact (sigma o r = -sigma on all four fixing axes with eta jump +i->-i; off pi/2 on EVERY axis sigma o r = +si","claim_id":"SEAM.BIT.TWISTCLASS.01","dependencies_as_recorded":"SEAM.TAU.FLAG.01; SEAM.BIT.RPBLIND.01; SEAM.BIT.TWISTBLIND.01; SEAM.BIT.FREEDOM.01; v510; v512; v521; v525","external_data_as_recorded":"-","id":"claim:SEAM.BIT.TWISTCLASS.01","location_as_recorded":"tfpt_3;tfpt_research_contracts;introduction","path":"verification/status_ledger.csv","row_number":595,"scripts_as_recorded":"v528_seam_bit_twist_class_definition.py","status_as_recorded":"SUCCESS ([E] exact integer/symbolic + 40-digit certificates; [C] measurement sketch principle-only); the bit remains formal input; NO marker moves","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"F1=KILL (Kill-Test-2 fires at toy level: RP breaks for every g>0; straddle law 24/24; Kill-Test-1 does NOT fire); F2=KILL (tenth side-blind test 9->10); F3=ERFOLG (grading+Z8+FK+OS quotient); [C] fence one toy/one class -- narrows WOIT route, does not close it; no marker moves","checked_by_registry":false,"claim_excerpt":"THE MINIMAL INTERACTING FIDKOWSKI-KITAEV SEAM TOY (2026-07-23; one module, 24 checks, ~97 s; triple-verdicted -- the FIRST firing Kill-Test-2 shadow). F1 = KILL, F2 = KILL, F3 = ERFOLG. (1) F1 = KILL (THE MOST IMPORTANT PART): Theta exists exactly on the interacting model (U_r^2=2^8, Theta^2=+1, clock-tower inversion conj_V·V=4096, [Theta,H_g]=0 exact, Theta Omega_g = Omega_g) -- Kill-Test 1 does NOT fire; BUT Kill-T","claim_id":"SEAM.INT.FKTOY.01","dependencies_as_recorded":"WOIT.OS.TWISTOR.01; WOIT.BETA2.OS.01; SEAM.BIT.TWISTBLIND.01; SEAM.BIT.TWISTCLASS.01; SEAM.TAU.FLAG.01; SEAM.EQUIV.TWISTOR.01; v510; v512; v519; v524; v525","external_data_as_recorded":"Fidkowski-Kitaev Phys. Rev. B 81 (2010); Woit arXiv:2104.05099 -- literature framing, no data","id":"claim:SEAM.INT.FKTOY.01","location_as_recorded":"tfpt_3;tfpt_research_contracts;introduction","path":"verification/status_ledger.csv","row_number":596,"scripts_as_recorded":"v529_seam_interacting_toy_fk.py","status_as_recorded":"F1=KILL / F2=KILL / F3=ERFOLG ([E] exact Fraction/Clifford + float-track certificates; [C] flat-band parent / one interaction class fence); WOIT.OS.TWISTOR.01 stays Open; NO marker moves","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"V1=KILL (the literal leading-order cone formalization is empty everywhere); V2=ERFOLG (THE SELECTION LAW: RP holds for exactly ONE member x sign -- delta=pi/2 with positive coupling; asymmetric members die; straddle law refined: symmetric straddling protects); first dynamical selection of the alignment bit at toy level; [C] fence one toy/one class; no marker moves","checked_by_registry":false,"claim_excerpt":"THE RP CONE ON THE INTERACTING FK QUARTETS -- THE FIRST DYNAMICAL SELECTION OF THE ALIGNMENT BIT (2026-07-24; one module, 15 checks, ~7 s; double-verdicted; the named v534 candidate of the 2026-07-23 review round executed). V1 = KILL, V2 = ERFOLG. (1) V1 = KILL (the literal contract formalization): independent couplings lambda_q on the four mark quartets of M(delta), leading OS-Gram correction dG via first-order PT (","claim_id":"SEAM.STRADDLE.CONE.01","dependencies_as_recorded":"SEAM.INT.FKTOY.01; SEAM.BIT.TWISTCLASS.01; WOIT.OS.TWISTOR.01; WOIT.BETA2.OS.01; SEAM.BIT.TWISTBLIND.01; v510; v519; v524; v528; v529","external_data_as_recorded":"Fidkowski-Kitaev Phys. Rev. B 81 (2010) -- literature framing, no data","id":"claim:SEAM.STRADDLE.CONE.01","location_as_recorded":"tfpt_3;tfpt_research_contracts;introduction","path":"verification/status_ledger.csv","row_number":597,"scripts_as_recorded":"v534_seam_straddle_cone.py","status_as_recorded":"V1=KILL / V2=ERFOLG ([E] exact integer/Fraction census + float-track certificates; [C] flat-band parent / one interaction class fence); WOIT.OS.TWISTOR.01 stays Open; NO marker moves","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the center quotient A = [[8,2],[5,3]] (atoms), self-code (7,11,13), CP code (1,7,11,13), factorisation det(C+kI) = (k+1)det(A+kI); [C] Lie readings; [O] stratum ablation; no marker moves","checked_by_registry":false,"claim_excerpt":"THE CENTER QUOTIENT COMPILER (2026-07-23; external review round, all identities machine-confirmed before promotion; 14 checks, <1 s, sympy exact): the Sheet-Diamond center C = M(1,0) (v95) carries the fixed primitive line Cv = v with v = (-1,1,0), and the induced operator on the quotient lattice Z^3/Zv (unimodular basis P = (v,e1,e3), P^-1 C P = [[1,4,2],[0,8,2],[0,5,3]]) is EXACTLY the atom matrix A = [[8,2],[5,3]] ","claim_id":"DIAMOND.CENTER.QUOTIENT.01","dependencies_as_recorded":"DIAMOND.CENTER.01; DIAMOND.CENTER.RESOLVENT.01; COX.CLOCK.01; v95; v223; v414","external_data_as_recorded":"-","id":"claim:DIAMOND.CENTER.QUOTIENT.01","location_as_recorded":"tfpt_2","path":"verification/status_ledger.csv","row_number":598,"scripts_as_recorded":"v530_center_quotient_compiler.py","status_as_recorded":"Identity [E] (exact integer linear algebra: fixed line, unimodular quotient, self-coding row sums, resolvent factorisation, honest uniqueness controls -- sympy exact, Wolfram-mirrored) + [C] (the Lie-dimension readings of the quotient ladder, audit-typed like v414) + [O] (full selector-stratum ablation)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] Stage A answered on the 8-dim primitive-character alternative: T30 = C_Phi5 (x) C_Phi6, exact order 30, chi = Phi_30, traces = c_30(k) = c_5 c_6; [O] flip-atlas intertwiner + Stage B stay open; no marker moves beyond the Stage A prose sharpening","checked_by_registry":false,"claim_excerpt":"COXETER STAGE A CLOSED ON THE PRIMITIVE-CHARACTER SPACE (2026-07-23; 15 checks, <1 s, sympy exact): the tfpt_1 two-stage Coxeter audit asked for a natural order-30 operator with characteristic polynomial Phi_30 on the even-flip atlas OR its 8-dimensional primitive-character space. The explicit integer operator T30 = Comp(Phi_5) (x) Comp(Phi_6) (the v418 carrier clock tensor the family/CP hexagon, 8x8) delivers the ch","claim_id":"COX.STAGEA.TENSOR.01","dependencies_as_recorded":"COX.CLOCK.01; COX.COUPLE.01; v223; v418; v55","external_data_as_recorded":"-","id":"claim:COX.STAGEA.TENSOR.01","location_as_recorded":"tfpt_1","path":"verification/status_ledger.csv","row_number":599,"scripts_as_recorded":"v531_coxeter_tensor_stage_a.py","status_as_recorded":"Identity [E] (exact order/charpoly/trace arithmetic + honest kill-scope + coprimality controls -- sympy exact, Wolfram-mirrored) + [C] (the identification with the E8 Coxeter clock, as v223/v314) + [O] (the flip-atlas intertwiner COX.FLIP.INTERTWINER; Stage B metrization)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E, audit] dual-degree checksum: (60,192,240,252) -> sum 744 = 3*248 (= j constant coefficient, recomputed), prod |W(E8)|, gcd 12, /12 = (5,16,20,21); D16 control 1488 = 3*496 (NOT E8-exclusive); primes-below-30 totative fingerprint with maximality scan; audit-only, no marker moves","checked_by_registry":false,"claim_excerpt":"THE E8 DUAL-DEGREE MODULAR CHECKSUM 744 + THE PRIME-TOTATIVE FINGERPRINT (2026-07-23; AUDIT-TYPED under the no-free-pattern rule -- feeds no derivation, kills no alternative alone, registered with its own negative controls; 11 checks, ~2 s, sympy exact): [E] the E8 invariant degrees (2,8,12,14,18,20,24,30) (v66) pair dually d_i + d_{9-i} = 32 = h+2; the four dual products (2*30, 8*24, 12*20, 14*18) = (60,192,240,252)","claim_id":"E8.DEGREE.MODULAR.01","dependencies_as_recorded":"E8.DEG.01 (v66); CELEST.WP4.01 (v496); COXETER.PRIME2.01; ARITH.HULL.01","external_data_as_recorded":"-","id":"claim:E8.DEGREE.MODULAR.01","location_as_recorded":"tfpt_3;tfpt_1","path":"verification/status_ledger.csv","row_number":600,"scripts_as_recorded":"v532_e8_degree_modular_checksum.py","status_as_recorded":"Identity [E, audit-only] (exact integer/q-series arithmetic incl. the j-series recomputation and all controls -- sympy exact, Wolfram-mirrored); explicitly NON-exclusive (D16 control passes); the fingerprint feeds no derivation (no-free-pattern rule honoured)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the sheet path J->K->C->F is one translation orbit alpha_{t+1} = alpha_t + 2 in Z[(1+sqrt(-7))/2] with norms (2,4,14,32) and constant discriminant -7; [C]/[O] common-solver Moebius action = preregistered next test; no marker moves","checked_by_registry":false,"claim_excerpt":"THE SHEET TRANSFER IS A NORM LINE OF DISCRIMINANT -7 (2026-07-23; 12 checks, <1 s, sympy exact): the branch-preserving F_transfer path J -> K -> C -> F = M(1, -2..1) (FTR.PATH.01/v224, v412) carries the determinant D(t) = det M(1,t) = 4t^2 + 14t + 14 = ((4t+7)^2 + 7)/4 = N_{Q(sqrt-7)/Q}(alpha_t) with alpha_t = (4t+7+sqrt(-7))/2. [E] INTEGRALITY: -7 = 1 mod 4 and 4t+7 odd => alpha_t lies in the maximal order Z[(1+sqrt","claim_id":"FTR.DISC7.NORM.01","dependencies_as_recorded":"FTR.PATH.01; DIAMOND.SHEET.SOURCE.J.01 (v412); DIAMOND.SHEET.CALCULUS.01 (v413); v224","external_data_as_recorded":"-","id":"claim:FTR.DISC7.NORM.01","location_as_recorded":"tfpt_2;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":601,"scripts_as_recorded":"v533_ftransfer_disc7_norm.py","status_as_recorded":"Identity [E] (exact norm/integrality/translation/discriminant arithmetic + negative controls -- sympy exact, Wolfram-mirrored) + [E, audit] (split prime 2, Heegner class number) + [C]/[O] (the arithmetic F_transfer frame: common Moebius action of the four solvers = preregistered next test; GATE.FTRANSFER unchanged)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] sum_k rho^{d_k} = 4 rho (arg = pi/3 exactly, sheet-EVEN) and sum_k rho^{m_k} = 4 (arg = 0 exactly, sheet-ODD) on the hexagonal CM unit -- the E8 channel typing has an exact fiber realisation and the phase channel is sheet-blind; arg(prod c) = 0 exactly on both TFPT sectors (the CP residual is a FIBER datum, not a magnitude datum); Tier-1 invariance EMPTY per algebra (every pi/3-carrier is kappa-odd); Im(rho det)/det = Im rho = sin(pi/3) exactly (the orientation reading is degree +1 in the frame normalisation, 21 sin(pi/3) is frame data, the sign a declared orientation); two inequivalent Tier-2 characters (-1,+1) vs (-1,-1) carry the same pi/3 (DEGENERATE), neither frame-coupled; Jarlskog anchor J = 3.327021e-5 = v88 passes (a)-(c), fails only the pi/3-carrier test. Four ledger rows narrowed, no marker moves; R1/R2 OPEN.","checked_by_registry":false,"claim_excerpt":"THE CP CHANNEL / INVARIANT IDENTITIES (2026-07-29; one module, 25 checks, ~1 s; promotion of the exact cores of discovery T177 (contract CP.INVARIANT, probe cp_invariant_probe.py, 49/49, verdict DEGENERATE) -- THE CP MIRROR AS ALGEBRA: the prime-front toolkit (gauge-degree bookkeeping under declared group actions) turned on the four CP ledger rows REDTEAM.D.01 / E8.CHAN.01 / CP.MOD.01 / DUAL.FRAME.01; every statement","claim_id":"CP.CHANNEL.IDENT.01","dependencies_as_recorded":"REDTEAM.D.01; E8.CHAN.01; CP.MOD.01; DUAL.FRAME.01; CP.MU6.01; FLAV.CP.01; REG.FREEZE.01; v88; v220; v225; v227; T177","external_data_as_recorded":"-","id":"claim:CP.CHANNEL.IDENT.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":602,"scripts_as_recorded":"v561_cp_channel_identities.py","status_as_recorded":"Identity [E] (exact identities and certified numerics with mutation controls -- the hexagonal channel identity sum rho^{d_k} = 4 rho / sum rho^{m_k} = 4 sympy-exact with the sheet-even/odd parity typing, arg(prod c) = 0 exactly on both magnitude sectors with the branch-order law, Tier-1 emptiness by the conjugation-commutation theorem, the frame removal Im(rho det)/det = Im rho exact with the degree +1 account, the two inequivalent Tier-2 characters as verified homomorphisms, and the Jarlskog anchor J = 3.327021e-5 = v88 at unitarity 1.1e-41) -- NARROWINGS of four existing ledger readings only; no marker moves; R1/R2 typed OPEN","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] natural class fiber-only (6 brackets = +-Delta, 21 vanish identically; generic degree 1..4 Euler factorisation exact); metric door non-canonical (character split (-1,-1,+1) vs (-1,-1,-1); continuum 441 sin(pi/3)/(25t+117)); single-sine <=> n in {1,2,3,4,6} = phi(n) <= 2 (identity + enumeration to 24); anchor tuple (-1,-1,-1) selects sheet-odd, J = 3.327021e-5 = v88; unique canonical anchor-matching carrier = fiber-pure sin(pi/3); 22/22 checks","checked_by_registry":false,"claim_excerpt":"THE FRAME DOOR OF THE CP MIRROR, DECIDED (2026-07-30; T178, contract FRAME.CARRIER, probe cp_frame_carrier_probe.py 31/31, verdict FIBER-PINNED; one module, 22 checks, ~2 s, sympy-exact generic-frame algebra + one 3x3 unitary matrix at 40 dps). T177/v561 left R1 (can a frame-coupled, scale-free, character-covariant pi/3-carrier exist at all) and R2 (which of the two degenerate Tier-2 characters is physical) open; bot","claim_id":"CP.FIBER.PIN.01","dependencies_as_recorded":"CP.CHANNEL.IDENT.01; REDTEAM.D.01; E8.CHAN.01; CP.MOD.01; DUAL.FRAME.01; CP.MU6.01; REG.FREEZE.01; v88; v225; v561; T177; T178","external_data_as_recorded":"-","id":"claim:CP.FIBER.PIN.01","location_as_recorded":"tfpt_5_redteam","path":"verification/status_ledger.csv","row_number":603,"scripts_as_recorded":"v564_cp_fiber_pin.py","status_as_recorded":"Identity [E] (exact theorems and certified character accounts with mutation controls -- Euler factorisation on fully generic homogeneous blocks, the one-generator bracket enumeration, the character split and the q_t continuum, the single-sine lemma with the crystallographic equivalence, the anchor tuple at 40 dps) + [C] (the Weyl 1946 FFT class boundary; the selection conditional on the Jarlskog anchor; the deck column a declared model); R1 decided, R2 selected, no marker moves","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] block theorem (4 cross entries forced zero; 16 -> 8 params); dichotomy eps = +-1 with the OS cut forced on the Minkowski branch (seam norm a(|z|^2 - 1)) and signature (2,2) by the mirror theorem; kill empty (rho4^2 = diag(-1,1,-1,1) not scalar); induced member unique z -> -conj(z) = theta_perp = the v524 Theta_phys carrier (placement offsets exactly -+pi/2; axis 11pi/8 = 3pi/8 mod pi); N = 8 regressions: Gram PD (16,0,0) min 3.3471e-3, eta_perp = +i, Theta^2 = +1 both sectors, time reversal + torsor closure exact; family A (4,4,0); 22/22 checks","checked_by_registry":false,"claim_excerpt":"THE WOIT-BETA3 MILESTONE EXECUTED (2026-07-30; one module, 22 checks, ~2 s; probe woit_os_beta3_pt_dual_probe.py 25/25, verdict SUCCESS per the frozen preregistration): 'the PT <-> PT* duality typed against sigma_std' -- contract wording: success = Woit's Minkowski conjugation identified with the family-D conjugation on the quotient; kill = the duality forces a clock-centralising (family A) structure. (1) THE COMPATI","claim_id":"WOIT.BETA3.DUALITY.01","dependencies_as_recorded":"WOIT.OS.TWISTOR.01; WOIT.THETA.FREE.01; WOIT.BETA1.GSO.01; WOIT.BETA2.OS.01; SEAM.BIT.RPBLIND.01; v492; v519; v522; v524","external_data_as_recorded":"-","id":"claim:WOIT.BETA3.DUALITY.01","location_as_recorded":"tfpt_research_contracts;tfpt_3","path":"verification/status_ledger.csv","row_number":604,"scripts_as_recorded":"v565_woit_beta3_pt_duality.py","status_as_recorded":"Identity [E] (exact sympy algebra on generic block parameters -- block theorem, branch dichotomy, signature-mirror theorem, kill emptiness, unique induced member, exact rational-pi placement arithmetic, exact lattice regressions) + two 40-digit inertia certificates + [C] (the declared conventions: seam line, seam preservation, RP-side placement, torsor relabeling; contract-level identification, not a derivation); verdict SUCCESS, kill branch empty by algebra, no marker moves","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] A = full 2|1 parabolic, dim 7, word det -81, closed 49/49, mutation-fragile; a = Spec(I + V(V-I)/2) = (1,1,2) with chi_H = x^3 - flag x^2 + Levi x - radical (4,5,2 double-coded); m = 2 unique (enumeration to 2000 + divisor argument); saturated Smith (1,1,1,3,3,3,3), index 81 = 3^4 = staircase sum; A2 Ext^1 = 1 (two module classes); p_n = 1 + tr V^n (240, rank 8 as traces); CR = 4/3 design with 28/25 control; Lorentz/pencil identities exact; 14/14 checks","checked_by_registry":false,"claim_excerpt":"THE PARABOLIC ANCHOR SELF-CODE (2026-07-31; external structural review audited by discovery probe parabolic_selfcode_audit_probe.py 23/23, verdict SELFCODE-VERIFIED, and promoted; one module, 14 checks, ~1 s, exact integer/symbolic sympy, no floats). The v218 sheet-diamond direction operators U = Q diag(1,0,0) (rank-1 winding) and V = Q diag(0,1,1) (rank-2 sheet, Spec V = {0,1,2}) carry a previously unstated exact op","claim_id":"DIAMOND.PARA.SELFCODE.01","dependencies_as_recorded":"DIAMOND.AXIS.01; ANCHOR.GEN.01; AX.P2.01; FLAV.QGEO.01; CONTRACT.F.01; SEAM.BIT.RPBLIND.01; FORM.LADDER.01; v23; v218; v224; v528; v533; v534","external_data_as_recorded":"-","id":"claim:DIAMOND.PARA.SELFCODE.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":605,"scripts_as_recorded":"v566_parabolic_anchor_selfcode.py","status_as_recorded":"Identity [E] (exact integer/symbolic algebra with mutation controls -- parabolic closure, double self-code, uniqueness enumeration + divisor argument, saturated Smith form, A2 quiver, trace code, cross-ratio identities, Lorentz/pencil identities) + [C] (the TFPT readings of the invariants; the bit-carrier and CR-test interpretations) + [O] (the No-Carrier-Reconstruction audit, the mark-local 81 mechanism, the CR-test execution); NO marker moves","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] 52 admissible under (S)(W)(E)(M)(Z) at B = 6; 28 under the seam-line demand; ONE anchor code x^3-4x^2+5x-2 = spectrum (1,1,2) on all 28 (carrier-free anchor); 81-pin -> exactly 2 (corpus Q vs q32 = 0 twin; all carrier-free certificates equal, separator = the forbidden column budget (9,5,1)); winding ablation 28 -> 1376 at bound 3; bound-stable at 9; 9/9 checks; verdict RECONSTRUCTS-TO-FAMILY","checked_by_registry":false,"claim_excerpt":"THE NO-CARRIER-RECONSTRUCTION AUDIT, STAGE A (2026-07-31; Priority 1 of the self-code review; one module, 9 checks, ~1 s, exact enumeration with integer prefilters + sympy verification; discovery probe carrier_free_q_reconstruction_probe.py 10/10, verdict RECONSTRUCTS-TO-FAMILY). THE QUESTION: can Q -- hence V and the v566 parabolic anchor self-code -- be reconstructed WITHOUT carrier/anchor inputs? THE CIRCULARITY L","claim_id":"QGEO.QRECON.01","dependencies_as_recorded":"DIAMOND.PARA.SELFCODE.01; FLAV.QGEO.01; GATE.QGEO.01; FLAV.KQ.01; AX.P2.01; ANCHOR.GEN.01; v10; v11; v218; v566","external_data_as_recorded":"-","id":"claim:QGEO.QRECON.01","location_as_recorded":"tfpt_1;tfpt_2","path":"verification/status_ledger.csv","row_number":606,"scripts_as_recorded":"v567_carrier_free_q_reconstruction.py","status_as_recorded":"Identity/enumeration [E] (exact admissible-set census 52/28/2 with integer prefilters verified by sympy on survivors; one anchor code class on all 28; separator dissection exact; ablations quantified) + [C] (the seam-line demand as declared geometric input; the bit-resonance observation) + [O] (Stage B = GATE.QGEO.01 relocation; the binary selector); verdict RECONSTRUCTS-TO-FAMILY; no marker moves","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] twins integrally distinct (H0 != H2 at equal index 81); v(c) = (1,2,2c) identically; ladder self-consistency <=> c = 2, unique on 28/28; witness = AnchorLadder 2^n / |Z2| / trace code; split member q32 = 1 (complement solve a=0,b=1) collapses to dim 5 -- excluded; mu4-grading candidate fails (5/7 homogeneous); F3[V]-action computed: charpoly x(x-1)^2(x+1) mod 3, eigenvalues {0,1,1,-1} != regular mu4, U-action zero, twins identical; 11/11 checks; verdict SELECTOR-FOUND","checked_by_registry":false,"claim_excerpt":"THE RESIDUAL RECONSTRUCTION BIT: LOCATED, SEPARATED, AND GIVEN A CANONICAL EXACT WITNESS (2026-07-31; Priorities 2+3 of the self-code review fused with the v567 residual bit; one module, 11 checks, ~1 s; discovery probe bit_selector_probe.py 10/10, verdict SELECTOR-FOUND). (1) THE BIT IS INTEGRALLY VISIBLE [E]: the two 81-twins of the v567 audit (q32 = 2 = |Z2| vs q32 = 0) generate DIFFERENT integral orders -- Hermit","claim_id":"DIAMOND.BIT.SELECT.01","dependencies_as_recorded":"QGEO.QRECON.01; DIAMOND.PARA.SELFCODE.01; DIAMOND.AXIS.01; SEAM.BIT.RPBLIND.01; FORM.LADDER.01; v10; v218; v528; v534; v566; v567","external_data_as_recorded":"-","id":"claim:DIAMOND.BIT.SELECT.01","location_as_recorded":"tfpt_1;tfpt_2","path":"verification/status_ledger.csv","row_number":607,"scripts_as_recorded":"v568_bit_selector_ladder.py","status_as_recorded":"Identity [E] (exact integer/symbolic algebra -- Hermite/Smith lattice comparison, the symbolic dominant-mode identity, the uniqueness census on the 28-member class, the split-complement solve, the candidate tests) + [C] (the anchored ladder selector as candidate canonical selection; its physical justification open) + [O] (the selection mechanism; the F3[V]-character question; Stage B); verdict SELECTOR-FOUND; no marker moves","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"CR-PASSES (discrete half): declared export (26,35,44,53), CR = 4/3 exact, y_F = 53 Moebius-forced; controls 28/25 and 1.3222 fail as they must; continuous half open; 9/9 checks","checked_by_registry":false,"claim_excerpt":"The preregistered cross-ratio check (self-code review Priority 4 / v566 S9), executed on its DISCRETE half (one module, 9 checks, <1 s; discovery probe cr_discrete_corners_probe.py 9/9, verdict CR-PASSES): the four solver corners are the in-repo Sheet-Diamond kernels J,K,C,F = M(1,t) = R + Q diag(1,t,t), t = -2..1 (FTR.PATH.01/v224, dets (2,4,14,32)); the corpus's one canonical declared solver reading, the Koide anch","claim_id":"FTR.CRDISC.01","dependencies_as_recorded":"CONTRACT.F.01; FTR.PATH.01; DIAMOND.PARA.SELFCODE.01; v183; v224; v533; v566","external_data_as_recorded":"-","id":"claim:FTR.CRDISC.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":608,"scripts_as_recorded":"v571_cr_discrete_corners.py","status_as_recorded":"Identity [E] + typed boundary [C] (exact symbolic identities on compiler kernels; the continuous-solver half open)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"ANCHOR-VISIBLE: spectrally blind (same inertia, never PSD), integrally separated exactly through anchor/ladder states (Smith slot 18 vs 2, factor 9 = N_fam^2); trace discriminant -81^2; 11/11 checks (half-sided restrictions blind too; the interacting construction is the one remaining RP route) (V-flow robustness; Gibbs pencil: compiler Gibbs-critical at s* = (8-4sqrt19)/15, alt never; critical mode = seam-row flow-fixed direction, the Ext-carrier slot); dynamical RP-slot open","checked_by_registry":false,"claim_excerpt":"The RP form on the 81-twins -- spectrally BLIND, integrally ANCHOR-VISIBLE (one module, 11 checks, ~1 s; discovery probe rp_bit_form_probe.py 11/11, verdict ANCHOR-VISIBLE): with the corpus reflection theta(X) = Sigma X^T Sigma (v10) and the declared states (trace; anchor (1,1,2); ladder (1,2,4); unit), the RP kernel K(x,y) = omega(theta(x) y) on the Hermite basis of each twin order has IDENTICAL inertia on both twin","claim_id":"DIAMOND.BIT.RPFORM.01","dependencies_as_recorded":"DIAMOND.BIT.SELECT.01; QGEO.QRECON.01; DIAMOND.PARA.SELFCODE.01; v10; v23; v534; v568","external_data_as_recorded":"-","id":"claim:DIAMOND.BIT.RPFORM.01","location_as_recorded":"tfpt_1;tfpt_2","path":"verification/status_ledger.csv","row_number":609,"scripts_as_recorded":"v572_rp_bit_form.py","status_as_recorded":"Identity [E] (exact integral/spectral computations; honest negative on the kinematic selection; RP-slot open)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"FORCED: type killed by rank theorem; N <= 3 by (E); double self-consistency (ladder + sat = N^4) pins (N, Q) = (3, compiler Q) uniquely; 11/11 checks; (E)/(M)/(L) ALL redundant, winding form = the uniformity choice (1 of 4) at B = 6 -- the reconstruction needs only involution existence, winding form with N_fam = 3 (E8-glue) and the self-code; gate narrowed by FIVE items; GATE.QGEO.01 narrowed by two items, not closed","checked_by_registry":false,"claim_excerpt":"Stage B of the No-Carrier-Reconstruction audit, first narrowing (one module, 11 checks, ~6 s; discovery probe stageb_winding_probe.py 12/12, verdict FORCED): the involution TYPE is killed by a rank theorem -- any involution with a two-dimensional positive eigenspace gives V' = Q P_- of rank <= 1 (char poly x^2 (x - t) identically in Q), so the binary trace code Spec V = {0,1,2} (v566) is unreachable: only the corpus ","claim_id":"QGEO.WINDING.SELF.01","dependencies_as_recorded":"QGEO.QRECON.01; DIAMOND.BIT.SELECT.01; DIAMOND.PARA.SELFCODE.01; FLAV.QGEO.01; v567; v568","external_data_as_recorded":"-","id":"claim:QGEO.WINDING.SELF.01","location_as_recorded":"tfpt_1;tfpt_2","path":"verification/status_ledger.csv","row_number":610,"scripts_as_recorded":"v574_stageb_winding.py","status_as_recorded":"Identity [E] + typed gate [C] (rank theorem symbolic; enumerations at declared bound; the remaining gate named)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"UNIFLOW-DEGENERATE: exports {(2/3)^6,(2/3)^6,1,-7} forced degenerate by the single-flow theorem; CR in {0,1,oo} in every assignment; the continuous half closes onto v425; 7/7 checks; anchors stay [O]","checked_by_registry":false,"claim_excerpt":"The CONTINUOUS half of the preregistered cross-ratio check, executed against the in-repo solver dynamics (one module, 7 checks, <1 s; discovery probe cr_continuous_uniflow_probe.py 7/7, verdict UNIFLOW-DEGENERATE): the frozen protocol exports -- the fixed-point multipliers of the native contractions, recomputed from primitives (F_pole = e^{-Delta} = (2/3)^6 via the v99 generator; F_Boltzmann = the SAME contraction by","claim_id":"FTR.CRCONT.01","dependencies_as_recorded":"FTR.CRDISC.01; CONTRACT.F.01; DYN.TRANSFER.UNIVERSAL.01; v99; v159; v320; v425; v571","external_data_as_recorded":"-","id":"claim:FTR.CRCONT.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":611,"scripts_as_recorded":"v575_cr_continuous_uniflow.py","status_as_recorded":"Identity [E] + typed closure [C] (exports recomputed; degeneracy theorem exact; the closure onto v425 typed)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"MOEBIUS-IN-OWN-CLOCK: seam {q,t} = -Delta^2/2 (own clock 0), QCD Schwarzian 0 in own time, relic degenerate; no shared wall-time jet invariant; clock = the obstruction; 6/6 checks","checked_by_registry":false,"claim_excerpt":"The jet/Schwarzian contract, executed natively (one module, 6 checks, <1 s; discovery probe native_jets_probe.py 6/6, verdict MOEBIUS-IN-OWN-CLOCK; the second review's Priority 6): the exact v99 Koide trajectory solves the generator identically and has wall-time Schwarzian {q,t} = -Delta^2/2 = -18 log(3/2)^2 exactly (constant, trajectory-independent; F_Boltzmann carries the SAME value by the v425 single-flow theorem)","claim_id":"FTR.JETS.01","dependencies_as_recorded":"FTR.CRCONT.01; FTR.CRDISC.01; DYN.TRANSFER.UNIVERSAL.01; v99; v159; v425; v575","external_data_as_recorded":"-","id":"claim:FTR.JETS.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":612,"scripts_as_recorded":"v578_native_jets.py","status_as_recorded":"Identity [E] + typed closure [C] (exact trajectories and Schwarzians; the joint test external)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"UNIT-BOX-SEPARATED: positive Ext coupling inside |J| < 1 heals exactly the compiler twin (J_c <= 15/16, thresholds exact with v572 pencil-factor numerators); alt twin rigid; golden-polynomial response pole observed; response-level, contract stays open; 8/8 checks","checked_by_registry":false,"claim_excerpt":"The interacting follow-up of v572, executed -- RANK-ONE EXT-SOURCE COUPLING ON THE GIBBS PENCIL SEPARATES THE 81-TWINS DIRECTIONALLY INSIDE THE UNIT COUPLING BOX (one module, 8 checks, ~1 s; discovery probe ext_source_response_probe.py 8/8, verdict UNIT-BOX-SEPARATED): the interacting kernel K(s,J) = K0 + s K_Pi + J v v^T (v from the shared Ext arrows E31/E32 of the radical row) has EXACT rational flip thresholds J_c","claim_id":"DIAMOND.BIT.EXTSOURCE.01","dependencies_as_recorded":"DIAMOND.BIT.RPFORM.01; DIAMOND.BIT.SELECT.01; QGEO.QRECON.01; v534; v568; v572","external_data_as_recorded":"-","id":"claim:DIAMOND.BIT.EXTSOURCE.01","location_as_recorded":"tfpt_1;tfpt_2","path":"verification/status_ledger.csv","row_number":613,"scripts_as_recorded":"v584_ext_source_response.py","status_as_recorded":"Exact [E] + typed consistency [C] (thresholds closed rational; verified numerically; response level only)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"EXISTENCE-UNCONDITIONAL: rigidity (Z/2)^3 on both twins; narrowing 6 -> 3 -> 2 -> 1 via v574 type theorem + seam reversal + zero-mode fixing; S0 explicit with Sigma-signature; the two demands' continuum derivation stays open; 7/7 checks","checked_by_registry":false,"claim_excerpt":"The sheet-involution existence question of GATE.QGEO.01, narrowed to a two-demand selection with UNCONDITIONAL existence (one module, 7 checks, <1 s; discovery probe involution_existence_probe.py 7/7, verdict EXISTENCE-UNCONDITIONAL): RIGIDITY -- the integral V-commuting involutions are exactly the spectral sign group (Z/2)^3: all eight sign choices on V's eigenspaces {0,1,2} are integer matrices, genuine involutions","claim_id":"QGEO.INVOL.01","dependencies_as_recorded":"QGEO.WINDING.SELF.01; QGEO.QRECON.01; DIAMOND.PARA.SELFCODE.01; v566; v567; v574","external_data_as_recorded":"-","id":"claim:QGEO.INVOL.01","location_as_recorded":"tfpt_1;tfpt_2","path":"verification/status_ledger.csv","row_number":614,"scripts_as_recorded":"v590_involution_existence.py","status_as_recorded":"Exact [E] + typed relocation [C] (exact sympy; demands declared; continuum derivation open)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"FINGERPRINTS-HIT: rank-3 Eisenstein module; projective D4 via deck (r^4 = omega); cusp-class group (Z/3)^4 = 81 with the per-mark mechanism; Lorentz (1,2) polarization (Chevalley-Weil + Paper II simultaneously); single-cusp Gram {0,0,2}; Q/V dictionary and RP map named open; 6/6 checks","checked_by_registry":false,"claim_excerpt":"Strategy I/II, first executed step -- the mu3-cover of P^1 branched at mu4 (the curve y^3 = x^4 - 1) carries FOUR independent compiler fingerprints (one module, 6 checks, <1 s; discovery probe mu4_cover_model_probe.py 6/6, verdict FINGERPRINTS-HIT): (1) genus 3 with five cusps (mu4 + infinity; monodromies (w,w,w,w,w^2) multiplying to 1) and Chevalley-Weil H^{1,0} = (1,2) per character -- H_1 is a RANK-3 module over t","claim_id":"QGEO.COVER.01","dependencies_as_recorded":"QGEO.INVOL.01; QGEO.WINDING.SELF.01; DIAMOND.PARA.SELFCODE.01; GATE.QGEO.01; v566; v574; v590","external_data_as_recorded":"-","id":"claim:QGEO.COVER.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":615,"scripts_as_recorded":"v597_mu4_cover_model.py","status_as_recorded":"Exact [E] fingerprints + typed candidate [C] (Burau convention validated; Q-identification open)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"DICT-THREE-ENTRIES: U ~ G2, Q_- ~ G1-G3 (diamond diagonal), ladder ~ 1+G1+G3 -- all exact; grading half absent from 7296 canonical combinations (kill not triggered; real structure the named suspect); 4/4 checks","checked_by_registry":false,"claim_excerpt":"The cover dictionary, round 2 -- THREE compiler objects located as canonical cusp-Gram combinations on the mu3-cover (one module, 4 checks, <1 s; discovery probe cover_dictionary_probe.py 4/4, verdict DICT-THREE-ENTRIES): with T_1..T_4 the D4-conjugate cusp twists and G_k their Grams -- U ~ G_2 (char x^2(x-3), the winding operator as a single-cusp Gram; v597 entry); Q_- ~ G_1 - G_3 (char x(x^2-3)): THE MU4 SHEET COUP","claim_id":"QGEO.DICT.01","dependencies_as_recorded":"QGEO.COVER.01; QGEO.INVOL.01; DIAMOND.PARA.SELFCODE.01; v566; v568; v597","external_data_as_recorded":"-","id":"claim:QGEO.DICT.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":616,"scripts_as_recorded":"v598_cover_dictionary.py","status_as_recorded":"Exact [E] entries + quantified negatives (numeric prefilter, symbolic confirmation)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"REAL-STRUCTURE-LANDED: R unique (R^2 = +1), four intertwinings exact; Gamma closes V/H/Q_+ at char level (H carries the anchor spectrum); constants 5/9/27 in the Gamma-decomposition; joint embedding open (4x6 candidates, 0 joint pairs); det J = 8, Lorentz (1,2); 18/18 checks","checked_by_registry":false,"claim_excerpt":"The real structure on the mu3-cover -- the v598 suspect constructed (one module, 18 checks, ~3 s; discovery probe real_structure_probe.py 18/18, verdict REAL-STRUCTURE-LANDED).  EXISTENCE AND UNIQUENESS [E]: complex conjugation on the base fixes the punctures {1,-1} and swaps {i,-i} (an orientation-reversing D4 reflection); it must act semi-linearly, R(v) = M conj(v), sending each cusp twist to the INVERSE of its ref","claim_id":"QGEO.REAL.01","dependencies_as_recorded":"QGEO.DICT.01; QGEO.COVER.01; QGEO.INVOL.01; DIAMOND.PARA.SELFCODE.01; v566; v597; v598","external_data_as_recorded":"-","id":"claim:QGEO.REAL.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":617,"scripts_as_recorded":"v599_real_structure.py","status_as_recorded":"Exact [E] existence/uniqueness/char identities + [X] quantified joint negative + [C] the TFPT readings (exact sympy; numeric prefilter with symbolic confirmation for the scan)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"JOINT-EMBEDDING-LANDED: (U*, V*) Gamma-even degree-2, Z[omega]-integral, chars + joint traces compiler-exact, word rank 7, conjugation solved, integer on saturated Fix(R), Smith (1,1,1,3,3,3,3) index 81 = v566; canonicity open; 15/15 checks","checked_by_registry":false,"claim_excerpt":"The joint embedding -- the compiler pair (U, V) is realized on the mu3-cover (one module, 15 checks, ~4 s; discovery probe joint_embedding_probe.py 15/15, verdict JOINT-EMBEDDING-LANDED).  THE PAIR [E]: in the Gamma-even DEGREE-2 sector (the v599 grading functor applied to cusp-Gram products), U* = -2E1 + (G1 Gamma(G1) + Gamma(G1) G1) + 3 and V* = -E3 + (1/2)(G2 Gamma(G2) + Gamma(G2) G2) + 1 are both integral over Z[","claim_id":"QGEO.EMBED.01","dependencies_as_recorded":"QGEO.REAL.01; QGEO.DICT.01; QGEO.COVER.01; QGEO.INVOL.01; DIAMOND.PARA.SELFCODE.01; GATE.QGEO.01; v566; v597; v598; v599","external_data_as_recorded":"-","id":"claim:QGEO.EMBED.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":618,"scripts_as_recorded":"v600_joint_embedding.py","status_as_recorded":"Exact [E] existence realization (integrality, conjugation, saturation index all exact sympy) + typed open canonicity [O]; NO marker moves","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"EQUIVARIANT-DUAL-LANDED: GJ_k idempotent equivariant projectors; pair family compiler-exact and equivariant by construction; conjugate to the TRANSPOSED compiler pair (dual parabolic); Klein group integral on the curve (8/8, S_0 explicit, A B = S_0); J-word-Gram inertia (3,2,2) typed open vs v572; 14/14 checks","checked_by_registry":false,"claim_excerpt":"The canonical equivariant realization (one module, 14 checks, ~12 s; discovery probe equivariant_dual_probe.py 14/14, verdict EQUIVARIANT-DUAL-LANDED).  THE REPAIR: the naive cusp-Gram presentation of v600 is not D4-equivariant because the standard hermitian dagger is basis-dependent -- the Burau image preserves J; the canonical building blocks are the J-ADAPTED cusp projectors GJ_k = (1-T_k) J^-1 (1-T_k)^dagger J.  ","claim_id":"QGEO.CANON.01","dependencies_as_recorded":"QGEO.EMBED.01; QGEO.REAL.01; QGEO.INVOL.01; DIAMOND.PARA.SELFCODE.01; v590; v597; v599; v600","external_data_as_recorded":"-","id":"claim:QGEO.CANON.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":619,"scripts_as_recorded":"v601_equivariant_dual.py","status_as_recorded":"Exact [E] equivariance/duality/Klein identities + [C] typed opens (exact sympy; one numeric inertia count of an exact hermitian matrix)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"DUALITY-FORMS-LANDED: J-adjoint exchanges the parabolic types (exact conjugations both ways); dictionary complete in J-projector language (anchor formula verbatim); Weil-twisted form positive definite (exact); B = M^dag J symmetric, det 8; corpus-transpose / mark-local / seam questions typed open; Lean FORM.QGEO.04 green; 17/17 checks","checked_by_registry":false,"claim_excerpt":"The duality-and-forms round (one module, 17 checks, ~8 s; discovery probe duality_forms_probe.py 17/17, verdict DUALITY-FORMS-LANDED).  THE DUALITY MECHANISM [E]: U_1 = 3 GJ_1 is J-self-adjoint; the J-adjoint of V_1 = 1 + GJ_4 - GJ_1 GJ_2 is the exact product reversal 1 + GJ_4 - GJ_2 GJ_1; and (U_1, V_1^J) is EXACTLY conjugate to the compiler line-stabilizer pair while (U_1, V_1) is conjugate to the transposed pair (","claim_id":"QGEO.DUALFORMS.01","dependencies_as_recorded":"QGEO.CANON.01; QGEO.EMBED.01; QGEO.REAL.01; DIAMOND.PARA.SELFCODE.01; v572; v590; v600; v601","external_data_as_recorded":"-","id":"claim:QGEO.DUALFORMS.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":620,"scripts_as_recorded":"v602_duality_forms.py","status_as_recorded":"Exact [E] duality/dictionary/positivity identities + [X/O] quantified negatives and typed opens (exact sympy; two numeric inertia counts of exact matrices) + Lean certificate FORM.QGEO.04","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"SEAM-REAL-LANDED: seam line unique, real (R-fixed), S_0-reversed (v590 demand geometric); infinity cusp separated (unreduced Burau, full twist {1, omega x3}); E_1 order-3 cokernel class (first per-mark witness); E_4 trivial, E_2/E_3 outside; translator negatives quantified; 15/15 checks","checked_by_registry":false,"claim_excerpt":"The seam-and-marks round (one module, 15 checks, ~7 s; discovery probe seam_marks_probe.py 15/15, verdict SEAM-REAL-LANDED).  THE SEAM LINE IS REAL [E]: the line-stabilizer pair (U_1, V_1^J) has a UNIQUE common eigenline v with U v = 0 and V v = v -- the compiler seam span(e3), transported; explicitly v = (0, (sqrt3-i)/(sqrt3+i), 1).  The real structure FIXES this line (R v ~ v): the seam is a real line of the cover.","claim_id":"QGEO.SEAMMARKS.01","dependencies_as_recorded":"QGEO.DUALFORMS.01; QGEO.CANON.01; QGEO.EMBED.01; QGEO.INVOL.01; v590; v600; v601; v602","external_data_as_recorded":"-","id":"claim:QGEO.SEAMMARKS.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":621,"scripts_as_recorded":"v603_seam_marks.py","status_as_recorded":"Exact [E] seam/infinity/witness identities + [X] quantified translator negatives + [C] typed per-mark framing (exact sympy)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"EQUIVARIANT-ORDER-LANDED: M^dag J M = J^T exact (R anti-isometry); J_fix integer, det 72; four-frame order FULL rank 18, divisors (1^15,3,3,3), index 27 = 3^3; coker(1-T_inf) = Z^2+(Z/3)^3, finite cusps torsion-free; 81 at marks / 27 at infinity; translator negatives extended (omega-bar named); 12/12 checks","checked_by_registry":false,"claim_excerpt":"The equivariant order and the infinity bridge (one module, 12 checks, ~4 s; discovery probe equivariant_order_probe.py 12/12, verdict EQUIVARIANT-ORDER-LANDED).  CORRECTION + THE INTEGRAL FORM [E]: R IS an anti-isometry of the polarization -- the correct compatibility equation M^dagger J M = J^T holds EXACTLY (a v599-diary side remark had tested the wrong equation M conj(J) M^dagger vs J); consequently J restricts to","claim_id":"QGEO.EQORDER.01","dependencies_as_recorded":"QGEO.SEAMMARKS.01; QGEO.DUALFORMS.01; QGEO.EMBED.01; QGEO.COVER.01; v597; v600; v601; v602; v603","external_data_as_recorded":"-","id":"claim:QGEO.EQORDER.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":622,"scripts_as_recorded":"v604_equivariant_order.py","status_as_recorded":"Exact [E] anti-isometry/order/localization identities + [C] typed localization reading + [X] quantified translator negatives (exact sympy; Smith normal forms over Z)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"TRANSLATOR-LANDED: theta_corpus = Jadj o inner(c) exact (c unique, 14c integral); seam = nonzero 3-torsion at infinity ((2,2,0) pattern); order chain indices 3^5/3^4 (the 81 survives); J_fix duality certified + Lean; c's geometric identity open; 11/11 checks","checked_by_registry":false,"claim_excerpt":"The translator round (one module, 11 checks, ~11 s; discovery probe translator_probe.py 11/11, verdict TRANSLATOR-LANDED).  THE TRANSLATOR EXISTS [E, centerpiece]: pulling the corpus RP anti-automorphism theta(X) = Sigma X^T Sigma back along the compiler conjugation and composing with the J-adjoint gives an algebra automorphism phi = Jadj o theta_pull -- and phi is INNER: the intertwiner space is 1-DIMENSIONAL, its g","claim_id":"QGEO.TRANSLATOR.01","dependencies_as_recorded":"QGEO.EQORDER.01; QGEO.SEAMMARKS.01; QGEO.DUALFORMS.01; QGEO.EMBED.01; v572; v600; v601; v602; v603; v604","external_data_as_recorded":"-","id":"claim:QGEO.TRANSLATOR.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":623,"scripts_as_recorded":"v605_translator.py","status_as_recorded":"Exact [E] translator/bridge/chain/duality identities + [C] typed opens (exact sympy; Smith transforms over Z; Lean addendum green)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"MODES-SEPARATED: all three V-eigenlines pure 3-torsion at infinity, classes pairwise distinct ((2,0,2)/(2,2,0)/(1,2,0)); canonical '+1' rule open; cubic field of c disc -783, S_3, not abelian (arithmetic route closed); 7/7 checks","checked_by_registry":false,"claim_excerpt":"The mode-separation round (one module, 7 checks, ~2 s; discovery probe mode_separation_probe.py 7/7, verdict MODES-SEPARATED).  ALL THREE MODES ARE PURE TORSION AT INFINITY [E]: the three eigenlines of the sheet operator V (eigenvalues 0, 1, 2), lifted to the unreduced integral module along the unique intertwiner (1-parameter, rank 3), all have ZERO free part in coker(1 - T_inf) = Z^2 + (Z/3)^3 -- like the seam (v605","claim_id":"QGEO.MODESEP.01","dependencies_as_recorded":"QGEO.TRANSLATOR.01; QGEO.SEAMMARKS.01; QGEO.EQORDER.01; v590; v603; v604; v605","external_data_as_recorded":"-","id":"claim:QGEO.MODESEP.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":624,"scripts_as_recorded":"v606_mode_separation.py","status_as_recorded":"Exact [E] torsion/separation identities + [C] typed frame caveat + [X] honest arithmetic negative (exact sympy; Smith transforms over Z)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"SELECTION-RULE-LANDED: torsion = F_3 space (omega trivial); r-action explicit, char (x+1)(x^2+1) mod 3, unique projective eigenline = top mode; seam/zero not fixed; labels mutually exclusive (R-real / deck-eigen / unlabeled); S_0 flips the labeled pair; 10/10 checks","checked_by_registry":false,"claim_excerpt":"The selection rule round (one module, 10 checks, ~2 s; discovery probe selection_rule_probe.py 10/10, verdict SELECTION-RULE-LANDED).  THE F_3 STRUCTURE [E]: the torsion of coker(1 - T_inf) is a genuine F_3 vector space -- omega-multiplication acts as the IDENTITY ((1-omega) acts as zero) -- and the deck rotation r (commuting with T_inf = r^4) acts F_3-linearly on it.  THE RIGIDITY [E]: the induced action is the expl","claim_id":"QGEO.SELRULE.01","dependencies_as_recorded":"QGEO.MODESEP.01; QGEO.TRANSLATOR.01; QGEO.INVOL.01; v590; v603; v605; v606","external_data_as_recorded":"-","id":"claim:QGEO.SELRULE.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":625,"scripts_as_recorded":"v607_selection_rule.py","status_as_recorded":"Exact [E] F_3/rigidity/labeling identities + [C] typed selection reading (exact sympy / F_3 arithmetic; Smith transforms over Z)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"GAMMA-FREE-SLICE-LANDED: chiral (16,0,0); anti-chiral (8,8,0) sector-exact (odd strictly ND -- mirror exclusion); clock spectrum {1, sqrt2-1} multiplicity-free; mark algebras PD dim 4, products generate, tau_2 = mark transport PD; gamma open on A_hol; 9/9 checks","checked_by_registry":false,"claim_excerpt":"The free gamma slice of the WOIT roadmap (one module, 9 checks, ~1 s; discovery probe gamma_free_slice_probe.py 9/9, verdict GAMMA-FREE-SLICE-LANDED; the v524 machinery imported read-only).  THE BASELINE [E]: the chiral N = 8 OS Gram is PD (16,0,0) -- H_phys exists (v524 Q1.3 reproduced).  THE FLIP LOCALIZES [E]: the anti-chiral (mirror) state's Gram has inertia (8,8,0) and the split is SECTOR-EXACT: even (8,0,0) PD,","claim_id":"WOIT.GAMMA.FREE.01","dependencies_as_recorded":"WOIT.OS.TWISTOR.01; WOIT.BETA2.OS.01; WOIT.THETA.FREE.01; v519; v524; v565","external_data_as_recorded":"-","id":"claim:WOIT.GAMMA.FREE.01","location_as_recorded":"tfpt_research_contracts;tfpt_3","path":"verification/status_ledger.csv","row_number":626,"scripts_as_recorded":"v608_gamma_free_slice.py","status_as_recorded":"Exact [E] sector/spectrum/incidence statements on the explicit v524 net + [C] the gamma reading (free slice; A_hol untouched)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"C-FACTORIZATION-LANDED: d unique (1-dim), det 1, Z[omega]-integral, Gamma(d)d = 1; c = lambda K_1 d exact with K_1 = J^-1 conj(F_2)^T M^-1; theta_corpus = Jadj o inner(K_1) o inner(d); c geometrically identified; 8/8 checks","checked_by_registry":false,"claim_excerpt":"The translator factorization (one module, 8 checks, ~8 s; discovery probe translator_factorization_probe.py 8/8, verdict C-FACTORIZATION-LANDED).  THE MIRROR INTERTWINER [E]: the intertwining system d A = Gamma(A) d for the realized pair (A in {U_1, V_1^J}; Gamma = the v599 real-structure conjugation) has a 1-DIMENSIONAL solution space -- d exists, is unique up to scale, and intertwines the pair with its mirror image","claim_id":"QGEO.CFACTOR.01","dependencies_as_recorded":"QGEO.TRANSLATOR.01; QGEO.MODESEP.01; QGEO.REAL.01; v599; v605; v606","external_data_as_recorded":"-","id":"claim:QGEO.CFACTOR.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":627,"scripts_as_recorded":"v609_translator_factorization.py","status_as_recorded":"Exact [E] uniqueness/unimodularity/integrality/involutivity/factorization identities + [C] the closed-identity reading (exact sympy)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"LANDSCAPE-MAPPED: differential characters (12,12,6); Jac ~ A_2(zeta_12) x E(omega) point-count-confirmed (10 exact zero-differences; surface traces only at p = 1 mod 12); anchor class most frequent nontrivial integer family (286); single spectra cheap, joint structure the distinction; periods named; 9/9 checks","checked_by_registry":false,"claim_excerpt":"The curve landscape round -- what else the mu3-cover carries (one module, 9 checks, ~1 s; discovery probe curve_landscape_probe.py 9/9, verdict LANDSCAPE-MAPPED).  THE JACOBIAN SPLITS [E chars + C reading]: the three holomorphic differentials of C: y^3 = x^4 - 1 carry (deck, rotation) characters of combined orders (12, 12, 6) (dx/y ~ (w^-1, i), dx/y^2 ~ (w, i), x dx/y^2 ~ (w, -1)); by standard CM theory the Jacobian ","claim_id":"QGEO.LANDSCAPE.01","dependencies_as_recorded":"QGEO.COVER.01; QGEO.DICT.01; QGEO.EMBED.01; v597; v598; v600","external_data_as_recorded":"-","id":"claim:QGEO.LANDSCAPE.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":628,"scripts_as_recorded":"v610_curve_landscape.py","status_as_recorded":"Exact [E] characters/point-counts/census + [C] CM-theory reading and named resources (deterministic integer computations; no floats beyond the census prefilter)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"PERIODS-CLASSICAL: five Beta identities exact (zeta_12-grid Gamma denominators); rotation characters act on periods exactly; Omega_E = B(1/3,1/6)/2; cross-factor PSLQ null (splitting-consistent); period dictionary named; 6/6 checks","checked_by_registry":false,"claim_excerpt":"The periods round -- the analytic layer of the cover is classical (one module, 6 checks, ~1 s; discovery probe periods_probe.py 6/6, verdict PERIODS-CLASSICAL).  EXACT BETA IDENTITIES [E, symbolic]: the five basic period integrals I_{k,j} = int_0^1 x^k (1-x^4)^{-j/3} dx equal (1/4) B((k+1)/4, 1-j/3) EXACTLY; the Gamma denominators (Gamma(11/12), Gamma(7/12), Gamma(5/12), Gamma(1/12)) all live on the ZETA_12 GRID -- t","claim_id":"QGEO.PERIODS.01","dependencies_as_recorded":"QGEO.LANDSCAPE.01; QGEO.COVER.01; v597; v610","external_data_as_recorded":"-","id":"claim:QGEO.PERIODS.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":629,"scripts_as_recorded":"v611_periods.py","status_as_recorded":"Exact [E] symbolic Beta identities + 40-digit certificates + PSLQ-null consistency + [C] the period-dictionary reading","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"POLARIZATION-FRAMED: r eigenvalues zeta_12 x {1,-1,-i} simple; J exactly diagonal in the rotation frame (values (1+sqrt3)/2, (1-sqrt3)/2, -1); the positive Hodge direction = the primitive zeta_12 eigenspace; product = det J/|det W|^2 = 1/2; period normalization named; 9/9 checks","checked_by_registry":false,"claim_excerpt":"The polarization frame round (one module, 9 checks, ~2 s; discovery probe polarization_frame_probe.py 9/9, verdict POLARIZATION-FRAMED).  THE ROTATION SPECTRUM [E]: the braid rotation r has three SIMPLE eigenvalues = zeta_12 x {1, -1, -i} (e^{i pi/6}, e^{-i 5pi/6}, e^{-i pi/3}), det r = -1 exactly -- the twelfth roots organize the spectrum.  J DIAGONALIZES IN THE ROTATION FRAME [E]: in the left-eigenvector basis W of","claim_id":"QGEO.POLFRAME.01","dependencies_as_recorded":"QGEO.PERIODS.01; QGEO.LANDSCAPE.01; QGEO.REAL.01; v597; v599; v610; v611","external_data_as_recorded":"-","id":"claim:QGEO.POLFRAME.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":630,"scripts_as_recorded":"v612_polarization_frame.py","status_as_recorded":"Exact [E] spectrum/diagonalization/signature identities + [C] the bridge reading (exact sympy)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"PERIOD-NORMALIZED: rotation deck-free on segments (12 wrap factors = 1); r = deck o rotation exactly (char(r) = char(omega*M), deck power unique); period rows realize the eigenframe (antihol <-> zeta_12); Hodge weights = explicit Gamma monomials, signature (2,1); J = -h per character (Riemann-Hodge positivity realized); 19/19 checks","checked_by_registry":false,"claim_excerpt":"The canonical period normalization -- the analytic bridge closes (one module, 19 checks, ~6 s; discovery probe canonical_periods_probe.py 19/19, verdict PERIOD-NORMALIZED; executes v612's named step B5).  DECK-FREE ROTATION [E, 40-digit certificates]: the quarter rotation x -> ix maps the four branch-point segments of y^3 = x^4 - 1 cyclically with NO deck correction (all 12 wrap factors exactly 1); the single omega-s","claim_id":"QGEO.PERNORM.01","dependencies_as_recorded":"QGEO.POLFRAME.01; QGEO.PERIODS.01; QGEO.LANDSCAPE.01; QGEO.REAL.01; v597; v599; v610; v611; v612","external_data_as_recorded":"-","id":"claim:QGEO.PERNORM.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":631,"scripts_as_recorded":"v613_canonical_periods.py","status_as_recorded":"Exact [E] dictionary/uniqueness identities + 40-digit certificates + Gamma-monomial closed forms + [C] the fork-basis residue (sympy + mpmath)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"TRANSPORT-CANONICAL: transported periods factorize exactly (rotation substitution identity); deck step = boundary monodromy t^4 = omega on every sheet (exponent 4 = |mu_4| forced); canonical transport matrix = omega*M (v613 dictionary canonical, r^4 = omega re-derived); 25-digit certificates; 12/12 checks","checked_by_registry":false,"claim_excerpt":"The Gauss-Manin transport round -- the deck step IS the boundary monodromy (one module, 12 checks, ~7 s; discovery probe transport_deck_probe.py 12/12, verdict TRANSPORT-CANONICAL; closes v613's named residue F1 at the transport level).  THE FACTORIZATION [E, symbolic]: transporting the segment cycles along the rigid quarter-rotation loop of the four branch points (p_k(tau) = e^{i pi tau/2} p_k, the rotation braid), ","claim_id":"QGEO.TRANSPORT.01","dependencies_as_recorded":"QGEO.PERNORM.01; QGEO.POLFRAME.01; v597; v612; v613","external_data_as_recorded":"-","id":"claim:QGEO.TRANSPORT.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":632,"scripts_as_recorded":"v614_transport_deck.py","status_as_recorded":"Exact [E] factorization/deck/uniqueness identities + 25-digit transport certificates + [C] the boundary-monodromy reading (sympy + mpmath)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"GAMMA-TOY-LANDED: interacting mirror flip sector-exact on every cut/coupling (odd strictly ND, bounded away from zero -- kill test (3) cannot fire on the survivor); mark transport Hermitian PD at every g (kill test (7) does not fire); odd transfer spectrum multiplicity-free; dead member has no RP home (bit selection and chirality co-locate); 11/11 checks","checked_by_registry":false,"claim_excerpt":"The interacting gamma slice at toy level (one module, 11 checks, ~2 s; discovery probe gamma_toy_interacting_probe.py 11/11, verdict GAMMA-TOY-LANDED).  The gamma battery executed ON the RP-surviving interaction class (the alignment bit: delta = pi/2, positive coupling, v534) of the 16-Majorana FK seam toy (v529).  TWO PARENTS [float]: chiral (2-point I + iC, the v519 kernel) and MIRROR (I - iC), both gap 1.  SURVIVO","claim_id":"WOIT.GAMMA.TOY.01","dependencies_as_recorded":"WOIT.GAMMA.FREE.01; SEAM.STRADDLE.CONE.01; SEAM.INT.FKTOY.01; WOIT.THETA.FREE.01; WOIT.BETA2.OS.01; v519; v524; v529; v534; v608","external_data_as_recorded":"-","id":"claim:WOIT.GAMMA.TOY.01","location_as_recorded":"tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":633,"scripts_as_recorded":"v615_gamma_toy_interacting.py","status_as_recorded":"Float-track certificates (tolerances declared) + exact combinatorics + [C] toy fence (numpy/sympy)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"SU2-KINEMATIC-SEPARATED: rho_tw = right-j; internal su(2) fiber-preserving, commutes with spacetime, intersection {0} (kill test (6) kinematic branch does not fire); clock = left-u o right-u exact; deck = left-i; broken to U(1) with mark torsor = internal mu4; 17/17 checks","checked_by_registry":false,"claim_excerpt":"The internal SU(2), kinematic separation at twistor level (one module, 17 checks, <1 s; discovery probe su2_internal_kinematic_probe.py 17/17, verdict SU2-KINEMATIC-SEPARATED; the first executed slice of gamma kill test (6)).  THE QUATERNION SPLIT [E]: on C^4 = H^2 the right multiplications close the (opposite) quaternion algebra exactly, and Woit's Euclidean structure IS an internal direction: rho_tw = right-j VERBA","claim_id":"WOIT.SU2.KIN.01","dependencies_as_recorded":"WOIT.GAMMA.TOY.01; WOIT.BETA3.DUALITY.01; WOIT.THETA.FREE.01; v519; v565; v608; v615","external_data_as_recorded":"-","id":"claim:WOIT.SU2.KIN.01","location_as_recorded":"tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":634,"scripts_as_recorded":"v616_su2_internal_kinematic.py","status_as_recorded":"Exact [E] operator identities (sympy) + [C] the kinematic fence","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"SEAM-FORCES-COVER: Z4-Mobius rigidity (mu4 forced, harmonic CR orbit); weights forced uniform j in {1,2}; y^3 = x^4-1 exact, genus 3; seam reflections = the v599 (k,5-k) pattern with the v519 cut points; residue = cyclic-3 choice + physical<->conformal identification; 14/14 checks","checked_by_registry":false,"claim_excerpt":"The seam forcing round -- the conformal seam axioms force the mu3-cover y^3 = x^4 - 1 up to the conjugate sheet (one module, 14 checks, <1 s; discovery probe seam_cover_forcing_probe.py 14/14, verdict SEAM-FORCES-COVER; a constructive slice of the bedrock premise QGEO.SYM.01).  Z4-MOBIUS RIGIDITY [E]: any 4-point configuration on P^1 cyclically permuted by an order-4 Mobius map is Mobius-equivalent to mu4 (multiplier","claim_id":"QGEO.SEAMFORCE.01","dependencies_as_recorded":"QGEO.COVER.01; QGEO.REAL.01; QGEO.SEAMMARKS.01; QGEO.PERNORM.01; v597; v599; v603; v613","external_data_as_recorded":"-","id":"claim:QGEO.SEAMFORCE.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":635,"scripts_as_recorded":"v617_seam_cover_forcing.py","status_as_recorded":"Exact [E] rigidity/census/genus identities (sympy) + [C] the residue typing","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"N3-PINNED: seam-admissible primitive-Lorentz orders = {3, 5} exactly (N = 6 reduces to N = 3); compiler constants 27/81 pin N = 3 uniquely (vs 125/625 for N = 5); residue = N_fam = 3 (E8-anchored); 9/9 checks","checked_by_registry":false,"claim_excerpt":"The cyclic-N census -- the seam admits N in {3, 5} as primitive-Lorentz orders and the compiler's integral constants pin N = 3 (one module, 9 checks, <1 s; discovery probe cyclic_n_census_probe.py 9/9, verdict N3-PINNED; makes the first v617 bedrock residue CONDITIONAL).  RAMIFICATION [E]: points over infinity = gcd(N, 4): full ramification everywhere iff N in {3, 5} among N = 2..6.  GENUS [E]: Riemann-Hurwitz table ","claim_id":"QGEO.NCENSUS.01","dependencies_as_recorded":"QGEO.SEAMFORCE.01; QGEO.COVER.01; QGEO.PERNORM.01; v597; v600; v613; v617","external_data_as_recorded":"-","id":"claim:QGEO.NCENSUS.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":636,"scripts_as_recorded":"v620_cyclic_n_census.py","status_as_recorded":"Exact [E] ramification/genus/Chevalley-Weil/pinning identities (sympy) + [C] the conditional typing","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"CLOCK-SURVIVES-INTERACTING: free v524 pattern reproduced at N = 16; at g > 0 Hermiticity survives exactly on {4, 6, 7} (mu4-commensurate); clock step PD over the whole grid; mechanism = alpha_4-invariance exact (quartet stabilizer); 6/6 checks","checked_by_registry":false,"claim_excerpt":"The interacting Klein-Landau semigroup -- the clock survives the interaction as a positive transfer exactly on the mu4-commensurate steps (one module, 6 checks, ~2 s; discovery probe interacting_semigroup_probe.py 6/6, verdict CLOCK-SURVIVES-INTERACTING; the gamma net-dynamics slice after v615/v616).  FREE BASELINE [E-float]: at g = 0 all seven steps tau_k (dims 29, 22, 16, 11, 7, 4, 2) are Hermitian with normalized ","claim_id":"WOIT.GAMMA.SEMI.01","dependencies_as_recorded":"WOIT.GAMMA.TOY.01; WOIT.BETA2.OS.01; SEAM.STRADDLE.CONE.01; v524; v534; v615; v616","external_data_as_recorded":"-","id":"claim:WOIT.GAMMA.SEMI.01","location_as_recorded":"tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":637,"scripts_as_recorded":"v621_interacting_semigroup.py","status_as_recorded":"Float-track certificates (declared tolerances) + exact Clifford combinatorics + [C] toy fence","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"SEAM-IDENTIFIED: v519 kernel = discrete NS mode sum exactly (flat band = NS spectrum; Ramond must-fail); mark-bond midpoints = mu4 exactly; group dictionary exact; straddle law = axis-through-marks geometry; residue = covering-level identification; 10/10 checks","checked_by_registry":false,"claim_excerpt":"The seam identification round -- the physical seam IS the conformal seam (one module, 10 checks, ~1 s; discovery probe seam_identification_probe.py 10/10, verdict SEAM-IDENTIFIED; closes the second v617 bedrock residue at the kernel + dictionary level).  THE KERNEL IDENTITY [E, exact]: the v519 chiral seam kernel c(d) = (2/N)/sin(pi d/N) for odd d and 0 for even d is EXACTLY the antiperiodic (NS) chiral mode sum on t","claim_id":"QGEO.SEAMID.01","dependencies_as_recorded":"QGEO.SEAMFORCE.01; QGEO.NCENSUS.01; WOIT.THETA.FREE.01; SEAM.STRADDLE.CONE.01; v519; v534; v617; v620","external_data_as_recorded":"-","id":"claim:QGEO.SEAMID.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":638,"scripts_as_recorded":"v622_seam_identification.py","status_as_recorded":"Exact [E] mode-sum/dictionary identities (sympy) + must-fail control + [C] the covering residue typing","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"COVERED-SEAM-SKELETON: one 48-site covered seam (uniform weights; alternating pair disconnects -- independent kill); lifted clock exact order 12 with L^4 = deck (r^4 = omega as lattice combinatorics); N = 48 kernel identity; 12-grid mode split with untwisted = base verbatim, twisted pair = omega on bilinears; 12 marks in a single 12-cycle; 9/9 checks","checked_by_registry":false,"claim_excerpt":"The covered seam round -- the lattice skeleton of the covering-level identification (one module, 9 checks, ~4 s; discovery probe covered_seam_probe.py 9/9, verdict COVERED-SEAM-SKELETON; the named residue of v622, first executed slice).  CONNECTIVITY CENSUS [E]: lifting the 16-site seam to the mu3-cover, the covered seam is ONE 48-site circle for the uniform weights j = 1, 2 and DISCONNECTS into 3 circles for the tri","claim_id":"QGEO.COVERSEAM.01","dependencies_as_recorded":"QGEO.SEAMID.01; QGEO.SEAMFORCE.01; QGEO.NCENSUS.01; QGEO.PERNORM.01; v597; v613; v614; v617; v620; v622","external_data_as_recorded":"-","id":"claim:QGEO.COVERSEAM.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":639,"scripts_as_recorded":"v623_covered_seam.py","status_as_recorded":"Exact [E] combinatorics + mode-sum identities (sympy) + [C] the orbifold residue typing","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"LATTICE-AUDIT-PASSED: four-mark closure forces d = 4 three ways (conditional); bytecode exact (240 + 8 = 248); Lorentz congruence P^T J_det P = J_fix exact (index 6); B-test retyped ill-posed; Suzuki citations verified; 14/14 checks | 2026-08-28 v993: architecture conditionality lifted at census level (this row's v624 checks unchanged)","checked_by_registry":false,"claim_excerpt":"The external-review lattice audit (one module, 14 checks, <1 s; discovery probe external_lattice_audit_probe.py 14/14, verdict LATTICE-AUDIT-PASSED; external review 2026-08-02, three claimed derivations machine-checked, one follow-up retyped honestly).  THE FOUR-MARK CLOSURE [E, conditional]: generalizing the glue to D_{d+1} + A_{d-1}, THREE independent selectors each force d = 4 -- the disc-group census (Z_d = Z_4 w","claim_id":"EXTREV.LATTICE.01","dependencies_as_recorded":"AX.P2.01; QGEO.EQORDER.01; QGEO.DUALFORMS.01; PRIME.UNIFC.01; v47; v602; v604; v618","external_data_as_recorded":"-","id":"claim:EXTREV.LATTICE.01","location_as_recorded":"tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":640,"scripts_as_recorded":"v624_external_lattice_audit.py","status_as_recorded":"Exact [E] closure/bytecode/congruence identities + [X] the ill-posed retype + [C] conditional typing (sympy; citations web-verified)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"E8-IS-A-CODE: Construction A(Hamming [8,4,4]) = E8 exactly; single-bit errors correctable; the error-correction reading is a theorem; no physics claim, no marker moves.","checked_by_registry":false,"claim_excerpt":"The E8 code round (one module, 7 checks, ~2 s; discovery probe e8_code_probe.py 7/7, verdict E8-IS-A-CODE). Construction A on the self-dual extended Hamming code [8,4,4] yields the even unimodular rank-8 lattice = E8 (shells 240/2160 = the v625 theta); every single-bit error is exhaustively correctable (16 x 8, unique nearest codewords); the compiler ties (8 = rank, 4 = d = |mu4|, 16 = half-spinor, 14 = 2 x 7 parabol","claim_id":"E8.CODE.01","dependencies_as_recorded":"PRIME.SHADOW.01; EXTREV.LATTICE.01; v1; v625","external_data_as_recorded":"-","id":"claim:E8.CODE.01","location_as_recorded":"tfpt_3","path":"verification/status_ledger.csv","row_number":641,"scripts_as_recorded":"v626_e8_code.py","status_as_recorded":"Exact [E] code/lattice identities + [C] typed compiler ties (integer combinatorics; Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"ORBIFOLD-CASIMIR-EXACT: the kinematic half of the Z3 orbifold statement is exact; the interacting statement (twist-field OPE, crossing, RP) stays the named residue; GATE.QGEO does not move.","checked_by_registry":false,"claim_excerpt":"The orbifold Casimir round (one module, 5 checks, ~1 s; discovery probe orbifold_casimir_probe.py 5/5, verdict ORBIFOLD-CASIMIR-EXACT). The covered seam's three deck-mode classes {1/6, 1/2, 5/6} carry EXACTLY the Z3-twist Casimir data: exact closed form E0(nu, N) = -cos(pi(2nu-1)/(2N))/(2 sin(pi/(2N))); finite-size coefficient exactly pi(6nu^2 - 6nu + 1)/12; sector table (1/72, -1/24, 1/72); degenerate twisted pair; ","claim_id":"QGEO.ORBCAS.01","dependencies_as_recorded":"QGEO.COVERSEAM.01; QGEO.SEAMID.01; v622; v623","external_data_as_recorded":"-","id":"claim:QGEO.ORBCAS.01","location_as_recorded":"tfpt_3","path":"verification/status_ledger.csv","row_number":642,"scripts_as_recorded":"v628_orbifold_casimir.py","status_as_recorded":"Exact [E] closed forms and expansions (sympy exact; Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"INCIDENCE-CENSUS-DECIDED: the naive 48 x 5 construction fails at the first hurdle; 48 x 5 = 240 stays an audit fingerprint; 60 = D_start is a free clock-orbit count on the roots.","checked_by_registry":false,"claim_excerpt":"The root incidence census (one module, 6 checks, ~1 s; discovery probe root_incidence_probe.py 6/6, verdict INCIDENCE-CENSUS-DECIDED). The naive 48 x 5 incidence to the 240 E8 roots is KILLED for the compiler-canonical order-12 element (orbit census 19 x 12 + 3 x 4, not 20 free zeta_12 orbits); positive residue: the mu4 clock alone acts FREELY with EXACTLY 60 orbits (60 = D_start) and the family 3-cycle fixes exactly","claim_id":"E8.INCIDENCE.01","dependencies_as_recorded":"EXTREV.LATTICE.01; QGEO.COVERSEAM.01; v623; v624; v626","external_data_as_recorded":"-","id":"claim:E8.INCIDENCE.01","location_as_recorded":"tfpt_3","path":"verification/status_ledger.csv","row_number":643,"scripts_as_recorded":"v629_root_incidence.py","status_as_recorded":"Exact [E] census (Fraction combinatorics) + honest kill + [C] typed observations (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"COMMON-ACTION-DISCRETE / UNIFLOW-CONTINUOUS -- NOT KILLED: the kill criterion 'four incompatible arithmetic actions' is not met; one parabolic class on the discrete half (exact conjugations), uniflow degeneration on the native continuous half; residual = the external anchor clocks/jets, fenced by CONTRACT.F.01; no marker moves.","checked_by_registry":false,"claim_excerpt":"The F_transfer PGL2 round (one module, 25 checks, ~1 s; discovery probe ftransfer_pgl2_probe.py 25/25, verdict COMMON-ACTION-DISCRETE / UNIFLOW-CONTINUOUS -- NOT KILLED). The v533 preregistration executed in its LITERAL group form: the discrete transfer path alpha_t (disc -7 norm line, norms 2/4/14/32) carries the parabolic base translation T: alpha -> alpha + 2; the declared v183 Koide reading induces the parabolic ","claim_id":"FTR.PGL2.01","dependencies_as_recorded":"CONTRACT.F.01; FTR.DISC7.NORM.01; FTR.CRDISC.01; FTR.CRCONT.01; v533; v571; v575; v578","external_data_as_recorded":"-","id":"claim:FTR.PGL2.01","location_as_recorded":"tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":644,"scripts_as_recorded":"v632_ftransfer_pgl2.py","status_as_recorded":"Exact [E] PGL2/intertwining identities + [C] typed reading (sympy exact; Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"ZI-E8-QUOTIENT-CONFIRMED + CASCADE-KILLED: the 'complex E8' reading of the 60 free clock orbits is exact (hermitian-unimodular Z[i]-E8, ST31 hyperplane system); the quotient-cascade route 60 -> 6 carries no canonical structure -- a typed negative; no marker moves.","checked_by_registry":false,"claim_excerpt":"The mu4-quotient round (one module, 17 checks, ~3 s; discovery probe orbit60_quotient_probe.py 17/17, verdicts ZI-E8-QUOTIENT-CONFIRMED + CASCADE-KILLED). The quotient of the 240 E8 roots by the free mu4 clock IS the hermitian-unimodular Z[i]-E8 with the 60-hyperplane system of ST31: H(x,y) = <x,y> + i<x,Jy> has H(v,v) = 2 on all 60 line reps; the Z[i]-span of the reps is the FULL E8 lattice (HNF covolume 256 in doub","claim_id":"E8.ZIQUOTIENT.01","dependencies_as_recorded":"E8.INCIDENCE.01; EXTREV.LATTICE.01; v626; v629","external_data_as_recorded":"-","id":"claim:E8.ZIQUOTIENT.01","location_as_recorded":"tfpt_3","path":"verification/status_ledger.csv","row_number":645,"scripts_as_recorded":"v633_orbit60_quotient.py","status_as_recorded":"Exact [E] quotient/lattice identities + [E, KILL] typed cascade negative (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"ST31-STRUCTURE-DECIDED: G31 = full unitary stabilizer, degrees (8,12,20,24) Molien-unique, sigma = c^4 / J = c^9 exact, real structure (Z4 o 2^{1+4}).Sp4(2) computed; |G31| = |W(D5)|*|W(A3)| stays NUMEROLOGY (killed three ways); the compiler clock is NOT the regular 12-element; no marker moves.","checked_by_registry":false,"claim_excerpt":"The ST31 structure round (one module, 56 checks, ~10 s; discovery probe st31_structure_probe.py 56/56). G31 = <the 60 unitary reflections> has order 46080 (BFS + independent Schreier-Sims) and IS the FULL unitary stabilizer of the mu4-quotient structure (exact backtracking count over Gram-matching images of a Z[i]-unimodular basis); degrees (8,12,20,24) UNIQUE via Molien among all divisor quadruples with product 4608","claim_id":"E8.ST31.01","dependencies_as_recorded":"E8.ZIQUOTIENT.01; E8.INCIDENCE.01; v629; v633","external_data_as_recorded":"-","id":"claim:E8.ST31.01","location_as_recorded":"tfpt_3","path":"verification/status_ledger.csv","row_number":646,"scripts_as_recorded":"v634_st31_structure.py","status_as_recorded":"Exact [E] group/Molien/Springer census + [E, KILL] the numerology kill + honest clock typing (Python-only per GATE.WOLFRAM.02; Lean order identities).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"DICTIONARY-SHARP: the equivariant placement is RM(1,3) on AG(3,2) with an exact dictionary (information bits one per mu4 pair, syndrome flag with the sigma 3-cycle, decode = projection); only 2/30 placements carry it; residual: the anchor-pair orientation; no physics claim, no marker moves.","checked_by_registry":false,"claim_excerpt":"The code-semantics rounds, kill + stage 2 (one module, 27 checks, ~3 s; discovery probes code_semantics_kill_probe.py 13/13 CODE-SEMANTICS-RELABELLED and code_semantics_stage2_probe.py 27/27 DICTIONARY-SHARP). Stage 1 (kill): the naive v626 placement is DEAD for the family 3-cycle pisig; exactly 2/30 S8-placements of the extended Hamming code carry BOTH compiler symmetries mod 2 (piJ = mu4 in-pair swap, pisig = famil","claim_id":"E8.CODESEM.01","dependencies_as_recorded":"E8.CODE.01; E8.INCIDENCE.01; v626; v629","external_data_as_recorded":"-","id":"claim:E8.CODESEM.01","location_as_recorded":"tfpt_3","path":"verification/status_ledger.csv","row_number":647,"scripts_as_recorded":"v638_code_semantics.py","status_as_recorded":"Exact [E] code/dictionary identities + [E, kill] the 30-census control (exact arithmetic; Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"TWIST-OPE-COHERENT-RP-OPEN: the interacting slice stands at the abelian vertex level (weights 1/36, exponent 2/9, crossing, closed four-point, OPE data); RP validated in the real Z2 class, the complex Z3 pairing typed open (parafermionic Klein twist); GATE.QGEO does not move.","checked_by_registry":false,"claim_excerpt":"The twist-field/OPE round (one module, 25 checks, ~1 s; discovery probe orbifold_twist_ope_probe.py 25/25, verdict TWIST-OPE-COHERENT-RP-OPEN). The interacting/CFT-level slice of the Z3 orbifold residue (v623/v628): h_sigma = 1/36 from THREE independent exact routes (v628 Casimir coefficient = 2(h - c/24); zeta-function mode sum -zeta(-1,nu)/2; bosonization pair h(1/2-eta)+h(1/2+eta) = eta^2/2), with the convention t","claim_id":"QGEO.TWISTOPE.01","dependencies_as_recorded":"QGEO.ORBCAS.01; QGEO.COVERSEAM.01; QGEO.SEAMID.01; v519; v622; v623; v628","external_data_as_recorded":"-","id":"claim:QGEO.TWISTOPE.01","location_as_recorded":"tfpt_3","path":"verification/status_ledger.csv","row_number":648,"scripts_as_recorded":"v639_twist_ope.py","status_as_recorded":"Exact [E] weights/crossing + [E-float] two-/four-point and OPE + [O] typed open items + [X-slice] honest RP negative (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"KLEIN-RP-POSITIVE: the Z3 twist sector is reflection positive on the seam-double lattice under the parafermionic Klein-twist pairing (mirror x charge conjugation, omega^{k q} phases, eta = (1,1) unique among 36), N-stable 48..384, both axes, including the full mixed OS Gram; the naive pairing keeps its N-stable violation (must-fail); continuum OS/modularity typed open; GATE.QGEO does not move.","checked_by_registry":false,"claim_excerpt":"Parafermionic Klein-twist reflection positivity of the Z3 twist sector (one module, 17 checks, ~30 s; discovery probe parafermion_klein_rp_probe.py 17/17, verdict KLEIN-RP-POSITIVE).  The named open item of QGEO.TWISTOPE.01 (the naive antiunitary Z3 pairing fails positivity N-stably at -4.5e-3) is RESOLVED at the lattice OS level: the positivity-carrying pairing composes the mirror with CHARGE CONJUGATION -- Theta_K(","claim_id":"QGEO.KLEINRP.01","dependencies_as_recorded":"QGEO.TWISTOPE.01; QGEO.ORBCAS.01; QGEO.COVERSEAM.01; v519; v622; v623; v628; v639","external_data_as_recorded":"-","id":"claim:QGEO.KLEINRP.01","location_as_recorded":"tfpt_3","path":"verification/status_ledger.csv","row_number":649,"scripts_as_recorded":"v645_klein_rp.py","status_as_recorded":"Exact [E] reality/uniqueness/must-fail structure + [E-float] PSD Grams (N-stable) + [C] typed continuum remainder (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"RM13-REVERSE-TWO-PART: the anchor decomposition (0,1,1,2)/norm 6 is exact with the sigma action selecting the anchor sector (selection equivariance-specific, weights generic); the bytecode p-sequence has NO code reading (0/11 families, 18/27/81 no hit) -- honest negative, route closed; kill control selective; no marker moves.","checked_by_registry":false,"claim_excerpt":"The RM(1,3) reverse reading -- are compiler numbers CODE operations? (one module, 20 checks, ~1 s; discovery probe rm13_reverse_probe.py 20/20; exact integer arithmetic).  An honestly TWO-PART answer.  THE ANCHOR IDENTITY [E, central]: the sigma-fixed syndromes of the equivariant placement C* are EXACTLY {0, s(e6), s(e7), q} with coset-leader weights (0, 1, 1, 2) and norm-square sum 6 = (1,1,2).(1,1,2); the anchor is","claim_id":"E8.RM13REV.01","dependencies_as_recorded":"E8.CODESEM.01; E8.CODE.01; EXTREV.LATTICE.01; v624; v626; v638","external_data_as_recorded":"-","id":"claim:E8.RM13REV.01","location_as_recorded":"tfpt_3","path":"verification/status_ledger.csv","row_number":650,"scripts_as_recorded":"v646_rm13_reverse.py","status_as_recorded":"Exact [E] anchor identity + honest [E] generic/specific split + honest negative (no code reading of the p-sequence) + selective kill control (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"ST31-DEGREE-ANCHORED: the mu4 center is a power of both regular clocks (w^6 = +-J, chi_w = x^4 + i x^2 - 1 primitive-zeta24; u^5 = +-J central); c = w^2 killed by the parity theorem (19/3 odd -- proof-grade); u^4 free with census {5:48}, 48 = 240/5; 48 = seam sites stays a typed observation; no marker moves.","checked_by_registry":false,"claim_excerpt":"The ST31 degree-24/-20 round (one module, 25 checks, ~4 s; discovery probe st31_degree24_probe.py 25/25; exact Fraction/Z[i] arithmetic).  THE REGULAR 24-CLOCK [E, structural]: an explicit w with free census {24:10} and |C_G31(w)| = 24 (Springer); on the 60 lines it reads as the free 6-clock {6:10}; EXACT center relations w^12 = -1 and w^6 = J^3 -- the mu4 center is a POWER of the regular 24-clock (mu4 = <w^6>, <w>/m","claim_id":"E8.ST31DEG.01","dependencies_as_recorded":"E8.ST31.01; E8.ZIQUOTIENT.01; E8.INCIDENCE.01; v629; v633; v634","external_data_as_recorded":"-","id":"claim:E8.ST31DEG.01","location_as_recorded":"tfpt_3","path":"verification/status_ledger.csv","row_number":651,"scripts_as_recorded":"v647_st31_degree24.py","status_as_recorded":"Exact [E] structural clock relations + [E] parity-theorem kill + [C] typed observations (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"DISCIPLINE-CERTIFIED: frozen minimum bars -- 214 kill/negative rows, 1469 negative-control occurrences in 233 of 643 modules, 47 contract rows (29 with named kill criteria; FTR.PGL2 and the W1 chain verified as executed), replay 12/12 deterministic, 5 classical anchors recomputed, 54 committed Lean modules; the limit typed [C]: process discipline, not physics truth -- the open gates stay open.","checked_by_registry":false,"claim_excerpt":"The discipline audit (one module, 17 checks, ~200 s; discovery probe discipline_audit_probe.py 17/17, verdict DISCIPLINE-MEASURED).  The suite parses ITSELF and freezes its process-discipline metrics as minimum bars.  [E] D1 LEDGER CENSUS: 715 rows / 710 active (display classes E/C/O/X/AXIOM/OTHER = 169/222/282/37/2/3 at freeze), and 214 rows documenting kills / honest negatives / ill-posed retirements / retypes (key","claim_id":"META.DISCIPLINE.01","dependencies_as_recorded":"REG.FREEZE.01; FTR.PGL2.01; PRIME.WEIL.OPERATOR.01; AUDIT.NULLMC.01; v84; v100","external_data_as_recorded":"classical literature values (Jacobi 1834; Shephard-Todd 1954; Suzuki arXiv:2606.09096)","id":"claim:META.DISCIPLINE.01","location_as_recorded":"tfpt_3","path":"verification/status_ledger.csv","row_number":652,"scripts_as_recorded":"v649_discipline_audit.py","status_as_recorded":"Exact [E] machine census + deterministic replay + external anchor recomputes + [C] typed limit (read-only meta-module; Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"ORB-MODULAR-COHERENT: nine sectors match |theta/eta|^2 at < 1%, S measured with a clean N^{-4} rate (the N^{-2} artifact is itself S-covariant and cancels), T exact as the Z6 Dehn shift, h_sigma = 1/36 with the 1/6 gap, deck^3 = -1 exact as Z6 trace arithmetic; chiral phases/continuum OS typed open; GATE.QGEO does not move.","checked_by_registry":false,"claim_excerpt":"The modular data of the Z3 orbifold of the seam on the lattice (one module, 17 checks, ~25 s; discovery probe orbifold_modular_probe.py 17/17, verdict ORB-MODULAR-COHERENT).  SECTORS [E]: all nine twisted-sector partition functions Z[g,h] of the seam double (free complex fermion, N x L cylinder) are real positive with exact conjugation degeneracies and match the continuum |theta[g/3,h/3]/eta|^2 at < 1% on ln Z (N = 4","claim_id":"QGEO.ORBMOD.01","dependencies_as_recorded":"QGEO.TWISTOPE.01; QGEO.KLEINRP.01; QGEO.ORBCAS.01; v622; v623; v628; v639; v645","external_data_as_recorded":"-","id":"claim:QGEO.ORBMOD.01","location_as_recorded":"tfpt_3","path":"verification/status_ledger.csv","row_number":653,"scripts_as_recorded":"v650_orbifold_modular.py","status_as_recorded":"Exact [E] sectors/characters/spin structure + [E-float] measured S-covariance (N^{-4}) + [C] typed continuum remainder (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"ORB-ASSEMBLY-SEAM: H^2(Z3,U(1)) = 0 enumerated (no discrete torsion), six candidates -> exactly {B, C3} survive {integer spectrum, vacuum, S, T} (T kills the naive Z3 exactly at 3.5e-3), the seam data pick B (measured c = 0 grounds + Klein eta = (1,1)); chiral phase measured; GATE.QGEO does not move.","checked_by_registry":false,"claim_excerpt":"The full Z3-orbifold assembly of the seam (one module, 17 checks, ~35 s; discovery probe orbifold_assembly_probe.py 17/17, verdict ORB-ASSEMBLY-SEAM).  COHOMOLOGY [E]: H^2(Z3, U(1)) = 0 by machine enumeration (27 mu3-valued 2-cocycles = 9 coboundaries x 3 classes, every cocycle symmetric) -- NO discrete torsion for a pure Z3 orbifold; residual phase tables are exact charge-class relabelings.  GRID [E]: all 35 nonvani","claim_id":"QGEO.ORBASM.01","dependencies_as_recorded":"QGEO.ORBMOD.01; QGEO.KLEINRP.01; QGEO.TWISTOPE.01; v622; v623; v628; v639; v645","external_data_as_recorded":"-","id":"claim:QGEO.ORBASM.01","location_as_recorded":"tfpt_3","path":"verification/status_ledger.csv","row_number":654,"scripts_as_recorded":"v651_orbifold_assembly.py","status_as_recorded":"Machine [E] cohomology/census + [E-float] S rates and exact T + data-backed [C] B-vs-C3 pick (hardened by v652) (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"ARF-B-STRUCTURAL: B vs C3 decided structurally -- the 6^6 classification leaves {B, C3}, the one-Fock-space pin forces B, and the mu6 ladder measures the C3-excised states directly (factors 85.0/9.0); the v639 2/9 read is B-vs-C3-blind; new tau datum 1/18; GATE.QGEO does not move.","checked_by_registry":false,"claim_excerpt":"Arf/GSO hardening of the B-vs-C3 discriminator (one module, 15 checks, ~30 s; discovery probe orbifold_arf_probe.py 15/15, verdict ARF-B-STRUCTURAL).  THE LADDER [E]: the mu6 defect ladder on the seam double measures the C3-excised states DIRECTLY -- exponents 2 Delta = (1/18, 2/9, 1/2) at rel devs < 8e-4 (N = 96..1536 and within-ring), the half-twist (tau) Klein Gram exactly real symmetric and PSD, exact charge-reso","claim_id":"QGEO.ORBARF.01","dependencies_as_recorded":"QGEO.ORBASM.01; QGEO.ORBMOD.01; QGEO.KLEINRP.01; QGEO.TWISTOPE.01; v622; v623; v628; v639","external_data_as_recorded":"-","id":"claim:QGEO.ORBARF.01","location_as_recorded":"tfpt_3","path":"verification/status_ledger.csv","row_number":655,"scripts_as_recorded":"v652_orbifold_arf.py","status_as_recorded":"Exact [E] classification/pin/excision data + [C] typed premise remainder (resolved by v653) (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"BOND-DEFECT-CANONICAL: twist = deck = bond defect as a lattice theorem in Q(zeta_6) (exact unitary equivalence, D_can = L^4, D_can^3 = -1 operator identities), position = gauge + mark pin, alternatives census complete incl. the honest isospectral chain (string data discriminate); continuum CFT + seam identification stay [C]; GATE.QGEO does not move.","checked_by_registry":false,"claim_excerpt":"The bond-defect premise upgraded to a lattice THEOREM (one module, 18 checks, ~40 s; discovery probe bond_defect_premise_probe.py 18/18, verdict BOND-DEFECT-CANONICAL).  THE THEOREM [E]: the deck-character blocks of the covered seam ARE the one-bond-defect chains, unitarily and exactly (A_r = sqrt(3) R P_r on all modes, exact in Q(zeta_6), at 16/48 AND 48/144; defect phase = deck character): twist sector = deck bound","claim_id":"QGEO.BONDDEF.01","dependencies_as_recorded":"QGEO.ORBARF.01; QGEO.ORBASM.01; QGEO.TWISTOPE.01; v622; v623; v628; v639","external_data_as_recorded":"-","id":"claim:QGEO.BONDDEF.01","location_as_recorded":"tfpt_3","path":"verification/status_ledger.csv","row_number":656,"scripts_as_recorded":"v653_bond_defect.py","status_as_recorded":"Lattice theorem [E] (exact unitary equivalence + gauge pin + exclusion census, honest isospectral documentation) + [C] typed continuum remainder (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"D4-THEOREM: every Springer-regular d-clock has x^{d/4} = +-i Id (generator of mu4; exponents 3 mod 4); converse exact at d in {8, 20, 24}, unique exception at d = 12 = the compiler-clock class (chi_c = (x-i)^2(x^2+ix-1), c^3 = J^3); order-8 landscape complete; 'free => regular' killed; no marker moves.","checked_by_registry":false,"claim_excerpt":"The ST31 degree-8 round + the unified d/4-theorem (one module, 30 checks, ~10 s; discovery probe st31_degree8_probe.py 30/30; exact Fraction/Z[i] arithmetic).  ORDER-8 LANDSCAPE [E]: 10560 order-8 elements, 4800 with free census {8:30}, only 480 with x^2 central; the regular witness has |C| = 192 (Springer), chi_v = (x^2 + i)^2 EXACT (all eigenvalues primitive zeta8, doubled), v^2 a GENERATOR of mu4; HONEST KILL: 'fr","claim_id":"E8.ST31D8.01","dependencies_as_recorded":"E8.ST31.01; E8.ST31DEG.01; E8.ZIQUOTIENT.01; v629; v633; v634; v647","external_data_as_recorded":"-","id":"claim:E8.ST31D8.01","location_as_recorded":"tfpt_3","path":"verification/status_ledger.csv","row_number":657,"scripts_as_recorded":"v654_st31_degree8.py","status_as_recorded":"Exact [E] census/theorem/controls + honest kill ('free => regular' false) (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"LOOKELSEWHERE-QUANTIFIED: 42 slots / 19 hits / 6 kills, global p = 5.08e-3 conservative (ensemble significant), pseudo-theory control 0.2%/0.3%, NO single observation significant; re-types executed (6 = p_2(a) p = 0.169; CODESEM battery p = 0.593; 14/16 FORCED); the substance is the [E] theorems.","checked_by_registry":false,"claim_excerpt":"The look-elsewhere audit -- the bingo budget of the typed [C] numeric coincidences, quantified (one module, 14 checks, ~2 s; discovery probe look_elsewhere_probe.py 14/14, verdict LOOKELSEWHERE-QUANTIFIED; seed 20260802, 100k MC, exact Poisson-binomial tails).  THE BUDGET [E]: N = 42 structure slots, K = 19 hits against the compiler target list FROZEN before the computation; the 6 killed readings enter as 0-hit trial","claim_id":"META.LOOKELSEWHERE.01","dependencies_as_recorded":"META.DISCIPLINE.01; EXTREV.LATTICE.01; E8.CODE.01; E8.CODESEM.01; E8.INCIDENCE.01; E8.ST31.01; v100; v624; v626; v629; v633; v634; v638; v646; v647","external_data_as_recorded":"-","id":"claim:META.LOOKELSEWHERE.01","location_as_recorded":"tfpt_3","path":"verification/status_ledger.csv","row_number":658,"scripts_as_recorded":"v664_look_elsewhere.py","status_as_recorded":"Exact [E] budget census + MC quantification + executed re-types (read-only meta-module; Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"ORB-OS-CONTINUUM-SLICE: correlator convergence with understood FH rates (2/3 sigma, 4/3 tau channel law; limits < 0.05% at CFT after one FH term), RP survives the limit (lambda_min extrapolations bounded away from zero, margins 7x..358x, must-fail flips), the cluster property exact in space and Euclidean time (2 Delta = 0.222220 vs 2/9 at 8e-6; time gap = the epsilon level), characters at 1e-12 with the measured N^-2 rate; E0/E2/E3/E4 measured at the convergence level, E1 discrete; the formal limit (GNS, uniform bounds, operator convergence) is the named remainder; GATE.QGEO does not move.","checked_by_registry":false,"claim_excerpt":"The first continuum-OS slice of the seam orbifold B -- the Osterwalder-Schrader reconstruction data measured at the CONVERGENCE level (one module, 19 checks, ~3 s; discovery probe orbifold_continuum_os_probe.py 19/19, verdict ORB-OS-CONTINUUM-SLICE).  MACHINERY [machine]: Toeplitz == mode-sum covariance (1.2e-15); zero-mode-dressed Klein reality for the full mu6 angle family (5.4e-15); the NEW Euclidean-time machiner","claim_id":"QGEO.ORBOS.01","dependencies_as_recorded":"QGEO.ORBMOD.01; QGEO.ORBASM.01; QGEO.ORBARF.01; QGEO.BONDDEF.01; QGEO.KLEINRP.01; QGEO.TWISTOPE.01; GATE.QGEO.01; v622; v623; v639; v645; v650","external_data_as_recorded":"-","id":"claim:QGEO.ORBOS.01","location_as_recorded":"tfpt_3","path":"verification/status_ledger.csv","row_number":659,"scripts_as_recorded":"v679_orbifold_continuum_os.py","status_as_recorded":"Machine-exact wiring + Exact [E] convergence/cluster/character slices + [MEASURED] RP-limit extrapolations with must-fail control + [C] honest typing of the formal-limit remainder (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"GAUSSIAN-CODE-BRIDGE-EXACT: E8(Z[i])/(1+i) = F2^4 (SNF exact, presentation-independent), 240 = 15 x 16 census (zero class provably empty), 60 = 15 x 4, sigma = RM(1,3) family permutation (18 equivariant gauges), coordinate block = F1+F2+F3; all must-fail controls fire (naive placement, non-piJ placement, Z[i]^4).","checked_by_registry":false,"claim_excerpt":"The Gaussian code bridge (review contract E8.GAUSSIAN.CODE.01) -- E8(Z[i])/(1+i) IS the information space of RM(1,3): the mu4 complex structure J makes E8 a rank-4 Z[i]-lattice L; reduction modulo the ramified Gaussian prime (1+i) gives L/(1+i)L = F2^4 EXACTLY (one module, 26 checks, ~3 s, exact integer/Fraction arithmetic, sympy only for the Smith normal form; discovery probe gaussian_code_bridge_probe.py 26/26, ver","claim_id":"E8.GAUSSCODE.01","dependencies_as_recorded":"E8.CODE.01; E8.CODESEM.01; E8.ST31.01; E8.ZIQUOTIENT.01; v626; v634; v638","external_data_as_recorded":"-","id":"claim:E8.GAUSSCODE.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":660,"scripts_as_recorded":"v689_gaussian_code_bridge.py","status_as_recorded":"Exact [E] SNF/census/semantics identities + [E, kill] three must-fail controls (exact arithmetic; Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"QUARTIC-HALF-ALIVE: the vanishing half {2,14,18,30} proven symbolically but TRIVIAL (mu4 orbit factor, honest typing); the substance: F8/F12/F20/F24 algebraically independent G31 basic invariants (holomorphic restriction generates the FULL G31 ring, Chevalley cited); Jacobian carries the 60 mirrors (60/60 point-verified); controls fire exactly as demanded.","checked_by_registry":false,"claim_excerpt":"The quartic invariant restriction (review contract E8.QUARTIC.HALF.01) -- is G31 the holomorphic mu4 shadow of the E8 Coxeter compiler?  ALIVE, with the honest split (one module, 22 checks, ~1 s, exact Gaussian-integer/Fraction arithmetic, no floats; discovery probe quartic_half_probe.py 22/22, verdict QUARTIC-HALF-ALIVE).  THE VANISHING HALF [PROOF, typed honest]: {2,14,18,30} is TRUE but TRIVIAL -- W(J alpha) = -i ","claim_id":"E8.QUARTICHALF.01","dependencies_as_recorded":"E8.ST31.01; E8.ST31DEG.01; v634; v647; v654","external_data_as_recorded":"Chevalley Amer. J. Math. 77 (1955) (basic invariants, cited); Molien series (v634)","id":"claim:E8.QUARTICHALF.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":661,"scripts_as_recorded":"v690_quartic_half.py","status_as_recorded":"Symbolic [PROOF] mu4-orbit vanishing + [E] G31 invariance/independence/mirror census + [E, kill] complex-structure controls + [cited] Chevalley basic-invariant theorem (exact arithmetic; Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"EXECUTED (first slice): v689 closes the census + semantics exactly (26/26); remaining: theorem writeup.","checked_by_registry":false,"claim_excerpt":"Review contract (external review, theorem candidate, registered 2026-08-03): E8(Z[i])/(1+i) is the information space of RM(1,3) -- the mu4 complex structure J makes E8 a rank-4 Z[i]-lattice; the (1+i)-quotient is F2^4; the 240 roots fall 15 x 16; sigma acts as the RM(1,3) family permutation.  FIRST SLICE EXECUTED by v689 (26/26, GAUSSIAN-CODE-BRIDGE-EXACT): the full 6-step census verbatim, exact arithmetic, all must-","claim_id":"E8.GAUSSIAN.CODE.01","dependencies_as_recorded":"E8.GAUSSCODE.01; E8.CODESEM.01; E8.CODE.01","external_data_as_recorded":"-","id":"claim:E8.GAUSSIAN.CODE.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":662,"scripts_as_recorded":"-","status_as_recorded":"Review contract; first slice machine-closed [E] (v689); remaining: theorem writeup.","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"EXECUTED (first slice): v690 proves the vanishing half (trivial, honestly typed) and establishes the basic-invariant substance; remaining: symbolic Jacobian factorization + writeup.","checked_by_registry":false,"claim_excerpt":"Review contract (external review, theorem candidate, registered 2026-08-03): restricting the W(E8) invariant root power sums to the holomorphic mu4 eigenspace V^{1,0} kills exactly the half {2,14,18,30} and keeps {8,12,20,24} = Deg(G31) -- 'G31 is the holomorphic mu4 shadow of the E8 compiler'.  FIRST SLICE EXECUTED by v690 (22/22, QUARTIC-HALF-ALIVE) WITH the honest correction: the vanishing half is TRUE but TRIVIAL","claim_id":"E8.QUARTIC.HALF.01","dependencies_as_recorded":"E8.QUARTICHALF.01; E8.ST31.01","external_data_as_recorded":"Chevalley Amer. J. Math. 77 (1955)","id":"claim:E8.QUARTIC.HALF.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":663,"scripts_as_recorded":"-","status_as_recorded":"Review contract; first slice machine-closed [E]/[PROOF] with honest typing correction (v690); remaining: Jacobian factorization symbolics + writeup.","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"ORBIT60-PARKED: all canonical cascade routes dead; no involution of cycle type 2^27 1^6 in the line group (order 11520; 375 involutions, 21 classes); W(E8) Coxeter does not descend; no A5 signature (order-5 elements exist but nothing natural); the must-fail numerology control fires -- parked per the review protocol.","checked_by_registry":false,"claim_excerpt":"The ORBIT60 census -- the 60 mu4-lines of E8 as a combinatorial object: quotient graph, sigma/clock/Coxeter dynamics on the ORBIT SPACE, and a STRICT park test for the cascade 60 -> 6 (one module, 18 checks, ~1 s; discovery probe orbit60_census_probe.py 18/18, verdict ORBIT60-PARKED).  THE FIVE ROUTES, all adjudicated: (i) degree rules DEAD (all quotient graphs regular -- no distinguished pair sequence from incidence","claim_id":"E8.ORBIT60.01","dependencies_as_recorded":"E8.ST31.01; v629; v633; v634","external_data_as_recorded":"-","id":"claim:E8.ORBIT60.01","location_as_recorded":"tfpt_3","path":"verification/status_ledger.csv","row_number":664,"scripts_as_recorded":"v700_orbit60_census.py","status_as_recorded":"Honest [E, park] five-route adjudication with the involution-witness census and the must-fail numerology control (exact group computations; Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"The three digamma channels ARE the three deck sectors of the 48-site NS lift (exact tower traces, dev 3.4e-16, scalar forced 1, must-fail x82) -- the geometry anchor of the chain arc; GATE.QGEO untouched; no RH statement.","checked_by_registry":false,"claim_excerpt":"TFPT scope of original v705: only D1 NS-circle clock/deck finite algebra, 48 modes with three 16-mode sectors. The prime/digamma application is maintained in Prime Front.","claim_id":"QGEO.DECKSECTOR.01","dependencies_as_recorded":"PRIME.KEYSTONE.01; QGEO.ORBIFOLD.01; v623; v628","external_data_as_recorded":"-","id":"claim:QGEO.DECKSECTOR.01","location_as_recorded":"tfpt_3","path":"verification/status_ledger.csv","row_number":665,"scripts_as_recorded":"v705_chain_deck_sector.py","status_as_recorded":"Exact [E] deck-sector trace identity (3.4e-16, scalar forced 1, must-fail x82); deterministic (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"QGEO-CAR-RATES-SUMMABLE: all 6+1 channels Schatten-norm Cauchy (N up to 3072/6144), FH renormalization fit-free lattice-derived (Barnes G 8.8e-7), RP cone stable, kill criteria clear; majorant lemma (L1)-(L3) named with constants + classical proof route; GATE.QGEO does NOT move.","checked_by_registry":false,"claim_excerpt":"QGEO-CAR -- the quasi-free CAR route to the formal orbifold continuum limit (GATE.QGEO), first slice (one module, 22 checks, ~10 s; discovery probe qgeo_car_continuum_probe.py 22/22, verdict QGEO-CAR-RATES-SUMMABLE).  THE STRATEGY EXECUTED: not measure compactness -- the orbifold correlators are DETERMINANTS of a one-particle covariance, so the limit runs through SCHATTEN-NORM control plus Araki's quasi-free CAR theo","claim_id":"QGEO.CARLIMIT.01","dependencies_as_recorded":"GATE.QGEO.01; QGEO.CONEDYN.01","external_data_as_recorded":"-","id":"claim:QGEO.CARLIMIT.01","location_as_recorded":"tfpt_3","path":"verification/status_ledger.csv","row_number":666,"scripts_as_recorded":"v715_qgeo_car_continuum.py","status_as_recorded":"[MEASURED] Schatten-norm Cauchy rates (6+1 channels, geometrically summable) + [E] lattice-derived FH renormalization (Barnes G, 8.8e-7) + named (L1)-(L3) majorant lemma; deterministic (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"RAMIFIED-SEES-NSR: the NS/R grading IS the parity character of E8(Z[i])/(1+i) = F2^4 (exact, controls fire); the Ramond projection is (1+i)-adic -- first exact witness for the groupoid reading of G_net; the Q-system identification stays the OPEN contract half (kills registered); no status move.","checked_by_registry":false,"claim_excerpt":"PHYS moonshot slice (T2 / G_net) -- is the Ramond projection (1+i)-adic? (one module, 9 checks, ~1 s; discovery probe phys_ramified_ns_r_probe.py 9/9, verdict RAMIFIED-SEES-NSR).  THE THEOREM CHECK: on the explicit even-coordinate E8 with the integral complex structure J (pair rotation, J^2 = -I, orthogonal, lattice-stable -- a concrete witness of the v634/v689 Gaussian E8), (1+i)L is CONTAINED in the even/NS sublatt","claim_id":"GNET.RAMIFIED.01","dependencies_as_recorded":"GATE.METRIC.10; GATE.METRIC.08; E8.GAUSSCODE.01; PRIME.MOONSHOT.01","external_data_as_recorded":"-","id":"claim:GNET.RAMIFIED.01","location_as_recorded":"tfpt_3;tfpt_1;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":667,"scripts_as_recorded":"v722_phys_ramified_ns_r.py","status_as_recorded":"Exact [E] integer-arithmetic slice ((1+i)L in the even sublattice on a Z-basis; 15x16 purity census; parity homomorphism) with both controls firing; contract half typed OPEN (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"STT-KILLED + INTERNAL-PAIR-CONFIRMED: strong thermal time is dead on the declared clock exports (QCD clock parabolic, not reachable by any modular flow); the pole/Boltzmann pair is internal ((2/3)^6 exact, v425); the external clock contract STANDS, sharpened to the typed census {one unit, theta_i, C_p}; no status move.","checked_by_registry":false,"claim_excerpt":"PHYS moonshot slice (T3 / F_transfer) -- can thermal time replace the external clock contract?  The conjugacy-class KILL test (one module, 11 checks, ~1 s; discovery probe phys_modular_clock_probe.py 11/11, verdict STT-KILLED + INTERNAL-PAIR-CONFIRMED).  STRONG THERMAL TIME (Connes-style: ONE modular flow sigma_t and four CONSTANT clock conversions t_k = c_k t) requires all four native time-1 maps in modular-exponent","claim_id":"FTRANSFER.STT.01","dependencies_as_recorded":"FR.POLE.SOLVE.01; FIRSTPRINCIPLES.BOUNDARY.01; ANCHOR.VGEO.02; v425; v153; v632","external_data_as_recorded":"-","id":"claim:FTRANSFER.STT.01","location_as_recorded":"tfpt_3;tfpt_2;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":668,"scripts_as_recorded":"v723_phys_modular_clock.py","status_as_recorded":"Exact [E] symbolic kill (parabolic + no-diagonalizable-log lemma) + [E] internal-pair confirmation ((2/3)^6 exact); the external clock contract confirmed and sharpened (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"T3B-DEAD: the four solver classes do NOT arise from conditioned modular flows of one internal mother state (all four loxodromic/complex; cocycle composition exact; one KMS scale); with FTRANSFER.STT.01 both thermal-time routes are closed -- the external clock contract stands; no status move.","checked_by_registry":false,"claim_excerpt":"T3-B -- conditioned modular flows from ONE internal mother state, the second thermal-time KILL (one module, 12 mechanical checks, ~1 s; discovery probe phys_t3b_conditioned_modular_flows.py 12/12, verdict T3B-DEAD).  THE CONSTRUCTION (frozen before any target test): the sheet geodesic M(1,t), t = -2..1, delivers the four intertwiners J, K, C, F and the target-independent tangent S = dM/dt; S builds the chiral mother ","claim_id":"FTRANSFER.COCYCLE.01","dependencies_as_recorded":"FTRANSFER.STT.01; FIRSTPRINCIPLES.BOUNDARY.01; v258; v578; v632","external_data_as_recorded":"-","id":"claim:FTRANSFER.COCYCLE.01","location_as_recorded":"tfpt_3;tfpt_2;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":669,"scripts_as_recorded":"v724_phys_t3b_modular_flows.py","status_as_recorded":"[E] exact cocycle composition + [X] honest class-gate kill (0/4 matches, Lindblad escape refused); the second thermal-time route closed (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"TORSOR CLOSURE PASS: the v_geo interface is structurally closed as an R+ scale torsor (export table complete, dimension matrix rank 1, all conditions lambda-homogeneous, two-anchor consistency 0.11%); calibration theorem stated; FENCE: no scale derivation (No-Unit); moonshot named: H_EW = 37.1776.","checked_by_registry":false,"claim_excerpt":"T1 CLOSURE -- the calibration/scale-torsor audit of the v_geo interface (one module, 21 checks, ~1 s; discovery probe phys_vgeo_torsor_audit_probe.py 21/21, verdict TORSOR-SCHLIESSUNG PASS).  THE STRUCTURE THEOREM (machine-audited on the corpus, sources read-only: v153/v152/v274/v401/v364/v75/v68/v60/v20/v272/v3/rt_E/v714): the v_geo interface is a well-defined R+ SCALE TORSOR -- (1) the corpus exports ALL dimensiona","claim_id":"VGEO.TORSOR.01","dependencies_as_recorded":"ANCHOR.VGEO.01; ANCHOR.VGEO.02; VGEO.SHARPEN.01; SCALE.OVERDET.01; METROLOGY.CLOSURE.01; FIRSTPRINCIPLES.BOUNDARY.01","external_data_as_recorded":"CODATA Mbar; Planck-2018 rho_Lambda^{1/4} = 2.24 meV; PDG lepton masses (corpus-documented references, read-only)","id":"claim:VGEO.TORSOR.01","location_as_recorded":"tfpt_3;tfpt_2;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":670,"scripts_as_recorded":"v725_phys_vgeo_torsor_audit.py","status_as_recorded":"Structural [E] torsor audit (export table, rank 1, lambda-homogeneity, leave-one-anchor-out 0.11%) with conditionalities named; closure in calibration form, NO scale derivation (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"T2-SLICE-GO (PP-INDEX-4-ON-LADDER): optimal Pimsner-Popa constant exactly 1/4 and Watatani index exactly 4 on the CAR ladder with mu4 DERIVED from the clock; Ramond healed state-preservingly by the Klein dressing; (1+i) dictionary closes with v722; Q-system identification = the open contract half; no status move.","checked_by_registry":false,"claim_excerpt":"PHYS T2 main slice -- Pimsner-Popa / Watatani index 4 on the CAR ladder, with the mu4 action DERIVED from the clock and the Ramond zero-mode test (one module, 57 checks, ~7 s; discovery probe phys_car_pp_index_probe.py 57/57, verdict T2-SLICE-GO (PP-INDEX-4-ON-LADDER)).  THE DERIVATION (circularity rule): mu4 is NOT inserted -- the clock L = S^{N/12} of the v679/v716 frame gives the half-turn H = L^6 whose order 4 is","claim_id":"GNET.PPINDEX.01","dependencies_as_recorded":"GATE.METRIC.08; GATE.METRIC.10; GNET.RAMIFIED.01; v679","external_data_as_recorded":"-","id":"claim:GNET.PPINDEX.01","location_as_recorded":"tfpt_3;tfpt_1;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":671,"scripts_as_recorded":"v726_phys_car_pp_index.py","status_as_recorded":"Exact [E] index results (PP = 1/4 optimal, Watatani = 4 with forced quasi-basis weights; mu4 derived, not inserted) + [E] state-preserving Ramond healing + [M] outerness witnesses (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"ORBIT-PACKET-EXACT: Burnside 7, the canonical 5 x 48 packet split (1 fixed + 4 moved = g_car), the (1,1,2) anchor from the leader weights, the q = 16 normal form; P1/P2 come back as exact internal reconstruction (circularity fence: reconstruction, not derivation); sigma-class-specific (free order-3 census gives Burnside 5); Lean companion OrbitPacket.lean.","checked_by_registry":false,"claim_excerpt":"The Gaussian ORBIT PACKET lemma (one module, 26 checks, ~1 s; discovery probe orbit_packet_probe.py 26/26, verdict ORBIT-PACKET-EXACT).  BURNSIDE EXACT: the sigma orbit census on the 15 nonzero Gaussian classes gives N_orbit = (15 + 3 + 3)/3 = 7 (3 fixed classes + 4 moved orbits).  THE CANONICAL PACKET SPLIT: 240 = 5 x 48 -- one fixed block + 4 moved blocks of 12 Gaussian lines (48 roots) each, pairwise disjoint, lab","claim_id":"E8.ORBITPACKET.01","dependencies_as_recorded":"E8.GAUSSCODE.01; E8.GAUSSIAN.CODE.01; v638; v623","external_data_as_recorded":"-","id":"claim:E8.ORBITPACKET.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":672,"scripts_as_recorded":"v736_orbit_packet.py","status_as_recorded":"Exact [E] integer/finite-group census; P1/P2 typed as reconstruction behind the circularity fence, NOT derivation (Python-only per GATE.WOLFRAM.02; companion Lean module kernel-checked).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"SEAM48-DEAD: the 48 x 5 incidence matrix is not identically 1 (0:96/1:64/2:64/3:16), representative-independent, must-fail control fires; residues: the 4 moved blocks carry the v623 character table exactly, the fixed block deviates by the 12 lifted marks, u^5 = +/-J exact; 240 = 48 x 5 stays a factorization without coordinatization.","checked_by_registry":false,"claim_excerpt":"The seam-48 intertwiner test -- the sharpest structural kill of the review morning (one module, 24 machinery checks, ~4 s; discovery probe seam48_intertwiner_probe.py 24/24 machinery, verdict SEAM48-DEAD).  THE QUESTION (external review, preregistered kill): do the five canonical 48-blocks (from the proven sigma orbit structure of the 15 x 16 Gaussian classes) and the 48 regular five-cycles of the CERTIFIED regular o","claim_id":"E8.SEAM48.01","dependencies_as_recorded":"E8.GAUSSCODE.01; E8.ORBITPACKET.01; v623; v736","external_data_as_recorded":"-","id":"claim:E8.SEAM48.01","location_as_recorded":"tfpt_1;tfpt_3","path":"verification/status_ledger.csv","row_number":673,"scripts_as_recorded":"v737_seam48_intertwiner.py","status_as_recorded":"Exact [E] machinery; the preregistered kill fires -- honest structural negative (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"L1-SECTOR-PROVEN-MODULO-ELEMENTARY: (L1) proven modulo elementary steps for all 6 sectors -- exact summation instead of EM, leading term at 6e-4, gamma = 2 derived, 39744+108 inequalities 0 violations, r1 = 1 sharp; residues (a) elementary / (b) hard-technical / (c) medium named, not claimed; GATE.QGEO does not move; 2026-08-05 (v778): residue (a) fully closed in the corrected (1 + ln M) form (the literal v715 all-refinements clause repaired; log coefficient certified, measured slope J/pi^2); (b)/(c) stay open.","checked_by_registry":false,"claim_excerpt":"The (L1) sector lemma of the CAR continuum majorant, proven modulo elementary steps with explicit constants (one module, 11 checks, ~1 s; discovery probe qgeo_car_l1_sector_lemma_probe.py 11/11, verdict L1-SECTOR-PROVEN-MODULO-ELEMENTARY).  THE LEMMA: || K_2N^(q) - K_N^(q) ||_{S1(Lambda_eps)} <= B_q(eps)/N for all 6 undressed sectors on the fixed grid -- the occupied-arc mode sums are EXACT geometric sums (no Riemann","claim_id":"QGEO.CARL1.01","dependencies_as_recorded":"QGEO.CARLIMIT.01; GATE.QGEO.01; v715","external_data_as_recorded":"-","id":"claim:QGEO.CARL1.01","location_as_recorded":"tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":674,"scripts_as_recorded":"v745_qgeo_car_l1_sector_lemma.py","status_as_recorded":"Proof-near [E] sector lemma (exact geometric sums, derived gamma = 2, 39744+108 inequalities at 0 violations) with the named residues typed (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"GNET-LOCAL-FUNCTOR-ALIVE: net axioms exact (isotony/graded locality/clock covariance), Watatani index LOCALLY exactly 4 for every interval ell >= 2, Ramond = half-line/bond defect (solitonic; leakage sqrt(2/N)); 4 must-fails fire; the five continuum theorems named, not claimed.","checked_by_registry":false,"claim_excerpt":"The G_net local net functor -- net axioms exact, Watatani index locally exactly 4, Ramond as half-line/bond defect (one module, 16 checks, ~2 s; discovery probe phys_gnet_local_functor_probe.py 16/16, verdict GNET-LOCAL-FUNCTOR-ALIVE).  THE NET AXIOMS ARE EXACT: isotony, graded locality and clock covariance hold exactly for the interval assignment on the quotient circle.  THE INDEX IS LOCAL: the Watatani index of the","claim_id":"GNET.LOCALNET.01","dependencies_as_recorded":"QGEO.BONDDEF.01; GATE.METRIC.11; QGEO.DECKSECTOR.01; v722","external_data_as_recorded":"-","id":"claim:GNET.LOCALNET.01","location_as_recorded":"tfpt_3;tfpt_2","path":"verification/status_ledger.csv","row_number":675,"scripts_as_recorded":"v746_phys_gnet_local_functor.py","status_as_recorded":"Exact [E] finite net axioms + exact local index 4 + [C] the named continuum theorems (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"EXECUTED 2026-08-05 (v777): the K1 kill fired sympy-exactly as the frozen prior expected -- NO-COMMON-CONNECTION ({-Delta^2/2, -Delta^2/2, 0}); all four dictionary legs construction-valid (571x / 1.15e-4 / 0.83% / 0.0602); K1 duty discharged (the needed reparametrization is the forbidden non-affine Moebius clock); the fibered-groupoid refinement carries (constant seam cocycle {0, +-Delta^2/2}); nothing upgrades CONTRACT.F.01; no marker move.","checked_by_registry":false,"claim_excerpt":"Preregistered theory-contract search target (frozen 2026-08-04, experiments/ftransfer-clocks/hypotheses/ftransfer_clocks_v1.yaml; EXECUTED 2026-08-05, v777): the external-clock contract for the F_transfer jets.  THE FOUR FROZEN CLOCKS (exactly one physical clock per solver, fixed in advance): F_pole = proper time tau (on-shell/pole-mass chart; one v99 seam unit = one proper-phase e-fold), F_Boltzmann = inverse temper","claim_id":"FTRANSFER.CLOCKS.01","dependencies_as_recorded":"CONTRACT.F.01; FTR.JETS.01; FTR.PGL2.01; FTRANSFER.STT.01; FTRANSFER.COCYCLE.01; v578; v632; v723; v724","external_data_as_recorded":"PDG 2024 (pole masses, alpha_s), FIRAS T0, Planck 2018 background, Saikawa-Shirai 2018 g_*s tabulation (curated + SHA-frozen data tables in experiments/ftransfer-clocks/data/, byte-verified at every run; executed 2026-08-05)","id":"claim:FTRANSFER.CLOCKS.01","location_as_recorded":"tfpt_research_contracts;tfpt_3;tfpt_4","path":"verification/status_ledger.csv","row_number":676,"scripts_as_recorded":"v777_ftransfer_clock_jets.py","status_as_recorded":"Executed preregistered search target (frozen 2026-08-04 [X]; executed + promoted 2026-08-05, v777): the K1 kill fired exactly as the frozen prior expected (NO-COMMON-CONNECTION); the fibered-groupoid refinement carries; the four observables stay [C]/[O]; no marker move (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"PROJ-HAMMING-EXACT: (V, hbar) is the symplectic F2^4 of the unimodular hermitian E8 lattice; B B^T = 4I + 3J exact, eigenvalues 7^1 (+2)^9 (-2)^5, K^2 = (4/49) I + (45/49) Pi0; NS/R = hbar(., FSUM) = the anchor bit; 248 = 120 + 128; the v737 distribution derived and the 5 x 48 coordinatization exists via exactly one ubar-invariant spread (kill explained, not revised); no RH statement.","checked_by_registry":false,"claim_excerpt":"The projective Hamming incidence lemma on V = L/(1+i)L -- the symplectic F2^4 of the unimodular hermitian E8 lattice, and the v737 resolution (one module, 36 checks, ~5 s; discovery probe projective_hamming_incidence_probe.py 36/36, verdict PROJ-HAMMING-EXACT).  THE LEMMA FROM THE CONCRETE LATTICE: h = H/4 is Z[i]-valued with hermitian Gram determinant 1 (the UNIMODULAR hermitian E8 lattice over Z[i]); doubly-even =>","claim_id":"E8.PROJHAMMING.01","dependencies_as_recorded":"E8.GAUSSCODE.01; E8.ORBITPACKET.01; E8.SEAM48.01; v689; v634; v722; v736; v737; v738","external_data_as_recorded":"-","id":"claim:E8.PROJHAMMING.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":677,"scripts_as_recorded":"v752_projective_hamming_incidence.py","status_as_recorded":"Exact [E] finite lemma (integer/Fraction arithmetic; Lean companion module; Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"FANO-DISC7-DECORATIVE: preregistered four-condition test, break exactly at condition 2 -- 2 splits in Q(sqrt(-7)) => 2-rank <= 2 < 3, the code F2-structures are arithmetically unrealizable; the three-cycle half is real (Fano sigma-bar = x2 multiplier, C corner = fixed point); the seven-correlation is permanently typed decorative; no RH statement.","checked_by_registry":false,"claim_excerpt":"The preregistered Fano -> discriminant(-7) bridge -- the three-cycle half is real, the parity half dies arithmetically: the seven-correlation is typed decorative for good (one module, 26 checks, ~1 s, ONE preregistered [FAIL] line C2.d = the COND2 break; discovery probe fano_disc7_bridge_probe.py, verdict FANO-DISC7-DECORATIVE).  THE FOUR-CONDITION TEST breaks exactly at condition 2: the NS/R parity bit has NO arithm","claim_id":"QGEO.FANODISC7.01","dependencies_as_recorded":"E8.PROJHAMMING.01; PRIME.HECKEMODRAM.01; QGEO.CAR.01; v533; v571; v632; v722; v738","external_data_as_recorded":"-","id":"claim:QGEO.FANODISC7.01","location_as_recorded":"tfpt_3","path":"verification/status_ledger.csv","row_number":678,"scripts_as_recorded":"v757_fano_disc7_bridge.py","status_as_recorded":"Exact [E] machinery; the preregistered break fires -- honest structural negative, correlation typed decorative (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"ARF-SPINOR-EXACT: unique sigma-selected Arf refinement q* (census 4 -> 2 -> 1; q_wt IS q*), parity lift iota ~ C_even(5) with beta = hbar exact, 16 = 1 + 5bar + 10 as Stab(q*) ~ S5 Arf geometry, K6 duad bijection, B = I + A_KG(6,2) with exact ovoid eigenvectors, spreads (1,2), hypercharge table -> v310/v14 dictionary, moments (16,0,120,0) with chain 40/41/240/248, Pati--Salam 8+8 with B-L exact, chi_NSR = anchor bit; A3^Fam != A3^PS discipline; matter reading fenced (v775); Lean companion 23 theorems; no RH statement.","checked_by_registry":false,"claim_excerpt":"The Arf/spinor compiler on V = L/(1+i)L = F2^4 -- Priority 1 of the Arf compiler programme, the exact finite-algebra layer (one module, 46 checks, ~2 s; discovery probe arf_spinor_compiler_probe.py 46/46, verdict ARF-SPINOR-EXACT, zero kills, both must-fail controls fire).  THE COMPILER, EXACT END TO END: hbar rebuilt from the concrete v752 lattice (Gram J - I in the family/anchor basis, census 240 = 15 x 16, sigma s","claim_id":"ARF.SPINORCOMPILER.01","dependencies_as_recorded":"E8.PROJHAMMING.01; PRIME.HECKEPOLARITY.01; CAR.SM.01; AX.P2.01; v752; v753; v2; v310; v14","external_data_as_recorded":"-","id":"claim:ARF.SPINORCOMPILER.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":679,"scripts_as_recorded":"v774_arf_spinor_compiler.py","status_as_recorded":"Exact [E] finite algebra (integer/Fraction/F2 arithmetic; Lean companion ArfSpinorCompiler.lean, 23 kernel theorems; Python-only per GATE.WOLFRAM.02); the physical code->matter reading FENCED (killed by v775/ARF.ROOTCLASS.01).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"ROOTCLASS-MIXED: no D5(+)A3/SU(5) convention makes even one full set of 15 classes pure -- counting bound (128 spinor roots, >= 7 adjoint-side classes for EVERY embedding), 0/56 splits pass, all 8 spinor classes mix 8 weight pairs; the code->matter table must not enter any main claim (fence incl. the right-handed-neutrino mailbox reading); no RH statement.","checked_by_registry":false,"claim_excerpt":"THE FIRED PHYSICAL KILL of the Arf compiler programme -- gaussian_class_d5_weight_purity, Priority 2, preregistered (one module, 18 checks, ~2 s; discovery probe gaussian_class_d5_purity_probe.py 18/18, verdict ROOTCLASS-MIXED, all 3 must-fail controls fire; FROZEN_SPEC SHA-256 58d9be9b935d92bbc3ddb838092d0cb7f8c1e5dad09e06ec28e850116ee3ef25, hashed BEFORE any root data).  THE QUESTION: does each nonzero Gaussian cla","claim_id":"ARF.ROOTCLASS.01","dependencies_as_recorded":"ARF.SPINORCOMPILER.01; E8.PROJHAMMING.01; PRIME.HECKEPOLARITY.01; v752; v1; v47; v310","external_data_as_recorded":"-","id":"claim:ARF.ROOTCLASS.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":680,"scripts_as_recorded":"v775_gaussian_class_d5_purity.py","status_as_recorded":"Exact [E] finite census kill -- the fired preregistered physical kill; the fence is binding on all main claims (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"BOUNDARY-CODE-UNIQUE: census 135 -> 30 -> 14 -> 2 -> 1 without Hamming/E8 input; flag datum = one deck-invariant Z2; Construction A -> E8 exact; q* unique; g_car = 1 + 4 = 5 as OUTPUT; residuals R1 (universe premise, the relocated+shrunk circularity), R2 (deck placement semantic), R3 (anchor naming) typed; open contract: derive evenness/self-duality from the seam axioms; NO P2-removal claim; no RH statement.","checked_by_registry":false,"claim_excerpt":"Boundary code uniqueness -- the non-circular selection chain boundary -> code -> E8 -> F2^4 -> 5 slots EXISTS with g_car = 5 as OUTPUT, and the residual premise is named (one module, 31 checks, ~2 s; discovery probe boundary_hamming_uniqueness_probe.py 31/31, verdict BOUNDARY-CODE-UNIQUE; frozen design SHA-256 c1893641...).  THE CHAIN, REBUILT WITHOUT HAMMING/E8 INPUT: direct enumeration gives 135 self-dual binary co","claim_id":"ARF.BOUNDARY.CODE.01","dependencies_as_recorded":"ARF.SPINORCOMPILER.01; AX.P2.01; E8.GAUSSCODE.01; E8.PROJHAMMING.01; v689; v736; v638; v752","external_data_as_recorded":"-","id":"claim:ARF.BOUNDARY.CODE.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":681,"scripts_as_recorded":"v776_boundary_hamming_uniqueness.py","status_as_recorded":"Exact [E] finite selection chain (census / Construction A / Arf selector, all exact arithmetic) + OPEN research contract [O]: derive the doubly-even self-dual universe premise from the seam axioms; NO P2-removal claim (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"GRIDSUP-SPLIT-CLOSED-LOG-LAW + FOURIER-LOGSUM-CLOSED: (a1)-(a3) closed elementarily with explicit constants (zero census violations), (a4) closed by the certified grid Fourier log-sum theorem ||F||_1 <= c0 + (J/4) ln(M+3); repaired (L1) clause [B0 + (J/2) ln(M+3)]/N verified; Araki summability unaffected; measured slope J/pi^2 (bound valid, not sharp); (b)/(c) open; GATE.QGEO does not move; no RH statement.","checked_by_registry":false,"claim_excerpt":"Remainder (a) of the (L1) majorant lemma FULLY closed in the corrected (1 + ln M) form -- one module from two probes (19 + 19 checks, ~40 s; discovery probes qgeo_grid_supremum_probe.py 19/19 GRIDSUP-SPLIT-CLOSED-LOG-LAW and qgeo_fourier_logsum_probe.py 19/19 FOURIER-LOGSUM-CLOSED, both 2026-08-05).  THE FOUR-WAY SPLIT of the v745 residue (a): (a1) the continuum entrywise supremum CLOSED -- Taylor constant 5/8 symbol","claim_id":"QGEO.GRIDSUP.01","dependencies_as_recorded":"QGEO.CARL1.01; QGEO.CARLIMIT.01; v745; v715","external_data_as_recorded":"-","id":"claim:QGEO.GRIDSUP.01","location_as_recorded":"tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":682,"scripts_as_recorded":"v778_qgeo_gridsup_logsum.py","status_as_recorded":"Theorem-level [E] closure of residue (a) in the corrected (1 + ln M) form (exact twisted-circulant + summation-by-parts + census, zero violations); the v715 literal clause corrected; residues (b)/(c) open; GATE.QGEO does not move (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"GNS-PRECURSORS-COHERENT + GNET-ARF-NO-CORRESPONDENCE: exact Haar tower intertwining, commuting index-4 expectation squares, geometric state Cauchy ~1/4, machine-exact index census with zero degradation, twisted-duality defect 0 with ratio 4; dim law d_c = 4^(l-1) + 2^(l-1) cos(pi c/2) => C[Z4] obstruction exactly 2^-l (explains the l = 1 anomaly); the 1+5+10 echo exact but non-geometric (rank 3 vs 4, GL census 0/20160); K_matter does not govern transport; the two fours stay in their registers; no RH statement.","checked_by_registry":false,"claim_excerpt":"The G_net continuum strand -- finite-level precursors of the GNS limit net COHERENT, the exact C[Z4] obstruction dim law, and the honest Arf negative; one module from two probes (27 + 27 checks, ~50 s; discovery probes gnet_gns_limit_probe.py 27/27 GNS-PRECURSORS-COHERENT and gnet_arf_qsystem_probe.py 27/27 GNET-ARF-NO-CORRESPONDENCE, both 2026-08-05).  THE PRECURSORS (typed finite evidence FOR the five v746 continuu","claim_id":"GNET.GNSLIMIT.01","dependencies_as_recorded":"GNET.LOCALNET.01; GNET.PPINDEX.01; GATE.METRIC.08; GATE.METRIC.11; ARF.SPINORCOMPILER.01; v746; v726; v754","external_data_as_recorded":"-","id":"claim:GNET.GNSLIMIT.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":683,"scripts_as_recorded":"v779_gnet_gns_arf.py","status_as_recorded":"Exact [E] finite coherence data + exact [E] dim law + measured [MEASURED] precursors and the honest negative, all typed finite evidence for the named continuum theorems -- never the theorems (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"ONE-OBJECT-PARTIAL + CLOCK-FIBER-DEAD: even unimodular diagonal glue of A_{d-1}+D_{d+1} iff d = 4 (census 2..12, v92 reproduced, E8 certificate); g_car = 5 / N_fam = 3 / |mu4| = 4 as one-object corollaries; c3 = 1/(2 pi d)|_{d=4} typed corpus-legitimate rewriting, NOT a P1 derivation; the Z12 x_{Z6} Z30 clock action on the 60 lines dead at three levels (group order 23040, max element order 12); controls fire; no RH statement.","checked_by_registry":false,"claim_excerpt":"The d = 4 forcing census + the 60-line clock synchronization kill, one module from two probes (21/21 + 23/23 checks, ~5 s; discovery probes one_object_reduction_probe.py ONE-OBJECT-PARTIAL and clock_fiber_product_probe.py CLOCK-FIBER-DEAD, both 2026-08-05).  THE FORCING CENSUS (exact Fraction arithmetic, d = 2..12): the TFPT glue pattern (cyclic isotropic glue, evenness q = 0 mod 2Z, unimodularity |H|^2 = 4d) admits ","claim_id":"E8.ONEOBJECT.01","dependencies_as_recorded":"v1; v23; v53; v92; v623; v629; v633; v634; ARF.ROOTCLASS.01","external_data_as_recorded":"-","id":"claim:E8.ONEOBJECT.01","location_as_recorded":"tfpt_1;tfpt_3","path":"verification/status_ledger.csv","row_number":684,"scripts_as_recorded":"v781_one_object_clock_census.py;v807_lorentz_nullselector.py","status_as_recorded":"Exact [E] lattice/discriminant-form census results and an exact [E] group-theoretic kill, both behind explicit fences; the c_3 link stays typed INTERPRETATION (no P1 derivation); no marker move (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"TRANSITION-BUS-TORSOR: 15 coordinate 8-frames; pair fibers = canonical v_perp-torsors; NO deck-equivariant V x (V-0) labeling exists (proof-grade obstruction); the frozen symplectic predicate reproduces all 57600 inner products incl. the sign law; 240 = 5 x 3 x 16 spread layer; A15 comparison quantified; controls fire; no RH statement.","checked_by_registry":false,"claim_excerpt":"The transition-bus structure theorem (35/35 checks, ~2 s; discovery probe e8_transition_bus_probe.py TRANSITION-BUS-TORSOR, 2026-08-05).  The 240 roots of the unimodular hermitian Gaussian E8 lattice are 15 disjoint coordinate 8-frames (cross-polytopes) over the class map V = L/(1+i)L; on L/2L the quadratic form q(y) = <y,y>/4 mod 2 is well defined and the 120 root PAIRS are exactly the 120 q = 1 points of the plus-t","claim_id":"E8.TRANSITIONBUS.01","dependencies_as_recorded":"v752; v689; ARF.SPINORCOMPILER.01; ARF.ROOTCLASS.01","external_data_as_recorded":"-","id":"claim:E8.TRANSITIONBUS.01","location_as_recorded":"tfpt_1;tfpt_3","path":"verification/status_ledger.csv","row_number":685,"scripts_as_recorded":"v782_e8_transition_bus.py","status_as_recorded":"Exact [E] finite structure theorem (torsor + predicate + obstruction census) behind the interpretation fence ('transition bus / instruction set' language stays interpretation); no marker move (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"CLIFFORD-PARTIAL(H4): the 60 Gaussian lines = the 60 two-qubit stabilizer rays entry-exactly over Z[i] (60/60, census 4+24+32); G31 = index-2 subgroup of the Clifford matrix group (coset zeta8 G31, projectively equal); 46080 = mu4 x Pauli16 x Sp(4,2) with classes = contexts and spreads = MUB pentads; the index bit = the sqrt2/Hadamard Galois bit (H4 as predeclared); controls fire; no matter reading; no RH statement.","checked_by_registry":false,"claim_excerpt":"The two-qubit stabilizer identification of the compiler carrier (32/32 checks, ~4 s; discovery probe two_qubit_clifford_probe.py CLIFFORD-PARTIAL(H4), 2026-08-05).  H1 EXACT: under the single predeclared chart U (the coordinate-class frame v_k = 2 e_{2k} -> the computational basis; z_k = r_2k + i r_2k+1, J -> multiplication by i) the 60 Gaussian E8 lines ARE the 60 pure two-qubit stabilizer rays, entry-exactly over Z","claim_id":"E8.CLIFFORD2Q.01","dependencies_as_recorded":"v689; v752; v634; E8.GAUSSIAN.CODE.01; ARF.ROOTCLASS.01","external_data_as_recorded":"-","id":"claim:E8.CLIFFORD2Q.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":686,"scripts_as_recorded":"v783_two_qubit_clifford.py","status_as_recorded":"Exact [E] finite group/lattice identification (H1-H3) with the H4 layer honestly PARTIAL (the index bit identified as the sqrt2/Hadamard Galois bit, not J <-> -J); no marker move (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"CURVE-CODE-PARTIAL: (A[2], e_2) = (V, hbar) as bare symplectic spaces only; the correspondence dies at two exact layers -- deck acts syntheme-side [3,3]-free vs code duad-side [3,1,1,1] (outer S6), and curve theta even/Arf-0 (1+6+9) vs q* odd/Arf-1 (1+5+10); joint census 0 with positive control 6; every period certified as integral O-recognition; no RH statement.","checked_by_registry":false,"claim_excerpt":"The curve/code 2-torsion decider (33/33 checks, ~9 s; discovery probe curve_code_2torsion_probe.py CURVE-CODE-PARTIAL, 2026-08-05).  The frozen CM-model route through the seam curve C: y^3 = x^4 - 1 (genus 3, Jacobian splits per v610): exact differential characters (zeta^11, zeta^7, zeta^10) reproduce v610 L1; A = the zeta_12 CM abelian surface with EVERY generator period certified as an integral O = Z[zeta_12] recog","claim_id":"CURVE.CODE.2TORSION.01","dependencies_as_recorded":"v610; v611; v752; v753; ARF.SPINORCOMPILER.01; ARF.ROOTCLASS.01","external_data_as_recorded":"-","id":"claim:CURVE.CODE.2TORSION.01","location_as_recorded":"tfpt_1;tfpt_3","path":"verification/status_ledger.csv","row_number":687,"scripts_as_recorded":"v784_curve_code_2torsion.py","status_as_recorded":"Exact [E] finite algebra + certified-recognition CM layer; the correspondence honestly PARTIAL with both breaking layers named exactly (syntheme-vs-duad and Arf 0-vs-1); no marker move (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"KMS-COSET-THEOREM: S = -(ln lambda)^2/2 from the time-1 PGL2 holonomy multiplier per clock e-fold; classifier Schwarzian-free and derivative-free (non-circularity gated); blind assignment F_pole/F_Boltzmann modular (|ln lambda| = Delta), F_QCD autonomous, F_relic degenerate; unblinding exact (sympy zero); controls fire incl. the Moebius-clock positive case; the executor -> groupoid -> coset chain whole; no RH statement.","checked_by_registry":false,"claim_excerpt":"the coset assignment of the fibered clock functor is a THEOREM from KMS/modular typing (18/18 checks incl. the three must-fire controls, ~3 s; discovery probe ftransfer_kms_coset_probe.py, 2026-08-05, verdict KMS-COSET-THEOREM; frozen before the first run).  THE THEOREM: S_transported = -(ln lambda)^2/2 with lambda the PGL2 multiplier of the flow's time-1 holonomy per clock e-fold -- the coset is COMPUTED from the ty","claim_id":"FTRANSFER.KMSCOSET.01","dependencies_as_recorded":"CONTRACT.F.01; FTRANSFER.CLOCKS.01; v777; v578; v99; v425","external_data_as_recorded":"-","id":"claim:FTRANSFER.KMSCOSET.01","location_as_recorded":"tfpt_research_contracts;tfpt_3","path":"verification/status_ledger.csv","row_number":688,"scripts_as_recorded":"v792_ftransfer_kms_coset.py","status_as_recorded":"Theorem-grade [E] sympy-exact derivation chain + blind classification with the non-circularity of the classifier gated on its own source; completes the fiber classification of the executed clock contract; no marker move (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"BRIDGE-CANONICAL: the Sylvester duality beta (code odd forms -> curve spreads) with beta sigma = tau beta and beta(q*) = S* is unique up to the order-6 joint stabilizer (18 + 18 -> 6 + 6, one orbit incl. the tau/tau^2 swap); q_Theta pulls back constantly to q_even* = q* + hbar(., A) -- the anchor shift resolves the v784 Arf mismatch; 5bar/10, 3+2 and t_A -> rho = J transport exactly; chi_NSR an exact two-variant torsor; inner identification stays dead; no RH statement.","checked_by_registry":false,"claim_excerpt":"the canonical OUTER bridge between the code's duad side and the curve's syntheme side of the S6 duality (24/24 checks, ~11 s; discovery probe duad_syntheme_bridge_probe.py, 2026-08-05, verdict BRIDGE-CANONICAL).  THE CONSTRUCTION (Sylvester duality made explicit): a bridge is a bijection beta: Omega_code -> T_curve (code odd Arf forms -> curve isotropic spreads/totals), canonically inducing the incidence-preserving d","claim_id":"CURVE.CODE.OUTERSPIN.01","dependencies_as_recorded":"CURVE.CODE.2TORSION.01; ARF.SPINORCOMPILER.01; v784; v774; v752; v610; v611; ARF.ROOTCLASS.01","external_data_as_recorded":"-","id":"claim:CURVE.CODE.OUTERSPIN.01","location_as_recorded":"tfpt_1;tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":689,"scripts_as_recorded":"v796_duad_syntheme_bridge.py","status_as_recorded":"Exact [E] finite census theorem (torsor uniqueness incl. the tau/tau^2 swap; constant Arf resolution; exact transports) behind the structure-label fence; the inner identification stays dead (v784); no marker move (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"MODULAR-S-PARTIAL: the per-factor Hadamard IS the metaplectic S-lift at tau = i, landing exactly in the missing coset zeta8 G31 (S^2 = I, T^2 = Pauli parity, (TK)^3 = zeta8 I); the deck J = the metaplectic anomaly of the total Fourier (R2 solved); zeta8 = (1+J)/sqrt2 the half-deck swapping the seam pair; strict census EMPTY (0/46080 fix q*), one G31-conjugacy class of retyped survivors, sigma-orbit Arf defects XOR to the anchor A (R3 named, not fixed); no RH statement.","checked_by_registry":false,"claim_excerpt":"the missing Clifford index-2 bit IS the metaplectic lift of the modular S transformation at its fixed point tau = i -- coset decision positive, deck placed, anchor named; the frozen uniqueness decider fails sharply (27/27 checks, ~50 s; discovery probe seam_clifford_modular_s_probe.py, 2026-08-06, verdict MODULAR-S-PARTIAL).  COSET DECISION POSITIVE (exact cyclotomic arithmetic): the per-binary-factor Weil/metaplecti","claim_id":"SEAM.CLIFFORD.MODULAR_S.01","dependencies_as_recorded":"E8.CLIFFORD2Q.01; ARF.BOUNDARY.CODE.01; ARF.SPINORCOMPILER.01; v783; v774; v752; v689; ARF.ROOTCLASS.01","external_data_as_recorded":"-","id":"claim:SEAM.CLIFFORD.MODULAR_S.01","location_as_recorded":"tfpt_1;tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":690,"scripts_as_recorded":"v798_seam_clifford_modular_s.py","status_as_recorded":"Exact [E] cyclotomic coset/metaplectic identities (BFS certificates; exact tau = i relations) with the strict uniqueness census EMPTY by its own frozen gate -- the Arf defect unavoidable, a sharp typed fact; R2 placed, R3 named; no marker move (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"TYPEII-FORCED: exhaustively over all subspaces of F2^8 (dim <= 4), locality <=> self-orthogonal, integer spin <=> doubly even, S-closure/|disc| = 1 <=> self-dual; survivor set = exactly the 30 e8-hat copies; no boundary-legal non-Type-II code; R1 -> R1' = the three physical axioms A1-A3; imported ingredients classical, cited, instance-verified; NO P2 marker move; no RH statement.","checked_by_registry":false,"claim_excerpt":"Type II (doubly-even self-dual) is FORCED from three physical seam axioms -- the direct attack on residual R1 of ARF.BOUNDARY.CODE.01, decided exhaustively (19/19 checks, ~5 s; discovery probe seam_code_typeii_probe.py, 2026-08-06, verdict TYPEII-FORCED).  THE THREE EQUIVALENCE CENSUSES, exhaustive over ALL 308,993 subspaces of F2^8 of dim 0..4 (totals = the Gaussian binomials 1, 255, 10795, 97155, 200787; dim > 4 ex","claim_id":"SEAM.CODE.TYPEII.01","dependencies_as_recorded":"ARF.BOUNDARY.CODE.01; AX.P2.01; ARF.SPINORCOMPILER.01; v776; v752; E8.GAUSSCODE.01","external_data_as_recorded":"-","id":"claim:SEAM.CODE.TYPEII.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":691,"scripts_as_recorded":"v799_seam_code_typeii.py","status_as_recorded":"Exact [E] exhaustive finite equivalence chain at length 8 (all 308,993 subspaces) modulo the cited classical lattice-VOA/theta ingredients, each machine-verified in every instance used; the OPE-linearity scope note typed; R1 -> R1' [C] residual registered; NO P2 marker move (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"TORSOR-FOURIER-PARTIAL: 120 canonical projective Fourier rays (phase law exact on 960 shifts, Gram = 16 I); deck/Pauli diagonal, G31 monomial through Sp(4,2); the carrier block = the 8 R-fibers' 64 rays = (1+5+10) x (1+3) under W(D5) x W(A3) with sigma = family 3-cycle + anchor -- the carrier Pascal at character level, impossible at point level (v775); weight/character bases exactly mutually unbiased (the honest cap); the 45 deck-even modes = the 45 context Pauli observables under the certified chart; no RH statement.","checked_by_registry":false,"claim_excerpt":"the projective Fourier modes of the 15 Gaussian root torsors -- carrier-block purity at CHARACTER level with the mutually-unbiased honest cap (30/30 checks, ~60 s; discovery probe e8_torsor_fourier_probe.py, 2026-08-06, verdict TORSOR-FOURIER-PARTIAL; FROZEN_SPEC SHA-hashed before any root data).  THE CONSTRUCTION: because the v782 class fibers are torsors WITHOUT origin, their character data is canonical where their","claim_id":"E8.TORSOR.FOURIER.01","dependencies_as_recorded":"E8.TRANSITIONBUS.01; E8.CLIFFORD2Q.01; ARF.ROOTCLASS.01; PRIME.POSITIVE_DESCENT.01; v782; v783; v775; v752; v791","external_data_as_recorded":"-","id":"claim:E8.TORSOR.FOURIER.01","location_as_recorded":"tfpt_1;tfpt_3","path":"verification/status_ledger.csv","row_number":692,"scripts_as_recorded":"v800_e8_torsor_fourier.py","status_as_recorded":"Exact [E] integer/cyclotomic character theory (canonical rays, exact Clebsch spectrum, exact overlap census) with the predeclared P3 failure typed -- the weight and character gradings mutually unbiased; ROOTCLASS-MIXED (v775) intact and re-confirmed; no marker move (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"MARTINGALE-HYPOTHESES-MET: exact Haar filtration with one index-4 expectation for the whole tower; state defects summable at measured rate ~0.25 per doubling (<= the 2^-l envelope, one power better); unique limit by telescoping verified on every rung; split/normality precursors uniform (determinant witness >= 0.99); decimation converges to the WRONG degenerate limit (coherent bond load-bearing); QGEO residues (b)/(c) bypassed for existence, relocated into normality; steps 5-7 typed open; no RH statement.","checked_by_registry":false,"claim_excerpt":"the noncommutative-martingale route to the G_net GNS limit -- its finite hypotheses MEASURED, all met (15/15 checks, controls 4/4, ~7 s; discovery probe gnet_martingale_probe.py, 2026-08-06, verdict MARTINGALE-HYPOTHESES-MET).  THE PROGRAMME: replace continuum heuristics by martingale convergence -- if the local-state defects along the certified Haar inductive system are SUMMABLE in trace norm, the limit state exists","claim_id":"GNET.MARTINGALE.LIMIT.01","dependencies_as_recorded":"GNET.GNSLIMIT.01; GATE.METRIC.11; QGEO.GRIDSUP.01; v779; v746","external_data_as_recorded":"-","id":"claim:GNET.MARTINGALE.LIMIT.01","location_as_recorded":"tfpt_2;tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":693,"scripts_as_recorded":"v802_gnet_martingale.py","status_as_recorded":"Measured [MEASURED] martingale hypotheses under frozen gates (all met; rate one power better than the dim-law envelope, reported not forced) + typed analytic remainder; the QGEO majorant residues relocated into the normality step, not proven; no marker move (Python-only per GATE.WOLFRAM.02).","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"JETCODE-EXACT + AFFINE-NSR-EXACT: Z[i]/(2) = F2[eps]/(eps^2) unique iso; W = L/2L free rank 4 (Hermite-certified); exact self-extension with ker eps = im eps; J = 1 + eps reproduces the v782 torsor on all 240 roots; 0/65536 mu4-equivariant splittings -- non-splitness IS the no-origin obstruction; 240 roots = oriented q = 1 unit jets (15 x 8 x 2); Stab(chi_NSR) = AGL(3,2) order 1344 = Aut(H8), same natural 8-point action; affine functions = RM(1,3) = H8 (1344 equivalences); typed internal reconstruction, no P2 removal; no matter semantics.","checked_by_registry":false,"claim_excerpt":"E8.RAMIFIED.JETCODE.01 (+ E8.AFFINE.NSR.01): the jet-code normal form of the Gaussian E8 compiler + the NS/R bit as an affine 8-point geometry, ONE module from two probes (18/18 + 15/15 checks, ~3 s; discovery probes e8_ramified_jetcode_probe.py JETCODE-EXACT and e8_affine_nsr_probe.py AFFINE-NSR-EXACT, both 2026-08-06, FROZEN_SPEC SHA-hashed before any root data).  PART 1, THE JET CODE (all [E neu], machine-certifie","claim_id":"E8.RAMIFIED.JETCODE.01","dependencies_as_recorded":"E8.TRANSITIONBUS.01; ARF.BOUNDARY.CODE.01; v752; v689; v782; v776; v646; v148; v227; v301","external_data_as_recorded":"-","id":"claim:E8.RAMIFIED.JETCODE.01","location_as_recorded":"tfpt_1;tfpt_3","path":"verification/status_ledger.csv","row_number":694,"scripts_as_recorded":"v803_e8_jetcode_affine_nsr.py","status_as_recorded":"Exact [E] ring/module/extension structure theorems (integer/F2/Z[i] arithmetic, exhaustive censuses) behind the interpretation fence; the reconstruction-chain reading typed [H neu]; carries E8.AFFINE.NSR.01","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"SYNDROME-DEAD: max rank 222/256 over all four frozen phase conventions (two post-hoc diagnostics score worse: 215/160); the +-r proportionality obstruction structural for the whole diagonal-phase family; SURVIVES: 16 + 240 = 256 counting, the 16 v112 neutral kernels ARE the diagonal MASA, same-class products A_0-valued with mu4 coefficients exactly, the fine groupoid law associative 0/3375; successor needs root-individual (non-linear-in-r) operator data; no matter semantics.","checked_by_registry":false,"claim_excerpt":"E8.SYNDROME.ALGEBRA.01: the honest kill -- E8 is NOT an error-correction hull in the sharpest sense, one probe (13/13 checks incl. the 3 must-fire controls, ~6 s; discovery probe e8_syndrome_algebra_probe.py, 2026-08-06, verdict SYNDROME-DEAD, the kill fired exactly as preregistered).  THE QUESTION: do the 240 root operators U_r |x> = i^{c(r).x} |x XOR v> plus the 16 neutral kernels form a 256-dimensional mu4-twisted","claim_id":"E8.SYNDROME.ALGEBRA.01","dependencies_as_recorded":"E8.PROJHAMMING.01; ARF.ROOTCLASS.01; v752; v111; v112; v775","external_data_as_recorded":"-","id":"claim:E8.SYNDROME.ALGEBRA.01","location_as_recorded":"tfpt_1;tfpt_3","path":"verification/status_ledger.csv","row_number":695,"scripts_as_recorded":"v805_e8_syndrome_algebra.py","status_as_recorded":"DEAD as frozen [E kill, preregistered adjudication fired]: the twisted V-graded basis reading of E8 killed at rank level; the surviving structures typed exactly; successor criterion named","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"PETERSEN-RADIAL-EXACT + SIXTHROOT-SPECTRAL-ONLY: charges (-4,+1,+6) = the SU(5) decuple against v774; Petersen SRG certified, |Aut| = 120 census; shells (1,3,6) charge-pure; the flavor hexagon = the distance-2 shell edge-by-edge; equitable quotient with hypercharge eigenvector (6,-4,1) -> -2; spec(P^6) = {1, 64/729, 1/729} = the deployed transport spectrum; 10-dim multiplicities (x5 = g_car fast, x4 = |mu4| slow) typed [H neu] -- no corpus 10-dim operator; B unique symmetric doubly stochastic PSD sixth root in the corpus basis, B^6 GL(3,Q)-conjugate to v486's M^6 and the cusp-diagonal form but bit-equal to neither -- the corpus freezes the spectrum, not the basis.","checked_by_registry":false,"claim_excerpt":"CARRIER.PETERSEN.RADIAL.01 (+ TRANSPORT.SIXTHROOT.01): the K5 edge machine, the Petersen carrier geometry with the radial dynamics whose sixth power IS the deployed transport spectrum, + the bit-exact decider on the PSD sixth root, ONE module from two probes (19/19 + 16/16 checks, ~1 s; discovery probes carrier_petersen_radial_probe.py PETERSEN-RADIAL-EXACT and transport_sixthroot_probe.py SIXTHROOT-SPECTRAL-ONLY, bo","claim_id":"CARRIER.PETERSEN.RADIAL.01","dependencies_as_recorded":"ARF.SPINORCOMPILER.01; v774; v54; v56; v124; v486; v327; v212; v397; v14; v700","external_data_as_recorded":"-","id":"claim:CARRIER.PETERSEN.RADIAL.01","location_as_recorded":"tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":696,"scripts_as_recorded":"v808_petersen_sixthroot.py","status_as_recorded":"Exact [E neu] finite graph/matrix structure theorems (integer/Fraction; charpolys sympy-gated) behind the carrier-geometry fence; the 10-dim multiplicity prediction typed [H neu]; carries TRANSPORT.SIXTHROOT.01 (spectral-only decider)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"DOILY-EXACT: NN^T = B + 2I entrywise; spec {9, 4^9, 0^5}; N/3 singular values {1, 2/3, 0} -- the recovery base rate as the unique nontrivial singular value, (2/3)^6 typed pending six-step composition; Petersen edges = synthemes 15/15; every census bridge factors exactly N_code = P_Delta^T N_curve^T P_Gamma -- a duality, not an isomorphism (inner route 0/720); Arf switch set T6 = the six within-block duads; N/3 doubly stochastic, typed classical not CPTP.","checked_by_registry":false,"claim_excerpt":"CURVE.CODE.DOILY.01: the certified outer bridge sharpened into an incidence-operator statement with a spectral payoff, one probe (21/21 checks incl. the 3 must-fire controls, ~1 s; discovery probe curve_code_doily_probe.py, 2026-08-06, verdict DOILY-EXACT).  THE EXACT IDENTITY: the K6 doily incidence N (15 duads x 15 synthemes on the six odd Arf refinements) satisfies NN^T = 3I + A_KG(6,2) = B + 2I entrywise, with B ","claim_id":"CURVE.CODE.DOILY.01","dependencies_as_recorded":"CURVE.CODE.OUTERSPIN.01; CURVE.CODE.2TORSION.01; v752; v774; v796; v221; v240; v425","external_data_as_recorded":"-","id":"claim:CURVE.CODE.DOILY.01","location_as_recorded":"tfpt_3","path":"verification/status_ledger.csv","row_number":697,"scripts_as_recorded":"v809_curve_code_doily.py","status_as_recorded":"Exact [E] incidence-operator identities and spectra (integer/Fraction, annihilator-certified) with the (2/3)^6 identification typed [H neu -> decidable] pending the six-step composition; the inner identification stays dead","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"CUTCODE-EXACT + MOMENT-INCIDENCE-PARTIAL: delta injective isometric on all 256 cells; Arf split = the (0|5)+(1|4)+(2|3) cut classification; Clebsch 40 = 5 + 20 + 15 with forbidden blocks empty and within-10 = Petersen (census 120); roots/lines grade 80 + 160 / 20 + 40 -- Arf/cut grading, NOT matter; Tr_{S+}X^2 = 4|X|^2 = 4 h(E8) = 120 from one symbolic identity; charpoly exact, 72 audit-only; the 210 = C(10,4) map DECORATIVE -- equivariant bijection killed by the fixed-point obstruction (exhaustive); the partial 80 -> 5 x 16 miss-slot map and Newton tie survive as audit.","checked_by_registry":false,"claim_excerpt":"CARRIER.CUTCODE.01 (+ CARRIER.MOMENT.INCIDENCE.01): the Arf split as the cut classification of K5 + the one-line master moment with the frozen 210 decision, ONE module from two probes (17/17 + 16/16 checks, ~1 s; discovery probes carrier_cutcode_probe.py CUTCODE-EXACT and carrier_moment_incidence_probe.py MOMENT-INCIDENCE-PARTIAL, both 2026-08-06).  PART 1, THE CUT CODE [E neu]: the cut map delta: F2^5 -> F2^10 (edge","claim_id":"CARRIER.CUTCODE.01","dependencies_as_recorded":"ARF.SPINORCOMPILER.01; ARF.ROOTCLASS.01; v774; v2; v55; v109; v111; v700; v752","external_data_as_recorded":"-","id":"claim:CARRIER.CUTCODE.01","location_as_recorded":"tfpt_1;tfpt_3","path":"verification/status_ledger.csv","row_number":698,"scripts_as_recorded":"v810_cutcode_moment.py","status_as_recorded":"Exact [E neu] cut-map/shell-grading censuses (F2/integer, exhaustive) + the frozen 210 decision landing PARTIAL (decorative, per the preregistered rule); the 5/20/15 and charpoly readings audit fingerprints [C]; carries CARRIER.MOMENT.INCIDENCE.01","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"FILTRATION-FINGERPRINT-ONLY: Q (4,5,6) / K (6,9,10) / L (10,14,16) = exact counts of the K_{3,2}/prism/K5/H8 incidence chain, order-exact, with level-wise additivity mirroring L = K + Q; deployed matrices located (v11/v12/v37/v4); NO entry-level reconstruction from any frozen candidate (25/20/47 per level); exhaustive false-positive rates 0.005-0.75% -- the misses are informative; typed audit fingerprint.","checked_by_registry":false,"claim_excerpt":"FLAVOR.GRAPH.FILTRATION.01: the flavor-matrix filtration Q -> K -> L as an incidence-compiler fingerprint -- budgets exact, entries NOT reconstructible, one probe (16/16 checks incl. the 4 must-fire controls, ~1 s; discovery probe flavor_graph_filtration_probe.py, 2026-08-06, verdict FILTRATION-FINGERPRINT-ONLY).  THE BUDGET IDENTIFICATIONS ARE EXACT AND ORDER-EXACT: Q row budgets (4, 5, 6) = (|E(K3) u E(K2)|, |V(K5)","claim_id":"FLAVOR.GRAPH.FILTRATION.01","dependencies_as_recorded":"FLAV.PENCIL.01; v11; v12; v37; v4; v752","external_data_as_recorded":"-","id":"claim:FLAVOR.GRAPH.FILTRATION.01","location_as_recorded":"tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":699,"scripts_as_recorded":"v812_flavor_graph_filtration.py","status_as_recorded":"Exact [E] order-exact budget identifications (pure integers, exhaustive false-positive controls) with the entry-level reconstruction NEGATIVE; typed audit fingerprint at budget level","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"P1-IDENTITY-CLOSED: I*beta*c3 = 1 exact; the index c3-free (zero occurrences, four sources), beta independently measured (v526, wrong-beta excluded; the radian pin is the one shared convention and cancels); c3 stays the P1 axiom the identity EXPLAINS; finite evenness precursor measured: w1 = w3 = 1/4 exactly every level, symmetric zero-sum offset +-2^-(l+1) -- the no-anomaly shape; the sea state does NOT equidistribute (dev 0.188) -- the bridge must normalize the modular response; controls: index 2 -> 1/(4pi), booked elsewhere by the corpus; contract registered OPEN [O], kill = an asymmetric sector offset.","checked_by_registry":false,"claim_excerpt":"P1.INDEX.KMS.01: the closed normalization identity c3 = 1/(I_Jones * beta_angle) = 1/(4 * 2pi) = 1/(8pi), its convention audit, and the sharpened P1 contract, one probe (13/13 checks incl. the 2 must-fire controls, ~0.1 s; discovery probe p1_index_kms_probe.py, 2026-08-06, verdict P1-IDENTITY-CLOSED).  THE IDENTITY [E]: I * beta * c3 = 4 * 2pi * 1/(8pi) = 1 EXACT in formal Fraction x pi^k arithmetic (no floats; S2.1-","claim_id":"P1.INDEX.KMS.01","dependencies_as_recorded":"AX.P1.01; GATE.METRIC.11; GATE.METRIC.12; ANCHOR.GEN.01; v154; v726; v746; v779; v526; v239; v208; v8; v23","external_data_as_recorded":"-","id":"claim:P1.INDEX.KMS.01","location_as_recorded":"tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":700,"scripts_as_recorded":"v813_p1_index_kms.py","status_as_recorded":"Exact [E] identity chain (formal Fraction x pi^k) + gated independence audit + measured finite evenness precursor; OPEN [O] contract with the one open bridge (even modular-response normalization) and the kill criterion named; c3 stays the P1 axiom","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"SIXSTEP-CLOCK-ONLY + TRANSPORT10-PROPOSED: the (2/3)^6 rate canonical on three spatial routes, each with a typed obstruction; the deployed 6 is the clock exponent (sixth-power blindness makes per-step data mandatory); T_v221 == B^6 bit-exact (SIXTHROOT upgrades to BITEXACT-vs-v221, dated note on the v808 row); T10 = P10^6 in the Lambda^2 basis passes all gates -- proposal, no deploy claim; NO RH claim","checked_by_registry":false,"claim_excerpt":"K5.SIXSTEP.TRANSPORT.01: the six-step composition and the 10-dim transport deploy -- the (2/3)^6 rate is canonical on three spatial routes, the deployed six is the clock exponent, and the canonical T10 proposal passes every gate, one probe (23/23 checks incl. the 3 must-fire controls, ~0.2 s; discovery probe k5_sixstep_transport_probe.py, 2026-08-06, verdicts SIXSTEP-CLOCK-ONLY / TRANSPORT10-PROPOSED).  THE CORRECTIO","claim_id":"K5.SIXSTEP.TRANSPORT.01","dependencies_as_recorded":"CARRIER.PETERSEN.RADIAL.01; TRANSPORT.SIXTHROOT.01; CURVE.CODE.DOILY.01; v221; v124; v486; v37; v774; v808; v809","external_data_as_recorded":"-","id":"claim:K5.SIXSTEP.TRANSPORT.01","location_as_recorded":"tfpt_1;tfpt_3","path":"verification/status_ledger.csv","row_number":701,"scripts_as_recorded":"v814_k5_sixstep_transport.py","status_as_recorded":"Exact [E neu] operator identities and censuses (three spatial routes, sixth-power blindness, corpus census, bit-exact v221 location); [H neu] the walk-vs-clock reading and the T10 deployment proposal; dated BITEXACT correction to TRANSPORT.SIXTHROOT.01 carried","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"MASTER-BOTH-INSTANCES: G_net hypotheses re-verified (Choi PSD, delta rate 0.267/doubling); THE NEW NUMBER -- prime packet state defects summable at 0.701/doubling ~ sqrt-dilution 2^{-1/2}, mh2(p) = -1/15 exact for every odd prime; the selection problem eliminated on both sides; K4: positivity NOT implied by summability; open per instance: G_net normality/split, prime sector floor (-> PRIME.FLOOR.RATIO.01); NO RH claim","checked_by_registry":false,"claim_excerpt":"Abstract positive-descent theorem and G_net finite hypothesis checks; the prime packet instance is maintained by Prime Front. Original module ID retained; original complete mixed record is preserved in extraction provenance.","claim_id":"TFPT.POSITIVE_DESCENT.MASTER.01","dependencies_as_recorded":"PRIME.POSITIVE_DESCENT.01; GNET.MARTINGALE.LIMIT.01; PRIME.FLOOR.RATIO.01; v791; v802; v793","external_data_as_recorded":"-","id":"claim:TFPT.POSITIVE_DESCENT.MASTER.01","location_as_recorded":"tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":702,"scripts_as_recorded":"v817_positive_descent_master.py","status_as_recorded":"Abstract master theorem with kernel-checked Lean core (PositiveDescentMaster.lean: telescoping + tail, positivity closure, sector commutation); both instances measured at finite level; hypotheses (6)/(7) typed per instance; positivity a separate hypothesis (K4)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"ANCHOR-AFFINE-EXACT + FLAVOR-BIDIR-CHECKSUM (selective): the whole compiler budget from ONE affine recursion T(x) = 2x - 2 (orbit 4, 6, 10, 18, 34; fixed point 2); the flavor matrix R decodes the same anchor bidirectionally (rows p_1, p_3, 13; columns p_2, p_4, 8) and the accepted down-row (1,5,2) is the UNIQUE candidate of 12 passing the full identity set -- the kill test is the anchor contraction (R a)_2 = 10 = p_3","checked_by_registry":false,"claim_excerpt":"ANCHOR.AFFINE.01 + FLAVOR.BIDIR.01: the anchor affine normal form and the flavor bidirectional checksum -- two exact corpus compressions, ONE module from two probes (18/18 + 15/15 checks, verdicts ANCHOR-AFFINE-EXACT and FLAVOR-BIDIR-CHECKSUM (selective); discovery probes anchor_affine_probe.py and flavor_bidir_probe.py, 2026-08-07, re-run identically at promotion, promoted VERBATIM).  PART A: the anchor a = (1,1,2) ","claim_id":"ANCHOR.AFFINE.01","dependencies_as_recorded":"v1; v2; v6; v222; v230; v415","external_data_as_recorded":"-","id":"claim:ANCHOR.AFFINE.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3","path":"verification/status_ledger.csv","row_number":703,"scripts_as_recorded":"v832_anchor_flavor_checksum.py","status_as_recorded":"Exact identity-grade compression [Identity]: both parts exact sympy/integer arithmetic; the compression is a normal form of existing corpus surfaces (tfpt_1 anchor power compiler + budget lines, tfpt_2 flavor spectral selector + bilinear table); no marker move (Python-only per GATE.WOLFRAM.02)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"RAMIFICATION-LADDER-EXACT: the four documented roles of pi2 = 1+i -- norm doubling / empty zero class, the 4-bit address, the non-split jet with deck = 1 + eps, the metaplectic zeta8 with the Clifford index-2 coset and the RM-CSS phase bit -- are ONE ladder (33/33 exact); defect-free controls (split ring, split extension, scrambled nilpotent) all fire","checked_by_registry":false,"claim_excerpt":"GAUSSIAN.RAMLADDER.01: the (1+i) ramification ladder -- the four documented roles of the ramified Gaussian prime pi2 = 1+i are ONE machine-checked object with four rungs, each re-certified from scratch, ONE module from one probe (33/33 checks, verdict RAMIFICATION-LADDER-EXACT; discovery probe gaussian_ramification_probe.py, 2026-08-07, re-run identically at promotion, promoted VERBATIM, ~5 s).  RUNG 1, NORM DOUBLING","claim_id":"GAUSSIAN.RAMLADDER.01","dependencies_as_recorded":"v689; v783; v798; v803; v819","external_data_as_recorded":"-","id":"claim:GAUSSIAN.RAMLADDER.01","location_as_recorded":"tfpt_1;tfpt_3","path":"verification/status_ledger.csv","row_number":704,"scripts_as_recorded":"v833_gaussian_ramification_ladder.py","status_as_recorded":"Exact identity/lattice-grade compression [Identity/Lattice]: all four rungs re-certified from scratch in exact arithmetic; unifies note_e8_gaussian_code/v689 (census, norm doubling), v803 (non-split jet), v783/v798/v819 (metaplectic zeta8, Clifford coset, RM-CSS phase bit); no marker move (Python-only per GATE.WOLFRAM.02)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"PG32-FLAGS-EXACT + INCIDENCE-SPLIT: 105 = 45 + 60 is the Sp(4,2)-orbit decomposition on both sides; the polarity dictionary is exact, equivariant and incidence-preserving on the 60 non-isotropic rungs; the 45 doily rungs carry the typed obstruction ((t+U) n U empty 45/45, flag Gram 18I+3J != 22I+6J) -- '105 checks = 105 flags' is a deck-equivariant bijection, NOT an incidence isomorphism","checked_by_registry":false,"claim_excerpt":"PG32.FLAGS.01: the PG(3,2) flag normal form for the 105 + 35 vacuum completion, with the incidence kill test typed as a split, ONE module from one probe (26/26 checks, verdict PG32-FLAGS-EXACT + INCIDENCE-SPLIT; discovery probe pg32_flag_completion_probe.py, 2026-08-07, re-run identically at promotion, promoted VERBATIM, < 1 s).  COUNTING NORMAL FORM: [4 choose 2]_2 = 35; 140 affine 2-flats of AG(4,2) = 35 through th","claim_id":"PG32.FLAGS.01","dependencies_as_recorded":"v689; v774; v819; v821; v822","external_data_as_recorded":"-","id":"claim:PG32.FLAGS.01","location_as_recorded":"tfpt_3","path":"verification/status_ledger.csv","row_number":705,"scripts_as_recorded":"v834_pg32_flag_completion.py","status_as_recorded":"Exact lattice/identity-grade compression with the kill typed as a split [Identity/Lattice]: 60-sector exact via the symplectic polarity (equivariant incidence dictionary), 45-sector obstructed on the doily (typed negative); compresses v819 S4 / v821 / v822 RM surfaces into the PG(3,2) normal form; no marker move (Python-only per GATE.WOLFRAM.02)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"MESSAGE-LADDER-EXACT + DOILY-PASCAL-RANK-EXACT: M_0..M_4 = (15, 30, 60, 120, 240) = 15 * 2^n with one named structure per rung (address space / h(E8) from the rebuilt root system / Gaussian lines / positive system / root census) and the coda 248 = 15*16 + 8; N N^T = B + 2I entrywise; rank N = 10 = A_Lambda, ker = 5 = g_car, multiplicity 9 = N_fam^2, top 3 = N_fam, recovery 2/3, six-step (2/3)^6 = 64/729 exact; NO (1/3)^6 doily mode (v814, no upgrade); all controls fire","checked_by_registry":false,"claim_excerpt":"v844 -- MESSAGE.LADDER.01 + DOILY.PASCAL.RANK.01: the E8 addressing formula and the Doily-Pascal rank theorem -- two exact corpus compressions, ONE module from two probes (23/23 + 16/16 checks, verdicts MESSAGE-LADDER-EXACT and DOILY-PASCAL-RANK-EXACT; discovery probes binary_message_ladder_probe.py and doily_pascal_rank_probe.py, 2026-08-07, re-run identically at promotion, promoted VERBATIM with no downscoping, ~2 ","claim_id":"MESSAGE.LADDER.01","dependencies_as_recorded":"v832; v833; v774; v814; v330; v486; v327; v775","external_data_as_recorded":"-","id":"claim:MESSAGE.LADDER.01","location_as_recorded":"tfpt_1;tfpt_3","path":"verification/status_ledger.csv","row_number":706,"scripts_as_recorded":"v844_message_doily_rank.py","status_as_recorded":"Exact identity-grade compression [Identity]: both parts exact integer/Fraction/sympy arithmetic certified against the rebuilt lattice objects (h(E8) = 30 derived from the rebuilt root system, not cited); the (1/3)^6 typed gap re-affirmed with NO upgrade (v814 cited); no marker move (Python-only per GATE.WOLFRAM.02)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"NORMAL-FORM-ASSEMBLED: C_fin = (V, hbar, q*, sigma, iota) read off the Gaussian quotient -- selector-unique q*, faithful S5 stabilizer (|Sp(4,2)| = 720, Stab = 120, orbits [1,5,10]), Pascal (1,10,5), ovoid projective reading, budget 240 = 16*15 / 248 = 16*15 + 8 against the actual census; the code-to-matter reading stays DEAD (bounds saturated 8 + 7, weight kill 8 pairs never 1); P2 narrowed to v799 R1' ([C]), not eliminated; all controls fire","checked_by_registry":false,"claim_excerpt":"v845 -- NORMALFORM.CFIN.01: the finite compiler normal form C_fin = (V, hbar, q*, sigma, iota) assembled as ONE machine-checked object from the Gaussian quotient, with the code-to-matter kill built in as a checked NEGATIVE and the remaining P2 bridge typed -- the round's central corpus compression, ONE module from one probe (28/28 checks, declared SPEC v2, verdict NORMAL-FORM-ASSEMBLED; discovery probe finite_compile","claim_id":"NORMALFORM.CFIN.01","dependencies_as_recorded":"AX.P2.01; v752; v774; v775; v799; v776; v833; MESSAGE.LADDER.01","external_data_as_recorded":"-","id":"claim:NORMALFORM.CFIN.01","location_as_recorded":"tfpt_1;tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":707,"scripts_as_recorded":"v845_cfin_normal_form.py","status_as_recorded":"Exact identity-grade normal form [Identity] with the built-in checked NEGATIVE (v775 ROOTCLASS-MIXED re-anchored via the 128-spinor counting bound + the saturated 8 + 7 census) and the typed P2 bridge: C_fin does NOT derive A1-A3 / the linearity scope / the v776 uniqueness selection -- P2 NARROWED to the v799 residual R1' ([C]), NOT eliminated; SPEC v2 declared (v836 precedent, no numeric result changed); no marker move (Python-only per GATE.WOLFRAM.02)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"CFIN-UNIQUE: admissible tuple census at omega = hbar = 14400, G-orbits = 1 (orbit-stabilizer 14400 x 6 = 86400 = |Sp(4,2) x S_5| exact); Aut(C_fin) ~= C6 (element orders [1,2,3,3,6,6], faithful into Sp(4,2), the S_5 slot permutation determined by the symplectic part); the Gaussian diagram fixes the carrier triple up to the 18-element centralizer torsor, q* selector-unique, 120 iota-completions in one orbit; strict terminal reading FAILS (typed either way); controls fire (dot form 0 refinements; wrong Arf class: empty iota set; no sigma: canonicity dies 16 -> 8 -> 4 != 1)","checked_by_registry":false,"claim_excerpt":"CFIN.UNIQUE.01: finite compiler uniqueness, one orbit and C6 automorphisms; cofinal Weil mirror moved to Prime Front. Original module ID retained; original complete mixed record is preserved in extraction provenance.","claim_id":"CFIN.UNIQUE.01","dependencies_as_recorded":"AX.P2.01; NORMALFORM.CFIN.01; MESSAGE.LADDER.01; v774; v833; v844; v845","external_data_as_recorded":"-","id":"claim:CFIN.UNIQUE.01","location_as_recorded":"tfpt_1;tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":708,"scripts_as_recorded":"v849_cfin_unique_cofinal_lean.py","status_as_recorded":"Exact identity-grade uniqueness theorem [Identity] for the finite compiler object: exhaustive finite verification over F_2^4 (no floats, no RNG, no fit; orbit-stabilizer exact); the strict terminal-object reading FAILS honestly and is typed (unique up to NON-unique isomorphism, a one-object groupoid); P2 stays NARROWED to the v799 residual R1' (why THIS normal form), NOT eliminated; no marker move (Python-only per GATE.WOLFRAM.02)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"ARF-VACUUM-SYNDROME-EXACT + OVOID-DECODER-EXACT: a(t+U) = hb(u,v) on all 140 flats; census 15/20/45/60; the local Hecke theorem 12/16 -> 28/-4 at all 15 points with x^perp/<x> semantics; pencil [15,11,3] > {[15,10,4], 2 x [15,10,3]} > [15,9,4] with the canonicity lemma (one Arf functional on H) and the vacuum bit = the RM(2,4) parity bit; N^T v_a = 0, Gram 36I - 6J, SNF diag(1^10, 0^5) torsion-free (det +-1 minor exhibited), N+ = N^T/4 - J/36 (four Penrose axioms exact in Q), P5 = I/2 - B/4 + J/12 (tr 5 = g_car), decoder exact on the predeclared set, ker = the S6 standard representation (11/11 classes), three rings (R ovoid span / Z torsion-free / F2 code A_q = [15,5,6] via v_a mod 2 = q_a)","checked_by_registry":false,"claim_excerpt":"v852 -- ARF.VACUUM.SYNDROME.01 + OVOID.DECODER.01: the Arf-vacuum syndrome theorem and the integral five-mode decoder -- the corpus's flat counts, orbit splits, Hecke matches and code enumerators compress into ONE two-bit syndrome table on the Hamming code, and the doily recovery channel gains an explicit integral inverse with the S6 standard representation identified, ONE module from two probes (24/24 + 23/23 checks","claim_id":"ARF.VACUUM.SYNDROME.01","dependencies_as_recorded":"NORMALFORM.CFIN.01; MESSAGE.LADDER.01; v774; v819; v820; v821; v834; v844; v845","external_data_as_recorded":"-","id":"claim:ARF.VACUUM.SYNDROME.01","location_as_recorded":"tfpt_1;tfpt_3","path":"verification/status_ledger.csv","row_number":709,"scripts_as_recorded":"v852_arf_vacuum_ovoid.py","status_as_recorded":"Exact identity-grade compression [Identity]: both parts exhaustive finite algebra (F_2 / Z / Q; SNF, Penrose axioms, S6 class characters exact; SET equalities, not counts); the corpus surfaces v819/v820/v821/v834/v535/v785 compressed into ONE two-bit syndrome table and the v774/v814 doily channel into ONE integral decoder; controls fire (dot form, Arf-0 labeling break, frozen-LCG permutation/pairing); no marker move (Python-only per GATE.WOLFRAM.02)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"ARF-BENT-CSS-EXACT + MANGOLDT-COMMUTATOR-EXACT: s_q-hat = -4 s_q on all 16 (W^2 = 16I, perfect autocorrelation 16 delta); (16,6,2) difference set {0} u 5bar; A_q = C_iso^perp = [15,5,6] with the 31-word structural census; [[15,5,3]] -> [[16,4,4]] (the 60 minimal words = the 60 isotropic planes, the s_Arf = 0 rows of the v852 table; vacuum transformation typed: slot +1, logical qubit -1, distance 3 -> 4); the -4 triple point Hecke = Gauss = Walsh = a_3 (v785: 32 = 28 - (-4)); the 16 bent translates a second Gram-16I frame mutually unbiased vs the characters (+-4; reported, no upgrade); L = -M[D,Z] = -[D, log Z] = T(Lambda) exact three ways (BCH truncates; log Z rational), L^k = ordered chains (nilpotency floor(log2 N) + 1), the four-comb discipline at operator level (Epstein leak [6,14,21,...] exact, first unramified 21 = 3x7, repaired by a_A + a_B = 1 * chi_{-20}; ideal-level Dedekind Lambda_K with norm aggregation (1 + chi4) Lambda), the carrier bridge (the deployed mu-pairing IS row one of L; rows are shifts; L^2 - [D,L] = T(mu*log^2) -- the Selberg hierarchy)","checked_by_registry":false,"claim_excerpt":"ARF.BENT.CSS.01: exact bent phase and CSS code identities; Mangoldt incidence experiment moved to Prime Front. Original module ID retained; original complete mixed record is preserved in extraction provenance.","claim_id":"ARF.BENT.CSS.01","dependencies_as_recorded":"ARF.VACUUM.SYNDROME.01; PRIME.RELATION.MULT.01; v535; v774; v785; v800; v819; v820; v852","external_data_as_recorded":"-","id":"claim:ARF.BENT.CSS.01","location_as_recorded":"tfpt_1;tfpt_3","path":"verification/status_ledger.csv","row_number":710,"scripts_as_recorded":"v853_bent_css_mangoldt.py","status_as_recorded":"Exact identity-grade compression [Identity] with the operator-level relation bridge typed HONESTLY as classical incidence algebra (mu*log = Lambda in matrix clothes -- the value is the packaging + the four-comb discipline transport at operator level, NOT new mathematics); the -4 triple point is ONE machine-checked integer (Hecke = Gauss = Walsh = a_3); the bent/character MUB partner of v800 REPORTED with no upgrade; controls fire; no marker move (Python-only per GATE.WOLFRAM.02)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"SIMPLEX-FOURIER-EXACT + INTERTWINER-IDENTIFIED + WINDING-QUADRATIC-EXACT: rhat = (240; -16 x15), P = (J-I)/15 with spec {1, (-1/15)^15}, two-step 1/225 exact; ramification + equidistribution at every level <= 16; packet numerator == code Walsh at every level (both [-16, 112, -448, 1136, ...]); mh2(odd n) = -1/15 for every odd n <= 16500 (integer identity, 1911 primes); q_wind = t^2 - 5t + 2 exact by the adjugate lemma; triple lock s = 6; Delta(6) = 39200 = 2 x 140^2, sole 2xsquare hit; s* ~ 2.8250 the unique Delta-root in (2,3); 7 controls fire, 2 invariances hold","checked_by_registry":false,"claim_excerpt":"v857 -- E8.SIMPLEX.FOURIER.01 + FLAVOR.WINDING.QUADRATIC.01: the E8 audits, part I -- the Gaussian census IS a Fourier law and v817's per-prime measurement is the prime restriction of a CHARACTER THEOREM (mh2(n) = -1/15 as an integer identity at EVERY odd n <= 16500), and the tfpt_2 winding line collapses to ONE rank-one determinant quadratic q_wind = t^2 - g_car t + |Z2| with the triple lock s = 6 and the reality th","claim_id":"E8.SIMPLEX.FOURIER.01","dependencies_as_recorded":"CFIN.UNIQUE.01; MESSAGE.LADDER.01; ARF.BENT.CSS.01; v4; v94; v817; v833; v844","external_data_as_recorded":"-","id":"claim:E8.SIMPLEX.FOURIER.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":711,"scripts_as_recorded":"v857_simplex_fourier_winding.py","status_as_recorded":"Exact corpus compression [typed evidence line: 26/26 + 20/20 checks, zero fails, exact integer/Fraction/sympy arithmetic throughout; the identification typed SPECTRAL-only (the packet and code gradings do not refine each other); the spinor halving stays numerical fiat; q_wind(6) = 8 = det R typed a measured coincidence; the integer-window 2xsquare census measured, not narrated]; audits of DEPLOYED claims (v817/v833/v844, tfpt_2 I.5 keyboxes) -- normal forms and identities, no new physical claim; NO RH claim; no marker move (Python-only per GATE.WOLFRAM.02)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"CLOCK-ALPHABET-SELECTIVE: Deg(G31)/4 = {2,3,5,6} = {|Z2|, N_fam, g_car, |R+(A3)|}; gcd 4 = |mu4|, lcm 120 = |R+(E8)|, lcm/gcd 30 = h(E8); (sum d/4)(sum(d-1)/4) = 16 x 15 = 240 realized on the roots (4 lines/class); (8,12,20,24) the unique product-46080/sum-64 quadruple; 607-group scan: G31 sole full-battery passer (weak-triple impostors G(20,10,4)/G(20,20,4)/G29; sum-64 coincidences G(8,2,4)/G(10,10,4)/W(H4)); family boundary m <= 120 empty; fence killed by computed centers 4 vs 1","checked_by_registry":false,"claim_excerpt":"v858 -- E8.G31.CLOCK_ALPHABET.01: the E8 audits, part II -- the compiler clock alphabet is a NORMAL FORM of G31: Deg(G31)/4 = {2, 3, 5, 6} = {|Z2|, N_fam, g_car, |R+(A3)|} with the audit identity (sum d/4)(sum (d-1)/4) = 16 x 15 = 240 REALIZED on the roots, (8, 12, 20, 24) the UNIQUE integer quadruple with product 46080 and sum 64, the 607-group rank-4 kill scan typed (G31 the SOLE full-battery passer; weak-triple an","claim_id":"E8.G31.CLOCK_ALPHABET.01","dependencies_as_recorded":"v634; v654; CFIN.UNIQUE.01","external_data_as_recorded":"-","id":"claim:E8.G31.CLOCK_ALPHABET.01","location_as_recorded":"tfpt_1;tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":712,"scripts_as_recorded":"v858_g31_clock_alphabet.py","status_as_recorded":"Exact corpus compression + selectivity audit [typed evidence line: 19/19 checks, zero fails; the honesty line kept (degree-only audits cannot separate G31 from the reducible torus Z8 x Z12 x Z20 x Z24 -- frozen scope the irreducible rank-4 Shephard-Todd list); the Molien uniqueness and the full W(D5)-fence structural refutation CITED (v634), not recomputed; X1/X2 controls fire]; a normal form plus an armed kill rule for a deployed object; NO RH claim; no marker move (Python-only per GATE.WOLFRAM.02)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"FEEDBACK-NORMALFORM-EXACT: P^{-1} R_s P = [[s+4,0,3],[0,0,-2],[4,1,5]] exact symbolic in s; chi_{R_s} = (t-s-|mu4|) q_wind - 12t; quotient Z2^2 typed NOT mu4; all sibling controls fire.","checked_by_registry":false,"claim_excerpt":"THE FEEDBACK NORMAL FORM OF THE WINDING LINE (2026-08-08 round 36, v874; discovery probe flavor_feedback_probe.py 14/14, verdict FEEDBACK-NORMALFORM-EXACT; exact sympy/integer arithmetic in every decision).  THEOREM: with the integral basis P = [2*1 | e3 | R e3] (det P = -4, SNF diag(1,2,2)) the WHOLE winding line R_s = R + s 1 e1^T conjugates EXACTLY (symbolic in s) to M(s) = [[s+4,0,3],[0,0,-2],[4,1,5]]: a gain cha","claim_id":"FLAVOR.FEEDBACK.NORMALFORM.01","dependencies_as_recorded":"E8.SIMPLEX.FOURIER.01; E8.G31.CLOCK_ALPHABET.01; v4; v857; v858","external_data_as_recorded":"-","id":"claim:FLAVOR.FEEDBACK.NORMALFORM.01","location_as_recorded":"tfpt_2_standard_model;tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":713,"scripts_as_recorded":"v874_feedback_decoder_lean.py","status_as_recorded":"Honest promotion of an exact integer theorem [typed evidence line: 14/14 checks, zero fails, verdict FEEDBACK-NORMALFORM-EXACT; all decisions exact sympy; frozen spec SHA f5f40996...]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"WINDING-DECODER-EXACT: q({2,3,5,6}) = (-4,-4,2,8); D(y) = (y+4)^2(y-2)(y-8) with budget coefficients (2,48,32,256); |mu4| q(|Z2|)/|R(E8)| = -1/15 == the Walsh message eigenvalue; typed audit-not-functor.","checked_by_registry":false,"claim_excerpt":"THE WINDING DECODER OF THE CLOCK ALPHABET (2026-08-08 round 36, v874; discovery probe g31_winding_decoder_probe.py 11/11, verdict WINDING-DECODER-EXACT; exact arithmetic).  THEOREM: the v857 winding quadratic q_wind(t) = t^2 - g_car t + |Z2| maps the G31 clock alphabet {2, 3, 5, 6} = {|Z2|, N_fam, g_car, |R+(A3)|} (v858) to the atom quadruple (-|mu4|, -|mu4|, |Z2|, h(D5)) = (-4, -4, 2, 8) -- with q(2) = q(3) FORCED b","claim_id":"E8.WINDING.DECODER.01","dependencies_as_recorded":"E8.G31.CLOCK_ALPHABET.01; E8.SIMPLEX.FOURIER.01; E8.SHELL.GLOBAL.01; FLAVOR.FEEDBACK.NORMALFORM.01; v857; v858","external_data_as_recorded":"-","id":"claim:E8.WINDING.DECODER.01","location_as_recorded":"tfpt_1_architecture_e8;tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":714,"scripts_as_recorded":"v874_feedback_decoder_lean.py","status_as_recorded":"Honest promotion of an exact integer theorem [typed evidence line: 11/11 checks, zero fails, verdict WINDING-DECODER-EXACT; frozen spec SHA 6a54768d...]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Formal [F]: the feedback normal form is a Lean theorem family (11 theorems), standard axioms only, no sorry, full build green.","checked_by_registry":false,"claim_excerpt":"LEAN 4 FORMALISATION of the feedback normal form (2026-08-08 round 36; TfptCarrier/FlavorFeedback.lean, 16 declarations, 11 theorems) -- AUDIT: PASS, no sorry, no native_decide, no domain axioms (#print axioms = propext, Classical.choice, Quot.sound on every theorem; lake build green 3418 jobs).  Kernel-checked over Z with a SYMBOLIC s (no numeric specialization smuggled in): the three action identities R_s b0 = (s+4","claim_id":"FORM.FLAVOR.FEEDBACK.01","dependencies_as_recorded":"FLAVOR.FEEDBACK.NORMALFORM.01; FORM.QGEO.01","external_data_as_recorded":"Lean 4 (leanprover/lean4 v4.29.1) + Mathlib","id":"claim:FORM.FLAVOR.FEEDBACK.01","location_as_recorded":"tfpt_2_standard_model;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":715,"scripts_as_recorded":"lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean","status_as_recorded":"Formal [F] (Lean kernel; the action identities, the inverse-free conjugation, charpoly in Z[X], the SNF determinantal divisors -- with the Z2^2-not-mu4 typing doc-level)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"SHELL-GLOBAL-THEOREM: Sp(4,2) transitivity + (1+i) doubling + Theta_L = 240 sigma_3 => Thetahat_u/Theta_L = -1/15 at ALL odd shells; census n <= 16500 retained as ward; non-transitive control breaks the law.","checked_by_registry":false,"claim_excerpt":"THE GLOBAL GAUSSIAN SHELL THEOREM (2026-08-08 round 36, v875; discovery probe gaussian_shell_global_probe.py 15/15, verdict SHELL-GLOBAL-THEOREM) -- the census->theorem upgrade: the v857 value law 'Thetahat_u/Theta_L = -1/15 on odd shells' holds for ALL shells, no census cap.  THEOREM: on V = L/(1+i)L of the Gaussian E8, for EVERY n >= 1: Theta_v(n) = (Theta_L(n) - Theta_0(n))/15 for all v != 0 (the division exact), ","claim_id":"E8.SHELL.GLOBAL.01","dependencies_as_recorded":"E8.SIMPLEX.FOURIER.01; E8.G31.CLOCK_ALPHABET.01; v857; v858; v868","external_data_as_recorded":"-","id":"claim:E8.SHELL.GLOBAL.01","location_as_recorded":"tfpt_1_architecture_e8;tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":716,"scripts_as_recorded":"v875_shell_global_lean.py","status_as_recorded":"Honest promotion of a proved shell law [typed evidence line: 15/15 checks, zero fails, verdict SHELL-GLOBAL-THEOREM; frozen spec SHA a4b2f6d9...]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Formal [F]: the shell consequence chain is a Lean theorem family (7 theorems from the named hypothesis bundle), standard axioms only, no sorry, full build green.","checked_by_registry":false,"claim_excerpt":"LEAN 4 FORMALISATION of the global shell theorem's consequence chain (2026-08-08 round 36; TfptCarrier/GaussianShells.lean) -- AUDIT: PASS, no sorry, no native_decide, no domain axioms (#print axioms = propext, Classical.choice, Quot.sound on all 7 theorems; lake build green 3418 jobs).  THE PATTERN (the house discipline): the ARITHMETIC CONSEQUENCE CHAIN is kernel-checked while the finite/structural inputs stay NAME","claim_id":"FORM.E8.SHELL.GLOBAL.01","dependencies_as_recorded":"E8.SHELL.GLOBAL.01; FORM.QGEO.01","external_data_as_recorded":"Lean 4 (leanprover/lean4 v4.29.1) + Mathlib","id":"claim:FORM.E8.SHELL.GLOBAL.01","location_as_recorded":"tfpt_1_architecture_e8;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":717,"scripts_as_recorded":"lean4-carrier-rigidity/TfptCarrier/GaussianShells.lean","status_as_recorded":"Formal [F] (Lean kernel; the consequence chain from the named ShellSystem hypotheses -- every statement an exact integer identity)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Ledger integrity enforced: unique claim_id (active + global), acyclic supersession with existing targets, unique active supersession targets modulo the frozen 2-pair allowlist, dependency cross-reference census frozen remove-only.","checked_by_registry":false,"claim_excerpt":"THE STATUS-LEDGER INTEGRITY GUARD (2026-08-08 round 36, v878_ledger_integrity.py 10/10; a CI sentinel, no new physics).  THE TRIGGER: the round-36 ledger audit found the first PRIMARY-KEY violation -- claim_id FORM.QGEO.03 double-booked (2026-06-15 CohomologyGrading formalisation; 2026-06-18 SeamDeckClosure flat all-orders closure).  THE FIX (this round, dated QA note on FORM.QGEO.04): the SeamDeckClosure row RENAMED","claim_id":"GATE.LEDGER.01","dependencies_as_recorded":"FORM.QGEO.01; FORM.QGEO.02; FORM.QGEO.04","external_data_as_recorded":"-","id":"claim:GATE.LEDGER.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":718,"scripts_as_recorded":"v878_ledger_integrity.py","status_as_recorded":"Identity [I] (CSV integrity sentinel; frozen baselines remove-only)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"FINITE-ANCHOR-CLOSED (S1): q* = polar quadric + forced linear part (1,1,1,1); weight-only (0,1,1,0,0); sigma splits 5 = 1+1+3, 10 = 1+3+3+3","checked_by_registry":false,"claim_excerpt":"v880 (part 1) -- the closed census-free normal form of the distinguished quadratic refinement: q*(x) = sum_{i<j} x_i x_j + sum_i x_i = C(|x|+1, 2) mod 2, WEIGHT-ONLY with value table (0,1,1,0,0); the 16 refinements of the bit form ARE the 16 linear shifts of the polar quadric and the frozen v845 selector acts on the linear part as c1=c2=c3 (4) -> c4=1 (2) -> c1=1 (1), FORCING c = (1,1,1,1) -- the 2^16 search is repla","claim_id":"CFIN.QSTAR.NORMALFORM.01","dependencies_as_recorded":"NORMALFORM.CFIN.01; v845; v774","external_data_as_recorded":"-","id":"claim:CFIN.QSTAR.NORMALFORM.01","location_as_recorded":"tfpt_1;tfpt_3","path":"verification/status_ledger.csv","row_number":719,"scripts_as_recorded":"v880_finite_anchor_theorems.py","status_as_recorded":"Exact identity-grade theorem [Identity]: closed boolean normal form, census-free derivation; no marker move (Python-only per GATE.WOLFRAM.02)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"FINITE-ANCHOR-CLOSED (S2/S5): doily lines = anchor multiset {2,1,1}, Vieta (4,5,2); secants = wrong anchor (1,2,2); external = (1,1,1); ladder and flavor identities in anchor notation","checked_by_registry":false,"claim_excerpt":"v880 (part 2) -- the EXCLUSIVE anchor classification of PG(3,2) lines: EVERY of the 15 doily (isotropic) lines carries the local weight multiset {2 - q*} = {2,1,1} = the anchor a = (1,1,2) (per-line charpoly (t-2)(t-1)^2, elementary symmetric (4,5,2) with e2 = g_car, e3 = |Z2|), and NO other line does: the 20 non-isotropic lines split EXACTLY as 10 secants ({0,0,1} = the WRONG anchor (1,2,2), Vieta (5,8,4)) + 10 exte","claim_id":"DOILY.ANCHOR.CLASSIFY.01","dependencies_as_recorded":"CFIN.QSTAR.NORMALFORM.01; MESSAGE.LADDER.01; v832; v844; v857","external_data_as_recorded":"-","id":"claim:DOILY.ANCHOR.CLASSIFY.01","location_as_recorded":"tfpt_1;tfpt_3","path":"verification/status_ledger.csv","row_number":720,"scripts_as_recorded":"v880_finite_anchor_theorems.py","status_as_recorded":"Exact identity-grade theorem [Identity]: the anchor law characterizes the doily among ALL 35 lines (exclusivity census 15 + 10 + 10); no marker move","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"FINITE-ANCHOR-CLOSED (S3): support partition + exact wedge factorization + bijection 15 = 5 x 3 + converse (nonzero exactly on doily lines)","checked_by_registry":false,"claim_excerpt":"v880 (part 3) -- the doily IS the multiplication table Lambda^2 E x Lambda^2 E -> Lambda^4 E of the five-slot carrier: via the v845 parity lift the three iota-supports of every doily line partition {1..5} as {i} u {j,k} u {l,m}; b_jk ^ b_lm = +-f_i EXACT (integer exterior algebra); the map line -> (i; {j,k},{l,m}) is a BIJECTION onto all 5 x 3 = 15 configurations (three perfect matchings per carrier slot); CONVERSE: ","claim_id":"DOILY.HODGE.FACTOR.01","dependencies_as_recorded":"CFIN.QSTAR.NORMALFORM.01; v845; v774; v854","external_data_as_recorded":"-","id":"claim:DOILY.HODGE.FACTOR.01","location_as_recorded":"tfpt_1;tfpt_3","path":"verification/status_ledger.csv","row_number":721,"scripts_as_recorded":"v880_finite_anchor_theorems.py","status_as_recorded":"Exact identity-grade theorem [Identity]: the incidence geometry IS the Clifford multiplication; no marker move","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"FINITE-ANCHOR-CLOSED (S4): one-step exhaustion <=> g = 5 (unique among odd g); the Calderon premise stays [O] -- the sharpened but open half of P2","checked_by_registry":false,"claim_excerpt":"v880 (part 4) -- QUADRATIC ONE-STEP EXHAUSTION FORCES g_car = 5 ([E] theorem / [O] premise split): the demand Lambda^2 E ^ Lambda^2 E = Lambda^{g-1} E (one quadratic composition step exhausts the top nontrivial half-spinor sector) holds for EXACTLY one odd g in {3, 5, 7, 9, 11}, namely g = 5 (exact rank 5 = dim Lambda^4; S+ = 1 + 10 + 5 = 16); even control g = 4 breaks the half-spinor demand.  THE THEOREM IS [E]; the","claim_id":"P2.QUADRATIC.EXHAUSTION.01","dependencies_as_recorded":"AX.P2.01; NORMALFORM.CFIN.01; v799; v845","external_data_as_recorded":"-","id":"claim:P2.QUADRATIC.EXHAUSTION.01","location_as_recorded":"tfpt_1;tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":722,"scripts_as_recorded":"v880_finite_anchor_theorems.py","status_as_recorded":"Exact algebraic theorem [Identity] with the [O]/[C] physical premise EXPLICITLY typed and NOT claimed: P2 unchanged","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"CLOSED [E]: doily = the Plucker monomial incidence of Gr(2,5) with exact signs; Specht channels (1, 0, 2/3); (16,6,2,10) anchor signature; S6 -> S5 vacuum selection","checked_by_registry":false,"claim_excerpt":"THE GR(2,5) PLUCKER READING + THE S6 SPECHT CHANNELS + THE HADAMARD ANCHOR + THE VACUUM SELECTION (closed 2026-08-09, round CV; promoted round CVIII in v888; probe s6_plucker_hadamard_probe.py 27/27 S6PLUCKER-CLOSED, exact integer/sympy): (1) the 15 doily lines ARE the 15 monomials of the five Plucker quadrics of Gr(2,5) -- bijection 15/15 with PERFECT sign match (every quadric reads (+,-,+) = the v880 Hodge table; c","claim_id":"DOILY.PLUCKER.GR25.01","dependencies_as_recorded":"CFIN.QSTAR.NORMALFORM.01; DOILY.ANCHOR.CLASSIFY.01; DOILY.HODGE.FACTOR.01; v880; v845; v844","external_data_as_recorded":"-","id":"claim:DOILY.PLUCKER.GR25.01","location_as_recorded":"tfpt_1;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":723,"scripts_as_recorded":"v888_finite_pfaffian_signature.py","status_as_recorded":"Closed finite theorems [E]: four exact statements; the physical vacuum-selection mechanism stays [O]; no marker move","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"CLOSED [E]: g^2 = sigma exact; the hexagon = the Aut(C_fin) 6-orbit on Lambda^2 E; (2/3)^6 = the recovery value; 0/600 non-automorphisms factor","checked_by_registry":false,"claim_excerpt":"THE FLAVOR HEXAGON IS THE COMPILER AUTOMORPHISM ORBIT (closed 2026-08-09, round CV; promoted round CVIII in v888; probe cfin_aut_flavor_probe.py 19/19 C6FLAVOR-MEASURED + INTERTWINED): Aut(C_fin) recomputed by exhaustive enumeration = C_6; the pinned generator g satisfies g^2 = the deployed family 3-cycle sigma EXACTLY (sharp, not inverse) and g^3 = the W-edge sheet swap (the S_2 factor of Stab_{S5}(W); honest: no sh","claim_id":"CFIN.AUT.FLAVOR.C6.01","dependencies_as_recorded":"v845; v849; v808; v857","external_data_as_recorded":"-","id":"claim:CFIN.AUT.FLAVOR.C6.01","location_as_recorded":"tfpt_1;tfpt_2;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":724,"scripts_as_recorded":"v888_finite_pfaffian_signature.py","status_as_recorded":"Closed finite theorem [E] (the intertwiner exists and is exact; the exponent reading is typed as consistent, not as the unique derivation); no marker move","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"CLOSED [E]: fermionic Pfaffian signs gauge-matched via canonical chi = Laplace/volume-form/C6 character; self-hosting forces g = 5 (N_fam = 3); mod-30 clock distinguished; operative-Coxeter-30 dead","checked_by_registry":false,"claim_excerpt":"THE FERMIONIC PFAFFIAN SIGNATURE OF THE FINITE COMPILER (closed 2026-08-09, round CVII; promoted round CVIII in v888; probe k6_pfaffian_selfhosting_probe.py 42/42 K6PFAFFIAN-CLOSED, exact integer/sympy, first frozen run): (1) THE K6 MOTIF THEOREM (CFIN.K6.MOTIF.01): under the corpus duad labeling the 35 lines of PG(3,2) are EXACTLY 15 perfect matchings of K6 (= the doily) + 10 triangles through the vacuum vertex (= t","claim_id":"DOILY.PFAFFIAN.WICK.01","dependencies_as_recorded":"DOILY.PLUCKER.GR25.01; DOILY.HODGE.FACTOR.01; P2.QUADRATIC.EXHAUSTION.01; v880; v868","external_data_as_recorded":"-","id":"claim:DOILY.PFAFFIAN.WICK.01","location_as_recorded":"tfpt_1;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":725,"scripts_as_recorded":"v888_finite_pfaffian_signature.py","status_as_recorded":"Closed finite theorems [E] + one honest kill (the operative-30 reading); the Wick-compiler premise stays [O]; no marker move","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open [O]: block functor constructed; the mixing mechanism has a constructed candidate state (v898) -- the physical realization is the demand","checked_by_registry":false,"claim_excerpt":"THE WICK FUNCTOR ARC [O] (constructed/obstructed/resolved 2026-08-09, rounds CVIII-CX; promoted round CXI in v896): (1) THE SIX ROLES EXIST in the deployed seam system (D5 slot pairs + A3 boundary block on the 16-dim one-particle space; so(16) sector law, q* edge grading, C6 intertwining all exact) but the deployed vacuum kernel is channel-diagonal (all 15 duad two-point functions vanish); (2) THE PROVED SCALAR OBSTR","claim_id":"SEAM.CFIN.WICKFUNCTOR.01","dependencies_as_recorded":"DOILY.PFAFFIAN.WICK.01; P2.QUADRATIC.EXHAUSTION.01; v888; v113","external_data_as_recorded":"-","id":"claim:SEAM.CFIN.WICKFUNCTOR.01","location_as_recorded":"tfpt_1;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":726,"scripts_as_recorded":"v896_wick_block_functor.py","status_as_recorded":"Open contract [O] (structure exact, obstruction proved, block candidate constructed; the physical mixing mechanism is the demand)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"CONSTRUCTED: the C6-covariant mixing KMS state passes all block-functor gates; exact Schur generation of all 10 carrier duads; RP-THETA-OPEN measured exclusionary at family level (v903); [O] unmoved","checked_by_registry":false,"claim_excerpt":"THE CHANNEL-MIXING CANDIDATE STATE (constructed 2026-08-09, round CXIII; promoted round CXV in v898): the v896 demand -- a channel-mixing state realizing the block Wick functor's value level -- now has a CONSTRUCTED CANDIDATE on the deployed 16-dim one-particle space.  (1) THE KMS ROUTE: the C6-covariant mixing KMS state EXISTS -- K = i h with h = -(A16_dep + A_int/8) at beta = 1 (the FIRST point of the frozen grid) ","claim_id":"SEAM.CFIN.KMSMIX.01","dependencies_as_recorded":"SEAM.CFIN.WICKFUNCTOR.01; v888; v113; v426; v440","external_data_as_recorded":"-","id":"claim:SEAM.CFIN.KMSMIX.01","location_as_recorded":"tfpt_1;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":727,"scripts_as_recorded":"v898_kms_schur_mixing.py","status_as_recorded":"Constructed candidate + exact generation identity [Numerical/Identity]: the mixing demand answered at candidate level; RP-THETA-OPEN measured exclusionary at family level (v903); the [O] premise unmoved","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"MEASURED: strict RP forces t = 0 (mixing and RP mutually exclusive); u >= t forced; 2pi-KMS locus = (t=0 beta=2pi); no root is 1/8","checked_by_registry":false,"claim_excerpt":"THE RP/MODULAR CARVING OF THE SEAM STATE SPACE (measured 2026-08-10, round CXXIV; promoted in v903): on the v898 family the reflections and the modular route CARVE for the first time.  (1) THE REFLECTION CENSUS: two spatial thetas are deployable on the 16-dim one-particle space (the sheet swap theta_S = the 16-dim lift of the v440 collar reflection, and the orientation-REVERSED 2-cycle theta_abT); the untwisted 2-cyc","claim_id":"SEAM.STATE.DERIVATION.01","dependencies_as_recorded":"SEAM.CFIN.KMSMIX.01; SEAM.CFIN.WICKFUNCTOR.01; v898; v440; v519; v526","external_data_as_recorded":"-","id":"claim:SEAM.STATE.DERIVATION.01","location_as_recorded":"tfpt_1;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":728,"scripts_as_recorded":"v903_seam_rp_exclusion.py","status_as_recorded":"Measured carving [Numerical/Identity]: RP and mixing mutually exclusive; u >= t forced; the modular locus is one point; no marker move","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"NEGATIVE: t = 1/8 is a decoration (55/55 t pass all frozen v898 gates; allowed set (0 infinity); PIN-ABSENT); thermal mixing kept as structure fact","checked_by_registry":false,"claim_excerpt":"DEAD READING (negative result, first-class; measured 2026-08-10, round CXVI; promoted in v903): 'THE MIXING STRENGTH t = 1/8 = 2pi c3/|Z2| IS A COMPILER VALUE' IS A DECORATION, NOT A DERIVATION -- the seat audit is clean (the chain beta-angle x c3/|Z2| = 2pi x (1/(8pi))/2 = 1/8 is EXACT and via v813 equivalent to 1/(I_Jones |Z2|); c3 = P1 axiom, the angle 2pi MEASURED (v526/v519/v239), |Z2| = 2 deployed (v53/v456/v44","claim_id":"SEAM.CFIN.MIXING.NORMALIZATION.01","dependencies_as_recorded":"AX.P1.01; SEAM.CFIN.KMSMIX.01; v813; v526; v898","external_data_as_recorded":"-","id":"claim:SEAM.CFIN.MIXING.NORMALIZATION.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":729,"scripts_as_recorded":"v903_seam_rp_exclusion.py","status_as_recorded":"Dead reading registered [Numerical] (negative result): the t = 1/8 reading is a decoration -- allowed set unbounded and pin absent; no marker move","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"NEGATIVE: N_fam = 3 as minimal mediation rank REFUTED (rank 1 suffices by exact sign law + integer witness; deployed S rank 2 exactly); purity = dimension bookkeeping","checked_by_registry":false,"claim_excerpt":"DEAD READING (negative result, first-class; measured 2026-08-10, round CXVII; promoted in v903): 'N_fam = 3 IS THE MINIMAL BOUNDARY-MEDIATION RANK' IS REFUTED at theorem grade for this finite size (a census/sign-level theorem, not a search negative).  PREMISES SHARPENED: O16 is EXACTLY the identity on the A3 boundary -- C6 covariance constrains only the COUPLING (24-dim, orbit-repeated 2x6 blocks, projector ward + sy","claim_id":"SEAM.CFIN.MINIMAL.MEDIATOR.01","dependencies_as_recorded":"SEAM.CFIN.KMSMIX.01; SEAM.CFIN.WICKFUNCTOR.01; v898","external_data_as_recorded":"-","id":"claim:SEAM.CFIN.MINIMAL.MEDIATOR.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":730,"scripts_as_recorded":"v903_seam_rp_exclusion.py","status_as_recorded":"Dead reading registered [Identity/Numerical] (negative result): rank 1 suffices -- the minimal-mediation reading of N_fam = 3 is refuted; purity pins 3 as dimension bookkeeping; no marker move","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"MEASURED: twisted census 16/48 involutive and 6 admissible; 0/6 with strict RP at t > 0 (TWISTED-RP-EXCLUSIONARY); exclusion survives every C6 twist","checked_by_registry":false,"claim_excerpt":"THE COMPLETE TWISTED-OS CENSUS IS EXCLUSIONARY (measured 2026-08-10, round CXXXI; promoted in v903): the COMPLETE census of C6-twisted reflections Theta_g = U_g o theta (2 bases x 6 C6 powers x 4 degree twists = 48 candidates) admits EXACTLY 16 involutions (Theta^2 = 1 <=> 3 | k, eta-independent; the law q^2 = img^{2k} verified indexwise -- the 3-cycle of pi forces k in {0, 3}), of which 6 are Gram-hermitian at the b","claim_id":"SEAM.CFIN.TWISTED.RP.01","dependencies_as_recorded":"SEAM.STATE.DERIVATION.01; SEAM.CFIN.KMSMIX.01; v898; v519","external_data_as_recorded":"-","id":"claim:SEAM.CFIN.TWISTED.RP.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":731,"scripts_as_recorded":"v903_seam_rp_exclusion.py","status_as_recorded":"Measured complete census [Numerical] (negative result): 0 of 6 admissible twisted reflections admit strict RP at t > 0; no marker move","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"MEASURED: DILATION-SPLIT -- marginal theta_abT witness on the cone boundary; t^2*3m/(1-m^2) = 1/200 exact; strict collar obstructed (defect magnitude 2t)","checked_by_registry":false,"claim_excerpt":"THE DILATION ROUTE SPLITS (measured 2026-08-10, round CXXXII; promoted in v903): on the explicit C6-covariant parent family over the v898 split 16 = 10 (+) 6 the dilation mechanism is REALIZED for the 2-cycle reflection -- every one of the 28 CAR-valid s = 0 points is theta_abT-MARGINAL RP (parent a_J = 0, 1p Gram eigenvalues EXACTLY {0, 0}: the cone boundary), and the Schur compression of the v898 M2 parent (kappa =","claim_id":"SEAM.CFIN.RP.DILATION.01","dependencies_as_recorded":"SEAM.STATE.DERIVATION.01; SEAM.CFIN.TWISTED.RP.01; SEAM.CFIN.KMSMIX.01; v898","external_data_as_recorded":"-","id":"claim:SEAM.CFIN.RP.DILATION.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":732,"scripts_as_recorded":"v903_seam_rp_exclusion.py","status_as_recorded":"Measured split [Numerical/Identity]: a marginal cone-boundary witness with the exact 1/200 floor; the strict collar route obstructed by an exact linear law; no marker move","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"MEASURED: Pf(A_dep + t A_int) = -(t-1)(3t^2-1)(9t^3+21t^2-t-1) exact; t_gap unique in (0 1/4] (Sturm); kernel dim exactly 2; coupling load-bearing","checked_by_registry":false,"claim_excerpt":"t_gap IS THEOREM-SHAPED (measured 2026-08-10, round CXXXIII; promoted in v903): t_gap = 0.2309488708... is the UNIQUE positive root of the irreducible cubic q(t) = 9t^3 + 21t^2 - t - 1 (exact Sturm count: 1 on (0, infinity) and 1 on (0, 1/4] -- the root is interior to the deployed region), which divides the EXACT Pfaffian of the FIXED integer pencil: Pf(A_dep + t A_int) = -(t-1)(3t^2-1) q(t) EXACTLY (degree <= 8 iden","claim_id":"SEAM.CFIN.GAP.PENCIL.01","dependencies_as_recorded":"SEAM.STATE.DERIVATION.01; SEAM.CFIN.RP.DILATION.01; v898","external_data_as_recorded":"-","id":"claim:SEAM.CFIN.GAP.PENCIL.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":733,"scripts_as_recorded":"v903_seam_rp_exclusion.py","status_as_recorded":"Measured exact pencil identity [Identity/Numerical]: t_gap as a generalized eigenvalue with Sturm uniqueness; three surfaces one variety; no marker move","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"MEASURED: strict 2-cycle RP impossible on the whole covariant class (M1 = diag(a_J, -a_J) exact); the s = 0 stratum is marginal not isolated; Pf4(eps) = (eps - 1/200)(eps + 1/200) -- crossover at the 1/200 floor","checked_by_registry":false,"claim_excerpt":"STRICT 2-CYCLE RP IS IMPOSSIBLE ON THE WHOLE COVARIANT CLASS (measured 2026-08-10, round CXXXVIII(60); promoted in v908): the closure-vs-isolated dilemma of the v903 marginal witness is REFUTED AS A DILEMMA -- the theta_abT sector Grams see ONLY the channel-{4,5} 4x4 seat (ward 1e-14), covariance allows there EXACTLY the J coordinate (integer defect 2 for I/X/Z units, 0 for J; c4 = c5 forced), and the exact symbolic ","claim_id":"SEAM.CFIN.MARGINAL.STABILITY.01","dependencies_as_recorded":"SEAM.STATE.DERIVATION.01; SEAM.CFIN.RP.DILATION.01; SEAM.CFIN.KMSMIX.01; v898; v903","external_data_as_recorded":"-","id":"claim:SEAM.CFIN.MARGINAL.STABILITY.01","location_as_recorded":"tfpt_1;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":734,"scripts_as_recorded":"v908_seam_equilibrium_wiring.py","status_as_recorded":"Measured covariant exclusion [Identity/Numerical]: interior empty (exact +-a_J law), floor exchange Pf4 = (eps - 1/200)(eps + 1/200); escape only by symmetry breaking at price 2 eps; no marker move","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"CLOSED (NOT-NEEDED): stationary => sigma == 0 exactly and drive buys no RP; V_J/V_Z equilibrium witnesses with J coordinate exactly 1/200; PURE-I is the maximally obstructed direction -- SEAM.STATE.WIRING.SELECTOR.01 registered next","checked_by_registry":false,"claim_excerpt":"NO NESS NEEDED -- THE PRICE OF THE MIXING IS EXACTLY ZERO ENTROPY PRODUCTION (demand closed as NOT-NEEDED; measured 2026-08-10, round CXXXIX(60); promoted in v908): strict theta_S (collar) hermiticity is a TWO-SEAT LINEAR LAW of the coupling -- the 1p seat A_{x+1,y} + A_{x,y+1} kills the X-, the deg-2 empty seat A_{x,y} + A_{x+1,y+1} the I-subblock coordinates; exact rank 12, kernel 12 = the {J, Z} coordinates of the","claim_id":"SEAM.CFIN.NESS.PARENT.01","dependencies_as_recorded":"SEAM.CFIN.MARGINAL.STABILITY.01; SEAM.STATE.DERIVATION.01; SEAM.CFIN.KMSMIX.01; v898; v903","external_data_as_recorded":"-","id":"claim:SEAM.CFIN.NESS.PARENT.01","location_as_recorded":"tfpt_1;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":735,"scripts_as_recorded":"v908_seam_equilibrium_wiring.py","status_as_recorded":"Demand closed NOT-NEEDED [Identity/Numerical]: equilibrium J/Z witnesses carry the full 1/200 mixing at zero entropy production; the deployed wiring is PURE-I (maximally obstructed); wiring-selector contract registered; no marker move","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"CLOSED (DEPLOYMENT-CHOICE): exactly one admissible wiring component mod rule gauge; pure-I interior + integer-gauge-connected to pure-J; theta_S conventional (five demand classes silent); strict-collar RP exactly frame-covariant, exclusion = frame statement; Z/X exclusion orbit-invariant","checked_by_registry":false,"claim_excerpt":"THE WIRING FREEDOM THEOREM -- IS PURE-I COMPILER-FORCED?  ANSWERED: NO -- DEPLOYMENT-CHOICE, NOT COMPILER THEOREM (the v908-registered contract, closed 2026-08-12, rounds 69-71 notes CCXIII/CCXV/CCXXI; promoted in v911).  (1) THE EXACT GROEBNER CENSUS (30/30, WIRING-DEGENERATE): the C6-equivariant commutant of the coupling space is EXACTLY 24-dim (the boundary C6 action is the identity), the IOTA rule subspace 8-dim ","claim_id":"SEAM.STATE.WIRING.SELECTOR.01","dependencies_as_recorded":"SEAM.CFIN.NESS.PARENT.01; SEAM.CFIN.MARGINAL.STABILITY.01; SEAM.STATE.DERIVATION.01; v898; v903; v908","external_data_as_recorded":"-","id":"claim:SEAM.STATE.WIRING.SELECTOR.01","location_as_recorded":"tfpt_1;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":736,"scripts_as_recorded":"v911_wiring_freedom.py","status_as_recorded":"Contract closed as measured freedom theorem [Identity/Numerical]: one admissible wiring orbit (C_rot), Z/X excluded gauge-invariantly; pure-I = deployment representative; RP exclusion frame-relative (option 2); 'pure-I is compiler-forced' FORBIDDEN; [O] premise of v898/v903 unmoved; no marker move","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Kinematics certified [E]: reciprocal-in-D_4 + conformal rigidity (2D needs tau, 3D automatic) + Stinespring reduced-channel reset + lens-crossover uplift + KMS closure (tick = e^{-H_mod}) + holonomy dictionary (seam strings = GSO 2-torsion) + selector-uniqueness necessity + frozen top-hat kernel; the cyclic/CCC reading stays [C]; the dynamics stay WOIT.OS.TWISTOR.01 [O]","checked_by_registry":false,"claim_excerpt":"THE CCC CROSSOVER KINEMATICS DICTIONARY [E] (rounds DL-DLV, notes 2026-08-24; promoted 2026-08-24).  EXACT (v957; six probes 28/28 + 29/29 + 18/18 + 21/21 + 14/14 + 7/7 embedded byte-exact, hashes pinned): (1) Penrose's reciprocal gauge Omega*tau(Omega) = -1 is the element tau = rho^2 sigma of the proven mu_4 Moebius stabiliser D_4; tau reverses the clock (= the Z_2 sheet parity), swaps the aeon poles {0, inf}, fixes","claim_id":"CCC.SEAM.KINEMATICS.01","dependencies_as_recorded":"QGEO.CONF.01 (the seam premise); v221 (transport); v492 (deck/clock, A_3 ALE); v519/v521/v522 (Theta, side-blindness, GSO wrap); v526 (KMS normalisation); v529/v534 (straddle law + selector, cited); VGEO.TORSOR.01 (unit calibration untouched); rounds DL-DLV","external_data_as_recorded":"Planck 2018 cosmography (typed external: eta_rec, eta_0, Omega_K, Omega_L, H_0, n_s, r bounds -- kernel freeze and fork pricing only)","id":"claim:CCC.SEAM.KINEMATICS.01","location_as_recorded":"origin_theory;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":737,"scripts_as_recorded":"v957_ccc_crossover_kinematics.py","status_as_recorded":"Certified kinematics dictionary [E] (fine types Identity/Formal (Moebius/D_4 algebra, Stinespring isometry, Hopf equivariance, commutant dimensions, symbolic Einstein/Weyl checks, KMS/detailed-balance identities, Theta-reality censuses -- exact on corpus objects) and Numerical (linking integrals, Obata scans, band arithmetic pinned); the CCC/cyclic READING itself stays [C] and is NOT upgraded; WOIT.OS.TWISTOR.01 stays [O] with all kill tests live)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open [O]: D1 interacting algebra on the crossover (WOIT gamma) + D2 field-level Stinespring + D3 cosmology fork decision = the remaining demands; D4 EXECUTED with a robust null (p_global 0.673, BH-q 0.673, injection recovery 100 percent, K1-K6 NA; results.json) -- no kill fired; kinematic base certified in v957","checked_by_registry":false,"claim_excerpt":"THE CCC CROSSOVER CONTRACT [O] (registered 2026-08-24 from the external TFPT-vs-CCC adjudication of the six gates; the kinematic base is CCC.SEAM.KINEMATICS.01 [E]/v957).  DEMAND (the dynamical crossover, in order): (D1) the interacting seam algebra A_hol realised ON the lens crossover X = S^3/Z_4 with reflection positivity protected on the mid-gap cut class while the aeon transfer uses the through-mark class (the tw","claim_id":"CCC.SEAM.CROSSOVER.01","dependencies_as_recorded":"CCC.SEAM.KINEMATICS.01 (the certified base); WOIT.OS.TWISTOR.01 (gamma = D1); SEAM.THERMAL.KMS.01 (the kappa chain); v529/v534 (the straddle fence); experiments/ccc-crossover-disc (the frozen search)","external_data_as_recorded":"Planck 2018 / BICEP-Keck bounds and LiteBIRD/CMB-S4 sensitivities (typed external, fork pricing); Planck PR3 SMICA map COM_CMB_IQU-smica_2048_R3.00_full.fits (D4 data pass, SHA-256 60952c645eb33d151905ddf5837477e15ca02a3261feca4ceca3c3feece4f9ac, 2013312960 bytes)","id":"claim:CCC.SEAM.CROSSOVER.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":738,"scripts_as_recorded":"v957_ccc_crossover_kinematics.py","status_as_recorded":"Open contract [O] (research contract; the kinematic base [E] via v957; the dynamics = WOIT.OS.TWISTOR.01 gamma on the crossover geometry; D4 executed 2026-08-24 with a robust preregistered null -- no kill fired, no type change; the contract stays open via D1-D3)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Firewall in force: no 1+1D theorem closes a 3+1D claim; every closure carries dimension typing of hypotheses and conclusion; route ordering registered","checked_by_registry":false,"claim_excerpt":"THE DIMENSION-UPLIFT FIREWALL (registered 2026-08-27 from the external deep review: 'chiral 1+1D seam net does NOT imply a local, interacting 3+1D quantum world').  STANDING RULE, in force immediately: (F1) no theorem whose hypotheses live in 1+1D (chiral net, VOA, lattice collar, seam circle) may be cited as CLOSING a claim about 3+1D physics; (F2) every contract closure must state the spacetime dimension of its hyp","claim_id":"DIMENSION.UPLIFT.FIREWALL.01","dependencies_as_recorded":"SEAM.EQUIV.01; WOIT.OS.TWISTOR.01; CCC.SEAM.KINEMATICS.01 (kinematic only)","external_data_as_recorded":"-","id":"claim:DIMENSION.UPLIFT.FIREWALL.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":739,"scripts_as_recorded":"-","status_as_recorded":"Firewall (standing discipline rule, in force; the uplift theorems it names stay Open)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open: the named seam->bulk 4D reconstruction theorem (seven demands B1-B7); no corpus result closes any part","checked_by_registry":false,"claim_excerpt":"THE SEAM-TO-BULK 4D RECONSTRUCTION CONTRACT [O] (registered 2026-08-27): the theorem previously only implicit between the SEAM.EQUIV.01 conclusion (a chiral c=8 boundary object, 1+1D) and the WOIT.OS.TWISTOR.01 goal (a Poincare-covariant causal chiral 4D theory) is made explicit as its own named target.  DEMAND: from seam data alone construct a 4D family of local algebras (equivalently Schwinger functions) and prove ","claim_id":"SEAM.BULK4D.RECON.01","dependencies_as_recorded":"DIMENSION.UPLIFT.FIREWALL.01; SEAM.EQUIV.01; WOIT.OS.TWISTOR.01; QFT4D.OS.RECON.01; CHIRAL4D.NOMIRROR.01","external_data_as_recorded":"-","id":"claim:SEAM.BULK4D.RECON.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":740,"scripts_as_recorded":"-","status_as_recorded":"Open (research contract)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the finite kernel half: Q = log T is an exact Markov generator (row sums 0, off-diagonals ln(9/8), 2ln3, 2ln3 > 0, uniformization positivity for all t >= 0); [O] the field-level embedding","checked_by_registry":false,"claim_excerpt":"THE MARKOV EMBEDDING CONTRACT (registered 2026-08-27; 'three meanings of dynamics' split, step (a)->(b)).  FINITE KERNEL HALF [E] (v971, sympy-exact): for the v221 seam transfer kernel T (spectrum exactly {1, 64/729, 1/729}) the principal logarithm Q = log T is an EXACT classical Markov generator -- e^Q = T by exact spectral calculus; row sums symbolically zero; off-diagonals exactly {ln(9/8), 2 ln 3, 2 ln 3} = {0.11","claim_id":"DYN.MARKOV.EMBED.01","dependencies_as_recorded":"v221 (kernel); v957 (T = e^{-H_mod}); CONTRACT.F.01 (axiom 3 positivity); v723/v724/v777 (external clocks)","external_data_as_recorded":"-","id":"claim:DYN.MARKOV.EMBED.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":741,"scripts_as_recorded":"v971_markov_embedding_generator.py","status_as_recorded":"Contract [E] (finite kernel embedding, sympy-exact; v971) + [O] (field level)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] (2026-08-28, v984): discrete collision/QCA-band dilation.  [E] (2026-08-28, v987): kernel OS continuation exact + size-uniform free band + interacting congruence family + quantum SWAP coupling (d(theta)~theta^1.99, CPTP, LR radius 1).  [O] continuous field-level OS reconstruction, thermodynamic-limit branch selection, any 3+1D reading; no marker move.  | 2026-08-29 v999: finite ladder COMPLETE (incl. continuous-time weak-collision HP); open = thermodynamic field limit only.  Display stays [O].","checked_by_registry":false,"claim_excerpt":"THE UNITARY DILATION CONTRACT [O] (registered 2026-08-27; 'three meanings of dynamics' split, step (b)->(c)).  The continuous semigroup e^{tQ} (DYN.MARKOV.EMBED.01) is irreversible statistical dynamics; fundamental quantum dynamics needs T = e^{-aH} -> (OS) -> U(t) = e^{-itH} with H positive self-adjoint.  DEMAND: (D1) a Stinespring/Hamiltonian dilation of the semigroup with (quasi-)local generator; (D2) size consist","claim_id":"DYN.UNITARY.DILATION.01","dependencies_as_recorded":"DYN.MARKOV.EMBED.01; CCC.SEAM.CROSSOVER.01 (D2); QFT4D.OS.RECON.01","external_data_as_recorded":"-","id":"claim:DYN.UNITARY.DILATION.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":742,"scripts_as_recorded":"v984_markov_qca_dilation.py; v987_os_dilation_package.py; v999_weak_collision_hp.py","status_as_recorded":"Open [O] + finite ladder complete [E]/[N] (discrete/kernel/field-free/interacting-classical/quantum-coupled/continuous-time; open = thermodynamic field limit only)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the Birkhoff fibre of B is the sign-character line t in [0,1/18]; loop-current discriminator Psi_t(A) = 6t A; qubit Choi law -3t/2 with EB criticality 2/3 + 1/3 = 1; full-level NPT -(1/3)(2/3)^n; the deployed Kraus dilation is EB (Q = 0, C_0 = 0); binary-message KKT certificates; [C] defect-Birkhoff value coincidence (forcing functor OPEN as TRANSFER.DEFECT.BIRKHOFF.01)","checked_by_registry":false,"claim_excerpt":"THE HIDDEN CIRCULATION CONTRACT, executed half (registered 2026-08-27; external-review round, companion of the DYN.MARKOV.EMBED.01/DYN.UNITARY.DILATION.01 split).  [E] (v976, sympy/Fraction-exact): (1) the Birkhoff fibre of the seam single step B (exact sixth root of the v221 kernel; B = (1/2)I + (1/18)P12 + (2/9)P13 + (2/9)P23 bit-exact) is EXACTLY a one-parameter line w_t, t in [0, 1/18], because the decomposition ","claim_id":"TRANSFER.HIDDEN.CIRCULATION.01","dependencies_as_recorded":"DYN.UNITARY.DILATION.01; DYN.MARKOV.EMBED.01; QEC.SEAM.01; v221_seam_qecc.py; v652_orbifold_arf.py","external_data_as_recorded":"-","id":"claim:TRANSFER.HIDDEN.CIRCULATION.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":743,"scripts_as_recorded":"v976_seam_lift_birkhoff.py","status_as_recorded":"Identity [E] (executed half: fibre line, discriminator, criticality, EB no-go, KKT) + literature [C]; fibre-point selection open","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] B unistochastic with exact SU(3) lift {U, U*}, J = +-1/27; 5-12-13 plaquette code (norms {10,13,130,169}); center bridge disc chi_A = 65 = det(A-I)^2 + (det A/2)^2 with sibling negatives; rationality selection (J_n rational only at n = 1); census unique full-code point = deployed (2/3, 1/3); no fixed microstep (Dirichlet witness); [C] coherification literature; PMNS near-miss stays negative; sgn J and the intertwiner OPEN","checked_by_registry":false,"claim_excerpt":"THE COHERENT WILSON CONTRACT, executed half (registered 2026-08-27; external-review round, companion of TRANSFER.HIDDEN.CIRCULATION.01).  [E] (v977, sympy-exact): (1) UNISTOCHASTICITY: the seam single step B equals |U_ij|^2 entrywise for an exact U in SU(3); the angles are forced by B (sin^2 th13 = 2/9, sin^2 th12 = 1/14, sin^2 th23 = 2/7), cos delta = -4/sqrt(65) is uniquely solved, so the complete lift set up to re","claim_id":"TRANSFER.COHERENT.WILSON.01","dependencies_as_recorded":"TRANSFER.HIDDEN.CIRCULATION.01; DYN.UNITARY.DILATION.01; v530_center_quotient_compiler.py; v738_hecke_mod_ramified.py; v270_pmns_jarlskog_assembly.py","external_data_as_recorded":"-","id":"claim:TRANSFER.COHERENT.WILSON.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":744,"scripts_as_recorded":"v977_transfer_unistochastic_wilson.py","status_as_recorded":"Identity [E] (executed half: unistochastic lift, Wilson code, center bridge, selectivity census) + literature [C]; branch selection and intertwiner open","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open: the nonperturbative 4D OS package (RP, Euclidean covariance, clustering, uniform bounds, continuum limit, reconstruction); the all-orders EG/BRST leg is fenced as local-perturbative-under-hypotheses","checked_by_registry":false,"claim_excerpt":"THE 4D OSTERWALDER-SCHRADER PACKAGE CONTRACT [O] (registered 2026-08-27; step (3) of the DIMENSION.UPLIFT.FIREWALL.01 route ordering).  INPUT: TFPT fixes the discrete data (representation content, charge lattice, coupling relations, boundary conditions -- the seam as internal/topological boundary module); the genuine 4D Euclidean lattice carries spacetime, gauge fields, Higgs, fermions.  DEMAND: (O1) reflection posit","claim_id":"QFT4D.OS.RECON.01","dependencies_as_recorded":"DIMENSION.UPLIFT.FIREWALL.01; QFT4D.EG.ALLORDER.01 (fenced perturbative leg)","external_data_as_recorded":"-","id":"claim:QFT4D.OS.RECON.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":745,"scripts_as_recorded":"-","status_as_recorded":"Open (research contract; binding phrasing rule in force for the perturbative leg)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open: explicit GW/overlap chiral lattice operator for the TFPT content.  EXECUTED (v989): 1+1D Gauss census (single-exponent iff vectorlike; two-exponent always).  No 3+1D closure.  EXECUTED (v997): SMG mechanism toy-proved [E] (N=8 unique Spin(7) singlet, gap 14 volume-independent; N=4 2^L contrast; physical edge pi/L exact).  4D Spin(10) theorem stays [O].  No 3+1D closure.  WAVE-5 (2026-08-29, v1002): number-preserving Casimir projector route excluded (census N=8:0, k=2:27, k=3:1463, |W(D5)|=1920).  Display unmoved Open. | ROUND3 2026-09-05: finite derivative-filtered block only; no invariant mirror-response gap, Weyl cone, many-body realization or 4D closure. Display stays [O]. | ROUND-4 CURRENT: v1027 repairs canonical DET excitations under the singlet premise and preserves signed z=1 dispersion for fixed c-number gauge fields. It changes flatDeltaQ to additiveDeltaNa. No hard bare-mirror gap, quantum-link CAR diagonalization, chiral SM or continuum closure; [O] unchanged.","checked_by_registry":false,"claim_excerpt":"THE CHIRAL 4D LATTICE MATTER CONTRACT [O] (registered 2026-08-27; step (4) of the firewall route ordering).  The seam's c_- = 8 and Chern/inflow structure are a boundary-ANOMALY signal, not yet 4D matter.  DEMAND: an explicit chiral lattice operator (Ginsparg-Wilson/overlap type) for the TFPT representation content with proofs of (C1) a local gauge-invariant fermion measure; (C2) perturbative AND global anomaly freed","claim_id":"CHIRAL4D.NOMIRROR.01","dependencies_as_recorded":"DIMENSION.UPLIFT.FIREWALL.01; QFT4D.OS.RECON.01; WOIT.OS.TWISTOR.01 (kill test 3)","external_data_as_recorded":"-","id":"claim:CHIRAL4D.NOMIRROR.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":746,"scripts_as_recorded":"v989_lattice_gate_battery.py; v997_spin2_smg_witnesses.py; v1002_spin10_mirror_projector.py; v1023_derivative_filtered_wall.py","status_as_recorded":"Open (research contract; 1+1D chiral Gauss census executed; SMG mechanism toy-proved [E]; Nielsen-Ninomiya as Gauss statement; 4D Spin(10) theorem stays [O]; no 3+1D closure) | Round-3 v1023 adds an exact finite block lemma [E]/conditional GW reading [C]; NOMIRROR remains Open [O].","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Firewall in force: every BW/CHM use declares assumption-vs-result; Einstein-derivation chain typed conditional on the 4D package; census of all current usages recorded","checked_by_registry":false,"claim_excerpt":"THE BISOGNANO-WICHMANN DIRECTION FIREWALL (registered 2026-08-27, with audit census).  BW is a theorem WITHIN an already-local Poincare-covariant QFT with suitable vacuum (wedge modular flow = boost); it does NOT generate Lorentz spacetime from an arbitrary modular flow (Poincare-covariant nets violating BW exist: Mund arXiv:hep-th/0101227, Morinelli arXiv:1703.06831).  Correct order: 4D net + locality + vacuum + spe","claim_id":"GRAV.NONCIRCULAR.01","dependencies_as_recorded":"QFT4D.OS.RECON.01; QGEO.SYM.01; QG.AMB.01; SEAM.EQUIV.01","external_data_as_recorded":"-","id":"claim:GRAV.NONCIRCULAR.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":747,"scripts_as_recorded":"-","status_as_recorded":"Firewall (standing discipline rule, in force; audit census recorded)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Principle registered: eigenvalue + projection + coupling = signature.  EXECUTED (v990): finite W[J] mixed-derivative transduction shadow (link transduces, e^c control = 0).  Per-bundle middle-arrow proofs stay Open.","checked_by_registry":false,"claim_excerpt":"THE TRANSDUCTION PRINCIPLE CONTRACT (registered 2026-08-27; elevates the S15 typing rule to a named principle).  PRINCIPLE: observable signature = internal eigenvalue [compiler] + nonvanishing projection B P_r != 0 [transduction] + physical coupling operator [physics].  WITHOUT THE MIDDLE ARROW, NEITHER A NON-OBSERVATION FALSIFIES NOR AN OBSERVATION CONFIRMS.  Minimal model machine-checked at exploration level (exper","claim_id":"OBS.TRANSDUCTION.01","dependencies_as_recorded":"v221 (kernel); FO.01 (exploration minimal model); FRB/GW scorecard rows (readout typing)","external_data_as_recorded":"-","id":"claim:OBS.TRANSDUCTION.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":748,"scripts_as_recorded":"v990_wj_transduction_mechanism.py","status_as_recorded":"Contract (principle registered; finite W[J] transduction shadow executed; per-bundle proofs stay Open)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open: joint likelihood with atom-induced covariance, effective dof, prespecified null + formula grammar, real holdout.  EXECUTED [N] (v992): v1 chi2=11.80/9, p=0.225, nu_eff=1, 0th percentile of 200 scrambled decoders, LOO stable; promotion conditions typed.  Display marker stays Open.","checked_by_registry":false,"claim_excerpt":"THE JOINT LIKELIHOOD CONTRACT [O] (registered 2026-08-27; from hit-counting to overdetermined relations).  The 27+ individually matched values descend from the same few atoms (phi_0, c_3, g_car, mu_4) and are statistically CORRELATED: counting hits overstates independent evidence.  DEMAND: reorganize the evidence into overdetermined relation bundles, each carried by one proof object -- (i) the flavor invariant sum ru","claim_id":"PRED.JOINTLIKELIHOOD.01","dependencies_as_recorded":"v84 (frozen registry); v100 (null MC, reinterpreted); v375 (scorecard); OBS.TRANSDUCTION.01","external_data_as_recorded":"-","id":"claim:PRED.JOINTLIKELIHOOD.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":749,"scripts_as_recorded":"v992_joint_likelihood_v1.py","status_as_recorded":"Open (statistics-construction contract; v1 executed [N]; promotion conditions typed)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] JP made decidable (unique B) + free FK certified on all 8 cuts + confusion 23/12/0/0 + quartic class EMPTY on the basis => the straddle law refined to the ODD-SPLIT LAW (JP-predicted, measurement-confirmed); toy level, fence inherited","checked_by_registry":false,"claim_excerpt":"THE ODD-SPLIT LAW (measured 2026-08-27; promoted in v972): the v529 straddle law refined on the 16-Majorana FK seam toy via the Jaffe-Pedrocchi Majorana-RP class made DECIDABLE -- the crossing coefficient matrix B is UNIQUE (left-monomial pairs biject onto crossing monomials), so 'B Hermitian AND -B PSD' is a finite check.  (1) THE INSTRUMENT: the checker certifies the free FK Hamiltonian on all 8 bond cuts (twist et","claim_id":"SEAM.INT.ODDSPLIT.01","dependencies_as_recorded":"SEAM.INT.FKTOY.01; WOIT.OS.TWISTOR.01; v529; v903","external_data_as_recorded":"Jaffe-Pedrocchi arXiv:1406.1384; Wei-Li-Xiang arXiv:1601.01994 -- literature framing, no data","id":"claim:SEAM.INT.ODDSPLIT.01","location_as_recorded":"tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":750,"scripts_as_recorded":"v972_seam_interaction_front.py","status_as_recorded":"Measured/Exact [E] (toy level; JP sufficient-only; v529 fence inherited); no marker moves","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the avoiding family generates the full even algebra (rank 15) and carries a positive OS/GNS structure at g = 1 while the straddled control fails; kill-test-2 counterweight narrowed, not removed; toy level","checked_by_registry":false,"claim_excerpt":"OS VIABILITY ON THE QUARTET-AVOIDING FAMILY (measured 2026-08-27; promoted in v972): the v529 kill-test-2 counterweight -- (1) the straddle census 24/24 reproduced; (2) the clock-invariant m = 4 member's quartet-avoiding cut family generates the FULL even seam algebra (rank 15, dim 32768 = 2^15; the single-cut members m = 2/6 carry a typed deficit of EXACTLY 1); (3) OS/GNS on the avoiding cut k = 3 at g = 1 is POSITI","claim_id":"SEAM.INT.OSAVOID.01","dependencies_as_recorded":"SEAM.INT.FKTOY.01; SEAM.INT.ODDSPLIT.01; WOIT.OS.TWISTOR.01; v529","external_data_as_recorded":"-","id":"claim:SEAM.INT.OSAVOID.01","location_as_recorded":"tfpt_3;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":751,"scripts_as_recorded":"v972_seam_interaction_front.py","status_as_recorded":"Measured [E] (toy level; v529 fence inherited); no marker moves","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] census: theta_abT kills exactly one coordinate (32-dim marginal hyperplane {a_J = 0}); theta_S leaves a 17-dim neutral subspace with strict witnesses; the v903 exclusivity typed ray-/reflection-relative; premise unmoved  EXECUTED UPDATE (2026-08-28, v995): finite KMS rigidity [E] -- all 33 mixing directions killed; covariance redundant; 196608 -> 0. Type-III/continuum stays [O].  WAVE-5 (2026-08-29): continuum leg listed as a child of SEAM.MMST.TYPEIII.CHARGED.01 [O]; finite KMS rigidity unmoved.  Display unmoved.","checked_by_registry":false,"claim_excerpt":"THE RP MIXING CENSUS (measured 2026-08-27; promoted in v972): the v903 exclusivity is RAY- and REFLECTION-relative, NOT slice-wide.  The full 33-dim C6-covariant mixing slice censused under BOTH deployable reflections: (1) theta_abT sees exactly ONE coordinate -- a_J, killed 1st order odd / 2nd order even, kernel value -1/(1+c^2) = -0.8240271368 at c = tanh(1/2) -- and 32/33 directions are identically invisible => a ","claim_id":"SEAM.STATE.RPMIXING.01","dependencies_as_recorded":"SEAM.STATE.DERIVATION.01; SEAM.CFIN.KMSMIX.01; v903; v898","external_data_as_recorded":"-","id":"claim:SEAM.STATE.RPMIXING.01","location_as_recorded":"tfpt_1;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":752,"scripts_as_recorded":"v972_seam_interaction_front.py; v995_kms_subnet_rigidity.py","status_as_recorded":"Measured census [E] (sector-truncated; float64 exploration grade warded by exact identities) + finite KMS rigidity [E] (v995); type-III/continuum stays [O]; no marker moves","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] the executable OS skeleton is shared 5/5 with all divergences control-typed to the checkerboard mechanism; an executable-level narrowing -- does NOT close either route or the parent","checked_by_registry":false,"claim_excerpt":"THE CROSS-ROUTE OS SKELETON (2026-08-27, v973): the two continuum routes of the seam equivalence target -- the MMST scaling-limit route (the p+ip collar edge) and the twistor route's Z4 lattice object -- share the EXECUTABLE OS skeleton: all FIVE WOIT kill-test main invariants (alpha: forced eta = +i, Theta^2 = +1, bond RP; beta1: GSO 2-torsion; beta2: OS quotient exists + KMS expansion lambda_max > 1; beta3: perp de","claim_id":"SEAM.EQUIV.SKELETON.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.EQUIV.MMST.01; SEAM.EQUIV.TWISTOR.01; WOIT.OS.TWISTOR.01","external_data_as_recorded":"-","id":"claim:SEAM.EQUIV.SKELETON.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":753,"scripts_as_recorded":"v973_seam_route_narrowing.py","status_as_recorded":"Exact [E] (executable skeleton; fine types Lattice/Numerical for the collar battery, Identity for the S0 mechanism gates)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Exact witnesses for both faces; target stays open","checked_by_registry":false,"claim_excerpt":"THE TWO NAMED FACES OF ALPHA.QUILLEN.EXACT.01 CARRY COMPUTED WITNESSES (2026-08-27, seam/alpha promotion wave; probes seam_bfk_conical_det_probe 21/21 SPEC d06b3bbec70e7efc / laughlin_pump_em1_probe 20/20 SPEC f9b5cb0bf20d0293 / quillen_rigidity_chain_probe 18/18 SPEC b4ee0dd0141da6ab, embedded byte-exact in v974). [E] BFK FACE EXECUTED: the Mayer-Vietoris determinant gluing on the seam circle at the four mu4 marks -","claim_id":"ALPHA.QUILLEN.FACES.01","dependencies_as_recorded":"ALPHA.QUILLEN.EXACT.01; SEAM.CONTACT.UNIT.01; SEAM.CONTACT.UNIT.02; EM.WARD.01; ALPHA.QUILLEN.INFLOW.01; SEAM.STATE.RPMIXING.01","external_data_as_recorded":"-","id":"claim:ALPHA.QUILLEN.FACES.01","location_as_recorded":"tfpt_1;origin_theory;tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":754,"scripts_as_recorded":"v974_alpha_faces_computed.py","status_as_recorded":"Exact/computed witnesses [E] + typed conditional [C]; the target row stays [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Conditional [C]: d = 4 unique + minimal + overdetermined under {d > 2, [g_YM] = 0, real SD/ASD 2-form split, Weyl chirality} on d = 2..12; A2 and A3 each pin {4} alone, A1 & A4 alone = {4, 6, 8, 10, 12}; mu4 enters nowhere; axiom provenance from {c3, g_car} is the open half","checked_by_registry":false,"claim_excerpt":"THE CONDITIONAL 4D DIMENSION SELECTOR [C] (registered 2026-08-27 from the external bird's-eye review, the master-route wave; machine-checked in v975, 16/16 sympy-exact).  STATEMENT: under the named TFPT-compatible physics axiom set A1 (d > 2: propagating local gauge fields, d-2 >= 1 transverse polarizations), A2 (dimensionless Yang-Mills coupling), A3 (real self-dual/anti-self-dual 2-form sectors: the Euclidean Hodge","claim_id":"DIMENSION.SELECTOR.4D.01","dependencies_as_recorded":"DIMENSION.UPLIFT.FIREWALL.01; SEAM.BULK4D.RECON.01; QFT4D.OS.RECON.01; CHIRAL4D.NOMIRROR.01","external_data_as_recorded":"-","id":"claim:DIMENSION.SELECTOR.4D.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":755,"scripts_as_recorded":"v975_dimension_selector_4d.py","status_as_recorded":"Conditional [C] (exact selector under the named axiom set A1-A4; axiom provenance from the compiler open)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] (v983): lattice-arithmetic generator lambda = (omega_s, omega_f).  [E-measured] (v988): S3 exact + S1/S2 quantitative skeleton on toy and v367 QWZ collar.  [C conditional] (v988): lemma reduced to cited quasi-free class + MMST identification.  [O] open rest = C7 modular invariance + net-level G2/G3/G4; no closure; 1+1D in and out.  [E] (v993): [lambda]^2 = [v] parity shadow of U^2 = (-1)^F; rank-8 ADE census unique (D5, A3) -- D+A architecture is an OUTPUT.  [E-measured] (v994): 5/7 MMST identification criteria (c=8.005, character [1,0,248,0,4124,0,34752], k=1, det D8=4->det E8=1).  [C] (v994): C6 written-out in psi_lambda_convergence_theorem_en.tex (2/pi^2 vs 0.203).| 2026-08-29 v998: C7 arithmetic shadow exact (shared with SEAM.EQUIV.MMST.01); net-level C7 stays cited.  Display unmoved.  WAVE-5 (2026-08-29): parent scaling-limit theorem SEAM.MMST.TYPEIII.CHARGED.01 [O] named; G1-G4 analytic half still [O].  Display unmoved.","checked_by_registry":false,"claim_excerpt":"THE SIMPLE-CURRENT GENERATOR CONTRACT [O] (registered 2026-08-27 from the external bird's-eye review; the seam-gap compression conjecture).  CONTEXT: v973 carved the cited-theorem coverage of the seam target -- the so(16)_1 fermion-bilinear half is COVERED (strong convergence, Virasoro/correlator control, polynomial errors), the NAMED residual is N1 (the mu4/GSO extension SO(16)_1 -> (E8)_1 as a NET statement: the 12","claim_id":"SEAM.SIMPLECURRENT.GENERATOR.01","dependencies_as_recorded":"SEAM.EQUIV.01; SEAM.EQUIV.MMST.01 (the v973 N1-N4 carve); v125; v154; DIMENSION.UPLIFT.FIREWALL.01; v993","external_data_as_recorded":"-","id":"claim:SEAM.SIMPLECURRENT.GENERATOR.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":756,"scripts_as_recorded":"v983_simple_current_generator.py; v988_psi_lambda_reduction.py; v993_minimal_defect_selector.py; v994_mmst_criteria_battery.py; v998_seam_modular_closure.py","status_as_recorded":"Open [O] + lattice shadow [E] (v983) + quantitative S1/S2 skeleton [E-measured] + reduction-to-cited-class [C conditional] + MMST criteria 5/7 executed [E-measured] (v994) + C6 written-out [C]; open rest = C7 modular invariance + net-level G2/G3/G4; no closure","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open: one explicit finite 4D lattice family with seven finite gates T1-T7.  EXECUTED (v989, toy level): T4 exact, T5/T6 2D mechanism, T7 toy, Euclidean T2 kill (N_t-exact), Hamiltonian route clears T2 by construction.  No gate of the 4D contract closed; display marker stays Open.","checked_by_registry":false,"claim_excerpt":"THE EXPLICIT 4D LATTICE ACTION CONTRACT [O] (registered 2026-08-27 from the external bird's-eye review; route step (2) of the DIMENSION.UPLIFT.FIREWALL.01 ordering made concrete -- THE single object on which nearly all open 4D questions become simultaneously testable).  DEMAND: exhibit ONE fully explicit finite family of 4D Euclidean lattice theories Z_a[J] = int DU Dpsi DPhi exp(-S_a[U, psi, Phi] + J O) with S_a = S","claim_id":"TFPT4D.LATTICE.ACTION.01","dependencies_as_recorded":"DIMENSION.UPLIFT.FIREWALL.01; QFT4D.OS.RECON.01; CHIRAL4D.NOMIRROR.01; DYN.UNITARY.DILATION.01; DIMENSION.SELECTOR.4D.01; SEAM.BULK4D.RECON.01","external_data_as_recorded":"-","id":"claim:TFPT4D.LATTICE.ACTION.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":757,"scripts_as_recorded":"v989_lattice_gate_battery.py","status_as_recorded":"Open (research contract; T1-T7 harness + Euclidean T2 kill + Hamiltonian-route T2 clearance executed at toy level; no gate closed)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open: Res_seam det D_4D ~= det D_seam with connection + bulk holonomy == discrete orientation.  [E] (v991): finite 2+1D/1D QWZ bulk-edge correspondence (C_bulk = W_seam = +1, M=3 control 0=0, conjugation mutant).  Continuum Bismut-Freed stays [O]; no 4D unification. | LATE EVENING (2026-08-30 v1014): finite restriction isomorphism verified; orientation fixes conjugate branch; residual U(1) is the A0 anchor.  Continuum stays [O].","checked_by_registry":false,"claim_excerpt":"THE DETERMINANT-LINE UNIFICATION HYPOTHESIS [O] (registered 2026-08-27 from the external bird's-eye review; a precise research hypothesis, NOT a result).  OBSERVATION: three separately open structures may be projections of ONE geometric object -- (1) the seam extension is described by a Q-system/simple current (SEAM.SIMPLECURRENT.GENERATOR.01), (2) the chiral fermion measure lives on a determinant line (CHIRAL4D.NOMI","claim_id":"SEAM.DETLINE.UNIFICATION.01","dependencies_as_recorded":"ALPHA.QUILLEN.EXACT.01; ALPHA.QUILLEN.FACES.01; CHIRAL4D.NOMIRROR.01; SEAM.SIMPLECURRENT.GENERATOR.01; TFPT4D.LATTICE.ACTION.01","external_data_as_recorded":"-","id":"claim:SEAM.DETLINE.UNIFICATION.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":758,"scripts_as_recorded":"v991_detline_bulk_edge.py; v1014_bridge_refinements.py","status_as_recorded":"Open [O] + finite bulk-edge shadow [E] (2+1D/1D QWZ; continuum Bismut-Freed stays Open)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open: one generating functional W[J] = log Z[J] from which all four F_transfer bridges derive.  EXECUTED (v990): finite 1+1D Z6 W[J] derivative identities + transduction shadow.  No upgrade permitted by this row.","checked_by_registry":false,"claim_excerpt":"THE GENERATING FUNCTIONAL CONTRACT [O] (registered 2026-08-27 from the external bird's-eye review; the constructive successor named by the FR.TRANSFER.01 guard).  The four continuous-transfer interfaces (F_pole: source masses -> pole, Koide v183; F_Boltzmann: CP source -> eta_B, v169/v184; F_relic: (f_a, m_a, theta_i, N_DW) -> Omega_a, v185; F_QCD: (alpha_s, b3, Lambda_QCD, lattice) -> m_p/m_e, v164) are currently fo","claim_id":"FTRANSFER.GENERATING.01","dependencies_as_recorded":"FR.TRANSFER.01; TFPT4D.LATTICE.ACTION.01; QFT4D.OS.RECON.01","external_data_as_recorded":"-","id":"claim:FTRANSFER.GENERATING.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":759,"scripts_as_recorded":"v990_wj_transduction_mechanism.py","status_as_recorded":"Open (research contract; finite W[J] derivative identities + transduction shadow executed at 1+1D Z6; no upgrade permitted)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Decision: physical completeness = finite local unitary lattice QFT (Hamiltonian route); continuum OS limit retyped as mathematical reinforcement.  No [E] claim, no marker move; QFT4D.OS.RECON.01 unchanged as the math program.  | 2026-08-29: quasilocal family {H_Lambda} is the fundamental object; continuum (a->0) optional; thermodynamic limit + controlled IR universality mandatory.  Decision typing UNCHANGED. | WAVE-7 (2026-08-30, v1008): 2+1D scaffold-coherent (K=0 theorem, contractive-root selector, wall/mirror, Z6 assembly); no marker move. | AFTERNOON (2026-08-30 v1011): 3+1D minimal object viable; fully coupled link-wall dynamics demonstrated at minimal scale; Kronecker limitation removed.  Decision typing UNCHANGED. | LATE EVENING (2026-08-30 v1013): mandatory-dynamics leg CLOSED at class level (LR + tau_t + A^G + state existence proved); remaining phase uniqueness, limit gap, IR universality.  Decision typing UNCHANGED.","checked_by_registry":false,"claim_excerpt":"THE LATTICE-FUNDAMENTAL READING (registered 2026-08-28 as a typed DECISION, not an [E] claim and not a marker move).  DECISION: TFPT's PHYSICAL completeness criterion is the finite, local, unitary lattice quantum theory -- Hamiltonian route: Gauss-law Hilbert space, hermitian local H, T = e^{-aH} positive by construction, Lieb-Robinson cone -- while the exact continuum Osterwalder-Schrader limit (QFT4D.OS.RECON.01) i","claim_id":"QFT4D.LATTICE.FUNDAMENTAL.01","dependencies_as_recorded":"TFPT4D.LATTICE.ACTION.01; QFT4D.OS.RECON.01; CHIRAL4D.NOMIRROR.01; DYN.UNITARY.DILATION.01","external_data_as_recorded":"-","id":"claim:QFT4D.LATTICE.FUNDAMENTAL.01","location_as_recorded":"tfpt_research_contracts;tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":760,"scripts_as_recorded":"v989_lattice_gate_battery.py; v1008_master_assembly_scaffold.py; v1011_3p1d_ladder_battery.py; v1013_thermodynamic_dynamics.py","status_as_recorded":"Decision (registered route/typing; no [E] claim, no marker move; QFT4D.OS.RECON.01 unchanged as the math program)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open [O] + H0 grammar kill [E] (v996): naive census-only extension of the U(1) alpha grammar to SU(2)/SU(3) excluded (sign kill, 64 conventions 0 hits); genuinely nonabelian Casimir/instanton structure required -- typed. Honest: alpha_s(M_Z) is currently an external input. ln-2 detline rate is a numerical Bismut-Freed shadow.  WAVE-5 (2026-08-29, exploration probes gauge_stiffness_fixpoint/stepscaling; NOT a new module): mechanism executed at FIXED VOLUME BUT thermodynamic step-scaling DIVERGENT; typed hurdle >= 2+1D.  WAVE-7 (2026-08-30, v1008): 2+1D scaffold-coherent (K=0, contractive selector, q^2 law); 4D fixpoint stays [O]. Display unmoved Open. | AFTERNOON (2026-08-30 v1011): BINDING constraint -- holonomy stiffness collapses in the confined phase; the matching point of the coupling functional must be defined in the deconfined/weak regime; charged channels enhance (~2.014x at weak g) but do not prevent collapse at minimal volume.  Display stays [O].","checked_by_registry":false,"claim_excerpt":"THE GAUGE-COUPLING FIXPOINT CONTRACT [O] (registered 2026-08-28, review wave 3).  DEMAND: all three gauge couplings (g1, g2, g3 / equivalently alpha, sin^2 theta_W, alpha_s) arise as stationary points of ONE nonabelian zeta-det / inflow functional on the determinant line -- the nonabelian upgrade of the U(1) face ALPHA.QUILLEN.EXACT.01.  ACCEPTANCE: unique stationary points, positive Hessian, alpha_s(M_Z) without mea","claim_id":"GAUGE.DETLINE.FIXPOINT.01","dependencies_as_recorded":"ALPHA.QUILLEN.EXACT.01; SEAM.DETLINE.UNIFICATION.01; EM.FP.01","external_data_as_recorded":"-","id":"claim:GAUGE.DETLINE.FIXPOINT.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":761,"scripts_as_recorded":"v996_gauge_grammar_kill.py; v1008_master_assembly_scaffold.py; v1011_3p1d_ladder_battery.py","status_as_recorded":"Open (research contract; naive grammar extension excluded [E]; genuinely nonabelian structure required -- typed; alpha_s(M_Z) currently an external input)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open [O] + quadratic witnesses [E] (v997): R+R^2 clean (massless TT pole, two helicities, scalaron at M_scal exact); local a4 Weyl^2 truncation necessarily carries an opposite-residue spin-2 ghost -- typed. Content pinned on the untruncated form factor. Einstein equation stays downstream/conditional; GRAV.NONCIRCULAR.01 binding.  | 2026-08-29 v1000: quadratic Hamiltonian half executed (positivity, 2 helicities at 5852 momenta, omega=k-k^3/24).  Display stays [O]. | WAVE-6 (2026-08-30): GRAV.WEINBERG.WITTEN.01 is the binding firewall before any spin-2 marker move; display stays [O] | EVENING (2026-08-30 v1012): interacting TT half-step: conservation/positivity/sum-rules/Z-persistence executed; missing TFPT content, k->0 volume scaling, Ward identities.  Display stays [O]. | ROUND3 2026-09-05: uniform full gap and direct finite-range TT are excluded mechanisms; critical gauge-constrained escape remains open. No graviton claim. | ROUND-4 CURRENT: v1029 gives a local quadratic first-class constraint target with two z=1 nonzero-momentum modes. The full periodic target is unbounded below at k=0; an additional global zero-mode removal is indispensable. No common-parent embedding/nonlinear universal coupling; [O] unchanged.","checked_by_registry":false,"claim_excerpt":"THE SPIN-2 EMERGENCE CONTRACT [O] (registered 2026-08-28, review wave 3).  DEMAND: from the SAME spectral determinant that carries the gauge fixpoints, a massless transversal spin-2 pole with two helicities, universal T_munu coupling, diffeomorphism Ward identities, and positive H / RP transfer.  RELATION: the entanglement-equilibrium Einstein equation (v358/v359) stays a DOWNSTREAM / CONDITIONAL readout -- it presup","claim_id":"GRAV.SPIN2.EMERGENCE.01","dependencies_as_recorded":"GRAV.NONCIRCULAR.01; GAUGE.DETLINE.FIXPOINT.01; QFT4D.OS.RECON.01; QG.G2.01","external_data_as_recorded":"-","id":"claim:GRAV.SPIN2.EMERGENCE.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":762,"scripts_as_recorded":"v997_spin2_smg_witnesses.py; v1000_spin2_sk_witnesses.py; v1012_toe_gate_witnesses.py; v1024_parent_internal_boundaries.py","status_as_recorded":"Open (research contract; quadratic witnesses [E] + quadratic Hamiltonian half executed; content pinned on the untruncated form factor; Einstein eq stays a downstream/conditional readout) | Round-3 v1024 supplies finite gap/TT locality no-gos [E]; spin-2 emergence remains Open [O].","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open [O] + mechanism executed (v1000): KMS/FDT ~1e-17; rho_0 contrast 3.5e-3 vs static 1e-16; 3pi/5 unique in the mu4 lift [C].  WAVE-7 (2026-08-30, v1009): finite uniqueness closed [E-finite]; V1000_CONSEQUENCE_MISMATCH + CENTER_FLATNESS_PREMISE_FALSE typed; weaker admissible set needed.  Display stays [O]. | EVENING (2026-08-30 v1012): double diagnosis -- hard sectors response-dead, KMS-affine sets selection-vacuous; canonical state requires a different principle (e.g. Euclidean-cap/orientation-branch).  Display stays [O]. | MONDAY MORNING (2026-08-31 v1016): R4 first viable non-entropic selector (D_tr 0.143 + response alive + saddle preserved; finite-proxy caveat).  Display stays [O]. | ROUND3 2026-09-05: 12D cap is arbitrary and D4-breaking, not global rho_0; divisibility/commutant scopes explicit. Display stays [O]. | ROUND-4 CURRENT: v1028 constructs a symmetric gap-one internal cap, but D4 leaves a2D invariant-vector space and the vacuum-preserving extension selects no unique full-parent state. Order-five unitary is not a Weyl pair or derived selector; [O] unchanged.","checked_by_registry":false,"claim_excerpt":"THE SCHWINGER-KELDYSH INITIAL-STATE CONTRACT [O] (registered 2026-08-28, review wave 3; mechanism executed 2026-08-29).  DEMAND: cosmological transfers (F_relic, F_Boltzmann, and any nonequilibrium 4D readout) need the pair (S, rho_0), not W[J] alone -- the Euclidean-cap / KMS initial state.  TYPED CANDIDATE: the theta_i = 3 pi/5 saddle S_init = -kappa cos(5 theta - 3 pi) as the selection.  ARITHMETIC: stationary poi","claim_id":"FTRANSFER.SK.RHO0.01","dependencies_as_recorded":"FTRANSFER.GENERATING.01; FR.TRANSFER.01; TFPT4D.LATTICE.ACTION.01","external_data_as_recorded":"-","id":"claim:FTRANSFER.SK.RHO0.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":763,"scripts_as_recorded":"v1000_spin2_sk_witnesses.py; v1009_rho0_minimizer.py; v1012_toe_gate_witnesses.py; v1016_state_gap_batteries.py; v1024_parent_internal_boundaries.py","status_as_recorded":"Open (research contract; mechanism executed [N]/[C]; FTRANSFER.GENERATING.01 covers equilibrium only) | Round-3 v1024 gives a finite internal candidate and algebraic boundaries [E/N]; global rho_0 and SK uniqueness remain Open [O].","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open [O]: TOE_Complete := AND(T1..T8); TOE_Validated := Complete AND independent holdouts passed.  Named AND of existing 4D/dilation/detline/SK/flavor/gravity/SK contracts; not a closure.  Compiler Rest sits beside Rest_TOE.  WAVE-5 (2026-08-29): T2 master scaling-limit theorem named SEAM.MMST.TYPEIII.CHARGED.01 [O] (children listed there, not back).  Display unmoved.  WAVE-6 (2026-08-30): T7 child GRAV.WEINBERG.WITTEN.01 [O] (Weinberg-Witten firewall before any spin-2 marker move). Display unmoved. | EVENING (2026-08-30 v1012): T5 four witnesses + propagating-mode precondition; T7 interacting stress mechanism; T8 selection-principle vacuity typed (needs a non-entropic selection); T6/nu scaffold-level triple bound complete.  Display unmoved. | LATE EVENING (2026-08-30 v1013/v1014): T3 mandatory-dynamics leg closed at class level; remaining axiom-core and continuum gaps run through one externalized theorem (MMST/Quillen).  Display unmoved. | MONDAY MORNING (2026-08-31 v1015): T1 structure-postulate route fully premise-supported at finite level.  Display unmoved. | ROUND3 2026-09-05: current T1-T8 matrix recorded; no marker moves; shared 3+1D parent absent. The one-theorem statement is compiler/W-bridge scope only. | ROUND-4 CURRENT (v1026-v1030): uniform relaxed TEL-B norm proved; canonical DET-CAR and signed z=1 wall only for fixed classical gauge fields with an explicitly changed additive parent; full Gauss site/cube dimensions3/0mod5; symmetric internal D4 cap noncanonical; local tensor target needs global zero-mode removal; ALG2 frame theorem conditional. All T1-T8 remain [O]; no shared complete3+1D parent.","checked_by_registry":false,"claim_excerpt":"THE MASTER TOE-COMPLETENESS CONTRACT [O] (registered 2026-08-29, review wave 4).  Eight gates, all named; NOTHING claimed closed.  T1 structure postulate -> P1/P2/compiler (AX.P1.01, AX.P2.01, TFPT.IRREDUCIBLE.01, DIMENSION.SELECTOR.4D.01).  T2 seam = (E8)_1 proven (SEAM.EQUIV.01, SEAM.EQUIV.MMST.01, SEAM.EQUIV.TWISTOR.01, SEAM.SIMPLECURRENT.GENERATOR.01, SEAM.DETLINE.UNIFICATION.01, SEAM.STATE.RPMIXING.01).  T3 quas","claim_id":"TFPT.TOE.COMPLETE.01","dependencies_as_recorded":"AX.P1.01; AX.P2.01; TFPT.IRREDUCIBLE.01; DIMENSION.SELECTOR.4D.01; SEAM.EQUIV.01; SEAM.EQUIV.MMST.01; SEAM.EQUIV.TWISTOR.01; SEAM.SIMPLECURRENT.GENERATOR.01; SEAM.DETLINE.UNIFICATION.01; SEAM.STATE.RPMIXING.01; QFT4D.LATTICE.FUNDAMENTAL.01; TFPT4D.LATTICE.ACTION.01; DYN.UNITARY.DILATION.01; DYN.MARKOV.EMBED.01; CHIRAL4D.NOMIRROR.01; QFT4D.OS.RECON.01; SEAM.BULK4D.RECON.01; ALPHA.QUILLEN.EXACT.01; GAUGE.DETLINE.FIXPOINT.01; FLAV.NUSCALE.01; FLAV.NUSCALE.04; FLAV.NUSCALE.03; FLAV.NUSCALE.02; FLAV.NUSCALE.05; FLAV.NUSCALE.06; GRAV.SPIN2.EMERGENCE.01; GRAV.NONCIRCULAR.01; GRAV.WEINBERG.WITTEN.01; FTRANSFER.SK.RHO0.01; FTRANSFER.GENERATING.01; OBS.TRANSDUCTION.01; PRED.JOINTLIKELIHOOD.01","external_data_as_recorded":"-","id":"claim:TFPT.TOE.COMPLETE.01","location_as_recorded":"tfpt_research_contracts;tfpt_4_frontier;introduction","path":"verification/status_ledger.csv","row_number":764,"scripts_as_recorded":"v1012_toe_gate_witnesses.py; v1013_thermodynamic_dynamics.py; v1014_bridge_refinements.py; v1015_axiom_core_closure.py; v1022_telb_round3_certificates.py; v1023_derivative_filtered_wall.py; v1024_parent_internal_boundaries.py; v1025_telb_c1_c2a_certificates.py; v1026_telb_round4_closure.py; v1027_signed_det_car_wall.py; v1028_gauss_d4_cap.py; v1029_local_tensor_constraints.py; v1030_alg2_sector_frame.py","status_as_recorded":"Open (research contract; named AND of eight gates; no closure, no marker move) | Round-3 v1022-v1025 adds certified subgates and no-gos only; Round-4 v1026-v1030 adds narrow proved and conditional subresults only; all T1-T8 gates and TOE remain Open [O].","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[C]/[N] pentagon-class misalignment candidate (v1001): phi=288 deg, theta=2pi/35, LEE 2.7%, v3 SHA a4c28732fa687620, Sigma=0.0599 eV, m_beta=9.0 meV, m_bb [1.5,3.8] meV, delta_CP=287.66 deg; v270-theta23 tension 1.85 sigma TYPED; census 0/1607.  Mechanism Q_+-to-flavor [O].  No closure.  WAVE-5 (2026-08-29, v1003): both structural nulls (D4-even Schur; scale cancellation 1.885e-4) are binding on FLAV.NU.TEXTURE.MECHANISM.01 [O].  Pentagon-class candidate unmoved; no seesaw closure.","checked_by_registry":false,"claim_excerpt":"THE PENTAGON-CLASS MISALIGNMENT CANDIDATE (registered 2026-08-29, review wave 4, v1001).  Candidate [C]/[N]; mechanism = the Q_+-to-flavor operator [O]; NO closure; FLAV.NUSCALE.05 unmoved.  [E] U_e = I inventory theorem: no charged-lepton mass matrix in the compiler; companion algebra G-self-adjoint with eigenvalues (16/7, 4/3, 7/6).  [E] misalignment U = U_v9 R13(theta, phi) solves the 13/23 pair analytically (held","claim_id":"FLAV.NUSCALE.06","dependencies_as_recorded":"FLAV.NUSCALE.05; FLAV.NUSCALE.02; FLAV.NUSCALE.01; AX.P2.01","external_data_as_recorded":"-","id":"claim:FLAV.NUSCALE.06","location_as_recorded":"tfpt_2_standard_model;tfpt_research_contracts;tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":765,"scripts_as_recorded":"v1001_nu_pentagon_chain.py; v1003_nu_structural_nulls.py","status_as_recorded":"Candidate [C]/[N] + mechanism [O] (pentagon-class misalignment; no seesaw closure; FLAV.NUSCALE.05 unmoved)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Candidate [C] (v1002/v1007): T1/T2 proved; T3 MZ cited-verified (t*>0, gap>=1/2); dynamical [N] + boxed BDL/1/192.  Open: compact-group dynamical links, domain-wall geometry, 4D volume theorem.  No marker upgrade of NOMIRROR.  WAVE-7 2026-08-30. | MONDAY MORNING (2026-08-31 v1016): DFP volume-uniform gap cited-verified for finite-group open chains; dynamical-link leg closed at that level; remaining rotor/wall/3+1D.  Display stays [C]. | ROUND3 2026-09-05: derivative-filtered witness is not a DET16/DET32 realization and supplies no 4D theorem. Candidate stays [C].","checked_by_registry":false,"claim_excerpt":"THE DET16 RANK-ONE MIRROR PROJECTOR CANDIDATE (registered 2026-08-29, review wave 5, v1002).  Candidate [C]: exact finite-cluster gapping mechanism on the full 2^16 chiral Spin(10) Fock space.  [E-finite] Omega^dag Omega = P_16, Omega Omega^dag = P_0, defect 0; P_phi hermitian idempotent (2.8e-18), rank 1; h_mir spectrum {0^1, 1^65535}, gap exactly 1; all 45 so(10) Fock commutators = 0 (det rho_16 = 1); parity commut","claim_id":"CHIRAL4D.MIRROR.DET16.01","dependencies_as_recorded":"CHIRAL4D.NOMIRROR.01; DIMENSION.UPLIFT.FIREWALL.01","external_data_as_recorded":"articles/2026-08-30/det16_mirror_gap_theorem_en.tex (12 pp; T1/T2 proved, T3 MZ cited-verified, 1/192 boxed, BDL boxed)","id":"claim:CHIRAL4D.MIRROR.DET16.01","location_as_recorded":"tfpt_research_contracts;tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":766,"scripts_as_recorded":"v1002_spin10_mirror_projector.py; v1007_det16_stability_battery.py; v1016_state_gap_batteries.py; v1023_derivative_filtered_wall.py","status_as_recorded":"Candidate [C] (exact finite-cluster gapping; open: dynamical gauge fields, domain-wall geometry, 4D volume theorem) | Round-3 v1023 is a separate finite block lemma and does not upgrade DET16.","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open [O] + five lemmas in-house (v1006): L3, UGF K_G=pi^2/4, TEL-a N^{-2} isometries, integer D5+A3 pairings, Z4 outerness in the limit.  Residual boxed TEL-B-EXTERNAL + ALG-EXH.  WAVE-7 2026-08-30.  Display stays [O]. | MONDAY MORNING (2026-08-31 v1016): TEL-B narrowed to scalar dyadic A_R<43 (factor-350 headroom; UV-supported remainder); uniform CAR nuclearity proved as specialist input; ALG-EXH unchanged.  Display stays [O]. | ROUND3 2026-09-05: TEL-B reduced to CF/DG; C1/C2a/TV closed; ALG2 correction binding. Charged/type-III parent stays [O]. | ROUND-4 CURRENT: v1026 proves the relaxed uniform norm ||R_N||HS<2.995906<3 for every evenN>=16 (CF/DG/CROSS plus validated Fourier aliases). Historical2.11 and finite1.7833 are not promoted. The residual is microscopic one-edge FE-GEN, actual-word/joint-adjoint tails, ALG-EXH and MMST identification; v1030 is conditional. Aggregate [O] unchanged.","checked_by_registry":false,"claim_excerpt":"THE MASTER SCALING-LIMIT THEOREM FOR THE CHARGED/TYPE-III IDENTIFICATION [O] (registered 2026-08-29, review wave 5).  DEMAND: ONE scaling-limit theorem Psi_lambda,N -> Psi_lambda strongly on the finite-energy core + crossed-product continuity, from which B ≅ (E8)_1, mu = 1, type III_1, unique rotational KMS, unique conditional expectation, deck equidistribution, and modular invariance all follow as corollaries.  CHIL","claim_id":"SEAM.MMST.TYPEIII.CHARGED.01","dependencies_as_recorded":"SEAM.SIMPLECURRENT.GENERATOR.01; SEAM.STATE.RPMIXING.01; ALPHA.QUILLEN.EXACT.01; AX.P1.01","external_data_as_recorded":"articles/2026-08-29/holomorphic_kms_extension_en.tex (KLM; Longo-Tanimoto) -- cited theorems, no data; articles/2026-08-30/mmst_charged_scaling_limit_en.tex (21 pp; five lemmas in-house; residual TEL-B-EXTERNAL + ALG-EXH); articles/2026-08-30/externalization_mmst_handoff_v2_en.html","id":"claim:SEAM.MMST.TYPEIII.CHARGED.01","location_as_recorded":"tfpt_research_contracts;tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":767,"scripts_as_recorded":"v1006_mmst_lemma_battery.py; v1016_state_gap_batteries.py; v1022_telb_round3_certificates.py; v1025_telb_c1_c2a_certificates.py","status_as_recorded":"Open (research contract; master scaling-limit theorem; children listed here not back) | Round-3: C1/C2a/TV and scalar C2b subclaims proved [E]; ALG2 implication refuted [X]; CF/DG and ALG-EXH remain Open [O].","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open [O] (v1003): mechanism must be D4-odd AND supply a ~2e-4 even-odd cancellation; pure seam data excluded [X-typed].  NUSCALE.05/.06 unmoved; no seesaw closure. | EVENING (2026-08-30 v1012): kappa null completes the scaffold bound: mechanism scale strictly beyond frozen finite objects -- 4D functional required.  Display stays [O]. | ROUND3 2026-09-05: finite intertwiner only; projective full-Fock boundary explicit; no neutrino mass texture. Display stays [O]. | ROUND-4 CURRENT: v1028 exactly counts full Gauss dimensions and constructs a D4-symmetric cap only on the selected even pair subspace. The invariant-vector space is2D; the actual symmetric fermion lift forbids all Majorana bilinears. No mass texture; [O] unchanged.","checked_by_registry":false,"claim_excerpt":"THE NEUTRINO-TEXTURE MECHANISM CONTRACT [O] (registered 2026-08-29, review wave 5, v1003).  Both structural nulls are BINDING CONSTRAINTS.  [E] charged-sector data h=(1,1,1), d=(64,60,64) (coset min norms all 2).  [X] Schur-texture NULL: all 8 preregistered (K,B) combinations fail; D4 reflection forces lambda_1=lambda_3; hierarchy (eps, 2eps, 3) structurally unreachable from D4-even seam data; required K spectrum [35","claim_id":"FLAV.NU.TEXTURE.MECHANISM.01","dependencies_as_recorded":"FLAV.NUSCALE.05; FLAV.NUSCALE.06","external_data_as_recorded":"-","id":"claim:FLAV.NU.TEXTURE.MECHANISM.01","location_as_recorded":"tfpt_2_standard_model;tfpt_research_contracts;tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":768,"scripts_as_recorded":"v1003_nu_structural_nulls.py; v1012_toe_gate_witnesses.py; v1024_parent_internal_boundaries.py","status_as_recorded":"Open (research contract; both structural nulls are binding constraints; NUSCALE.05/.06 unmoved) | Round-3 v1024 provides a finite parent-internal witness [E/N]; the physical texture/scale remains Open [O].","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open [O]: required canonical identification (dual-number + Frobenius + Gray torsor + deck + CP) geometric/mechanical, not basis-chosen; rank clock and socle-CP as outputs.  Kill: second inequivalent identification, or mu4-equivariance failure.  Classical cite vs new-in-corpus [E-finite] vs interpretive [C] typed on v1004.  WAVE-6 2026-08-30. | AFTERNOON (2026-08-30 v1010): SHARPENED -- strong all-structure identification finitely obstructed at F2 (clock order 2 vs 4, CP Jordan rank 2 vs 4) and at all upstairs homes (Z/4: J^2=-I vs Gray P^2!=-I, D8 vs C4xC2; Gaussian k=2 order collapse, k=3 rank/relation clash; affine cannot repair linear parts).  Only the coarse D-module+pairing bridge exists (witness constructed; |Aut(X)|=36864, |Aut(Y)|=8).  Ring-internal identities (rank clock, socle CP, self-clock) of v1004 UNAFFECTED.  Display stays [O].","checked_by_registry":false,"claim_excerpt":"THE MILNOR LOCAL-RING IDENTIFICATION CONTRACT [O] (registered 2026-08-30, review wave 6, v1004).  REQUIRED: a CANONICAL identification between the raw seam collar / E8 transition bus and the reduced Milnor algebra F2[y,z]/(y^2,z^4) preserving simultaneously the dual-number action, Frobenius pairing, Gray torsor, deck action and CP.  ACCEPTANCE: the identification must be geometric/mechanical (not basis-chosen), must ","claim_id":"SEAM.MILNOR.LOCALRING.01","dependencies_as_recorded":"SEAM.EQUIV.01; AX.P2.01","external_data_as_recorded":"-","id":"claim:SEAM.MILNOR.LOCALRING.01","location_as_recorded":"tfpt_research_contracts;tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":769,"scripts_as_recorded":"v1004_milnor_frobenius_gray.py; v1010_simplicity_bridge_census.py","status_as_recorded":"Open (research contract; canonical geometric identification of the raw seam collar with F2[y,z]/(y^2,z^4) unproven; Milnor algebra + exponents classical)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open [O]: Weinberg-Witten firewall -- no microscopic Lorentz-covariant local conserved T_munu; Lorentz, diffeomorphism Ward and spin-2 emerge in the SAME IR limit.  Acceptance: positive TT density, two helicities, massless pole, emergent diff Ward, universal soft coupling, named evaded premise.  Kill: microscopic covariant local T_munu + massless composite spin-2.  Child of T7.  WAVE-6 2026-08-30.","checked_by_registry":false,"claim_excerpt":"THE WEINBERG-WITTEN FIREWALL [O] (registered 2026-08-30, review wave 6).  BINDING BEFORE ANY spin-2 marker move.  DEMAND: the microscopic Hamiltonian family must NOT possess a fundamental Lorentz-covariant local conserved T_munu; Lorentz symmetry, diffeomorphism Ward identities and the spin-2 mode must emerge in the SAME IR limit.  ACCEPTANCE: positive TT spectral density, exactly two helicities, massless pole, emerg","claim_id":"GRAV.WEINBERG.WITTEN.01","dependencies_as_recorded":"GRAV.SPIN2.EMERGENCE.01; GRAV.NONCIRCULAR.01","external_data_as_recorded":"-","id":"claim:GRAV.WEINBERG.WITTEN.01","location_as_recorded":"tfpt_research_contracts;tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":770,"scripts_as_recorded":"-","status_as_recorded":"Open (research contract; binding firewall before any spin-2 marker move; no script)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] Identity: seven exact E8 readout cells (Seifert/Phi_30, Hamming, srg(120,56,28,24), N(n)=240 sigma_3(n), tau, C2 x C4, E6 oplus A2 glue); C7 OPEN (rem:c7-audit); NO RH claim","checked_by_registry":false,"claim_excerpt":"THE SEVEN EXACT E8 READOUT CELLS [E] Identity (round r609, promoted 2026-09-02; module v1018, re-derived, no probe imports).  (1) Seifert/Euler: S+S^T=A_E8, charpoly(-S^{-1}S^T)=Phi_30, rank(S-S^T)=8, orientation-independent charpoly (exponents=totatives of 30; degrees {2,8,12,14,18,20,24,30}, sum(2m_i+1)=248).  (2) Hamming H_8 enumerator 1+14 y^4+y^8, 240=16+14*16, S(3,4,8).  (3) srg(120,56,28,24) eigenvalues 56/8/-","claim_id":"E8.DIRECTED.READOUT.01","dependencies_as_recorded":"v1018","external_data_as_recorded":"-","id":"claim:E8.DIRECTED.READOUT.01","location_as_recorded":"note_e8_gaussian_code;introduction;tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":771,"scripts_as_recorded":"v1018_e8_directed_readout.py","status_as_recorded":"Proven finite statement [E] (Identity, exact over Z/Q via sympy); C7 Gauss-code transform stays OPEN (rem:c7-audit); NO RH claim","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] Identity: det(I-xC)=Phi_30, Tr C=-1, U=1 oplus C, Z_C and D_E8 zeta quotients (classical Moebius); Numerical Euler products at X=10^5 (residuals 4.76e-4 at s=0.75, 4.16e-12 at s=1.5); class statement + Beurling-genericity; fence verbatim (no marker upgrade); NO-GO E8.COXETER.REGULARIZED_SPLIT.NO_GO.01 on det_2; NO RH claim","checked_by_registry":false,"claim_excerpt":"THE COXETER-EULER COMPLETION OF E8 [E] Identity + Numerical (round r617, promoted 2026-09-02; module v1019, re-derived, no probe imports).  Exact: C=-S^{-1}S^T, det(I-xC)=Phi_30, Tr C=-1; Moebius Phi_30=(1-x^2)(1-x^3)(1-x^5)(1-x^30)/[(1-x)(1-x^6)(1-x^10)(1-x^15)] (classical cyclotomic Euler-product inversion); U=1 oplus C, det(I-xU)=(1-x)Phi_30=1-x^2-x^3+x^6+x^7-x^9, Tr U=0.  Global Z_C(s)=zeta(2s)zeta(3s)zeta(5s)zet","claim_id":"E8.COXETER.EULER.COMPLETION.01","dependencies_as_recorded":"v1019","external_data_as_recorded":"-","id":"claim:E8.COXETER.EULER.COMPLETION.01","location_as_recorded":"introduction;tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":772,"scripts_as_recorded":"v1019_coxeter_euler_completion.py","status_as_recorded":"Proven finite statement [E] (Identity, exact over Z/Q via sympy) plus Numerical Euler-product checks (mpmath, X=10^5); fence/no-go carry NO marker upgrade; NO RH claim","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Open: the prime-completion contract (uniqueness in the category of seam-generated completions with trivial relative commutant); finite free-fermion witness in v1020 (B vs B (+) C separated by dim C at every momentum, generated a.e. in p); no closure; SEAM.BULK4D.RECON.01/B7 re-scoped, not superseded; DIMENSION.UPLIFT.FIREWALL.01 F2 dimension typing in force","checked_by_registry":false,"claim_excerpt":"THE PRIME-COMPLETION CONTRACT [O] (registered 2026-09-04, v1020): replaces the \"unique from seam data alone\" reading of SEAM.BULK4D.RECON.01/B7 by uniqueness IN THE CATEGORY OF SEAM-GENERATED (PRIME) COMPLETIONS.  DEMAND: (1) an explicit family of seam-derived subalgebras A_i (seam CAR algebra, its time evolution, inclusions/intersections); (2) generatedness A_bulk = vN(v_i A_i); (3) NO-SPECTATOR: trivial relative co","claim_id":"BULK.PRIME_COMPLETION.01","dependencies_as_recorded":"SEAM.BULK4D.RECON.01; DIMENSION.UPLIFT.FIREWALL.01","external_data_as_recorded":"-","id":"claim:BULK.PRIME_COMPLETION.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":773,"scripts_as_recorded":"v1020_spectator_sector_obstruction.py","status_as_recorded":"Open (research contract)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] subclaims only: C_star<0.1525 and sup|phi_N|<0.509/N for every even N>=16. C2b, ALG-EXH, MMST and TOE remain [O]. | ROUND-4 SUPERSESSION: v1026 closes the former CF/DG residual and relaxed norm; v1025 C1/C2a inputs remain valid. ALG-EXH and MMST remain OPEN.","checked_by_registry":false,"claim_excerpt":"TEL-B C1/C2a SUBCLAIM CONTRACT (registered 2026-09-05, v1025; no parent marker move). C1: a native 100-bit Arb/Acb certificate integrates 3888 analytic rectangles, adds a closed axis-strip majorant and the exact imaginary term 1/12, obtaining C_star <= 0.1520453048... < 0.1525. C2a: exact cotangent reindexing, the Peano kernel and shifted Euler summation prove N sup_k |phi_N(k)| < 0.509 for every even N>=16; v1025 ou","claim_id":"SEAM.MMST.TELB.C1C2A.01","dependencies_as_recorded":"SEAM.MMST.TYPEIII.CHARGED.01; TFPT.TOE.COMPLETE.01","external_data_as_recorded":"-","id":"claim:SEAM.MMST.TELB.C1C2A.01","location_as_recorded":"tfpt_research_contracts;tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":774,"scripts_as_recorded":"v1025_telb_c1_c2a_certificates.py","status_as_recorded":"Proven subclaims [E]: C1 native interval certificate plus analytic axis bound; C2a analytic all-even-N theorem plus outward constant certificate. Parent contracts remain Open [O].","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"TV residual closed; C1/C2a closed by v1025; C2b reduced to CF and DG; ALG2 inference killed and replacement premise named. No parent marker move. | ROUND-4 SUPERSESSION: v1026 closes CF/DG and the relaxed all-even-N>=16 norm below2.995906<3; the old full-C2b-open wording is historical. TV and potential inputs remain valid. v1030 gives only a conditional sector/frame interface; microscopic ALG-EXH/MMST remain OPEN.","checked_by_registry":false,"claim_excerpt":"TEL-B ROUND-3 MIXED CERTIFICATE (registered 2026-09-05, v1022; no parent marker move). Native 256-bit Arb/Acb over 5812 rational cells gives TV_p(F'') <= 15.817695962988924... < 15.928674 and K3_TV < 2.517464500835. The analytic C2b scalar reduction, with executable Arb arithmetic in v1022, gives c_epsilon=0.288547359238..., c_zeta=0.110677064901..., sum=0.399224424139...<0.400. Full C2b remains open exactly at CF<=0","claim_id":"SEAM.MMST.TELB.ROUND3.01","dependencies_as_recorded":"SEAM.MMST.TELB.C1C2A.01; SEAM.MMST.TYPEIII.CHARGED.01; TFPT.TOE.COMPLETE.01","external_data_as_recorded":"-","id":"claim:SEAM.MMST.TELB.ROUND3.01","location_as_recorded":"tfpt_research_contracts;tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":775,"scripts_as_recorded":"v1022_telb_round3_certificates.py","status_as_recorded":"Mixed: TV interval-certified [E]; C2b scalar reduction is analytic proof plus Arb arithmetic [E]; old ALG2 implication refuted [X]; CF/DG, ALG-EXH, MMST and TOE remain Open [O].","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E-finite]/[C]: exact 2x2 singular-value block and deterministic covariance witness only. No invariant mirror-response gap, Weyl cone, many-body or 4D theorem.","checked_by_registry":false,"claim_excerpt":"DERIVATIVE-FILTERED WALL BLOCK LEMMA (registered 2026-09-05, v1023; no parent marker move). For H_df=Delta b^dagger b+lambda(b+g D_GW p)^dagger(b+g D_GW p), every singular-value block has determinant lambda g^2 Delta s^2, preserves ker D_GW on the physical summand, has an adiabatically mirror-continuated high branch >=Delta+lambda and a quadratic low branch with coefficient lambda g^2 Delta/(Delta+lambda). Finite gau","claim_id":"CHIRAL4D.MIRROR.DFILTER.BLOCK.01","dependencies_as_recorded":"CHIRAL4D.NOMIRROR.01; CHIRAL4D.MIRROR.DET16.01; TFPT.TOE.COMPLETE.01","external_data_as_recorded":"-","id":"claim:CHIRAL4D.MIRROR.DFILTER.BLOCK.01","location_as_recorded":"tfpt_research_contracts;tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":776,"scripts_as_recorded":"v1023_derivative_filtered_wall.py","status_as_recorded":"Proven finite block identity [E]; GW/gauge reading conditional [C]; DET16 [C], NOMIRROR [O], T4 and TOE [O] unchanged.","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Finite parent-internal intertwiner only; projective full-Fock boundary explicit. T6 and TOE remain [O].","checked_by_registry":false,"claim_excerpt":"FINITE PARENT-INTERNAL A3-D4 INTERTWINER (registered 2026-09-05, v1024; no parent marker move). A positive, fermion-even, gauge-compatible, non-additive seam/neutrino-pair term is constructed inside one finite parent, with local gap 0.25 conditional on the inherited parent bound and mixed resolvent 0.104712041885. The selected pair-operator triplet carries ordinary D4, while the full Fock lift is projective: C_f^8=1,","claim_id":"FLAV.NU.PARENT.INTERTWINER.01","dependencies_as_recorded":"FLAV.NU.TEXTURE.MECHANISM.01; TFPT.TOE.COMPLETE.01","external_data_as_recorded":"-","id":"claim:FLAV.NU.PARENT.INTERTWINER.01","location_as_recorded":"tfpt_research_contracts;tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":777,"scripts_as_recorded":"v1024_parent_internal_boundaries.py","status_as_recorded":"Proven finite witness [E/N]; physical neutrino texture and scale remain Open [O].","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Uniform full gap and direct finite-range TT projection are excluded as T7 mechanisms. Critical gauge-constrained escape remains open; no spin-2 closure.","checked_by_registry":false,"claim_excerpt":"GAPPED-PARENT SPIN-2 BOUNDARY (registered 2026-09-05, v1024; no parent marker move). A uniform strictly positive full-parent gap excludes a massless spin-2 pole. The exact transverse-traceless projector has direction-dependent k->0 limits and therefore cannot be a strictly finite-range microscopic projector. A viable T7 route must use a critical physical sequence together with local tensor gauge constraints; the fini","claim_id":"GRAV.PARENT.GAP.NO_GO.01","dependencies_as_recorded":"GRAV.SPIN2.EMERGENCE.01; GRAV.WEINBERG.WITTEN.01; TFPT.TOE.COMPLETE.01","external_data_as_recorded":"-","id":"claim:GRAV.PARENT.GAP.NO_GO.01","location_as_recorded":"tfpt_research_contracts;tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":778,"scripts_as_recorded":"v1024_parent_internal_boundaries.py","status_as_recorded":"Proven finite no-go/boundary [E]; massless spin-2 emergence, Ward identities and universal coupling remain Open [O].","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"Internal 12D cap is not a canonical global state; commutant/divisibility statements have explicit scope. T8 and TOE remain [O].","checked_by_registry":false,"claim_excerpt":"FINITE PARENT-INTERNAL Z5 CAP AND ENLARGEMENT BOUNDARIES (registered 2026-09-05, v1024; no parent marker move). A 12-dimensional internal cap has gap 0.197423715893 and preserves the finite parent vacuum/gap, but the selector is arbitrary, breaks D4 and is not a global rho_0. On the unprojected parent a full Z5 Weyl pair requires 5|D; Gauss-projected physical dimensions are not counted. Any unital M_n -> M_nd enlarge","claim_id":"FTRANSFER.PARENT.Z5CAP.01","dependencies_as_recorded":"FTRANSFER.SK.RHO0.01; BULK.PRIME_COMPLETION.01; TFPT.TOE.COMPLETE.01","external_data_as_recorded":"-","id":"claim:FTRANSFER.PARENT.Z5CAP.01","location_as_recorded":"tfpt_research_contracts;tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":779,"scripts_as_recorded":"v1024_parent_internal_boundaries.py","status_as_recorded":"Finite candidate and exact algebraic boundaries [E/N]; global rho_0, Gauss-projected Weyl realization and unique SK functional remain Open [O].","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] narrow uniform norm theorem only; all T1-T8 remain [O]","checked_by_registry":false,"claim_excerpt":"For the fixed M=1 Ny=8 collar, CF<0.065697, DG<0.042959, C2b<0.466902 and one-sided CROSS<0.282637/N imply Bound-B squared<0.714386. Validated 512-node Acb Fourier core plus the complete all-volume alias envelope gives ||R_N||HS<2.995906<3 for all even N>=16. Historical 2.11 and finite Rsm<=1.7833 are not proved. Microscopic FE-GEN/ALG-EXH and MMST remain open.","claim_id":"SEAM.MMST.TELB.NORM.01","dependencies_as_recorded":"SEAM.MMST.TELB.ROUND3.01; SEAM.MMST.TELB.C1C2A.01","external_data_as_recorded":"python-flint 0.9.0 native; no external observation","id":"claim:SEAM.MMST.TELB.NORM.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":780,"scripts_as_recorded":"v1026_telb_round4_closure.py","status_as_recorded":"Identity (analytic theorem with native interval certificate; fixed regulator)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[C] fixed-classical-background signed-wall theorem; T3/T4 remain [O]","checked_by_registry":false,"claim_excerpt":"Even onsite unitary conjugation constructs canonical DET excitations under the determinant-singlet premise. The additive Delta*N_a replaces the flat Delta*Q. Signed wall det h(s)=M*s*(1+c*s), cL<1 and B<M give the original kernel, linear low branch and high band>=M for fixed classical gauge backgrounds; example M=4 B=3. Bare mirror retains low-band weight; free overlap illustration is a nonchiral four-component Dirac","claim_id":"CHIRAL4D.MIRROR.SIGNED.CAR.01","dependencies_as_recorded":"CHIRAL4D.MIRROR.DFILTER.BLOCK.01; CHIRAL4D.MIRROR.DET16.01","external_data_as_recorded":"none","id":"claim:CHIRAL4D.MIRROR.SIGNED.CAR.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":781,"scripts_as_recorded":"v1027_signed_det_car_wall.py","status_as_recorded":"Identity (conditional Hamiltonian-class and exact finite regression)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] finite counts and selected-subspace cap; T6/T8 remain [O]","checked_by_registry":false,"claim_excerpt":"Full 192-mode site exterior character and exact mod5 Frobenius reduction give Gauss dimension3 mod5 for one site and0 mod5 for the open 2x2x2 cube with the specified nine-irrep link truncation; parity sectors4 mod5 at one site. Abstract Weyl divisibility obstruction is not universal after Gauss projection. Symmetric 12D D4 cap has unique selected-sector ground and gap1, but the invariant-vector space has dimension2; ","claim_id":"PARENT.GAUSS.D4.ROUND4.01","dependencies_as_recorded":"FLAV.NU.TEXTURE.MECHANISM.01; FTRANSFER.SK.RHO0.01","external_data_as_recorded":"none","id":"claim:PARENT.GAUSS.D4.ROUND4.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":782,"scripts_as_recorded":"v1028_gauss_d4_cap.py","status_as_recorded":"Identity (exact finite projected counts and conditional symmetry obstructions)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[C] radiative target after global zero-mode removal; T7 remains [O]","checked_by_registry":false,"claim_excerpt":"Polynomial first-class constraints for a quadratic tensor target leave exactly two positive linear-dispersion modes at nonzero momentum. Staggered differences give a finite stencil and no extra zero corners. At k=0 all constraints vanish and the trace momentum gives H0=-3r^2/4; positivity requires removing the whole global canonical block. Fixed finite-site exact CCR are impossible; collective low-energy emergence is","claim_id":"GRAV.SPIN2.LOCAL.CONSTRAINT.01","dependencies_as_recorded":"GRAV.SPIN2.EMERGENCE.01","external_data_as_recorded":"Linearized GR context only","id":"claim:GRAV.SPIN2.LOCAL.CONSTRAINT.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":783,"scripts_as_recorded":"v1029_local_tensor_constraints.py","status_as_recorded":"Identity (quadratic target only; global zero-mode prescription required)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[C] conditional certificate interface; ALG-EXH and T2 remain [O]","checked_by_registry":false,"claim_excerpt":"Given full neutral block algebras, nonzero charged corners generate the full finite matrix algebra iff their sector graph is connected. A noncollapsing actual-word frame with uniform word norm M gives section norm<=2*M*D^(3/2)/sigma. Compression is not multiplicative and double-cutoff convergence is insufficient: a joint real-linear y/y-adjoint frame and high-output tails for x, x*, y and y* are separately required. ","claim_id":"SEAM.MMST.ALG2.FRAME.01","dependencies_as_recorded":"SEAM.MMST.TYPEIII.CHARGED.01; SEAM.MMST.TELB.ROUND3.01","external_data_as_recorded":"none","id":"claim:SEAM.MMST.ALG2.FRAME.01","location_as_recorded":"tfpt_research_contracts","path":"verification/status_ledger.csv","row_number":784,"scripts_as_recorded":"v1030_alg2_sector_frame.py","status_as_recorded":"Identity (conditional finite-algebra and uniform-frame bridge)","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] free-target theorem only; T7 and TOE remain [O]","checked_by_registry":false,"claim_excerpt":"Declared local tensor target after removal of the entire unstable global zero block: C=r^4 P_TT, positive pure quasi-free Weyl/Fock state with 2(V-1) real oscillators and thermodynamic then distributional continuum limit. Full written analytic proof plus 53 exact and 16 floating checks; finite-dimensional exact CCR excluded. No microscopic TFPT derivation or nonlinear coupling.","claim_id":"GRAV.FREE.CURVATURE.FOCK.01","dependencies_as_recorded":"GRAV.SPIN2.LOCAL.CONSTRAINT.01; GRAV.SPIN2.EMERGENCE.01","external_data_as_recorded":"none","id":"claim:GRAV.FREE.CURVATURE.FOCK.01","location_as_recorded":"tfpt_research_contracts;tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":785,"scripts_as_recorded":"v1031_quantum_tensor_curvature.py","status_as_recorded":"Identity in declared zero-mean free target [E]; TFPT identification [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"[E] free curvature theorem plus 34 exact checks; T7 and TOE [O]","checked_by_registry":false,"claim_excerpt":"On the null cone the linearized Riemann sandwich of the de Donder form equals a rank-two positive TT polarization factorization. The polynomial kernel defines a positive-energy Lorentz-covariant local free curvature Wightman field with helicities +/-2 and the same global Fock space as the electric curvature target. Local-net equality and a finite-range lattice realization of every curvature component are not asserted","claim_id":"GRAV.FREE.CURVATURE.COVARIANT.01","dependencies_as_recorded":"GRAV.FREE.CURVATURE.FOCK.01; GRAV.SPIN2.EMERGENCE.01","external_data_as_recorded":"Free massless-field context; no external observation","id":"claim:GRAV.FREE.CURVATURE.COVARIANT.01","location_as_recorded":"tfpt_research_contracts;tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":786,"scripts_as_recorded":"v1032_covariant_curvature.py","status_as_recorded":"Identity in declared free continuum target [E]; TFPT identification [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"35 checks: 12 exact; 7 source; 16 numerical. 2026-09-06 numerical amendment: basis-independent zero-space mixture and bounds over every pure filling; finite-grid only. T2 and TOE [O]","checked_by_registry":false,"claim_excerpt":"Adding an auxiliary local Z4 flux register constructs order-four charged corners in the common QWZ matter Fock space. Scalar matter gauge transformations alone cannot change seam holonomy. The simple eight-channel quarter twist has h=1/4 rather than h_lambda=1; every norm-two same-phase integer dressing has odd parity. The D5/A3 quotient and cocycle/GSO identification are not supplied. Sharp and smooth string numeric","claim_id":"SEAM.MMST.DISORDER.REGISTER.01","dependencies_as_recorded":"SEAM.MMST.TYPEIII.CHARGED.01; SEAM.MMST.ALG2.FRAME.01","external_data_as_recorded":"Full repository source inputs; no observational data","id":"claim:SEAM.MMST.DISORDER.REGISTER.01","location_as_recorded":"tfpt_research_contracts;mmst_charged_scaling_limit_en","path":"verification/status_ledger.csv","row_number":787,"scripts_as_recorded":"v1033_charged_disorder.py","status_as_recorded":"Identity in explicitly enlarged model and exact obstruction [E]; finite/scaling regressions [N]; microscopic identification [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"36 checks: 29 exact; 6 source; 1 floating. T3/T4 and TOE [O]","checked_by_registry":false,"claim_excerpt":"The actual v1008 factorized onsite model at n=4 J=2 and |d|<=3/5 has uniform gap >=1+sqrt(3)/2. An ordinary hopping bond has zero vacuum expectation but nonzero action and therefore cannot obey the proposed lower form bound by onsite vacuum-complement projectors. This refutes that bound, not the existence of every interacting gap. Newly chosen bond magnitude 3/5 is distinct from the actual sin(k) source coefficient 3","claim_id":"CHIRAL4D.MIRROR.FACTORIZED.BOUND.01","dependencies_as_recorded":"CHIRAL4D.NOMIRROR.01; CHIRAL4D.MIRROR.SIGNED.CAR.01","external_data_as_recorded":"Full repository source inputs; no observational data","id":"claim:CHIRAL4D.MIRROR.FACTORIZED.BOUND.01","location_as_recorded":"tfpt_research_contracts;tfpt_4_frontier","path":"verification/status_ledger.csv","row_number":788,"scripts_as_recorded":"v1034_parent_mirror.py","status_as_recorded":"Identity for factorized model and relative-bound obstruction [E]; finite regression [N]; interacting gap [O]","type":"claim_ledger_row"},{"active_as_recorded":"true","canonical_status_as_recorded":"59 checks: 55 exact; 4 floating. T7 and TOE [O]","checked_by_registry":false,"claim_excerpt":"For the declared staggered tensor target and prescribed conserved sources use c0=-s^T q and ci=i Bp with the real paired Fourier Hamiltonian. 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The dedicated papers should contain only their own source body plus directly necessary local technical material. Cross-paper background is referenced through dependency boxes; extended backend material is assigned to the Technical Companion.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Purpose","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3727,"byte_start":561,"id":"section:b3937fd5bd5ebd921462","kind":"section","labels":[],"line_end":53,"line_start":13,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/coverage_audit"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/coverage_audit.tex","status_markers_as_written":[],"summary_excerpt":"@p0.18 p0.18 p0.54 @ Original lines & Primary owner & Content\\\\ 225–848 & Paper 0 & Title metadata, original abstract, architecture box, reading guide, big picture.\\\\ 849–1305 & Paper 1 & Primitive core and primitive relative spectral dynamics.\\\\ 1306–2314 & Paper 2 & Carrier algebraic normal form, stabilizer, packet, traces, abelian index.\\\\ 2315–2695 & Paper 3 & Kernel numerics and electromagnetic closure.\\\\ 2696–3","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Primary Coverage Map","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4038,"byte_start":3727,"id":"section:379dddc9b543ddaac718","kind":"section","labels":[],"line_end":58,"line_start":54,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/coverage_audit"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/coverage_audit.tex","status_markers_as_written":[],"summary_excerpt":"Every dedicated paper contains its primary source body and ends with a ``Not used here'' list. 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The source status follows the TFPT 4.5 split: boundary and carrier inputs are core, electromagnetic/flavor/metrology inputs are bridge readouts, QFT closure is conditional, and cosmology rows are downstream comparis","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Standalone Minimal Kernel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1602,"byte_start":1411,"id":"section:78a580896c6c7a997120","kind":"section","labels":[],"line_end":24,"line_start":22,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_alpha_em_closure"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_alpha_em_closure.tex","status_markers_as_written":[],"summary_excerpt":"Electromagnetic closure [formula in source] Carrier budget and exact seam opening enter before the root is evaluated.root or residual failure","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dependency Graph","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2309,"byte_start":1602,"id":"section:a26008db0d714512c3f2","kind":"section","labels":[],"line_end":52,"line_start":25,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_alpha_em_closure"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_alpha_em_closure.tex","status_markers_as_written":[],"summary_excerpt":"The electromagnetic row uses the exact seam opening, not the frozen retained seed. With [formula in source] define [formula in source] The closure function is [formula in source] The prediction is the unique positive root [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2561,"byte_start":2309,"id":"section:ca6b8093074a2738f1e7","kind":"section","labels":[],"line_end":55,"line_start":53,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_alpha_em_closure"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_alpha_em_closure.tex","status_markers_as_written":[],"summary_excerpt":"The exact opening [formula in source] must remain inside the root equation. Freezing it at [formula in source] shifts the result by about [formula in source] in [formula in source] and is not the benchmark definition.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"No-Knobs and Failure Surface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2967,"byte_start":2561,"id":"section:7ddb1ad50f77c2d8ea92","kind":"section","labels":[],"line_end":64,"line_start":56,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_alpha_em_closure"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_alpha_em_closure.tex","status_markers_as_written":[],"summary_excerpt":"The standalone claim is limited to the displayed target and dependency class. 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Any update of the upstream boundary kernel, carrier theorem, or sector map must be propagated into this prediction before the numerical row is distributed.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Minimal Submission Claim","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":762,"byte_start":0,"id":"section:df2452663e1a38780f45","kind":"frontmatter","labels":[],"line_end":15,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_alpha_mz_scheme"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_alpha_mz_scheme.tex","status_markers_as_written":[],"summary_excerpt":"tfptblue TFPT Prediction: Running Electromagnetic Scheme Projection at the Z Pole Stefan Hamann Alessandro Rizzo tfptgray Standalone prediction note –","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"tfptblue TFPT Prediction: Running Electromagnetic Scheme Projection at the Z Pole","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1274,"byte_start":762,"id":"section:17305e6ac46ac41ea9b1","kind":"section","labels":[],"line_end":21,"line_start":16,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_alpha_mz_scheme"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_alpha_mz_scheme.tex","status_markers_as_written":[],"summary_excerpt":"The paper is intentionally one-row: it does not reprove the full TFPT series. It states the minimal closed-branch input needed for this prediction, shows the sector map, and gives the direct failure mode. The source status follows the TFPT 4.5 split: boundary and carrier inputs are core, electromagnetic/flavor/metrology inputs are bridge readouts, QFT closure is conditional, and cosmology rows are downstream comparis","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Standalone Minimal Kernel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1464,"byte_start":1274,"id":"section:9151299f7583c664a277","kind":"section","labels":[],"line_end":24,"line_start":22,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_alpha_mz_scheme"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_alpha_mz_scheme.tex","status_markers_as_written":[],"summary_excerpt":"Scheme projection [formula in source] This row projects the exact alpha(0) readout through a declared scheme map.scheme mismatch","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dependency Graph","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1871,"byte_start":1464,"id":"section:22cffe3ac7b8302eb443","kind":"section","labels":[],"line_end":41,"line_start":25,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_alpha_mz_scheme"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_alpha_mz_scheme.tex","status_markers_as_written":[],"summary_excerpt":"The physical electromagnetic input is the exact closure value [formula in source] The Z-pole comparison row is obtained only after the declared scheme map [formula in source] is applied. The representative in the ledger is [formula in source] Its status is therefore scheme projection, not a separate primitive prediction.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2050,"byte_start":1871,"id":"section:249054de342013d95f2b","kind":"section","labels":[],"line_end":44,"line_start":42,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_alpha_mz_scheme"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_alpha_mz_scheme.tex","status_markers_as_written":[],"summary_excerpt":"The row must not be used as an independent fitting input. It is downstream of alpha(0) and the declared threshold convention.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"No-Knobs and Failure Surface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2456,"byte_start":2050,"id":"section:b9c67e30b1f6f6013de6","kind":"section","labels":[],"line_end":53,"line_start":45,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_alpha_mz_scheme"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_alpha_mz_scheme.tex","status_markers_as_written":[],"summary_excerpt":"The standalone claim is limited to the displayed target and dependency class. It does not assert that every comparison row of the full TFPT ledger has the same proof status. Any update of the upstream boundary kernel, carrier theorem, or sector map must be propagated into this prediction before the numerical row is distributed.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Minimal Submission Claim","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":747,"byte_start":0,"id":"section:e116cfa04264caba06ee","kind":"frontmatter","labels":[],"line_end":15,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_axion_haloscope_window"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_axion_haloscope_window.tex","status_markers_as_written":[],"summary_excerpt":"tfptblue TFPT Prediction: Axion Haloscope Window from the Seam-Transfer Cosmology Interface Stefan Hamann Alessandro Rizzo tfptgray Standalone prediction note –","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"tfptblue TFPT Prediction: Axion Haloscope Window from the Seam-Transfer Cosmology Interface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1259,"byte_start":747,"id":"section:169867abcf31e9646d0f","kind":"section","labels":[],"line_end":21,"line_start":16,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_axion_haloscope_window"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_axion_haloscope_window.tex","status_markers_as_written":[],"summary_excerpt":"The paper is intentionally one-row: it does not reprove the full TFPT series. It states the minimal closed-branch input needed for this prediction, shows the sector map, and gives the direct failure mode. The source status follows the TFPT 4.5 split: boundary and carrier inputs are core, electromagnetic/flavor/metrology inputs are bridge readouts, QFT closure is conditional, and cosmology rows are downstream comparis","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Standalone Minimal Kernel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1427,"byte_start":1259,"id":"section:db2f67d43343eb720a7a","kind":"section","labels":[],"line_end":24,"line_start":22,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_axion_haloscope_window"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_axion_haloscope_window.tex","status_markers_as_written":[],"summary_excerpt":"Axion interfacehaloscope windowThe row is downstream of seam transfer and determinant-line phase.window exclusion","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dependency Graph","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1962,"byte_start":1427,"id":"section:a18b045adf620997933c","kind":"section","labels":[],"line_end":46,"line_start":25,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_axion_haloscope_window"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_axion_haloscope_window.tex","status_markers_as_written":[],"summary_excerpt":"The determinant-line axion interface fixes [formula in source] with seam-transfer and scalaron inputs supplying the cosmology interface. The closed-branch target recorded in the ledger is [formula in source] The associated coupled sensitivity row is [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2163,"byte_start":1962,"id":"section:0784777c38b399845dce","kind":"section","labels":[],"line_end":49,"line_start":47,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_axion_haloscope_window"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_axion_haloscope_window.tex","status_markers_as_written":[],"summary_excerpt":"The practical scan target is [formula in source] . Exclusion in the relevant coupled window pressures the intrinsic axion row.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"No-Knobs and Failure Surface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2569,"byte_start":2163,"id":"section:a87e1eef23242aef73a7","kind":"section","labels":[],"line_end":58,"line_start":50,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_axion_haloscope_window"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_axion_haloscope_window.tex","status_markers_as_written":[],"summary_excerpt":"The standalone claim is limited to the displayed target and dependency class. It does not assert that every comparison row of the full TFPT ledger has the same proof status. Any update of the upstream boundary kernel, carrier theorem, or sector map must be propagated into this prediction before the numerical row is distributed.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Minimal Submission Claim","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":717,"byte_start":0,"id":"section:ce33691530aa309a4189","kind":"frontmatter","labels":[],"line_end":15,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_birefringence_beta"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_birefringence_beta.tex","status_markers_as_written":[],"summary_excerpt":"tfptblue TFPT Prediction: Cosmic Birefringence from Determinant-Line Response Stefan Hamann Alessandro Rizzo tfptgray Standalone prediction note –","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"tfptblue TFPT Prediction: Cosmic Birefringence from Determinant-Line Response","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1229,"byte_start":717,"id":"section:9d7ec3f7e4b7b6f459e8","kind":"section","labels":[],"line_end":21,"line_start":16,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_birefringence_beta"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_birefringence_beta.tex","status_markers_as_written":[],"summary_excerpt":"The paper is intentionally one-row: it does not reprove the full TFPT series. It states the minimal closed-branch input needed for this prediction, shows the sector map, and gives the direct failure mode. The source status follows the TFPT 4.5 split: boundary and carrier inputs are core, electromagnetic/flavor/metrology inputs are bridge readouts, QFT closure is conditional, and cosmology rows are downstream comparis","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Standalone Minimal Kernel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1388,"byte_start":1229,"id":"section:ecc1d0b9a08ab05dca83","kind":"section","labels":[],"line_end":24,"line_start":22,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_birefringence_beta"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_birefringence_beta.tex","status_markers_as_written":[],"summary_excerpt":"Determinant response [formula in source] The response row is sectorized away from the old seed quartet.calibrated null","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dependency Graph","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1856,"byte_start":1388,"id":"section:22c12b8686e650e940fe","kind":"section","labels":[],"line_end":43,"line_start":25,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_birefringence_beta"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_birefringence_beta.tex","status_markers_as_written":[],"summary_excerpt":"The retained UV expression is [formula in source] In degrees this gives the row recorded as [formula in source] The physical dependency class is not the old seed quartet but the determinant-line response [formula in source] The comparison row is made against calibrated CMB rotation analyses without EB self-nulling.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2059,"byte_start":1856,"id":"section:7f7893b26894c1c6ac0b","kind":"section","labels":[],"line_end":46,"line_start":44,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_birefringence_beta"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_birefringence_beta.tex","status_markers_as_written":[],"summary_excerpt":"The direct falsifier is a calibrated achromatic CMB rotation analysis consistent with [formula in source] inside [formula in source] under the declared convention.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"No-Knobs and Failure Surface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2465,"byte_start":2059,"id":"section:4c84354a785d610478f9","kind":"section","labels":[],"line_end":55,"line_start":47,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_birefringence_beta"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_birefringence_beta.tex","status_markers_as_written":[],"summary_excerpt":"The standalone claim is limited to the displayed target and dependency class. It does not assert that every comparison row of the full TFPT ledger has the same proof status. Any update of the upstream boundary kernel, carrier theorem, or sector map must be propagated into this prediction before the numerical row is distributed.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Minimal Submission Claim","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":678,"byte_start":0,"id":"section:0d7a27d0aaf6ad55ad0f","kind":"frontmatter","labels":[],"line_end":15,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_ckm_phase"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_ckm_phase.tex","status_markers_as_written":[],"summary_excerpt":"tfptblue TFPT Prediction: CKM Phase from Exact Holonomy Transport Stefan Hamann Alessandro Rizzo tfptgray Standalone prediction note –","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"tfptblue TFPT Prediction: CKM Phase from Exact Holonomy Transport","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1190,"byte_start":678,"id":"section:9bd98329e43e5390386c","kind":"section","labels":[],"line_end":21,"line_start":16,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_ckm_phase"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_ckm_phase.tex","status_markers_as_written":[],"summary_excerpt":"The paper is intentionally one-row: it does not reprove the full TFPT series. It states the minimal closed-branch input needed for this prediction, shows the sector map, and gives the direct failure mode. 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A stable exclusion at [formula in source] would break the current flavor bridge.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"No-Knobs and Failure Surface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2430,"byte_start":2024,"id":"section:1e9026cb771db00f48df","kind":"section","labels":[],"line_end":53,"line_start":45,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_ckm_phase"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_ckm_phase.tex","status_markers_as_written":[],"summary_excerpt":"The standalone claim is limited to the displayed target and dependency class. It does not assert that every comparison row of the full TFPT ledger has the same proof status. Any update of the upstream boundary kernel, carrier theorem, or sector map must be propagated into this prediction before the numerical row is distributed.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Minimal Submission Claim","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4016,"byte_start":0,"id":"section:f2bd5a6066b402971cd9","kind":"frontmatter","labels":[],"line_end":104,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_alpha_em_closure","document:_archive/tfpt-45/predictions/tfpt_prediction_alpha_mz_scheme","document:_archive/tfpt-45/predictions/tfpt_prediction_axion_haloscope_window","document:_archive/tfpt-45/predictions/tfpt_prediction_birefringence_beta","document:_archive/tfpt-45/predictions/tfpt_prediction_ckm_phase","document:_archive/tfpt-45/predictions/tfpt_prediction_eht_achromatic_intercept","document:_archive/tfpt-45/predictions/tfpt_prediction_eta_b_leptogenesis","document:_archive/tfpt-45/predictions/tfpt_prediction_lambda_c_cabibbo","document:_archive/tfpt-45/predictions/tfpt_prediction_neutrino_sum","document:_archive/tfpt-45/predictions/tfpt_prediction_neutrinoless_double_beta","document:_archive/tfpt-45/predictions/tfpt_prediction_no_second_higgs","document:_archive/tfpt-45/predictions/tfpt_prediction_omega_b_cosmology","document:_archive/tfpt-45/predictions/tfpt_prediction_pi0_hadronic","document:_archive/tfpt-45/predictions/tfpt_prediction_pmns_phase_octant","document:_archive/tfpt-45/predictions/tfpt_prediction_rare_kaons","document:_archive/tfpt-45/predictions/tfpt_prediction_strong_cp_edm_null","document:_archive/tfpt-45/predictions/tfpt_prediction_theta13_neutrino","document:_archive/tfpt-45/predictions/tfpt_two_page_summary"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_common.tex","status_markers_as_written":[],"summary_excerpt":"The standalone input package is the boundary-polarized closed branch [formula in source] The prediction uses only the sector map named in its audit box. Numerical comparison conventions are not theorem inputs; they enter only at the final interface row.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1534,"byte_start":0,"id":"section:9ebcf46fc01a6671cdd3","kind":"frontmatter","labels":[],"line_end":25,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_eht_achromatic_intercept"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_eht_achromatic_intercept.tex","status_markers_as_written":[],"summary_excerpt":"tfptblue TFPT Prediction: Achromatic Residual Polarization Intercept around Compact Objects\\\\[0.35em] An EHT/ngEHT Test of the Local Dyonic [formula in source] Channel Stefan Hamann Alessandro Rizzo tfptgray Standalone prediction note –","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"tfptblue TFPT Prediction: Achromatic Residual Polarization Intercept around Compact Objects\\\\[0.35em] An EHT/ngEHT Test of the Local Dyonic [formula in source] Channel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2016,"byte_start":1534,"id":"section:f4f9104548479b7ba3e3","kind":"section","labels":[],"line_end":35,"line_start":26,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_eht_achromatic_intercept"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_eht_achromatic_intercept.tex","status_markers_as_written":[],"summary_excerpt":"This row uses the same closed-branch input package as the cosmic-birefringence prediction. The new content is the projection map onto the local dyonic geometry of a magnetised compact object. Source status follows the TFPT 4.5 split: boundary, carrier, and electromagnetic-closure inputs are core; the determinant-line response is a bridge readout; cosmology and astrophysical projections are downstream comparison surfa","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Standalone Minimal Kernel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2259,"byte_start":2016,"id":"section:7bbc051982f6dc912052","kind":"section","labels":[],"line_end":39,"line_start":36,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_eht_achromatic_intercept"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_eht_achromatic_intercept.tex","status_markers_as_written":[],"summary_excerpt":"Determinant-line response, dyonic projection [formula in source] Local [formula in source] projection on the horizon collar after GRMHD subtraction.calibrated null","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dependency Graph","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4251,"byte_start":2259,"id":"section:db28b89591a66acba2e4","kind":"section","labels":["eq:beta-bh","sec:eht-derivation"],"line_end":80,"line_start":40,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_eht_achromatic_intercept"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_eht_achromatic_intercept.tex","status_markers_as_written":[],"summary_excerpt":"The determinant-line response of TFPT yields the cosmological birefringence row through [formula in source] The same admissibility data emits a local astrophysical [formula in source] amplitude for a magnetised horizon-scale region. Tracing the dyonic appendix of the TFPT 4.2 source through the closure chain [formula in source] local response, the local rotation rate takes the structured form where [formula in source","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"From the Determinant-Line Response to a Local Channel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6671,"byte_start":4251,"id":"section:8ab87107860676e42270","kind":"section","labels":["eq:chi-RM","eq:chi-res","sec:eht-protocol"],"line_end":127,"line_start":81,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_eht_achromatic_intercept"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_eht_achromatic_intercept.tex","status_markers_as_written":[],"summary_excerpt":"The conventional rotation-measure decomposition of the linear-polarization angle is i.e. the wavelength-squared coefficient [formula in source] captures conventional Faraday rotation and the intercept [formula in source] collects the achromatic part: intrinsic emission orientation, calibration, and any new physics insensitive to [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Observation Protocol","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7486,"byte_start":6671,"id":"section:f29fa336a853bde0ce5a","kind":"section","labels":[],"line_end":144,"line_start":128,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_eht_achromatic_intercept"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_eht_achromatic_intercept.tex","status_markers_as_written":[],"summary_excerpt":"The prediction is robust because three independent null tests must be passed simultaneously before it can be claimed:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Three Independent Nulls","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8280,"byte_start":7486,"id":"section:b09446298f62691bb136","kind":"section","labels":[],"line_end":160,"line_start":145,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_eht_achromatic_intercept"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_eht_achromatic_intercept.tex","status_markers_as_written":[],"summary_excerpt":"The local dyonic amplitude in controls the precision-zone correction of the [formula in source] -kernel: [formula in source] This cross-link is structural, not numerical: the same TFPT branch number that puts the electromagnetic closure into the precision zone of CODATA also controls the size of the local dyonic intercept. EHT-class polarimetry therefore probes the same admissibility data as the [formula in source] r","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cross-Link to the [formula in source] -KernelCross-Link to the alpha-Kernel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9058,"byte_start":8280,"id":"section:8d98be6de842bac7733f","kind":"section","labels":[],"line_end":172,"line_start":161,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_eht_achromatic_intercept"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_eht_achromatic_intercept.tex","status_markers_as_written":[],"summary_excerpt":"The TFPT coupling [formula in source] is fixed by the same kernel that fixes [formula in source] and [formula in source] : there is no free coupling in [formula in source] and [formula in source] , the inflow geometry, and the emission radius. 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It does not claim a full microscopic black-hole solution and does not reinterpret rotation-measure analyses. Any update of the upstream boundary kernel, carrier theorem, electromagnetic closure, or determinant-line response must be propagated i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Minimal Submission Claim","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":678,"byte_start":0,"id":"section:cafe6f8301edfa6e0939","kind":"frontmatter","labels":[],"line_end":15,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_eta_b_leptogenesis"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_eta_b_leptogenesis.tex","status_markers_as_written":[],"summary_excerpt":"tfptblue TFPT Prediction: Baryon Asymmetry from the Leptogenesis Interface Stefan Hamann Alessandro Rizzo tfptgray Standalone prediction note –","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"tfptblue TFPT Prediction: Baryon Asymmetry from the Leptogenesis Interface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1190,"byte_start":678,"id":"section:9bcfe97f47177c60dd4b","kind":"section","labels":[],"line_end":21,"line_start":16,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_eta_b_leptogenesis"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_eta_b_leptogenesis.tex","status_markers_as_written":[],"summary_excerpt":"The paper is intentionally one-row: it does not reprove the full TFPT series. It states the minimal closed-branch input needed for this prediction, shows the sector map, and gives the direct failure mode. The source status follows the TFPT 4.5 split: boundary and carrier inputs are core, electromagnetic/flavor/metrology inputs are bridge readouts, QFT closure is conditional, and cosmology rows are downstream comparis","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Standalone Minimal Kernel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; 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A stable [formula in source] value outside [formula in source] or a GN-plane mismatch would break the present flavor bridge.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"No-Knobs and Failure Surface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2575,"byte_start":2169,"id":"section:c7fc45e9edda3ce3a584","kind":"section","labels":[],"line_end":48,"line_start":40,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_rare_kaons"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_rare_kaons.tex","status_markers_as_written":[],"summary_excerpt":"The standalone claim is limited to the displayed target and dependency class. 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not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1427,"byte_start":1222,"id":"section:98f18a9cbf130ce2eacb","kind":"section","labels":[],"line_end":24,"line_start":22,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_strong_cp_edm_null"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_strong_cp_edm_null.tex","status_markers_as_written":[],"summary_excerpt":"Admissibility and determinant-line closure [formula in source] Strong CP belongs to admissibility/QFT closure, not to the flavor paper.nonzero EDM","summary_method":"opening prose excerpt; 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Any update of the upstream boundary kernel, carrier theorem, or sector map must be propagated into this prediction before the numerical row is distributed.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Minimal Submission Claim","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":720,"byte_start":0,"id":"section:1bcee2531ff770848b6e","kind":"frontmatter","labels":[],"line_end":16,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_theta13_neutrino"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_theta13_neutrino.tex","status_markers_as_written":[],"summary_excerpt":"tfptblue TFPT Prediction: Neutrino Reactor Angle from the Closed PMNS Branch Stefan Hamann Alessandro Rizzo tfptgray Standalone prediction note –","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"tfptblue TFPT Prediction: Neutrino Reactor Angle from the Closed PMNS Branch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1232,"byte_start":720,"id":"section:73a2158720a0c219a3d8","kind":"section","labels":[],"line_end":22,"line_start":17,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_theta13_neutrino"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_theta13_neutrino.tex","status_markers_as_written":[],"summary_excerpt":"The paper is intentionally one-row: it does not reprove the full TFPT series. It states the minimal closed-branch input needed for this prediction, shows the sector map, and gives the direct failure mode. The source status follows the TFPT 4.5 split: boundary and carrier inputs are core, electromagnetic/flavor/metrology inputs are bridge readouts, QFT closure is conditional, and cosmology rows are downstream comparis","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Standalone Minimal Kernel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1419,"byte_start":1232,"id":"section:30f41891f55be0fdb58f","kind":"section","labels":[],"line_end":25,"line_start":23,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_theta13_neutrino"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_theta13_neutrino.tex","status_markers_as_written":[],"summary_excerpt":"Neutrino closure [formula in source] The UV identity is a shadow; the operational row belongs to PMNS/neutrino closure.NuFIT exclusion","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dependency Graph","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1898,"byte_start":1419,"id":"section:00c73f44bae2515989d5","kind":"section","labels":[],"line_end":46,"line_start":26,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_theta13_neutrino"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_theta13_neutrino.tex","status_markers_as_written":[],"summary_excerpt":"The compact UV identity is [formula in source] After sectorization, the physical row is read as [formula in source] The benchmark target recorded in the prediction table is [formula in source] The comparison convention used in the ledger is the NuFIT normal-ordering representative.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2101,"byte_start":1898,"id":"section:744094073e11ac0fe487","kind":"section","labels":[],"line_end":49,"line_start":47,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_theta13_neutrino"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_theta13_neutrino.tex","status_markers_as_written":[],"summary_excerpt":"The row must not be presented as a free seed projection. Its operational status is neutrino closure; the seed expression is only a compact UV shadow.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"No-Knobs and Failure Surface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2507,"byte_start":2101,"id":"section:dc6ce5a7586729a2ff97","kind":"section","labels":[],"line_end":58,"line_start":50,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_prediction_theta13_neutrino"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_prediction_theta13_neutrino.tex","status_markers_as_written":[],"summary_excerpt":"The standalone claim is limited to the displayed target and dependency class. It does not assert that every comparison row of the full TFPT ledger has the same proof status. Any update of the upstream boundary kernel, carrier theorem, or sector map must be propagated into this prediction before the numerical row is distributed.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Minimal Submission Claim","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":783,"byte_start":0,"id":"section:736a2efa33976ca96e05","kind":"frontmatter","labels":[],"line_end":20,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_two_page_summary"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_two_page_summary.tex","status_markers_as_written":[],"summary_excerpt":"-2.2em tfptblue TFPT in Two Pages\\\\[-0.15em] Boundary polarization, carrier rigidity, and testable readouts Stefan Hamann Alessandro Rizzo -1.0em","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"-2.2em tfptblue TFPT in Two Pages\\\\[-0.15em] Boundary polarization, carrier rigidity, and testable readouts","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; 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not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2400,"byte_start":1593,"id":"section:36f0b02b84019afaeed5","kind":"section","labels":[],"line_end":68,"line_start":50,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_two_page_summary"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_two_page_summary.tex","status_markers_as_written":[],"summary_excerpt":"@p0.20 p0.23 Y@ Layer & Status & Role \\\\ Boundary kernel & Core theorem & Builds [formula in source] from [formula in source] .\\\\ Carrier packet & Core theorem & Generates the Standard-Model-like representation packet.\\\\ EM/flavor & Bridge/readout & Fixes [formula in source] , CKM, PMNS, and sectorized seed shadows.\\\\ QFT/strong CP & Conditional closure & Uses stated admissibility, positivity, and gap hypotheses.\\\\ M","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Status Discipline","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3904,"byte_start":2400,"id":"section:032609bafdcc07e1c7a5","kind":"section","labels":[],"line_end":91,"line_start":69,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_two_page_summary"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_two_page_summary.tex","status_markers_as_written":[],"summary_excerpt":"@p0.19 p0.22 p0.22 Y@ Row & Target & Dependency class & Kill/pressure criterion \\\\ [formula in source] & [formula in source] & exact EM closure & failure of the self-consistent root.\\\\ [formula in source] & [formula in source] & flavor readout & stable CKM mismatch.\\\\ [formula in source] & [formula in source] & neutrino closure & robust NO global-fit exclusion.\\\\ [formula in source] & [formula in source] & determinan","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Prediction Surface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4272,"byte_start":3904,"id":"section:f31643b0f549bcfcd0a8","kind":"section","labels":[],"line_end":98,"line_start":92,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/predictions/tfpt_two_page_summary"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/predictions/tfpt_two_page_summary.tex","status_markers_as_written":[],"summary_excerpt":"The prediction papers do not treat every row as the same kind of truth. Some are theorem-level null tests, some are physical observables, some are scheme projections, and some are downstream comparison targets. Each standalone prediction paper states its dependency class and kill criterion before giving the formula chain.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"What This Is Not","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":660,"byte_start":0,"id":"section:ea795c3e0c284769b5cc","kind":"frontmatter","labels":[],"line_end":19,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/series_index"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/series_index.tex","status_markers_as_written":[],"summary_excerpt":"tfptblue TFPT 4.5 Paper Series Index\\\\[0.35em] Split by Burden of Proof Stefan Hamann Alessandro Rizzo tfptgray Working index generated from –","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"tfptblue TFPT 4.5 Paper Series Index\\\\[0.35em] Split by Burden of Proof","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2158,"byte_start":660,"id":"section:a01f4705d32ce8754839","kind":"section","labels":[],"line_end":39,"line_start":20,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/series_index"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/series_index.tex","status_markers_as_written":[],"summary_excerpt":"@p0.12 p0.34 Y@ File & Title & Role \\\\ 00_orientation_note.tex & TFPT in One Map & Thin entry document and dependency map. \\\\ 01_boundary_kernel.tex & Boundary Polarization and the Primitive Kernel of TFPT & Primitive boundary kernel. \\\\ 02_carrier_rigidity_standard_model_packet.tex & Carrier Rigidity, Hypercharge, and the Standard Model Packet & Carrier theorem and SM packet. \\\\ 03_electromagnetic_closure_flavor_tra","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Documents","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2624,"byte_start":2158,"id":"section:d5180dd192386a37265e","kind":"section","labels":[],"line_end":50,"line_start":40,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/series_index"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/series_index.tex","status_markers_as_written":[],"summary_excerpt":"Paper 1: boundary primitive kernel. Paper 2: carrier rigidity and Standard-Model packet. Paper 3: electromagnetic and flavor readouts. Paper 4: admissibility, strong CP, positivity, OS/local-net/scattering closure. Paper 5: geometric branch and dimensionless metrology. Paper 6: downstream cosmology interfaces.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Mathematical Dependency Order","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3002,"byte_start":2624,"id":"section:36d50e75a98758ea3fed","kind":"section","labels":[],"line_end":61,"line_start":51,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/series_index"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/series_index.tex","status_markers_as_written":[],"summary_excerpt":"Paper 0 as public orientation. Paper 2 as first visible core result. Paper 1 as formal foundation backbone. Paper 3 as prediction paper. Papers 4 and 5 as analytic and metrological stabilization. Paper 6 as downstream expansion.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Recommended Public Order","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3503,"byte_start":3002,"id":"section:57cff0e7b98afca06c28","kind":"section","labels":[],"line_end":74,"line_start":62,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/series_index"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/series_index.tex","status_markers_as_written":[],"summary_excerpt":"Every paper begins with the same four-part box: Inputs from previous papers. New theorem contribution. Not claimed here. Falsification or audit surface. This is a deliberate anti-evasion device: each document states how it can fail. Each paper also ends with a short ``Not used here'' list so that excluded material does not re-enter through a back-door support appendix.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Per-Paper Front-Box Rule","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4206,"byte_start":3503,"id":"section:9f019dcfbe1de2ca9e1e","kind":"section","labels":[],"line_end":91,"line_start":75,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/series_index"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/series_index.tex","status_markers_as_written":[],"summary_excerpt":"@p0.22 Y@ Paper & Explicit exclusions \\\\ Paper 1 & Carrier, SM group, [formula in source] , flavor, gravity, cosmology, E8. \\\\ Paper 2 & Exact [formula in source] , CKM, PMNS, masses, OS reconstruction, cosmology, E8. \\\\ Paper 3 & Full QFT closure, gravity, CMB, E8, large mass tables. \\\\ Paper 4 & [formula in source] detail calculation, CMB, E8, full empirical tables. \\\\ Paper 5 & Late-time [formula in source] , CMB,","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Global Exclusion Discipline","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4630,"byte_start":4206,"id":"section:d9f561d00f7b45997b87","kind":"section","labels":[],"line_end":100,"line_start":92,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/series_index"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/series_index.tex","status_markers_as_written":[],"summary_excerpt":"All documents in this folder are based on . The dedicated papers are intentionally clean splits: they keep their own primary source body and refer cross-paper material through dependency boxes. The Technical Companion is the designated home for full appendix-level ballast, extended ledgers, optional continuations, E8 grammar, horizons, record algebra, and transient channels.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Source","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6495,"byte_start":0,"id":"section:b772146c3488ec2fc03c","kind":"frontmatter","labels":[],"line_end":202,"line_start":1,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/source_extracts/00_shared_architecture_source.tex","status_markers_as_written":[],"summary_excerpt":"From the one-sided boundary datum [formula in source] the manuscript derives the Calder\\'on polarization [formula in source] , the boundary involution [formula in source] , the exact-double deck involution [formula in source] , and the doubled closed datum [formula in source] The hard core is now read through three decoders. First, the carrier decoder [formula in source] satisfies [formula in source] and in the primi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3888,"byte_start":0,"id":"section:07a68b6b3fbab2251fa7","kind":"frontmatter","labels":[],"line_end":92,"line_start":1,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/source_extracts/99_bibliography_source.tex","status_markers_as_written":[],"summary_excerpt":"aps1975 M. F. Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian geometry. I, Math. Proc. Cambridge Philos. 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Singer, Spectral asymmetry and Riemannian geometry. I, Math. Proc. Cambridge Philos. 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Leach, How long before the end of inflation was observable inflation?, Phys. Rev. D 68 (2003), 103503; arXiv:astro-ph/0305263.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2261,"byte_start":0,"id":"section:b1e90a348a191d124915","kind":"frontmatter","labels":[],"line_end":53,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/03_electromagnetic_closure_flavor_transport"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/source_extracts/bibliography_precision.tex","status_markers_as_written":[],"summary_excerpt":"codata2022 P. J. Mohr, D. B. Newell, and B. N. Taylor, CODATA recommended values of the fundamental physical constants: 2022 update, NIST / CODATA reference set, https://physics.nist.gov/cuu/Constants/, accessed March 2026.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1476,"byte_start":0,"id":"section:3ca9d7787d313bc094db","kind":"frontmatter","labels":[],"line_end":34,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/technical_companion.tex","status_markers_as_written":[],"summary_excerpt":"tfptblue Technical Companion to TFPT\\\\[0.35em] Conventions, Positivity, APS Interfaces, and Comparison Maps Stefan Hamann Alessandro Rizzo tfptgray Companion document for the TFPT 4.5 paper series –","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"tfptblue Technical Companion to TFPT\\\\[0.35em] Conventions, Positivity, APS Interfaces, and Comparison Maps","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1733,"byte_start":1476,"id":"section:6d075708b89859807d61","kind":"section","labels":[],"line_end":40,"line_start":35,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/technical_companion.tex","status_markers_as_written":[],"summary_excerpt":"The companion exists to keep the six papers short enough to be reviewed by the right audiences. A reader checking the carrier theorem should not be forced to read CMB sky maps, E8 scale grammar, record algebra, or horizon continuations.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Purpose","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2060,"byte_start":1733,"id":"section:b36fc927d5178a4e63ec","kind":"section","labels":[],"line_end":52,"line_start":41,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/technical_companion.tex","status_markers_as_written":[],"summary_excerpt":"The first part collects: symbol guide, relative objects, layered datum and admissibility conventions, APS and superconnection setup, positivity conventions, theorem-status vocabulary.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Core Convention Blocks","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2449,"byte_start":2060,"id":"section:81073067a9ab9e39fb4e","kind":"section","labels":[],"line_end":64,"line_start":53,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/technical_companion.tex","status_markers_as_written":[],"summary_excerpt":"This part holds expanded details for: relative reflection positivity with fermions, admissible OS reconstruction, asymptotic scattering, dressed massless interface, exact admissible flow and 1PI expansion details, Yukawa kernels and positivity lemmas.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Analytic Backend","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2836,"byte_start":2449,"id":"section:b006166411e5169234e3","kind":"section","labels":[],"line_end":77,"line_start":65,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/technical_companion.tex","status_markers_as_written":[],"summary_excerpt":"This part holds: constants atlas, extended benchmarks, compact and full empirical ledgers, residual readout and interface refinements, operational prediction matrix, target and kill-test rows, novelty boundary and literature positioning.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Comparison Backend","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3334,"byte_start":2836,"id":"section:b84dce1b35eaf7e39c87","kind":"section","labels":[],"line_end":92,"line_start":78,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/technical_companion.tex","status_markers_as_written":[],"summary_excerpt":"This part holds material that should not drive the primitive theorem chain: E8 stage atlas, optional arithmetic continuations, infrared seam-transfer continuations, horizon continuations, record algebra and pointer dynamics, information-theoretic readings, cut-and-project readings, transient event channels.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Downstream and Optional Continuations","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3680,"byte_start":3334,"id":"section:82adb67b496d093b5581","kind":"section","labels":[],"line_end":99,"line_start":93,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/technical_companion.tex","status_markers_as_written":[],"summary_excerpt":"This section contains the main technical development assigned to this paper by the TFPT 4.5 clean split. Cross-paper background is referenced through dependency and scope boxes; extended backend material is kept in the Technical Companion.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Main Technical Development","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4491,"byte_start":3680,"id":"section:eaad73e5e7234d8b607f","kind":"section","labels":["app:dyonic-calibration"],"line_end":114,"line_start":100,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/technical_companion.tex","status_markers_as_written":[],"summary_excerpt":"This appendix records the analytic dyonic calibration model that supports the local achromatic intercept [formula in source] used in the EHT-class residual-intercept prediction. It is a calibration model, not a physical horizon-scale solution: the goal is to display how the fixed TFPT coupling [formula in source] is projected onto a magnetised compact-object geometry through model-dependent geometric weights.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dyonic Calibration Lemma and Local [formula in source] Intercept","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5316,"byte_start":4491,"id":"section:458af9ade18f94aaeaac","kind":"subsection","labels":["eq:dyonic-E","eq:dyonic-axion","eq:dyonic-f"],"line_end":134,"line_start":115,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/technical_companion.tex","status_markers_as_written":[],"summary_excerpt":"Consider a static, spherically symmetric ansatz with a magnetised dyonic interior and the admissible-branch axion field. Working at leading order in the boundary-normalised expansion, the axion profile, the radial electric field, and the metric function take the closed forms where [formula in source] is the standard Reissner–Nordström-like contribution and the quartic correction [formula in source] is the leading dyo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Analytic dyonic toy ansatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6312,"byte_start":5316,"id":"section:bc69831152bd4ac15f21","kind":"subsection","labels":["eq:beta-bh-companion"],"line_end":155,"line_start":135,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/technical_companion.tex","status_markers_as_written":[],"summary_excerpt":"The corresponding local rotation of the linear-polarization angle in the magnetised inflow region follows from the determinant-line / Chern–Simons response composed with the local [formula in source] projection, yielding where [formula in source] and [formula in source] encode the local effective dyonic weights in the bright magnetically dominated regions of the horizon-scale image, and [formula in source] is the top","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Local [formula in source] intercept","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7501,"byte_start":6312,"id":"section:5c373fe1e993adb684c4","kind":"subsection","labels":["lem:horizon-shift-sign","ssec:horizon-shift-correction"],"line_end":184,"line_start":156,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/technical_companion.tex","status_markers_as_written":[],"summary_excerpt":"A known wording slip in earlier draft notes describes the [formula in source] shift of ``microscopic increase'' of the outer horizon. This is reversed by direct inspection of the quartic term: with [formula in source] , the function [formula in source] acquires a positive contribution that grows as [formula in source] , so the outer root of [formula in source] migrates inward.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Horizon-shift sign correction","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8011,"byte_start":7501,"id":"section:33236e0f5cd1617c0929","kind":"subsection","labels":[],"line_end":196,"line_start":185,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/technical_companion.tex","status_markers_as_written":[],"summary_excerpt":"Equation lemma. It is not advertised as a realistic black-hole solution and does not replace a full GRMHD/synchrotron forward model. Its only purpose in the TFPT layer is to display the structural [formula in source] profile and the fixed coupling [formula in source] that enter the achromatic residual intercept of the linear polarization angle.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Calibration scope","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8816,"byte_start":8011,"id":"section:594e28e2de2967061b07","kind":"section","labels":["app:rg-fingerprints"],"line_end":211,"line_start":197,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/technical_companion.tex","status_markers_as_written":[],"summary_excerpt":"This appendix records an external stress-test protocol for the closed-branch admissibility data, formulated as a set of RG fingerprints to be reproduced by an independent two-loop renormalisation solver (e.g. PyR@TE) seeded with the TFPT input package. The fingerprints are external comparison targets, not internal theorem claims: their purpose is to give a sceptical reader a clean numerical reproduction surface.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"External RG Fingerprint Protocol","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9418,"byte_start":8816,"id":"section:dd0ee82a6ceb260ca7e5","kind":"subsection","labels":[],"line_end":225,"line_start":212,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/technical_companion.tex","status_markers_as_written":[],"summary_excerpt":"The configuration handed to the external solver freezes the closed-branch admissibility data [formula in source] together with the carrier rank data [formula in source] , family multiplicity [formula in source] , admissible occupancy [formula in source] , and Higgs index [formula in source] from Paper 2. The two-loop SM running is performed inside the standard [formula in source] system with the declared threshold ma","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TFPT branch input package","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10691,"byte_start":9418,"id":"section:faee8ca5d67e14cbdb1b","kind":"subsection","labels":[],"line_end":263,"line_start":226,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/technical_companion.tex","status_markers_as_written":[],"summary_excerpt":"The fingerprint targets to be reproduced by the external solver are:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Four fingerprints","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11609,"byte_start":10691,"id":"section:b290f664c462afc9ceed","kind":"subsection","labels":[],"line_end":280,"line_start":264,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/technical_companion.tex","status_markers_as_written":[],"summary_excerpt":"The four items above must be presented as external comparison fingerprints of the closed branch through standard SM running, not as new theorem-level claims. They are reproducible from a declared PyR@TE configuration that uses only the upstream TFPT inputs listed above. Until that reproduction is published as a companion artifact, the fingerprints are programmatic targets.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Status discipline","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12539,"byte_start":11609,"id":"section:a31b31afd7e157b578fe","kind":"section","labels":[],"line_end":302,"line_start":281,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/technical_companion.tex","status_markers_as_written":[],"summary_excerpt":"Use : Appendix-level empirical readout sections. Technical conventions and data layers. Constants atlas and downstream scale grammar. Relative APS and superconnection setup. Relative reflection positivity with fermions. Admissible OS reconstruction and asymptotic scattering. FRW reduction and cosmology interface proofs. Yukawa kernels and positivity lemmas. Information-theoretic and cut-and-project readings. Record a","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Source Extraction Map","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12837,"byte_start":12539,"id":"section:ee91623da6f8ee0986b4","kind":"section","labels":[],"line_end":309,"line_start":303,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/technical_companion.tex","status_markers_as_written":[],"summary_excerpt":"If a companion item becomes load-bearing for a theorem paper, it must be promoted into that paper's technical backend or cited as a named standard-theorem interface. 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TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5079,"byte_start":0,"id":"section:f59da1f9ad473c2dcc1f","kind":"frontmatter","labels":[],"line_end":120,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/tfpt45_theory_map"],"relation_ids":[],"semantic_review":false,"source":"_archive/tfpt-45/tfpt45_theory_map.tex","status_markers_as_written":["[P]"],"summary_excerpt":"tfptblue TFPT – Von Boundary Struktur zu beobachtbarer Realit\\\"at\\\\[0.35em] Eine Statuskarte der beanspruchten Ableitungskette, nicht aller Claims auf derselben Beweisstufe Stefan Hamann Alessandro Rizzo tfptgray TFPT 4.5 theory map –","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"tfptblue TFPT – Von Boundary Struktur zu beobachtbarer Realit\\\"at\\\\[0.35em] Eine Statuskarte der beanspruchten Ableitungskette, nicht aller Claims auf derselben Beweisstufe","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2280,"byte_start":0,"id":"section:e5917e0d5131b2a4e25a","kind":"frontmatter","labels":[],"line_end":45,"line_start":1,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/preamble.tex","status_markers_as_written":[],"summary_excerpt":"arrows.meta,positioning,calc disposition ink pageheadfoot muted TFPT / UNIVERSALRAUM Sitzungsstand 20.09.2026 nosep,leftmargin=1.5em,topsep=4pt =1.8em Y> X P[1]> p#1","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1583,"byte_start":0,"id":"section:11d4def5ecb6111d6dee","kind":"frontmatter","labels":[],"line_end":26,"line_start":1,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/001-chapter-leserbrief.tex","status_markers_as_written":[],"summary_excerpt":"ink FORSCHUNGSDOKUMENTATION 17mm 3237 TFPT und Universalraum 7mm Vom geometrischen Compiler zur gemeinsamen physikalischen Dynamik 12mm 9mm Zusammenhängende Darstellung der Untersuchungen, Beweise, Gegenbeispiele und offenen Forschungsfragen aus der Sitzung vom 18.–20. September 2026. Was dieser Bericht leistetDie Sitzung hat mehrere exakte Operatoranschlüsse und vollständige endliche Spektralsätze geliefert. Sie hat","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4426,"byte_start":1583,"id":"section:e220d28239ac26270ec0","kind":"chapter","labels":[],"line_end":42,"line_start":27,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/001-chapter-leserbrief.tex","status_markers_as_written":[],"summary_excerpt":"tocchapterLeserbrief Das Ziel dieser Sitzung war von Anfang an groß: eine gemeinsame, möglichst einfache Ursprungstheorie finden, die den TFPT-Compiler, Quantenprozesse, Materie, Raumzeit und Gravitation aus derselben Struktur verständlich macht. Die Untersuchungen dürfen deshalb nicht nur daran gemessen werden, ob irgendwo eine schöne Matrix entsteht. Entscheidend ist, ob die verschiedenen Matrizen dieselbe Quelle, ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Leserbrief","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4474,"byte_start":4426,"id":"section:38210718ca957c8fff23","kind":"chapter","labels":[],"line_end":43,"line_start":43,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/001-chapter-leserbrief.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Ziel, Maßstab und Gesamtzusammenhang","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5308,"byte_start":4474,"id":"section:7c0c0a45cd8710c44226","kind":"section","labels":[],"line_end":48,"line_start":44,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/001-chapter-leserbrief.tex","status_markers_as_written":[],"summary_excerpt":"Die gesuchte Gesamtlösung soll nicht nur bestehende Zahlen nachbilden. Sie müsste erklären, warum gerade die ursprünglichen Daten, die zulässigen Zustände, die Dynamik und ihre Auslesungen zusammen auftreten. Eine plausible gemeinsame Konstruktion müsste dabei die bereits vorhandenen TFPT-Beziehungen erhalten, statt sie durch frei gewählte Ersatzstrukturen zu reproduzieren.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was eine vollständige Lösung leisten müsste","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7112,"byte_start":5308,"id":"section:c21ec71efd29fbc808ec","kind":"section","labels":[],"line_end":66,"line_start":49,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/001-chapter-leserbrief.tex","status_markers_as_written":[],"summary_excerpt":"P1 setzt eine orientierte Naht, einen primitiven reflexionspositiven Randkern, Einheitswindung und die Normierung [formula in source] . P2 setzt die fünfteilige Trägerschnittstelle mit dem Schnitt [formula in source] . Diese Postulate sind strukturierte Eingaben. Sie sind nicht gleichbedeutend mit den später zusätzlich gewählten Gitterketten, Quellen-Hilberträumen oder Hamiltonoperatoren.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Ausgangspunkt der Theorie","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8693,"byte_start":7112,"id":"section:9bb2112d776d5073213d","kind":"section","labels":[],"line_end":87,"line_start":67,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/001-chapter-leserbrief.tex","status_markers_as_written":[],"summary_excerpt":"@lY@ Klasse & Bedeutung in diesem Bericht\\\\ A & Eine ausdrücklich gewählte Voraussetzung, etwa Graph, Kopplung, Polarisation oder Instrument.\\\\ E & Exakter mathematischer Befund unter den genannten Voraussetzungen; gegebenenfalls durch rationale oder ganzzahlige Zertifikate abgesichert.\\\\ N & Numerischer Befund. Kleine Residuen allein schließen unentdeckte tiefere Zustände nicht aus.\\\\ C & Bedingte physische oder dar","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Belegklassen und drei verschiedene Arten von Eindeutigkeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9689,"byte_start":8693,"id":"section:869c53fd73d15520e952","kind":"section","labels":[],"line_end":100,"line_start":88,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/001-chapter-leserbrief.tex","status_markers_as_written":[],"summary_excerpt":"Viele Ergebnisse der Sitzung liegen in der zweiten Zeile. Die erste Verbindung ist noch nicht vollständig hergeleitet; die dritte und vierte Zeile folgen nicht allein aus der Existenz einer schönen endlichen Realisierung. Diese Karte verhindert, dass ein neuer Teilsektor den ursprünglichen Auftrag unbemerkt ersetzt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie die Gesamtlösung hier geprüft wird","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9739,"byte_start":9689,"id":"section:6a2a4f5655be84475a5b","kind":"chapter","labels":[],"line_end":101,"line_start":101,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/001-chapter-leserbrief.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Von Readouts zur Frage nach dem Prozess","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11877,"byte_start":9739,"id":"section:7beb2d352ba35825540f","kind":"section","labels":[],"line_end":110,"line_start":102,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/001-chapter-leserbrief.tex","status_markers_as_written":[],"summary_excerpt":"Der Ausgangsimpuls war, in den Readouts und im Forschungsgraphen eine bislang übersehene Verbindung zu finden. Assoziative Texte sind dafür Suchhinweise: Sie können eine sinnvolle Frage aufwerfen. Ihre physikalische Wahrheit folgt aber weder aus sprachlicher Geschlossenheit noch daraus, dass ein System Begriffe wie Phase, Primzahl, Quelle oder Compiler gemeinsam ausgibt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was die frühen Logs tatsächlich beitragen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13331,"byte_start":11877,"id":"section:d031d3eb45237edc80be","kind":"section","labels":[],"line_end":125,"line_start":111,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/001-chapter-leserbrief.tex","status_markers_as_written":[],"summary_excerpt":"Ein wichtiger früher Test betraf die Rekonstruktion des Generators aus einer Zustands- oder Randbeschreibung. 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Auf dem zweidimensionalen Kontrastraum unterscheiden sich jedoch ihre Quantenkanäle: Die Multiplikatoren auf [formula in source] sind [formula in source] . Die unsic","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gleicher Populationstransfer, verschiedene Quantenfortsetzungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17017,"byte_start":15069,"id":"section:e34e3b7e4e07eb24a039","kind":"section","labels":[],"line_end":164,"line_start":152,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/001-chapter-leserbrief.tex","status_markers_as_written":[],"summary_excerpt":"Eine weitere Rekonstruktion benutzte die tatsächlichen 60 Reflexionen auf [formula in source] . Bei festgehaltenem Zeit-eins-Populationstransfer [formula in source] sind nur 16 dieser Ereignisse zugelassen: vier Achsenereignisse sowie vier relative Phasen [formula in source] auf jedem der drei Paare. Die Population fixiert die Summen der Paar-Raten; sie fixiert die Aufteilung auf diese Phasen nicht. 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Sein A3-Konformalgewicht beträgt [formula in source] . 16","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein bedingter affiner Anschluss der ganzen Ereignispfade","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4042,"byte_start":3992,"id":"section:a35898e53b742c8ac39b","kind":"chapter","labels":[],"line_end":39,"line_start":39,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die Quelle wird selbst quantendynamisch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5357,"byte_start":4042,"id":"section:e8fb3e63273b3bf974b9","kind":"section","labels":[],"line_end":56,"line_start":40,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Der entscheidende Modellwechsel besteht darin, das Wurzellabel nicht länger als unveränderlichen äußeren Zufall zu behandeln. Die 240 vollständigen Wurzeln erhalten orthogonale Kets [formula in source] . Zusammen mit zwei Viererregistern entsteht eine bewegliche Quelle. Diese Quantisierung ist eine zusätzliche Modellentscheidung. 17","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das einzelne Quellenpaket","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6575,"byte_start":5357,"id":"section:21bcb807b54b56633891","kind":"section","labels":[],"line_end":68,"line_start":57,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Zwei reine lokale Paketvakuua können nicht unabhängig auf [formula in source] – [formula in source] und [formula in source] – [formula in source] gesetzt werden: Das Register [formula in source] existiert nur einmal. Die gemeinsame Rechnung muss den gesamten Hilbertraum [formula in source] verwenden.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum Überlappung eine neue Aufgabe ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8130,"byte_start":6575,"id":"section:c12d1c94a6db13cfd0b4","kind":"section","labels":[],"line_end":97,"line_start":69,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Der gemeinsame Hamiltonoperator lautet nun [formula in source] Bei starker Quellenangleichung bleibt zunächst der ausgerichtete Raum [formula in source] übrig. Seine virtuelle gemeinsame Bewegung wird in führender Starkkopplungsordnung durch [formula in source] beschrieben. Die obersten Eigenwerte von [formula in source] sind [formula in source] einfach und [formula in source] achtfach. Für die Koordinatenmatrix [for","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der kontrollierte starke Quellenverbund","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9493,"byte_start":8130,"id":"section:dd6b3fbc27dbbbac4dc3","kind":"section","labels":[],"line_end":119,"line_start":98,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] Quellen auf einer offenen Kette hat der starke Grenzzustand die Form [formula in source] Der Wechsel der ganzen Ausrichtung erfordert [formula in source] primitive Quellschritte. Bei fester Länge folgt [formula in source] Die Fehlerkonstanten sind nicht uniform in [formula in source] . Man darf daraus keinen thermodynamischen Satz bei festen Kopplungen ableiten. 20","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum diese Lücke keine laufende Welle ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11435,"byte_start":9493,"id":"section:1b7165806ee825c5a69d","kind":"section","labels":[],"line_end":141,"line_start":120,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Die im Gespräch vorgelegte Antwortrechnung unterscheidet [formula in source] und [formula in source] . Bei [formula in source] wurden folgende Werte berichtet: @lrr@ Antwortgröße & Gemeinsam & Relativ\\\\ Erste aufgelöste Energie & 0,0068284 & 0,8398055\\\\ Mittlere Antwortenergie & 0,0101378 & 1,4441434\\\\ Statisches Gewicht & 0,2482573 & 0,0017427\\\\ Diese Zahlen werden hier als N, berichtete endliche Antwort, dokumentie","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Räumliche Antwort: was welcher Operator sehen kann","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12720,"byte_start":11435,"id":"section:13e8ed4a5e87662ce8bd","kind":"section","labels":[],"line_end":148,"line_start":142,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Eine Wurzelpermutation ist noch keine Automorphie der E8-Stromklammer. Beim Vertauschen zweier nichtkommutierender Wurzeln fehlen sonst die Vorzeichen. Für die 60 Reflexionen wurden phasentreue Kokzyklus-Lifts samt involutiven Korrekturen rekonstruiert; eine globale gemeinsame Sektion wurde damit nicht hergeleitet. 18","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Phasentreue E8-Lifts ändern die Dynamikfrage","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12775,"byte_start":12720,"id":"section:4fdbc2c3abcec9dfe5ea","kind":"chapter","labels":[],"line_end":149,"line_start":149,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Welche Bindungen bilden wirklich das Vakuum?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14481,"byte_start":12775,"id":"section:bff188da0183ae0b32c5","kind":"section","labels":[],"line_end":175,"line_start":150,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Im konjugierten Vierersektor der Quelle reduziert sich die lokale Anordnung auf [formula in source] . Bei [formula in source] besitzt [formula in source] das exakte Spektrum [formula in source] Die Quelle kann mit dem linken oder rechten Register ein invariantes Paar bilden; die beiden Möglichkeiten haben Überlappung [formula in source] . Für offene Ketten gilt [formula in source] Die vermeintlich freien Positionen i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein tieferer Sektor ist noch nicht der tiefste Zustand","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16886,"byte_start":14481,"id":"section:664d29917e7d651009fe","kind":"section","labels":[],"line_end":213,"line_start":176,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Der tatsächliche Vollraum bei [formula in source] besitzt [formula in source] Dieser Satz war im ersten Bindungsbericht noch die nicht geschlossene Assumption G. Erst der spätere relaxierte Kernbeweis schließt sie exakt. Die damaligen Lanczoswerte werden dadurch nicht rückwirkend zu einem Beweis. 24 26","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei Quellen: Bindungsbewegung im vollständigen tiefsten Raum","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18742,"byte_start":16886,"id":"section:4f05f771c489023154fd","kind":"section","labels":[],"line_end":234,"line_start":214,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Für drei Quellen ist der aus zwei äußeren Paketen gebildete Bindungsraum exakt invariant. In der orthonormalen Basis [formula in source] gilt [formula in source] Die zwei Paketprojektoren komprimieren beide auf [formula in source] . Daraus folgen im niedrigeren Eigenzustand dieses Blocks die berichteten Antworten [formula in source] [formula in source] Die Resonanz ist eine exakte Zeitantwort zwischen getrennten Pake","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Drei Quellen: genaue Resonanz, offene Globalität","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20820,"byte_start":18742,"id":"section:a6edc33a4a266b6ba167","kind":"section","labels":[],"line_end":267,"line_start":235,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Die Domänenwandarbeit hat zunächst feste Quellenmodule relaxiert. Die zentralen und äußeren Kerne sind darin jeweils echte eindeutige Grundzustände; die Module haben 409\\,600 Dimensionen. Der native Spiegelhop bleibt [formula in source] Das ist ein belastbarer endlicher Bewegungseffekt nach Relaxation. Es ist noch keine effektive Theorie beliebig langer Ketten. 26","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vier Quellen: der spätere Vollraumsatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20887,"byte_start":20820,"id":"section:e53b6a4ba24e7623fef7","kind":"chapter","labels":[],"line_end":268,"line_start":268,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Domänenwände, Ising-Kritikalität und ihr Vollraumtest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":22369,"byte_start":20887,"id":"section:310db0d3fe062049bf6e","kind":"section","labels":[],"line_end":288,"line_start":269,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Die Muster [formula in source] bei zwei Quellen und [formula in source] im Dreiquellen-Bindungsblock legen eine alternierende Ordnung nahe. Die vorgeschlagene Frage war sinnvoll: Könnte eine Wand zwischen zwei solchen Ordnungen das bewegliche Objekt sein, statt eines einzelnen Quellenlabels?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die plausible Idee und ihr kleinster Test","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":23671,"byte_start":22369,"id":"section:f4f91a2f34b4bcf32789","kind":"section","labels":[],"line_end":313,"line_start":289,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Auf geraden Ringen werden alle Links-/Rechts-Zuordnungen [formula in source] aufgenommen. Eine Kante trägt [formula in source] Materiebelegungen. Die Paketvektoren sind nicht vollständig orthogonal; die Grammatrix ist [formula in source] mit [formula in source] und einem nur zwischen zwei uniformen Zuordnungen wirkenden Austausch [formula in source] . Erst [formula in source] ist die korrekte orthonormierte Kompressi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die vollständige Paketzuordnung liefert eine Ising-Kompression","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":25376,"byte_start":23671,"id":"section:79ce52bd4c717f284af7","kind":"section","labels":[],"line_end":331,"line_start":314,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Der letzte Vertrag führt diesen Test aus. Für gerade [formula in source] , [formula in source] , [formula in source] und [formula in source] gilt auf der gesamten unveränderten Paketspanne [formula in source] Ein zulässiger ausgerichteter Vollraumzustand [formula in source] besitzt dagegen exakt [formula in source] . Beide leben im selben relevanten Gesamtphasensektor und sind bezüglich der gemeinsamen Quellgruppe Si","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der entscheidende Ausschluss der nackten kritischen Familie","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":26668,"byte_start":25376,"id":"section:320d83aad9449d3106a6","kind":"section","labels":[],"line_end":343,"line_start":332,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Die direkte Summe der bisherigen Hamiltonoperatoren über alle beschrifteten Graphen ist zunächst blockdiagonal. Sie verändert keine Kante. Ein Bindungshop auf einem festen Graphen ist kein Wechsel der Graphinzidenz. 27","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bindungsbewegung erzeugt noch keine dynamischen Orte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":26734,"byte_start":26668,"id":"section:769e5cf04a53cc5d2cca","kind":"chapter","labels":[],"line_end":344,"line_start":344,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Stromprodukte, Clock-Schließung und die letzte Brücke","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":27959,"byte_start":26734,"id":"section:54919ac38d300b883dae","kind":"section","labels":[],"line_end":363,"line_start":345,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Unter der bestehenden unitären [formula in source] -Vakuumprämisse liefert [formula in source] eine normtreue Einbettung. Die adjungierten Nullmoden handeln richtig, und [formula in source] . Mit der zusätzlichen Randzeitwahl [formula in source] entsteht eine lineare Antwort bei [formula in source] , [formula in source] . Für die quartischen Richtungen lautet das Gewicht [formula in source] Dies ist ein präziser posi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was aus den Quellenantworten im affinen Netz entsteht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1107,"byte_start":0,"id":"section:059a91ab06ce02258312","kind":"section","labels":[],"line_end":14,"line_start":1,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/003-section-das-alte-bell10-erscheint-aus-echten-stromproduk.tex","status_markers_as_written":[],"summary_excerpt":"Die tatsächlichen Grad-2-Produkte der 24 Ströme erzeugen einen 50-dimensionalen Raum. Für die 60 Produktvektoren [formula in source] gilt [formula in source] Der alte Bell10-Raum ist damit der eindeutige oberste Antwortbereich: zehn Eigenwerte sind [formula in source] , vierzig sind [formula in source] . [formula in source] ist kein Hamiltonoperator; die Differenz [formula in source] ist keine Energielücke. 21","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das alte Bell10 erscheint aus echten Stromprodukten wieder","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1899,"byte_start":1107,"id":"section:2e32a8e486fec37fb747","kind":"section","labels":[],"line_end":19,"line_start":15,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/003-section-das-alte-bell10-erscheint-aus-echten-stromproduk.tex","status_markers_as_written":[],"summary_excerpt":"Im festen CAR-Wörterbuch schickt [formula in source] die 112 D8-Wurzeln in 56 D8- und 56 Spinorwurzeln. Die kumulative [formula in source] -Bahn erreicht bei Potenz acht alle 240 Wurzelrichtungen. Schon D8 zusammen mit einem geeigneten Spinorstrom und seinem Adjungierten schließt durch nichtverschwindende Klammern in den Schritten [formula in source] . 22","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die tatsächliche Coxeterclock erzwingt mehr als D8","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4070,"byte_start":1899,"id":"section:ec1c5f07f098fbedcd43","kind":"section","labels":[],"line_end":41,"line_start":20,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/003-section-das-alte-bell10-erscheint-aus-echten-stromproduk.tex","status_markers_as_written":[],"summary_excerpt":"Die 60 alten Strahlen sind viergliedrige [formula in source] -Orbits vollständiger Wurzeln. Die tatsächliche Coxeterwirkung respektiert diese Quotienten bei festem [formula in source] nicht: Ein Orbit kann auf zwei Zielorbits aufgeteilt werden. Der korrekte kovariante Ausdruck ist [formula in source] Der letzte Vertrag macht diesen Befund quantitativ. Die Abbildung [formula in source] erfüllt [formula in source] und ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der feste komplexe Rahmen ist zu klein","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5083,"byte_start":4070,"id":"section:f4a3c6f86896bfcd0c7f","kind":"section","labels":[],"line_end":54,"line_start":42,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/003-section-das-alte-bell10-erscheint-aus-echten-stromproduk.tex","status_markers_as_written":[],"summary_excerpt":"Auf den Ring-Paketzuordnungen wirkt die Quellen- [formula in source] -Transformation als gemeinsamer Skalar. Sie bleibt nach Grammatrix-Orthonormierung skalar. Auf den tatsächlichen acht reellen Cartanrichtungen gilt dagegen [formula in source] , also gibt es keinen Fixvektor. Für eine äquivariante lineare Abbildung [formula in source] müsste gelten [formula in source] und damit [formula in source] . Eine mit der Sym","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum neutrale Paketfluktuationen keine acht Cartanströme tragen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6118,"byte_start":5083,"id":"section:bf4636105309d2f3c0fb","kind":"section","labels":[],"line_end":67,"line_start":55,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/003-section-das-alte-bell10-erscheint-aus-echten-stromproduk.tex","status_markers_as_written":[],"summary_excerpt":"Unter der ausdrücklichen Prämisse einer phasendiagonalen affinen Stromwirkung besitzt ein Generator die Form [formula in source] Die tatsächliche Coxeterwirkung mit charakteristischem Polynom [formula in source] erzwingt [formula in source] . Auf dem gemeinsamen irreduziblen Stromraum bleibt somit [formula in source] Die Regel ist bedingt stark: Ist der gemeinsame affine Prozess erst vorhanden, bleibt nur eine positi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was die Clock an der Zeitregel bereits erzwingt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7831,"byte_start":6118,"id":"section:380421659fb5c350d058","kind":"section","labels":[],"line_end":87,"line_start":68,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":["relation:1511ffa990297a83c12a","relation:6573cc31baa20758871b","relation:6e6952b1d58423367a92","relation:f180fb12bba35c77e395"],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/003-section-das-alte-bell10-erscheint-aus-echten-stromproduk.tex","status_markers_as_written":[],"summary_excerpt":"Der letzte Herkunftstest arbeitet wieder mit der tatsächlichen CAR-Quelle. Die dortige Einteilchendispersion ist [formula in source] . Auf einem festen, nicht umlaufenden Patch um eine Fermistelle liefert die Skalierung [formula in source] die Abschätzung [formula in source] Für passend verschachtelte Träger auf dem festen zusammenhängenden Halbzahl-Patch gilt für die positiven Moden [formula in source] zugleich der ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der positive Fermi-Patch: ein kontrollierter Anfang","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7882,"byte_start":7831,"id":"section:b173a9b819f548e21cef","kind":"chapter","labels":[],"line_end":88,"line_start":88,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/003-section-das-alte-bell10-erscheint-aus-echten-stromproduk.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Was die Sitzung insgesamt verändert hat","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9702,"byte_start":7882,"id":"section:d9e361810ccd7403b4bf","kind":"section","labels":[],"line_end":100,"line_start":89,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/003-section-das-alte-bell10-erscheint-aus-echten-stromproduk.tex","status_markers_as_written":[],"summary_excerpt":"Die Sitzung hat die Ursprungsidee nicht auf eine weitere Zahlenübereinstimmung reduziert. Sie hat mehrere belastbare Verbindungen hergestellt: Das Alphabet besitzt präzise Komposition. Integrale Trialität, native CAR-Wörterbücher, Chevalleyzeichen, quartischer Übertrag und Rahmenwirkungen sind explizit. Falsche Gleichsetzungen werden durch die tatsächlichen Wirkungen ausgeschlossen. Ein gemeinsamer Ereignisprozess ka","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die positiven Ergebnisse zusammen lesen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12023,"byte_start":9702,"id":"section:089d8afed3b3424a2643","kind":"section","labels":[],"line_end":121,"line_start":101,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/003-section-das-alte-bell10-erscheint-aus-echten-stromproduk.tex","status_markers_as_written":[],"summary_excerpt":"@P.25 P.42 P.25 @ Frühere naheliegende Deutung & Heutiger belastbarer Stand & Konsequenz\\\\ Frühere Deutung & Heutiger Stand & Konsequenz\\\\ Zustand bzw. Vorzeichenprojektor bestimmt den Generator & Energiegrößen und Kohärenzdynamik bleiben im Allgemeinen frei. & Mehrzeitgesetz oder Generatorursprung nötig.\\\\[4pt] Acht reale Richtungen sind die acht nativen CAR-Moden & Charaktere und Skalarkörper unterscheiden sich. & ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die wichtigsten Korrekturen im Verlauf","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14220,"byte_start":12023,"id":"section:9688158a2abfa6a4fad3","kind":"section","labels":[],"line_end":139,"line_start":122,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/003-section-das-alte-bell10-erscheint-aus-echten-stromproduk.tex","status_markers_as_written":[],"summary_excerpt":"Der Engpass ist nicht, dass uns eine weitere besonders elegante Zahl fehlt. Er besteht darin, dass die tragenden positiven Resultate noch unter verschiedenen Zusatzvoraussetzungen stehen. Der eine Satz setzt einen Quellen-Hamiltonoperator voraus; der nächste eine affine Vakuumdarstellung; ein dritter eine Markierung und einen Record; ein vierter acht gleiche freie Kinetiken. Diese Voraussetzungen werden nicht dadurch","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum wir noch keine Gesamtlösung haben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14277,"byte_start":14220,"id":"section:e24d5d9630bad1034c51","kind":"chapter","labels":[],"line_end":140,"line_start":140,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/003-section-das-alte-bell10-erscheint-aus-echten-stromproduk.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die größten anschließenden Forschungsfragen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15755,"byte_start":14277,"id":"section:01334cd8bd860ace5f7a","kind":"section","labels":[],"line_end":151,"line_start":141,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/003-section-das-alte-bell10-erscheint-aus-echten-stromproduk.tex","status_markers_as_written":[],"summary_excerpt":"Frage. Lässt sich aus P1/P2 eine einzige lokale Realisierung gewinnen, in der die tatsächlichen 16 Majoranas, die 120 D8-Ströme, die 128 Spinorströme und die markierten [formula in source] -Wirkungen gemeinsam handeln?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Priorität 1: dieselbe Quelle, dieselben geladenen Operatoren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17151,"byte_start":15755,"id":"section:7d1cb4ec727cf6da8e17","kind":"section","labels":[],"line_end":162,"line_start":152,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/003-section-das-alte-bell10-erscheint-aus-echten-stromproduk.tex","status_markers_as_written":[],"summary_excerpt":"Frage. Warum wählt die Rohquelle gerade einen gemeinsamen Generator [formula in source] und, soweit erforderlich, acht gleiche Kinetiken?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Priorität 2: aus einer Clock eine physische Zeit gewinnen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18667,"byte_start":17151,"id":"section:f5d55ba07c4e0ac07253","kind":"section","labels":[],"line_end":173,"line_start":163,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/003-section-das-alte-bell10-erscheint-aus-echten-stromproduk.tex","status_markers_as_written":[],"summary_excerpt":"Frage. Gibt es in der unveränderten Quellenfamilie bei festen positiven Kopplungen einen großen Zustandszweig mit lokalen [formula in source] -Anregungen und richtigem geladenen Antwortgewicht?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Priorität 3: eine dressierte kritische Phase über dem echten Vakuum","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19933,"byte_start":18667,"id":"section:264e27c56591d1e6ede7","kind":"section","labels":[],"line_end":182,"line_start":174,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/003-section-das-alte-bell10-erscheint-aus-echten-stromproduk.tex","status_markers_as_written":[],"summary_excerpt":"Frage. Welche aus der Quelle bestimmte Operation entscheidet nicht nur die Messwahrscheinlichkeit, sondern auch Nachzustand, Record, Ereigniszeit und Auffrischung?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Priorität 4: ein physisches Instrument samt Gedächtnis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":21262,"byte_start":19933,"id":"section:441275f097bd1888ed69","kind":"section","labels":[],"line_end":191,"line_start":183,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/003-section-das-alte-bell10-erscheint-aus-echten-stromproduk.tex","status_markers_as_written":[],"summary_excerpt":"Frage. Welche voneinander unterscheidbaren lokalen Algebren und welche Dynamik ihrer Inzidenz ergeben sich aus dem gemeinsamen Prozess, ohne die gesuchte Raumgeometrie schon einzusetzen?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Priorität 5: aus Beziehungen wirkliche Lokalität rekonstruieren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":22571,"byte_start":21262,"id":"section:99e8b1742e5e1cc48cfd","kind":"section","labels":[],"line_end":200,"line_start":192,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/003-section-das-alte-bell10-erscheint-aus-echten-stromproduk.tex","status_markers_as_written":[],"summary_excerpt":"Frage. Kann dieselbe erfolgreiche Realisierung anschließend das chirale Standardmodell und einen universell gekoppelten masselosen Spin-2-Zweig tragen?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Priorität 6: chirale Materie, 3+1D und Gravitation gemeinsam","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":23131,"byte_start":22571,"id":"section:1e89074d050f474806b1","kind":"section","labels":[],"line_end":203,"line_start":201,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20/sections/003-section-das-alte-bell10-erscheint-aus-echten-stromproduk.tex","status_markers_as_written":[],"summary_excerpt":"Unabhängig von diesen großen Fragen bleibt ein kleinerer dokumentarischer Nachweis sinnvoll: Der globale Drei-Quellen-Komplementboden aus dem früheren Bericht sollte entweder mit vollständigem Zertifikat rekonstruiert oder die entsprechende Vollraumbehauptung dauerhaft auf den invarianten Bindungsblock begrenzt werden. Gleiches gilt für die unreplayte allgemeine Leakageformel. 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Dokumentationsbeleg: SESSION/work/session-documentation-20260920/early_","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dokumentationsaudit und ergänzende Belege","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2282,"byte_start":0,"id":"section:baad60d2ed6f8d80d707","kind":"frontmatter","labels":[],"line_end":45,"line_start":1,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/preamble.tex","status_markers_as_written":[],"summary_excerpt":"arrows.meta,positioning,calc disposition ink pageheadfoot muted TFPT / UNIVERSALRAUM Gesamtsitzung · Fassung 2 nosep,leftmargin=1.5em,topsep=4pt =1.8em Y> X P[1]> p#1","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1703,"byte_start":0,"id":"section:ce177320fe0f0ea1e0ac","kind":"frontmatter","labels":[],"line_end":28,"line_start":1,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/001-chapter-leserbrief.tex","status_markers_as_written":[],"summary_excerpt":"ink FORSCHUNGSDOKUMENTATION 17mm 3237 TFPT und Universalraum 7mm Vom geometrischen Compiler zur gemeinsamen physikalischen Dynamik 12mm 9mm Zusammenhängende Darstellung der Untersuchungen, Beweise, Gegenbeispiele und offenen Forschungsfragen aus der Sitzung vom 18.–20. September 2026. 3mm Einschließlich der späteren Quellen-, Rand-, Paar- und Registeruntersuchungen. Was dieser Bericht leistetDie Sitzung hat mehrere e","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4741,"byte_start":1703,"id":"section:59c30eba3c935582bb49","kind":"chapter","labels":[],"line_end":44,"line_start":29,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/001-chapter-leserbrief.tex","status_markers_as_written":[],"summary_excerpt":"tocchapterLeserbrief Das Ziel dieser Sitzung war von Anfang an groß: eine gemeinsame, möglichst einfache Ursprungstheorie finden, die den TFPT-Compiler, Quantenprozesse, Materie, Raumzeit und Gravitation aus derselben Struktur verständlich macht. Die Untersuchungen dürfen deshalb nicht nur daran gemessen werden, ob irgendwo eine schöne Matrix entsteht. Entscheidend ist, ob die verschiedenen Matrizen dieselbe Quelle, ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Leserbrief","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4789,"byte_start":4741,"id":"section:e9f4681eaf4e3fa65a53","kind":"chapter","labels":[],"line_end":45,"line_start":45,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/001-chapter-leserbrief.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Ziel, Maßstab und Gesamtzusammenhang","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5623,"byte_start":4789,"id":"section:a0681a9ba40188a343a1","kind":"section","labels":[],"line_end":50,"line_start":46,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/001-chapter-leserbrief.tex","status_markers_as_written":[],"summary_excerpt":"Die gesuchte Gesamtlösung soll nicht nur bestehende Zahlen nachbilden. Sie müsste erklären, warum gerade die ursprünglichen Daten, die zulässigen Zustände, die Dynamik und ihre Auslesungen zusammen auftreten. Eine plausible gemeinsame Konstruktion müsste dabei die bereits vorhandenen TFPT-Beziehungen erhalten, statt sie durch frei gewählte Ersatzstrukturen zu reproduzieren.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was eine vollständige Lösung leisten müsste","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7427,"byte_start":5623,"id":"section:5abe63354d469f930c4a","kind":"section","labels":[],"line_end":68,"line_start":51,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/001-chapter-leserbrief.tex","status_markers_as_written":[],"summary_excerpt":"P1 setzt eine orientierte Naht, einen primitiven reflexionspositiven Randkern, Einheitswindung und die Normierung [formula in source] . P2 setzt die fünfteilige Trägerschnittstelle mit dem Schnitt [formula in source] . Diese Postulate sind strukturierte Eingaben. Sie sind nicht gleichbedeutend mit den später zusätzlich gewählten Gitterketten, Quellen-Hilberträumen oder Hamiltonoperatoren.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Ausgangspunkt der Theorie","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9008,"byte_start":7427,"id":"section:f002e47e0119f3456e55","kind":"section","labels":[],"line_end":89,"line_start":69,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/001-chapter-leserbrief.tex","status_markers_as_written":[],"summary_excerpt":"@lY@ Klasse & Bedeutung in diesem Bericht\\\\ A & Eine ausdrücklich gewählte Voraussetzung, etwa Graph, Kopplung, Polarisation oder Instrument.\\\\ E & Exakter mathematischer Befund unter den genannten Voraussetzungen; gegebenenfalls durch rationale oder ganzzahlige Zertifikate abgesichert.\\\\ N & Numerischer Befund. Kleine Residuen allein schließen unentdeckte tiefere Zustände nicht aus.\\\\ C & Bedingte physische oder dar","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Belegklassen und drei verschiedene Arten von Eindeutigkeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10004,"byte_start":9008,"id":"section:7e2d06215fa28f15760e","kind":"section","labels":[],"line_end":102,"line_start":90,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/001-chapter-leserbrief.tex","status_markers_as_written":[],"summary_excerpt":"Viele Ergebnisse der Sitzung liegen in der zweiten Zeile. Die erste Verbindung ist noch nicht vollständig hergeleitet; die dritte und vierte Zeile folgen nicht allein aus der Existenz einer schönen endlichen Realisierung. Diese Karte verhindert, dass ein neuer Teilsektor den ursprünglichen Auftrag unbemerkt ersetzt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie die Gesamtlösung hier geprüft wird","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10054,"byte_start":10004,"id":"section:fb39aeb805b49db59056","kind":"chapter","labels":[],"line_end":103,"line_start":103,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/001-chapter-leserbrief.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Von Readouts zur Frage nach dem Prozess","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12192,"byte_start":10054,"id":"section:c24bcccb7d4213e14483","kind":"section","labels":[],"line_end":112,"line_start":104,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/001-chapter-leserbrief.tex","status_markers_as_written":[],"summary_excerpt":"Der Ausgangsimpuls war, in den Readouts und im Forschungsgraphen eine bislang übersehene Verbindung zu finden. Assoziative Texte sind dafür Suchhinweise: Sie können eine sinnvolle Frage aufwerfen. Ihre physikalische Wahrheit folgt aber weder aus sprachlicher Geschlossenheit noch daraus, dass ein System Begriffe wie Phase, Primzahl, Quelle oder Compiler gemeinsam ausgibt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was die frühen Logs tatsächlich beitragen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13646,"byte_start":12192,"id":"section:5e24fd90f3f1e990d21a","kind":"section","labels":[],"line_end":127,"line_start":113,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/001-chapter-leserbrief.tex","status_markers_as_written":[],"summary_excerpt":"Ein wichtiger früher Test betraf die Rekonstruktion des Generators aus einer Zustands- oder Randbeschreibung. 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Die Rückrichtung [formula ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein Zustand ist weniger Information als eine Dynamik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15384,"byte_start":13646,"id":"section:d0ff4d3fd3e1799524e1","kind":"section","labels":[],"line_end":153,"line_start":128,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/001-chapter-leserbrief.tex","status_markers_as_written":[],"summary_excerpt":"Der konkrete Familien-Populationstransfer lautet [formula in source] Seine Birkhoff-Ausführungen besitzen in der Reihenfolge Identität, zwei Dreierzyklen und drei Transpositionen die Gewichte [formula in source] Alle haben denselben klassischen Schatten. Auf dem zweidimensionalen Kontrastraum unterscheiden sich jedoch ihre Quantenkanäle: Die Multiplikatoren auf [formula in source] sind [formula in source] . Die unsic","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gleicher Populationstransfer, verschiedene Quantenfortsetzungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17332,"byte_start":15384,"id":"section:00dc3f3848f12077c67a","kind":"section","labels":[],"line_end":166,"line_start":154,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/001-chapter-leserbrief.tex","status_markers_as_written":[],"summary_excerpt":"Eine weitere Rekonstruktion benutzte die tatsächlichen 60 Reflexionen auf [formula in source] . 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Der Compound-Pois","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die verborgene Phasenfaser und das Gedächtnis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19316,"byte_start":17332,"id":"section:dd4906932289f4b8e061","kind":"section","labels":[],"line_end":186,"line_start":167,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/001-chapter-leserbrief.tex","status_markers_as_written":[],"summary_excerpt":"Der festgehaltene vierte Sektor ist keine notwendige Folge des Dreiertransfers. Er entstand durch die gewählte Fortsetzung [formula in source] . Unter Positivität, Normierung, Schärfe auf den ersten drei Koordinaten und nativer Dreierkovarianz ist stattdessen die Auslesung [formula in source] eindeutig. Jeder der drei sichtbaren Ausgänge erhält denselben Anteil des vierten Platzes. Eine unsichtbare interne Richtung k","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die inklusive Dreierauslesung löst den eingefrorenen vierten Platz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":21269,"byte_start":19316,"id":"section:8a4e54893a998b8ac72e","kind":"section","labels":[],"line_end":206,"line_start":187,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/001-chapter-leserbrief.tex","status_markers_as_written":[],"summary_excerpt":"Die vier Marken [formula in source] liefern normierte Residuenlinien [formula in source] Alle vier Projektoren gehören tatsächlich zur nativen 60er-Bank. Die geometrische Deckung hat auf ihnen die Eigenwerte [formula in source] ; sie ist deshalb nicht die zentral auf [formula in source] wirkende Compiler-Viertelclock. In der Reihenfolge der nichttrivialen Charaktere [formula in source] liefert die inklusive Auslesung","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der diskrete Randanschluss funktioniert tatsächlich","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":22533,"byte_start":21269,"id":"section:d80fa727b950496dfd34","kind":"section","labels":[],"line_end":217,"line_start":207,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/001-chapter-leserbrief.tex","status_markers_as_written":[],"summary_excerpt":"Bereits die frühe Clockanalyse zeigte, warum der feste komplexe Viererraum zu klein ist. 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Die gemeinsame Rechnung muss den gesamten Hilbertraum [formula in source] verwenden.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum Überlappung eine neue Aufgabe ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8130,"byte_start":6575,"id":"section:829949f6740f3080729c","kind":"section","labels":[],"line_end":97,"line_start":69,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Der gemeinsame Hamiltonoperator lautet nun [formula in source] Bei starker Quellenangleichung bleibt zunächst der ausgerichtete Raum [formula in source] übrig. Seine virtuelle gemeinsame Bewegung wird in führender Starkkopplungsordnung durch [formula in source] beschrieben. Die obersten Eigenwerte von [formula in source] sind [formula in source] einfach und [formula in source] achtfach. Für die Koordinatenmatrix [for","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der kontrollierte starke Quellenverbund","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9494,"byte_start":8130,"id":"section:f05481dc7416abc61010","kind":"section","labels":[],"line_end":119,"line_start":98,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] Quellen auf einer offenen Kette hat der starke Grenzzustand die Form [formula in source] Der Wechsel der ganzen Ausrichtung erfordert [formula in source] primitive Quellschritte. Bei fester Länge folgt [formula in source] Die Fehlerkonstanten sind nicht uniform in [formula in source] . Man darf daraus keinen thermodynamischen Satz bei festen Kopplungen ableiten. 20","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum diese Lücke keine laufende Welle ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11436,"byte_start":9494,"id":"section:d7f6669e51dfd9358bad","kind":"section","labels":[],"line_end":141,"line_start":120,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Die im Gespräch vorgelegte Antwortrechnung unterscheidet [formula in source] und [formula in source] . Bei [formula in source] wurden folgende Werte berichtet: @lrr@ Antwortgröße & Gemeinsam & Relativ\\\\ Erste aufgelöste Energie & 0,0068284 & 0,8398055\\\\ Mittlere Antwortenergie & 0,0101378 & 1,4441434\\\\ Statisches Gewicht & 0,2482573 & 0,0017427\\\\ Diese Zahlen werden hier als N, berichtete endliche Antwort, dokumentie","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Räumliche Antwort: was welcher Operator sehen kann","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12722,"byte_start":11436,"id":"section:20c0d8177670b7ad48db","kind":"section","labels":[],"line_end":149,"line_start":142,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Eine Wurzelpermutation ist noch keine Automorphie der E8-Stromklammer. Beim Vertauschen zweier nichtkommutierender Wurzeln fehlen sonst die Vorzeichen. Für die 60 Reflexionen wurden phasentreue Kokzyklus-Lifts samt involutiven Korrekturen rekonstruiert; eine globale gemeinsame Sektion wurde damit nicht hergeleitet. 18","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Phasentreue E8-Lifts ändern die Dynamikfrage","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14127,"byte_start":12722,"id":"section:9b3bc14f9081a133ef52","kind":"section","labels":[],"line_end":160,"line_start":150,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Dieselben fünf Quartiken liefern auch einen anderen Schnitt: eine Quellenkomponente und drei Register, also [formula in source] . Mit ihren [formula in source] -Matrizen [formula in source] und [formula in source] gilt exakt [formula in source] Damit ist [formula in source] ein normierter Zustand mit derselben Dreiregisterdichte [formula in source] wie der starke Quellengrenzzustand. Die Quellenhälfte liegt im vorhan","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein positiver Anschluss des Dreiregisterzustands","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14182,"byte_start":14127,"id":"section:3df76abd4ac5ee62b180","kind":"chapter","labels":[],"line_end":161,"line_start":161,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Welche Bindungen bilden wirklich das Vakuum?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15888,"byte_start":14182,"id":"section:f73e8160f202e2c9c47e","kind":"section","labels":[],"line_end":187,"line_start":162,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Im konjugierten Vierersektor der Quelle reduziert sich die lokale Anordnung auf [formula in source] . Bei [formula in source] besitzt [formula in source] das exakte Spektrum [formula in source] Die Quelle kann mit dem linken oder rechten Register ein invariantes Paar bilden; die beiden Möglichkeiten haben Überlappung [formula in source] . Für offene Ketten gilt [formula in source] Die vermeintlich freien Positionen i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein tieferer Sektor ist noch nicht der tiefste Zustand","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18293,"byte_start":15888,"id":"section:96a8d75124ced35fcf88","kind":"section","labels":[],"line_end":225,"line_start":188,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Der tatsächliche Vollraum bei [formula in source] besitzt [formula in source] Dieser Satz war im ersten Bindungsbericht noch die nicht geschlossene Assumption G. Erst der spätere relaxierte Kernbeweis schließt sie exakt. Die damaligen Lanczoswerte werden dadurch nicht rückwirkend zu einem Beweis. 24 26","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei Quellen: Bindungsbewegung im vollständigen tiefsten Raum","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20149,"byte_start":18293,"id":"section:6ddb82f04d012f5d9525","kind":"section","labels":[],"line_end":246,"line_start":226,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Für drei Quellen ist der aus zwei äußeren Paketen gebildete Bindungsraum exakt invariant. In der orthonormalen Basis [formula in source] gilt [formula in source] Die zwei Paketprojektoren komprimieren beide auf [formula in source] . Daraus folgen im niedrigeren Eigenzustand dieses Blocks die berichteten Antworten [formula in source] [formula in source] Die Resonanz ist eine exakte Zeitantwort zwischen getrennten Pake","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Drei Quellen: genaue Resonanz, offene Globalität","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":22247,"byte_start":20149,"id":"section:d9d1915ab3d7c9f27ea5","kind":"section","labels":[],"line_end":279,"line_start":247,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Die Domänenwandarbeit hat zunächst feste Quellenmodule relaxiert. Die zentralen und äußeren Kerne sind darin jeweils echte eindeutige Grundzustände; die Module haben 409\\,600 Dimensionen. Der native Spiegelhop bleibt [formula in source] Das ist ein belastbarer endlicher Bewegungseffekt nach Relaxation. Es ist noch keine effektive Theorie beliebig langer Ketten. 26","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vier Quellen: der spätere Vollraumsatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":22314,"byte_start":22247,"id":"section:42f7f5a9722103c8ae34","kind":"chapter","labels":[],"line_end":280,"line_start":280,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Domänenwände, Ising-Kritikalität und ihr Vollraumtest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":24688,"byte_start":22314,"id":"section:fbed0e63223da1540c0c","kind":"section","labels":[],"line_end":307,"line_start":281,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Die Muster [formula in source] bei zwei Quellen und [formula in source] im Dreiquellen-Bindungsblock legen eine alternierende Ordnung nahe. Die vorgeschlagene Frage war sinnvoll: Könnte eine Wand zwischen zwei solchen Ordnungen das bewegliche Objekt sein, statt eines einzelnen Quellenlabels?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die plausible Idee und ihr kleinster Test","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":25990,"byte_start":24688,"id":"section:48fb6b4beebda45e5001","kind":"section","labels":[],"line_end":332,"line_start":308,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Auf geraden Ringen werden alle Links-/Rechts-Zuordnungen [formula in source] aufgenommen. Eine Kante trägt [formula in source] Materiebelegungen. Die Paketvektoren sind nicht vollständig orthogonal; die Grammatrix ist [formula in source] mit [formula in source] und einem nur zwischen zwei uniformen Zuordnungen wirkenden Austausch [formula in source] . Erst [formula in source] ist die korrekte orthonormierte Kompressi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die vollständige Paketzuordnung liefert eine Ising-Kompression","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":27695,"byte_start":25990,"id":"section:49ec4327dd4e162af347","kind":"section","labels":[],"line_end":350,"line_start":333,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Der letzte Vertrag führt diesen Test aus. Für gerade [formula in source] , [formula in source] , [formula in source] und [formula in source] gilt auf der gesamten unveränderten Paketspanne [formula in source] Ein zulässiger ausgerichteter Vollraumzustand [formula in source] besitzt dagegen exakt [formula in source] . Beide leben im selben relevanten Gesamtphasensektor und sind bezüglich der gemeinsamen Quellgruppe Si","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der entscheidende Ausschluss der nackten kritischen Familie","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":28987,"byte_start":27695,"id":"section:abc073334ae8b9909c08","kind":"section","labels":[],"line_end":362,"line_start":351,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"Die direkte Summe der bisherigen Hamiltonoperatoren über alle beschrifteten Graphen ist zunächst blockdiagonal. Sie verändert keine Kante. Ein Bindungshop auf einem festen Graphen ist kein Wechsel der Graphinzidenz. 27","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bindungsbewegung erzeugt noch keine dynamischen Orte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":29053,"byte_start":28987,"id":"section:3ec8fc4c90b4aebfbb58","kind":"chapter","labels":[],"line_end":363,"line_start":363,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/002-section-die-rahmenidentifikation-und-eine-wichtige-verwe.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Stromprodukte, Clock-Schließung und die letzte Brücke","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1225,"byte_start":0,"id":"section:4ca57bdf1d208c179637","kind":"section","labels":[],"line_end":19,"line_start":1,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/003-section-was-aus-den-quellenantworten-im-affinen-netz-ent.tex","status_markers_as_written":[],"summary_excerpt":"Unter der bestehenden unitären [formula in source] -Vakuumprämisse liefert [formula in source] eine normtreue Einbettung. Die adjungierten Nullmoden handeln richtig, und [formula in source] . Mit der zusätzlichen Randzeitwahl [formula in source] entsteht eine lineare Antwort bei [formula in source] , [formula in source] . Für die quartischen Richtungen lautet das Gewicht [formula in source] Dies ist ein präziser posi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was aus den Quellenantworten im affinen Netz entsteht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2332,"byte_start":1225,"id":"section:ca7f5f14a152ea8c08fc","kind":"section","labels":[],"line_end":33,"line_start":20,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/003-section-was-aus-den-quellenantworten-im-affinen-netz-ent.tex","status_markers_as_written":[],"summary_excerpt":"Die tatsächlichen Grad-2-Produkte der 24 Ströme erzeugen einen 50-dimensionalen Raum. Für die 60 Produktvektoren [formula in source] gilt [formula in source] Der alte Bell10-Raum ist damit der eindeutige oberste Antwortbereich: zehn Eigenwerte sind [formula in source] , vierzig sind [formula in source] . [formula in source] ist kein Hamiltonoperator; die Differenz [formula in source] ist keine Energielücke. 21","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das alte Bell10 erscheint aus echten Stromprodukten wieder","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3124,"byte_start":2332,"id":"section:f11bc327843c76b69200","kind":"section","labels":[],"line_end":38,"line_start":34,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/003-section-was-aus-den-quellenantworten-im-affinen-netz-ent.tex","status_markers_as_written":[],"summary_excerpt":"Im festen CAR-Wörterbuch schickt [formula in source] die 112 D8-Wurzeln in 56 D8- und 56 Spinorwurzeln. Die kumulative [formula in source] -Bahn erreicht bei Potenz acht alle 240 Wurzelrichtungen. Schon D8 zusammen mit einem geeigneten Spinorstrom und seinem Adjungierten schließt durch nichtverschwindende Klammern in den Schritten [formula in source] . 22","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die tatsächliche Coxeterclock erzwingt mehr als D8","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5295,"byte_start":3124,"id":"section:b48e984dffc6f2f78fbf","kind":"section","labels":[],"line_end":60,"line_start":39,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/003-section-was-aus-den-quellenantworten-im-affinen-netz-ent.tex","status_markers_as_written":[],"summary_excerpt":"Die 60 alten Strahlen sind viergliedrige [formula in source] -Orbits vollständiger Wurzeln. Die tatsächliche Coxeterwirkung respektiert diese Quotienten bei festem [formula in source] nicht: Ein Orbit kann auf zwei Zielorbits aufgeteilt werden. Der korrekte kovariante Ausdruck ist [formula in source] Der letzte Vertrag macht diesen Befund quantitativ. Die Abbildung [formula in source] erfüllt [formula in source] und ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der feste komplexe Rahmen ist zu klein","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6308,"byte_start":5295,"id":"section:cb0bfb64d4dfc00b5304","kind":"section","labels":[],"line_end":73,"line_start":61,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/003-section-was-aus-den-quellenantworten-im-affinen-netz-ent.tex","status_markers_as_written":[],"summary_excerpt":"Auf den Ring-Paketzuordnungen wirkt die Quellen- [formula in source] -Transformation als gemeinsamer Skalar. Sie bleibt nach Grammatrix-Orthonormierung skalar. Auf den tatsächlichen acht reellen Cartanrichtungen gilt dagegen [formula in source] , also gibt es keinen Fixvektor. Für eine äquivariante lineare Abbildung [formula in source] müsste gelten [formula in source] und damit [formula in source] . Eine mit der Sym","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum neutrale Paketfluktuationen keine acht Cartanströme tragen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7343,"byte_start":6308,"id":"section:face01c14fad46d07efa","kind":"section","labels":[],"line_end":86,"line_start":74,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/003-section-was-aus-den-quellenantworten-im-affinen-netz-ent.tex","status_markers_as_written":[],"summary_excerpt":"Unter der ausdrücklichen Prämisse einer phasendiagonalen affinen Stromwirkung besitzt ein Generator die Form [formula in source] Die tatsächliche Coxeterwirkung mit charakteristischem Polynom [formula in source] erzwingt [formula in source] . Auf dem gemeinsamen irreduziblen Stromraum bleibt somit [formula in source] Die Regel ist bedingt stark: Ist der gemeinsame affine Prozess erst vorhanden, bleibt nur eine positi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was die Clock an der Zeitregel bereits erzwingt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9058,"byte_start":7343,"id":"section:1c17a0507a642eaaf392","kind":"section","labels":[],"line_end":108,"line_start":87,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":["relation:2966da1e80ef9174519f","relation:48bec3e183dcdae12b64","relation:681e2a6f3b37853621b7","relation:dfd47b05fa6e4a851e5f"],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/003-section-was-aus-den-quellenantworten-im-affinen-netz-ent.tex","status_markers_as_written":[],"summary_excerpt":"Der letzte Herkunftstest arbeitet wieder mit der tatsächlichen CAR-Quelle. Die dortige Einteilchendispersion ist [formula in source] . Auf einem festen, nicht umlaufenden Patch um eine Fermistelle liefert die Skalierung [formula in source] die Abschätzung [formula in source] Für passend verschachtelte Träger auf dem festen zusammenhängenden Halbzahl-Patch gilt für die positiven Moden [formula in source] zugleich der ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der positive Fermi-Patch: ein kontrollierter Anfang","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9190,"byte_start":9058,"id":"section:2653bab9944a0eaa58f9","kind":"chapter","labels":[],"line_end":110,"line_start":109,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/003-section-was-aus-den-quellenantworten-im-affinen-netz-ent.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Quellenzeit, lokaler Randlimes und Carry","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10698,"byte_start":9190,"id":"section:12325c6f15e9ef686f57","kind":"section","labels":[],"line_end":135,"line_start":111,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/003-section-was-aus-den-quellenantworten-im-affinen-netz-ent.tex","status_markers_as_written":[],"summary_excerpt":"Die späten Contracts vom 20. September 2026 verfolgen eine einzige präzise Frage: Lässt sich der algebraisch bereits formulierte E8-/Spinor-Anschluss als derselbe physische Prozess wiederfinden, der Zustand, geladene Felder, Zeit, Cocycles und Auslesung der ursprünglichen Quelle gemeinsam trägt? Die Antwort der geprüften Texte ist partiell, aber deutlich. Mehrere starke Teilresultate sind inzwischen exakt formuliert:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Einordnung des Strangs","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13506,"byte_start":10698,"id":"section:349eb4d83a012ddb11e0","kind":"section","labels":[],"line_end":192,"line_start":136,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":["relation:34bdf8755066a9a0eba2","relation:7cf7420aae63ac60e553"],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/003-section-was-aus-den-quellenantworten-im-affinen-netz-ent.tex","status_markers_as_written":[],"summary_excerpt":"Der Contract 31 analysiert die tatsächlichen Hopping-Blöcke aus verification/v1033_charged_disorder.py, mit Masse eins, fester Breite [formula in source] , Sektor [formula in source] und dem gefüllten negativen See. Für","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was die unveränderte QWZ-Quelle tatsächlich enthält","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15742,"byte_start":13506,"id":"section:f1d4219f8762cb3f2b32","kind":"section","labels":[],"line_end":246,"line_start":193,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/003-section-was-aus-den-quellenantworten-im-affinen-netz-ent.tex","status_markers_as_written":[],"summary_excerpt":"33 prüft eine andere Geometrie als die früheren Festkreisvergleiche: [formula in source] und [formula in source] , bei unveränderter Masse, Breite und Hoppingstruktur. Für den tatsächlichen Streifenoperator und den oberen Randvektor [formula in source] gilt exakt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der lokale wachsende-Kreis-Limes","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18599,"byte_start":15742,"id":"section:b15a1bebaecdedd50970","kind":"section","labels":[],"line_end":318,"line_start":247,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/003-section-was-aus-den-quellenantworten-im-affinen-netz-ent.tex","status_markers_as_written":[],"summary_excerpt":"32 verbindet die vorhandene Gittervertexalgebra mit der Frage nach gemeinsamer Quellzeit. Der bekannte E8-Pfad ist nicht null: mit [formula in source] , [formula in source] und [formula in source] gilt [formula in source] , [formula in source] , und der einfache OPE-Pol führt von [formula in source] und [formula in source] nach [formula in source] . Die einzelne Phase hängt von der Cocycle-Konvention ab; der nichtver","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zeit, geladene Ströme und Viertelholonomie","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20466,"byte_start":18599,"id":"section:5e4cee6dc38c83d8f93f","kind":"section","labels":[],"line_end":369,"line_start":319,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/003-section-was-aus-den-quellenantworten-im-affinen-netz-ent.tex","status_markers_as_written":[],"summary_excerpt":"36 bestätigt die Quellformeln, markiert aber die Fensterbedingung: Die Stromgewichte gelten für die deklarierte Niedrigimpulsmenge, nicht als ungefilterter Vollquellensatz. Die E8-Cocycle trägt den Carry [formula in source] mit [formula in source] in der übernommenen Konvention. Ein phasenfreier Lift und der echte Cocycle unterscheiden sich nur in der Rephasierung, nicht in der Tatsache des Carry.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Carry: positive Quelle, aber externe Fahrregel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":57,"byte_start":0,"id":"section:34a10968b4f43d7695ed","kind":"chapter","labels":[],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/004-chapter-randgitter-dynamik-und-lokale-rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Randgitter, Dynamik und lokale Rekonstruktion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1836,"byte_start":57,"id":"section:5471a0d8f104058b6e5d","kind":"section","labels":[],"line_end":45,"line_start":3,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/004-chapter-randgitter-dynamik-und-lokale-rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Die späteren Arbeiten zur Rand-, Gitter- und Eichstruktur bilden eine logisch zusammenhängende Kette. Ihr Ausgangspunkt ist kein aus den TFPT-Prinzipien bereits abgeleiteter Materiesektor, sondern ein präzise deklarierter Kandidat: zehn chirale bosonisierte Kanäle mit","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ausgangspunkt und Geltungsbereich","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5590,"byte_start":1836,"id":"section:792e4664e03a4f0a3f4f","kind":"section","labels":[],"line_end":109,"line_start":46,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/004-chapter-randgitter-dynamik-und-lokale-rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"37 beginnt mit allen primitiven charakteristischen Nullvektoren minimaler euklidischer Länge im Gitter [formula in source] . Die Charakteristik erzwingt ungerade Komponenten; Minimalität gibt [formula in source] . Die globale Quellenladung, der Glue und die orientierte Farb-/Schwach-/Familienzerlegung reduzieren die Kandidaten stufenweise. 38 ersetzt dabei eine zunächst separat angenommene Blockpermutationssymmetrie ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Auswahl des Randkandidaten und erste physikalische Markierungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9039,"byte_start":5590,"id":"section:e2a57e30b7bb2dc74459","kind":"section","labels":[],"line_end":177,"line_start":110,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/004-chapter-randgitter-dynamik-und-lokale-rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"39 liefert die entscheidende lokale Struktur. Der gemeinsame orthogonale Kern von [formula in source] und [formula in source] ist","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das vollständige Gitter trägt die Statistik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11796,"byte_start":9039,"id":"section:d95cb6207db1a8e20937","kind":"section","labels":[],"line_end":218,"line_start":178,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/004-chapter-randgitter-dynamik-und-lokale-rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Hier gilt [formula in source] . Dieser Punkt liegt nicht auf dem direkten Energiepfad des vorigen Abschnitts; schon der Matrixeintrag [formula in source] , gegenüber null auf dem ganzen direkten Pfad, zeigt die zusätzliche kollektive Dichterichtung.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lokale Rekonstruktion am bedingten Konkurrenzpunkt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11856,"byte_start":11796,"id":"section:dbad3b4ae5b1e391a45a","kind":"chapter","labels":[],"line_end":219,"line_start":219,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/004-chapter-randgitter-dynamik-und-lokale-rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Gruppenobstruktion, Eichladung und geladene Lifts","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15302,"byte_start":11856,"id":"section:a0b878cc3850d863cf0c","kind":"section","labels":[],"line_end":261,"line_start":220,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/004-chapter-randgitter-dynamik-und-lokale-rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Die Quellprüfung 44 untersucht zuerst den naheliegenden Ursprung im nativen 64-CAR/60-CCR-Fockmodell. Dort ist die Nicht-Gauß-Struktur wirklich Teil des Zeitgenerators,","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die zentrale Gruppenobstruktion und die nichtlineare Randlösung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19041,"byte_start":15302,"id":"section:4dfa5e12c2ba2903814e","kind":"section","labels":[],"line_end":328,"line_start":262,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/004-chapter-randgitter-dynamik-und-lokale-rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"42 analysiert den vorhandenen kompakten U(1)-Rotorparenten, ohne ihn mit der zehnkanaligen Quelle gleichzusetzen. Auf einem endlichen verbundenen Graphen lautet die Gaußbedingung","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gaußreduktion, kompatible Ladung und Flussindex","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":21469,"byte_start":19041,"id":"section:adde62cd38b817aa0374","kind":"section","labels":[],"line_end":371,"line_start":329,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/004-chapter-randgitter-dynamik-und-lokale-rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Der neutrale Quotient legt die Wirkung auf geladene Felder nicht fest. 46 klassifiziert deshalb alle ganzzahligen additiven isometrischen Schnitte desselben Quotienten:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Geladene Lifts und der minimale lokale Reparaturraum","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2602,"byte_start":0,"id":"section:48b79ac10ae127882481","kind":"section","labels":[],"line_end":13,"line_start":1,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/005-section-gemeinsames-ergebnis-und-offene-herkunftsbr-cke.tex","status_markers_as_written":[],"summary_excerpt":"Die Kette ergibt ein klares Gesamtbild. Das vollständige ungerade Quellgitter kann lokale geladene Spinorfelder tragen, aber dann ist der volle gewünschte [formula in source] -Stromlift auf diesen Feldern nicht gegenseitig lokal. Der neutrale Quotient besitzt exakt die E8-Struktur, legt jedoch die geladene Operatorwirkung nicht fest. Ein gerades Nachbargitter realisiert den vollen Stromlift, entfernt dafür die ursprü","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gemeinsames Ergebnis und offene Herkunftsbrücke","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2759,"byte_start":2602,"id":"section:f403e230003f7d8cd38d","kind":"chapter","labels":[],"line_end":15,"line_start":14,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/005-section-gemeinsames-ergebnis-und-offene-herkunftsbr-cke.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Sektorrekonstruktion, Paarantwort und Herkunftsgrenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4310,"byte_start":2759,"id":"section:c78255cd86bb3bf42137","kind":"section","labels":[],"line_end":55,"line_start":16,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/005-section-gemeinsames-ergebnis-und-offene-herkunftsbr-cke.tex","status_markers_as_written":[],"summary_excerpt":"Der Kernbefund von 30 ist eine Trennung, die für alle späteren Ableitungen entscheidend bleibt. Im E8-Ziel sei [formula in source] , [formula in source] , [formula in source] , und [formula in source] projiziere auf den [formula in source] -Sektor, [formula in source] auf den Spinorsektor. Ein Spinorstrom ist off-diagonal und kann trotz [formula in source] einen geladenen Rückweg erzeugen:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Quelle und Projektions-/Gedächtnisfrage","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7540,"byte_start":4310,"id":"section:3202daa4fa68b1465175","kind":"section","labels":[],"line_end":140,"line_start":56,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/005-section-gemeinsames-ergebnis-und-offene-herkunftsbr-cke.tex","status_markers_as_written":[],"summary_excerpt":"mit [formula in source] . In diesem Feld- und Paarvergleich bleiben die Cosinus- und Massenterme ausgeschaltet. Verwendet wird die konforme Zeit dieser bedingten masselosen Randtheorie, ergänzt um den angegebenen Viertelladungsterm. Die 64 nativen Fermiongewichte werden als [formula in source] , die 60 Mediatorgewichte als [formula in source] eingesetzt. Exakt 480 der 2016 Paare haben das passende Produkt und","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Native Felder, Paarjets und die positive algebraische Seite","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10893,"byte_start":7540,"id":"section:a97a13198b43cc0d4db6","kind":"section","labels":[],"line_end":205,"line_start":141,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/005-section-gemeinsames-ergebnis-und-offene-herkunftsbr-cke.tex","status_markers_as_written":[],"summary_excerpt":"gibt es die vier Diskriminantklassen [formula in source] . Die Twist-Charaktere und die spinabhängige Arf-Kombination reproduzieren die fermionischen Spuren:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vier Sektoren, gleiche Zeit und die Grundzustandsgrenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14472,"byte_start":10893,"id":"section:bf5b124fa00159d711b6","kind":"section","labels":[],"line_end":268,"line_start":206,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/005-section-gemeinsames-ergebnis-und-offene-herkunftsbr-cke.tex","status_markers_as_written":[],"summary_excerpt":"34 hält die vorgelagerte Operatorfrage offen. Wenn ein Carrier [formula in source] liegt und sein Involutionsoperator nur die Einschränkung desselben Projektions- Involutionsoperators ist, dann ist seine negative Komponente identisch null. Eine nichttriviale [formula in source] -Yukawaform mit Signatur [formula in source] folgt daraus nicht. Im reinen selbstdualen CAR-Fall vertauscht die Konjugation die beiden Polari","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Rohträger, Herkunft und der verbleibende Nachweis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14561,"byte_start":14472,"id":"section:d90f62370c56c7276559","kind":"chapter","labels":["ch:register"],"line_end":270,"line_start":269,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/005-section-gemeinsames-ergebnis-und-offene-herkunftsbr-cke.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Das Vierphasenregister: Ausblenden oder gemeinsam kodieren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15885,"byte_start":14561,"id":"section:c43b7fa2a279a397da8a","kind":"section","labels":[],"line_end":281,"line_start":271,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/005-section-gemeinsames-ergebnis-und-offene-herkunftsbr-cke.tex","status_markers_as_written":[],"summary_excerpt":"Nach den Feld-, Gitter- und Paarvergleichen blieb eine einfache Möglichkeit offen: Vielleicht erzeugt bereits das vorhandene Phasenregister die gesuchte Wechselwirkung, wenn man seine vollständige Wirkung behält. Diese Frage wurde an der unveränderten freien QWZ-Quelle untersucht. Zwei verschiedene Reduktionsregeln müssen dabei streng getrennt werden. Die erste startet mit unabhängig präpariertem Register und Materie","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum diese letzte Untersuchung nötig war","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17612,"byte_start":15885,"id":"section:89c59a97e57eeab61147","kind":"section","labels":[],"line_end":296,"line_start":282,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/005-section-gemeinsames-ergebnis-und-offene-herkunftsbr-cke.tex","status_markers_as_written":[],"summary_excerpt":"Bei einer Produktpräparation [formula in source] und anschließendem vollständigem Registertrace entsteht exakt [formula in source] Registerkohärenzen überleben diesen Trace nicht. Eine solche Mischung ist auf der vollständigen Materiealgebra genau dann eine unitäre Entwicklung, wenn alle besetzten [formula in source] bis auf skalare Phasen übereinstimmen. Für eine zusammenhängende Zeitentwicklung im hier gewählten fr","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine Mischung freier Entwicklungen kann nichtgaußsche Antworten tragen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19141,"byte_start":17612,"id":"section:c61e79c467e4d20470f0","kind":"section","labels":[],"line_end":321,"line_start":297,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/005-section-gemeinsames-ergebnis-und-offene-herkunftsbr-cke.tex","status_markers_as_written":[],"summary_excerpt":"Seien [formula in source] , [formula in source] , [formula in source] und [formula in source] die gesamte Materieteilchenzahl. Mit gewöhnlichen Fermionoperatoren [formula in source] definiert man [formula in source] Hier bezeichnet [formula in source] die neue kombinierte Registergröße, nicht das Coxeterelement aus den früheren Kapiteln. Die [formula in source] sind Kodierungsabbildungen und nicht die Viertelclock [f","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine korrelierte Kodierung erhält geladene Felder und dieselbe Zeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20900,"byte_start":19141,"id":"section:af2211c3687a06a939af","kind":"section","labels":[],"line_end":348,"line_start":322,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/005-section-gemeinsames-ergebnis-und-offene-herkunftsbr-cke.tex","status_markers_as_written":[],"summary_excerpt":"Die Quelle liefert tatsächlich den Operator [formula in source] , wobei [formula in source] , [formula in source] , den markierten Phasenbogen beschreibt und [formula in source] gilt. Das Symbol [formula in source] ist hier nur eine Bogenmarkierung, keine elektrische Ladung. [formula in source] selbst erhält die Teilchenzahl und ist fermionisch gerade.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die ursprüngliche Phasenlinie braucht einen zusätzlichen Registerfaktor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":23783,"byte_start":20900,"id":"section:f6354174df4acb4156e8","kind":"section","labels":[],"line_end":371,"line_start":349,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/005-section-gemeinsames-ergebnis-und-offene-herkunftsbr-cke.tex","status_markers_as_written":[],"summary_excerpt":"Auf dem gesamten Fockraum ist [formula in source] im Allgemeinen kein einziger teilchenzahlunabhängiger quadratischer Operator. Im exakten Sechsmodenbeispiel der Originalquelle gilt etwa [formula in source] Die Ziffern bezeichnen besetzte Orbitale; [formula in source] in der ersten Formel ist ein Einteilchenzustand und kein Vakuum. Ein zusätzlicher Zuschauer ändert die Phase desselben Übergangs.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Höhere Fermionterme und der wirkliche räumliche Test","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":46,"byte_start":0,"id":"section:6725125937378e0a9459","kind":"chapter","labels":[],"line_end":1,"line_start":1,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/006-chapter-was-die-gesamte-sitzung-ergeben-hat.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Was die gesamte Sitzung ergeben hat","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1963,"byte_start":46,"id":"section:ed4a13310021a1e248cd","kind":"section","labels":[],"line_end":10,"line_start":2,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/006-chapter-was-die-gesamte-sitzung-ergeben-hat.tex","status_markers_as_written":[],"summary_excerpt":"Am Anfang stand die Hoffnung, dass eine sehr kleine geometrische Grammatik bereits das ganze Universum festlegt. Die Untersuchung hat dieses Ziel nicht erreicht. Sie hat aber aus einer allgemeinen Hoffnung eine wesentlich präzisere Kette von Fragen und nachprüfbaren Verbindungen gemacht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das verständliche Gesamtbild","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4552,"byte_start":1963,"id":"section:5ac3121fde7ae10d181c","kind":"section","labels":[],"line_end":25,"line_start":11,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/006-chapter-was-die-gesamte-sitzung-ergeben-hat.tex","status_markers_as_written":[],"summary_excerpt":"@P.22 P.34 P.36 @ Ebene & Belastbarer Gewinn & Verbleibende Brücke\\\\ Ebene & Belastbarer Gewinn & Verbleibende Brücke\\\\ Compiler und endliche Operatoren & Integrale Wörterbücher, native Ereignisse, Phasen- und Clockbedingungen sind in konkreten Darstellungen geprüft. & Ein Randpostulat bestimmt noch nicht automatisch die gesamte räumliche Energie und ihre Präparation.\\\\ Quantenquellen und Bindungen & Rückwirkung, übe","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Welche Ebenen jetzt miteinander verbunden sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6828,"byte_start":4552,"id":"section:9d0ad89ee1482151b6f7","kind":"section","labels":[],"line_end":36,"line_start":26,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/006-chapter-was-die-gesamte-sitzung-ergeben-hat.tex","status_markers_as_written":[],"summary_excerpt":"Erstens: Die Quelle muss ihre eigene Rückwirkung behalten. Eine unveränderliche Quelle kann eine schöne Ereignisstatistik erzeugen, aber das folgende Ereignis hängt davon ab, was nach dem ersten mit der Quelle geschieht. Die Rückwirkungsmodelle und Registerrechnungen zeigen konkret, an welcher Stelle diese Information verloren geht oder erhalten bleibt. 08 17 51 52","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was wir tatsächlich besser verstanden haben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8627,"byte_start":6828,"id":"section:d33fedb7fbd6d74ec400","kind":"section","labels":[],"line_end":45,"line_start":37,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/006-chapter-was-die-gesamte-sitzung-ergeben-hat.tex","status_markers_as_written":[],"summary_excerpt":"Es fehlt nicht nur ein letzter passender Zahlenwert. Die erste offene Auswahl liegt schon davor: Welche vollständige physische Quelle und welche Dynamik folgen aus den ursprünglichen Postulaten? Die Sitzung besitzt mehrere gute Kandidaten und exakte Teilverbindungen, aber noch keinen gemeinsamen Satz, der ihre unabhängigen Entscheidungen beseitigt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die Gesamtlösung weiterhin fehlt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9478,"byte_start":8627,"id":"section:86918813eac6bdd4bb40","kind":"section","labels":[],"line_end":50,"line_start":46,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/006-chapter-was-die-gesamte-sitzung-ergeben-hat.tex","status_markers_as_written":[],"summary_excerpt":"Die einfachen Ideen der Sitzung waren besonders produktiv, wenn sie eine entscheidende Annahme sichtbar machten: die Differenz von Summe und relativer Bewegung, ein einziger Zentrumstest, der gemeinsame Determinantenfaktor oder ein Register, das mit der Teilchenzahl weiterdreht. Diese kleinen Tests ersparten große Rechnungen an falschen Identifikationen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Rolle von Einfachheit und Eleganz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9535,"byte_start":9478,"id":"section:501b16e075e9ebf59a6b","kind":"chapter","labels":[],"line_end":51,"line_start":51,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/006-chapter-was-die-gesamte-sitzung-ergeben-hat.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die größten anschließenden Forschungsfragen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11174,"byte_start":9535,"id":"section:7f647af75fb6bd9d9cea","kind":"section","labels":[],"line_end":60,"line_start":52,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/006-chapter-was-die-gesamte-sitzung-ergeben-hat.tex","status_markers_as_written":[],"summary_excerpt":"Frage. Welche einzige, aus den Originalprinzipien begründete Quelle erzeugt die benötigte nichtquadratische Bewegung und die gemeinsame Energie der geladenen Felder?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Priorität 1: die Quelle wählt ihre Dynamik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12580,"byte_start":11174,"id":"section:401df4119cfa2205e0b1","kind":"section","labels":[],"line_end":69,"line_start":61,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/006-chapter-was-die-gesamte-sitzung-ergeben-hat.tex","status_markers_as_written":[],"summary_excerpt":"Frage. Wie tragen dieselben lokalen Zustände E8-Ströme, ungerade geladene Felder, die tatsächlichen Clocks und ihre Zeitentwicklung?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Priorität 2: geladene Fermionen und neutrale Ströme in einem lokalen Raum","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13956,"byte_start":12580,"id":"section:38f3943eba80a450815b","kind":"section","labels":[],"line_end":78,"line_start":70,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/006-chapter-was-die-gesamte-sitzung-ergeben-hat.tex","status_markers_as_written":[],"summary_excerpt":"Frage. Warum erzeugt die ursprüngliche Quelle unterschiedliche Down- und Lepton-Deformationen mit einer physisch unterscheidbaren relativen Phase?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Priorität 3: eine relative Flavorphase aus demselben Funktional","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15258,"byte_start":13956,"id":"section:09d3406262cac3ee18c7","kind":"section","labels":[],"line_end":87,"line_start":79,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/006-chapter-was-die-gesamte-sitzung-ergeben-hat.tex","status_markers_as_written":[],"summary_excerpt":"Frage. Gibt es in der physisch begründeten Hamiltonfamilie einen stabilen großen Zustandszweig, über dessen tatsächlichem Vakuum lokale geladene Anregungen linear dispergieren?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Priorität 4: eine große Phase mit wirklicher lokaler Bewegung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16624,"byte_start":15258,"id":"section:e49beba97afe6c7642a6","kind":"section","labels":[],"line_end":96,"line_start":88,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/006-chapter-was-die-gesamte-sitzung-ergeben-hat.tex","status_markers_as_written":[],"summary_excerpt":"Frage. Wie werden nicht nur Zustände und Energien, sondern die tatsächlichen Ereignisse, ihre Records und ihre Orte aus demselben Prozess bestimmt?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Priorität 5: Instrument, Anfangszustand und räumliche Beziehungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17849,"byte_start":16624,"id":"section:c5e8b8a67bf23eb98728","kind":"section","labels":[],"line_end":105,"line_start":97,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/006-chapter-was-die-gesamte-sitzung-ergeben-hat.tex","status_markers_as_written":[],"summary_excerpt":"Frage. Trägt die erfolgreiche Quelle anschließend chirale Materie, die gemessenen Kopplungen und einen universell gekoppelten masselosen Spin-2-Sektor?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Priorität 6: gemeinsame 3+1-dimensionale Physik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18289,"byte_start":17849,"id":"section:3606d7d740b210dc9624","kind":"section","labels":[],"line_end":108,"line_start":106,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/006-chapter-was-die-gesamte-sitzung-ergeben-hat.tex","status_markers_as_written":[],"summary_excerpt":"Zwei frühere Aussagen benötigen unabhängig davon eine Bereinigung: der vollständige Drei-Quellen-Komplementboden und die allgemeine Vierersektor-Leakageformel. In diesem Dossier bleiben die nicht wiederhergestellten Teile ausdrücklich außerhalb der gesicherten Vollsätze. Ihre Rekonstruktion würde den Bestand verbessern, ist aber von einem neuen Fortschritt zur Weltphysik zu unterscheiden.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dokumentarische Nacharbeiten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18345,"byte_start":18289,"id":"section:271294ad6ee24413b383","kind":"chapter","labels":[],"line_end":109,"line_start":109,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/006-chapter-was-die-gesamte-sitzung-ergeben-hat.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Provenienz, Reproduzierbarkeit und Reichweite","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20434,"byte_start":18345,"id":"section:be05be507da9594df963","kind":"section","labels":[],"line_end":122,"line_start":110,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/006-chapter-was-die-gesamte-sitzung-ergeben-hat.tex","status_markers_as_written":[],"summary_excerpt":"Diese zweite Fassung erfasst die gesamte in der Sitzung dokumentierte Ergebnisfolge vom 18. bis 20. September 2026 bis einschließlich der geladenen Registerrekonstruktion. Grundlage sind 55 vorherige Abschlussantworten, die vom Nutzer eingebrachten Anschlussberichte und die zugehörigen lokalen Forschungsartefakte. Die bereits vorhandene erste Fassung deckte die ersten 43 Abschlussantworten ab. Sie bleibt unverändert ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Abdeckung und Quellenstand","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":22093,"byte_start":20434,"id":"section:c1abeeec21fa02cc4ec0","kind":"section","labels":[],"line_end":131,"line_start":123,"occurrence":1,"owner_documents":["document:TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2"],"relation_ids":[],"semantic_review":false,"source":"documents/TFPT_Universalraum_Sitzungsdokumentation_2026-09-20_v2/sections/006-chapter-was-die-gesamte-sitzung-ergeben-hat.tex","status_markers_as_written":[],"summary_excerpt":"Für diese zweite Dokumentation wurden Quellenstände, Vertragszuordnungen, Korrekturen und die Abdeckung der späteren Sitzung abgeglichen. LaTeX-Kompilation, interne Verweise und die gerenderte Seitendarstellung werden gesondert geprüft. Die großen numerischen und exakten Forschungsläufe wurden zur PDF-Erstellung nicht vollständig wiederholt. 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TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reduced datum and carrier split","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4323,"byte_start":3607,"id":"section:8aaead3d793e00ad0fcd","kind":"subsection","labels":["eq:c3","eq:seam-flow","prop:seam-normalization","sec:seam-norm"],"line_end":133,"line_start":111,"occurrence":1,"owner_documents":["document:_archive/paper-latex/muon-g2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--muon-g2/sections/001-section-introduction-label-sec-introduction.tex","status_markers_as_written":[],"summary_excerpt":"TFPTkernel] If the seam loop carries one unit of relative spectral flow, then the seam constant is","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Seam normalization","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5849,"byte_start":4323,"id":"section:6f8fa3b3de71de178826","kind":"subsection","labels":["def:hard-topological-kernel","eq:defect-chain","eq:defects","eq:delta2-derivation","eq:delta2-numerical","lem:numerics","sec:defect-coefficients"],"line_end":194,"line_start":134,"occurrence":1,"owner_documents":["document:_archive/paper-latex/muon-g2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--muon-g2/sections/001-section-introduction-label-sec-introduction.tex","status_markers_as_written":[],"summary_excerpt":"TFPT31] The first- and second-order topological defect coefficients on the canonical admissible branch are","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Topological defect coefficients","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5901,"byte_start":5849,"id":"section:dcc8bc8051c453d17a3b","kind":"section","labels":["sec:vertex"],"line_end":196,"line_start":195,"occurrence":1,"owner_documents":["document:_archive/paper-latex/muon-g2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--muon-g2/sections/001-section-introduction-label-sec-introduction.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Seam vertex correction","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; 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At one loop the Schwinger term [formula in source] provides the leading contribution.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The vertex mechanism","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9193,"byte_start":6898,"id":"section:7bfc96aa78bd78894d11","kind":"subsection","labels":["eq:seam-vertex","thm:seam-vertex"],"line_end":284,"line_start":221,"occurrence":1,"owner_documents":["document:_archive/paper-latex/muon-g2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--muon-g2/sections/001-section-introduction-label-sec-introduction.tex","status_markers_as_written":[],"summary_excerpt":"The seam loop carries one unit of spectral flow over a complete [formula in source] phase cycle ( eq:seam-flow). When the topological defect coefficient [formula in source] is read as a vertex correction, it must be normalized by the total seam-loop phase [formula in source] . This normalization is the geometric analogue of the [formula in source] that appears in the Schwinger vertex: there, [formula in source] proje","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The [formula in source] 1/(2pi) projection","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10662,"byte_start":9193,"id":"section:78849d7ca0cc88c93fca","kind":"subsection","labels":["cor:carrier-decomposition","eq:carrier-decomposition"],"line_end":341,"line_start":285,"occurrence":1,"owner_documents":["document:_archive/paper-latex/muon-g2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--muon-g2/sections/001-section-introduction-label-sec-introduction.tex","status_markers_as_written":[],"summary_excerpt":"The seam vertex correction admits a fully explicit decomposition in terms of the carrier invariants.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Carrier-algebraic decomposition","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10722,"byte_start":10662,"id":"section:704e302068d97cf47f49","kind":"section","labels":["sec:comparison"],"line_end":343,"line_start":342,"occurrence":1,"owner_documents":["document:_archive/paper-latex/muon-g2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--muon-g2/sections/001-section-introduction-label-sec-introduction.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Comparison with experiment","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11301,"byte_start":10722,"id":"section:1042084f0bfc8615118d","kind":"subsection","labels":["eq:numerical-prediction","thm:numerical-prediction"],"line_end":370,"line_start":344,"occurrence":1,"owner_documents":["document:_archive/paper-latex/muon-g2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--muon-g2/sections/001-section-introduction-label-sec-introduction.tex","status_markers_as_written":[],"summary_excerpt":"From lem:numerics, [formula in source] . Dividing by [formula in source] yields [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Numerical evaluation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1110,"byte_start":0,"id":"section:d4de89874c0a5279af1e","kind":"subsection","labels":["tab:comparison"],"line_end":33,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/muon-g2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--muon-g2/sections/002-subsection-comparison-table.tex","status_markers_as_written":[],"summary_excerpt":"@> p0.32 > p0.30 > X@ Source & Value [formula in source] & Status \\\\ Experimental discrepancy [formula in source] & [formula in source] & Fermilab + BNL world average \\\\ TFPT seam vertex [formula in source] & [formula in source] & exact from carrier algebra \\\\ Deviation from central value & [formula in source] & [formula in source] \\\\ The TFPT prediction versus the measured muon [formula in source] discrepancy. The p","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Comparison table","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1880,"byte_start":1110,"id":"section:10da10df460d6f88697e","kind":"subsection","labels":[],"line_end":52,"line_start":34,"occurrence":1,"owner_documents":["document:_archive/paper-latex/muon-g2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--muon-g2/sections/002-subsection-comparison-table.tex","status_markers_as_written":[],"summary_excerpt":"The carrier split [formula in source] is the unique solution of [formula in source] and [formula in source] . The invariants [formula in source] , [formula in source] , and [formula in source] follow algebraically. The seam constant [formula in source] follows from the unit spectral flow normalization. The occupancy [formula in source] is the topological family closure output. The defect coefficients [formula in sour","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Parameter-free comparison","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3383,"byte_start":1880,"id":"section:e0269b5d716e81b061ab","kind":"section","labels":["prop:order-assignment","sec:why-delta2"],"line_end":88,"line_start":53,"occurrence":1,"owner_documents":["document:_archive/paper-latex/muon-g2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--muon-g2/sections/002-subsection-comparison-table.tex","status_markers_as_written":[],"summary_excerpt":"The first-order defect [formula in source] enters the exact seam generating function [formula in source] , which determines the fine-structure constant [formula in source] through the carrier-form closure equation [formula in source] By construction, [formula in source] is consumed by the electromagnetic closure: it is part of the input that fixes [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Why [formula in source] delta2 and not [formula in source] delta-top","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3427,"byte_start":3383,"id":"section:c99c9101d78856319977","kind":"section","labels":["sec:discussion"],"line_end":90,"line_start":89,"occurrence":1,"owner_documents":["document:_archive/paper-latex/muon-g2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--muon-g2/sections/002-subsection-comparison-table.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Discussion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3839,"byte_start":3427,"id":"section:e0da80715f0ae230abd8","kind":"subsection","labels":[],"line_end":99,"line_start":91,"occurrence":1,"owner_documents":["document:_archive/paper-latex/muon-g2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--muon-g2/sections/002-subsection-comparison-table.tex","status_markers_as_written":[],"summary_excerpt":"The TFPT derivation does not invoke supersymmetric partners (sleptons, charginos, neutralinos), dark photons, leptoquarks, or extended Higgs sectors. The anomaly is not a signal of new particles propagating in loops; it is the topological signature of the seam—the codimension-one locus where the involution-doubled manifold [formula in source] folds onto the physical quotient [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"No new particles","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4359,"byte_start":3839,"id":"section:70b0bad5d9fb3a20e96e","kind":"subsection","labels":[],"line_end":109,"line_start":100,"occurrence":1,"owner_documents":["document:_archive/paper-latex/muon-g2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--muon-g2/sections/002-subsection-comparison-table.tex","status_markers_as_written":[],"summary_excerpt":"The vertex projection [formula in source] is lepton-universal at the topological level: the seam defect does not depend on which lepton traverses the vertex. This is consistent with the fact that the electron anomalous magnetic moment [formula in source] is dominated by the QED Schwinger series and is measured to a precision where the [formula in source] topological correction would appear at the level of the [formul","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Universality","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5010,"byte_start":4359,"id":"section:fed91222860e0586e25f","kind":"subsection","labels":[],"line_end":121,"line_start":110,"occurrence":1,"owner_documents":["document:_archive/paper-latex/muon-g2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--muon-g2/sections/002-subsection-comparison-table.tex","status_markers_as_written":[],"summary_excerpt":"Recent lattice QCD evaluations of the hadronic vacuum polarization (HVP) BMW2021,RBC2024 suggest a smaller discrepancy than the dispersive approach. If the lattice central value is adopted, the experimental anomaly shrinks to [formula in source] (current estimates). The TFPT prediction [formula in source] would then sit at [formula in source] , still within the allowed band but less tightly centered. The resolution o","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lattice HVP and the residual tension","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5316,"byte_start":5010,"id":"section:ee6c0e9fac07b8cea4fc","kind":"subsection","labels":[],"line_end":128,"line_start":122,"occurrence":1,"owner_documents":["document:_archive/paper-latex/muon-g2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--muon-g2/sections/002-subsection-comparison-table.tex","status_markers_as_written":[],"summary_excerpt":"The prediction [formula in source] is exact and non-negotiable within TFPT. If future measurements of [formula in source] converge to a value outside the range [formula in source] , the seam vertex mechanism in its present form would be excluded.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Falsifiability","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6166,"byte_start":5316,"id":"section:c72accc067a46e65228c","kind":"section","labels":["sec:conclusion"],"line_end":161,"line_start":129,"occurrence":1,"owner_documents":["document:_archive/paper-latex/muon-g2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--muon-g2/sections/002-subsection-comparison-table.tex","status_markers_as_written":[],"summary_excerpt":"The muon [formula in source] anomaly admits a parameter-free explanation within the TFPT carrier algebra. The second-order topological defect [formula in source] projected through the seam-loop holonomy phase [formula in source] , yields [formula in source] This lies within [formula in source] of the Fermilab/BNL world average discrepancy [formula in source] and requires no supersymmetry, no dark photons, and no free","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conclusion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7249,"byte_start":6166,"id":"section:ab3d710a42f4182d87c0","kind":"section","labels":["app:chain"],"line_end":199,"line_start":162,"occurrence":1,"owner_documents":["document:_archive/paper-latex/muon-g2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--muon-g2/sections/002-subsection-comparison-table.tex","status_markers_as_written":[],"summary_excerpt":"For self-containedness, we collect the complete algebraic chain from the carrier split to the muon anomaly in one sequence.","summary_method":"opening prose excerpt; 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not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9735,"byte_start":7814,"id":"section:ee16e1fcab6db7fcbfbc","kind":"section","labels":["app:import"],"line_end":285,"line_start":217,"occurrence":1,"owner_documents":["document:_archive/paper-latex/muon-g2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--muon-g2/sections/002-subsection-comparison-table.tex","status_markers_as_written":[],"summary_excerpt":"The minimal import block for this application note is [formula in source] This block is intentionally small enough to be verified independently against the parent manuscript TFPT31 and the clean kernel note TFPTkernel.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Imported TFPT kernel block","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; 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TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Geometric Scale [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8643,"byte_start":5846,"id":"section:48b9b2d5dca0077ef61d","kind":"subsection","labels":["eq:CFE","fig:CFE"],"line_end":190,"line_start":115,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/002-subsection-closure-axioms-a7-a8.tex","status_markers_as_written":[],"summary_excerpt":"Effective Potential Parametersparams From the 11D Chern–Simons reduction (A5) and BFG structure (A6): Notation: We use [formula in source] (calligraphic) for this CFE parameter to distinguish it from [formula in source] (gravitational coupling).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Cubic Fixed-Point Equation (CFE)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8778,"byte_start":8643,"id":"section:a5a75b49defbafc020ad","kind":"subsection","labels":[],"line_end":193,"line_start":191,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/002-subsection-closure-axioms-a7-a8.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Geometric Self-Consistency (Backreaction)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12138,"byte_start":8778,"id":"section:5a72350523b9f8f38daf","kind":"subsubsection","labels":["eq:backreaction","tab:alpha"],"line_end":279,"line_start":194,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/002-subsection-closure-axioms-a7-a8.tex","status_markers_as_written":[],"summary_excerpt":"The ansatz [formula in source] is not ad hoc but the first-order term of a well-defined structural response. We derive it as follows.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Backreaction as Structural Response","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14805,"byte_start":12138,"id":"section:0d2813b60ea5f16c37fa","kind":"subsubsection","labels":["fig:deviation","sec:sensitivity"],"line_end":352,"line_start":280,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/002-subsection-closure-axioms-a7-a8.tex","status_markers_as_written":[],"summary_excerpt":"The sub-ppm precision of the [formula in source] prediction depends critically on the backreaction coefficient. We analyze the sensitivity to demonstrate this is not fine-tuning but a genuine geometric constraint.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Sensitivity Analysis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15007,"byte_start":14805,"id":"section:83e514c3e73261eee992","kind":"section","labels":[],"line_end":356,"line_start":353,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/002-subsection-closure-axioms-a7-a8.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"The Unified Field Equation (UFE)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1298,"byte_start":0,"id":"section:f458bc5df9389281b602","kind":"subsection","labels":["eq:UFE","eq:bianchi","eq:maxwell"],"line_end":34,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/003-subsection-torsionful-geometric-action.tex","status_markers_as_written":[],"summary_excerpt":"UFE ActionUFEaction On a manifold [formula in source] with metric [formula in source] and torsionful connection [formula in source] , the action is:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Torsionful Geometric Action","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2841,"byte_start":1298,"id":"section:135101359ae2b7313655","kind":"subsection","labels":[],"line_end":69,"line_start":35,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/003-subsection-torsionful-geometric-action.tex","status_markers_as_written":[],"summary_excerpt":"Gravitational Coupling Consistencykappa The gravitational coupling [formula in source] (with dimension [formula in source] ) is constrained by consistency with the dimensionless ratio:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gravitational Coupling from Invariants","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3033,"byte_start":2841,"id":"section:a98aaacc9e26538884fe","kind":"section","labels":[],"line_end":73,"line_start":70,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/003-subsection-torsionful-geometric-action.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Observable Predictions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3500,"byte_start":3033,"id":"section:6e5e11ecaea5b3fe11f0","kind":"subsection","labels":[],"line_end":85,"line_start":74,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/003-subsection-torsionful-geometric-action.tex","status_markers_as_written":[],"summary_excerpt":"Axion–Photon Couplinggagg The CFE fixes the axion–photon vertex uniquely: This determines cosmic birefringence without free parameters.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Axion–Photon Coupling","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4103,"byte_start":3500,"id":"section:f3135a4d80a75a8299e2","kind":"subsection","labels":[],"line_end":101,"line_start":86,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/003-subsection-torsionful-geometric-action.tex","status_markers_as_written":[],"summary_excerpt":"Cosmic Birefringence Predictionbirefringence A homogeneous axion field [formula in source] rotates the polarization plane of light by: With the minimal geometric choice [formula in source] :","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cosmic Birefringence","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9280,"byte_start":4103,"id":"section:55055f7edb1d2777c273","kind":"subsubsection","labels":["eq:shifted-axion-potential","fig:birefringence","sec:deltaa","tab:birefringence"],"line_end":213,"line_start":102,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/003-subsection-torsionful-geometric-action.tex","status_markers_as_written":[],"summary_excerpt":"Goal: Replace the excursion postulate [formula in source] by a minimal dynamical mechanism using only TFPT invariants.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dynamical Completion of the Excursion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11246,"byte_start":9280,"id":"section:07f8121d80f47c337dce","kind":"subsection","labels":["fig:twoloop"],"line_end":268,"line_start":214,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/003-subsection-torsionful-geometric-action.tex","status_markers_as_written":[],"summary_excerpt":"RG FingerprintsRGfingerprints The TFPT invariants leave signatures in the RG flow of gauge couplings: where [formula in source] GeV.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Two-Loop RG Fingerprints","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11453,"byte_start":11246,"id":"section:9fed06dd04243e76479c","kind":"section","labels":[],"line_end":272,"line_start":269,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/003-subsection-torsionful-geometric-action.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"The E [formula in source] Cascade and Block Constants","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14098,"byte_start":11453,"id":"section:9cdf32b7f01bf954c7e2","kind":"subsection","labels":[],"line_end":321,"line_start":273,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/003-subsection-torsionful-geometric-action.tex","status_markers_as_written":[],"summary_excerpt":"E [formula in source] Orbit Graphorbitgraph Let [formula in source] denote the set of nilpotent orbits of the exceptional Lie algebra [formula in source] . For each orbit [formula in source] , define: [formula in source] : the dimension of the orbit as a variety [formula in source] : the ``centralizer dimension'' [formula in source] : the height (sum of coefficients in weighted Dynkin diagram) The orbit graph [formul","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nilpotent Orbit Structure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18386,"byte_start":14098,"id":"section:65f1ff6b9d9bc0ed08c0","kind":"subsection","labels":["eq:ladder","fig:ladder"],"line_end":418,"line_start":322,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/003-subsection-torsionful-geometric-action.tex","status_markers_as_written":[],"summary_excerpt":"E [formula in source] Cascade LadderE8cascade For [formula in source] , the ladder values are: with:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Log-Exact Ladder Formula","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4491,"byte_start":0,"id":"section:e4c6a3eb57954c3ff455","kind":"subsection","labels":["fig:blocks","tab:blocks"],"line_end":111,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/004-subsection-block-constant-formula-and-derivation.tex","status_markers_as_written":[],"summary_excerpt":"For a 6D Weyl fermion zero mode on a boundary cycle [formula in source] with flat [formula in source] connection (holonomy [formula in source] ), the variation of [formula in source] under the connection is proportional to the quadratic charge index: The proportionality constant is fixed by the topological normalization [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Block Constant Formula and Derivation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5912,"byte_start":4491,"id":"section:3724d2aadc37436c2127","kind":"subsection","labels":[],"line_end":144,"line_start":112,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/004-subsection-block-constant-formula-and-derivation.tex","status_markers_as_written":[],"summary_excerpt":"The neutrino block at [formula in source] provides concrete predictions for the seesaw mechanism.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neutrino Seesaw Predictions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6122,"byte_start":5912,"id":"section:42c0d25b43c54467000e","kind":"section","labels":[],"line_end":148,"line_start":145,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/004-subsection-block-constant-formula-and-derivation.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Flavor Structure: The Z [formula in source] Architecture","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8753,"byte_start":6122,"id":"section:70d22cf219472bf1a18d","kind":"subsection","labels":[],"line_end":200,"line_start":149,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/004-subsection-block-constant-formula-and-derivation.tex","status_markers_as_written":[],"summary_excerpt":"On a conformally flat boundary geometry, the unique projectively invariant quantity from four marked points is the cross-ratio. Any boundary monodromy acts as a PSL [formula in source] transformation. Therefore, relations depending only on boundary monodromies must be rational functions of a M\\\"obius map.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Universal Phase [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10157,"byte_start":8753,"id":"section:a92ee1c4099bd398ada8","kind":"subsection","labels":[],"line_end":232,"line_start":201,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/004-subsection-block-constant-formula-and-derivation.tex","status_markers_as_written":[],"summary_excerpt":"Mass Ratios from M\\\"obius Mapmassratios The M\\\"obius map [formula in source] evaluated at cusps [formula in source] yields mass ratios:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"M\\\"obius Mass Relations","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11407,"byte_start":10157,"id":"section:98224b965c2ed93b2d3b","kind":"subsection","labels":[],"line_end":257,"line_start":233,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/004-subsection-block-constant-formula-and-derivation.tex","status_markers_as_written":[],"summary_excerpt":"Cabibbo AngleCabibbo The Cabibbo angle is fixed parameter-free by [formula in source] : PDG reference: [formula in source] . Deviation: [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cabibbo Angle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13373,"byte_start":11407,"id":"section:3ca03d51eec256d3f9da","kind":"subsection","labels":[],"line_end":300,"line_start":258,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/004-subsection-block-constant-formula-and-derivation.tex","status_markers_as_written":[],"summary_excerpt":"Identities, fonttitle= ] The PMNS matrix can be closed parameter-free using a single TFPT identity for [formula in source] combined with the trimaximal TM1 pattern.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"PMNS Neutrino Mixing: TM1 Pattern","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15810,"byte_start":13373,"id":"section:12adf4a45c18ae768277","kind":"section","labels":["eq:As","eq:R2action","eq:R2scale","eq:ns","eq:r","tab:inflation"],"line_end":352,"line_start":301,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/004-subsection-block-constant-formula-and-derivation.tex","status_markers_as_written":[],"summary_excerpt":"The TFPT topological correction scale is set by [formula in source] (cf.\\ [formula in source] ). 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The key results are:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conclusions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10658,"byte_start":9270,"id":"section:bc6f54202b572002ea11","kind":"section","labels":["tab:constants"],"line_end":217,"line_start":185,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/005-subsection-mode-separation-background-vs-oscillating.tex","status_markers_as_written":[],"summary_excerpt":"@ll@ Quantity & Value\\\\ [formula in source] & 0.0397887357729738339\\\\ [formula in source] & 0.0530516476972984453\\\\ [formula in source] & 0.000120304479547082053\\\\ [formula in source] & 0.0531719521768455273\\\\ [formula in source] (self-consistent) & 0.0531701963683282963\\\\ [formula in source] & 0.00423128951139541511\\\\ [formula in source] & [formula in source] \\\\ [formula in source] (E [formula in source] closure) & ","summary_method":"opening prose excerpt; 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no semantic paraphrase","title":"Derivation of the CFE from the Effective Potential","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":860,"byte_start":0,"id":"section:3184a8f7f9b790e992dd","kind":"section","labels":[],"line_end":29,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":["relation:11d317f37b9d4db5f1a9","relation:a20140d2c46429290934","relation:c60d489d0b2256115831"],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/006-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"The TFPT verification suite (v5) runs 10 independent modules:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verification Suite Summary","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1121,"byte_start":860,"id":"section:bb3398249a3014635dc5","kind":"section","labels":["app:E8cert"],"line_end":36,"line_start":30,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/006-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"This appendix provides the complete verification data for the E [formula in source] chain uniqueness theorem (Theorem","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"E [formula in source] Chain Certificate","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1625,"byte_start":1121,"id":"section:6b85f6173f0aa3a74656","kind":"subsection","labels":[],"line_end":46,"line_start":37,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/006-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"Each nilpotent orbit [formula in source] of [formula in source] is characterized by: Bala–Carter label: Standard notation (e.g., [formula in source] , [formula in source] , [formula in source] , ) Dimension: [formula in source] Centralizer dimension: [formula in source] Height: [formula in source] (sum of weighted Dynkin diagram coefficients)","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Orbit Data Structure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2301,"byte_start":1625,"id":"section:db3e7b318c92b24bea2b","kind":"subsection","labels":[],"line_end":71,"line_start":47,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/006-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"The complete chain from [formula in source] to [formula in source] :","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Unique Chain (Excerpt)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3069,"byte_start":2301,"id":"section:35ffe854593515c057a8","kind":"subsection","labels":[],"line_end":86,"line_start":72,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/006-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"The uniqueness is verified by: Constructing the complete Hasse diagram of [formula in source] from standard tables. Computing all cover relations with [formula in source] . Running dynamic programming to find all paths from [formula in source] to [formula in source] . Applying the cost function [formula in source] (second-difference smoothness). 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For a Weyl fermion coupled to a [formula in source] gauge field [formula in source] , the APS index theorem gives: where [formula in source] is the [formula in source] -invariant of the boundary Dirac operator.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4213,"byte_start":3700,"id":"section:bb16186726ec4baea5c3","kind":"subsection","labels":[],"line_end":118,"line_start":104,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/006-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"On the orientable double cover [formula in source] , the boundary decomposes as: (two boundary cycles plus the twist seam).","summary_method":"opening prose excerpt; 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TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5255,"byte_start":4959,"id":"section:097cc12ba3a578200de5","kind":"section","labels":["app:seam"],"line_end":144,"line_start":139,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/006-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"This appendix records the current status of Postulate A3 (effective seam boundary term) used in Axiom","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Orbifold Gauss–Bonnet and the Seam Term (Status and Open Formalization)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5577,"byte_start":5255,"id":"section:ef7719d27604bd5bbbb3","kind":"subsection","labels":[],"line_end":148,"line_start":145,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/006-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"We model the identification seam [formula in source] in the orientable double cover as contributing an effective boundary-type term in the (orbifold) Gauss–Bonnet balance. In TFPT bookkeeping, this yields three [formula in source] curvature contributions (two edges plus seam), fixing [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Postulate restatement","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6215,"byte_start":5577,"id":"section:84f4c5f9fbbd531979da","kind":"subsection","labels":[],"line_end":155,"line_start":149,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/006-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"Orbifold viewpoint: The M\\\"obius base can be viewed as a [formula in source] quotient; fixed-locus data naturally appear in geometric balance laws. Index-theory intuition: In orbifold/APS settings, fixed loci and matching conditions can contribute terms that are boundary-like in form. Cut-and-glue: Cutting along [formula in source] converts the seam matching condition into boundary data on a manifold-with-boundary, s","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Motivation (sketch)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6851,"byte_start":6215,"id":"section:a3bf36b8051691450b6c","kind":"subsection","labels":[],"line_end":162,"line_start":156,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/006-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"Exact orbifold Gauss–Bonnet statement: A precise theorem statement for the relevant [formula in source] quotient geometry, explicitly including fixed-locus (seam) contributions. Precise seam term definition: A differential-geometric definition of the seam contribution (as a boundary term or distributional curvature term) compatible with the variational normalization used in Section 2.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"What remains to be formalized (one-page ledger)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7293,"byte_start":6851,"id":"section:e1ccadcca1700b87f3bf","kind":"section","labels":["app:48deriv"],"line_end":173,"line_start":163,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/006-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"This appendix explains the integer coefficient in [formula in source] . The key point is that the canonical quantity is and the appearance of ``48'' is simply the same number expressed in units of [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of the Coefficient 48 in [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8017,"byte_start":7293,"id":"section:0e2d3cec61e3aab3077b","kind":"subsection","labels":[],"line_end":186,"line_start":174,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/006-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"The topological correction [formula in source] arises from the leading gauge-invariant correction to the tree-level geometric scale [formula in source] . The requirements are: Gauge invariance: The correction must be built from [formula in source] only (no explicit [formula in source] dependence at this order). Dimensionlessness: Since [formula in source] is dimensionless, the correction must be a pure power [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Physical Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8778,"byte_start":8017,"id":"section:9ce3987ffa4c786bf5a8","kind":"subsection","labels":[],"line_end":203,"line_start":187,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/006-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"The effective action on the M\\\"obius fiber includes the Chern–Simons term [formula in source] . The leading topological correction comes from the one-loop determinant of the Dirac operator coupled to this background.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Power Counting: Why [formula in source] ?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9286,"byte_start":8778,"id":"section:d018c0221eb35ffad5c6","kind":"subsection","labels":[],"line_end":216,"line_start":204,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/006-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"In the orbifold model underlying Axiom [formula in source] fixed points. Each [formula in source] fixed point contributes a deficit factor so the total deficit sum is In TFPT normalization this yields the canonical form [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Orbifold deficit sum rule (why the numerator is 3)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9587,"byte_start":9286,"id":"section:54ace52509521e298b6c","kind":"subsection","labels":[],"line_end":226,"line_start":217,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/006-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"Using [formula in source] : so [formula in source] and [formula in source] are exactly equivalent.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conversion to the [formula in source] normalization","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9997,"byte_start":9587,"id":"section:4c99d6e02694597efac7","kind":"subsection","labels":[],"line_end":231,"line_start":227,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/006-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"The deficit-sum explanation above is the intended bookkeeping origin of the integer coefficient and removes any appearance of numerology. A fully rigorous derivation (including a precise orbifold Gauss–Bonnet theorem statement and seam-term definition) is listed as open work in Appendix","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Status note","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10230,"byte_start":9997,"id":"section:cca7cc5d04fe9e7857c4","kind":"section","labels":["app:flavor"],"line_end":237,"line_start":232,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/006-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"This appendix derives the M\\\"obius structure of flavor relations from boundary monodromy.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Flavor Monodromy and Cross-Ratio","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10953,"byte_start":10230,"id":"section:a6208ab2650e4ebe7bd5","kind":"subsection","labels":[],"line_end":255,"line_start":238,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/006-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"On a conformally flat boundary, the metric is locally: Holomorphic automorphisms (Wilson lines of flat connections) act as M\\\"obius transformations:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Projective Invariance on Boundaries","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11387,"byte_start":10953,"id":"section:29005f891cd4f581f3b1","kind":"subsection","labels":[],"line_end":266,"line_start":256,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/006-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"Given four marked points [formula in source] on the boundary, the unique projective invariant is the cross-ratio:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cross-Ratio as Unique Invariant","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11925,"byte_start":11387,"id":"section:51d19bddd95fbc6afe5b","kind":"subsection","labels":[],"line_end":277,"line_start":267,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/006-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"The cusps [formula in source] arise from: Rationality: Quantized holonomies [formula in source] rational cusps. GUT compatibility: SU(5) hypercharge assignments give [formula in source] (quarks), [formula in source] (leptons), etc. Uniqueness: These are the only rational values that simultaneously separate the three SM sectors (up, down, lepton) and maintain GUT normalization.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cusp Selection","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12606,"byte_start":11925,"id":"section:d1038774a63a073fa6c0","kind":"subsection","labels":[],"line_end":296,"line_start":278,"occurrence":2,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/006-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"Leading term: [formula in source] from the abelian trace (same as [formula in source] numerator divided by 41/10's denominator structure).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13673,"byte_start":12606,"id":"section:a63f4e3fa05e41a205c9","kind":"section","labels":["app:repro"],"line_end":323,"line_start":297,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":["relation:19105e946d9995ca9448","relation:30f29665423d97f9a55b","relation:ac5c95bc7fd397b7329e"],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/006-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"Replication package: All numerical results can be reproduced using the TFPT verification suite (v5).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproducibility","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15725,"byte_start":13673,"id":"section:5bfeab8ea48c043fde16","kind":"section","labels":["app:identities"],"line_end":360,"line_start":324,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/006-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"This appendix labels frequently used equalities by logical status to prevent conflating definitions, algebraic rewrites, and genuine predictions.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Identity Catalogue and Status Labels","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17288,"byte_start":15725,"id":"section:410a2075bf4ba040574d","kind":"section","labels":[],"line_end":394,"line_start":361,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tffpt-theory-fullv2"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tffpt-theory-fullv2/sections/006-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"] F. W. Hehl, P. von der Heyde, G. D. Kerlick, J. M. Nester, ``General Relativity with Spin and Torsion: Foundations and Prospects,'' Rev.\\ Mod.\\ Phys.\\ 48, 393 (1976).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"References","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":965,"byte_start":0,"id":"section:3610c96b27fc666aaffc","kind":"frontmatter","labels":[],"line_end":34,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31-cosmolical-constant"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31-cosmolical-constant/preamble.tex","status_markers_as_written":[],"summary_excerpt":"detect-all, round-mode = none, exponent-mode = input, exponent-product = , group-separator = \\,, group-minimum-digits = 4","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1851,"byte_start":0,"id":"section:7990ffa89953221b68ac","kind":"frontmatter","labels":[],"line_end":15,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31-cosmolical-constant"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31-cosmolical-constant/sections/001-section-what-tfpt-is.tex","status_markers_as_written":[],"summary_excerpt":"A Seam-Induced Cosmological Constant from the Fine-Structure Constant and the Late-Time Hubble Scale Stefan Hamann Alessandro Rizzo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"A Seam-Induced Cosmological Constant from the Fine-Structure Constant and the Late-Time Hubble Scale","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7185,"byte_start":1851,"id":"section:a0e06086160c7b648ef3","kind":"section","labels":["eq:delta-def","eq:norm-split"],"line_end":87,"line_start":16,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31-cosmolical-constant"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31-cosmolical-constant/sections/001-section-what-tfpt-is.tex","status_markers_as_written":[],"summary_excerpt":"This Letter extracts the cosmological-constant branch of Conjecture 13.1 from the companion TFPT manuscript tfpt31. 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The starting point is therefore the admissible reduced datum from which the primitive layer is reconstructed before the later closure theorems are invoked.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Primitive relative spectral dynamics","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14946,"byte_start":7597,"id":"section:7b09885547820f3a6ccd","kind":"subsection","labels":["cor:minimal-carrier-compression","eq:carrier-polynomial","eq:explicit-hypercharge","eq:hypercharge-seam-inversion","eq:minimal-carrier-conditions","fig:minimal-carrier-glance","rem:carrier-discriminant","sec:minimal-carrier-proof"],"line_end":384,"line_start":168,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/002-subsection-primitive-relative-spectral-dynamics.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be a split carrier with traceless diagonal generator [formula in source] If one simultaneously requires then necessarily [formula in source] .","summary_method":"opening prose excerpt; 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TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Character, trace identities, and the abelian index","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9968,"byte_start":6622,"id":"section:1da34aa6147cb6d1a128","kind":"section","labels":["fig:primitive-start-sketch"],"line_end":250,"line_start":193,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/004-subsection-character-trace-identities-and-the-abelian-in.tex","status_markers_as_written":[],"summary_excerpt":"The carrier-first presentation should not leave the impression that TFPT is hard only at the level of group theory and representation bookkeeping. 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The electromagnetic [formula in s","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kernel output package","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3282,"byte_start":2771,"id":"section:35c2ded76227a1adec57","kind":"section","labels":[],"line_end":45,"line_start":42,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/005-subsection-kernel-output-package.tex","status_markers_as_written":[],"summary_excerpt":"This section collects the algebraic compressions that turn the carrier packet and kernel numerics from a list of internally consistent outputs into an overdetermined structure with genuine exclusion power. The compression identities are not new theorems; they are exact algebraic consequences of the already established carrier data. The exclusion theorems are the sharpest available evidence that the carrier packet act","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Compression identities and carrier exclusion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7796,"byte_start":3282,"id":"section:43694327db24a9f83eb8","kind":"subsection","labels":["cor:pythagorean-integrity-index","eq:rank-lock","lem:universal-5-4-compression","prop:rank-lock"],"line_end":210,"line_start":46,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/005-subsection-kernel-output-package.tex","status_markers_as_written":[],"summary_excerpt":"If the carrier identity [formula in source] , the canonical family data [formula in source] , and the optional occupancy compression [formula in source] are combined, then The unique integral solution is [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Rank lock and the [formula in source] - [formula in source] - [formula in source] 2-3-5 arithmetic","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11887,"byte_start":7796,"id":"section:89e7b6ea649277e9fc9f","kind":"subsection","labels":["cor:factorial-trace-delta2"],"line_end":381,"line_start":211,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/005-subsection-kernel-output-package.tex","status_markers_as_written":[],"summary_excerpt":"and [formula in source] ] Let [formula in source] be the two distinct carrier eigenvalues singled out by the factorized carrier polynomial. Then [formula in source] Here [formula in source] is the unweighted Vieta sum of the two distinct carrier eigenvalues, not the trace on [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Exact algebraic compressions on the minimal branch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3286,"byte_start":0,"id":"section:7d60994aaa0974cf746d","kind":"subsection","labels":["def:integrity-index-41","eq:41-chain-main","fig:41-chain-strip"],"line_end":72,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/006-subsection-the-texorpdfstring-41-41-integrity-index.tex","status_markers_as_written":[],"summary_excerpt":"The integer [formula in source] is not an isolated numerical curiosity. On the retained branch it is best read as a weighted integrity index rather than as a topological Euler-type object. 41 integrity index] Let [formula in source] On the canonical branch, [formula in source] and [formula in source] , so [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The [formula in source] 41 integrity index","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5728,"byte_start":3286,"id":"section:12ea62fe86c0bfaa85c8","kind":"subsection","labels":["eq:cabibbo-inversion","eq:catalan-cabibbo","eq:lambda-c-master","eq:seed-budget-identity"],"line_end":136,"line_start":73,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/006-subsection-the-texorpdfstring-41-41-integrity-index.tex","status_markers_as_written":[],"summary_excerpt":"The seed-driven observation rows [formula in source] are not four independent hits but four projections of [formula in source] . The Cabibbo angle admits an explicit inversion back to the seed: Setting [formula in source] the inversion formula becomes [formula in source] Hence where [formula in source] are the Catalan numbers. In the present paper the appropriate interpretation of this identity is noncrossing combina","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Single-seed compression and the Cabibbo inversion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10867,"byte_start":5728,"id":"section:72454b0c2c2ee1272cbb","kind":"subsection","labels":["fig:carrier-exclusion-matrix","thm:carrier-exclusion"],"line_end":233,"line_start":137,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/006-subsection-the-texorpdfstring-41-41-integrity-index.tex","status_markers_as_written":[],"summary_excerpt":"The strongest argument that the carrier packet selects the physical world is not a further precision hit. It is that wrong discrete worlds fail brutally.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Carrier exclusion theorems","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11433,"byte_start":10867,"id":"section:07a29e6c08c8bd5ee1cd","kind":"section","labels":[],"line_end":237,"line_start":234,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/006-subsection-the-texorpdfstring-41-41-integrity-index.tex","status_markers_as_written":[],"summary_excerpt":"This first closure-architecture block is the shortest route from the hard carrier packet to a broader Standard Model plus gravity compiler. It has three moves: the local patch-deficit count gives the carrier-side family count, the topological family closure globalizes it into the family space [formula in source] , the bosonic relative index selects the unique light Higgs doublet, and the local spectral-scale channel ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Closure architecture A: families, Higgs, and local spectral scale","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17942,"byte_start":11433,"id":"section:949d5451ed6b35cff53f","kind":"subsection","labels":["cor:boundary-bulk-occupancy","fig:family-triangle","prop:family-holonomy-su3","prop:orbifold-aps-compatibility","thm:orbifold-aps-family-master","thm:topological-family-closure"],"line_end":379,"line_start":238,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/006-subsection-the-texorpdfstring-41-41-integrity-index.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] denote the fundamental section of the seam complement. Define [formula in source] We use the distinguished cycle basis [formula in source] only as a concrete carrier-side basis of this family space; any later APS/Hodge realization is read as compatible analytic structure on the same topological family space. In this interpretation [formula in source] is neither an arbitrary flavor vector space","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Family monodromy and occupancy","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1250,"byte_start":0,"id":"section:a886efe54d35b7ad0524","kind":"subsection","labels":[],"line_end":18,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/007-subsection-occupancy-and-boundary-to-bulk-bridge.tex","status_markers_as_written":[],"summary_excerpt":"With the family bridge installed, the matter space becomes [formula in source] and the occupancy [formula in source] is already fixed by the topological family theorem and its bridge corollary. Here occupancy means the admissible chiral-state count after family lifting; it is not used as a primitive datum. The bridge point is not that family lifting creates a new numerical surcharge. Rather, the inherited hard kernel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Occupancy and boundary-to-bulk bridge","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2457,"byte_start":1250,"id":"section:2befd20907ccc6849223","kind":"subsection","labels":[],"line_end":43,"line_start":19,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/007-subsection-occupancy-and-boundary-to-bulk-bridge.tex","status_markers_as_written":[],"summary_excerpt":"Once the carrier packet and family closure architecture are fixed, the focused main-text closure problem splits into a geometric program [formula in source] and a transport program [formula in source] . Record algebra and prediction semantics are now tied directly to the admissible gap in the main theorem stack, while E [formula in source] scale grammar and horizon extrapolations are deferred to appendix-level contin","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"From bridge to geometric completion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6855,"byte_start":2457,"id":"section:c41c07d42f0d6743e148","kind":"subsection","labels":["cor:constant-scale-reduction","def:local-spectral-scale","thm:admissible-sector-on-reconstructed-geometry","thm:full-operator-reconstruction","thm:geometric-reconstruction-anchor","thm:geometric-reconstruction-from-Dgeo","thm:relative-geometric-reconstruction","thm:retained-branch-from-Padm"],"line_end":141,"line_start":44,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/007-subsection-occupancy-and-boundary-to-bulk-bridge.tex","status_markers_as_written":[],"summary_excerpt":"The geometric completion is formulated on a graded bundle [formula in source] with the geometric Dirac anchor [formula in source] , the declared reference operator [formula in source] , and APS-type boundary conditions on the seam [formula in source] ; see Appendix [formula in source] Here [formula in source] is the geometric Dirac anchor, while [formula in source] is the relative comparison operator entering the spe","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Relative APS and superconnection setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10809,"byte_start":6855,"id":"section:1589b2e56d1fc2c50f16","kind":"subsection","labels":["thm:callias-higgs-selection","thm:determinant-class-higgs-selection"],"line_end":243,"line_start":142,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/007-subsection-occupancy-and-boundary-to-bulk-bridge.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] Assume the total seam twist on the oriented double cover is one unit. Then the determinant holonomy classes satisfy [formula in source] Equivalently, for the asymptotic bosonic mass fields on the retained branch, [formula in source] The doublet winding is forced by the spin lift on the double cover, whereas center neutrality on the admissible branch forces determinant triviality in the triplet","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bosonic relative index and Higgs selection","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13901,"byte_start":0,"id":"section:586ede42ffd941cbae67","kind":"subsection","labels":["eq:carrier-dressed-v","eq:chi-effective-action","eq:induced-einstein","eq:relative-a2","eq:relative-a4","eq:relative-bosonic-endomorphism","fig:chi-bifurcation","fig:chi-bifurcation-clean","lem:two-sheet-zero-mode-normalization","prop:canonical-bosonic-normalization","tab:heat-kernel-map","thm:gravity-cosmology-closure"],"line_end":344,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/008-subsection-heat-kernel-coefficient-map-and-local-spectra.tex","status_markers_as_written":[],"summary_excerpt":"The local target action is written as The relative bosonic endomorphism used below is and the coefficient bookkeeping expected from the relative spectral expansion is summarized in tab:heat-kernel-map.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Heat-kernel coefficient map and local spectral-scale bifurcation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3540,"byte_start":0,"id":"section:8adc551aa0304f4c3593","kind":"frontmatter","labels":["thm:regulator-equivalence-bernstein-cone","thm:uv-bernstein-cone-completion"],"line_end":84,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/009-partial-t-gamma-k.tex","status_markers_as_written":[],"summary_excerpt":"Assume the projected RG flow preserves the admissible Bernstein cone and admits a nontrivial UV fixed point satisfying the pole and positivity audit below. The effective average action is sought in the form [formula in source] where the sector form factors are constrained by complete Bernstein functions [formula in source] The admissible RG flow is required to preserve both the retained sector and this cone: [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4044,"byte_start":3540,"id":"section:86597c87d0359ebaa342","kind":"section","labels":[],"line_end":88,"line_start":85,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/009-partial-t-gamma-k.tex","status_markers_as_written":[],"summary_excerpt":"The second closure-architecture block is the transport compiler. Its role is to turn the carrier packet and the family/occupancy closure into actual masses, mixings, hadronic admissibility, and strong-CP control. The logic is again staged: first the discrete phase operator and the transport kernel, then path-length masses and mixing data, then confinement and strong CP as transport-side admissibility statements.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Closure architecture B: Yukawas, masses, flavor, confinement, and strong CP","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8264,"byte_start":4044,"id":"section:bebafe5347dc3445330d","kind":"subsection","labels":["fig:z6-circle"],"line_end":157,"line_start":89,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/009-partial-t-gamma-k.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] This makes the phase grammar concrete rather than rhetorical. The six admissible phases are shown as a finite hexagonal transport geometry in fig:z6-circle: the cusp values live on the same real axis as the positive-real phase, the admissible gap is visible directly, and the holonomy phase can be read as a triangle on the same discrete transport base.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Discrete phase operator and transport grammar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16023,"byte_start":8264,"id":"section:5d3aa56c7dbe47dd5d27","kind":"subsection","labels":["def:gap-stable-admissibility","eq:finite-hexagonal-resolvent","eq:gap-lift-full-operator","eq:mobius-quotient","eq:transport-bridge-offset","eq:transport-spectrum","eq:yukawa-kernel","lem:finite-admissible-hexagon-gap","prop:finite-hexagonal-resolvent","prop:gap-lift-full-operator","thm:exact-transport-closure"],"line_end":388,"line_start":158,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/009-partial-t-gamma-k.tex","status_markers_as_written":[],"summary_excerpt":"For each fermion sector define the structural positive transport kernel by [formula in source] whenever the inverse exists on [formula in source] . The final admissible kernel is the restriction of this operator to the gap-stable branch selected below. The transport pole [formula in source] is the unique stationary point of the exact determinant functional [formula in source] with [formula in source] On the canonical","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Regularized Yukawa kernels and path-length masses","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11298,"byte_start":0,"id":"section:5e6ddf834fe8f17c17e6","kind":"frontmatter","labels":["cor:transport-length-sum-rule","eq:c6-cosine-polynomial","eq:ckm-holonomy-phase","eq:finite-positive-transport-kernel","eq:mass-bridge","eq:minimal-word-lengths","eq:path-length-yukawa","eq:yukawa-holonomy-matrix","prin:minimal-admissible-transport-packets","prop:exact-family-holonomy-phase","prop:finite-positive-transport-algebra","prop:holonomy-triangle-phase","rem:transport-rank-echo","tab:transport-dictionary"],"line_end":294,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/010-subsection-ckm-and-pmns-sharpening.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] Then [formula in source] The cosine operator [formula in source] has spectrum [formula in source] and satisfies Consequently the regularized positive transport kernel reduces to the cubic polynomial","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12926,"byte_start":11298,"id":"section:72d363d88ffbf7fe11c6","kind":"subsection","labels":["eq:ckm-magnitudes","eq:ckm-phase"],"line_end":339,"line_start":295,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/010-subsection-ckm-and-pmns-sharpening.tex","status_markers_as_written":[],"summary_excerpt":"The leading CKM magnitudes on the transport branch are As a small-area transport asymptotic, prop:holonomy-triangle-phase gives The benchmark row used later uses the exact holonomy phase [formula in source] while eq:ckm-phase is retained only as its small-area asymptotic expansion. Thus [formula in source] remains the base monodromy phase while [formula in source] is the leading family-transport area correction.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"CKM and PMNS sharpening","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15033,"byte_start":12926,"id":"section:3e2009d6c292cde99f80","kind":"subsection","labels":["fig:admissible-words"],"line_end":378,"line_start":340,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/010-subsection-ckm-and-pmns-sharpening.tex","status_markers_as_written":[],"summary_excerpt":"For each carrier word [formula in source] , let [formula in source] be its color-center charge and let [formula in source] be its seam parity. Physical hadronic words satisfy [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Confinement surrogate as admissible singlet selection","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3486,"byte_start":0,"id":"section:3e482338dcaeb5a67956","kind":"subsection","labels":["cor:strong-cp-rg-stability","def:sheet-cp-symmetry","eq:strong-cp","thm:sheet-cp-protection"],"line_end":66,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/011-subsection-transport-side-ingredients-for-the-strong-cp-.tex","status_markers_as_written":[],"summary_excerpt":"Define Define the admissible sheet-CP operator by [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Transport-side ingredients for the strong-CP theorem","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15237,"byte_start":3486,"id":"section:3e176e5cd9533053ba66","kind":"section","labels":["ass:remaining-closure-inputs","cor:factorized-admissibility-selector","def:admissibility-complex","def:relative-generating-functional","lem:admissibility-nilpotency","lem:admissible-reflection-positivity","lem:hodge-admissibility-projector","sec:closure-theorems","thm:master-closure"],"line_end":400,"line_start":67,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/011-subsection-transport-side-ingredients-for-the-strong-cp-.tex","status_markers_as_written":[],"summary_excerpt":"The preceding two sections introduced the carrier-compatible geometric and transport architecture. We now state the closure layer in the precise mode used throughout this manuscript: the theorems below are closed statements relative to the admissibility complex, the topological family theorem, and the explicit APS / positivity / reflection-stability inputs collected first.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Closure theorems from the admissibility complex","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6197,"byte_start":0,"id":"section:d8be05f5da7aef83748c","kind":"frontmatter","labels":["def:observer-algebra-prediction","def:stable-record-algebra","thm:admissible-vacuum-existence","thm:lorentzian-reconstruction","thm:nonperturbative-admissible-qft","thm:reflection-positivity-admissible","thm:strong-cp-closure"],"line_end":136,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/012-section-particle-and-mass-compiler.tex","status_markers_as_written":[],"summary_excerpt":"Define [formula in source] On the admissible branch, [formula in source] Moreover, [formula in source] so the free energy [formula in source] satisfies [formula in source] . If the CP-even admissible vacuum is unique, its minimum lies at [formula in source] . At the same time weak CP may survive through [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15329,"byte_start":6197,"id":"section:3559395957442aff0f78","kind":"section","labels":["def:intrinsic-observation-surfaces","fig:compiler-to-masses"],"line_end":392,"line_start":137,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/012-section-particle-and-mass-compiler.tex","status_markers_as_written":[],"summary_excerpt":"This section is the phenomenological heart of the manuscript. It is not meant to flatten all rows into one uniform notion of prediction. Instead it makes the relation between derived theorem outputs and intrinsic observation rows explicit: a declared numerical preconditioner, a kernel-output map, and a mass ledger that separates internal theorem outputs from their observation-surface images. Accordingly this section ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Particle and mass compiler","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2924,"byte_start":0,"id":"section:a103e4f44f09ea92c03f","kind":"frontmatter","labels":["fig:epistemic-output-matrix"],"line_end":47,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/013-subsection-rg-map-for-compiler-outputs.tex","status_markers_as_written":[],"summary_excerpt":"at (0,-1.2) [formula in source] \\\\G_ ^ glob [formula in source] S^+ [formula in source] [formula in source] , [formula in source] ; at (6.3,-1.2) [formula in source] \\ preconditioner; at (9.45,-1.2) E [formula in source] grammar\\ ;","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9214,"byte_start":2924,"id":"section:b467f395785119534d9f","kind":"subsection","labels":["cor:intrinsic-threshold-outputs","def:core-closure-functional","sec:rg-map-compiler-outputs","thm:observation-closure"],"line_end":175,"line_start":48,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/013-subsection-rg-map-for-compiler-outputs.tex","status_markers_as_written":[],"summary_excerpt":"The symbol [formula in source] denotes the declared comparison map from TFPT outputs to scheme-specified observables. Here it is the bookkeeping package [formula in source] and we write [formula in source] with the following restricted interpretation in the main text: [formula in source] is compared in the Thomson-limit on-shell convention, with the CODATA 2022 / NIST value taken as the normative low-energy reference","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"RG map for compiler outputs","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13151,"byte_start":9214,"id":"section:562ac0c91e68315bef91","kind":"subsection","labels":["eq:relative-gauge-split","prop:local-gauge-closure-matching"],"line_end":278,"line_start":176,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/013-subsection-rg-map-for-compiler-outputs.tex","status_markers_as_written":[],"summary_excerpt":"We write [formula in source] for the seam matching scale read from the first positive seam boundary mode and the common gauge coupling at that scale. In the same notation, [formula in source] is the determinant-sector involution used in admissibility, [formula in source] is the transport generator on the family side, [formula in source] denotes the seam cycle data when needed, and [formula in source] is the spin holo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Local gauge closure and seam matching","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14569,"byte_start":13151,"id":"section:aeb4fe4b8c0f6e5a83ac","kind":"subsection","labels":["tab:kernel-output-map"],"line_end":300,"line_start":279,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/013-subsection-rg-map-for-compiler-outputs.tex","status_markers_as_written":[],"summary_excerpt":"The roles of [formula in source] and [formula in source] should not remain implicit. They are the central hard numeric quantities of the present main-text kernel. The downstream E [formula in source] parameter [formula in source] is isolated in the next section rather than folded back into the kernel center.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Central hard-kernel quantities","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18908,"byte_start":14569,"id":"section:8407b09fe7671164c341","kind":"subsection","labels":["tab:sm-mass-ledger-ew","tab:sm-mass-ledger-quarks"],"line_end":359,"line_start":301,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/013-subsection-rg-map-for-compiler-outputs.tex","status_markers_as_written":[],"summary_excerpt":"For the mass surface itself the main text now uses four row-level status classes: exact algebraic, conditional geometric or closure, matched intrinsic observation, and optional extrapolation. The present ledgers use the middle two classes: conditional closure rows for theorem-facing masses and matched intrinsic observation rows for selected branch comparisons.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Mass-closure ledgers","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2934,"byte_start":0,"id":"section:b86dcc6b1f3b980a2040","kind":"section","labels":["lem:automatic-seam-transfer-convergence","sec:cosmology-closure","thm:cosmology-closure"],"line_end":86,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/014-section-downstream-cosmology-module-on-the-observation-c.tex","status_markers_as_written":[],"summary_excerpt":"On the admissible branch the seam transfer operator [formula in source] is positive and trace class. Moreover, [formula in source] Hence [formula in source] so the Fredholm determinant [formula in source] converges absolutely and defines a positive quantity.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Downstream cosmology module on the observation-closed branch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7319,"byte_start":2934,"id":"section:5fc4a6c3bc6151ad32ab","kind":"section","labels":["tab:benchmark"],"line_end":163,"line_start":87,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/014-section-downstream-cosmology-module-on-the-observation-c.tex","status_markers_as_written":[],"summary_excerpt":"The comparison values used in this section follow representative CODATA, PDG, NuFIT, Planck, and birefringence references codata2022,pdg2025,nufit2025,planck2018,minamiKomatsu2020,eskilt2023,sullivan2025. The snapshot policy is frozen at CODATA 2022 / NIST for [formula in source] , PDG 2025 for particle-mass and weak-mixing rows, NuFIT 2025 for neutrino-angle rows, and Planck 2018 for the baryon-fraction reconstructi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Primary benchmark map and prediction ledger","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12523,"byte_start":7319,"id":"section:1c2ea22a47f4f1325e00","kind":"subsection","labels":["tab:operational-prediction-set"],"line_end":214,"line_start":164,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/014-section-downstream-cosmology-module-on-the-observation-c.tex","status_markers_as_written":[],"summary_excerpt":"The six-row observation table is not the whole experimental surface of the manuscript. tab:operational-prediction-set collects the rows that are operationally testable on near- to medium-term timescales, while keeping their status, next test, kill criterion, and dependency structure explicit. The point is not to flatten them into one truth class. Rather, the Status column now uses only the manuscript's final output v","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Operational prediction set","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14980,"byte_start":12523,"id":"section:60033edd5e16c177830a","kind":"subsection","labels":["tab:prediction-ledger"],"line_end":244,"line_start":215,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/014-section-downstream-cosmology-module-on-the-observation-c.tex","status_markers_as_written":[],"summary_excerpt":"The main observation table shows only a narrow comparison surface. To keep the compiler structure visible, tab:prediction-ledger summarizes which output packages belong to which layer of the paper.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Compact prediction ledger","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15824,"byte_start":14980,"id":"section:262528400f2be9524405","kind":"subsection","labels":[],"line_end":256,"line_start":245,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/014-section-downstream-cosmology-module-on-the-observation-c.tex","status_markers_as_written":[],"summary_excerpt":"The present main-text surface is no longer intentionally mixed. Its rows now use the manuscript's four final classes: exact algebraic, conditional geometric or closure, matched intrinsic observation, and optional extrapolation. Carrier algebra and the exact [formula in source] row remain the sharpest numerically load-bearing entries, while the seed-driven observation rows remain useful because they are transparent an","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Realism audit of the present compiler surface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17817,"byte_start":15824,"id":"section:27a4ab818ca895f028de","kind":"subsection","labels":["fig:residual-plot"],"line_end":306,"line_start":257,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/014-section-downstream-cosmology-module-on-the-observation-c.tex","status_markers_as_written":[],"summary_excerpt":"The residuals for the restricted six-row observation table are shown in fig:residual-plot. The carrier-linked electromagnetic, birefringence, and baryon-density channels all remain within the displayed few-sigma window. The CKM phase is not plotted here because it is better treated in the operational prediction set and Appendix rather than inside the restricted six-row residual plot.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Residual map and principal comparison refinements","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19929,"byte_start":17817,"id":"section:59fd5df0b41c3690aa61","kind":"subsection","labels":["tab:falsification"],"line_end":333,"line_start":307,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/014-section-downstream-cosmology-module-on-the-observation-c.tex","status_markers_as_written":[],"summary_excerpt":"The present draft does not ask the reader to accept one undifferentiated compiler claim. Each main-text closure statement has a corresponding local or global failure mode, and those failure modes should be readable without first decoding the appendix tables.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Falsification matrix","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19983,"byte_start":19929,"id":"section:5c625d68f882fcaefa0a","kind":"section","labels":[],"line_end":335,"line_start":334,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/014-section-downstream-cosmology-module-on-the-observation-c.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Compiler theorem and intrinsic observation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20894,"byte_start":19983,"id":"section:1bdaa538a517385090cd","kind":"subsection","labels":["eq:closed-compiler-chain"],"line_end":362,"line_start":336,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/014-section-downstream-cosmology-module-on-the-observation-c.tex","status_markers_as_written":[],"summary_excerpt":"Collecting the admissible reduced datum, primitive reconstruction, the closure theorems from the admissibility complex, and the intrinsic observation layer, the compiler line is This line is not meant as a slogan. Each arrow is attached either to a hard theorem or to one of the closure theorems of sec:closure-theorems. In practical finite-threshold computations, [formula in source] is only the numerical preconditione","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Compiler chain","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1620,"byte_start":0,"id":"section:5ba7c7bb2bf5294a1869","kind":"subsection","labels":[],"line_end":28,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/015-subsection-compiler-theorem-from-the-admissibility-compl.tex","status_markers_as_written":[],"summary_excerpt":"Assume the admissible reduced datum summarized in tab:status-matrix, together with the closure theorems of sec:closure-theorems and the conditional closure selection theorem thm:observation-closure. Then every main-text observable in scope is classified by exactly one of the following status classes: exact algebraic, conditional geometric or closure, matched intrinsic observation, optional extrapolation.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Compiler theorem from the admissibility complex","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4395,"byte_start":1620,"id":"section:4e947639a598cbdead8b","kind":"subsection","labels":["tab:proof-obligations"],"line_end":59,"line_start":29,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/015-subsection-compiler-theorem-from-the-admissibility-compl.tex","status_markers_as_written":[],"summary_excerpt":"The compiler theorem above is only meaningful if the closure arrows are visibly attached to concrete input packages, output packages, and output classes. 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The main-text output surface is organized by four classes: exact algebraic, conditional geometric or closure, matched intrinsic observation, and optional extr","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Intrinsic observation layer","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6800,"byte_start":6465,"id":"section:7472bd8e84f98fd5f207","kind":"subsection","labels":[],"line_end":116,"line_start":109,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/015-subsection-compiler-theorem-from-the-admissibility-compl.tex","status_markers_as_written":[],"summary_excerpt":"Optional arithmetic continuations, appendix-level E [formula in source] scale grammar, and horizon semantics are kept as extrapolations and are not part of the theorem surface itself. They are retained only where they illuminate downstream interpretations without carrying any main-text proof burden.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Optional extrapolations","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7039,"byte_start":6800,"id":"section:6a8f6b29c8f65862fa11","kind":"section","labels":["app:tech"],"line_end":121,"line_start":117,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/015-subsection-compiler-theorem-from-the-admissibility-compl.tex","status_markers_as_written":[],"summary_excerpt":"This appendix collects the technical bookkeeping that supports the carrier-first presentation but would slow the early main-text flow if placed before the carrier theorem.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Technical conventions and data layers","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8474,"byte_start":7039,"id":"section:286c07c965fa1fa8ff34","kind":"subsection","labels":["tab:relative-objects"],"line_end":145,"line_start":122,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/015-subsection-compiler-theorem-from-the-admissibility-compl.tex","status_markers_as_written":[],"summary_excerpt":"The adjective relative is used in one fixed sense throughout the paper: every operator or action is compared to a declared reference object.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Relative objects","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11466,"byte_start":8474,"id":"section:6053877817fe7dd894c0","kind":"subsection","labels":["tab:layered-datum"],"line_end":208,"line_start":146,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/015-subsection-compiler-theorem-from-the-admissibility-compl.tex","status_markers_as_written":[],"summary_excerpt":"The technical bookkeeping behind the manuscript uses four levels: [formula in source] [formula in source] [formula in source] [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Layered datum and admissibility","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17291,"byte_start":11466,"id":"section:00e22b5635c7e33903b6","kind":"subsection","labels":["tab:symbol-guide"],"line_end":271,"line_start":209,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/015-subsection-compiler-theorem-from-the-admissibility-compl.tex","status_markers_as_written":[],"summary_excerpt":"The main text uses a small number of recurrent symbols across different layers. The table below records their first-duty meaning and status class, now including the seam-matching notation introduced in Definition 9.1, so that the manuscript can be read without repeatedly reverse-engineering the bookkeeping.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Symbol guide","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17506,"byte_start":17291,"id":"section:f9183dafeb09770fa09b","kind":"section","labels":["app:constants"],"line_end":276,"line_start":272,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/015-subsection-compiler-theorem-from-the-admissibility-compl.tex","status_markers_as_written":[],"summary_excerpt":"This appendix collects material that is useful for internal compression but should not dominate the main-text scope of explicit claims.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Constants atlas and downstream scale grammar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":22520,"byte_start":17506,"id":"section:38411439ae8e74a58951","kind":"subsection","labels":["fig:constant-cascade","tab:constants-atlas"],"line_end":360,"line_start":277,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/015-subsection-compiler-theorem-from-the-admissibility-compl.tex","status_markers_as_written":[],"summary_excerpt":"The seam loop is assumed to carry one unit of spectral flow, [formula in source] Because the spin lift closes only after [formula in source] , the normalized rotation modulus is [formula in source] The cascade in fig:constant-cascade is kept here as technical bookkeeping rather than as an early main-text dependency graphic.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Global rotation angle and constants atlas","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1570,"byte_start":0,"id":"section:b5a3fee6b574801aec1b","kind":"subsection","labels":[],"line_end":33,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/016-subsection-texorpdfstring-e-8-e8-as-downstream-scale-gra.tex","status_markers_as_written":[],"summary_excerpt":"In the present paper E [formula in source] is not used as a primitive cause. The retained parameter is [formula in source] On the retained branch this means [formula in source] The intended reading is a downstream scale grammar: the carrier packet fixes [formula in source] , [formula in source] then defines an optional ladder parameter, the ladder is allowed to organize scale spacing, but it does not replace the carr","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"E [formula in source] E8 as downstream scale grammar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4287,"byte_start":1570,"id":"section:46b756265183b589016a","kind":"subsection","labels":["tab:e8-full-atlas"],"line_end":68,"line_start":34,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/016-subsection-texorpdfstring-e-8-e8-as-downstream-scale-gra.tex","status_markers_as_written":[],"summary_excerpt":"The full real-domain atlas up to [formula in source] extends the main-text robust table with restricted-scan candidates and IR tail conjectures. Rows are classified as robust (restrictive grammar, unambiguous target), restricted-scan (plausible but less constrained), or tail conjecture (new trace class [formula in source] not yet derived from block structure).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Full stage atlas","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6114,"byte_start":4287,"id":"section:c2ae9139f3496bfc487a","kind":"subsection","labels":["eq:41-chain"],"line_end":109,"line_start":69,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/016-subsection-texorpdfstring-e-8-e8-as-downstream-scale-gra.tex","status_markers_as_written":[],"summary_excerpt":"The main-text compression identities are developed in the dedicated section on compression identities and carrier exclusion. This appendix subsection collects additional arithmetic continuations and the compression chain summary.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Compression identities on the minimal branch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10841,"byte_start":6114,"id":"section:307efb92649764c85580","kind":"subsection","labels":["rem:defect-factorization-gcd-lcm"],"line_end":259,"line_start":110,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/016-subsection-texorpdfstring-e-8-e8-as-downstream-scale-gra.tex","status_markers_as_written":[],"summary_excerpt":"The next relations mix the main-text carrier with optional appendix-level E [formula in source] , inflation, or geometric notation. 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It assumes that the carrier rank, family multiplicity, and seam normalization are all read as closed rather than only partially inherited.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conditional minimal-parameter picture","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13404,"byte_start":12431,"id":"section:7fbcd82c3450a8fb21a6","kind":"section","labels":["app:aps"],"line_end":338,"line_start":326,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/016-subsection-texorpdfstring-e-8-e8-as-downstream-scale-gra.tex","status_markers_as_written":[],"summary_excerpt":"The geometric completion uses APS-type relative data aps1975. In practice this means: one works with a declared pair [formula in source] rather than a single unanchored operator, boundary conditions on the seam [formula in source] are part of the definition of the relative index, the [formula in source] -term keeps track of the residual spectral asymmetry, the superconnection package is used in the same spirit as the","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Relative APS and superconnection setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13484,"byte_start":13404,"id":"section:76113a5085d9b7a4b303","kind":"section","labels":["app:os-fermions"],"line_end":341,"line_start":339,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/016-subsection-texorpdfstring-e-8-e8-as-downstream-scale-gra.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Relative reflection positivity with fermions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13971,"byte_start":13484,"id":"section:5ad137efe6871c43c935","kind":"subsection","labels":[],"line_end":351,"line_start":342,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/016-subsection-texorpdfstring-e-8-e8-as-downstream-scale-gra.tex","status_markers_as_written":[],"summary_excerpt":"The relative Euclidean theory used in the main closure section is not interpreted as a difference of measures. Instead it is organized as the normalized quotient [formula in source] Because the denominator is source independent on the admissible sector, the reference theory acts only as a fixed normalizer and does not interfere with reflection positivity.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Normalized quotient form","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15001,"byte_start":13971,"id":"section:8c8e88a1eada0a755553","kind":"subsection","labels":[],"line_end":369,"line_start":352,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/016-subsection-texorpdfstring-e-8-e8-as-downstream-scale-gra.tex","status_markers_as_written":[],"summary_excerpt":"The commutation relations [formula in source] ensure that reflection preserves the admissible subspace. The bosonic part then follows the standard Markov / reflection-stable Osterwalder–Schrader argument on admissible observables. For fermions, the admissible CAR kernel may be written as a reflected quadratic form; equivalently one may express the same condition as positivity of the associated Pfaffian structure on t","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bosonic and fermionic positivity on [formula in source] Padm","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1903,"byte_start":0,"id":"section:628e31c73eb3ec1b51e0","kind":"section","labels":["app:yukawa"],"line_end":34,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/017-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"This appendix is the proof motor for the transport positivity, strong-CP protection, and bounded-residual statements used in the main text. 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This statement is kept in the appendix so that the main theorem surface does not depend o","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Optional strong-coupling sharpening","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2972,"byte_start":2548,"id":"section:51c3bcf6773dc582b5b1","kind":"section","labels":["app:info-readings"],"line_end":55,"line_start":51,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/017-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"This appendix collects interpretive notes that help organize the algebraic structure of the carrier-first compiler. 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Since [formula in source] the Cabibbo scale is exactly the standard-deviation scale of a Bernoulli variable with success probability [formula in source] : [formula in source] Equivalently, the Fisher information of the Bernoulli family is [formula in source] so the Cabibbo bridge measures the inverse square-root Fisher scale of the retained seed. T","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Seed variance and surprisal readings","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8168,"byte_start":5530,"id":"section:f6451f20553467abdf89","kind":"subsection","labels":[],"line_end":168,"line_start":111,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/017-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"The strongest information-theoretic statement is no longer a loose analogy. 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The stronger generative theorem path described in the conclusion would refine this object to the global admissible vacuum functional [formula in source] whose variations also select the transport branch. 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The purpose is not to flatten the truth-mode hierarchy but to give the reader a single-page capability audit: which particles, which quantities, which derivation, which status, which reference value, which residual. The status language is the same throughout the paper:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Global particle ledger and status surface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16540,"byte_start":13599,"id":"section:fc02600046ead802d5e4","kind":"subsection","labels":["tab:sm-content-origin"],"line_end":319,"line_start":278,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/017-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"@> p0.09 > p0.11 > p0.10 > p0.04 > p0.18 > p0.20 > p0.08 @ Particle & Repr. & Ext.\\ source & [formula in source] & TFPT origin & Internal source & Status \\\\ 7@l Fermion sector (one family [formula in source] ): \\\\ [formula in source] & [formula in source] & [formula in source] & [formula in source] & carrier scaffold & hard carrier, [formula in source] & EA \\\\ [formula in source] & [formula in source] & [formula in s","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Table A: Standard Model content and origin map","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":21263,"byte_start":16540,"id":"section:162b2943036b7a704049","kind":"subsection","labels":["tab:full-mass-benchmark-surface"],"line_end":378,"line_start":320,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/017-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"round-mode=none, group-minimum-digits=20 ! @llllrlrrl@ Quantity & Sector & TFPT formula or source & Obs.\\ map & TFPT\\ & Unit & Reference\\ & Residual & Status \\\\ 9@l Exact algebraic surface: \\\\ [formula in source] & EM & exact [formula in source] closure & on-shell Thomson & 137.0359992 & — & 137.03599918 & [formula in source] & EA \\\\ [formula in source] & EM & unbroken [formula in source] & — & [formula in source] & ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Table B: full mass and benchmark surface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2928,"byte_start":0,"id":"section:fe91a750411eb227a486","kind":"subsection","labels":["tab:strict-benchmark-surface"],"line_end":49,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/018-subsection-strict-benchmark-surface.tex","status_markers_as_written":[],"summary_excerpt":"tab:strict-benchmark-surface extracts only the rows that are fair as direct theory-versus-data comparisons: exact algebraic outputs and matched intrinsic observation rows. Conditional closure rows and optional extrapolations are excluded.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Strict benchmark surface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3273,"byte_start":2928,"id":"section:e5207e7749a3a9f853c7","kind":"section","labels":["app:benchmarks"],"line_end":54,"line_start":50,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/018-subsection-strict-benchmark-surface.tex","status_markers_as_written":[],"summary_excerpt":"This appendix turns the broader prediction surface into explicit experimental bookkeeping. The point is not to promote every row to main-text benchmark status, but to keep next test, kill criterion, and dependency structure visible wherever the theory already commits to a concrete target.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Extended benchmarks","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7103,"byte_start":3273,"id":"section:fb7cd8f2a88d6711411a","kind":"subsection","labels":["tab:extended-benchmarks"],"line_end":88,"line_start":55,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/018-subsection-strict-benchmark-surface.tex","status_markers_as_written":[],"summary_excerpt":"The appendix matrix keeps the same truth-mode discipline as the main text, but its final column adds a short row-level qualifier whenever an appendix-level auxiliary continuation needs to be made explicit.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Operational prediction matrix","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9236,"byte_start":7103,"id":"section:66f008470993a457ffaa","kind":"subsection","labels":["tab:kill-tests"],"line_end":113,"line_start":89,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/018-subsection-strict-benchmark-surface.tex","status_markers_as_written":[],"summary_excerpt":"round-mode=none, group-minimum-digits=20 ! @> p0.22 > p0.24 > p0.12 > p0.38 @ Test row & TFPT target or prohibition & Status reading & Failure mode \\\\ Second light Higgs doublet & no additional seam-even\\ doublet & kill\\ & robust discovery would\\ the bosonic-index route \\\\ Calibrated birefringence null & [formula in source] \\ the minimal branch & kill\\ & externally calibrated null\\ with zero at the\\ tolerance would r","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Target and kill-test rows","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10093,"byte_start":9236,"id":"section:143a8b1e4b5d0d27c81e","kind":"subsection","labels":[],"line_end":138,"line_start":114,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/018-subsection-strict-benchmark-surface.tex","status_markers_as_written":[],"summary_excerpt":"The axion rows are read as intrinsic observation outputs of the downstream cosmology module rather than as an independent hard theorem. 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This interface depends on the downstream PQ / scale-gramma","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Axion interface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13407,"byte_start":10093,"id":"section:4170ca510337d8f11b99","kind":"subsection","labels":["tab:mass-source-supplement"],"line_end":182,"line_start":139,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/018-subsection-strict-benchmark-surface.tex","status_markers_as_written":[],"summary_excerpt":"The compact main-text mass ledgers intentionally suppress explicit formula detail. The source rows collected here retain that information without forcing the main text to read like a mixed formula notebook.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Supplementary mass-source rows","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16125,"byte_start":13407,"id":"section:c5c52d149c66e7fb784e","kind":"subsection","labels":["tab:extended-compiler-ledger","tab:yukawa-residuals"],"line_end":234,"line_start":183,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/018-subsection-strict-benchmark-surface.tex","status_markers_as_written":[],"summary_excerpt":"round-mode=none, group-minimum-digits=20 @> p0.15 > p0.33 > p0.15 Y@ Row & TFPT source or target & TFPT value & Status note \\\\ [formula in source] & exact unbroken [formula in source] direction & [formula in source] & exact structural row \\\\ [formula in source] & exact color gauge direction before confinement & [formula in source] & exact structural row \\\\ [formula in source] & intrinsic threshold output at [formula ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Extended compiler ledger","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18765,"byte_start":16125,"id":"section:6fd67203a9a402700a66","kind":"subsection","labels":[],"line_end":288,"line_start":235,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-31"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-31/sections/018-subsection-strict-benchmark-surface.tex","status_markers_as_written":[],"summary_excerpt":"The paper uses standard tools from relative spectral geometry, APS index theory, transport/resolvent language, and conventional RG comparison. The claim of novelty is not that these background ingredients are new in isolation, but that the minimal [formula in source] carrier packet, the compression identities, and the carrier-first compiler architecture are organized into one tightly overdetermined program. Conversel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Novelty boundary and literature positioning","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4363,"byte_start":0,"id":"section:77ead172a259110848bf","kind":"frontmatter","labels":[],"line_end":131,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/preamble.tex","status_markers_as_written":[],"summary_excerpt":"skins,breakable arrows.meta,positioning,calc,fit,backgrounds,matrix,decorations.pathmorphing compat=1.18","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TFPT: Carrier Algebra, Closure Theorems, and Benchmark Bridge\\\\[0.5em] An overdetermined rank-5 spectral theory on the oriented double cover","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3828,"byte_start":0,"id":"section:a676cbdeaac57368fcf5","kind":"frontmatter","labels":[],"line_end":24,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/001-section-reading-guide-and-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"A minimal carrier [formula in source] on the oriented double cover is shown to be the unique rank-5 split satisfying [formula in source] and [formula in source] . This carrier already forces the global Standard Model group [formula in source] , one chiral family with [formula in source] from the positive half-spinor, the hypercharge–seam inversion [formula in source] , and a self-consistent electromagnetic closure eq","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13899,"byte_start":3828,"id":"section:44d833b825fd27c41145","kind":"section","labels":["fig:dependency-map","tab:status-matrix"],"line_end":127,"line_start":25,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/001-section-reading-guide-and-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"The paper is organized in three reading layers: Big picture: one section explains what TFPT claims in plain language before the detailed datum and conventions begin. Detail: the main body then runs from primitive core and hard carrier kernel through kernel numerics, the two closure-architecture sections, the closure theorem stack, the particle/mass compiler, and the benchmark interface. Proof sketches: the main text ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reading guide and claim map","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":22738,"byte_start":13899,"id":"section:859e405bbfdc63ffac7c","kind":"section","labels":["eq:compiler-chain","eq:tfpt-master","eq:tfpt-selectors","fig:status-ladder","fig:tfpt-headline-claims"],"line_end":267,"line_start":128,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/001-section-reading-guide-and-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"TFPT is presented here as a carrier-first theory of admissible vacua on the oriented double cover. The primitive datum fixes the relative spectral starting package [formula in source] before any carrier decomposition is imposed. The later hard carrier theorem then enforces the minimal split [formula in source] and hence the global Standard Model group, hypercharge, one chiral family, seam normalization, and the carri","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Big picture: what TFPT actually claims","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":22788,"byte_start":22738,"id":"section:c51633c7ce50b8b60650","kind":"section","labels":[],"line_end":269,"line_start":268,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/001-section-reading-guide-and-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Primitive core and hard carrier kernel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":25064,"byte_start":22788,"id":"section:7c2542b2b2bd544da229","kind":"subsection","labels":[],"line_end":299,"line_start":270,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/001-section-reading-guide-and-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"We use natural units [formula in source] . Relative operators are formulated in Euclidean signature and compared through a declared Wick-rotation bridge when Lorentzian language is needed. Higgs fields are denoted by [formula in source] , Hamiltonians by [formula in source] , and the cosmological Hubble rate by [formula in source] ; this avoids overloading the letter [formula in source] . Newton's constant is always ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Primitive core and conventions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":31354,"byte_start":25064,"id":"section:fbde52fd99878a3f9fb5","kind":"subsection","labels":["ass:bernstein-positivity","eq:bernstein-test-function","fig:aps-split"],"line_end":405,"line_start":300,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/001-section-reading-guide-and-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"The carrier theorem is not intended to float above an unspecified microscopic dynamics. The primitive TFPT datum is therefore stated already at the operator level, before the later closure theorems are invoked.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Primitive relative spectral dynamics","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7349,"byte_start":0,"id":"section:afd9bdbaf6943b9ab562","kind":"subsection","labels":["cor:minimal-carrier-compression","eq:carrier-polynomial","eq:explicit-hypercharge","eq:hypercharge-seam-inversion","eq:minimal-carrier-conditions","fig:minimal-carrier-glance","rem:carrier-discriminant","sec:minimal-carrier-proof"],"line_end":217,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/002-subsection-minimal-carrier-theorem.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be a split carrier with traceless diagonal generator [formula in source] If one simultaneously requires then necessarily [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Minimal carrier theorem","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9385,"byte_start":0,"id":"section:df63c604dd2e17a19645","kind":"subsection","labels":["fig:family-occupancy-map","prop:parity-code-family","tab:one-family"],"line_end":270,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/003-subsection-global-gauge-group-and-one-family-packet.tex","status_markers_as_written":[],"summary_excerpt":"The determinant-preserving connected stabilizer of the minimal carrier split is [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Global gauge group and one-family packet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6228,"byte_start":0,"id":"section:50da8d791aaec7ab1461","kind":"subsection","labels":["cor:family-degree-filters","eq:abelian-index","eq:family-character","eq:family-x-polynomial","eq:split-weight-enumerator","eq:x-mod-2","eq:x-mod-3","eq:x-mod-5","prop:family-hypercharge-compression","prop:split-weight-enumerator"],"line_end":182,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/004-subsection-character-trace-identities-and-the-abelian-in.tex","status_markers_as_written":[],"summary_excerpt":"For the present paragraph let [formula in source] Define also the split weight enumerator [formula in source] Then Moreover, Consequently, [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Character, trace identities, and the abelian index","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9529,"byte_start":6228,"id":"section:11bb6e14b4f653f56ab3","kind":"section","labels":["fig:primitive-start-sketch"],"line_end":240,"line_start":183,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/004-subsection-character-trace-identities-and-the-abelian-in.tex","status_markers_as_written":[],"summary_excerpt":"The carrier-first presentation should not leave the impression that TFPT is hard only at the level of group theory and representation bookkeeping. The numerical kernel already fixes a nontrivial output layer. Here that layer is pulled forward and read as the first established output package of the carrier/compiler architecture rather than as a later list of disconnected constants.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kernel numerics and electromagnetic closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14733,"byte_start":9529,"id":"section:80b48520de3406e2d409","kind":"subsection","labels":["eq:carrier-cfe","eq:hard-topological-kernel","eq:phi-opening","fig:alpha-closure-flow"],"line_end":354,"line_start":241,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/004-subsection-character-trace-identities-and-the-abelian-in.tex","status_markers_as_written":[],"summary_excerpt":"On the retained hard branch the inherited topological corrections are Numerically, [formula in source] On the retained branch we write In version 3.1 the electromagnetic closure is evaluated with this retained second-order opening. Higher terms are outside the present theorem surface. The carrier form of the electromagnetic closure equation is then equation [formula in source] On the canonical family branch these har","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Carrier form of the electromagnetic closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2725,"byte_start":0,"id":"section:d86d2ec13c1df84c914c","kind":"subsection","labels":["eq:hard-kernel-values","eq:kernel-benchmark-formulas"],"line_end":41,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/005-subsection-kernel-output-package.tex","status_markers_as_written":[],"summary_excerpt":"The benchmark row for [formula in source] is defined by the positive self-consistent root of eq:carrier-cfe, not by freezing the opening at its retained seed value. On the canonical branch that positive root remains [formula in source] For the remaining one-seed relations we keep the retained branch opening The two symbols belong to the same retained branch but play different jobs. The electromagnetic [formula in sou","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kernel output package","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3236,"byte_start":2725,"id":"section:296ec45eeea1fa038184","kind":"section","labels":[],"line_end":45,"line_start":42,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/005-subsection-kernel-output-package.tex","status_markers_as_written":[],"summary_excerpt":"This section collects the algebraic compressions that turn the carrier packet and kernel numerics from a list of internally consistent outputs into an overdetermined structure with genuine exclusion power. The compression identities are not new theorems; they are exact algebraic consequences of the already established carrier data. The exclusion theorems are the sharpest available evidence that the carrier packet act","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Compression identities and carrier exclusion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7832,"byte_start":3236,"id":"section:6e18fb2f8a4df39e7520","kind":"subsection","labels":["cor:pythagorean-integrity-index","eq:rank-lock","lem:universal-5-4-compression","prop:rank-lock"],"line_end":209,"line_start":46,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/005-subsection-kernel-output-package.tex","status_markers_as_written":[],"summary_excerpt":"If the carrier identity [formula in source] , the canonical family data [formula in source] , and the optional occupancy compression [formula in source] are combined, then The unique integral solution is [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Rank lock and the [formula in source] - [formula in source] - [formula in source] 2-3-5 arithmetic","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11365,"byte_start":7832,"id":"section:5d8077c1fcd487c1bd16","kind":"subsection","labels":["cor:factorial-trace-delta2"],"line_end":348,"line_start":210,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/005-subsection-kernel-output-package.tex","status_markers_as_written":[],"summary_excerpt":"and [formula in source] ] Let [formula in source] be the two distinct carrier eigenvalues singled out by the factorized carrier polynomial. Then [formula in source] Here [formula in source] is the unweighted Vieta sum of the two distinct carrier eigenvalues, not the trace on [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Exact algebraic compressions on the minimal branch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3155,"byte_start":0,"id":"section:477315b4e10843c7b18e","kind":"subsection","labels":["def:integrity-index-41","eq:41-chain-main","fig:41-chain-strip"],"line_end":71,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/006-subsection-the-texorpdfstring-41-41-integrity-index.tex","status_markers_as_written":[],"summary_excerpt":"The integer [formula in source] is not an isolated numerical curiosity. On the retained branch it is best read as a weighted integrity index rather than as a topological Euler-type object. 41 integrity index] Let [formula in source] On the canonical branch, [formula in source] and [formula in source] , so [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The [formula in source] 41 integrity index","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5561,"byte_start":3155,"id":"section:c5adc221d3253e692e46","kind":"subsection","labels":["eq:cabibbo-inversion","eq:catalan-cabibbo","eq:lambda-c-master","eq:seed-budget-identity"],"line_end":129,"line_start":72,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/006-subsection-the-texorpdfstring-41-41-integrity-index.tex","status_markers_as_written":[],"summary_excerpt":"The bridge rows [formula in source] are not four independent hits but four projections of [formula in source] . The Cabibbo angle admits an explicit inversion back to the seed: Setting [formula in source] the inversion formula becomes [formula in source] Hence where [formula in source] are the Catalan numbers. In the present paper the safe interpretation of this identity is noncrossing combinatorics on the seed side;","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Single-seed compression and the Cabibbo inversion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10689,"byte_start":5561,"id":"section:d78768f921da5fbf4423","kind":"subsection","labels":["fig:carrier-exclusion-matrix","thm:carrier-exclusion"],"line_end":226,"line_start":130,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/006-subsection-the-texorpdfstring-41-41-integrity-index.tex","status_markers_as_written":[],"summary_excerpt":"The strongest argument that the carrier packet selects the physical world is not a further precision hit. It is that wrong discrete worlds fail brutally.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Carrier exclusion theorems","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11247,"byte_start":10689,"id":"section:864204c71f3c179f91e1","kind":"section","labels":[],"line_end":230,"line_start":227,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/006-subsection-the-texorpdfstring-41-41-integrity-index.tex","status_markers_as_written":[],"summary_excerpt":"This first closure-architecture block is the shortest route from the hard carrier packet to a broader Standard Model plus gravity compiler. It has three moves: the local patch-deficit count gives the carrier-side family count, the APS family theorem globalizes it into the family space [formula in source] , the bosonic relative index selects the unique light Higgs doublet, and the local spectral-scale channel generate","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Closure architecture A: families, Higgs, and local spectral scale","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18201,"byte_start":11247,"id":"section:caa94be03666373f199f","kind":"subsection","labels":["cor:boundary-bulk-occupancy","eq:family-patch-deficit","eq:orbifold-aps-family-master","fig:family-triangle","prop:family-holonomy-su3","thm:orbifold-aps-family-master"],"line_end":377,"line_start":231,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/006-subsection-the-texorpdfstring-41-41-integrity-index.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] denote the fundamental section of the seam complement. Define [formula in source] We use the distinguished cycle basis [formula in source] only as a concrete carrier-side basis of this family space, not as a replacement for its APS/Hodge realization. In this interpretation [formula in source] is neither an arbitrary flavor vector space nor a loose bookkeeping trick; it is a cycle space attache","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Family monodromy and occupancy","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1242,"byte_start":0,"id":"section:1255c69aefbb29dd94dc","kind":"subsection","labels":[],"line_end":13,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/007-subsection-occupancy-and-boundary-to-bulk-bridge.tex","status_markers_as_written":[],"summary_excerpt":"With the family bridge installed, the matter space becomes [formula in source] and the occupancy [formula in source] is already fixed by the imported family theorem and its bridge corollary. Here occupancy means the admissible chiral-state count after family lifting; it is not used as a primitive datum. The bridge point is not that family lifting creates a new numerical surcharge. Rather, the inherited hard kernel va","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Occupancy and boundary-to-bulk bridge","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2297,"byte_start":1242,"id":"section:42732488c09e2f86aebb","kind":"subsection","labels":[],"line_end":31,"line_start":14,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/007-subsection-occupancy-and-boundary-to-bulk-bridge.tex","status_markers_as_written":[],"summary_excerpt":"Once the carrier packet and family closure architecture are fixed, the focused main-text closure problem splits into a geometric program [formula in source] and a transport program [formula in source] . Record algebra and prediction semantics are now tied directly to the admissible gap in the main theorem stack, while E [formula in source] scale grammar and horizon extrapolations remain conditional layers.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"From bridge to geometric completion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6584,"byte_start":2297,"id":"section:7452f96c4ab09dfafebd","kind":"subsection","labels":["cor:constant-scale-reduction","def:local-spectral-scale","thm:relative-geometric-reconstruction"],"line_end":121,"line_start":32,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/007-subsection-occupancy-and-boundary-to-bulk-bridge.tex","status_markers_as_written":[],"summary_excerpt":"The geometric completion is formulated on a graded bundle [formula in source] with a declared reference pair [formula in source] and APS-type boundary conditions on the seam [formula in source] ; see Appendix [formula in source] Here [formula in source] is the geometric-branch reorganization of the primitive seed package [formula in source] introduced earlier in eq:tfpt-master. on the admissible branch] Assume the ad","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Relative APS and superconnection setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10538,"byte_start":6584,"id":"section:b9f473fc5382f86b9e50","kind":"subsection","labels":["thm:callias-higgs-selection","thm:determinant-class-higgs-selection"],"line_end":223,"line_start":122,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/007-subsection-occupancy-and-boundary-to-bulk-bridge.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] Assume the total seam twist on the oriented double cover is one unit. Then the determinant holonomy classes satisfy [formula in source] Equivalently, for the asymptotic bosonic mass fields on the retained branch, [formula in source] The doublet winding is forced by the spin lift on the double cover, whereas center neutrality on the admissible branch forces determinant triviality in the triplet","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bosonic relative index and Higgs selection","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16640,"byte_start":0,"id":"section:952a6ed0a13ca376c57e","kind":"subsection","labels":["eq:carrier-dressed-v","eq:chi-effective-action","eq:induced-einstein","eq:relative-a2","eq:relative-a4","eq:relative-bosonic-endomorphism","fig:chi-bifurcation","fig:chi-bifurcation-clean","lem:two-sheet-zero-mode-normalization","prop:canonical-bosonic-normalization","tab:heat-kernel-map","thm:gravity-cosmology-closure"],"line_end":418,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/008-subsection-heat-kernel-coefficient-map-and-local-spectra.tex","status_markers_as_written":[],"summary_excerpt":"The local target action is written as The relative bosonic endomorphism used below is and the coefficient bookkeeping expected from the relative spectral expansion is summarized in tab:heat-kernel-map.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Heat-kernel coefficient map and local spectral-scale bifurcation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":504,"byte_start":0,"id":"section:52ded6136a72da95df31","kind":"section","labels":[],"line_end":4,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/009-section-closure-architecture-b-yukawas-masses-flavor-con.tex","status_markers_as_written":[],"summary_excerpt":"The second closure-architecture block is the transport compiler. Its role is to turn the carrier packet and the family/occupancy closure into actual masses, mixings, hadronic admissibility, and strong-CP control. The logic is again staged: first the discrete phase operator and the transport kernel, then path-length masses and mixing data, then confinement and strong CP as transport-side admissibility statements.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Closure architecture B: Yukawas, masses, flavor, confinement, and strong CP","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4423,"byte_start":504,"id":"section:f18df8126ee3bfc3ba0f","kind":"subsection","labels":["fig:z6-circle"],"line_end":72,"line_start":5,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/009-section-closure-architecture-b-yukawas-masses-flavor-con.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] This makes the phase grammar concrete rather than rhetorical. The six admissible phases are shown as a finite hexagonal transport geometry in fig:z6-circle: the cusp values live on the same real axis as the positive-real phase, the admissible gap is visible directly, and the holonomy phase can be read as a triangle on the same discrete transport base.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Discrete phase operator and transport grammar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16506,"byte_start":4423,"id":"section:5c6c63a53f9b184de954","kind":"subsection","labels":["def:gap-stable-admissibility","eq:c6-cosine-polynomial","eq:ckm-holonomy-phase","eq:finite-hexagonal-resolvent","eq:finite-positive-transport-kernel","eq:gap-lift-full-operator","eq:mass-bridge","eq:mobius-quotient","eq:path-length-yukawa","eq:transport-bridge-offset","eq:transport-spectrum","eq:yukawa-holonomy-matrix","eq:yukawa-kernel","lem:finite-admissible-hexagon-gap","prop:finite-hexagonal-resolvent","prop:finite-positive-transport-algebra","prop:gap-lift-full-operator","prop:holonomy-triangle-phase","rem:transport-rank-echo"],"line_end":395,"line_start":73,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/009-section-closure-architecture-b-yukawas-masses-flavor-con.tex","status_markers_as_written":[],"summary_excerpt":"The transport pole [formula in source] is defined as the unique stationary point in the retained interval [formula in source] of the determinant transport functional [formula in source] Here [formula in source] Taking the regularization to [formula in source] and solving the exact stationarity condition on the retained branch gives","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Regularized Yukawa kernels and path-length masses","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8425,"byte_start":0,"id":"section:b5817e9da3a8ea128458","kind":"frontmatter","labels":["cons:minimal-family-connection","cor:transport-length-sum-rule","eq:minimal-word-lengths","prin:minimal-admissible-transport-packets","tab:transport-dictionary"],"line_end":203,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/010-subsection-ckm-and-pmns-sharpening.tex","status_markers_as_written":[],"summary_excerpt":"On the minimal admissible branch the word-length candidates are These are not free parameters; they are the corrected minimal admissible diagonal word-length packets on the [formula in source] graph that keep the residual factors of tab:yukawa-residuals in the bounded [formula in source] range. Once the hierarchy ordering is fixed, the admissible graph distance is determined up to full [formula in source] -step windi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10840,"byte_start":8425,"id":"section:33745c80ca078f7a420c","kind":"subsection","labels":["eq:ckm-magnitudes","eq:ckm-phase","eq:neutrino-masses"],"line_end":273,"line_start":204,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/010-subsection-ckm-and-pmns-sharpening.tex","status_markers_as_written":[],"summary_excerpt":"The leading CKM magnitudes on the transport branch are To second transport order, prop:holonomy-triangle-phase gives The benchmark row used later keeps the truncation at that order, [formula in source] so [formula in source] remains the base monodromy phase while [formula in source] is the leading family-transport area correction.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"CKM and PMNS sharpening","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12889,"byte_start":10840,"id":"section:5a55b33b36e50ef95999","kind":"subsection","labels":["fig:admissible-words"],"line_end":312,"line_start":274,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/010-subsection-ckm-and-pmns-sharpening.tex","status_markers_as_written":[],"summary_excerpt":"For each carrier word [formula in source] , let [formula in source] be its color-center charge and let [formula in source] be its seam parity. Physical hadronic words satisfy [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Confinement as admissible word selection","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16334,"byte_start":12889,"id":"section:f950d9a3b863c5a4646b","kind":"subsection","labels":["cor:strong-cp-rg-stability","def:sheet-cp-symmetry","eq:strong-cp","thm:sheet-cp-protection"],"line_end":378,"line_start":313,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/010-subsection-ckm-and-pmns-sharpening.tex","status_markers_as_written":[],"summary_excerpt":"Define Define the admissible sheet-CP operator by [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Transport-side ingredients for the strong-CP theorem","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15617,"byte_start":0,"id":"section:387a99c38504d64571c0","kind":"section","labels":["ass:remaining-closure-inputs","cor:factorized-admissibility-selector","def:admissibility-complex","def:relative-generating-functional","lem:admissibility-nilpotency","lem:admissible-reflection-positivity","lem:hodge-admissibility-projector","sec:closure-theorems","thm:admissible-vacuum-existence","thm:lorentzian-reconstruction","thm:reflection-positivity-admissible","thm:strong-cp-closure"],"line_end":388,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/011-section-closure-theorems-from-the-admissibility-complex.tex","status_markers_as_written":[],"summary_excerpt":"The preceding two sections introduced the carrier-compatible geometric and transport architecture. We now state the closure layer in the precise mode used throughout this manuscript: the theorems below are closed statements relative to the admissibility complex, the imported family master theorem, and the explicit APS / positivity / reflection-stability inputs collected first.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Closure theorems from the admissibility complex","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3380,"byte_start":0,"id":"section:359f85dfe4f5f725bf3e","kind":"frontmatter","labels":["def:observer-algebra-prediction","def:stable-record-algebra","thm:nonperturbative-admissible-qft"],"line_end":74,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/012-section-particle-and-mass-compiler.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] Assume the transport gap estimate of prop:gap-lift-full-operator together with the positivity bounds of thm:callias-higgs-selection. Then, after removing the exact gauge zero modes, the reconstructed admissible Hamiltonian satisfies [formula in source] Hence connected admissible Euclidean correlators obey exponential clustering: [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15193,"byte_start":3380,"id":"section:d7d8ee8a23b4765be497","kind":"section","labels":["def:intrinsic-observation-surfaces","fig:compiler-to-masses","fig:epistemic-output-matrix"],"line_end":359,"line_start":75,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/012-section-particle-and-mass-compiler.tex","status_markers_as_written":[],"summary_excerpt":"This section is the phenomenological heart of the manuscript. It is not meant to flatten all rows into one uniform notion of prediction. Instead it makes the compiler interface explicit: a declared RG map, a kernel-output map, and a mass ledger that separates genuinely derived quantities from solver-level candidates and anchor-dependent comparison rows. Accordingly this section is best read through three ledgers: a p","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Particle and mass compiler","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5514,"byte_start":0,"id":"section:350948a3667fbc66579c","kind":"subsection","labels":["sec:rg-map-compiler-outputs"],"line_end":112,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/013-subsection-rg-map-for-compiler-outputs.tex","status_markers_as_written":[],"summary_excerpt":"The symbol [formula in source] denotes the declared comparison map from TFPT outputs to scheme-specified observables. Here it is the bookkeeping package [formula in source] and we write [formula in source] with the following restricted interpretation in the main text: [formula in source] is compared in the Thomson-limit on-shell convention, with the CODATA 2022 / NIST value taken as the normative low-energy reference","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"RG map for compiler outputs","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9440,"byte_start":5514,"id":"section:8b0fe6c8af37a808326c","kind":"subsection","labels":["eq:relative-gauge-split","prop:local-gauge-closure-matching"],"line_end":215,"line_start":113,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/013-subsection-rg-map-for-compiler-outputs.tex","status_markers_as_written":[],"summary_excerpt":"We write [formula in source] for the seam matching scale read from the first positive seam boundary mode and the common gauge coupling at that scale. In the same notation, [formula in source] is the determinant-sector involution used in admissibility, [formula in source] is the transport generator on the family side, [formula in source] denotes the seam cycle data when needed, and [formula in source] is the spin holo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Local gauge closure and seam matching","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10858,"byte_start":9440,"id":"section:b2a49722fbd2e3fbdfe7","kind":"subsection","labels":["tab:kernel-output-map"],"line_end":237,"line_start":216,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/013-subsection-rg-map-for-compiler-outputs.tex","status_markers_as_written":[],"summary_excerpt":"The roles of [formula in source] and [formula in source] should not remain implicit. They are the central hard numeric quantities of the present main-text kernel. The downstream E [formula in source] parameter [formula in source] is isolated in the next section rather than folded back into the kernel center.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Central hard-kernel quantities","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14738,"byte_start":10858,"id":"section:5851dc3f4ef8418c302c","kind":"subsection","labels":["tab:sm-mass-ledger-ew","tab:sm-mass-ledger-quarks"],"line_end":290,"line_start":238,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/013-subsection-rg-map-for-compiler-outputs.tex","status_markers_as_written":[],"summary_excerpt":"For the mass surface itself the main text now uses only three row-level status words: derived, candidate, and anchor-dependent. The explicit candidate formulas, neutrino rows, and transport-ratio source data are moved to the appendix so that the main text shows a compact comparison-ready ledger rather than a mixed formula dump.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Mass-closure ledgers","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15175,"byte_start":14738,"id":"section:44a4c21b596380c27de9","kind":"section","labels":[],"line_end":297,"line_start":291,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/013-subsection-rg-map-for-compiler-outputs.tex","status_markers_as_written":[],"summary_excerpt":"E [formula in source] is not part of the primitive carrier ontology and should not compete with the seam data, the carrier theorem, or the closure stack for explanatory priority. In the present main-text form it plays one restricted role only: a downstream scale grammar attached to the already fixed carrier norm. [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"E [formula in source] E8 as downstream scale grammar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16699,"byte_start":15175,"id":"section:91219d896b87a8b45f7b","kind":"subsection","labels":["eq:e8-block-formula"],"line_end":318,"line_start":298,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/013-subsection-rg-map-for-compiler-outputs.tex","status_markers_as_written":[],"summary_excerpt":"A physical E [formula in source] representation is not the stage label [formula in source] alone, but the full block triple [formula in source] . The compressed block formula is where [formula in source] is the unreduced Planck mass (not [formula in source] ), [formula in source] is the ladder stage with [formula in source] , [formula in source] is a mild block-multiplicity label ( [formula in source] ), and [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Block formula and reading discipline","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18676,"byte_start":16699,"id":"section:41d0b47c0db1a821a95c","kind":"subsection","labels":[],"line_end":344,"line_start":319,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/013-subsection-rg-map-for-compiler-outputs.tex","status_markers_as_written":[],"summary_excerpt":"] Under the restricted trace grammar, stages [formula in source] and [formula in source] have no unambiguous physical target. If [formula in source] is allowed to scan over all simple rationals, these stages can mimic almost any scale between [formula in source] and [formula in source] GeV. They mark the exact boundary where E [formula in source] without a derived block-trace theorem becomes too permissive. The open ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Permissiveness barrier","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4151,"byte_start":0,"id":"section:27ed65835598bc44e479","kind":"section","labels":["tab:benchmark"],"line_end":58,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/014-section-primary-benchmark-map-and-prediction-ledger.tex","status_markers_as_written":[],"summary_excerpt":"The comparison values used in this section follow representative CODATA, PDG, NuFIT, Planck, and birefringence references codata2022,pdg2025,nufit2025,planck2018,minamiKomatsu2020,eskilt2023,sullivan2025. The snapshot policy is frozen at CODATA 2022 / NIST for [formula in source] , PDG 2025 for particle-mass and weak-mixing rows, NuFIT 2025 for neutrino-angle rows, and Planck 2018 for the baryon-fraction reconstructi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Primary benchmark map and prediction ledger","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9305,"byte_start":4151,"id":"section:29c3d8eae3fa494798a0","kind":"subsection","labels":["tab:operational-prediction-set"],"line_end":92,"line_start":59,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/014-section-primary-benchmark-map-and-prediction-ledger.tex","status_markers_as_written":[],"summary_excerpt":"The six-row benchmark table is not the whole experimental surface of the manuscript. tab:operational-prediction-set collects the rows that are operationally testable on near- to medium-term timescales, while keeping their status, next test, kill criterion, and dependency structure explicit. The point is not to flatten them into one truth class. Rather, the Status column keeps the manuscript's global truth-mode vocabu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Operational prediction set","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11338,"byte_start":9305,"id":"section:aeefc7afb4631af9d16d","kind":"subsection","labels":["tab:prediction-ledger"],"line_end":119,"line_start":93,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/014-section-primary-benchmark-map-and-prediction-ledger.tex","status_markers_as_written":[],"summary_excerpt":"The main benchmark table shows only a narrow comparison surface. To keep the compiler structure visible, tab:prediction-ledger summarizes which output packages belong to which layer of the paper.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Compact prediction ledger","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12646,"byte_start":11338,"id":"section:88d5f46d5372a2a592cb","kind":"subsection","labels":[],"line_end":123,"line_start":120,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/014-section-primary-benchmark-map-and-prediction-ledger.tex","status_markers_as_written":[],"summary_excerpt":"The present comparison surface is deliberately uneven, and that unevenness is informative rather than embarrassing. Carrier algebra and the self-consistent [formula in source] row are the sharpest parts of the manuscript. The seed-driven bridge rows are useful because they are transparent and mutually constrained, not because they are independent. In the mass sector, the manuscript should be read as a mixed surface: ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Realism audit of the present compiler surface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14670,"byte_start":12646,"id":"section:8715967a753fdda95ef1","kind":"subsection","labels":["fig:residual-plot"],"line_end":169,"line_start":124,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/014-section-primary-benchmark-map-and-prediction-ledger.tex","status_markers_as_written":[],"summary_excerpt":"The residuals for the restricted six-row table are shown in fig:residual-plot. The carrier-linked electromagnetic, birefringence, and baryon-density channels all remain within the displayed few-sigma window. The CKM phase is not plotted here because it is better treated, at present, in the operational prediction set and Appendix","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Residual map and principal comparison refinements","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16766,"byte_start":14670,"id":"section:58cfad0a94b05014928f","kind":"subsection","labels":["tab:falsification"],"line_end":196,"line_start":170,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/014-section-primary-benchmark-map-and-prediction-ledger.tex","status_markers_as_written":[],"summary_excerpt":"The present draft does not ask the reader to accept one undifferentiated compiler claim. Each main-text closure statement has a corresponding local or global failure mode, and those failure modes should be readable without first decoding the appendix tables.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Falsification matrix","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16815,"byte_start":16766,"id":"section:22ae61db89883f4a3ad5","kind":"section","labels":[],"line_end":198,"line_start":197,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/014-section-primary-benchmark-map-and-prediction-ledger.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Compiler theorem and benchmark bridge","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17624,"byte_start":16815,"id":"section:e574c445789ea812b1e6","kind":"subsection","labels":["eq:conditional-compiler-chain"],"line_end":219,"line_start":199,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/014-section-primary-benchmark-map-and-prediction-ledger.tex","status_markers_as_written":[],"summary_excerpt":"Collecting the present primitive layer, the hard carrier kernel, the closure theorems from the admissibility complex, and the benchmark bridge, the compiler line is This line is not meant as a slogan. 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The compression identities and exclus","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conclusion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":25684,"byte_start":24488,"id":"section:f5b7c77d5740c6e700e1","kind":"subsection","labels":[],"line_end":283,"line_start":273,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/014-section-primary-benchmark-map-and-prediction-ledger.tex","status_markers_as_written":[],"summary_excerpt":"The theorem stack proved here is narrower than a full theory-of-everything claim, and the manuscript should say so explicitly. 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The table below records their first-duty meaning and status class, now including the seam-matching notation introduced in Definition 9.1, so that the manuscript can be read without repeatedly reverse-engineering the bookkeeping.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Symbol guide","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14305,"byte_start":14090,"id":"section:614896384ca1a7bc0784","kind":"section","labels":["app:constants"],"line_end":273,"line_start":269,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/015-subsection-internal-closure-candidates-beyond-the-theore.tex","status_markers_as_written":[],"summary_excerpt":"This appendix collects material that is useful for internal compression but should not dominate the main-text scope of explicit claims.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Constants atlas and downstream scale grammar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19321,"byte_start":14305,"id":"section:43c43a5f9b812e42137f","kind":"subsection","labels":["fig:constant-cascade","tab:constants-atlas"],"line_end":357,"line_start":274,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/015-subsection-internal-closure-candidates-beyond-the-theore.tex","status_markers_as_written":[],"summary_excerpt":"The seam loop is assumed to carry one unit of spectral flow, [formula in source] Because the spin lift closes only after [formula in source] , the normalized rotation modulus is [formula in source] The cascade in fig:constant-cascade is kept here as technical bookkeeping rather than as an early main-text dependency graphic.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Global rotation angle and constants atlas","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1570,"byte_start":0,"id":"section:ba8b7d5369f0293e20ee","kind":"subsection","labels":[],"line_end":33,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/016-subsection-texorpdfstring-e-8-e8-as-downstream-scale-gra.tex","status_markers_as_written":[],"summary_excerpt":"In the present paper E [formula in source] is not used as a primitive cause. 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They are useful compression patterns, but their interpretation should remain conditional or conjectural.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Optional arithmetic continuations","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12431,"byte_start":10841,"id":"section:019834987ef886fa1880","kind":"subsection","labels":[],"line_end":325,"line_start":260,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/016-subsection-texorpdfstring-e-8-e8-as-downstream-scale-gra.tex","status_markers_as_written":[],"summary_excerpt":"The next package is stronger but also more conditional. It assumes that the carrier rank, family multiplicity, and seam normalization are all read as closed rather than only partially inherited.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conditional minimal-parameter picture","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13404,"byte_start":12431,"id":"section:c880a135a716502ed610","kind":"section","labels":["app:aps"],"line_end":338,"line_start":326,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/016-subsection-texorpdfstring-e-8-e8-as-downstream-scale-gra.tex","status_markers_as_written":[],"summary_excerpt":"The geometric completion uses APS-type relative data aps1975. In practice this means: one works with a declared pair [formula in source] rather than a single unanchored operator, boundary conditions on the seam [formula in source] are part of the definition of the relative index, the [formula in source] -term keeps track of the residual spectral asymmetry, the superconnection package is used in the same spirit as the","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Relative APS and superconnection setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13484,"byte_start":13404,"id":"section:7e8931a716ddb1ed2a6f","kind":"section","labels":["app:os-fermions"],"line_end":341,"line_start":339,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/016-subsection-texorpdfstring-e-8-e8-as-downstream-scale-gra.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Relative reflection positivity with fermions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13971,"byte_start":13484,"id":"section:d8f7df8480e38ff536ad","kind":"subsection","labels":[],"line_end":351,"line_start":342,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/016-subsection-texorpdfstring-e-8-e8-as-downstream-scale-gra.tex","status_markers_as_written":[],"summary_excerpt":"The relative Euclidean theory used in the main closure section is not interpreted as a difference of measures. Instead it is organized as the normalized quotient [formula in source] Because the denominator is source independent on the admissible sector, the reference theory acts only as a fixed normalizer and does not interfere with reflection positivity.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Normalized quotient form","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15001,"byte_start":13971,"id":"section:4c430390750b2f4bc074","kind":"subsection","labels":[],"line_end":369,"line_start":352,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/016-subsection-texorpdfstring-e-8-e8-as-downstream-scale-gra.tex","status_markers_as_written":[],"summary_excerpt":"The commutation relations [formula in source] ensure that reflection preserves the admissible subspace. The bosonic part then follows the standard Markov / reflection-stable Osterwalder–Schrader argument on admissible observables. For fermions, the admissible CAR kernel may be written as a reflected quadratic form; equivalently one may express the same condition as positivity of the associated Pfaffian structure on t","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bosonic and fermionic positivity on [formula in source] Padm","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1903,"byte_start":0,"id":"section:8e415d3107ebae026b73","kind":"section","labels":["app:yukawa"],"line_end":34,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/017-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"This appendix is the proof motor for the transport positivity, strong-CP protection, and bounded-residual statements used in the main text. The transport program is based on the regularized kernel [formula in source] Three remarks are important. The regulator [formula in source] is not optional: without it the kernel becomes ill-defined exactly where the admissibility question is most delicate. Positivity of the kern","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Yukawa kernels and positivity lemmas","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2327,"byte_start":1903,"id":"section:d6206fa4e8bae41f8d6a","kind":"section","labels":["app:info-readings"],"line_end":39,"line_start":35,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/017-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"This appendix collects interpretive notes that help organize the algebraic structure of the carrier-first compiler. When an exact algebraic statement appears below, it refers back to a main-text proposition; the appendix itself does not upgrade any status label beyond the declared hard / closure / benchmark / conditional discipline.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Information-theoretic and cut-and-project readings","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3497,"byte_start":2327,"id":"section:d74dc45180243dc49be1","kind":"subsection","labels":["tab:checksum-41"],"line_end":62,"line_start":40,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/017-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"The canonical [formula in source] -chain admits a compact integrity-table reading:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Integrity-index overdetermination of the canonical branch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4885,"byte_start":3497,"id":"section:d8104cc44f73e37a6875","kind":"subsection","labels":[],"line_end":94,"line_start":63,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/017-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"The bridge identities also admit a disciplined probabilistic reading. Since [formula in source] the Cabibbo scale is exactly the standard-deviation scale of a Bernoulli variable with success probability [formula in source] : [formula in source] Equivalently, the Fisher information of the Bernoulli family is [formula in source] so the Cabibbo bridge measures the inverse square-root Fisher scale of the retained seed. T","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Seed variance and surprisal readings","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7523,"byte_start":4885,"id":"section:b1f5bb8f8b18d9216f59","kind":"subsection","labels":[],"line_end":152,"line_start":95,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/017-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"The strongest information-theoretic statement is no longer a loose analogy. By prop:parity-code-family, the one-family packet is exactly the even-parity subspace on five occupation bits, [formula in source] so the carrier packet is kinematically the classical even-parity [formula in source] code. The split formula [formula in source] shows that the coarse parity bits of the [formula in source] -sector and [formula in","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Exact parity-code and information-compression reading","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8047,"byte_start":7523,"id":"section:e12b9f93b1e75872eef2","kind":"subsection","labels":[],"line_end":160,"line_start":153,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/017-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"The split [formula in source] also admits a possible cut-and-project interpretation, with a three-dimensional visible sector and a two-dimensional internal sector. Such a reading would become mathematically sharp only after an explicit rank- [formula in source] lattice or module, a projection rule, and a seam/window selection theorem are written down. Until then, the quasicrystal language is only a conditional geomet","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conditional cut-and-project reading","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8318,"byte_start":8047,"id":"section:040ad48dae48d7b0b977","kind":"section","labels":["app:record"],"line_end":165,"line_start":161,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/017-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"This appendix elaborates the main-text record and prediction constructions while keeping the more speculative horizon extrapolations outside the core theorem stack.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Appendix elaboration on record algebra, horizons, and prediction semantics","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9084,"byte_start":8318,"id":"section:c5bfead61abde864740d","kind":"subsection","labels":[],"line_end":175,"line_start":166,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/017-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"At finite volume or with a declared cutoff, an admissible vacuum candidate is written as [formula in source] with lower boundedness and coercivity understood exactly as in the main-text closure axioms. The stronger generative theorem path described in the conclusion would refine this object to the global admissible vacuum functional [formula in source] whose variations also select the transport branch. In this append","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Minimal admissible vacuum","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9505,"byte_start":9084,"id":"section:49b907aeeaf9b9e69a2d","kind":"subsection","labels":[],"line_end":189,"line_start":176,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/017-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"One useful coarse-grained record algebra is [formula in source] As [formula in source] decreases, more stable channels open. The intended arrow-of-time claim is therefore [formula in source] but only as a record-growth principle, not as a replacement for detailed nonequilibrium dynamics.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Record growth principle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10101,"byte_start":9505,"id":"section:9826edb1581b125d8287","kind":"subsection","labels":[],"line_end":205,"line_start":190,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/017-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"An observer is modeled as a stable pointer subalgebra [formula in source] With orthogonal projectors [formula in source] one writes the measurement channel [formula in source] In finite-dimensional sectors, positivity, additivity on orthogonal decompositions, and phase invariance lead to the standard Born-type assignment [formula in source] The claim is therefore only a constrained evaluation principle on admissible ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Observer algebra and Born-type evaluation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10498,"byte_start":10101,"id":"section:bf73337a034acbcc74a2","kind":"subsection","labels":[],"line_end":213,"line_start":206,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/017-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"If a horizon is modeled as an inner seam, the manuscript uses only an approximate factorization language, [formula in source] or, better, an algebraic split on an appropriate code subspace. This appendix intentionally avoids selling the factorization as exact fundamental structure.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Horizons as conjectural inner seams","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10858,"byte_start":10498,"id":"section:903ec48c89af15161371","kind":"subsection","labels":[],"line_end":227,"line_start":214,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/017-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"The main-text prediction map can be decorated by explicit experimental metadata as [formula in source] with [formula in source] This is kept only as an optional formal extension.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Prediction semantics","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11203,"byte_start":10858,"id":"section:6d389648ce9df07257d1","kind":"section","labels":["app:benchmarks"],"line_end":232,"line_start":228,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/017-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"This appendix turns the broader prediction surface into explicit experimental bookkeeping. The point is not to promote every row to main-text benchmark status, but to keep next test, kill criterion, and dependency structure visible wherever the theory already commits to a concrete target.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Extended benchmarks","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15074,"byte_start":11203,"id":"section:e7290dacc5098064c738","kind":"subsection","labels":["tab:extended-benchmarks"],"line_end":264,"line_start":233,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/017-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"The appendix matrix keeps the same truth-mode discipline as the main text, but its final column adds a short row-level qualifier whenever a conditional branch, interface, or cross-check needs to be made explicit.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Operational prediction matrix","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17220,"byte_start":15074,"id":"section:a2206248773a028a8ad3","kind":"subsection","labels":["tab:kill-tests"],"line_end":289,"line_start":265,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/017-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"round-mode=none, group-minimum-digits=20 ! @> p0.22 > p0.24 > p0.12 > p0.38 @ Test row & TFPT target or prohibition & Status reading & Failure mode \\\\ Second light Higgs doublet & no additional seam-even\\ doublet & kill\\ & robust discovery would\\ the bosonic-index route \\\\ Calibrated birefringence null & [formula in source] \\ the minimal branch & kill\\ & externally calibrated null\\ with zero at the\\ tolerance would r","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Target and kill-test rows","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18041,"byte_start":17220,"id":"section:4701e5b7c0e3eca252f2","kind":"subsection","labels":[],"line_end":313,"line_start":290,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/017-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"The downstream axion rows should be read as an experimental interface rather than as an extra hard theorem. 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The source rows collected here retain that information without forcing the main text to read like a mixed formula notebook.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Supplementary mass-source rows","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3181,"byte_start":0,"id":"section:e0d221356499ee43bb88","kind":"subsection","labels":["tab:extended-compiler-ledger","tab:yukawa-residuals"],"line_end":50,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/018-subsection-extended-compiler-ledger.tex","status_markers_as_written":[],"summary_excerpt":"round-mode=none, group-minimum-digits=20 @> p0.15 > p0.33 > p0.15 Y@ Row & TFPT source or target & TFPT value & Status note \\\\ [formula in source] & exact unbroken [formula in source] direction & [formula in source] & exact structural row \\\\ [formula in source] & exact color gauge direction before confinement & [formula in source] & exact structural row \\\\ [formula in source] & boundary electroweak anchor at [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Extended compiler ledger","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5821,"byte_start":3181,"id":"section:9afa3d31cc1e046fb670","kind":"subsection","labels":[],"line_end":104,"line_start":51,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-32"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-32/sections/018-subsection-extended-compiler-ledger.tex","status_markers_as_written":[],"summary_excerpt":"The paper uses standard tools from relative spectral geometry, APS index theory, transport/resolvent language, and conventional RG comparison. 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Conversel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Novelty boundary and literature positioning","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8285,"byte_start":0,"id":"section:7b31691c5975a5b854fe","kind":"frontmatter","labels":[],"line_end":231,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/preamble.tex","status_markers_as_written":["[C]","[L]"],"summary_excerpt":"1.04 skins,breakable arrows.meta,positioning,calc,fit,backgrounds,matrix,decorations.pathmorphing compat=1.18","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"tfptblue TFPT: Boundary Polarization, Carrier Rigidity, and Closed-Form Theorems\\ the Admissibility Datum\\\\[0.6em] tfptgray A boundary-polarized spectral theory\\ one-sided admissible data","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6343,"byte_start":0,"id":"section:8f58244db841b5498bc2","kind":"frontmatter","labels":[],"line_end":204,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/001-section-reading-guide-and-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"From the one-sided boundary datum [formula in source] the manuscript derives the Calder\\'on polarization [formula in source] , the boundary involution [formula in source] , the exact-double deck involution [formula in source] , and the doubled closed datum [formula in source] The hard core is now read through three decoders. 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The eight items below are therefore not a promise of later c","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Version 4.5 completion surface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10979,"byte_start":0,"id":"section:a1f74a23b50f03cd31c4","kind":"section","labels":["eq:compiler-chain","eq:tfpt-master","eq:tfpt-selectors","fig:status-ladder","fig:tfpt-headline-claims","rem:selector-versus-dynamics"],"line_end":235,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/002-section-big-picture-what-tfpt-actually-claims.tex","status_markers_as_written":[],"summary_excerpt":"TFPT is presented here as a boundary-polarized closed theory of admissible vacua on the oriented double cover. 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Moreover, [formula in source] On the minimal branch [formula in source] , this reduces to [formula in sou","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12868,"byte_start":1978,"id":"section:ba2ddb79add6eb5c715e","kind":"subsection","labels":["fig:family-occupancy-map","prop:parity-code-family","tab:one-family","thm:global-sm-theorem","thm:physical-gauge-group","thm:physical-gauge-group-faithful"],"line_end":393,"line_start":70,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/005-subsection-internal-carrier-stabilizer-and-one-family-pa.tex","status_markers_as_written":[],"summary_excerpt":"The determinant-preserving connected stabilizer of the minimal carrier split is [formula in source] The corresponding Lie algebra factorization [formula in source] is only the differential, local form of the same statement; throughout the manuscript this quotient is intended as the internal carrier-stabilizer form whenever a group symbol is written, and the local algebra notation is used only when explicitly stated.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Internal carrier stabilizer and one-family packet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7977,"byte_start":0,"id":"section:08bd70d43340123ff942","kind":"subsection","labels":["cor:family-degree-filters","cor:multiplicative-family-character","eq:abelian-index","eq:family-character","eq:family-x-polynomial","eq:multiplicative-family-character","eq:split-weight-enumerator","eq:x-mod-2","eq:x-mod-3","eq:x-mod-5","prop:family-hypercharge-compression","prop:split-weight-enumerator"],"line_end":244,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/006-subsection-character-trace-identities-and-the-abelian-in.tex","status_markers_as_written":[],"summary_excerpt":"For the present paragraph let [formula in source] Define also the split weight enumerator [formula in source] Then Moreover, Consequently, [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Character, trace identities, and the abelian index","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11568,"byte_start":7977,"id":"section:eb8f8f5590793a6d60f4","kind":"section","labels":["fig:primitive-start-sketch","thm:primitive-seam-generator"],"line_end":314,"line_start":245,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/006-subsection-character-trace-identities-and-the-abelian-in.tex","status_markers_as_written":[],"summary_excerpt":"The boundary-to-carrier presentation should not leave the impression that TFPT is hard only at the level of group theory and representation bookkeeping. The numerical kernel already fixes a nontrivial output layer. Here that layer is pulled forward and read as the first established output package of the carrier/output architecture rather than as a later list of disconnected constants.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kernel numerics and electromagnetic closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9065,"byte_start":0,"id":"section:1c84beaba7ae11480980","kind":"subsection","labels":["def:exact-seam-generating-function","eq:carrier-cfe","eq:phi-opening","fig:alpha-closure-flow","prop:carrier-susceptibility-exponent","prop:log-det-variation-u1","thm:alpha-canonical","thm:exact-electromagnetic-closure"],"line_end":264,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/007-subsection-carrier-form-of-the-electromagnetic-closure.tex","status_markers_as_written":[],"summary_excerpt":"At this stage the electromagnetic closure is kept in generic closed form. The hard carrier data fix [formula in source] while the later family and Higgs theorems will specialize the abelian index coefficient and the topological bridge coefficient.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Carrier form of the electromagnetic closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11852,"byte_start":9065,"id":"section:48cb9c0bae8df900b7ba","kind":"subsection","labels":["eq:hard-kernel-values","eq:kernel-benchmark-formulas"],"line_end":311,"line_start":265,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/007-subsection-carrier-form-of-the-electromagnetic-closure.tex","status_markers_as_written":[],"summary_excerpt":"The benchmark row for [formula in source] is defined by the positive self-consistent root of eq:carrier-cfe, not by freezing the opening at its retained seed value. On the canonical branch that positive root remains [formula in source] For the remaining one-seed relations we keep the retained branch opening The two symbols belong to the same admissible branch but play different jobs. The electromagnetic [formula in s","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kernel output package","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12533,"byte_start":11852,"id":"section:e08e291a9c441074c35d","kind":"section","labels":[],"line_end":320,"line_start":312,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/007-subsection-carrier-form-of-the-electromagnetic-closure.tex","status_markers_as_written":[],"summary_excerpt":"This section collects the algebraic compressions that turn the carrier packet and kernel numerics from a list of internally consistent outputs into an overdetermined structure. These compression identities are derived consistency statements on the retained branch: their formal derivation closes only once the bosonic-rank and branch-Yukawa carrier theorems have fixed the rigid [formula in source] split. By contrast, t","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Compression identities and numerical comparison of alternative discrete worlds","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5453,"byte_start":0,"id":"section:ba6ca9cf87cc0989cd75","kind":"subsection","labels":["cor:pythagorean-integrity-index","cor:rank-5-master-compression","eq:rank-lock","lem:universal-5-4-compression","prop:rank-lock"],"line_end":215,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/008-subsection-derived-texorpdfstring-48-4-cdot12-48-4-12-id.tex","status_markers_as_written":[],"summary_excerpt":"48=4·12 identity on the retained branch] On the retained branch, once the family multiplicity and carrier ranks have been fixed, one recovers [formula in source] with [formula in source] Equivalently, the former rank-lock formula is a derived consistency identity evaluated at the closed branch point:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derived [formula in source] 48=4·12 identity and the [formula in source] - [formula in source] - [formula in source] 2-3-5 arithmetic","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5494,"byte_start":0,"id":"section:99d7dc60f98b931b4193","kind":"subsection","labels":["cor:factorial-trace-delta2","cor:family-integrality-repair","prop:dual-root-generation"],"line_end":225,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/009-subsection-carrier-compressions-on-the-minimal-branch.tex","status_markers_as_written":[],"summary_excerpt":"and [formula in source] ] Let [formula in source] be the two distinct carrier eigenvalues singled out by the factorized carrier polynomial. Then [formula in source] Here [formula in source] is the unweighted Vieta sum of the two distinct carrier eigenvalues, not the trace on [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Carrier compressions on the minimal branch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5851,"byte_start":5494,"id":"section:b2d91f2e68e5222c3efc","kind":"subsection","labels":["eq:41-chain-main"],"line_end":237,"line_start":226,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/009-subsection-carrier-compressions-on-the-minimal-branch.tex","status_markers_as_written":[],"summary_excerpt":"The abelian coefficient is first carried only in the generic form The arithmetic specialization to [formula in source] is deferred until the family multiplicity and the Higgs sector have both been theorematically closed.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Generic abelian index identity","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6036,"byte_start":0,"id":"section:9ba2ad3652302f4aab83","kind":"subsection","labels":["cor:baryon-reactor-bridge-law","cor:ckm-pmns-bridge-law","cor:matter-radiation-quotient","cor:uv-half-circle","eq:cabibbo-inversion","eq:catalan-cabibbo","eq:lambda-c-master","eq:seed-budget-identity","prop:retained-seed-decoder"],"line_end":217,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/010-subsection-uv-seed-shadow-identities-and-the-cabibbo-inv.tex","status_markers_as_written":[],"summary_excerpt":"The retained scalar seed [formula in source] still satisfies exact UV identities. In the present version these identities are auxiliary kernel bookkeeping rather than the independence grammar of the physical observable layer. In particular, the Cabibbo angle admits an explicit inversion back to the UV seed: Setting [formula in source] the inversion formula becomes [formula in source] Hence where [formula in source] a","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"UV seed-shadow identities and the Cabibbo inversion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11206,"byte_start":6036,"id":"section:a068c24ae37acbec774d","kind":"subsection","labels":["fig:carrier-exclusion-matrix","thm:carrier-exclusion"],"line_end":326,"line_start":218,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/010-subsection-uv-seed-shadow-identities-and-the-cabibbo-inv.tex","status_markers_as_written":[],"summary_excerpt":"The strongest numerical pressure test on the carrier packet is not a further precision hit. It is that nearby wrong discrete worlds miss the electromagnetic closure decisively.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Carrier comparison of alternative discrete worlds","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11812,"byte_start":11206,"id":"section:84c5dfa00325cd0e3ed2","kind":"section","labels":[],"line_end":335,"line_start":327,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/010-subsection-uv-seed-shadow-identities-and-the-cabibbo-inv.tex","status_markers_as_written":[],"summary_excerpt":"This first closure-architecture block is the shortest route from the hard carrier packet to the closed theorem body. It has three moves: primitive winding balance in the seam normal plane forces the four-corner structure of the fundamental section, that winding theorem globalizes into the family space [formula in source] , the determinant line selects the unique light Higgs doublet together with the compact seam phas","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Closure architecture A: families, Higgs, and local spectral scale","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9277,"byte_start":0,"id":"section:f93d9c337f284ca103cb","kind":"subsection","labels":["cor:boundary-bulk-occupancy","cor:derived-occupancy-identity","fig:family-triangle","prop:family-holonomy-su3","prop:orbifold-aps-compatibility","thm:harmonic-family-modes","thm:topological-family-closure"],"line_end":238,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/011-subsection-family-monodromy-and-occupancy.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] denote the compact seam quotient with four [formula in source] corner points [formula in source] , and define the punctured family section [formula in source] Its rigid harmonic model is the Möbius class [formula in source] Set [formula in source] We use the distinguished cycle basis [formula in source] only as a concrete carrier-side basis of this family space; any later APS/Hodge realization","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Family monodromy and occupancy","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10535,"byte_start":9277,"id":"section:366b58c1c4566820af76","kind":"subsection","labels":[],"line_end":260,"line_start":239,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/011-subsection-family-monodromy-and-occupancy.tex","status_markers_as_written":[],"summary_excerpt":"With the family bridge installed, the matter space becomes [formula in source] and the occupancy [formula in source] is already fixed by the harmonic family-mode theorem and its bridge corollary. Here occupancy means the admissible chiral-state count after family lifting; it is not used as a primitive datum. The bridge point is not that family lifting creates a new numerical surcharge. Rather, the inherited hard kern","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Occupancy and boundary-to-bulk bridge","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11729,"byte_start":10535,"id":"section:d014659b600b203559c9","kind":"subsection","labels":[],"line_end":285,"line_start":261,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/011-subsection-family-monodromy-and-occupancy.tex","status_markers_as_written":[],"summary_excerpt":"Once the carrier packet and family closure architecture are fixed, the focused main-text closure problem splits into a geometric program [formula in source] and a transport program [formula in source] . Record algebra and prediction semantics are now tied directly to the admissible gap in the main theorem stack, while E [formula in source] scale grammar and horizon extrapolations are deferred to appendix-level contin","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"From bridge to geometric completion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16820,"byte_start":11729,"id":"section:f4b3e5c9e90e812c5a32","kind":"subsection","labels":["cor:constant-scale-reduction","def:canonical-residues","def:local-spectral-scale","thm:admissible-sector-on-reconstructed-geometry","thm:full-operator-reconstruction","thm:geometric-reconstruction-anchor","thm:geometric-reconstruction-from-Dgeo","thm:relative-geometric-reconstruction","thm:retained-branch-from-Padm"],"line_end":406,"line_start":286,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/011-subsection-family-monodromy-and-occupancy.tex","status_markers_as_written":[],"summary_excerpt":"The geometric completion is formulated on a graded bundle [formula in source] with the geometric Dirac anchor [formula in source] , the declared reference operator [formula in source] , and APS-type boundary conditions on the seam [formula in source] ; see Appendix [formula in source] Here [formula in source] is the geometric Dirac anchor, while [formula in source] is the relative comparison operator entering the spe","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Relative APS and superconnection setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6469,"byte_start":0,"id":"section:36807fbbfb0ac619ac70","kind":"subsection","labels":["cor:bosonic-rank-two","thm:callias-higgs-selection","thm:compact-determinant-higgs-index","thm:compact-higgs-unique","thm:determinant-class-higgs-selection","thm:determinant-clutching"],"line_end":227,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/012-subsection-bosonic-relative-index-and-higgs-selection.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] over the compactified oriented normal sphere [formula in source] . Then the primitive charge generator [formula in source] together with center neutrality and seam-evenness forces the clutching map [formula in source] for [formula in source] , while center neutrality forces [formula in source] for [formula in source] . Therefore [formula in source] This pair is the unique minimal nonnegative a","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bosonic relative index and Higgs selection","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7945,"byte_start":6469,"id":"section:a8170205e9cf2fc7925e","kind":"subsection","labels":["eq:41-chain-specialized","fig:41-chain-strip"],"line_end":265,"line_start":228,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/012-subsection-bosonic-relative-index-and-higgs-selection.tex","status_markers_as_written":[],"summary_excerpt":"Once the derived corner theorem and the Higgs uniqueness theorem are in place, the generic abelian-index identity eq:41-chain-main specializes to The extra [formula in source] is precisely the arithmetic contribution of the unique light seam-even Higgs doublet.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Closed [formula in source] 41 chain after family and Higgs closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14527,"byte_start":0,"id":"section:11f2fdbfe208c49fbee6","kind":"subsection","labels":["cor:hierarchy-compression-vgeo","def:branch-source-masses","def:physical-ew-scale","eq:carrier-dressed-v","eq:chi-effective-action","eq:induced-einstein","eq:relative-bosonic-endomorphism","fig:chi-bifurcation","lem:two-sheet-zero-mode-normalization","prop:canonical-bosonic-normalization","tab:heat-kernel-map","thm:canonical-einstein-residue","thm:ew-geometric-to-physical-matching"],"line_end":394,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/013-subsection-canonical-spectral-einstein-functional-and-ge.tex","status_markers_as_written":[],"summary_excerpt":"The local target action is written as the low-curvature expansion of a canonical spectral Einstein functional: The relative bosonic endomorphism used below is and the resulting low-curvature residue decomposition is summarized in tab:heat-kernel-map.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Canonical spectral Einstein functional and geometric Hodge closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":899,"byte_start":0,"id":"section:0846d1154a18e9dc69e7","kind":"frontmatter","labels":[],"line_end":30,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/014-subsection-native-charged-current-hard-matching-and-the-.tex","status_markers_as_written":[],"summary_excerpt":"Each ingredient of [formula in source] is a functional readout of [formula in source] . In particular, [formula in source] Thus [formula in source] is not introduced as a comparison factor after the fact; it is the native charged-current residue functional of the renormalized branch.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13405,"byte_start":899,"id":"section:8ad66868c75283cac0be","kind":"subsection","labels":["def:charged-ew2-seam-projector","eq:charged-ew2-seam-projector","eq:charged-seam-ew2-pullback","eq:tfpt-point-closed-deltar","fig:chi-bifurcation-clean","lem:charged-seam-projector-ew2","thm:charged-current-point-closure","thm:dirac-pole-matching","thm:pole-level-readout"],"line_end":385,"line_start":31,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/014-subsection-native-charged-current-hard-matching-and-the-.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the primitive seam normalization constant and let [formula in source] be the admissible transport pole of thm:algebraic-transport-pole. The charged two-loop electroweak seam projector is Equivalently, using the canonical occupancy bridge [formula in source] , [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Native charged-current hard matching and the charged seam projector","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4097,"byte_start":0,"id":"section:c7a0a8b6c4c64e8489b1","kind":"frontmatter","labels":["thm:gravity-cosmology-closure"],"line_end":144,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/015-subsection-absolute-spectral-planck-closure.tex","status_markers_as_written":[],"summary_excerpt":"The same geometric closure sector defines the canonical spectral gravity branch [formula in source] On admissible geometric fluctuations, let [formula in source] denote the geometric BRST/Hodge differential that quotients diffeomorphism and local-frame gauge directions, and set [formula in source] On the low-curvature local branch one recovers the effective action [formula in source] with [formula in source] Thus the","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11821,"byte_start":4097,"id":"section:e7ca24fbecc58ca35003","kind":"subsection","labels":["cor:computable-spectral-planck-root","cor:planck_normalization_stationary_branch","cor:schwarzschild_de_sitter_vacuum_branch","lem:strict-convexity-rho-planck","thm:absolute-spectral-planck-closure","thm:boundary-spectral-unit-rigidity","thm:stationary_geometric_scale_equation"],"line_end":393,"line_start":145,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/015-subsection-absolute-spectral-planck-closure.tex","status_markers_as_written":[],"summary_excerpt":"The stationary gravitational scale is no longer treated as a downstream completion block. It is read in boundary-normalized form directly on the main theorem surface.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Absolute spectral Planck closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9122,"byte_start":0,"id":"section:c29e22153c537e809ced","kind":"frontmatter","labels":["thm:constructive-geometric-measure","thm:geometric-uv-fixed-point","thm:sectorial-hamilton-decomposition","thm:spectral-uv-completion"],"line_end":237,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/016-section-closure-architecture-b-yukawas-masses-flavor-had.tex","status_markers_as_written":[],"summary_excerpt":"On the admissible Lorentzian reconstruction, the full Hamiltonian splits as [formula in source] The gap / clustering closure applies to the matter block and the massive scalaron block. The transverse-traceless graviton block is massless, but it is controlled by Osterwalder–Schrader reflection positivity together with the positive TT quadratic form of thm:gravity-cosmology-closure.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9706,"byte_start":9122,"id":"section:d23e161d38756738de10","kind":"section","labels":[],"line_end":245,"line_start":238,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/016-section-closure-architecture-b-yukawas-masses-flavor-had.tex","status_markers_as_written":[],"summary_excerpt":"The second closure-architecture block is the transport closure. Its role is to turn the carrier packet and the family/occupancy closure into actual masses, mixings, hadronic admissibility, and control of the strong-CP sector. The logic is again staged: first the discrete phase operator and the transport kernel, then residue and winding data, then matrix-factorized Yukawas, hadronic selection, determinant-line phase e","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Closure architecture B: Yukawas, masses, flavor, hadronic admissibility, and the strong-CP sector","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14751,"byte_start":9706,"id":"section:bfdaa4bee08ac0c43d5e","kind":"subsection","labels":["fig:holonomy-triangle","fig:z6-circle"],"line_end":332,"line_start":246,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/016-section-closure-architecture-b-yukawas-masses-flavor-had.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] This makes the phase grammar concrete rather than rhetorical. The six admissible phases are shown as a finite hexagonal transport geometry in fig:z6-circle: the cusp values live on the same real axis as the positive-real phase, the admissible gap is visible directly, and the holonomy phase can be read as a triangle on the same discrete transport base.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Discrete phase operator and transport grammar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10153,"byte_start":0,"id":"section:35e6f8e393c2de55dcf6","kind":"subsection","labels":["def:canonical-cycle-holonomy","def:structural-transport-kernel","eq:transport-bridge-offset","lem:regularized-transport-pole-stability","prop:closed-form-transport-pole","prop:generator-family-holonomy","thm:algebraic-transport-pole","thm:d4-monodromy-rigidity","thm:d4-riemann-hilbert-rigidity","thm:rigid-family-local-system","thm:transport-pole-algebraic"],"line_end":395,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/017-subsection-regularized-yukawa-kernels-and-path-length-ma.tex","status_markers_as_written":[],"summary_excerpt":"For each fermion sector define the structural positive transport kernel by [formula in source] whenever the inverse exists on [formula in source] . The final admissible kernel is the restriction of this operator to the gap-stable branch selected below. The transport pole [formula in source] is fixed by the structural stationarity of the exact determinant functional [formula in source] with [formula in source] On the ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Regularized Yukawa kernels and path-length masses","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12270,"byte_start":0,"id":"section:7bcf0cbfcdb0ec95b3da","kind":"frontmatter","labels":["cor:single-winding-transport","def:gap-stable-admissibility","eq:finite-hexagonal-resolvent","eq:gap-lift-full-operator","eq:mobius-quotient","eq:transport-spectrum","eq:yukawa-kernel","lem:finite-admissible-hexagon-gap","prop:finite-hexagonal-resolvent","prop:gap-lift-full-operator","thm:canonical-transport-kernel","thm:exact-transport-closure"],"line_end":371,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/018-source.tex","status_markers_as_written":[],"summary_excerpt":"By thm:topological-family-closure, the family section is the rigid four-punctured sphere [formula in source] and it carries the full [formula in source] symmetry inherited from the seam winding data. The determinant line is fixed to be trivial, and the local puncture conjugacy classes are fixed by the admissible cusp labels. Therefore thm:d4-monodromy-rigidity determines one monodromy representation [formula in sourc","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12176,"byte_start":0,"id":"section:8acbf6cfc2ae774d5880","kind":"frontmatter","labels":["cor:transport-length-sum-rule","cor:uniform-positive-c6-green","eq:c6-cosine-polynomial","eq:ckm-holonomy-phase","eq:finite-positive-transport-kernel","eq:mass-bridge","eq:minimal-word-lengths","eq:path-length-yukawa","eq:yukawa-holonomy-matrix","eq:yukawa-matrix-factorization","prin:minimal-admissible-transport-packets","prop:exact-family-holonomy-phase","prop:finite-positive-transport-algebra","prop:holonomy-triangle-phase","prop:strict-positive-c6-green","rem:transport-rank-echo"],"line_end":350,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/019-source.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] Then [formula in source] The cosine operator [formula in source] has spectrum [formula in source] and satisfies Consequently the regularized positive transport kernel reduces to the cubic polynomial","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7270,"byte_start":0,"id":"section:aa2a4e5518b218924f6b","kind":"frontmatter","labels":["cor:carrier-asymmetry-leptons","cor:charged-lepton-seed-decoder","cor:quark-source-ratios","prop:transport-matrix-normal-form","tab:transport-dictionary","thm:charged-lepton-compression"],"line_end":271,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/020-subsection-ckm-and-pmns-closure.tex","status_markers_as_written":[],"summary_excerpt":"Collect the closed-branch diagonal lengths into the generation matrix [formula in source] with rows [formula in source] and columns [formula in source] . Then [formula in source] with [formula in source] Moreover, [formula in source] The generation-column sums are [formula in source] so [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10878,"byte_start":7270,"id":"section:b19f26bb5efa29236070","kind":"subsection","labels":["cor:cubic-vub-law","eq:ckm-magnitudes","eq:ckm-phase","prop:ckm-phase-asymptotic","thm:ckm-closure","thm:neutrino-closure"],"line_end":374,"line_start":272,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/020-subsection-ckm-and-pmns-closure.tex","status_markers_as_written":[],"summary_excerpt":"On the canonical admissible branch the quark mixing matrix [formula in source] is a branch invariant fixed by the hard holonomy form of thm:exact-transport-closure. Its leading transport magnitudes are Its exact CP phase is [formula in source] on the canonical branch.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"CKM and PMNS closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2362,"byte_start":0,"id":"section:de9df9321a6cdbe8923c","kind":"subsection","labels":["fig:admissible-words"],"line_end":44,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/021-subsection-hadronic-admissibility-as-singlet-selection.tex","status_markers_as_written":[],"summary_excerpt":"For each carrier word [formula in source] , let [formula in source] be its color-center charge and let [formula in source] be its seam parity. Physical hadronic words satisfy [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Hadronic admissibility as singlet selection","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8256,"byte_start":2362,"id":"section:bc26f09ff13cd1480915","kind":"subsection","labels":["cor:strong-cp-rg-stability","def:sheet-cp-symmetry","eq:strong-cp","lem:retained-gamma5-hermiticity","thm:sheet-cp-protection","thm:structural-strong-cp"],"line_end":201,"line_start":45,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/021-subsection-hadronic-admissibility-as-singlet-selection.tex","status_markers_as_written":[],"summary_excerpt":"Define Define the admissible sheet-CP operator by [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Transport-side ingredients for the strong-CP sector","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16180,"byte_start":0,"id":"section:84843d6bca191a75f2d7","kind":"section","labels":["ass:remaining-closure-inputs","cor:factorized-admissibility-selector","def:full-admissibility-complex","def:relative-generating-functional","fig:admissibility-stack","lem:admissible-reflection-positivity","prop:master-closure-roadmap","sec:closure-theorems","thm:apsdom-upgrade","thm:master-closure","thm:padm-upgrade"],"line_end":397,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/022-section-closure-theorems-from-the-admissibility-complex.tex","status_markers_as_written":[],"summary_excerpt":"The preceding two sections introduced the carrier-compatible geometric and transport architecture. The primitive admissibility projector [formula in source] was already placed in the primitive section so that the proof direction runs from the boundary datum through the derived closed datum to [formula in source] , and only then to the later sector theorems. What remains in this section is therefore (i) the upgrade of","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Closure theorems from the admissibility complex","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12372,"byte_start":0,"id":"section:b888ccd1fb28a680fc41","kind":"frontmatter","labels":["cor:yukawa-discharges-kpp","def:primitive-yukawa-generator","fig:carrier-closure-cut","lem:lowest-primitive-yukawa-generator","lem:nontrivial-topological-support","lem:topological-sector-positivity","lem:unique-cubic-weak-invariant","thm:strong-cp-closure","thm:strong-cp-closure-positive","thm:yukawa-forces-32"],"line_end":370,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/023-source.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the graded algebra of carrier-invariant Yukawa trilinears. A homogeneous nonzero invariant is called primitive if it is indecomposable, equivalently if it does not lie in the ideal generated by positive-degree invariants of strictly lower carrier degree.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17315,"byte_start":0,"id":"section:b17e53e1ba3c05273208","kind":"frontmatter","labels":["fig:gap-hardening-chain","lem:boundary-decoupling-admissible","lem:diagonal-weights-separate-basis","lem:parent-gap-from-transfer-block","thm:admissible-vacuum-existence","thm:admissible-vacuum-finite-volume","thm:cp-even-vacuum-uniqueness","thm:lorentzian-reconstruction","thm:reflection-positivity-admissible","thm:thermodynamic-limit","thm:uniform-parent-gap-injective"],"line_end":381,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/024-source.tex","status_markers_as_written":["[A]"],"summary_excerpt":"thm:sheet-cp-protection gives [formula in source] By lem:topological-sector-positivity, the admissible partition function admits a sector decomposition [formula in source] The antiunitary sheet symmetry of thm:sheet-cp-protection gives [formula in source] so the sector weights satisfy [formula in source] . Hence [formula in source] By lem:nontrivial-topological-support, one has [formula in source] . Therefore for eve","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5133,"byte_start":0,"id":"section:1a572b4f6da34adb8a73","kind":"frontmatter","labels":["lem:norm-stable-gap-parent-path","rem:vacuum-honest-status","thm:eta-zero-parent-domination","thm:gap-stability-thermo-limit","thm:nonperturbative-admissible-qft"],"line_end":122,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/025-subsection-admissible-schwinger-functions-minkowski-loca.tex","status_markers_as_written":[],"summary_excerpt":"eta=0] Fix finite volume [formula in source] and let [formula in source] be the primitive blocked admissible transfer operator with Perron vector [formula in source] . Let [formula in source] be the blocked admissible parent Hamiltonian of lem:parent-gap-from-transfer-block, with [formula in source] Let the physical admissible Hamiltonian be written as [formula in source] where each added term is positive semidefinit","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17333,"byte_start":5133,"id":"section:9ed5721442babfbf52cf","kind":"subsection","labels":["cor:master-closure-corollary","def:admissible-schwinger-functions","def:laboratory-scattering-sector","def:stable-record-algebra","fig:selector-versus-dynamics","rem:ir-dressed-massless-sectors","rem:resonant-states-admissible","thm:admissible-local-minkowski-net","thm:dressed-massless-interface","thm:full-admissible-os-closure","thm:lsz-stable-massive","thm:stable-massive-scattering"],"line_end":401,"line_start":123,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/025-subsection-admissible-schwinger-functions-minkowski-loca.tex","status_markers_as_written":["[A]"],"summary_excerpt":"Let [formula in source] denote a low-curvature branch region on which [formula in source] and [formula in source] All scattering statements below are formulated on [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Admissible Schwinger functions, Minkowski locality, and scattering closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":951,"byte_start":0,"id":"section:5f992a3216988ebd9b64","kind":"section","labels":["sec:rg-map-compiler-outputs"],"line_end":13,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/026-section-intrinsic-closed-branch-and-canonical-rigid-obje.tex","status_markers_as_written":[],"summary_excerpt":"The closed branch is not selected by a comparison functional. At the top of the main-text theorem stack now stands a thinner operational seed layer: quasilocal Euclidean dynamics, reflection positivity, finite relative action, a nontrivial seam class, and one elliptic collar generator. That seed induces the one-sided admissible boundary datum. Once the induced datum is fixed, the remaining closure problem splits into","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Intrinsic closed branch and canonical rigid object","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4175,"byte_start":951,"id":"section:a06af9918677fc215e09","kind":"subsection","labels":["ax:physical-operationality","cor:minimal-operational-seed","def:operational-seed-category","def:operational-seed-complexity","sec:operational-seed-generation","thm:operational-collar-completion"],"line_end":91,"line_start":14,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/026-section-intrinsic-closed-branch-and-canonical-rigid-obje.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] denote the category whose objects are tuples [formula in source] satisfying: [formula in source] is a quasilocal Euclidean observable net with positive-time reflection [formula in source] ; [formula in source] is reflection positive and clustering on the admissible local algebra, with finite relative action with respect to the declared reference sector; [formula in source] is a nontrivial seam","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Operational seed and boundary generation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10334,"byte_start":4175,"id":"section:c8c3e743c447d7fd1f59","kind":"subsection","labels":["def:admissible-spectral-bordism-category","def:lexicographic-admissible-complexity","def:tfpt-core-class","thm:initial-admissible-bordism"],"line_end":229,"line_start":92,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/026-section-intrinsic-closed-branch-and-canonical-rigid-obje.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] denote the category whose objects are tuples [formula in source] such that: [formula in source] is an elliptic Dirac-type operator on a one-sided collar with reflection-regular boundary behavior; the retained Euclidean sector is reflection positive; the relative action with respect to the declared reference sector is finite; the seam class is nontrivial, equivalently [formula in source] . Morp","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Initial admissible bordisms and induced boundary data","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11555,"byte_start":0,"id":"section:1f96b3c508aeec1fdf9a","kind":"subsection","labels":["cor:derived-post-carrier-kernel","def:boundary-primitive-kernel","def:core-closure-functional","def:intrinsic-closure-map","def:post-carrier-primitive-kernel","def:projected-modular-free-energy","def:sector-solution-sets","thm:continuous-closure-from-master-functional","thm:discrete-sector-from-primitive-kernel","thm:joint-discrete-admissible-sector"],"line_end":381,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/027-subsection-primitive-completion-from-the-boundary-kernel.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the boundary primitive kernel attached to an admissible one-sided boundary datum. Here [formula in source] are fixed by the primitive seam generator theorem. No carrier split, no hypercharge operator, no family geometry, no determinant class, no transport pole, no effective strong angle, and no vacuum datum are part of this definition.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Primitive completion from the boundary kernel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9231,"byte_start":0,"id":"section:69c1f3cce88bf37d1cba","kind":"frontmatter","labels":["cor:canonical-rigid-object-unique-branch","cor:no-alternatives-tfpt","def:tfpt-rigid-category","def:tfpt-rigid-pre-category","thm:branch-uniqueness","thm:canonical-rigid-reconstruction-essential-injective","thm:internal-analytic-closure","thm:internal-analytic-closure-hard","thm:intrinsic-closed-branch","thm:no-alternatives-tfpt","thm:observation-closure","thm:rigid-reconstruction-core","thm:singleton-fiber-product-branch","thm:spectral-completeness-rigid-tfpt"],"line_end":230,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/028-source.tex","status_markers_as_written":[],"summary_excerpt":"For every admissible boundary primitive kernel [formula in source] , the intrinsic closed branch is the singleton fiber product [formula in source] and therefore [formula in source] No Jacobian on mixed discrete and continuous variables is needed.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13547,"byte_start":0,"id":"section:37d20452b796e47ac2a2","kind":"section","labels":["cor:ir-seam-transfer-bounds","fig:cosmology-output-flow","lem:automatic-seam-transfer-convergence","prop:seam-action-cosmology","sec:cosmology-closure","thm:axion-seam-phase","thm:boundary-winding-control","thm:cosmology-closure","thm:frw-cosmology-derivation","thm:leptogenesis-closure"],"line_end":385,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/029-section-frw-reduction-seam-transfer-and-the-scalaron-bra.tex","status_markers_as_written":["[A]"],"summary_excerpt":"The trace-class seam transfer belongs to the main reconstruction surface. The cosmological constant and the reduced scalaron / determinant-line dynamics are therefore fixed directly on the closed branch. Axion, reheating, and leptogenesis quantities are read through explicit interface formulas built from the same theorem-level objects [formula in source] , [formula in source] , and the positive scalaron sector [formu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"FRW reduction, seam transfer, and the scalaron branch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3662,"byte_start":0,"id":"section:6e322457dcbc73dce9bf","kind":"subsection","labels":["tab:falsification"],"line_end":61,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/030-subsection-falsification-matrix.tex","status_markers_as_written":[],"summary_excerpt":"The present draft does not ask the reader to accept one undifferentiated output claim. Each main-text closure statement has a corresponding local or global failure mode, and those failure modes should be readable without first decoding the appendix tables.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Falsification matrix","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12510,"byte_start":3662,"id":"section:aece9c239123e301af67","kind":"subsection","labels":["tab:proof-obligation-ledger"],"line_end":128,"line_start":62,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":["relation:3d134d8b0a044326c0df","relation:4e3e629248a5e402e384","relation:779e256810980526ce8e"],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/030-subsection-falsification-matrix.tex","status_markers_as_written":[],"summary_excerpt":"To keep proof status, interface assumptions, and comparison-only layers visibly separated, we record the present audit path explicitly. We use five status classes: ] full proof in manuscript; ] full proof modulo an explicit standard theorem; ] proof sketch in main text with full proof deferred; ] readout or comparison only; ] programmatic closure target with a fixed mathematical statement but without a claimed proof ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Proof-obligation ledger","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13466,"byte_start":12510,"id":"section:4e6820f6519ea6e01376","kind":"section","labels":["sec:downstream_closure_modules"],"line_end":149,"line_start":129,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/030-subsection-falsification-matrix.tex","status_markers_as_written":["[P]"],"summary_excerpt":"The present section records the downstream closure modules that start from the already fixed branch object [formula in source] Nothing in this section changes the upstream theorem chain. The exact proof status of these downstream closures is recorded in the proof-obligation ledger, and each statement below is phrased only as far as it factors through already fixed branch data. The stationary geometric scale, boundary","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Downstream closure modules from the closed branch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15639,"byte_start":13466,"id":"section:5752b502d049d3f4df75","kind":"subsection","labels":["cor:hawking_temperature_stationary_branch","prop:kerr_compact_object_corrections","prop:wald_entropy_scalaron_branch","thm:modular_horizon_thermality","thm:tensor_scalaron_wave_channel_closure"],"line_end":212,"line_start":150,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/030-subsection-falsification-matrix.tex","status_markers_as_written":["[P]"],"summary_excerpt":"Assume the split property and stationarity of the exterior wedge algebra on the vacuum branch. Then for the outside algebra one has [formula in source] where [formula in source] is the horizon modular generator. Hence the reduced outside state is KMS and the horizon temperature is [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[P] Stationary horizons, modular thermality, and compact objects","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19200,"byte_start":0,"id":"section:35125602f375466da992","kind":"subsection","labels":["lem:decorrelation-weil-bound","rem:ergodic-vs-scalar","rem:finite-field-seam-mixer","rem:multiplicity-audit","rem:o20a-operator-level","rem:stage2-open-obligations","rem:stage2-traffic-light","thm:cmb_seam_phase_realization","thm:cmb_transfer_closure_closed_branch","thm:primordial_mode_closure_seam_state","thm:reheating_fixed_efolds"],"line_end":380,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/031-subsection-p-primordial-perturbation-closure-and-cmb-tra.tex","status_markers_as_written":["[P]"],"summary_excerpt":"The number of e folds on the closed branch is fixed by [formula in source] where the closed-branch reheating density [formula in source] is determined by the branch reheating scale [formula in source] , and the constant [formula in source] absorbs the standard pivot conversion [formula in source] at [formula in source] . The combined [formula in source] kernel [formula in source] is the standard Liddle–Leach form Lid","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[P] Primordial perturbation closure and CMB transfer","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13720,"byte_start":0,"id":"section:d9d0069a504ad95c6183","kind":"frontmatter","labels":["conj:canonical-trace-word","conj:polarisation-cross-check","conj:seam-record-state","cor:late_time_hubble_readout","cor:matter_power_spectrum_readout","def:closed-branch-density-readouts","rem:five-layer-roadmap","rem:good-vs-this-cmb-world","rem:smica-v2-result","thm:flavored_boltzmann_closure_baryogenesis"],"line_end":303,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":["relation:29df4c74d4c9b69d7bf1","relation:7e9b16f6477f6681ad2a","relation:eb4ad3ea1fd43634125a"],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/032-subsection-p-late-time-dark-sector-and-structure-growth.tex","status_markers_as_written":[],"summary_excerpt":"At the present level of the construction, the ergodic seam lift is statistically indistinguishable from a Gaussian realization at the closed-branch [formula in source] : the cross-correlation [formula in source] between the closed-branch realization and an independent Gaussian draw at the same [formula in source] is consistent with zero in every multipole band, within the [formula in source] envelope expected from tw","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14774,"byte_start":13720,"id":"section:b1685635efc8572b05c1","kind":"subsection","labels":["cor:no_fuzzy_halo_regime","thm:axion_schrodinger_poisson_closure","thm:relative_admissible_vacuum_energy_finiteness"],"line_end":333,"line_start":304,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/032-subsection-p-late-time-dark-sector-and-structure-growth.tex","status_markers_as_written":["[P]"],"summary_excerpt":"The late-time axion sector is governed by [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[P] Late time dark sector and structure growth","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4090,"byte_start":0,"id":"section:bb1856117fea93947068","kind":"subsection","labels":["def:scheme-fixed-yukawa-kernel","thm:closed_pole_mass_completion","thm:hadron_pole_masses_singlet_spectrum","thm:higgs_pole_readout_rg_branch"],"line_end":82,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/033-subsection-p-pole-masses-higgs-readout-and-full-flavor-o.tex","status_markers_as_written":["[P]"],"summary_excerpt":"Let [formula in source] and let [formula in source] denote the renormalized admissible flow. For every mass-independent renormalization scheme [formula in source] and every renormalization scale [formula in source] , the closed-branch quark mass readout is the scheme-and-scale-fixed map [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[P] Pole masses, Higgs readout, and full flavor output","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4604,"byte_start":4090,"id":"section:d093d02243ed49c9da96","kind":"subsection","labels":["prop:global_admissible_code_subspace"],"line_end":96,"line_start":83,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/033-subsection-p-pole-masses-higgs-readout-and-full-flavor-o.tex","status_markers_as_written":["[P]"],"summary_excerpt":"The physical sector is the global admissible code subspace [formula in source] and supports stable record algebras and pointer reductions of the form [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[P] Admissible code subspace, entanglement, and pointer dynamics","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5368,"byte_start":4604,"id":"section:91e23bd74c9c9e386383","kind":"subsection","labels":["conj:topological_phase_slip_burst_channel"],"line_end":118,"line_start":97,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/033-subsection-p-pole-masses-higgs-readout-and-full-flavor-o.tex","status_markers_as_written":["[P]"],"summary_excerpt":"Local determinant phase slips of the compact mode [formula in source] can source transient radio bursts with characteristic energy scale [formula in source] and photon conversion power [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[P] Topological transient channels and astrophysical bursts","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5430,"byte_start":5368,"id":"section:0ec57280249ff4d51792","kind":"section","labels":[],"line_end":120,"line_start":119,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/033-subsection-p-pole-masses-higgs-readout-and-full-flavor-o.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Canonical rigid object and falsification interface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8289,"byte_start":5430,"id":"section:46b3a399052d92fecfdc","kind":"subsection","labels":["eq:closed-output-chain"],"line_end":202,"line_start":121,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/033-subsection-p-pole-masses-higgs-readout-and-full-flavor-o.tex","status_markers_as_written":[],"summary_excerpt":"Collecting the operational-seed generation theorem, the minimal-packaging theorem for the induced boundary class, the boundary datum, the boundary primitive kernel, the joint discrete admissibility theorem, the derived selector, and the continuous closure theorems of sec:closure-theorems, the main-text reconstruction now takes the rigid two-stage form Here [formula in source] is the canonical rigid object of thm:no-a","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Canonical rigid object","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9779,"byte_start":8289,"id":"section:b31a10ff01cf118b3bfa","kind":"subsection","labels":["cor:canonical-rigid-object"],"line_end":229,"line_start":203,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/033-subsection-p-pole-masses-higgs-readout-and-full-flavor-o.tex","status_markers_as_written":[],"summary_excerpt":"By thm:intrinsic-closed-branch,thm:canonical-rigid-reconstruction-essential-injective,thm:spectral-completeness-rigid-tfpt, there exists a canonical rigid object [formula in source] in [formula in source] such that [formula in source] and every rigid closed admissible realization is uniquely unitarily equivalent to [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Canonical rigid-object corollary","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13810,"byte_start":9779,"id":"section:e9771601a33e45b03c38","kind":"subsection","labels":["sec:structural-falsification-map","tab:proof-obligations"],"line_end":271,"line_start":230,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/033-subsection-p-pole-masses-higgs-readout-and-full-flavor-o.tex","status_markers_as_written":[],"summary_excerpt":"The main text closes the theorem chain at [formula in source] and then attaches one structural side card, the falsification map [formula in source] This map reports which local or global structural failure mode would break each arrow of the reconstruction. It is hard-separated from the appendix-level empirical comparison map [formula in source] , which acts only after [formula in source] has been fixed and is collect","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Structural falsification map","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14418,"byte_start":13810,"id":"section:45030528c6d88ae5f6de","kind":"section","labels":["sec:universality-operational"],"line_end":281,"line_start":272,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/033-subsection-p-pole-masses-higgs-readout-and-full-flavor-o.tex","status_markers_as_written":[],"summary_excerpt":"Above the closed theorem stack ending at [formula in source] , the present version records one theorem-level input reduction and a stratified output-side observable chain. On the input side, the reduction is internal to a deliberately weakened ambient class. On the output side, the passage from [formula in source] to the renormalized low-energy package [formula in source] and then to the physical observable layer [fo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Internal reduction theorem and renormalized observable hierarchy","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15837,"byte_start":0,"id":"section:c948fca30a92ee00d8d0","kind":"subsection","labels":["def:physadm","def:rigid-closure-functor","def:universal-reduction","fig:internal-reduction-orbit","prop:universal-carrier-reduction","prop:universal-family-reduction","prop:universal-glueing","prop:universal-transport-reduction","thm:universality-tfpt"],"line_end":389,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/034-subsection-weakened-ambient-class.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] denote the category whose objects are tuples [formula in source] satisfying the following ambient admissibility axioms: Real even boundary datum: [formula in source] is an admissible real even one-sided boundary datum with reflection-regular collar. Quasilocal positive dynamics: [formula in source] is a quasilocal dynamics with reflection positivity and an admissible vacuum sector. Morphisms a","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Weakened ambient class","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13635,"byte_start":0,"id":"section:90a3ec631ca02894df43","kind":"subsection","labels":["cor:em-ir-boundary-condition","cor:one-loop-shadow-exact-flow","def:admissible-effective-average-action","def:canonical-measurement-orbit","def:minimal-observable-basis","def:obs-category","def:physical-observable-category","def:renormalized-low-energy-package","def:scheme-groupoid","thm:admissible-1pi-graph-expansion","thm:exact-admissible-rg-flow","thm:operational-completeness"],"line_end":372,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/035-subsection-renormalized-physical-and-scheme-readout-laye.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be an admissible infrared regulator commuting with the structural sector selection. Define [formula in source] and set [formula in source] The renormalized admissible effective action is [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Renormalized, physical, and scheme readout layers","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5573,"byte_start":0,"id":"section:4a44bb4eb3bf37932f99","kind":"frontmatter","labels":["cor:cosmology-axion-target","cor:no-double-counting","cor:response-birefringence-target","fig:admissible-rg-flow"],"line_end":137,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/036-section-absolute-dimensionless-metrology-from-the-bounda.tex","status_markers_as_written":[],"summary_excerpt":"0.96 ! (hadm) at (-5.0,0.9) [formula in source] \\ sector; (wk) at (-1.6,0.9) [formula in source] \\ generator; (gk) at (1.8,0.9) [formula in source] \\ admissible flow; (gren) at (5.2,0.9) [formula in source] \\ 1PI action;","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6434,"byte_start":5573,"id":"section:f9b9a00330cfb491fd8c","kind":"section","labels":["sec:absolute-dimensionless-metrology"],"line_end":166,"line_start":138,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/036-section-absolute-dimensionless-metrology-from-the-bounda.tex","status_markers_as_written":[],"summary_excerpt":"The closed branch should not be read as a source of isolated SI numbers. Its hard content is an internal dimensionless metrology: the boundary datum carries its own spectral unit, the stationary geometric branch fixes the gravitational normalization relative to that unit, the renormalized 1PI action fixes physical electroweak and pole readouts, and only afterwards does one choose an external comparison scheme. In the","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Absolute dimensionless metrology from the boundary branch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6827,"byte_start":6434,"id":"section:a2467601ac733c0c2dfd","kind":"subsection","labels":["def:boundary-spectral-unit"],"line_end":178,"line_start":167,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/036-section-absolute-dimensionless-metrology-from-the-bounda.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the intrinsic boundary mass unit fixed by thm:boundary-spectral-unit-rigidity. For a physical quantity [formula in source] of mass dimension [formula in source] , define its boundary-normalized readout by [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Boundary spectral unit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8701,"byte_start":6827,"id":"section:a62625046c2faf99cfe4","kind":"subsection","labels":["cor:dimensionless-geometric-hierarchy","cor:dimensionless-planck-metrology","thm:unique-stationary-spectral-planck-root"],"line_end":251,"line_start":179,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/036-section-absolute-dimensionless-metrology-from-the-bounda.tex","status_markers_as_written":[],"summary_excerpt":"By thm:absolute-spectral-planck-closure, the admissible geometric branch carries the unique positive stationary root [formula in source] [formula in source] This root is the boundary-normalized Planck datum of the stationary branch.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Stationary spectral Planck root","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10729,"byte_start":8701,"id":"section:9d47b967013d2762cd3e","kind":"subsection","labels":["thm:carrier-exhausted-ir-seam-eigenvalue","thm:sector-dressed-spectral-scale-bifurcation"],"line_end":307,"line_start":252,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/036-section-absolute-dimensionless-metrology-from-the-bounda.tex","status_markers_as_written":[],"summary_excerpt":"The primitive response [formula in source] bifurcates on the closed branch into distinct dressed spectral channels: [formula in source] Here [formula in source] is the stationary Einstein/Higgs background scale, while [formula in source] is the transport-dressed hadronic scale. They share one boundary origin but are not identified on the closed theorem surface.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Infrared seam and sector bifurcation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6936,"byte_start":0,"id":"section:b4835bee9765c14ba1b8","kind":"subsection","labels":["cor:dimensionless-gravitational-ew-metrology","cor:point-closed-planck-reconstruction","def:tfpt-metrology-functor","thm:dimensionless-ew-residue-matching","thm:dimensionless-pole-mass-readout","thm:dimensionless-tfpt-metrology"],"line_end":220,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/037-subsection-physical-readout-and-metrology-functor.tex","status_markers_as_written":[],"summary_excerpt":"On the renormalized branch, define [formula in source] Then the quantities [formula in source] are determined by [formula in source] . Consequently [formula in source] and hence [formula in source] is an internal readout of the closed branch.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Physical readout and metrology functor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6958,"byte_start":6936,"id":"section:d8caa4b81a98aed11886","kind":"section","labels":[],"line_end":222,"line_start":221,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/037-subsection-physical-readout-and-metrology-functor.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Conclusion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9891,"byte_start":6958,"id":"section:9407b37097378311849a","kind":"subsection","labels":[],"line_end":313,"line_start":223,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/037-subsection-physical-readout-and-metrology-functor.tex","status_markers_as_written":[],"summary_excerpt":"TFPT is organized around the one-sided boundary datum [formula in source] induced by the minimal operational seed, and reconstructs in a two-stage closure order [formula in source] This reconstruction first fixes the joint discrete datum and only afterwards the continuous Euler–Lagrange branch, thereby identifying the canonical rigid object of the boundary-polarized branch: [formula in source] The selector-to-dynamic","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Closed theorem stack and interface layers","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11052,"byte_start":9891,"id":"section:4ceb90b0ad274be15e72","kind":"subsection","labels":[],"line_end":330,"line_start":314,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/037-subsection-physical-readout-and-metrology-functor.tex","status_markers_as_written":[],"summary_excerpt":"From [formula in source] exactly two side maps are attached, both hard-separated from the theorem chain: Structural falsification map (main text). The map [formula in source] of sec:structural-falsification-map reports the structural failure mode that would break each arrow of the reconstruction. It uses no scheme conventions, no thresholds, and no comparison data. Empirical comparison map (appendix only). The map [f","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Two side maps from [formula in source] T-star","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13528,"byte_start":11052,"id":"section:9096ea138c6033d1fe30","kind":"subsection","labels":["subsec:conditional-closure-status"],"line_end":397,"line_start":331,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/037-subsection-physical-readout-and-metrology-functor.tex","status_markers_as_written":[],"summary_excerpt":"The closed-branch theorem stack is supplemented by a single, explicitly labeled conditional closure layer, organized so that every numerical readout can be promoted to a theorem as soon as a single named lift hypothesis is discharged. The four downstream readouts and their current status are [formula in source] The compressed integrated story is [formula in source] and in the matter sector [formula in source] The fou","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conditional closure layer and status of the four downstream readouts","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2783,"byte_start":0,"id":"section:2f282dcf2ebf7295731a","kind":"subsection","labels":[],"line_end":93,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/038-subsection-main-claim.tex","status_markers_as_written":[],"summary_excerpt":"A compressed decoder reading of the closed branch is [formula in source] [formula in source] In this condensed form, [formula in source] generates the carrier structure, the primitive winding class [formula in source] fixes the counting, and the retained seed [formula in source] decodes the bridge observables.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Main claim","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9550,"byte_start":2783,"id":"section:919fefdb9847c483fe25","kind":"section","labels":["app:comparison","cor:retained-seed-factorization","sec:appendix-empirical-readout","tab:benchmark"],"line_end":210,"line_start":94,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/038-subsection-main-claim.tex","status_markers_as_written":[],"summary_excerpt":"This appendix does not define the theorem-level physical observable object itself. The canonical scheme-facing object is the orbit [formula in source] The tables below record only chosen representatives [formula in source] in declared scheme objects [formula in source] . The appendix is therefore the carrier of the comparison map [formula in source] and remains hard-separated from the theorem chain [formula in source","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Appendix-level empirical readout","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15800,"byte_start":9550,"id":"section:6df85258fbb8746d44be","kind":"subsection","labels":["tab:operational-prediction-set"],"line_end":280,"line_start":211,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/038-subsection-main-claim.tex","status_markers_as_written":[],"summary_excerpt":"The narrow empirical readout table is not the whole experimental surface of the manuscript. tab:operational-prediction-set collects the rows that are operationally testable on near- to medium-term timescales, while keeping their status, next test, kill criterion, and dependency structure explicit. The point is not to flatten them into one truth class. Rather, the Status column now uses only the manuscript's final out","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Operational prediction set","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18007,"byte_start":15800,"id":"section:2affad0005f6cf01ce72","kind":"subsection","labels":["tab:basis-factorization"],"line_end":308,"line_start":281,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/038-subsection-main-claim.tex","status_markers_as_written":[],"summary_excerpt":"To make the renormalized / physical / scheme hierarchy explicit row by row, the visible appendix surface factors through the basis packages of [formula in source] as follows.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Basis factorization of readout rows","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20945,"byte_start":18007,"id":"section:b9901fa20638c8059738","kind":"subsection","labels":["tab:prediction-ledger"],"line_end":340,"line_start":309,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/038-subsection-main-claim.tex","status_markers_as_written":[],"summary_excerpt":"The main empirical readout table shows only a narrow readout surface. To keep the output structure visible, tab:prediction-ledger summarizes which output packages belong to which layer of the paper.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Compact prediction ledger","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":21711,"byte_start":20945,"id":"section:4e414d05871badb11c62","kind":"subsection","labels":[],"line_end":351,"line_start":341,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/038-subsection-main-claim.tex","status_markers_as_written":[],"summary_excerpt":"The present main-text readout surface is no longer intentionally mixed. Its rows now use the manuscript's closed classes: theorem, physical observable, scheme projection, and appendix continuation. Carrier algebra and the exact [formula in source] row remain the sharpest numerically load-bearing entries, while the former seed-driven rows are now reorganized by sector rather than counted as one compressed shadow packa","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Empirical readout and kill-test logic","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1974,"byte_start":0,"id":"section:324225233202f3fb9b8d","kind":"subsection","labels":["fig:residual-plot"],"line_end":50,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/039-subsection-residual-readout-and-interface-refinements.tex","status_markers_as_written":[],"summary_excerpt":"The residuals for the restricted six-row readout table are shown in fig:residual-plot. The carrier-linked electromagnetic, birefringence, and baryon-density channels all remain within the displayed few-sigma window. The CKM phase is not plotted here because it is better treated in the operational prediction set and Appendix rather than inside the restricted six-row residual plot.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Residual readout and interface refinements","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2219,"byte_start":1974,"id":"section:4cb4f13db21ad725f507","kind":"section","labels":["app:tech"],"line_end":55,"line_start":51,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/039-subsection-residual-readout-and-interface-refinements.tex","status_markers_as_written":[],"summary_excerpt":"This appendix collects the technical bookkeeping that supports the boundary-to-carrier presentation but would slow the early main-text flow if placed before the carrier theorem.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Technical conventions and data layers","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3949,"byte_start":2219,"id":"section:c4606d829410598efa3f","kind":"subsection","labels":["tab:relative-objects"],"line_end":80,"line_start":56,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/039-subsection-residual-readout-and-interface-refinements.tex","status_markers_as_written":[],"summary_excerpt":"The adjective relative is used in one fixed sense throughout the paper: every operator or action is compared to a declared reference object.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Relative objects","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7315,"byte_start":3949,"id":"section:cc15ea405e7627424fac","kind":"subsection","labels":["tab:layered-datum"],"line_end":152,"line_start":81,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/039-subsection-residual-readout-and-interface-refinements.tex","status_markers_as_written":[],"summary_excerpt":"The technical bookkeeping behind the manuscript uses five levels: [formula in source] [formula in source] [formula in source] [formula in source] [formula in source] Here [formula in source] is the primitive boundary kernel, while [formula in source] is the derived theorem-level post-carrier kernel reconstructed from the joint discrete datum and the full selector.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Layered datum and admissibility","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15656,"byte_start":7315,"id":"section:765505a6ce3e296919eb","kind":"subsection","labels":["tab:symbol-guide","tab:symbol-guide-appendix","tab:symbol-guide-theorem"],"line_end":250,"line_start":153,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/039-subsection-residual-readout-and-interface-refinements.tex","status_markers_as_written":[],"summary_excerpt":"The symbol guide is split into two tables to keep theorem-level objects lexically separate from appendix-only comparison and readout objects. tab:symbol-guide-theorem contains only symbols that participate in the main-text theorem chain; tab:symbol-guide-appendix contains only symbols that live in the appendix-level comparison and readout layer.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Symbol guide","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15871,"byte_start":15656,"id":"section:461e6cbd8501ba68a4fc","kind":"section","labels":["app:constants"],"line_end":255,"line_start":251,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/039-subsection-residual-readout-and-interface-refinements.tex","status_markers_as_written":[],"summary_excerpt":"This appendix collects material that is useful for internal compression but should not dominate the main-text scope of explicit claims.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Constants atlas and downstream scale grammar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20894,"byte_start":15871,"id":"section:4df7445c4b167eda40fb","kind":"subsection","labels":["fig:constant-cascade","tab:constants-atlas"],"line_end":339,"line_start":256,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/039-subsection-residual-readout-and-interface-refinements.tex","status_markers_as_written":[],"summary_excerpt":"On the canonical branch the seam loop carries one unit of spectral flow, [formula in source] Because the spin lift closes only after [formula in source] , the normalized rotation modulus is [formula in source] The cascade in fig:constant-cascade is kept here as technical bookkeeping rather than as an early main-text dependency graphic.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Global rotation angle and constants atlas","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":22464,"byte_start":20894,"id":"section:53cfe06135093cf58823","kind":"subsection","labels":[],"line_end":372,"line_start":340,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/039-subsection-residual-readout-and-interface-refinements.tex","status_markers_as_written":[],"summary_excerpt":"In the present paper E [formula in source] is not used as a primitive cause. The retained parameter is [formula in source] On the retained branch this means [formula in source] The intended reading is a downstream scale grammar: the carrier packet fixes [formula in source] , [formula in source] then defines an optional ladder parameter, the ladder is allowed to organize scale spacing, but it does not replace the carr","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"E [formula in source] E8 as downstream scale grammar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2723,"byte_start":0,"id":"section:1351bbbecbaa2db706ff","kind":"subsection","labels":["tab:e8-full-atlas"],"line_end":35,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/040-subsection-full-stage-atlas.tex","status_markers_as_written":[],"summary_excerpt":"The full real-domain atlas up to [formula in source] extends the main-text robust table with restricted-scan candidates and IR tail conjectures. Rows are classified as robust (restrictive grammar, unambiguous target), restricted-scan (plausible but less constrained), or tail conjecture (new trace class [formula in source] not yet derived from block structure).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Full stage atlas","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4854,"byte_start":2723,"id":"section:bd53a3cef50154519903","kind":"subsection","labels":["eq:41-chain"],"line_end":84,"line_start":36,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/040-subsection-full-stage-atlas.tex","status_markers_as_written":[],"summary_excerpt":"The main-text compression identities are developed in the dedicated section on compression identities and numerical comparison of alternative discrete worlds. This appendix subsection collects additional arithmetic continuations and the compression chain summary.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Compression identities on the minimal branch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9629,"byte_start":4854,"id":"section:e7475ced262ab1c62a03","kind":"subsection","labels":["rem:defect-factorization-gcd-lcm"],"line_end":247,"line_start":85,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/040-subsection-full-stage-atlas.tex","status_markers_as_written":[],"summary_excerpt":"The next relations mix the main-text carrier with optional appendix-level E [formula in source] , inflation, or geometric notation. They are useful compression patterns, but their interpretation should remain conditional or conjectural.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Optional arithmetic continuations","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11233,"byte_start":9629,"id":"section:0bbff7ca2fc04ee89530","kind":"subsection","labels":[],"line_end":313,"line_start":248,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/040-subsection-full-stage-atlas.tex","status_markers_as_written":[],"summary_excerpt":"The next package is stronger but also more conditional. It assumes that the carrier rank, family multiplicity, and seam normalization are all read as closed rather than only partially inherited.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conditional minimal-parameter picture","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14570,"byte_start":11233,"id":"section:f95ff39969033d19b94d","kind":"subsection","labels":["app:ir-seam-continuations","conj:ir-seam-car-continuation","conj:ir-seam-rec-continuation","cor:conditional-lambda-ir-readout"],"line_end":395,"line_start":314,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/040-subsection-full-stage-atlas.tex","status_markers_as_written":[],"summary_excerpt":"Theorem theorem-level seam-transfer expression for [formula in source] and its determinant bounds. The numerical scales recorded below require one further infrared assumption and therefore are organized as a labeled conditional closure layer, separated from the theorem core. Each member of the layer is stated as a conjecture or as a corollary conditional on the named seam-lift hypothesis, never as a theorem-level con","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Infrared continuations of the seam transfer","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":973,"byte_start":0,"id":"section:196d87fa99d5859c2e5d","kind":"section","labels":["app:aps"],"line_end":13,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/041-section-relative-aps-and-superconnection-setup.tex","status_markers_as_written":[],"summary_excerpt":"The geometric completion uses APS-type relative data aps1975. In practice this means: one works with a declared pair [formula in source] rather than a single unanchored operator, boundary conditions on the seam [formula in source] are part of the definition of the relative index, the [formula in source] -term keeps track of the residual spectral asymmetry, the superconnection package is used in the same spirit as the","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Relative APS and superconnection setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1053,"byte_start":973,"id":"section:b39ee7a8d6c6a6429e02","kind":"section","labels":["app:os-fermions"],"line_end":16,"line_start":14,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/041-section-relative-aps-and-superconnection-setup.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Relative reflection positivity with fermions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1540,"byte_start":1053,"id":"section:f941095bd6edafb8fff2","kind":"subsection","labels":[],"line_end":26,"line_start":17,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/041-section-relative-aps-and-superconnection-setup.tex","status_markers_as_written":[],"summary_excerpt":"The relative Euclidean theory used in the main closure section is not interpreted as a difference of measures. Instead it is organized as the normalized quotient [formula in source] Because the denominator is source independent on the admissible sector, the reference theory acts only as a fixed normalizer and does not interfere with reflection positivity.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Normalized quotient form","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2570,"byte_start":1540,"id":"section:a6ea9486ed3c5d85bcaf","kind":"subsection","labels":[],"line_end":44,"line_start":27,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/041-section-relative-aps-and-superconnection-setup.tex","status_markers_as_written":[],"summary_excerpt":"The commutation relations [formula in source] ensure that reflection preserves the admissible subspace. The bosonic part then follows the standard Markov / reflection-stable Osterwalder–Schrader argument on admissible observables. For fermions, the admissible CAR kernel may be written as a reflected quadratic form; equivalently one may express the same condition as positivity of the associated Pfaffian structure on t","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bosonic and fermionic positivity on [formula in source] Padm","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2983,"byte_start":2570,"id":"section:bb2abd3fac8cbb0764ac","kind":"section","labels":["app:os-scattering"],"line_end":52,"line_start":45,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/041-section-relative-aps-and-superconnection-setup.tex","status_markers_as_written":[],"summary_excerpt":"This appendix upgrades the admissible Schwinger, reconstruction, and scattering block from a named standard interface to a manuscript-level proof package. 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Moreover, for every compact [formula in source] and every source monomial of total degree [formula in source] , its moments obey polynomial bounds determined by the same uniform heat-kernel estimates and finite local moments of the admissible constructive measure","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Tempered admissible Schwinger families","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7489,"byte_start":5106,"id":"section:c6e2a3eef390913d77e6","kind":"subsection","labels":["thm:tailored-os-car-reconstruction"],"line_end":129,"line_start":89,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/041-section-relative-aps-and-superconnection-setup.tex","status_markers_as_written":[],"summary_excerpt":"Padm] Let [formula in source] be the admissible Schwinger family on the Euclidean continuation of [formula in source] . If reflection positivity, temperedness, graded Euclidean covariance, graded symmetry, and clustering hold on [formula in source] , then there exist: a Hilbert space [formula in source] with vacuum vector [formula in source] , a strongly continuous positive-energy semigroup [formula in source] with s","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"OS and CAR reconstruction on [formula in source] Padm","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9834,"byte_start":7489,"id":"section:c72cacd99b4e8651172f","kind":"subsection","labels":["cor:lsz-admissible-massive","lem:one-particle-projectors-from-poles","thm:haag-ruelle-admissible-massive"],"line_end":174,"line_start":130,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/041-section-relative-aps-and-superconnection-setup.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] have an isolated simple pole with positive residue at [formula in source] . Then the corresponding one-particle contribution defines a positive spectral projector on the admissible Hilbert space.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Stable massive Haag–Ruelle and LSZ closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10487,"byte_start":9834,"id":"section:ff4d2e0b478627dfdbed","kind":"subsection","labels":[],"line_end":189,"line_start":175,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/041-section-relative-aps-and-superconnection-setup.tex","status_markers_as_written":[],"summary_excerpt":"The massless sector is not treated by bare Fock asymptotics in the present manuscript. The relevant object is the infrared-dressed interface package [formula in source] constructed from the soft charges of the admissible local net on the low-curvature region [formula in source] . This is exactly the interface package used in the main-text theorem thm:dressed-massless-interface.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dressed massless interface in the low-curvature region","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14200,"byte_start":10487,"id":"section:1d252781b8a8cfc51971","kind":"section","labels":["app:frw-interface-proofs","lem:determinant-line-axion-reduction","lem:minisuperspace-reduction-hodge-branch","lem:seam-transfer-vacuum-term","thm:full-frw-interface-theorem"],"line_end":270,"line_start":190,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/041-section-relative-aps-and-superconnection-setup.tex","status_markers_as_written":[],"summary_excerpt":"This appendix section upgrades the cosmology interface block from a proof sketch to a manuscript proof. The point is to keep the theorem-level content at the level of closed-branch interface data, while leaving late-time numerical continuation in the comparison layer.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"FRW reduction and cosmology interface proofs","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16170,"byte_start":14200,"id":"section:dca1b7585c6b0caa6278","kind":"section","labels":["app:yukawa"],"line_end":308,"line_start":271,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/041-section-relative-aps-and-superconnection-setup.tex","status_markers_as_written":[],"summary_excerpt":"This appendix is the proof motor for the transport positivity, determinant-phase suppression, and bounded-residual statements used in the main text. The transport program is based on the regularized kernel [formula in source] Three remarks are important. The regulator [formula in source] is not optional: without it the kernel becomes ill-defined exactly where the admissibility question is most delicate. Positivity of","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Yukawa kernels and positivity lemmas","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16835,"byte_start":16170,"id":"section:a2b72ab09ed8375f6e50","kind":"subsection","labels":[],"line_end":324,"line_start":309,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/041-section-relative-aps-and-superconnection-setup.tex","status_markers_as_written":[],"summary_excerpt":"As an appendix-level dynamical sharpening of the hadronic admissibility theorem, one may further require the admissible center-neutral Wilson functional to obey strong-coupling dominance. On that optional route the relative Wilson loop satisfies [formula in source] and the physical Hilbert space contains no color-nonsinglet asymptotic states. This statement is kept in the appendix so that the main theorem surface doe","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Optional strong-coupling sharpening","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17277,"byte_start":16835,"id":"section:318adfb05d8570fc4b51","kind":"section","labels":["app:info-readings"],"line_end":332,"line_start":325,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/041-section-relative-aps-and-superconnection-setup.tex","status_markers_as_written":[],"summary_excerpt":"This appendix collects interpretive notes that help organize the algebraic structure of the boundary-polarized closed form. When a theorem-level statement appears below, it refers back to a main-text proposition; the appendix itself does not upgrade any status label beyond the declared theorem / derived-consequence / comparison / appendix discipline.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Information-theoretic and cut-and-project readings","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18471,"byte_start":17277,"id":"section:58094f78499b2836d5b7","kind":"subsection","labels":["tab:checksum-41"],"line_end":358,"line_start":333,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/041-section-relative-aps-and-superconnection-setup.tex","status_markers_as_written":[],"summary_excerpt":"The canonical [formula in source] -chain admits a compact overdetermination reading:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[formula in source] 41-chain overdetermination of the canonical branch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1388,"byte_start":0,"id":"section:a1df9050a4cb2c541113","kind":"subsection","labels":[],"line_end":32,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/042-subsection-seed-variance-and-surprisal-readings.tex","status_markers_as_written":[],"summary_excerpt":"The bridge identities also admit a disciplined probabilistic reading. Since [formula in source] the Cabibbo scale is exactly the standard-deviation scale of a Bernoulli variable with success probability [formula in source] : [formula in source] Equivalently, the Fisher information of the Bernoulli family is [formula in source] so the Cabibbo bridge measures the inverse square-root Fisher scale of the retained seed. T","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Seed variance and surprisal readings","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4026,"byte_start":1388,"id":"section:2853218407aa0c6ea728","kind":"subsection","labels":[],"line_end":90,"line_start":33,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/042-subsection-seed-variance-and-surprisal-readings.tex","status_markers_as_written":[],"summary_excerpt":"The strongest information-theoretic statement is no longer a loose analogy. By prop:parity-code-family, the one-family packet is exactly the even-parity subspace on five occupation bits, [formula in source] so the carrier packet is kinematically the classical even-parity [formula in source] code. The split formula [formula in source] shows that the coarse parity bits of the [formula in source] -sector and [formula in","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Exact parity-code and information-compression reading","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5890,"byte_start":4026,"id":"section:4ef0741923e4d5fd4767","kind":"subsection","labels":["thm:cut-project-model-set"],"line_end":147,"line_start":91,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/042-subsection-seed-variance-and-surprisal-readings.tex","status_markers_as_written":[],"summary_excerpt":"The appendix-level quasicrystal language is kept outside the hard core, but it can be stated exactly as a compatible model-set construction.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cut-and-project model-set realization","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6338,"byte_start":5890,"id":"section:ac489236b970d87f40b7","kind":"section","labels":["app:record"],"line_end":155,"line_start":148,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/042-subsection-seed-variance-and-surprisal-readings.tex","status_markers_as_written":[],"summary_excerpt":"This appendix elaborates the main-text record constructions and the stable pointer-algebra package used in the downstream closure discussion. Horizon thermality and prediction / transient semantics are separated into the following appendix sections so that record theory, black-hole continuation, and phenomenological event channels do not blur into one mixed extrapolation block.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Record algebra and pointer dynamics","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7104,"byte_start":6338,"id":"section:7205857189439efe131f","kind":"subsection","labels":[],"line_end":165,"line_start":156,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/042-subsection-seed-variance-and-surprisal-readings.tex","status_markers_as_written":[],"summary_excerpt":"At finite volume or with a declared cutoff, an admissible vacuum candidate is written as [formula in source] with lower boundedness and coercivity understood exactly as in the main-text closure axioms. The stronger generative theorem path described in the conclusion would refine this object to the global admissible vacuum functional [formula in source] whose variations also select the transport branch. In this append","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Minimal admissible vacuum","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7525,"byte_start":7104,"id":"section:419480dc9d913d11759d","kind":"subsection","labels":[],"line_end":179,"line_start":166,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/042-subsection-seed-variance-and-surprisal-readings.tex","status_markers_as_written":[],"summary_excerpt":"One useful coarse-grained record algebra is [formula in source] As [formula in source] decreases, more stable channels open. The intended arrow-of-time claim is therefore [formula in source] but only as a record-growth principle, not as a replacement for detailed nonequilibrium dynamics.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Record growth principle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8526,"byte_start":7525,"id":"section:0beea4f90e481bfb1f7f","kind":"subsection","labels":["thm:born-pointer-algebra"],"line_end":208,"line_start":180,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/042-subsection-seed-variance-and-surprisal-readings.tex","status_markers_as_written":[],"summary_excerpt":"An observer is modeled as a stable pointer subalgebra [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Observer algebra and Born-type evaluation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8933,"byte_start":8526,"id":"section:1348d515afbf38663cdc","kind":"section","labels":["app:horizons"],"line_end":216,"line_start":209,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/042-subsection-seed-variance-and-surprisal-readings.tex","status_markers_as_written":[],"summary_excerpt":"This appendix section records the horizon-side analytic input that supports the downstream modular thermality program. In the present version the split-inclusion theorem is the firm appendix-level statement, while the full modular KMS upgrade and compact-object thermality package remain visible downstream closure targets.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Horizons, modular flow, and black hole thermality","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10176,"byte_start":8933,"id":"section:d02349b21f0bbe529fa5","kind":"subsection","labels":["thm:horizon-split-inclusion"],"line_end":251,"line_start":217,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/042-subsection-seed-variance-and-surprisal-readings.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the local admissible net reconstructed in thm:admissible-local-minkowski-net, and assume in addition the split property. Then for every nested triple [formula in source] there exists a type-I factor [formula in source] such that [formula in source] Hence on a suitable code subspace one obtains an approximate tensor factorization [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Split inclusion horizon approximation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10523,"byte_start":10176,"id":"section:ada9ffd5266f47b5875e","kind":"section","labels":["app:prediction-semantics"],"line_end":258,"line_start":252,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/042-subsection-seed-variance-and-surprisal-readings.tex","status_markers_as_written":[],"summary_excerpt":"This appendix section collects the optional semantic decorations of the prediction map and the status note for transient event channels. These items organize downstream interpretation, but they do not add new upstream theorem arrows to the rigid core.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Prediction semantics and transient event channels","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10883,"byte_start":10523,"id":"section:f99a3c8705ea8bc36ea7","kind":"subsection","labels":[],"line_end":272,"line_start":259,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/042-subsection-seed-variance-and-surprisal-readings.tex","status_markers_as_written":[],"summary_excerpt":"The main-text prediction map can be decorated by explicit experimental metadata as [formula in source] with [formula in source] This is kept only as an optional formal extension.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Prediction semantics","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11212,"byte_start":10883,"id":"section:d5f0606de0ade3b6d3de","kind":"subsection","labels":[],"line_end":278,"line_start":273,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/042-subsection-seed-variance-and-surprisal-readings.tex","status_markers_as_written":[],"summary_excerpt":"The topological burst channel of conj:topological_phase_slip_burst_channel is kept at programmatic-target status. What is fixed in the present version is only the admissible phase-slip channel and its scaling form, not yet a complete defect dynamics or radiative-transfer derivation.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Transient event status","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13302,"byte_start":11212,"id":"section:f0d7c577331ae100cba2","kind":"section","labels":["app:global-particle-ledger","rem:counting-convention"],"line_end":310,"line_start":279,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/042-subsection-seed-variance-and-surprisal-readings.tex","status_markers_as_written":[],"summary_excerpt":"This appendix collects the full Standard Model output of the boundary-polarized manuscript into a theoretical surface and an empirical comparison surface. The purpose is not to flatten the hierarchy but to keep theorem-level outputs, derived consequences, physical observables, scheme projections, and appendix continuations visibly distinct:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Closed theoretical outputs and empirical comparison surface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16431,"byte_start":13302,"id":"section:209e2228224b86417e5f","kind":"subsection","labels":["tab:sm-content-origin"],"line_end":349,"line_start":311,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/042-subsection-seed-variance-and-surprisal-readings.tex","status_markers_as_written":[],"summary_excerpt":"@> p0.09 > p0.11 > p0.10 > p0.04 > p0.18 > p0.20 > p0.08 @ Particle & Repr. & Ext.\\ source & [formula in source] & TFPT origin & Internal source & Status \\\\ 7@l Fermion sector (one family [formula in source] ): \\\\ [formula in source] & [formula in source] & [formula in source] & [formula in source] & carrier scaffold & hard carrier, [formula in source] & Theorem \\\\ [formula in source] & [formula in source] & [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Table 1: Closed theoretical outputs","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6529,"byte_start":0,"id":"section:c4896b30855616e301ff","kind":"subsection","labels":["tab:full-mass-benchmark-surface"],"line_end":58,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/043-subsection-table-2-empirical-comparison-rows.tex","status_markers_as_written":[],"summary_excerpt":"round-mode=none, group-minimum-digits=20 ! @lllllrlrrl@ Quantity & Sector & TFPT formula or source & Metrology\\ & Comparison\\ & TFPT\\ & Unit & Reference\\ & Residual & Status \\\\ 10@l Closed theoretical outputs: \\\\ [formula in source] & EM & exact [formula in source] closure & [formula in source] \\ readout & on-shell Thomson & 137.0359992 & — & 137.03599918 & [formula in source] & Physical observable \\\\ [formula in sou","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Table 2: Empirical comparison rows","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10694,"byte_start":6529,"id":"section:6aafabe5adaef45cb6de","kind":"subsection","labels":["tab:strict-benchmark-surface"],"line_end":107,"line_start":59,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/043-subsection-table-2-empirical-comparison-rows.tex","status_markers_as_written":[],"summary_excerpt":"tab:strict-benchmark-surface extracts only the rows that are fair as direct theory-versus-data comparisons. Derived consequences that still depend on internal branch formulas are excluded.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Empirical comparison surface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11039,"byte_start":10694,"id":"section:735e76d51ff15c2bcf88","kind":"section","labels":["app:benchmarks"],"line_end":112,"line_start":108,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/043-subsection-table-2-empirical-comparison-rows.tex","status_markers_as_written":[],"summary_excerpt":"This appendix turns the broader prediction surface into explicit experimental bookkeeping. The point is not to promote every row to main-text benchmark status, but to keep next test, kill criterion, and dependency structure visible wherever the theory already commits to a concrete target.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Extended benchmarks","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14946,"byte_start":11039,"id":"section:15241c486d0ed809b928","kind":"subsection","labels":["tab:extended-benchmarks"],"line_end":146,"line_start":113,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/043-subsection-table-2-empirical-comparison-rows.tex","status_markers_as_written":[],"summary_excerpt":"The appendix matrix keeps the same truth-mode discipline as the main text, but its final column adds a short row-level qualifier whenever an appendix-level auxiliary continuation needs to be made explicit.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Operational prediction matrix","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17106,"byte_start":14946,"id":"section:d832cd95a8269cc8eadf","kind":"subsection","labels":["tab:kill-tests"],"line_end":171,"line_start":147,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/043-subsection-table-2-empirical-comparison-rows.tex","status_markers_as_written":[],"summary_excerpt":"round-mode=none, group-minimum-digits=20 ! @> p0.22 > p0.24 > p0.12 > p0.38 @ Test row & TFPT target or prohibition & Status reading & Failure mode \\\\ Second light Higgs doublet & no additional seam-even\\ doublet & kill\\ & robust discovery would\\ the bosonic-index route \\\\ Calibrated birefringence null & [formula in source] \\ the minimal branch & kill\\ & externally calibrated null\\ with zero at the\\ tolerance would r","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Target and kill-test rows","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17954,"byte_start":17106,"id":"section:38267f67b1fbdce36bc8","kind":"subsection","labels":[],"line_end":198,"line_start":172,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/043-subsection-table-2-empirical-comparison-rows.tex","status_markers_as_written":[],"summary_excerpt":"The axion rows are cosmology readouts generated from the same determinant-line / seam-transfer / scalaron interface data that also fix reheating and the heavy-neutrino scale. On the closed cosmology branch, [formula in source] In standard haloscope units this gives [formula in source] so the practical scan prescription is a conservative window [formula in source] at the quoted coupled sensitivity. The present appendi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Axion interface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":23593,"byte_start":17954,"id":"section:fcc8754b4160c1961727","kind":"subsection","labels":["cor:charged-lepton-source-compression","tab:mass-source-supplement"],"line_end":279,"line_start":199,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/043-subsection-table-2-empirical-comparison-rows.tex","status_markers_as_written":[],"summary_excerpt":"The compact main-text mass ledgers intentionally suppress explicit formula detail. The source rows collected here retain that information without forcing the main text to read like a mixed formula notebook. In the present version they are explicitly UV asymptotic source rows: the physical masses belong to the pole-level functor [formula in source] on [formula in source] , whereas the formulas below record the closed-","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Supplementary UV asymptotic mass-source rows","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":26931,"byte_start":23593,"id":"section:877c9d619d76859f1144","kind":"subsection","labels":["tab:extended-compiler-ledger","tab:yukawa-residuals"],"line_end":332,"line_start":280,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/043-subsection-table-2-empirical-comparison-rows.tex","status_markers_as_written":[],"summary_excerpt":"round-mode=none, group-minimum-digits=20 @> p0.14 > p0.28 > p0.18 > p0.15 Y@ Row & TFPT source or target & Metrology\\ & Scheme\\ & Status note \\\\ [formula in source] & exact unbroken [formula in source] direction & [formula in source] \\\\m_ / _ =0 [formula in source] 0 [formula in source] m_g [formula in source] d_O=1 [formula in source] & [formula in source] & exact structural row \\\\ [formula in source] & threshold ou","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Extended comparison ledger","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":31312,"byte_start":26931,"id":"section:9a33edaabb541632e5dc","kind":"subsection","labels":[],"line_end":426,"line_start":333,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-42"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-42/sections/043-subsection-table-2-empirical-comparison-rows.tex","status_markers_as_written":[],"summary_excerpt":"The paper uses standard tools from relative spectral geometry, APS index theory, transport/resolvent language, and conventional RG comparison. The claim of novelty is not that these background ingredients are new in isolation, but that the minimal [formula in source] carrier packet, the compression identities, and the boundary-polarized closed architecture are organized into one tightly overdetermined program. Conver","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Novelty boundary and literature positioning","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2993,"byte_start":0,"id":"section:67daee60346c0b933996","kind":"frontmatter","labels":[],"line_end":105,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/preamble.tex","status_markers_as_written":[],"summary_excerpt":"compat=1.18 arrows.meta,positioning,decorations.markings,decorations.pathmorphing,calc,patterns,shapes.geometric","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Topological Fixed Point Theory (TFPT)\\\\[0.5em] A Parameter-Free Derivation of the Fine-Structure Constant\\\\ from Topology, Geometry, and Quantum Consistency","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5973,"byte_start":0,"id":"section:fe4583371d2171707f36","kind":"frontmatter","labels":[],"line_end":95,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/001-section-introduction-the-problem-of-parameters.tex","status_markers_as_written":[],"summary_excerpt":"We present the complete axiomatic foundation of Topological Fixed Point Theory (TFPT), which derives the fine-structure constant [formula in source] and other fundamental quantities from eight minimal assumptions rooted in topology, geometry, and quantum field theory. The theory rests on two fundamental invariants: the topological coupling [formula in source] from 11D Chern–Simons quantization and the geometric scale","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8335,"byte_start":5973,"id":"section:5770e609f8218d83f3ae","kind":"section","labels":["fig:flow"],"line_end":143,"line_start":96,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/001-section-introduction-the-problem-of-parameters.tex","status_markers_as_written":[],"summary_excerpt":"The Standard Model of particle physics contains approximately 19 free parameters that must be determined experimentally. Among these, the fine-structure constant [formula in source] stands out as a dimensionless number whose value has no explanation within conventional frameworks.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Introduction: The Problem of Parameters","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8754,"byte_start":8335,"id":"section:a9627800b53213d2641d","kind":"section","labels":[],"line_end":151,"line_start":144,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/001-section-introduction-the-problem-of-parameters.tex","status_markers_as_written":[],"summary_excerpt":"TFPT is built on eight axioms, organized into three categories: geometric structure, quantum field theory, and closure conditions. Each axiom is either derived from established physics or explicitly marked as a new postulate.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Axiomatic Foundation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16214,"byte_start":8754,"id":"section:703c5ce40387d29746d0","kind":"subsection","labels":["fig:doublecover"],"line_end":311,"line_start":152,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/001-section-introduction-the-problem-of-parameters.tex","status_markers_as_written":[],"summary_excerpt":"Riemann–Cartan GeometryRC The fundamental spacetime connection possesses torsion; the Levi-Civita connection is a limiting case when torsion vanishes.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Geometric Axioms (A1–A4)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19596,"byte_start":16214,"id":"section:404db12cb6cf7414800a","kind":"subsection","labels":[],"line_end":390,"line_start":312,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/001-section-introduction-the-problem-of-parameters.tex","status_markers_as_written":[],"summary_excerpt":"Units and constants: Natural units: [formula in source] ; energies in GeV, lengths in GeV [formula in source] . Reference data: CODATA 2022, PDG 2024. Metric signature: [formula in source] . Levi-Civita tensor: [formula in source] , [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Quantum Field Theory Axioms (A5–A6)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4318,"byte_start":0,"id":"section:3d805e068a87630f17e4","kind":"subsection","labels":[],"line_end":72,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/002-subsection-closure-axioms-a7-a8.tex","status_markers_as_written":[],"summary_excerpt":"Standard Model Hypercharge TraceSMT The hypercharge trace invariant, summed over all SM fermions with GUT normalization [formula in source] , is: In TFPT this quantity appears as the spectral quadratic index of the hypercharge-coupled boundary operators in the regulated determinant (Appendix","summary_method":"opening prose excerpt; 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TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Geometric Scale [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10071,"byte_start":6448,"id":"section:06e7c3ca3e39a3161ea2","kind":"subsection","labels":["eq:CFE","fig:CFE"],"line_end":210,"line_start":122,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/002-subsection-closure-axioms-a7-a8.tex","status_markers_as_written":[],"summary_excerpt":"Effective Potential Parametersparams From the 11D Chern–Simons reduction (A5) and modulus-closure structure (A6): Notation: We use [formula in source] (calligraphic) for this CFE parameter to distinguish it from [formula in source] (gravitational coupling).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Cubic Fixed-Point Equation (CFE)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10206,"byte_start":10071,"id":"section:ed295ac5dc720b1d85c6","kind":"subsection","labels":[],"line_end":213,"line_start":211,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/002-subsection-closure-axioms-a7-a8.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Geometric Self-Consistency (Backreaction)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14714,"byte_start":10206,"id":"section:d084a5b5bae6193d9de0","kind":"subsubsection","labels":["eq:backreaction","tab:alpha"],"line_end":318,"line_start":214,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/002-subsection-closure-axioms-a7-a8.tex","status_markers_as_written":[],"summary_excerpt":"The response [formula in source] is the closed form consequence of defect sector reweighting on the orientable double cover. The linear form is the [formula in source] expansion, not a separate assumption.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Backreaction as Structural Response","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17335,"byte_start":14714,"id":"section:9375a5387ab4477bfe64","kind":"subsubsection","labels":["fig:deviation","sec:sensitivity"],"line_end":390,"line_start":319,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/002-subsection-closure-axioms-a7-a8.tex","status_markers_as_written":[],"summary_excerpt":"The sub-ppm precision of the [formula in source] prediction depends critically on the backreaction coefficient. We analyze the sensitivity to demonstrate this is not fine-tuning but a genuine geometric constraint.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Sensitivity Analysis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":202,"byte_start":0,"id":"section:50cd36bd2c3b2e9c0d99","kind":"section","labels":[],"line_end":4,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/003-section-the-unified-field-equation-ufe.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"The Unified Field Equation (UFE)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2083,"byte_start":202,"id":"section:7d88ca302af6191a1a98","kind":"subsection","labels":["eq:UFE","eq:bianchi","eq:maxwell"],"line_end":48,"line_start":5,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/003-section-the-unified-field-equation-ufe.tex","status_markers_as_written":[],"summary_excerpt":"UFE ActionUFEaction On a manifold [formula in source] with metric [formula in source] and torsionful connection [formula in source] , the action is:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Torsionful Geometric Action","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3626,"byte_start":2083,"id":"section:10d9c779ca40ac7649a3","kind":"subsection","labels":[],"line_end":83,"line_start":49,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/003-section-the-unified-field-equation-ufe.tex","status_markers_as_written":[],"summary_excerpt":"Gravitational Coupling Consistencykappa The gravitational coupling [formula in source] (with dimension [formula in source] ) is constrained by consistency with the dimensionless ratio:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gravitational Coupling from Invariants","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3818,"byte_start":3626,"id":"section:6dcbfa5d1c74c4b52222","kind":"section","labels":[],"line_end":87,"line_start":84,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/003-section-the-unified-field-equation-ufe.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Observable Predictions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4285,"byte_start":3818,"id":"section:4050ae2b761d824de261","kind":"subsection","labels":[],"line_end":99,"line_start":88,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/003-section-the-unified-field-equation-ufe.tex","status_markers_as_written":[],"summary_excerpt":"Axion–Photon Couplinggagg The CFE fixes the axion–photon vertex uniquely: This determines cosmic birefringence without free parameters.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Axion–Photon Coupling","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5352,"byte_start":4285,"id":"section:fd8cfd9286b095644a08","kind":"subsection","labels":[],"line_end":124,"line_start":100,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/003-section-the-unified-field-equation-ufe.tex","status_markers_as_written":[],"summary_excerpt":"Topological Excursion Quantizationtopoexcursion The topological axion excursion is quantized in discrete sector changes: with [formula in source] the minimal nontrivial class. The corresponding birefringence is [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cosmic Birefringence","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10674,"byte_start":5352,"id":"section:3efc1763b268977a4a98","kind":"subsubsection","labels":["eq:shifted-axion-potential","fig:birefringence","sec:deltaa","tab:birefringence"],"line_end":236,"line_start":125,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/003-section-the-unified-field-equation-ufe.tex","status_markers_as_written":[],"summary_excerpt":"Goal: Provide one minimal dynamical realization compatible with the topological quantization (Definition","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dynamical Completion of the Excursion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12640,"byte_start":10674,"id":"section:811f5111c0547562d272","kind":"subsection","labels":["fig:twoloop"],"line_end":291,"line_start":237,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/003-section-the-unified-field-equation-ufe.tex","status_markers_as_written":[],"summary_excerpt":"RG FingerprintsRGfingerprints The TFPT invariants leave signatures in the RG flow of gauge couplings: where [formula in source] GeV.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Two-Loop RG Fingerprints","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12847,"byte_start":12640,"id":"section:59bee2c86cea527acc50","kind":"section","labels":[],"line_end":295,"line_start":292,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/003-section-the-unified-field-equation-ufe.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"The E [formula in source] Cascade and Block Constants","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15492,"byte_start":12847,"id":"section:5c6890c1bcec128c5b90","kind":"subsection","labels":[],"line_end":344,"line_start":296,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/003-section-the-unified-field-equation-ufe.tex","status_markers_as_written":[],"summary_excerpt":"E [formula in source] Orbit Graphorbitgraph Let [formula in source] denote the set of nilpotent orbits of the exceptional Lie algebra [formula in source] . For each orbit [formula in source] , define: [formula in source] : the dimension of the orbit as a variety [formula in source] : the ``centralizer dimension'' [formula in source] : the height (sum of coefficients in weighted Dynkin diagram) The orbit graph [formul","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nilpotent Orbit Structure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4582,"byte_start":0,"id":"section:e6e8c1a8b3302e0927d8","kind":"subsection","labels":["eq:ladder","fig:ladder"],"line_end":100,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/004-subsection-log-exact-ladder-formula.tex","status_markers_as_written":[],"summary_excerpt":"E [formula in source] Cascade LadderE8cascade For [formula in source] , the ladder values are: with:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Log-Exact Ladder Formula","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9073,"byte_start":4582,"id":"section:17befb00fbc452d61723","kind":"subsection","labels":["fig:blocks","tab:blocks"],"line_end":211,"line_start":101,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/004-subsection-log-exact-ladder-formula.tex","status_markers_as_written":[],"summary_excerpt":"For a 6D Weyl fermion zero mode on a boundary cycle [formula in source] with flat [formula in source] connection (holonomy [formula in source] ), the variation of [formula in source] under the connection is proportional to the quadratic charge index: The proportionality constant is fixed by the topological normalization [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Block Constant Formula and Derivation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10494,"byte_start":9073,"id":"section:255182c00f03a0b74096","kind":"subsection","labels":[],"line_end":244,"line_start":212,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/004-subsection-log-exact-ladder-formula.tex","status_markers_as_written":[],"summary_excerpt":"The neutrino block at [formula in source] provides concrete predictions for the seesaw mechanism.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neutrino Seesaw Predictions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10704,"byte_start":10494,"id":"section:fa97e576eb4a71e25d7a","kind":"section","labels":[],"line_end":248,"line_start":245,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/004-subsection-log-exact-ladder-formula.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Flavor Structure: The Z [formula in source] Architecture","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13335,"byte_start":10704,"id":"section:9a6cf004f64d626a8f44","kind":"subsection","labels":[],"line_end":300,"line_start":249,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/004-subsection-log-exact-ladder-formula.tex","status_markers_as_written":[],"summary_excerpt":"On a conformally flat boundary geometry, the unique projectively invariant quantity from four marked points is the cross-ratio. Any boundary monodromy acts as a PSL [formula in source] transformation. Therefore, relations depending only on boundary monodromies must be rational functions of a M\\\"obius map.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Universal Phase [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14739,"byte_start":13335,"id":"section:d34366260bdf9c429b4a","kind":"subsection","labels":[],"line_end":332,"line_start":301,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/004-subsection-log-exact-ladder-formula.tex","status_markers_as_written":[],"summary_excerpt":"Mass Ratios from M\\\"obius Mapmassratios The M\\\"obius map [formula in source] evaluated at cusps [formula in source] yields mass ratios:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"M\\\"obius Mass Relations","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16091,"byte_start":14739,"id":"section:30f4a0c0bdcc7dbcafdf","kind":"subsection","labels":[],"line_end":358,"line_start":333,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/004-subsection-log-exact-ladder-formula.tex","status_markers_as_written":[],"summary_excerpt":"Cabibbo AngleCabibbo The Cabibbo angle is fixed parameter-free by [formula in source] : PDG reference: [formula in source] . Deviation: [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cabibbo Angle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1966,"byte_start":0,"id":"section:f69d05e13c1deba52260","kind":"subsection","labels":[],"line_end":43,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/005-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"Identities, fonttitle= ] The PMNS matrix can be closed parameter-free using a single TFPT identity for [formula in source] combined with the trimaximal TM1 pattern.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"PMNS Neutrino Mixing: TM1 Pattern","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3685,"byte_start":1966,"id":"section:e268a265e935cc113747","kind":"section","labels":["eq:As","eq:R2action","eq:ns","eq:r","tab:inflation"],"line_end":84,"line_start":44,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/005-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"The TFPT topological correction scale is set by [formula in source] (cf.\\ [formula in source] ). In effective gravity, the leading higher-curvature completion compatible with general covariance is an [formula in source] term.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Inflation: [formula in source] Completion (Starobinsky Limit)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4925,"byte_start":3685,"id":"section:9122988a0588846d0bbd","kind":"subsection","labels":["sec:r2derive"],"line_end":109,"line_start":85,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/005-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"Relevant Torsion DegreesR2torsion Decompose torsion into irreducible parts [formula in source] (axial, trace, tensor). In the minimal UFE setting the dominant coupling is through axial torsion [formula in source] , and the torsion sector is treated at quadratic order so it can be integrated out in the one-loop effective action.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[formula in source] Term from the Torsionful Effective Action","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5774,"byte_start":4925,"id":"section:81858557a0af040e72c6","kind":"subsection","labels":["eq:R2scale"],"line_end":129,"line_start":110,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/005-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"TFPT [formula in source] ScaleR2coeff Using the GR renormalization condition (A8) to fix the scheme, the coefficient of the [formula in source] term yields Here the square root applies only to [formula in source] , consistent with the numerical value above.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Coefficient Identification and GR Renormalization","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7309,"byte_start":5774,"id":"section:fd303e568e3e81e54fda","kind":"subsection","labels":["sec:bounce"],"line_end":162,"line_start":130,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/005-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"Bounce-to-Inflation Backgroundbouncebg Assume a non-singular bounce driven by the torsion-induced [formula in source] term (Lemma above), followed by a transition into the [formula in source] inflationary phase. We take the CMB pivot scales to exit the horizon during the [formula in source] phase.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bounce + [formula in source] Perturbations and Transfer Function","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7510,"byte_start":7309,"id":"section:18fe0def9da49b078985","kind":"section","labels":[],"line_end":166,"line_start":163,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/005-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Axion Cosmology and Dark Matter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9687,"byte_start":7510,"id":"section:409df341e1b33d68d749","kind":"subsection","labels":[],"line_end":205,"line_start":167,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/005-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"The TFPT axion sector is split into two distinct fields to avoid an internal contradiction (a single [formula in source] eV axion cannot remain quasi-static over Hubble times):","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Two-Field Structure: Topological vs.\\ QCD Axion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12474,"byte_start":9687,"id":"section:148e9be3410771be48ac","kind":"subsection","labels":[],"line_end":257,"line_start":206,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/005-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"Axion Dark Matter ParametersaxionDM For the QCD axion field [formula in source] from the E [formula in source] cascade (PQ block at [formula in source] ):","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dark Matter Relic Density","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14010,"byte_start":12474,"id":"section:b0359716445b4d18d22d","kind":"section","labels":["tab:beta"],"line_end":286,"line_start":258,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/005-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"The parameter [formula in source] provides a compact dictionary for expressing multiple quantities. Most equalities in this section are algebraic rewrites of earlier definitions rather than independent new inputs (see Appendix Inflation observables additionally depend on a dynamical completion (here: the conditional [formula in source] sector in Theorem","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[formula in source] -Centric Identity Summary","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16427,"byte_start":14010,"id":"section:b26ca7abe6aad5e79152","kind":"section","labels":["tab:status"],"line_end":326,"line_start":287,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/005-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"@p3cmp4cmp3cml@ Domain & Quantity & Deviation & Status\\\\ 4l Structural (parameter-free)\\\\ CFE & [formula in source] & [formula in source] ppm & green!60!black Closed-form consequence of defect sector reweighting on the orientable double cover\\\\ UFE & [formula in source] & 0.5–1.7 [formula in source] & green!60!black Solid\\\\ Cabibbo & [formula in source] & [formula in source] & green!60!black Solid\\\\ 4l RG-dressed\\\\ T","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Summary of Claims and Status","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17063,"byte_start":16427,"id":"section:77b7aa6081f9cae7dd93","kind":"section","labels":[],"line_end":340,"line_start":327,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/005-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"The following are not required: Slow-roll inflation (specific model) String landscape or anthropic selection Extra dimensions as free parameters Dark matter entirely from axions New particles beyond minimal axion sector Any fitted or adjusted parameters","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"What TFPT Does Not Assume","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18348,"byte_start":17063,"id":"section:b83ac41055cdd297365c","kind":"section","labels":[],"line_end":368,"line_start":341,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/005-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"TFPT demonstrates that the fine-structure constant [formula in source] can be derived from first principles using eight minimal axioms rooted in topology, geometry, and quantum consistency. The key results are:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conclusions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1387,"byte_start":0,"id":"section:082efec8052f7da9a4f1","kind":"section","labels":["tab:constants"],"line_end":33,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"@ll@ Quantity & Value\\\\ [formula in source] & 0.0397887357729738339\\\\ [formula in source] & 0.0530516476972984453\\\\ [formula in source] & 0.000120304479547082053\\\\ [formula in source] & 0.0531719521768455273\\\\ [formula in source] (self-consistent) & 0.053170209119023745\\\\ [formula in source] & 0.00423128951139541511\\\\ [formula in source] & [formula in source] \\\\ [formula in source] (E [formula in source] closure) & [","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Numerical Constants (High Precision)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8804,"byte_start":1387,"id":"section:188b729a423721ba1587","kind":"section","labels":["eq:CFE-appendix","eq:potential","eq:stationarity"],"line_end":187,"line_start":34,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"In background-field gauge, the one-loop effective potential for the electromagnetic coupling modulus takes the form. Here [formula in source] is the induced potential for [formula in source] after rewriting [formula in source] :","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of the CFE from the Effective Potential","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9880,"byte_start":8804,"id":"section:efccd6aa3ef98dcb26f3","kind":"section","labels":[],"line_end":220,"line_start":188,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":["relation:562a964eccad8ba4c9b8","relation:92dcdaae85811bf4057d","relation:df5821902ef3de18b179"],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"The TFPT verification suite (v5) runs 10 independent modules, with two additional modules planned for the [formula in source] effective action and bounce perturbations that complete the inflation/bounce closure:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verification Suite Summary","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10141,"byte_start":9880,"id":"section:ad71b3c13296b82d1d5e","kind":"section","labels":["app:E8cert"],"line_end":227,"line_start":221,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"This appendix provides the complete verification data for the E [formula in source] chain uniqueness theorem (Theorem","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"E [formula in source] Chain Certificate","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10645,"byte_start":10141,"id":"section:6562bef77b0a2a47fef3","kind":"subsection","labels":[],"line_end":237,"line_start":228,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"Each nilpotent orbit [formula in source] of [formula in source] is characterized by: Bala–Carter label: Standard notation (e.g., [formula in source] , [formula in source] , [formula in source] , ) Dimension: [formula in source] Centralizer dimension: [formula in source] Height: [formula in source] (sum of weighted Dynkin diagram coefficients)","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Orbit Data Structure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11321,"byte_start":10645,"id":"section:3f32dd65e0061cf6f60e","kind":"subsection","labels":[],"line_end":262,"line_start":238,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"The complete chain from [formula in source] to [formula in source] :","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Unique Chain (Excerpt)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12089,"byte_start":11321,"id":"section:6158cbfedc1dac1b49e9","kind":"subsection","labels":[],"line_end":277,"line_start":263,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"The uniqueness is verified by: Constructing the complete Hasse diagram of [formula in source] from standard tables. Computing all cover relations with [formula in source] . Running dynamic programming to find all paths from [formula in source] to [formula in source] . Applying the cost function [formula in source] (second-difference smoothness). Verifying that the minimum-cost path is unique (cost gap to second-best ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verification Algorithm","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12329,"byte_start":12089,"id":"section:50db69b4c472df7bd752","kind":"section","labels":["app:boundary"],"line_end":284,"line_start":278,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"This appendix derives the block index formula [formula in source] from the APS index theorem.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Boundary Trace Derivation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12720,"byte_start":12329,"id":"section:1054120bac361235aedf","kind":"subsection","labels":[],"line_end":294,"line_start":285,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"Consider a 6D manifold [formula in source] with boundary [formula in source] . For a Weyl fermion coupled to a [formula in source] gauge field [formula in source] , the APS index theorem gives: where [formula in source] is the [formula in source] -invariant of the boundary Dirac operator.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13233,"byte_start":12720,"id":"section:9182e009d884f4280f17","kind":"subsection","labels":[],"line_end":309,"line_start":295,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"On the orientable double cover [formula in source] , the boundary decomposes as: (two boundary cycles plus the twist seam).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Flat Connection on Boundary Cycles","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13751,"byte_start":13233,"id":"section:e9139d31ed0b4d061a84","kind":"subsection","labels":[],"line_end":319,"line_start":310,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"The regulated determinant of the hypercharge-coupled Dirac operator contains a universal UV logarithmic term whose coefficient is the quadratic charge trace: Thus [formula in source] appears as a spectral index coefficient, independent of IR thresholds, matching its role in the CFE.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spectral Trace Coefficient and [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14497,"byte_start":13751,"id":"section:a950717b2da5823b1426","kind":"subsection","labels":[],"line_end":339,"line_start":320,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"Step 1: Each boundary cycle contributes a factor proportional to [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14745,"byte_start":14497,"id":"section:c15b922a76a054d23f09","kind":"section","labels":["app:seam"],"line_end":345,"line_start":340,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"This appendix provides the [formula in source] -invariant gluing derivation used in Axiom","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Seam Gluing and the [formula in source] -Invariant Normalization","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15347,"byte_start":14745,"id":"section:c3bdb2280b873d750721","kind":"subsection","labels":[],"line_end":356,"line_start":346,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the orientable double cover of the M\\\"obius fiber and cut it along the seam [formula in source] to obtain a manifold-with-boundary [formula in source] with boundary components [formula in source] . Let [formula in source] be the Dirac operator on [formula in source] with APS boundary conditions on [formula in source] and a unitary matching operator [formula in source] identifying [formula i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cut Space and Operators","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15926,"byte_start":15347,"id":"section:b2cd593845c8a801d122","kind":"subsection","labels":[],"line_end":369,"line_start":357,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"The APS gluing theorem expresses the [formula in source] -invariant of the glued manifold in terms of the cut manifold plus a discrete spectral-flow correction: where [formula in source] is the spectral flow of the matching operator. In TFPT bookkeeping this contributes a quantized seam term to the curvature normalization.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gluing Formula for the [formula in source] -Invariant","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":284,"byte_start":0,"id":"section:78aaf645e907e2d5033c","kind":"subsection","labels":[],"line_end":7,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"For the M\\\"obius [formula in source] identification, the matching satisfies [formula in source] . The minimal nontrivial class is modeled by the unitary phase","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"M\\\"obius Matching and the Minimal Gluing Class","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":950,"byte_start":284,"id":"section:aa7edc2915180874aea4","kind":"subsection","labels":[],"line_end":24,"line_start":8,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"Interpolate boundary conditions by a phase [formula in source] , which gives the eigenvalues As [formula in source] runs from [formula in source] to [formula in source] , exactly one eigenvalue crosses zero, so [formula in source] and [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spectral Flow Computation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1371,"byte_start":950,"id":"section:ce0d2e0d4e6c937c734d","kind":"subsection","labels":[],"line_end":33,"line_start":25,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"The two physical boundary cycles contribute [formula in source] , and the seam gluing adds [formula in source] , so the total curvature is [formula in source] . The stationarity normalization [formula in source] therefore yields","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Normalization of [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1813,"byte_start":1371,"id":"section:d920158704431b9f1017","kind":"section","labels":["app:48deriv"],"line_end":44,"line_start":34,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"This appendix explains the integer coefficient in [formula in source] . The key point is that the canonical quantity is and the appearance of ``48'' is simply the same number expressed in units of [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of the Coefficient 48 in [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2537,"byte_start":1813,"id":"section:2d9cc02721cd43cbe0bc","kind":"subsection","labels":[],"line_end":57,"line_start":45,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"The topological correction [formula in source] arises from the leading gauge-invariant correction to the tree-level geometric scale [formula in source] . The requirements are: Gauge invariance: The correction must be built from [formula in source] only (no explicit [formula in source] dependence at this order). Dimensionlessness: Since [formula in source] is dimensionless, the correction must be a pure power [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Physical Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3298,"byte_start":2537,"id":"section:a7a83179ab1a2bc94fbc","kind":"subsection","labels":[],"line_end":74,"line_start":58,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"The effective action on the M\\\"obius fiber includes the Chern–Simons term [formula in source] . The leading topological correction comes from the one-loop determinant of the Dirac operator coupled to this background.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Power Counting: Why [formula in source] ?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3693,"byte_start":3298,"id":"section:952d3c2cec115d20459a","kind":"subsection","labels":[],"line_end":84,"line_start":75,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"The non-orientable identification acts as a [formula in source] operation on the base, but in the spin bundle the same element lifts to order [formula in source] because a [formula in source] rotation acts as [formula in source] on spinors and only a [formula in source] rotation is trivial. This produces a universal deficit factor per minimal sector.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spin-Lifted Deficit Factor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4199,"byte_start":3693,"id":"section:95dbb645d067a4e3d5ce","kind":"subsection","labels":[],"line_end":94,"line_start":85,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"Cutting along [formula in source] yields boundary components [formula in source] . The four local corner patches [formula in source] , [formula in source] , [formula in source] , [formula in source] constitute the fundamental domain. Summing the spin-lifted deficit factor over these sectors yields In TFPT normalization this yields the canonical form [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Sector Count from Cut Geometry","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4500,"byte_start":4199,"id":"section:ba052e0288a7739aec1c","kind":"subsection","labels":[],"line_end":104,"line_start":95,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"Using [formula in source] : so [formula in source] and [formula in source] are exactly equivalent.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conversion to the [formula in source] normalization","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4814,"byte_start":4500,"id":"section:0dde3d2251dd28b73ba7","kind":"subsection","labels":[],"line_end":110,"line_start":105,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"The spin-lift argument fixes the [formula in source] deficit factor robustly, and the sector count is fixed by seam symmetry. The seam normalization is provided by the [formula in source] -gluing derivation in Appendix","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Status note","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5047,"byte_start":4814,"id":"section:0eab60977b88c1256e80","kind":"section","labels":["app:flavor"],"line_end":116,"line_start":111,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"This appendix derives the M\\\"obius structure of flavor relations from boundary monodromy.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Flavor Monodromy and Cross-Ratio","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5770,"byte_start":5047,"id":"section:3cedcb53c22231f6ea49","kind":"subsection","labels":[],"line_end":134,"line_start":117,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"On a conformally flat boundary, the metric is locally: Holomorphic automorphisms (Wilson lines of flat connections) act as M\\\"obius transformations:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Projective Invariance on Boundaries","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6204,"byte_start":5770,"id":"section:e06c2296394d9c849126","kind":"subsection","labels":[],"line_end":145,"line_start":135,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"Given four marked points [formula in source] on the boundary, the unique projective invariant is the cross-ratio:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cross-Ratio as Unique Invariant","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6742,"byte_start":6204,"id":"section:3e4c6e7716cbca8d8c00","kind":"subsection","labels":[],"line_end":156,"line_start":146,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"The cusps [formula in source] arise from: Rationality: Quantized holonomies [formula in source] rational cusps. GUT compatibility: SU(5) hypercharge assignments give [formula in source] (quarks), [formula in source] (leptons), etc. Uniqueness: These are the only rational values that simultaneously separate the three SM sectors (up, down, lepton) and maintain GUT normalization.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cusp Selection","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7423,"byte_start":6742,"id":"section:56bd6747c27e02598c5e","kind":"subsection","labels":[],"line_end":175,"line_start":157,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"Leading term: [formula in source] from the abelian trace (same as [formula in source] numerator divided by 41/10's denominator structure).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8668,"byte_start":7423,"id":"section:397bfd1e9f74b6603a74","kind":"section","labels":["app:repro"],"line_end":204,"line_start":176,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":["relation:063efae9f98b0e479c88","relation:343750fc1f508fd487dc","relation:e9b9c97cc7ebfe1a733f"],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"Replication package: All numerical results can be reproduced using the TFPT verification suite (v5).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproducibility","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10769,"byte_start":8668,"id":"section:f93e7dffcdac0bc7be6f","kind":"section","labels":["app:identities"],"line_end":241,"line_start":205,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"This appendix labels frequently used equalities by logical status to prevent conflating definitions, algebraic rewrites, and genuine predictions.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Identity Catalogue and Status Labels","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11581,"byte_start":10769,"id":"section:8d2939f1c554334c8d9c","kind":"section","labels":["app:r2"],"line_end":255,"line_start":242,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"K1: Field content and torsionful Lagrangian fixed by the minimal UFE sector. K2: Quadratic fluctuation operator is of Laplace type after background-field gauge fixing. K3: Heat-kernel coefficient [formula in source] captures the curvature-squared terms in [formula in source] . K4: Matching to [formula in source] after imposing the GR renormalization condition.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"One-Loop Effective Action in Riemann–Cartan and the [formula in source] Coefficient","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11939,"byte_start":11581,"id":"section:a7e9094b61060a2409b0","kind":"subsection","labels":[],"line_end":261,"line_start":256,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"We evaluate the one-loop effective action in a Riemann–Cartan background with torsion decomposed into axial [formula in source] , trace [formula in source] , and tensor [formula in source] . The minimal UFE choice treats torsion at quadratic order, so integrating out torsion is Gaussian and parameter-free once [formula in source] fixes the normalization of the coupling.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.1 Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12302,"byte_start":11939,"id":"section:7416b7898474f3575c7c","kind":"subsection","labels":[],"line_end":270,"line_start":262,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"After background-field gauge fixing, the quadratic operator for torsion fluctuations can be written in Laplace type, with [formula in source] built from curvature and torsion invariants. The contribution to [formula in source] is [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.2 Operator Form","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12672,"byte_start":12302,"id":"section:79f732d83b71790b7cdd","kind":"subsection","labels":[],"line_end":278,"line_start":271,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"The local part of [formula in source] is governed by the heat-kernel expansion where [formula in source] contains the curvature-squared terms. The torsion-dependent pieces combine into an effective [formula in source] operator in the low-energy action.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.3 Heat-Kernel Coefficients","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12873,"byte_start":12672,"id":"section:26f431f18ee407a2e4ba","kind":"subsection","labels":[],"line_end":282,"line_start":279,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"The GR limit (A8) fixes the renormalization scheme by requiring that the [formula in source] limit reduces to the Einstein–Hilbert action with coefficient [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.4 Renormalization Condition","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13238,"byte_start":12873,"id":"section:8f1725552636d4d857c0","kind":"subsection","labels":[],"line_end":291,"line_start":283,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"With the TFPT normalization of the torsion sector, the induced [formula in source] coefficient is fixed by [formula in source] , yielding which reproduces","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.5 TFPT Closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13688,"byte_start":13238,"id":"section:b20bca9c8966ce00aa28","kind":"section","labels":["app:bounce"],"line_end":301,"line_start":292,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"This appendix provides a minimal outline; the full numerical transfer-function evaluation is scheduled for the bounce_perturbations verification module.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bounce Perturbations and the Transfer Function","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14002,"byte_start":13688,"id":"section:d9e87b6aad6ab546be24","kind":"subsection","labels":[],"line_end":306,"line_start":302,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"The bounce background is modeled by a smooth scale factor [formula in source] where the torsion-induced [formula in source] term regularizes [formula in source] for scalar perturbations. The transition to the [formula in source] inflationary phase is implemented by matching [formula in source] and its derivatives at [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.1 Background Solution","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14295,"byte_start":14002,"id":"section:6536915a687d0600ffc8","kind":"subsection","labels":[],"line_end":311,"line_start":307,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"Mode functions are initialized in an adiabatic vacuum well before the bounce and integrated through the bounce and into the [formula in source] era. The numerical scheme records the transfer function by comparing late-time solutions to the pure [formula in source] baseline.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.2 Numerical Integration Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14604,"byte_start":14295,"id":"section:bf4ffbd07b64a6e4ea88","kind":"subsection","labels":[],"line_end":319,"line_start":312,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"Define the transfer function as with [formula in source] for modes well inside the horizon during the bounce and deviations confined to [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.3 Transfer Function","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14983,"byte_start":14604,"id":"section:5bf5d23f735cfedf0952","kind":"subsection","labels":[],"line_end":325,"line_start":320,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"Large-scale suppression or oscillatory features in [formula in source] are predicted at [formula in source] . Current CMB large-scale bounds constrain the allowable feature amplitude, providing a direct observational test of the bounce completion.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.4 Falsification Targets","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16873,"byte_start":14983,"id":"section:3bcafb6e9255ac116ea7","kind":"section","labels":[],"line_end":366,"line_start":326,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv21"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv21/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"] F. W. Hehl, P. von der Heyde, G. D. Kerlick, J. M. Nester, ``General Relativity with Spin and Torsion: Foundations and Prospects,'' Rev.\\ Mod.\\ Phys.\\ 48, 393 (1976).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"References","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2993,"byte_start":0,"id":"section:10a1d8cc14dfd8f7eaf2","kind":"frontmatter","labels":[],"line_end":105,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/preamble.tex","status_markers_as_written":[],"summary_excerpt":"compat=1.18 arrows.meta,positioning,decorations.markings,decorations.pathmorphing,calc,patterns,shapes.geometric","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Topological Fixed Point Theory (TFPT)\\\\[0.5em] A Parameter-Free Derivation of the Fine-Structure Constant\\\\ from Topology, Geometry, and Quantum Consistency","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6473,"byte_start":0,"id":"section:79bdfaf90806d822de39","kind":"frontmatter","labels":[],"line_end":97,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/001-section-introduction-the-problem-of-parameters.tex","status_markers_as_written":[],"summary_excerpt":"We present the complete axiomatic foundation of Topological Fixed Point Theory (TFPT), which derives the fine-structure constant [formula in source] and other fundamental quantities from eight minimal assumptions rooted in topology, geometry, and quantum field theory. The theory rests on two fundamental invariants: the topological coupling [formula in source] from 11D Chern–Simons quantization and the geometric scale","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8835,"byte_start":6473,"id":"section:1b16c6794f58780121e2","kind":"section","labels":["fig:flow"],"line_end":145,"line_start":98,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/001-section-introduction-the-problem-of-parameters.tex","status_markers_as_written":[],"summary_excerpt":"The Standard Model of particle physics contains approximately 19 free parameters that must be determined experimentally. Among these, the fine-structure constant [formula in source] stands out as a dimensionless number whose value has no explanation within conventional frameworks.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Introduction: The Problem of Parameters","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9254,"byte_start":8835,"id":"section:8f6f6ccee4d1d1c5c784","kind":"section","labels":[],"line_end":153,"line_start":146,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/001-section-introduction-the-problem-of-parameters.tex","status_markers_as_written":[],"summary_excerpt":"TFPT is built on eight axioms, organized into three categories: geometric structure, quantum field theory, and closure conditions. Each axiom is either derived from established physics or explicitly marked as a new postulate.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Axiomatic Foundation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16714,"byte_start":9254,"id":"section:4a83b858aece5de4bd21","kind":"subsection","labels":["fig:doublecover"],"line_end":313,"line_start":154,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/001-section-introduction-the-problem-of-parameters.tex","status_markers_as_written":[],"summary_excerpt":"Riemann–Cartan GeometryRC The fundamental spacetime connection possesses torsion; the Levi-Civita connection is a limiting case when torsion vanishes.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Geometric Axioms (A1–A4)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20410,"byte_start":16714,"id":"section:d8331cdde639dcd10021","kind":"subsection","labels":[],"line_end":393,"line_start":314,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/001-section-introduction-the-problem-of-parameters.tex","status_markers_as_written":[],"summary_excerpt":"Units and constants: Natural units: [formula in source] ; energies in GeV, lengths in GeV [formula in source] . Reference data: CODATA 2022, PDG 2024. Metric signature: [formula in source] . Levi-Civita tensor: [formula in source] , [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Quantum Field Theory Axioms (A5–A6)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4318,"byte_start":0,"id":"section:81c4ccb87c14c049cb93","kind":"subsection","labels":[],"line_end":72,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/002-subsection-closure-axioms-a7-a8.tex","status_markers_as_written":[],"summary_excerpt":"Standard Model Hypercharge TraceSMT The hypercharge trace invariant, summed over all SM fermions with GUT normalization [formula in source] , is: In TFPT this quantity appears as the spectral quadratic index of the hypercharge-coupled boundary operators in the regulated determinant (Appendix","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Closure Axioms (A7–A8)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4523,"byte_start":4318,"id":"section:60e63c33304aaad41fb1","kind":"section","labels":[],"line_end":76,"line_start":73,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/002-subsection-closure-axioms-a7-a8.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Derivation of Fundamental Constants","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6448,"byte_start":4523,"id":"section:d7087868b3b58656d561","kind":"subsection","labels":[],"line_end":121,"line_start":77,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/002-subsection-closure-axioms-a7-a8.tex","status_markers_as_written":[],"summary_excerpt":"Existence and Uniqueness of [formula in source] phi0 From Axioms A3 and A4, the geometric scale is uniquely determined:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Geometric Scale [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10101,"byte_start":6448,"id":"section:5944eb61aca94ebf6f89","kind":"subsection","labels":["eq:CFE","fig:CFE"],"line_end":210,"line_start":122,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/002-subsection-closure-axioms-a7-a8.tex","status_markers_as_written":[],"summary_excerpt":"Effective Potential Parametersparams From the 11D Chern–Simons reduction (A5) and modulus-closure structure (A6): Notation: We use [formula in source] (calligraphic) for this CFE parameter to distinguish it from [formula in source] (gravitational coupling).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Cubic Fixed-Point Equation (CFE)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10236,"byte_start":10101,"id":"section:4a585901c491ce88713a","kind":"subsection","labels":[],"line_end":213,"line_start":211,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/002-subsection-closure-axioms-a7-a8.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Geometric Self-Consistency (Backreaction)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15379,"byte_start":10236,"id":"section:7bfc3cbb6b08ec2373eb","kind":"subsubsection","labels":["eq:backreaction","tab:alpha"],"line_end":329,"line_start":214,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/002-subsection-closure-axioms-a7-a8.tex","status_markers_as_written":[],"summary_excerpt":"The response [formula in source] is the closed form consequence of defect sector reweighting on the orientable double cover. The linear form is the [formula in source] expansion, not a separate assumption.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Backreaction as Structural Response","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18000,"byte_start":15379,"id":"section:f56abb78d8bbaf71d79b","kind":"subsubsection","labels":["fig:deviation","sec:sensitivity"],"line_end":401,"line_start":330,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/002-subsection-closure-axioms-a7-a8.tex","status_markers_as_written":[],"summary_excerpt":"The sub-ppm precision of the [formula in source] prediction depends critically on the backreaction coefficient. We analyze the sensitivity to demonstrate this is not fine-tuning but a genuine geometric constraint.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Sensitivity Analysis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":202,"byte_start":0,"id":"section:8636a69caaf950ec48ed","kind":"section","labels":[],"line_end":4,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/003-section-the-unified-field-equation-ufe.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"The Unified Field Equation (UFE)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3548,"byte_start":202,"id":"section:eca4e8e062790f2964a5","kind":"subsection","labels":["eq:UFE","eq:bianchi","eq:maxwell"],"line_end":61,"line_start":5,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/003-section-the-unified-field-equation-ufe.tex","status_markers_as_written":[],"summary_excerpt":"UFE ActionUFEaction On a manifold [formula in source] with metric [formula in source] and torsionful connection [formula in source] , the action is: Here [formula in source] denotes the Ricci scalar constructed from the full torsionful connection [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Torsionful Geometric Action","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5051,"byte_start":3548,"id":"section:648f2f80f128793550e7","kind":"subsection","labels":[],"line_end":96,"line_start":62,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/003-section-the-unified-field-equation-ufe.tex","status_markers_as_written":[],"summary_excerpt":"Gravitational Coupling Consistencykappa The gravitational coupling [formula in source] (with dimension [formula in source] ) is constrained by consistency with the dimensionless ratio:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gravitational Coupling from Invariants","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5243,"byte_start":5051,"id":"section:e1c71b6b348f18458e5e","kind":"section","labels":[],"line_end":100,"line_start":97,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/003-section-the-unified-field-equation-ufe.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Observable Predictions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5710,"byte_start":5243,"id":"section:03934240990a7fbb935d","kind":"subsection","labels":[],"line_end":112,"line_start":101,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/003-section-the-unified-field-equation-ufe.tex","status_markers_as_written":[],"summary_excerpt":"Axion–Photon Couplinggagg The CFE fixes the axion–photon vertex uniquely: This determines cosmic birefringence without free parameters.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Axion–Photon Coupling","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7053,"byte_start":5710,"id":"section:6a8a9f5007e4a25ad6bb","kind":"subsection","labels":[],"line_end":139,"line_start":113,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/003-section-the-unified-field-equation-ufe.tex","status_markers_as_written":[],"summary_excerpt":"Topological Excursion Quantizationtopoexcursion The topological axion excursion is quantized in discrete sector changes: with [formula in source] the minimal nontrivial class. The corresponding birefringence is [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cosmic Birefringence","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12375,"byte_start":7053,"id":"section:c24af750584761f7e90d","kind":"subsubsection","labels":["eq:shifted-axion-potential","fig:birefringence","sec:deltaa","tab:birefringence"],"line_end":251,"line_start":140,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/003-section-the-unified-field-equation-ufe.tex","status_markers_as_written":[],"summary_excerpt":"Goal: Provide one minimal dynamical realization compatible with the topological quantization (Definition","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dynamical Completion of the Excursion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14685,"byte_start":12375,"id":"section:4df73a5cf1b70eb71472","kind":"subsection","labels":["fig:twoloop"],"line_end":306,"line_start":252,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/003-section-the-unified-field-equation-ufe.tex","status_markers_as_written":[],"summary_excerpt":"RG FingerprintsRGfingerprints The TFPT invariants leave signatures in the RG flow of gauge couplings: These values are obtained by two-loop RG running from PDG boundary conditions at [formula in source] using the declared PyR@TE model (checked by two_loop_rg_fingerprints in tfpt-suite/; not direct measurements at the quoted scales). Here [formula in source] GeV.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Two-Loop RG Fingerprints","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14892,"byte_start":14685,"id":"section:54811be7ad8b4853c0f4","kind":"section","labels":[],"line_end":310,"line_start":307,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/003-section-the-unified-field-equation-ufe.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"The E [formula in source] Cascade and Block Constants","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17537,"byte_start":14892,"id":"section:c24722e672d4a8e58a23","kind":"subsection","labels":[],"line_end":359,"line_start":311,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/003-section-the-unified-field-equation-ufe.tex","status_markers_as_written":[],"summary_excerpt":"E [formula in source] Orbit Graphorbitgraph Let [formula in source] denote the set of nilpotent orbits of the exceptional Lie algebra [formula in source] . For each orbit [formula in source] , define: [formula in source] : the dimension of the orbit as a variety [formula in source] : the ``centralizer dimension'' [formula in source] : the height (sum of coefficients in weighted Dynkin diagram) The orbit graph [formul","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nilpotent Orbit Structure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4582,"byte_start":0,"id":"section:ccd042507df59a8d1cec","kind":"subsection","labels":["eq:ladder","fig:ladder"],"line_end":100,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/004-subsection-log-exact-ladder-formula.tex","status_markers_as_written":[],"summary_excerpt":"E [formula in source] Cascade LadderE8cascade For [formula in source] , the ladder values are: with:","summary_method":"opening prose excerpt; 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Any boundary monodromy acts as a PSL [formula in source] transformation. Therefore, relations depending only on boundary monodromies must be rational functions of a M\\\"obius map.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Universal Phase [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14739,"byte_start":13335,"id":"section:c10386b9ef40f4363822","kind":"subsection","labels":[],"line_end":332,"line_start":301,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/004-subsection-log-exact-ladder-formula.tex","status_markers_as_written":[],"summary_excerpt":"Mass Ratios from M\\\"obius Mapmassratios The M\\\"obius map [formula in source] evaluated at cusps [formula in source] yields mass ratios:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"M\\\"obius Mass Relations","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16344,"byte_start":14739,"id":"section:6f1bcf96faefa91aa66e","kind":"subsection","labels":[],"line_end":358,"line_start":333,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/004-subsection-log-exact-ladder-formula.tex","status_markers_as_written":[],"summary_excerpt":"Cabibbo AngleCabibbo The Cabibbo angle is fixed parameter-free by [formula in source] : PDG reference: [formula in source] . Deviation: [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cabibbo Angle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1966,"byte_start":0,"id":"section:fd4bc0be2130193c6e16","kind":"subsection","labels":[],"line_end":43,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/005-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"Identities, fonttitle= ] The PMNS matrix can be closed parameter-free using a single TFPT identity for [formula in source] combined with the trimaximal TM1 pattern.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"PMNS Neutrino Mixing: TM1 Pattern","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3685,"byte_start":1966,"id":"section:11526387978d591bbd8d","kind":"section","labels":["eq:As","eq:R2action","eq:ns","eq:r","tab:inflation"],"line_end":84,"line_start":44,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/005-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"The TFPT topological correction scale is set by [formula in source] (cf.\\ [formula in source] ). In effective gravity, the leading higher-curvature completion compatible with general covariance is an [formula in source] term.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Inflation: [formula in source] Completion (Starobinsky Limit)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4925,"byte_start":3685,"id":"section:7804e724e666c40bbbd6","kind":"subsection","labels":["sec:r2derive"],"line_end":109,"line_start":85,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/005-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"Relevant Torsion DegreesR2torsion Decompose torsion into irreducible parts [formula in source] (axial, trace, tensor). In the minimal UFE setting the dominant coupling is through axial torsion [formula in source] , and the torsion sector is treated at quadratic order so it can be integrated out in the one-loop effective action.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[formula in source] Term from the Torsionful Effective Action","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5802,"byte_start":4925,"id":"section:a2a99b369e27b25dbe86","kind":"subsection","labels":["eq:R2scale"],"line_end":129,"line_start":110,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/005-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"TFPT [formula in source] ScaleR2coeff Using the GR renormalization condition (A8) to fix the scheme, the coefficient of the [formula in source] term yields Here the square root applies only to [formula in source] , consistent with the numerical value above.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Coefficient Identification and GR Renormalization","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7337,"byte_start":5802,"id":"section:a58fb4918c59ec658569","kind":"subsection","labels":["sec:bounce"],"line_end":162,"line_start":130,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/005-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"Bounce-to-Inflation Backgroundbouncebg Assume a non-singular bounce driven by the torsion-induced [formula in source] term (Lemma above), followed by a transition into the [formula in source] inflationary phase. 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support/formula-only content is not paraphrased","title":"Axion Cosmology and Dark Matter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9715,"byte_start":7538,"id":"section:d8934d13884fd29d4d23","kind":"subsection","labels":[],"line_end":205,"line_start":167,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/005-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"The TFPT axion sector is split into two distinct fields to avoid an internal contradiction (a single [formula in source] eV axion cannot remain quasi-static over Hubble times):","summary_method":"opening prose excerpt; 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Most equalities in this section are algebraic rewrites of earlier definitions rather than independent new inputs (see Appendix Inflation observables additionally depend on a dynamical completion (here: the conditional [formula in source] sector in Theorem","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[formula in source] -Centric Identity Summary","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18220,"byte_start":14399,"id":"section:e7ce89f8559459d93580","kind":"section","labels":["tab:status"],"line_end":337,"line_start":286,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/005-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"@p3cmp4cmp3cml@ Domain & Quantity & Deviation & Status\\\\ 4l Structural (parameter-free)\\\\ CFE & [formula in source] & [formula in source] ppm & green!60!black Closed-form consequence of defect sector reweighting on the orientable double cover\\\\ UFE & [formula in source] & 0.5–1.7 [formula in source] & green!60!black Solid\\\\ Cabibbo & [formula in source] & [formula in source] & green!60!black Solid\\\\ 4l RG-dressed\\\\ T","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Summary of Claims and Status","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18856,"byte_start":18220,"id":"section:70aceda6bf8a0d46ccc0","kind":"section","labels":[],"line_end":351,"line_start":338,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/005-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"The following are not required: Slow-roll inflation (specific model) String landscape or anthropic selection Extra dimensions as free parameters Dark matter entirely from axions New particles beyond minimal axion sector Any fitted or adjusted parameters","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"What TFPT Does Not Assume","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20141,"byte_start":18856,"id":"section:528adb89168a764dda21","kind":"section","labels":[],"line_end":379,"line_start":352,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/005-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"TFPT demonstrates that the fine-structure constant [formula in source] can be derived from first principles using eight minimal axioms rooted in topology, geometry, and quantum consistency. The key results are:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conclusions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1387,"byte_start":0,"id":"section:43af2e360abc4637ddde","kind":"section","labels":["tab:constants"],"line_end":33,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"@ll@ Quantity & Value\\\\ [formula in source] & 0.0397887357729738339\\\\ [formula in source] & 0.0530516476972984453\\\\ [formula in source] & 0.000120304479547082053\\\\ [formula in source] & 0.0531719521768455273\\\\ [formula in source] (self-consistent) & 0.053170209119023745\\\\ [formula in source] & 0.00423128951139541511\\\\ [formula in source] & [formula in source] \\\\ [formula in source] (E [formula in source] closure) & [","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Numerical Constants (High Precision)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8804,"byte_start":1387,"id":"section:67dec930ed4a0951926e","kind":"section","labels":["eq:CFE-appendix","eq:potential","eq:stationarity"],"line_end":187,"line_start":34,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"In background-field gauge, the one-loop effective potential for the electromagnetic coupling modulus takes the form. Here [formula in source] is the induced potential for [formula in source] after rewriting [formula in source] :","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of the CFE from the Effective Potential","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9880,"byte_start":8804,"id":"section:46bc02793ebae03e1be1","kind":"section","labels":[],"line_end":220,"line_start":188,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":["relation:09b6ebe10b2fd657008e","relation:7fa3441fa81dc0a15d05","relation:d0d99967e2764d18dbd6"],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"The TFPT verification suite (v5) runs 10 independent modules, with two additional modules planned for the [formula in source] effective action and bounce perturbations that complete the inflation/bounce closure:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verification Suite Summary","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10141,"byte_start":9880,"id":"section:12f7b1eca79b36522f76","kind":"section","labels":["app:E8cert"],"line_end":227,"line_start":221,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"This appendix provides the complete verification data for the E [formula in source] chain uniqueness theorem (Theorem","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"E [formula in source] Chain Certificate","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10645,"byte_start":10141,"id":"section:e606725d1ec3f9b3e024","kind":"subsection","labels":[],"line_end":237,"line_start":228,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"Each nilpotent orbit [formula in source] of [formula in source] is characterized by: Bala–Carter label: Standard notation (e.g., [formula in source] , [formula in source] , [formula in source] , ) Dimension: [formula in source] Centralizer dimension: [formula in source] Height: [formula in source] (sum of weighted Dynkin diagram coefficients)","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Orbit Data Structure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11321,"byte_start":10645,"id":"section:79beb0a8831431946f23","kind":"subsection","labels":[],"line_end":262,"line_start":238,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"The complete chain from [formula in source] to [formula in source] :","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Unique Chain (Excerpt)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12089,"byte_start":11321,"id":"section:cf9ca0eb32a78484f335","kind":"subsection","labels":[],"line_end":277,"line_start":263,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"The uniqueness is verified by: Constructing the complete Hasse diagram of [formula in source] from standard tables. Computing all cover relations with [formula in source] . Running dynamic programming to find all paths from [formula in source] to [formula in source] . Applying the cost function [formula in source] (second-difference smoothness). Verifying that the minimum-cost path is unique (cost gap to second-best ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verification Algorithm","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12329,"byte_start":12089,"id":"section:22830a3e703266cb5577","kind":"section","labels":["app:boundary"],"line_end":284,"line_start":278,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"This appendix derives the block index formula [formula in source] from the APS index theorem.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Boundary Trace Derivation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12720,"byte_start":12329,"id":"section:054a586e4fa055d672b9","kind":"subsection","labels":[],"line_end":294,"line_start":285,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"Consider a 6D manifold [formula in source] with boundary [formula in source] . For a Weyl fermion coupled to a [formula in source] gauge field [formula in source] , the APS index theorem gives: where [formula in source] is the [formula in source] -invariant of the boundary Dirac operator.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13233,"byte_start":12720,"id":"section:c29f788a57c716f9f7ea","kind":"subsection","labels":[],"line_end":309,"line_start":295,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"On the orientable double cover [formula in source] , the boundary decomposes as: (two boundary cycles plus the twist seam).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Flat Connection on Boundary Cycles","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13751,"byte_start":13233,"id":"section:1ceed334e6d11d4cf184","kind":"subsection","labels":[],"line_end":319,"line_start":310,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"The regulated determinant of the hypercharge-coupled Dirac operator contains a universal UV logarithmic term whose coefficient is the quadratic charge trace: Thus [formula in source] appears as a spectral index coefficient, independent of IR thresholds, matching its role in the CFE.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spectral Trace Coefficient and [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14497,"byte_start":13751,"id":"section:6f156757227df61f2de9","kind":"subsection","labels":[],"line_end":339,"line_start":320,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"Step 1: Each boundary cycle contributes a factor proportional to [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14745,"byte_start":14497,"id":"section:28cbe89c6a53fdd895c3","kind":"section","labels":["app:seam"],"line_end":345,"line_start":340,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"This appendix provides the [formula in source] -invariant gluing derivation used in Axiom","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Seam Gluing and the [formula in source] -Invariant Normalization","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15347,"byte_start":14745,"id":"section:f583b38405d13c1096bd","kind":"subsection","labels":[],"line_end":356,"line_start":346,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the orientable double cover of the M\\\"obius fiber and cut it along the seam [formula in source] to obtain a manifold-with-boundary [formula in source] with boundary components [formula in source] . Let [formula in source] be the Dirac operator on [formula in source] with APS boundary conditions on [formula in source] and a unitary matching operator [formula in source] identifying [formula i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cut Space and Operators","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15926,"byte_start":15347,"id":"section:8f81c4f904ca1876ec00","kind":"subsection","labels":[],"line_end":369,"line_start":357,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/006-section-numerical-constants-high-precision.tex","status_markers_as_written":[],"summary_excerpt":"The APS gluing theorem expresses the [formula in source] -invariant of the glued manifold in terms of the cut manifold plus a discrete spectral-flow correction: where [formula in source] is the spectral flow of the matching operator. In TFPT bookkeeping this contributes a quantized seam term to the curvature normalization.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gluing Formula for the [formula in source] -Invariant","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":284,"byte_start":0,"id":"section:f939d71b3c301107fb9c","kind":"subsection","labels":[],"line_end":7,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"For the M\\\"obius [formula in source] identification, the matching satisfies [formula in source] . The minimal nontrivial class is modeled by the unitary phase","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"M\\\"obius Matching and the Minimal Gluing Class","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":950,"byte_start":284,"id":"section:c65208ce48869314e351","kind":"subsection","labels":[],"line_end":24,"line_start":8,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"Interpolate boundary conditions by a phase [formula in source] , which gives the eigenvalues As [formula in source] runs from [formula in source] to [formula in source] , exactly one eigenvalue crosses zero, so [formula in source] and [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spectral Flow Computation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1371,"byte_start":950,"id":"section:c5c21c85b6ba54188911","kind":"subsection","labels":[],"line_end":33,"line_start":25,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"The two physical boundary cycles contribute [formula in source] , and the seam gluing adds [formula in source] , so the total curvature is [formula in source] . The stationarity normalization [formula in source] therefore yields","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Normalization of [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1813,"byte_start":1371,"id":"section:9f511f04bd16a07a60db","kind":"section","labels":["app:48deriv"],"line_end":44,"line_start":34,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"This appendix explains the integer coefficient in [formula in source] . The key point is that the canonical quantity is and the appearance of ``48'' is simply the same number expressed in units of [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of the Coefficient 48 in [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2537,"byte_start":1813,"id":"section:ee42e0b09ec08b705f66","kind":"subsection","labels":[],"line_end":57,"line_start":45,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"The topological correction [formula in source] arises from the leading gauge-invariant correction to the tree-level geometric scale [formula in source] . The requirements are: Gauge invariance: The correction must be built from [formula in source] only (no explicit [formula in source] dependence at this order). Dimensionlessness: Since [formula in source] is dimensionless, the correction must be a pure power [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Physical Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3298,"byte_start":2537,"id":"section:6bd51ab22c346df853c7","kind":"subsection","labels":[],"line_end":74,"line_start":58,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"The effective action on the M\\\"obius fiber includes the Chern–Simons term [formula in source] . The leading topological correction comes from the one-loop determinant of the Dirac operator coupled to this background.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Power Counting: Why [formula in source] ?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3693,"byte_start":3298,"id":"section:c25ffcc7bdddeb7a7632","kind":"subsection","labels":[],"line_end":84,"line_start":75,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"The non-orientable identification acts as a [formula in source] operation on the base, but in the spin bundle the same element lifts to order [formula in source] because a [formula in source] rotation acts as [formula in source] on spinors and only a [formula in source] rotation is trivial. This produces a universal deficit factor per minimal sector.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spin-Lifted Deficit Factor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4199,"byte_start":3693,"id":"section:6d5fda9a04c25d0d19d9","kind":"subsection","labels":[],"line_end":94,"line_start":85,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"Cutting along [formula in source] yields boundary components [formula in source] . The four local corner patches [formula in source] , [formula in source] , [formula in source] , [formula in source] constitute the fundamental domain. Summing the spin-lifted deficit factor over these sectors yields In TFPT normalization this yields the canonical form [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Sector Count from Cut Geometry","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4500,"byte_start":4199,"id":"section:5f3f235665bc53ce064f","kind":"subsection","labels":[],"line_end":104,"line_start":95,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"Using [formula in source] : so [formula in source] and [formula in source] are exactly equivalent.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conversion to the [formula in source] normalization","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4814,"byte_start":4500,"id":"section:efa00888414c5cf3c810","kind":"subsection","labels":[],"line_end":110,"line_start":105,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"The spin-lift argument fixes the [formula in source] deficit factor robustly, and the sector count is fixed by seam symmetry. The seam normalization is provided by the [formula in source] -gluing derivation in Appendix","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Status note","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5047,"byte_start":4814,"id":"section:90ce82a5acc368eaa23f","kind":"section","labels":["app:flavor"],"line_end":116,"line_start":111,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"This appendix derives the M\\\"obius structure of flavor relations from boundary monodromy.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Flavor Monodromy and Cross-Ratio","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5770,"byte_start":5047,"id":"section:f0d58b24c37619710e53","kind":"subsection","labels":[],"line_end":134,"line_start":117,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"On a conformally flat boundary, the metric is locally: Holomorphic automorphisms (Wilson lines of flat connections) act as M\\\"obius transformations:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Projective Invariance on Boundaries","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6204,"byte_start":5770,"id":"section:51847e107bdbed2b614f","kind":"subsection","labels":[],"line_end":145,"line_start":135,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"Given four marked points [formula in source] on the boundary, the unique projective invariant is the cross-ratio:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cross-Ratio as Unique Invariant","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6742,"byte_start":6204,"id":"section:5b77dff132224f718261","kind":"subsection","labels":[],"line_end":156,"line_start":146,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"The cusps [formula in source] arise from: Rationality: Quantized holonomies [formula in source] rational cusps. GUT compatibility: SU(5) hypercharge assignments give [formula in source] (quarks), [formula in source] (leptons), etc. Uniqueness: These are the only rational values that simultaneously separate the three SM sectors (up, down, lepton) and maintain GUT normalization.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cusp Selection","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7423,"byte_start":6742,"id":"section:45a90177e3d089ffc953","kind":"subsection","labels":[],"line_end":175,"line_start":157,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"Leading term: [formula in source] from the abelian trace (same as [formula in source] numerator divided by 41/10's denominator structure).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8827,"byte_start":7423,"id":"section:d4b96114fb81cbb3762c","kind":"section","labels":["app:repro"],"line_end":204,"line_start":176,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":["relation:1a744a4991e8bb2efeda","relation:1e30c900a0403d236c40","relation:227a54d3bfff7bfaccdb"],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"Replication package: All numerical results can be reproduced using the TFPT verification suite (v5).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproducibility","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11120,"byte_start":8827,"id":"section:e26027f0eb812634d524","kind":"section","labels":["app:identities"],"line_end":242,"line_start":205,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"This appendix labels frequently used equalities by logical status to prevent conflating definitions, algebraic rewrites, and genuine predictions.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Identity Catalogue and Status Labels","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11932,"byte_start":11120,"id":"section:fc36fc9abb91f849de4f","kind":"section","labels":["app:r2"],"line_end":256,"line_start":243,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"K1: Field content and torsionful Lagrangian fixed by the minimal UFE sector. K2: Quadratic fluctuation operator is of Laplace type after background-field gauge fixing. K3: Heat-kernel coefficient [formula in source] captures the curvature-squared terms in [formula in source] . K4: Matching to [formula in source] after imposing the GR renormalization condition.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"One-Loop Effective Action in Riemann–Cartan and the [formula in source] Coefficient","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12290,"byte_start":11932,"id":"section:1396be75dc128a9bbdf5","kind":"subsection","labels":[],"line_end":262,"line_start":257,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"We evaluate the one-loop effective action in a Riemann–Cartan background with torsion decomposed into axial [formula in source] , trace [formula in source] , and tensor [formula in source] . The minimal UFE choice treats torsion at quadratic order, so integrating out torsion is Gaussian and parameter-free once [formula in source] fixes the normalization of the coupling.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.1 Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12653,"byte_start":12290,"id":"section:f3a795c31b83c464ed83","kind":"subsection","labels":[],"line_end":271,"line_start":263,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"After background-field gauge fixing, the quadratic operator for torsion fluctuations can be written in Laplace type, with [formula in source] built from curvature and torsion invariants. The contribution to [formula in source] is [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.2 Operator Form","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13023,"byte_start":12653,"id":"section:4c145ca6f7fa292d37bc","kind":"subsection","labels":[],"line_end":279,"line_start":272,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"The local part of [formula in source] is governed by the heat-kernel expansion where [formula in source] contains the curvature-squared terms. The torsion-dependent pieces combine into an effective [formula in source] operator in the low-energy action.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.3 Heat-Kernel Coefficients","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13224,"byte_start":13023,"id":"section:86bbbaa4c71290269707","kind":"subsection","labels":[],"line_end":283,"line_start":280,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"The GR limit (A8) fixes the renormalization scheme by requiring that the [formula in source] limit reduces to the Einstein–Hilbert action with coefficient [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.4 Renormalization Condition","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13589,"byte_start":13224,"id":"section:ee725d7e5bdc9cead9c6","kind":"subsection","labels":[],"line_end":292,"line_start":284,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"With the TFPT normalization of the torsion sector, the induced [formula in source] coefficient is fixed by [formula in source] , yielding which reproduces","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.5 TFPT Closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14067,"byte_start":13589,"id":"section:a290fd0ec6bd85dcedc4","kind":"section","labels":["app:bounce"],"line_end":302,"line_start":293,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"This appendix provides a minimal outline; the full numerical transfer-function evaluation is implemented in the bounce_perturbations verification module (see tfpt-suite/).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bounce Perturbations and the Transfer Function","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14381,"byte_start":14067,"id":"section:0cb50095bbaaec5fdc61","kind":"subsection","labels":[],"line_end":307,"line_start":303,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"The bounce background is modeled by a smooth scale factor [formula in source] where the torsion-induced [formula in source] term regularizes [formula in source] for scalar perturbations. The transition to the [formula in source] inflationary phase is implemented by matching [formula in source] and its derivatives at [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.1 Background Solution","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14674,"byte_start":14381,"id":"section:e3133a6ec8297f5d0b32","kind":"subsection","labels":[],"line_end":312,"line_start":308,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"Mode functions are initialized in an adiabatic vacuum well before the bounce and integrated through the bounce and into the [formula in source] era. The numerical scheme records the transfer function by comparing late-time solutions to the pure [formula in source] baseline.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.2 Numerical Integration Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14983,"byte_start":14674,"id":"section:5b7f468e2e2c191679d0","kind":"subsection","labels":[],"line_end":320,"line_start":313,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"Define the transfer function as with [formula in source] for modes well inside the horizon during the bounce and deviations confined to [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.3 Transfer Function","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15362,"byte_start":14983,"id":"section:1eda4bf85c73ba7564c7","kind":"subsection","labels":[],"line_end":326,"line_start":321,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"Large-scale suppression or oscillatory features in [formula in source] are predicted at [formula in source] . Current CMB large-scale bounds constrain the allowable feature amplitude, providing a direct observational test of the bounce completion.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.4 Falsification Targets","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17252,"byte_start":15362,"id":"section:d109e3b022fb22886c7f","kind":"section","labels":[],"line_end":367,"line_start":327,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv24"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv24/sections/007-subsection-m-obius-matching-and-the-minimal-gluing-class.tex","status_markers_as_written":[],"summary_excerpt":"] F. W. Hehl, P. von der Heyde, G. D. Kerlick, J. M. Nester, ``General Relativity with Spin and Torsion: Foundations and Prospects,'' Rev.\\ Mod.\\ Phys.\\ 48, 393 (1976).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"References","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":23569,"byte_start":0,"id":"section:5cb8442e876f729ca70b","kind":"frontmatter","labels":[],"line_end":591,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/preamble.tex","status_markers_as_written":[],"summary_excerpt":"compat=1.18 groupplots arrows.meta,positioning,decorations.markings,decorations.pathmorphing,calc,patterns,shapes.geometric","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Topological Fixed Point Theory (TFPT)\\\\[0.5em] A Parameter-Free Derivation of the Fine-Structure Constant\\\\ from Topology, Geometry, and Quantum Consistency","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2082,"byte_start":0,"id":"section:c539f356c8955bd431ce","kind":"frontmatter","labels":[],"line_end":24,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/001-section-kernel-and-discrete-grammar.tex","status_markers_as_written":[],"summary_excerpt":"We present the complete axiomatic foundation of Topological Fixed Point Theory (TFPT), which derives the fine-structure constant [formula in source] and other fundamental quantities from eight minimal assumptions rooted in topology, geometry, and quantum field theory. The theory rests on two fundamental invariants: the topological coupling [formula in source] from 11D Chern–Simons quantization and the geometric scale","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13803,"byte_start":2082,"id":"section:6b876a777857acc978fa","kind":"section","labels":["fig:compiler","fig:crosslink","tab:constant-factory"],"line_end":196,"line_start":25,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/001-section-kernel-and-discrete-grammar.tex","status_markers_as_written":[],"summary_excerpt":"Structural input (fixed, not fitted): the Standard Model abelian trace [formula in source] (determined by SM particle content and GUT normalization; not a TFPT knob).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kernel and Discrete Grammar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16280,"byte_start":13803,"id":"section:df2fe7929023aae9cd6e","kind":"section","labels":["fig:flow"],"line_end":244,"line_start":197,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/001-section-kernel-and-discrete-grammar.tex","status_markers_as_written":[],"summary_excerpt":"The Standard Model of particle physics contains approximately 19 free parameters that must be determined experimentally. Among these, the fine-structure constant [formula in source] stands out as a dimensionless number whose value has no explanation within conventional frameworks.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Introduction: The Problem of Parameters","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16699,"byte_start":16280,"id":"section:23d49a2e7da2a44cea57","kind":"section","labels":[],"line_end":252,"line_start":245,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/001-section-kernel-and-discrete-grammar.tex","status_markers_as_written":[],"summary_excerpt":"TFPT is built on eight axioms, organized into three categories: geometric structure, quantum field theory, and closure conditions. Each axiom is either derived from established physics or explicitly marked as a new postulate.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Axiomatic Foundation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":24159,"byte_start":16699,"id":"section:c4679245b235aacce773","kind":"subsection","labels":["fig:doublecover"],"line_end":412,"line_start":253,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/001-section-kernel-and-discrete-grammar.tex","status_markers_as_written":[],"summary_excerpt":"Riemann–Cartan GeometryRC The fundamental spacetime connection possesses torsion; the Levi-Civita connection is a limiting case when torsion vanishes.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Geometric Axioms (A1–A4)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3704,"byte_start":0,"id":"section:8d4861c93ff0b0f1bb33","kind":"subsection","labels":[],"line_end":80,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/002-subsection-quantum-field-theory-axioms-a5-a6.tex","status_markers_as_written":[],"summary_excerpt":"Units and constants: Natural units: [formula in source] ; energies in GeV, lengths in GeV [formula in source] . Reference data: CODATA 2022, PDG 2024. Metric signature: [formula in source] . Levi-Civita tensor: [formula in source] , [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Quantum Field Theory Axioms (A5–A6)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8022,"byte_start":3704,"id":"section:2db2f4cdd4072fb315de","kind":"subsection","labels":[],"line_end":152,"line_start":81,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/002-subsection-quantum-field-theory-axioms-a5-a6.tex","status_markers_as_written":[],"summary_excerpt":"Standard Model Hypercharge TraceSMT The hypercharge trace invariant, summed over all SM fermions with GUT normalization [formula in source] , is: In TFPT this quantity appears as the spectral quadratic index of the hypercharge-coupled boundary operators in the regulated determinant (Appendix","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Closure Axioms (A7–A8)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8227,"byte_start":8022,"id":"section:fcde0f67dd1a7906af75","kind":"section","labels":[],"line_end":156,"line_start":153,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/002-subsection-quantum-field-theory-axioms-a5-a6.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Derivation of Fundamental Constants","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10291,"byte_start":8227,"id":"section:0abb91b38dc79e489a0a","kind":"subsection","labels":[],"line_end":204,"line_start":157,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/002-subsection-quantum-field-theory-axioms-a5-a6.tex","status_markers_as_written":[],"summary_excerpt":"Existence and Uniqueness of [formula in source] phi0 From Axioms A3 and A4, the geometric scale is uniquely determined:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Geometric Scale [formula in source] The Geometric Scale phi0","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13944,"byte_start":10291,"id":"section:c898c04038f6bc36266d","kind":"subsection","labels":["eq:CFE","fig:CFE"],"line_end":293,"line_start":205,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/002-subsection-quantum-field-theory-axioms-a5-a6.tex","status_markers_as_written":[],"summary_excerpt":"Effective Potential Parametersparams From the 11D Chern–Simons reduction (A5) and modulus-closure structure (A6): Notation: We use [formula in source] (calligraphic) for this CFE parameter to distinguish it from [formula in source] (gravitational coupling).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Cubic Fixed-Point Equation (CFE)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14079,"byte_start":13944,"id":"section:e84eee49d5cc8fa58d13","kind":"subsection","labels":[],"line_end":296,"line_start":294,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/002-subsection-quantum-field-theory-axioms-a5-a6.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Geometric Self-Consistency (Backreaction)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20426,"byte_start":14079,"id":"section:dfe86a2a3a23348ef58c","kind":"subsubsection","labels":["eq:backreaction","tab:alpha"],"line_end":420,"line_start":297,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/002-subsection-quantum-field-theory-axioms-a5-a6.tex","status_markers_as_written":[],"summary_excerpt":"The response [formula in source] is the closed form consequence of defect sector reweighting on the orientable double cover. The linear form is the [formula in source] expansion, not a separate assumption.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Backreaction as Structural Response","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2259,"byte_start":0,"id":"section:45f7419ec4ad58b0714a","kind":"subsubsection","labels":["sec:sensitivity"],"line_end":46,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/003-subsubsection-sensitivity-analysis.tex","status_markers_as_written":[],"summary_excerpt":"The sub-ppm precision of the [formula in source] prediction depends critically on the backreaction coefficient. We analyze the sensitivity to demonstrate this is not fine-tuning but a genuine geometric constraint.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Sensitivity Analysis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4157,"byte_start":2259,"id":"section:bad424bbba9a98e6de60","kind":"subsection","labels":["sec:comparison-policy"],"line_end":71,"line_start":47,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/003-subsubsection-sensitivity-analysis.tex","status_markers_as_written":[],"summary_excerpt":"(MS [formula in source] ), fonttitle= ] Why this matters: Precision electroweak fits and PDG summaries use the MS [formula in source] coupling at [formula in source] , [formula in source] , as the comparison observable. CODATA [formula in source] is an on-shell/IR reference and is therefore treated as secondary diagnostic once scheme and threshold bookkeeping is made explicit.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Comparison and Scheme Policy (No Hidden Knobs)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4359,"byte_start":4157,"id":"section:6d2ff0f5077567a812a6","kind":"section","labels":[],"line_end":75,"line_start":72,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/003-subsubsection-sensitivity-analysis.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"The Unified Field Equation (UFE)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9516,"byte_start":4359,"id":"section:e8c3b33dff6dcab8cdb3","kind":"subsection","labels":["eq:UFE","eq:bianchi","eq:maxwell"],"line_end":172,"line_start":76,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/003-subsubsection-sensitivity-analysis.tex","status_markers_as_written":[],"summary_excerpt":"UFE ActionUFEaction On a manifold [formula in source] with metric [formula in source] and torsionful connection [formula in source] , the action is: Here [formula in source] denotes the Ricci scalar constructed from the full torsionful connection [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Torsionful Geometric Action","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13139,"byte_start":9516,"id":"section:414e5b9306da2bd98822","kind":"subsection","labels":["sec:torsion-regimes"],"line_end":243,"line_start":173,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/003-subsubsection-sensitivity-analysis.tex","status_markers_as_written":[],"summary_excerpt":"TFPT distinguishes between cosmological torsion (which may be active in the early universe and drive a bounce) and local vacuum torsion (which is constrained by laboratory and astrophysical bounds on Lorentz violation). To avoid hidden assumptions, we treat ``torsion today'' as an explicit regime choice rather than a vague qualitative statement.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Present-Day Torsion Regimes and Local Tests","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14642,"byte_start":13139,"id":"section:e18090b50a6280647d60","kind":"subsection","labels":[],"line_end":278,"line_start":244,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/003-subsubsection-sensitivity-analysis.tex","status_markers_as_written":[],"summary_excerpt":"Gravitational Coupling Consistencykappa The gravitational coupling [formula in source] (with dimension [formula in source] ) is constrained by consistency with the dimensionless ratio:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gravitational Coupling from Invariants","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14834,"byte_start":14642,"id":"section:d7a23827a2ab625aa107","kind":"section","labels":[],"line_end":282,"line_start":279,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/003-subsubsection-sensitivity-analysis.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Observable Predictions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15301,"byte_start":14834,"id":"section:bb00edbbeb9d44dca77d","kind":"subsection","labels":[],"line_end":294,"line_start":283,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/003-subsubsection-sensitivity-analysis.tex","status_markers_as_written":[],"summary_excerpt":"Axion–Photon Couplinggagg The CFE fixes the axion–photon vertex uniquely: This determines cosmic birefringence without free parameters.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Axion–Photon Coupling","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16644,"byte_start":15301,"id":"section:ad1bd2d43ab8364cc0ad","kind":"subsection","labels":[],"line_end":321,"line_start":295,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/003-subsubsection-sensitivity-analysis.tex","status_markers_as_written":[],"summary_excerpt":"Topological Excursion Quantizationtopoexcursion The topological axion excursion is quantized in discrete sector changes: with [formula in source] the minimal nontrivial class. The corresponding birefringence is [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cosmic Birefringence","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5322,"byte_start":0,"id":"section:81788e961f9a34bcdc7b","kind":"subsubsection","labels":["eq:shifted-axion-potential","fig:birefringence","sec:deltaa","tab:birefringence"],"line_end":112,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/004-subsubsection-dynamical-completion-of-the-excursion.tex","status_markers_as_written":[],"summary_excerpt":"Goal: Provide one minimal dynamical realization compatible with the topological quantization (Definition","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dynamical Completion of the Excursion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7868,"byte_start":5322,"id":"section:3bba4d004ae20c0e4581","kind":"subsection","labels":["fig:twoloop"],"line_end":165,"line_start":113,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/004-subsubsection-dynamical-completion-of-the-excursion.tex","status_markers_as_written":[],"summary_excerpt":"RG FingerprintsRGfingerprints The TFPT invariants leave signatures in the RG flow of gauge couplings: These values are obtained by two-loop RG running from PDG boundary conditions at [formula in source] using the declared PyR@TE model (checked by two_loop_rg_fingerprints in tfpt-suite/; not direct measurements at the quoted scales). The crossing scale for [formula in source] is [formula in source] GeV.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Two-Loop RG Fingerprints","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8143,"byte_start":7868,"id":"section:b9f571561e9c0abf7434","kind":"section","labels":["sec:e8"],"line_end":170,"line_start":166,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/004-subsubsection-dynamical-completion-of-the-excursion.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"The E [formula in source] Cascade and Block ConstantsThe E8 Cascade and Block Constants","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10788,"byte_start":8143,"id":"section:0400b64df246225b9453","kind":"subsection","labels":[],"line_end":219,"line_start":171,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/004-subsubsection-dynamical-completion-of-the-excursion.tex","status_markers_as_written":[],"summary_excerpt":"E [formula in source] Orbit Graphorbitgraph Let [formula in source] denote the set of nilpotent orbits of the exceptional Lie algebra [formula in source] . For each orbit [formula in source] , define: [formula in source] : the dimension of the orbit as a variety [formula in source] : the ``centralizer dimension'' [formula in source] : the height (sum of coefficients in weighted Dynkin diagram) The orbit graph [formul","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nilpotent Orbit Structure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15362,"byte_start":10788,"id":"section:722c044a4fabd4da41fb","kind":"subsection","labels":["eq:ladder","fig:ladder"],"line_end":325,"line_start":220,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/004-subsubsection-dynamical-completion-of-the-excursion.tex","status_markers_as_written":[],"summary_excerpt":"Holonomy degeneracy anchor for [formula in source] holonomydeg TFPT uses the SU(5) hypercharge holonomy data already fixed elsewhere in the construction. On the fundamental splitting, the holonomy spectrum separates into two eigenspaces of dimensions [formula in source] and [formula in source] , hence we define the discrete degeneracy count [formula in source] The minimal damping ratio compatible with a single additi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Log-Exact Ladder Formula","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4491,"byte_start":0,"id":"section:237f2533caab801d4b14","kind":"subsection","labels":["fig:blocks","tab:blocks"],"line_end":111,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/005-subsection-block-constant-formula-and-derivation.tex","status_markers_as_written":[],"summary_excerpt":"For a 6D Weyl fermion zero mode on a boundary cycle [formula in source] with flat [formula in source] connection (holonomy [formula in source] ), the variation of [formula in source] under the connection is proportional to the quadratic charge index: The proportionality constant is fixed by the topological normalization [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Block Constant Formula and Derivation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5912,"byte_start":4491,"id":"section:7c27ebea695743da0656","kind":"subsection","labels":[],"line_end":144,"line_start":112,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/005-subsection-block-constant-formula-and-derivation.tex","status_markers_as_written":[],"summary_excerpt":"The neutrino block at [formula in source] provides concrete predictions for the seesaw mechanism.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neutrino Seesaw Predictions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6178,"byte_start":5912,"id":"section:a76f40cc33b28df4cdc3","kind":"section","labels":[],"line_end":148,"line_start":145,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/005-subsection-block-constant-formula-and-derivation.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Flavor Structure: The Z [formula in source] ArchitectureFlavor Structure: The Z3 Architecture","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8849,"byte_start":6178,"id":"section:f3a1ffb884610a2574c6","kind":"subsection","labels":[],"line_end":200,"line_start":149,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/005-subsection-block-constant-formula-and-derivation.tex","status_markers_as_written":[],"summary_excerpt":"On a conformally flat boundary geometry, the unique projectively invariant quantity from four marked points is the cross-ratio. Any boundary monodromy acts as a PSL [formula in source] transformation. Therefore, relations depending only on boundary monodromies must be rational functions of a M\\\"obius map.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Universal Phase [formula in source] Universal Phase delta","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10253,"byte_start":8849,"id":"section:916878d34aeff2263855","kind":"subsection","labels":[],"line_end":232,"line_start":201,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/005-subsection-block-constant-formula-and-derivation.tex","status_markers_as_written":[],"summary_excerpt":"Mass Ratios from M\\\"obius Mapmassratios The M\\\"obius map [formula in source] evaluated at cusps [formula in source] yields mass ratios:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"M\\\"obius Mass Relations","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14095,"byte_start":10253,"id":"section:1b71820a1c7adc0f4931","kind":"subsection","labels":[],"line_end":319,"line_start":233,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/005-subsection-block-constant-formula-and-derivation.tex","status_markers_as_written":[],"summary_excerpt":"Cabibbo AngleCabibbo The Cabibbo angle is fixed parameter-free by [formula in source] : PDG reference: [formula in source] . Deviation: [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cabibbo Angle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15669,"byte_start":14095,"id":"section:dab6dce1b7061f48ba0c","kind":"subsubsection","labels":[],"line_end":342,"line_start":320,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/005-subsection-block-constant-formula-and-derivation.tex","status_markers_as_written":[],"summary_excerpt":"The shipped suite includes a deterministic CKM reconstruction pipeline with declared UV textures, two-loop RG dressing, and a reference-scale comparison at [formula in source] (module ckm_full_pipeline). The baseline benchmark gives a CKM matrix close to PDG at the level quantified by the reported [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Suite benchmark: RG-dressed CKM pipeline (explicit conventions)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2879,"byte_start":0,"id":"section:e5d979c0fbaa38a0bbe4","kind":"subsection","labels":[],"line_end":58,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/006-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"TFPT provides a closed prediction for [formula in source] via a single kernel identity plus the TM1 pattern. The remaining PMNS degrees of freedom [formula in source] are treated as an open interface requiring explicit Z [formula in source] -breaking and (eventually) correlated Yukawa/RG treatment; they must not be read as closed predictions at this stage.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"PMNS Neutrino Mixing: TM1 Pattern","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4661,"byte_start":2879,"id":"section:0de55ed5a55d69bf3169","kind":"section","labels":["eq:As","eq:R2action","eq:ns","eq:r","tab:inflation"],"line_end":99,"line_start":59,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/006-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"The TFPT topological correction scale is set by [formula in source] (cf.\\ [formula in source] ). In effective gravity, the leading higher-curvature completion compatible with general covariance is an [formula in source] term.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Inflation: [formula in source] Completion (Starobinsky Limit)Inflation: R2 Completion (Starobinsky Limit)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5964,"byte_start":4661,"id":"section:5e4c2c8a59455cb3b5bc","kind":"subsection","labels":["sec:r2derive"],"line_end":124,"line_start":100,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/006-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"Relevant Torsion DegreesR2torsion Decompose torsion into irreducible parts [formula in source] (axial, trace, tensor). In the minimal UFE setting the dominant coupling is through axial torsion [formula in source] , and the torsion sector is treated at quadratic order so it can be integrated out in the one-loop effective action.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[formula in source] Term from the Torsionful Effective ActionR2 Term from the Torsionful Effective Action","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6841,"byte_start":5964,"id":"section:33aaa77e94d07bc11538","kind":"subsection","labels":["eq:R2scale"],"line_end":144,"line_start":125,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/006-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"TFPT [formula in source] ScaleR2coeff Using the GR renormalization condition (A8) to fix the scheme, the coefficient of the [formula in source] term yields Here the square root applies only to [formula in source] , consistent with the numerical value above.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Coefficient Identification and GR Renormalization","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8442,"byte_start":6841,"id":"section:b7dbb22d61dd0c553106","kind":"subsection","labels":["sec:bounce"],"line_end":177,"line_start":145,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/006-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"Bounce-to-Inflation Backgroundbouncebg Assume a non-singular bounce driven by the torsion-induced [formula in source] term (Lemma above), followed by a transition into the [formula in source] inflationary phase. We take the CMB pivot scales to exit the horizon during the [formula in source] phase.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bounce + [formula in source] Perturbations and Transfer FunctionBounce + R2 Perturbations and Transfer Function","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8643,"byte_start":8442,"id":"section:9c3dc73acc8c09501e08","kind":"section","labels":[],"line_end":181,"line_start":178,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/006-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Axion Cosmology and Dark Matter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10820,"byte_start":8643,"id":"section:c1569d6e8c4ccf9c52ae","kind":"subsection","labels":[],"line_end":220,"line_start":182,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/006-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"The TFPT axion sector is split into two distinct fields to avoid an internal contradiction (a single [formula in source] eV axion cannot remain quasi-static over Hubble times):","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Two-Field Structure: Topological vs.\\ QCD Axion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13968,"byte_start":10820,"id":"section:b3308ecc8e6d63796873","kind":"subsection","labels":[],"line_end":271,"line_start":221,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/006-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"Axion Dark Matter ParametersaxionDM For the QCD axion field [formula in source] from the E [formula in source] cascade (PQ block at [formula in source] ):","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dark Matter Relic Density","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16020,"byte_start":13968,"id":"section:a2276a7072f25a857362","kind":"subsection","labels":["sec:dark-energy"],"line_end":306,"line_start":272,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/006-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"with no continuous knobs, fonttitle= ] We test the discrete defect-suppression candidate [formula in source] The two-defect sector uses [formula in source] and the corresponding [formula in source] (Sec.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dark Energy as a Defect-Suppressed Torsion Condensate (candidate)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17986,"byte_start":16020,"id":"section:dbe204242972dddce491","kind":"section","labels":["tab:beta"],"line_end":337,"line_start":307,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/006-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"The parameter [formula in source] provides a compact dictionary for expressing multiple quantities. Most equalities in this section are algebraic rewrites of earlier definitions rather than independent new inputs (see Appendix Inflation observables additionally depend on a dynamical completion (here: the conditional [formula in source] sector in Theorem","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[formula in source] -Centric Identity Summarybeta_rad-Centric Identity Summary","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":23206,"byte_start":17986,"id":"section:e5db14aa16ca4e7f0e2b","kind":"section","labels":["tab:status"],"line_end":400,"line_start":338,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/006-subsection-pmns-neutrino-mixing-tm1-pattern.tex","status_markers_as_written":[],"summary_excerpt":"@p3cmp4cmp3cmp5.2cm@ TFPT status dashboard. ``Exact'': [formula in source] ; ``Solid'': [formula in source] ; ``Minor'': [formula in source] ; ``Moderate'': [formula in source] . Domain & Quantity & Deviation & Status\\\\ Domain & Quantity & Deviation & Status\\\\ 4r Continued on next page.\\\\ 4l Structural (parameter-free)\\\\ CFE & [formula in source] & [formula in source] & green!60!black Derived (double cover + [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Summary of Claims and Status","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":636,"byte_start":0,"id":"section:c309179e21930c428fb5","kind":"section","labels":[],"line_end":14,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/007-section-what-tfpt-does-emph-not-assume.tex","status_markers_as_written":[],"summary_excerpt":"The following are not required: Slow-roll inflation (specific model) String landscape or anthropic selection Extra dimensions as free parameters Dark matter entirely from axions New particles beyond minimal axion sector Any fitted or adjusted parameters","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"What TFPT Does Not Assume","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2194,"byte_start":636,"id":"section:de77ecba6ba9c40a0b31","kind":"section","labels":[],"line_end":42,"line_start":15,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/007-section-what-tfpt-does-emph-not-assume.tex","status_markers_as_written":[],"summary_excerpt":"TFPT demonstrates that the fine-structure constant [formula in source] can be derived from first principles using eight minimal axioms rooted in topology, geometry, and quantum consistency. The key results are:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conclusions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4794,"byte_start":2194,"id":"section:b8149cc5edc87b2bacad","kind":"section","labels":["tab:constants"],"line_end":81,"line_start":43,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/007-section-what-tfpt-does-emph-not-assume.tex","status_markers_as_written":[],"summary_excerpt":"@ll@ Quantity & Value\\\\ [formula in source] & \\\\ [formula in source] & \\\\ [formula in source] & \\\\ [formula in source] & \\\\ [formula in source] (self-consistent) & 0.053170209119023745\\\\ [formula in source] & \\\\ [formula in source] & [formula in source] \\\\ [formula in source] & \\\\ [formula in source] (E [formula in source] ) & [formula in source] \\\\ [formula in source] (E [formula in source] exponent) & 0.58723319078","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Numerical Constants (High Precision)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12211,"byte_start":4794,"id":"section:9e986ea812c04ac4216f","kind":"section","labels":["eq:CFE-appendix","eq:potential","eq:stationarity"],"line_end":235,"line_start":82,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/007-section-what-tfpt-does-emph-not-assume.tex","status_markers_as_written":[],"summary_excerpt":"In background-field gauge, the one-loop effective potential for the electromagnetic coupling modulus takes the form. Here [formula in source] is the induced potential for [formula in source] after rewriting [formula in source] :","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of the CFE from the Effective Potential","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13472,"byte_start":12211,"id":"section:13891e8b420cf3f84576","kind":"section","labels":[],"line_end":252,"line_start":236,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/007-section-what-tfpt-does-emph-not-assume.tex","status_markers_as_written":[],"summary_excerpt":"The TFPT verification suite ( tfpt-suite/) turns paper claims into deterministic, assumption-explicit computations. All counts in this section are auto-generated from the suite artifacts (no hardcoded ``39 modules''): [formula in source] It ships: a conventional suite (registry-driven; core invariants, [formula in source] closure + policy bridge, RG/matching, flavor pipelines, cosmology/bounce wiring, torsion/birefri","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verification Suite Summary","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14762,"byte_start":13472,"id":"section:b63b138d6fb15db8d399","kind":"subsection","labels":["sec:known-gaps"],"line_end":282,"line_start":253,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/007-section-what-tfpt-does-emph-not-assume.tex","status_markers_as_written":[],"summary_excerpt":"@llrrrrrr@ Module & Mode & Checks & PASS & WARN & FAIL & Plots(exp) & Plots(ok)\\\\ alpha_on_shell_bridge & engineering & 7 & 6 & 1 & 0 & 0 & 0\\\\ matching_finite_pieces & engineering & 5 & 4 & 1 & 0 & 0 & 0\\\\ torsion_condensate & engineering & 8 & 5 & 3 & 0 & 0 & 0\\\\ alpha_on_shell_bridge & physics & 7 & 6 & 1 & 0 & 0 & 0\\\\ matching_finite_pieces & physics & 5 & 4 & 1 & 0 & 0 & 0\\\\ torsion_condensate & physics & 8 & 5 ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Known Gaps and Status (Auto-Generated)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6385,"byte_start":0,"id":"section:8b3aa891da48a1a2c113","kind":"subsection","labels":["sec:theoryv3-evidence"],"line_end":151,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/008-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"The theoryv3 analysis branch is a compact ``evidence layer'' for the discrete kernel and crosslink logic. Current inventory (auto-generated from tfpt-suite/2.5/theoryv3/out/): [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"theoryv3 Evidence Layer (Compressed, Auto-Generated)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6685,"byte_start":6385,"id":"section:22b3cbf63c265acaa292","kind":"section","labels":["app:E8cert"],"line_end":158,"line_start":152,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/008-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"This appendix provides the complete verification data for the E [formula in source] chain uniqueness theorem (Theorem","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"E [formula in source] Chain CertificateE8 Chain Certificate","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7189,"byte_start":6685,"id":"section:6eca807919461839c412","kind":"subsection","labels":[],"line_end":168,"line_start":159,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/008-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"Each nilpotent orbit [formula in source] of [formula in source] is characterized by: Bala–Carter label: Standard notation (e.g., [formula in source] , [formula in source] , [formula in source] , ) Dimension: [formula in source] Centralizer dimension: [formula in source] Height: [formula in source] (sum of weighted Dynkin diagram coefficients)","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Orbit Data Structure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7865,"byte_start":7189,"id":"section:68ab5294a2121105a3bf","kind":"subsection","labels":[],"line_end":193,"line_start":169,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/008-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"The complete chain from [formula in source] to [formula in source] :","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Unique Chain (Excerpt)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8633,"byte_start":7865,"id":"section:b8098ef60509670f5e29","kind":"subsection","labels":[],"line_end":208,"line_start":194,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/008-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"The uniqueness is verified by: Constructing the complete Hasse diagram of [formula in source] from standard tables. Computing all cover relations with [formula in source] . Running dynamic programming to find all paths from [formula in source] to [formula in source] . Applying the cost function [formula in source] (second-difference smoothness). Verifying that the minimum-cost path is unique (cost gap to second-best ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verification Algorithm","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8873,"byte_start":8633,"id":"section:0dad8674e27dbb1cd4bc","kind":"section","labels":["app:boundary"],"line_end":215,"line_start":209,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/008-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"This appendix derives the block index formula [formula in source] from the APS index theorem.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Boundary Trace Derivation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9264,"byte_start":8873,"id":"section:a03fb57da1052d60dc40","kind":"subsection","labels":[],"line_end":225,"line_start":216,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/008-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"Consider a 6D manifold [formula in source] with boundary [formula in source] . For a Weyl fermion coupled to a [formula in source] gauge field [formula in source] , the APS index theorem gives: where [formula in source] is the [formula in source] -invariant of the boundary Dirac operator.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9777,"byte_start":9264,"id":"section:57c9edaeb426dbe80262","kind":"subsection","labels":[],"line_end":240,"line_start":226,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/008-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"On the orientable double cover [formula in source] , the boundary decomposes as: (two boundary cycles plus the twist seam).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Flat Connection on Boundary Cycles","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10347,"byte_start":9777,"id":"section:03bfc6c8e0dd3ea5b9ea","kind":"subsection","labels":[],"line_end":250,"line_start":241,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/008-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"The regulated determinant of the hypercharge-coupled Dirac operator contains a universal UV logarithmic term whose coefficient is the quadratic charge trace: Thus [formula in source] appears as a spectral index coefficient, independent of IR thresholds, matching its role in the CFE.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spectral Trace Coefficient and [formula in source] Spectral Trace Coefficient and b1","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11128,"byte_start":10347,"id":"section:127383d97a6f43524144","kind":"subsection","labels":[],"line_end":270,"line_start":251,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/008-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"Step 1: Each boundary cycle contributes a factor proportional to [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of [formula in source] Derivation of kB","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11442,"byte_start":11128,"id":"section:2bb7e649337113d761fc","kind":"section","labels":["app:seam"],"line_end":276,"line_start":271,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/008-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"This appendix provides the [formula in source] -invariant gluing derivation used in Axiom","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Seam Gluing and the [formula in source] -Invariant NormalizationSeam Gluing and the eta-Invariant Normalization","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12044,"byte_start":11442,"id":"section:9f39db76556e4aa76be9","kind":"subsection","labels":[],"line_end":287,"line_start":277,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/008-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the orientable double cover of the M\\\"obius fiber and cut it along the seam [formula in source] to obtain a manifold-with-boundary [formula in source] with boundary components [formula in source] . Let [formula in source] be the Dirac operator on [formula in source] with APS boundary conditions on [formula in source] and a unitary matching operator [formula in source] identifying [formula i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cut Space and Operators","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12678,"byte_start":12044,"id":"section:98830004b1448b752aba","kind":"subsection","labels":[],"line_end":300,"line_start":288,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/008-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"The APS gluing theorem expresses the [formula in source] -invariant of the glued manifold in terms of the cut manifold plus a discrete spectral-flow correction: where [formula in source] is the spectral flow of the matching operator. In TFPT bookkeeping this contributes a quantized seam term to the curvature normalization.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gluing Formula for the [formula in source] -InvariantGluing Formula for the eta-Invariant","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12962,"byte_start":12678,"id":"section:d2d346035cf123b3aa77","kind":"subsection","labels":[],"line_end":307,"line_start":301,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/008-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"For the M\\\"obius [formula in source] identification, the matching satisfies [formula in source] . The minimal nontrivial class is modeled by the unitary phase","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"M\\\"obius Matching and the Minimal Gluing Class","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13628,"byte_start":12962,"id":"section:aa8c3a26601078cd30e2","kind":"subsection","labels":[],"line_end":324,"line_start":308,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/008-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"Interpolate boundary conditions by a phase [formula in source] , which gives the eigenvalues As [formula in source] runs from [formula in source] to [formula in source] , exactly one eigenvalue crosses zero, so [formula in source] and [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spectral Flow Computation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14093,"byte_start":13628,"id":"section:bd28f36a620c1d20a648","kind":"subsection","labels":[],"line_end":333,"line_start":325,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/008-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"The two physical boundary cycles contribute [formula in source] , and the seam gluing adds [formula in source] , so the total curvature is [formula in source] . The stationarity normalization [formula in source] therefore yields","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Normalization of [formula in source] Normalization of phi_tree","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14599,"byte_start":14093,"id":"section:47abd5dcfd20ab70b6d2","kind":"section","labels":["app:48deriv"],"line_end":344,"line_start":334,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/008-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"This appendix explains the integer coefficient in [formula in source] . The key point is that the canonical quantity is and the appearance of ``48'' is simply the same number expressed in units of [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of the Coefficient 48 in [formula in source] Derivation of the Coefficient 48 in delta_top","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15323,"byte_start":14599,"id":"section:5b09892798dc7fc23dc1","kind":"subsection","labels":[],"line_end":357,"line_start":345,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/008-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"The topological correction [formula in source] arises from the leading gauge-invariant correction to the tree-level geometric scale [formula in source] . The requirements are: Gauge invariance: The correction must be built from [formula in source] only (no explicit [formula in source] dependence at this order). Dimensionlessness: Since [formula in source] is dimensionless, the correction must be a pure power [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Physical Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16128,"byte_start":15323,"id":"section:4b379c6d14cd91aba1d3","kind":"subsection","labels":[],"line_end":374,"line_start":358,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/008-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"The effective action on the M\\\"obius fiber includes the Chern–Simons term [formula in source] . The leading topological correction comes from the one-loop determinant of the Dirac operator coupled to this background.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Power Counting: Why [formula in source] ?Power Counting: Why c3^4?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":395,"byte_start":0,"id":"section:8694b4600e2b6d4bb12e","kind":"subsection","labels":[],"line_end":10,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/009-subsection-spin-lifted-deficit-factor.tex","status_markers_as_written":[],"summary_excerpt":"The non-orientable identification acts as a [formula in source] operation on the base, but in the spin bundle the same element lifts to order [formula in source] because a [formula in source] rotation acts as [formula in source] on spinors and only a [formula in source] rotation is trivial. This produces a universal deficit factor per minimal sector.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spin-Lifted Deficit Factor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":901,"byte_start":395,"id":"section:392b0dd9e5e3fbad8c28","kind":"subsection","labels":[],"line_end":20,"line_start":11,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/009-subsection-spin-lifted-deficit-factor.tex","status_markers_as_written":[],"summary_excerpt":"Cutting along [formula in source] yields boundary components [formula in source] . The four local corner patches [formula in source] , [formula in source] , [formula in source] , [formula in source] constitute the fundamental domain. Summing the spin-lifted deficit factor over these sectors yields In TFPT normalization this yields the canonical form [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Sector Count from Cut Geometry","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1255,"byte_start":901,"id":"section:724dfc728daf97408454","kind":"subsection","labels":[],"line_end":30,"line_start":21,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/009-subsection-spin-lifted-deficit-factor.tex","status_markers_as_written":[],"summary_excerpt":"Using [formula in source] : so [formula in source] and [formula in source] are exactly equivalent.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conversion to the [formula in source] normalizationConversion to the c3 normalization","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1569,"byte_start":1255,"id":"section:c59112b1841b2fb91435","kind":"subsection","labels":[],"line_end":36,"line_start":31,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/009-subsection-spin-lifted-deficit-factor.tex","status_markers_as_written":[],"summary_excerpt":"The spin-lift argument fixes the [formula in source] deficit factor robustly, and the sector count is fixed by seam symmetry. The seam normalization is provided by the [formula in source] -gluing derivation in Appendix","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Status note","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1802,"byte_start":1569,"id":"section:8b6d1a7c233bf6da5062","kind":"section","labels":["app:flavor"],"line_end":42,"line_start":37,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/009-subsection-spin-lifted-deficit-factor.tex","status_markers_as_written":[],"summary_excerpt":"This appendix derives the M\\\"obius structure of flavor relations from boundary monodromy.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Flavor Monodromy and Cross-Ratio","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2525,"byte_start":1802,"id":"section:25ba077a9daef20524d4","kind":"subsection","labels":[],"line_end":60,"line_start":43,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/009-subsection-spin-lifted-deficit-factor.tex","status_markers_as_written":[],"summary_excerpt":"On a conformally flat boundary, the metric is locally: Holomorphic automorphisms (Wilson lines of flat connections) act as M\\\"obius transformations:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Projective Invariance on Boundaries","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2959,"byte_start":2525,"id":"section:87ef0a0774851a6b4da3","kind":"subsection","labels":[],"line_end":71,"line_start":61,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/009-subsection-spin-lifted-deficit-factor.tex","status_markers_as_written":[],"summary_excerpt":"Given four marked points [formula in source] on the boundary, the unique projective invariant is the cross-ratio:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cross-Ratio as Unique Invariant","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3497,"byte_start":2959,"id":"section:4439785b4d30eb05dc2a","kind":"subsection","labels":[],"line_end":82,"line_start":72,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/009-subsection-spin-lifted-deficit-factor.tex","status_markers_as_written":[],"summary_excerpt":"The cusps [formula in source] arise from: Rationality: Quantized holonomies [formula in source] rational cusps. GUT compatibility: SU(5) hypercharge assignments give [formula in source] (quarks), [formula in source] (leptons), etc. Uniqueness: These are the only rational values that simultaneously separate the three SM sectors (up, down, lepton) and maintain GUT normalization.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cusp Selection","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4221,"byte_start":3497,"id":"section:46cce393818f8dc56197","kind":"subsection","labels":[],"line_end":101,"line_start":83,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/009-subsection-spin-lifted-deficit-factor.tex","status_markers_as_written":[],"summary_excerpt":"Leading term: [formula in source] from the abelian trace (same as [formula in source] numerator divided by 41/10's denominator structure).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of [formula in source] Derivation of delta_star","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5629,"byte_start":4221,"id":"section:e6cd0f748cfa56b27a56","kind":"section","labels":["app:repro"],"line_end":130,"line_start":102,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":["relation:0fd4547770e055540bbb","relation:438e3203ccb5e8763c25","relation:a6106ae10129ff07526e"],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/009-subsection-spin-lifted-deficit-factor.tex","status_markers_as_written":[],"summary_excerpt":"Replication package: All numerical results can be reproduced using the TFPT verification suite (v5).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproducibility","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13883,"byte_start":5629,"id":"section:ae63c20b9d29f703f3fb","kind":"section","labels":["app:prediction-ledger","tab:prediction-ledger"],"line_end":190,"line_start":131,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/009-subsection-spin-lifted-deficit-factor.tex","status_markers_as_written":[],"summary_excerpt":"Purpose: Provide a single, reviewer-friendly list of predictions and candidates that is tied to the same JSON sources used by the verification suite, to prevent number drift between Abstract, theorems, tables, and appendices.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Prediction Ledger and Falsification","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16520,"byte_start":13883,"id":"section:4ad0c33dfa1d394a16cd","kind":"section","labels":["app:identities"],"line_end":229,"line_start":191,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/009-subsection-spin-lifted-deficit-factor.tex","status_markers_as_written":[],"summary_excerpt":"This appendix labels frequently used equalities by logical status to prevent conflating definitions, algebraic rewrites, and genuine predictions.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Identity Catalogue and Status Labels","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17418,"byte_start":16520,"id":"section:f8c0e4c2336aa70d12ed","kind":"section","labels":["app:r2"],"line_end":243,"line_start":230,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/009-subsection-spin-lifted-deficit-factor.tex","status_markers_as_written":[],"summary_excerpt":"K1: Field content and torsionful Lagrangian fixed by the minimal UFE sector. K2: Quadratic fluctuation operator is of Laplace type after background-field gauge fixing. K3: Heat-kernel coefficient [formula in source] captures the curvature-squared terms in [formula in source] . K4: Matching to [formula in source] after imposing the GR renormalization condition.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"One-Loop Effective Action in Riemann–Cartan and the [formula in source] CoefficientOne-Loop Effective Action in Riemann–Cartan and the R2 Coefficient","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17776,"byte_start":17418,"id":"section:9061def4ace19b489959","kind":"subsection","labels":[],"line_end":249,"line_start":244,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/009-subsection-spin-lifted-deficit-factor.tex","status_markers_as_written":[],"summary_excerpt":"We evaluate the one-loop effective action in a Riemann–Cartan background with torsion decomposed into axial [formula in source] , trace [formula in source] , and tensor [formula in source] . The minimal UFE choice treats torsion at quadratic order, so integrating out torsion is Gaussian and parameter-free once [formula in source] fixes the normalization of the coupling.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.1 Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18139,"byte_start":17776,"id":"section:a953d6efe84cab950539","kind":"subsection","labels":[],"line_end":258,"line_start":250,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/009-subsection-spin-lifted-deficit-factor.tex","status_markers_as_written":[],"summary_excerpt":"After background-field gauge fixing, the quadratic operator for torsion fluctuations can be written in Laplace type, with [formula in source] built from curvature and torsion invariants. The contribution to [formula in source] is [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.2 Operator Form","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18509,"byte_start":18139,"id":"section:589a53eb62e41825b9e2","kind":"subsection","labels":[],"line_end":266,"line_start":259,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/009-subsection-spin-lifted-deficit-factor.tex","status_markers_as_written":[],"summary_excerpt":"The local part of [formula in source] is governed by the heat-kernel expansion where [formula in source] contains the curvature-squared terms. The torsion-dependent pieces combine into an effective [formula in source] operator in the low-energy action.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.3 Heat-Kernel Coefficients","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18710,"byte_start":18509,"id":"section:0e27022fc66a4c176219","kind":"subsection","labels":[],"line_end":270,"line_start":267,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/009-subsection-spin-lifted-deficit-factor.tex","status_markers_as_written":[],"summary_excerpt":"The GR limit (A8) fixes the renormalization scheme by requiring that the [formula in source] limit reduces to the Einstein–Hilbert action with coefficient [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.4 Renormalization Condition","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19075,"byte_start":18710,"id":"section:2f2535146951560b41e4","kind":"subsection","labels":[],"line_end":279,"line_start":271,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/009-subsection-spin-lifted-deficit-factor.tex","status_markers_as_written":[],"summary_excerpt":"With the TFPT normalization of the torsion sector, the induced [formula in source] coefficient is fixed by [formula in source] , yielding which reproduces","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.5 TFPT Closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19553,"byte_start":19075,"id":"section:66f79df5de5bd7e12e8d","kind":"section","labels":["app:bounce"],"line_end":289,"line_start":280,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/009-subsection-spin-lifted-deficit-factor.tex","status_markers_as_written":[],"summary_excerpt":"This appendix provides a minimal outline; the full numerical transfer-function evaluation is implemented in the bounce_perturbations verification module (see tfpt-suite/).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bounce Perturbations and the Transfer Function","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19867,"byte_start":19553,"id":"section:98b381d6a8be440f6e8b","kind":"subsection","labels":[],"line_end":294,"line_start":290,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/009-subsection-spin-lifted-deficit-factor.tex","status_markers_as_written":[],"summary_excerpt":"The bounce background is modeled by a smooth scale factor [formula in source] where the torsion-induced [formula in source] term regularizes [formula in source] for scalar perturbations. The transition to the [formula in source] inflationary phase is implemented by matching [formula in source] and its derivatives at [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.1 Background Solution","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20160,"byte_start":19867,"id":"section:2fbcf9eded7cb6e55bbd","kind":"subsection","labels":[],"line_end":299,"line_start":295,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/009-subsection-spin-lifted-deficit-factor.tex","status_markers_as_written":[],"summary_excerpt":"Mode functions are initialized in an adiabatic vacuum well before the bounce and integrated through the bounce and into the [formula in source] era. The numerical scheme records the transfer function by comparing late-time solutions to the pure [formula in source] baseline.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.2 Numerical Integration Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20496,"byte_start":20160,"id":"section:68d5a4b77ca1bc1b4ad4","kind":"subsection","labels":[],"line_end":309,"line_start":300,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/009-subsection-spin-lifted-deficit-factor.tex","status_markers_as_written":[],"summary_excerpt":"Define the transfer function as with [formula in source] for modes well inside the horizon during the bounce and deviations confined to [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.3 Transfer Function","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9467,"byte_start":0,"id":"section:769f69e9022862dedd0b","kind":"subsection","labels":[],"line_end":273,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/010-subsection-texorpdfstring-l-4-the-k-to-ell-gate-cmb-obse.tex","status_markers_as_written":[],"summary_excerpt":"Deterministic (given the bounce completion): The transfer-function shape [formula in source] (this appendix; implemented in bounce_perturbations). Given an explicit expansion-history budget, the mapping [formula in source] and the resulting [formula in source] curves are deterministic (implemented in k_calibration and boltzmann_transfer).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.4 The [formula in source] Gate (CMB Observability as Policy Interface)L.4 The k->ell Gate (CMB Observability as Policy Interface)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9846,"byte_start":9467,"id":"section:970d0b3a3e0b2ee83469","kind":"subsection","labels":[],"line_end":279,"line_start":274,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/010-subsection-texorpdfstring-l-4-the-k-to-ell-gate-cmb-obse.tex","status_markers_as_written":[],"summary_excerpt":"Large-scale suppression or oscillatory features in [formula in source] are predicted at [formula in source] . Current CMB large-scale bounds constrain the allowable feature amplitude, providing a direct observational test of the bounce completion.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.5 Falsification Targets","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17056,"byte_start":9846,"id":"section:7cede861bc62a627e234","kind":"section","labels":["tab:reference-ledger"],"line_end":345,"line_start":280,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/010-subsection-texorpdfstring-l-4-the-k-to-ell-gate-cmb-obse.tex","status_markers_as_written":[],"summary_excerpt":"=0mu plus 1mu @p0.24 rrllp0.34 @ Reference ledger used by the TFPT suite (auto-generated). Key & Value & [formula in source] & Units & Version & Source (stable key)\\\\ Key & Value & [formula in source] & Units & Version & Source (stable key)\\\\ 6r Continued on next page.\\\\ A_s_planck2018 & 2.0989031673e-09 & 2.938464434e-11 & dimensionless & Planck 2018 & planck2018 Planck 2018 results VI (2020), base- [formula in sour","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reference Ledger (Auto-Generated)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19812,"byte_start":17056,"id":"section:962533e23a98bd5efff4","kind":"section","labels":[],"line_end":425,"line_start":346,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv25"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv25/sections/010-subsection-texorpdfstring-l-4-the-k-to-ell-gate-cmb-obse.tex","status_markers_as_written":[],"summary_excerpt":"99 hehl1976 F. W. Hehl, P. von der Heyde, G. D. Kerlick, J. M. Nester, ``General Relativity with Spin and Torsion: Foundations and Prospects,'' Rev.\\ Mod.\\ Phys.\\ 48, 393 (1976).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"References","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":23891,"byte_start":0,"id":"section:0fd3b387cccf967905f4","kind":"frontmatter","labels":[],"line_end":601,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/preamble.tex","status_markers_as_written":[],"summary_excerpt":"compat=1.18 groupplots arrows.meta,positioning,decorations.markings,decorations.pathmorphing,calc,patterns,shapes.geometric","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Topological Fixed Point Theory (TFPT)\\\\[0.5em] A Parameter-Free Derivation of the Fine-Structure Constant\\\\ from Topology, Geometry, and Quantum Consistency","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2080,"byte_start":0,"id":"section:67d79e574b6da1b1d2af","kind":"frontmatter","labels":[],"line_end":24,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/001-section-kernel-and-discrete-grammar.tex","status_markers_as_written":[],"summary_excerpt":"We present the complete axiomatic foundation of Topological Fixed Point Theory (TFPT), which derives the fine-structure constant [formula in source] and other fundamental quantities from eight minimal assumptions rooted in topology, geometry, and quantum field theory. The theory rests on two fundamental invariants: the topological coupling [formula in source] from 11D Chern–Simons quantization and the geometric scale","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13897,"byte_start":2080,"id":"section:fd7111709b834c4622d6","kind":"section","labels":["fig:compiler","fig:crosslink","tab:constant-factory"],"line_end":196,"line_start":25,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/001-section-kernel-and-discrete-grammar.tex","status_markers_as_written":[],"summary_excerpt":"Structural input (fixed, not fitted): the Standard Model abelian trace [formula in source] (determined by SM particle content and GUT normalization; not a TFPT knob).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kernel and Discrete Grammar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16374,"byte_start":13897,"id":"section:a391ac21750a3f27e243","kind":"section","labels":["fig:flow"],"line_end":244,"line_start":197,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/001-section-kernel-and-discrete-grammar.tex","status_markers_as_written":[],"summary_excerpt":"The Standard Model of particle physics contains approximately 19 free parameters that must be determined experimentally. Among these, the fine-structure constant [formula in source] stands out as a dimensionless number whose value has no explanation within conventional frameworks.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Introduction: The Problem of Parameters","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16793,"byte_start":16374,"id":"section:ff4a8bb060e30943bf21","kind":"section","labels":[],"line_end":252,"line_start":245,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/001-section-kernel-and-discrete-grammar.tex","status_markers_as_written":[],"summary_excerpt":"TFPT is built on eight axioms, organized into three categories: geometric structure, quantum field theory, and closure conditions. Each axiom is either derived from established physics or explicitly marked as a new postulate.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Axiomatic Foundation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":24257,"byte_start":16793,"id":"section:7c12c53352c7eb598083","kind":"subsection","labels":["fig:doublecover"],"line_end":412,"line_start":253,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/001-section-kernel-and-discrete-grammar.tex","status_markers_as_written":[],"summary_excerpt":"Riemann–Cartan GeometryRC The fundamental spacetime connection possesses torsion; the Levi-Civita connection is a limiting case when torsion vanishes.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Geometric Axioms (A1–A4)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3704,"byte_start":0,"id":"section:bc0d1ac0d4b322cbbabe","kind":"subsection","labels":[],"line_end":80,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/002-subsection-quantum-field-theory-axioms-a5-a6.tex","status_markers_as_written":[],"summary_excerpt":"Units and constants: Natural units: [formula in source] ; energies in GeV, lengths in GeV [formula in source] . Reference data: CODATA 2022, PDG 2024. Metric signature: [formula in source] . Levi-Civita tensor: [formula in source] , [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Quantum Field Theory Axioms (A5–A6)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8022,"byte_start":3704,"id":"section:83109c24c6033c609f3d","kind":"subsection","labels":[],"line_end":152,"line_start":81,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/002-subsection-quantum-field-theory-axioms-a5-a6.tex","status_markers_as_written":[],"summary_excerpt":"Standard Model Hypercharge TraceSMT The hypercharge trace invariant, summed over all SM fermions with GUT normalization [formula in source] , is: In TFPT this quantity appears as the spectral quadratic index of the hypercharge-coupled boundary operators in the regulated determinant (Appendix","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Closure Axioms (A7–A8)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8227,"byte_start":8022,"id":"section:4d48ee69c0595860d04f","kind":"section","labels":[],"line_end":156,"line_start":153,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/002-subsection-quantum-field-theory-axioms-a5-a6.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Derivation of Fundamental Constants","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10291,"byte_start":8227,"id":"section:6e6bb7a9e6f2f25a01d7","kind":"subsection","labels":[],"line_end":204,"line_start":157,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/002-subsection-quantum-field-theory-axioms-a5-a6.tex","status_markers_as_written":[],"summary_excerpt":"Existence and Uniqueness of [formula in source] phi0 From Axioms A3 and A4, the geometric scale is uniquely determined:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Geometric Scale [formula in source] The Geometric Scale phi0","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15257,"byte_start":10291,"id":"section:3417058b2895d3e003dc","kind":"subsection","labels":["eq:CFE","fig:CFE","fig:invariant_flow"],"line_end":327,"line_start":205,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/002-subsection-quantum-field-theory-axioms-a5-a6.tex","status_markers_as_written":[],"summary_excerpt":"Effective Potential Parametersparams From the 11D Chern–Simons reduction (A5) and modulus-closure structure (A6): Notation: We use [formula in source] (calligraphic) for this CFE parameter to distinguish it from [formula in source] (gravitational coupling).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Cubic Fixed-Point Equation (CFE)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15392,"byte_start":15257,"id":"section:9913c06ec7b20b9ec6ae","kind":"subsection","labels":[],"line_end":330,"line_start":328,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/002-subsection-quantum-field-theory-axioms-a5-a6.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Geometric Self-Consistency (Backreaction)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6444,"byte_start":0,"id":"section:2cf33a74c4300267f3bd","kind":"subsubsection","labels":["eq:backreaction","tab:alpha"],"line_end":126,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/003-subsubsection-backreaction-as-structural-response.tex","status_markers_as_written":[],"summary_excerpt":"The response [formula in source] is the closed form consequence of defect sector reweighting on the orientable double cover. The linear form is the [formula in source] expansion, not a separate assumption.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Backreaction as Structural Response","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8703,"byte_start":6444,"id":"section:a7af59241b7ac8b9f8b3","kind":"subsubsection","labels":["sec:sensitivity"],"line_end":172,"line_start":127,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/003-subsubsection-backreaction-as-structural-response.tex","status_markers_as_written":[],"summary_excerpt":"The sub-ppm precision of the [formula in source] prediction depends critically on the backreaction coefficient. We analyze the sensitivity to demonstrate this is not fine-tuning but a genuine geometric constraint.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Sensitivity Analysis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10634,"byte_start":8703,"id":"section:c22ae94cad3a55a733f0","kind":"subsection","labels":["sec:comparison-policy"],"line_end":197,"line_start":173,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/003-subsubsection-backreaction-as-structural-response.tex","status_markers_as_written":[],"summary_excerpt":"( [formula in source] ), fonttitle= ] Why this matters: Precision electroweak fits and PDG summaries use the [formula in source] coupling at [formula in source] , [formula in source] , as the comparison observable. CODATA [formula in source] is an on-shell/IR reference and is therefore treated as secondary diagnostic once scheme and threshold bookkeeping is made explicit.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Comparison and Scheme Policy (No Hidden Knobs)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10836,"byte_start":10634,"id":"section:e98025f14a3c14b7b602","kind":"section","labels":[],"line_end":201,"line_start":198,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/003-subsubsection-backreaction-as-structural-response.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"The Unified Field Equation (UFE)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11986,"byte_start":10836,"id":"section:0c6169d7f1fe50d1672e","kind":"subsection","labels":[],"line_end":230,"line_start":202,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/003-subsubsection-backreaction-as-structural-response.tex","status_markers_as_written":[],"summary_excerpt":"Quantum Vacuum TensorQVT Let Let [formula in source] denote the scalar invariant entering the coupling equation, Define the Quantum Vacuum Tensor","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Quantum Vacuum Tensor Packaging","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17143,"byte_start":11986,"id":"section:00754cf94e3c4d4aa8d1","kind":"subsection","labels":["eq:UFE","eq:bianchi","eq:maxwell"],"line_end":327,"line_start":231,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/003-subsubsection-backreaction-as-structural-response.tex","status_markers_as_written":[],"summary_excerpt":"UFE ActionUFEaction On a manifold [formula in source] with metric [formula in source] and torsionful connection [formula in source] , the action is: Here [formula in source] denotes the Ricci scalar constructed from the full torsionful connection [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Torsionful Geometric Action","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20766,"byte_start":17143,"id":"section:d00e4560a35568575ecb","kind":"subsection","labels":["sec:torsion-regimes"],"line_end":398,"line_start":328,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/003-subsubsection-backreaction-as-structural-response.tex","status_markers_as_written":[],"summary_excerpt":"TFPT distinguishes between cosmological torsion (which may be active in the early universe and drive a bounce) and local vacuum torsion (which is constrained by laboratory and astrophysical bounds on Lorentz violation). To avoid hidden assumptions, we treat ``torsion today'' as an explicit regime choice rather than a vague qualitative statement.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Present-Day Torsion Regimes and Local Tests","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3654,"byte_start":0,"id":"section:383c1162b4289e644d8a","kind":"subsubsection","labels":["fig:evpa_intercept","sec:eht-intercept"],"line_end":68,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/004-subsubsection-achromatic-polarization-rotation-around-co.tex","status_markers_as_written":[],"summary_excerpt":"Beyond the cosmic birefringence prediction (Theorem in the presence of a nonzero [formula in source] environment (see the companion note bhAchromaticRotationNote2025). EHT-style polarimetry provides the relevant data products for such an intercept test ehtm87pol2021. A simple dyonic toy model yields where [formula in source] is the emission radius and [formula in source] denote effective electromagnetic charges sourc","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Achromatic polarization rotation around compact objects (EHT intercept test)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5157,"byte_start":3654,"id":"section:fb6ba476bca237ff5a4e","kind":"subsection","labels":[],"line_end":103,"line_start":69,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/004-subsubsection-achromatic-polarization-rotation-around-co.tex","status_markers_as_written":[],"summary_excerpt":"Gravitational Coupling Consistencykappa The gravitational coupling [formula in source] (with dimension [formula in source] ) is constrained by consistency with the dimensionless ratio:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gravitational Coupling from Invariants","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5349,"byte_start":5157,"id":"section:00ee564ac43b07c15e9b","kind":"section","labels":[],"line_end":107,"line_start":104,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/004-subsubsection-achromatic-polarization-rotation-around-co.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Observable Predictions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5816,"byte_start":5349,"id":"section:ea7c7ba4378540ecf144","kind":"subsection","labels":[],"line_end":119,"line_start":108,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/004-subsubsection-achromatic-polarization-rotation-around-co.tex","status_markers_as_written":[],"summary_excerpt":"Axion–Photon Couplinggagg The CFE fixes the axion–photon vertex uniquely: This determines cosmic birefringence without free parameters.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Axion–Photon Coupling","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7159,"byte_start":5816,"id":"section:6136145a8e48cf90ef75","kind":"subsection","labels":[],"line_end":146,"line_start":120,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/004-subsubsection-achromatic-polarization-rotation-around-co.tex","status_markers_as_written":[],"summary_excerpt":"Topological Excursion Quantizationtopoexcursion The topological axion excursion is quantized in discrete sector changes: with [formula in source] the minimal nontrivial class. 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The crossing scale for [formula in source] is [formula in source] GeV.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Two-Loop RG Fingerprints","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15203,"byte_start":14928,"id":"section:6ee891e8b70e0741f7a5","kind":"section","labels":["sec:e8"],"line_end":313,"line_start":309,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/004-subsubsection-achromatic-polarization-rotation-around-co.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"The E [formula in source] Cascade and Block ConstantsThe E8 Cascade and Block Constants","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17848,"byte_start":15203,"id":"section:b9e75564902809c4669e","kind":"subsection","labels":[],"line_end":362,"line_start":314,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/004-subsubsection-achromatic-polarization-rotation-around-co.tex","status_markers_as_written":[],"summary_excerpt":"E [formula in source] Orbit Graphorbitgraph Let [formula in source] denote the set of nilpotent orbits of the exceptional Lie algebra [formula in source] . 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Any boundary monodromy acts as a PSL [formula in source] transformation. Therefore, relations depending only on boundary monodromies must be rational functions of a M\\\"obius map.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Universal Phase [formula in source] Universal Phase delta","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14827,"byte_start":13423,"id":"section:2c5aee1d29d0297d6532","kind":"subsection","labels":[],"line_end":338,"line_start":307,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/005-subsection-log-exact-ladder-formula.tex","status_markers_as_written":[],"summary_excerpt":"Mass Ratios from M\\\"obius Mapmassratios The M\\\"obius map [formula in source] evaluated at cusps [formula in source] yields mass ratios:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"M\\\"obius Mass Relations","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3805,"byte_start":0,"id":"section:b5fa604250960b503307","kind":"subsection","labels":[],"line_end":85,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/006-subsection-cabibbo-angle.tex","status_markers_as_written":[],"summary_excerpt":"Cabibbo AngleCabibbo The Cabibbo parameter is fixed by the birefringence invariant [formula in source] : Compared to the PDG reference value, this is a sub-permille level deviation (status: solid).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cabibbo Angle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5300,"byte_start":3805,"id":"section:640064610fdae853a5f3","kind":"subsubsection","labels":[],"line_end":107,"line_start":86,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/006-subsection-cabibbo-angle.tex","status_markers_as_written":[],"summary_excerpt":"The shipped suite includes a deterministic CKM reconstruction pipeline with declared UV textures, two-loop RG dressing, and a reference-scale comparison at [formula in source] (module ckm_full_pipeline). 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The remaining PMNS degrees of freedom [formula in source] are treated as an open interface requiring explicit Z [formula in source] -breaking and (eventually) correlated Yukawa/RG treatment; they must not be read as closed predictions at this stage.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"PMNS Neutrino Mixing: TM1 Pattern","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13690,"byte_start":11908,"id":"section:48872c42750f2aa1685c","kind":"section","labels":["eq:As","eq:R2action","eq:ns","eq:r","tab:inflation"],"line_end":305,"line_start":265,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/006-subsection-cabibbo-angle.tex","status_markers_as_written":[],"summary_excerpt":"The TFPT topological correction scale is set by [formula in source] (cf.\\ [formula in source] ). In effective gravity, the leading higher-curvature completion compatible with general covariance is an [formula in source] term.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Inflation: [formula in source] Completion (Starobinsky Limit)Inflation: R2 Completion (Starobinsky Limit)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14993,"byte_start":13690,"id":"section:7cd69f6277d8a19aa56f","kind":"subsection","labels":["sec:r2derive"],"line_end":330,"line_start":306,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/006-subsection-cabibbo-angle.tex","status_markers_as_written":[],"summary_excerpt":"Relevant Torsion DegreesR2torsion Decompose torsion into irreducible parts [formula in source] (axial, trace, tensor). In the minimal UFE setting the dominant coupling is through axial torsion [formula in source] , and the torsion sector is treated at quadratic order so it can be integrated out in the one-loop effective action.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[formula in source] Term from the Torsionful Effective ActionR2 Term from the Torsionful Effective Action","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15870,"byte_start":14993,"id":"section:5e1a0a3db9868e4010c2","kind":"subsection","labels":["eq:R2scale"],"line_end":350,"line_start":331,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/006-subsection-cabibbo-angle.tex","status_markers_as_written":[],"summary_excerpt":"TFPT [formula in source] ScaleR2coeff Using the GR renormalization condition (A8) to fix the scheme, the coefficient of the [formula in source] term yields Here the square root applies only to [formula in source] , consistent with the numerical value above.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Coefficient Identification and GR Renormalization","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17471,"byte_start":15870,"id":"section:fd369bdac4a4aa63fcf0","kind":"subsection","labels":["sec:bounce"],"line_end":383,"line_start":351,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/006-subsection-cabibbo-angle.tex","status_markers_as_written":[],"summary_excerpt":"Bounce-to-Inflation Backgroundbouncebg Assume a non-singular bounce driven by the torsion-induced [formula in source] term (Lemma above), followed by a transition into the [formula in source] inflationary phase. We take the CMB pivot scales to exit the horizon during the [formula in source] phase.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bounce + [formula in source] Perturbations and Transfer FunctionBounce + R2 Perturbations and Transfer Function","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":201,"byte_start":0,"id":"section:b798262d20dad2b4ca3f","kind":"section","labels":[],"line_end":4,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/007-section-axion-cosmology-and-dark-matter.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; 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Both are framed as outlook items rather than closed predictions at this stage fiveProblemsNote2025,blackHolesBh1Note2025.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Outlook (open interfaces).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19961,"byte_start":17362,"id":"section:99803af636c2d7a5c91d","kind":"section","labels":["tab:constants"],"line_end":310,"line_start":272,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/007-section-axion-cosmology-and-dark-matter.tex","status_markers_as_written":[],"summary_excerpt":"@ll@ Quantity & Value\\\\ [formula in source] & \\\\ [formula in source] & \\\\ [formula in source] & \\\\ [formula in source] & \\\\ [formula in source] (self-consistent) & 0.053170209119023745\\\\ [formula in source] & \\\\ [formula in source] & [formula in source] \\\\ [formula in source] & \\\\ [formula in source] (E [formula in source] ) & [formula in source] \\\\ [formula in source] (E [formula in source] exponent) & 0.58723319078","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Numerical Constants (High Precision)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7417,"byte_start":0,"id":"section:931acec25c903672fd06","kind":"section","labels":["eq:CFE-appendix","eq:potential","eq:stationarity"],"line_end":154,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/008-section-derivation-of-the-cfe-from-the-effective-potenti.tex","status_markers_as_written":[],"summary_excerpt":"In background-field gauge, the one-loop effective potential for the electromagnetic coupling modulus takes the form. Here [formula in source] is the induced potential for [formula in source] after rewriting [formula in source] :","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of the CFE from the Effective Potential","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8678,"byte_start":7417,"id":"section:ee5e8724493485ea83fe","kind":"section","labels":[],"line_end":171,"line_start":155,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/008-section-derivation-of-the-cfe-from-the-effective-potenti.tex","status_markers_as_written":[],"summary_excerpt":"The TFPT verification suite ( tfpt-suite/) turns paper claims into deterministic, assumption-explicit computations. All counts in this section are auto-generated from the suite artifacts (no hardcoded ``39 modules''): [formula in source] It ships: a conventional suite (registry-driven; core invariants, [formula in source] closure + policy bridge, RG/matching, flavor pipelines, cosmology/bounce wiring, torsion/birefri","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verification Suite Summary","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9968,"byte_start":8678,"id":"section:a004e8d3ba1417bea9a7","kind":"subsection","labels":["sec:known-gaps"],"line_end":201,"line_start":172,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/008-section-derivation-of-the-cfe-from-the-effective-potenti.tex","status_markers_as_written":[],"summary_excerpt":"@llrrrrrr@ Module & Mode & Checks & PASS & WARN & FAIL & Plots(exp) & Plots(ok)\\\\ alpha_on_shell_bridge & engineering & 7 & 6 & 1 & 0 & 0 & 0\\\\ matching_finite_pieces & engineering & 5 & 4 & 1 & 0 & 0 & 0\\\\ torsion_condensate & engineering & 8 & 5 & 3 & 0 & 0 & 0\\\\ alpha_on_shell_bridge & physics & 7 & 6 & 1 & 0 & 0 & 0\\\\ matching_finite_pieces & physics & 5 & 4 & 1 & 0 & 0 & 0\\\\ torsion_condensate & physics & 8 & 5 ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Known Gaps and Status (Auto-Generated)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16429,"byte_start":9968,"id":"section:4ffbee9aa83d653c88e2","kind":"subsection","labels":["sec:theoryv3-evidence"],"line_end":353,"line_start":202,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/008-section-derivation-of-the-cfe-from-the-effective-potenti.tex","status_markers_as_written":[],"summary_excerpt":"The theoryv3 analysis branch is a compact ``evidence layer'' for the discrete kernel and crosslink logic. Current inventory (auto-generated from tfpt-suite/2.5/theoryv3/out/): [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"theoryv3 Evidence Layer (Compressed, Auto-Generated)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16729,"byte_start":16429,"id":"section:91690a9f66fab8cfde21","kind":"section","labels":["app:E8cert"],"line_end":360,"line_start":354,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/008-section-derivation-of-the-cfe-from-the-effective-potenti.tex","status_markers_as_written":[],"summary_excerpt":"This appendix provides the complete verification data for the E [formula in source] chain uniqueness theorem (Theorem","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"E [formula in source] Chain CertificateE8 Chain Certificate","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17233,"byte_start":16729,"id":"section:845b03748438a8ddc85d","kind":"subsection","labels":[],"line_end":370,"line_start":361,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/008-section-derivation-of-the-cfe-from-the-effective-potenti.tex","status_markers_as_written":[],"summary_excerpt":"Each nilpotent orbit [formula in source] of [formula in source] is characterized by: Bala–Carter label: Standard notation (e.g., [formula in source] , [formula in source] , [formula in source] , ) Dimension: [formula in source] Centralizer dimension: [formula in source] Height: [formula in source] (sum of weighted Dynkin diagram coefficients)","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Orbit Data Structure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":676,"byte_start":0,"id":"section:88bcdf2874177774942e","kind":"subsection","labels":[],"line_end":25,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/009-subsection-the-unique-chain-excerpt.tex","status_markers_as_written":[],"summary_excerpt":"The complete chain from [formula in source] to [formula in source] :","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Unique Chain (Excerpt)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1444,"byte_start":676,"id":"section:c91cccb625cc0fa37890","kind":"subsection","labels":[],"line_end":40,"line_start":26,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/009-subsection-the-unique-chain-excerpt.tex","status_markers_as_written":[],"summary_excerpt":"The uniqueness is verified by: Constructing the complete Hasse diagram of [formula in source] from standard tables. Computing all cover relations with [formula in source] . Running dynamic programming to find all paths from [formula in source] to [formula in source] . Applying the cost function [formula in source] (second-difference smoothness). 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For a Weyl fermion coupled to a [formula in source] gauge field [formula in source] , the APS index theorem gives: where [formula in source] is the [formula in source] -invariant of the boundary Dirac operator.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2588,"byte_start":2075,"id":"section:57e89cd068dbee902c07","kind":"subsection","labels":[],"line_end":72,"line_start":58,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/009-subsection-the-unique-chain-excerpt.tex","status_markers_as_written":[],"summary_excerpt":"On the orientable double cover [formula in source] , the boundary decomposes as: (two boundary cycles plus the twist seam).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Flat Connection on Boundary Cycles","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3158,"byte_start":2588,"id":"section:702134858f47dbd0d78f","kind":"subsection","labels":[],"line_end":82,"line_start":73,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/009-subsection-the-unique-chain-excerpt.tex","status_markers_as_written":[],"summary_excerpt":"The regulated determinant of the hypercharge-coupled Dirac operator contains a universal UV logarithmic term whose coefficient is the quadratic charge trace: Thus [formula in source] appears as a spectral index coefficient, independent of IR thresholds, matching its role in the CFE.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spectral Trace Coefficient and [formula in source] Spectral Trace Coefficient and b1","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3939,"byte_start":3158,"id":"section:31ebe94d5caf9d39f05f","kind":"subsection","labels":[],"line_end":102,"line_start":83,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/009-subsection-the-unique-chain-excerpt.tex","status_markers_as_written":[],"summary_excerpt":"Step 1: Each boundary cycle contributes a factor proportional to [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of [formula in source] Derivation of kB","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4253,"byte_start":3939,"id":"section:6746a3645c1b0264ad60","kind":"section","labels":["app:seam"],"line_end":108,"line_start":103,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/009-subsection-the-unique-chain-excerpt.tex","status_markers_as_written":[],"summary_excerpt":"This appendix provides the [formula in source] -invariant gluing derivation used in Axiom","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Seam Gluing and the [formula in source] -Invariant NormalizationSeam Gluing and the eta-Invariant Normalization","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4855,"byte_start":4253,"id":"section:58c2aee516bb13722d72","kind":"subsection","labels":[],"line_end":119,"line_start":109,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/009-subsection-the-unique-chain-excerpt.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the orientable double cover of the M\\\"obius fiber and cut it along the seam [formula in source] to obtain a manifold-with-boundary [formula in source] with boundary components [formula in source] . Let [formula in source] be the Dirac operator on [formula in source] with APS boundary conditions on [formula in source] and a unitary matching operator [formula in source] identifying [formula i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cut Space and Operators","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5489,"byte_start":4855,"id":"section:366553b1645dc1f3465c","kind":"subsection","labels":[],"line_end":132,"line_start":120,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/009-subsection-the-unique-chain-excerpt.tex","status_markers_as_written":[],"summary_excerpt":"The APS gluing theorem expresses the [formula in source] -invariant of the glued manifold in terms of the cut manifold plus a discrete spectral-flow correction: where [formula in source] is the spectral flow of the matching operator. In TFPT bookkeeping this contributes a quantized seam term to the curvature normalization.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gluing Formula for the [formula in source] -InvariantGluing Formula for the eta-Invariant","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5773,"byte_start":5489,"id":"section:6f4b1ac614b8fc1b16c1","kind":"subsection","labels":[],"line_end":139,"line_start":133,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/009-subsection-the-unique-chain-excerpt.tex","status_markers_as_written":[],"summary_excerpt":"For the M\\\"obius [formula in source] identification, the matching satisfies [formula in source] . The minimal nontrivial class is modeled by the unitary phase","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"M\\\"obius Matching and the Minimal Gluing Class","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6439,"byte_start":5773,"id":"section:4f0770425c63c28c490e","kind":"subsection","labels":[],"line_end":156,"line_start":140,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/009-subsection-the-unique-chain-excerpt.tex","status_markers_as_written":[],"summary_excerpt":"Interpolate boundary conditions by a phase [formula in source] , which gives the eigenvalues As [formula in source] runs from [formula in source] to [formula in source] , exactly one eigenvalue crosses zero, so [formula in source] and [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spectral Flow Computation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6904,"byte_start":6439,"id":"section:7fbb555fc09a41dc82e6","kind":"subsection","labels":[],"line_end":165,"line_start":157,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/009-subsection-the-unique-chain-excerpt.tex","status_markers_as_written":[],"summary_excerpt":"The two physical boundary cycles contribute [formula in source] , and the seam gluing adds [formula in source] , so the total curvature is [formula in source] . The stationarity normalization [formula in source] therefore yields","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Normalization of [formula in source] Normalization of phi_tree","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7410,"byte_start":6904,"id":"section:d143d233bc408defb5a3","kind":"section","labels":["app:48deriv"],"line_end":176,"line_start":166,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/009-subsection-the-unique-chain-excerpt.tex","status_markers_as_written":[],"summary_excerpt":"This appendix explains the integer coefficient in [formula in source] . The key point is that the canonical quantity is and the appearance of ``48'' is simply the same number expressed in units of [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of the Coefficient 48 in [formula in source] Derivation of the Coefficient 48 in delta_top","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8134,"byte_start":7410,"id":"section:fb7e6f4a837131fa8fd3","kind":"subsection","labels":[],"line_end":189,"line_start":177,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/009-subsection-the-unique-chain-excerpt.tex","status_markers_as_written":[],"summary_excerpt":"The topological correction [formula in source] arises from the leading gauge-invariant correction to the tree-level geometric scale [formula in source] . The requirements are: Gauge invariance: The correction must be built from [formula in source] only (no explicit [formula in source] dependence at this order). Dimensionlessness: Since [formula in source] is dimensionless, the correction must be a pure power [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Physical Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8939,"byte_start":8134,"id":"section:172dfc79d7bf96658211","kind":"subsection","labels":[],"line_end":206,"line_start":190,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/009-subsection-the-unique-chain-excerpt.tex","status_markers_as_written":[],"summary_excerpt":"The effective action on the M\\\"obius fiber includes the Chern–Simons term [formula in source] . The leading topological correction comes from the one-loop determinant of the Dirac operator coupled to this background.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Power Counting: Why [formula in source] ?Power Counting: Why c3^4?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9334,"byte_start":8939,"id":"section:672da7827b1dc50a0b2c","kind":"subsection","labels":[],"line_end":216,"line_start":207,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/009-subsection-the-unique-chain-excerpt.tex","status_markers_as_written":[],"summary_excerpt":"The non-orientable identification acts as a [formula in source] operation on the base, but in the spin bundle the same element lifts to order [formula in source] because a [formula in source] rotation acts as [formula in source] on spinors and only a [formula in source] rotation is trivial. This produces a universal deficit factor per minimal sector.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spin-Lifted Deficit Factor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9840,"byte_start":9334,"id":"section:a07c42cd54c9222e96e6","kind":"subsection","labels":[],"line_end":226,"line_start":217,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/009-subsection-the-unique-chain-excerpt.tex","status_markers_as_written":[],"summary_excerpt":"Cutting along [formula in source] yields boundary components [formula in source] . The four local corner patches [formula in source] , [formula in source] , [formula in source] , [formula in source] constitute the fundamental domain. Summing the spin-lifted deficit factor over these sectors yields In TFPT normalization this yields the canonical form [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Sector Count from Cut Geometry","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10194,"byte_start":9840,"id":"section:2b5310aaec958561187c","kind":"subsection","labels":[],"line_end":236,"line_start":227,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/009-subsection-the-unique-chain-excerpt.tex","status_markers_as_written":[],"summary_excerpt":"Using [formula in source] : so [formula in source] and [formula in source] are exactly equivalent.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conversion to the [formula in source] normalizationConversion to the c3 normalization","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10508,"byte_start":10194,"id":"section:3dccd0ccdaa839abb89d","kind":"subsection","labels":[],"line_end":242,"line_start":237,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/009-subsection-the-unique-chain-excerpt.tex","status_markers_as_written":[],"summary_excerpt":"The spin-lift argument fixes the [formula in source] deficit factor robustly, and the sector count is fixed by seam symmetry. The seam normalization is provided by the [formula in source] -gluing derivation in Appendix","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Status note","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10741,"byte_start":10508,"id":"section:b49e86bc233c44cdb769","kind":"section","labels":["app:flavor"],"line_end":248,"line_start":243,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/009-subsection-the-unique-chain-excerpt.tex","status_markers_as_written":[],"summary_excerpt":"This appendix derives the M\\\"obius structure of flavor relations from boundary monodromy.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Flavor Monodromy and Cross-Ratio","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11523,"byte_start":10741,"id":"section:f23f77f45194e46a9d33","kind":"subsection","labels":[],"line_end":267,"line_start":249,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/009-subsection-the-unique-chain-excerpt.tex","status_markers_as_written":[],"summary_excerpt":"On a conformally flat boundary, the metric is locally: Holomorphic automorphisms (Wilson lines of flat connections) act as M\\\"obius transformations:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Projective Invariance on Boundaries","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11957,"byte_start":11523,"id":"section:00ce274305cb99aab9a9","kind":"subsection","labels":[],"line_end":278,"line_start":268,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/009-subsection-the-unique-chain-excerpt.tex","status_markers_as_written":[],"summary_excerpt":"Given four marked points [formula in source] on the boundary, the unique projective invariant is the cross-ratio:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cross-Ratio as Unique Invariant","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12495,"byte_start":11957,"id":"section:46e39d976eac34c716da","kind":"subsection","labels":[],"line_end":289,"line_start":279,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/009-subsection-the-unique-chain-excerpt.tex","status_markers_as_written":[],"summary_excerpt":"The cusps [formula in source] arise from: Rationality: Quantized holonomies [formula in source] rational cusps. GUT compatibility: SU(5) hypercharge assignments give [formula in source] (quarks), [formula in source] (leptons), etc. Uniqueness: These are the only rational values that simultaneously separate the three SM sectors (up, down, lepton) and maintain GUT normalization.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cusp Selection","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13219,"byte_start":12495,"id":"section:5889fc46f8a8d795511a","kind":"subsection","labels":[],"line_end":308,"line_start":290,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/009-subsection-the-unique-chain-excerpt.tex","status_markers_as_written":[],"summary_excerpt":"Leading term: [formula in source] from the abelian trace (same as [formula in source] numerator divided by 41/10's denominator structure).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of [formula in source] Derivation of delta_star","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14627,"byte_start":13219,"id":"section:66b0904859537d64179c","kind":"section","labels":["app:repro"],"line_end":337,"line_start":309,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":["relation:2ae16b23e89aac29a364","relation:80ef87d746931b4836d1","relation:c1004941dfa3193c4d43"],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/009-subsection-the-unique-chain-excerpt.tex","status_markers_as_written":[],"summary_excerpt":"Replication package: All numerical results can be reproduced using the TFPT verification suite (v5).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproducibility","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":23655,"byte_start":14627,"id":"section:f61801b6386cc7d105da","kind":"section","labels":["app:prediction-ledger","tab:prediction-ledger"],"line_end":400,"line_start":338,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/009-subsection-the-unique-chain-excerpt.tex","status_markers_as_written":[],"summary_excerpt":"Purpose: Provide a single, reviewer-friendly list of predictions and candidates that is tied to the same JSON sources used by the verification suite, to prevent number drift between Abstract, theorems, tables, and appendices.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Prediction Ledger and Falsification","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2617,"byte_start":0,"id":"section:777f6131def886d387e7","kind":"section","labels":["app:identities"],"line_end":39,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/010-section-identity-catalogue-and-status-labels.tex","status_markers_as_written":[],"summary_excerpt":"This appendix labels frequently used equalities by logical status to prevent conflating definitions, algebraic rewrites, and genuine predictions.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Identity Catalogue and Status Labels","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3515,"byte_start":2617,"id":"section:f76ee43ef5b3568b4dc7","kind":"section","labels":["app:r2"],"line_end":53,"line_start":40,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/010-section-identity-catalogue-and-status-labels.tex","status_markers_as_written":[],"summary_excerpt":"K1: Field content and torsionful Lagrangian fixed by the minimal UFE sector. K2: Quadratic fluctuation operator is of Laplace type after background-field gauge fixing. K3: Heat-kernel coefficient [formula in source] captures the curvature-squared terms in [formula in source] . K4: Matching to [formula in source] after imposing the GR renormalization condition.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"One-Loop Effective Action in Riemann–Cartan and the [formula in source] CoefficientOne-Loop Effective Action in Riemann–Cartan and the R2 Coefficient","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3873,"byte_start":3515,"id":"section:195ca7cad8b9eaed7467","kind":"subsection","labels":[],"line_end":59,"line_start":54,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/010-section-identity-catalogue-and-status-labels.tex","status_markers_as_written":[],"summary_excerpt":"We evaluate the one-loop effective action in a Riemann–Cartan background with torsion decomposed into axial [formula in source] , trace [formula in source] , and tensor [formula in source] . The minimal UFE choice treats torsion at quadratic order, so integrating out torsion is Gaussian and parameter-free once [formula in source] fixes the normalization of the coupling.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.1 Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4236,"byte_start":3873,"id":"section:ea415fd5fa57e9cba6a6","kind":"subsection","labels":[],"line_end":68,"line_start":60,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/010-section-identity-catalogue-and-status-labels.tex","status_markers_as_written":[],"summary_excerpt":"After background-field gauge fixing, the quadratic operator for torsion fluctuations can be written in Laplace type, with [formula in source] built from curvature and torsion invariants. The contribution to [formula in source] is [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.2 Operator Form","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4606,"byte_start":4236,"id":"section:27498a65f950502eaaf4","kind":"subsection","labels":[],"line_end":76,"line_start":69,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/010-section-identity-catalogue-and-status-labels.tex","status_markers_as_written":[],"summary_excerpt":"The local part of [formula in source] is governed by the heat-kernel expansion where [formula in source] contains the curvature-squared terms. The torsion-dependent pieces combine into an effective [formula in source] operator in the low-energy action.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.3 Heat-Kernel Coefficients","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4807,"byte_start":4606,"id":"section:bbea6a2bf4fbe2b345e5","kind":"subsection","labels":[],"line_end":80,"line_start":77,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/010-section-identity-catalogue-and-status-labels.tex","status_markers_as_written":[],"summary_excerpt":"The GR limit (A8) fixes the renormalization scheme by requiring that the [formula in source] limit reduces to the Einstein–Hilbert action with coefficient [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.4 Renormalization Condition","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5172,"byte_start":4807,"id":"section:0143de8054bfa12f5b32","kind":"subsection","labels":[],"line_end":89,"line_start":81,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/010-section-identity-catalogue-and-status-labels.tex","status_markers_as_written":[],"summary_excerpt":"With the TFPT normalization of the torsion sector, the induced [formula in source] coefficient is fixed by [formula in source] , yielding which reproduces","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.5 TFPT Closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5650,"byte_start":5172,"id":"section:efaad3dbb55d681dff66","kind":"section","labels":["app:bounce"],"line_end":99,"line_start":90,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/010-section-identity-catalogue-and-status-labels.tex","status_markers_as_written":[],"summary_excerpt":"This appendix provides a minimal outline; the full numerical transfer-function evaluation is implemented in the bounce_perturbations verification module (see tfpt-suite/).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bounce Perturbations and the Transfer Function","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5964,"byte_start":5650,"id":"section:4cdbd699d27fb04255ef","kind":"subsection","labels":[],"line_end":104,"line_start":100,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/010-section-identity-catalogue-and-status-labels.tex","status_markers_as_written":[],"summary_excerpt":"The bounce background is modeled by a smooth scale factor [formula in source] where the torsion-induced [formula in source] term regularizes [formula in source] for scalar perturbations. The transition to the [formula in source] inflationary phase is implemented by matching [formula in source] and its derivatives at [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.1 Background Solution","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6257,"byte_start":5964,"id":"section:e575d538166c155334fb","kind":"subsection","labels":[],"line_end":109,"line_start":105,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/010-section-identity-catalogue-and-status-labels.tex","status_markers_as_written":[],"summary_excerpt":"Mode functions are initialized in an adiabatic vacuum well before the bounce and integrated through the bounce and into the [formula in source] era. The numerical scheme records the transfer function by comparing late-time solutions to the pure [formula in source] baseline.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.2 Numerical Integration Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6593,"byte_start":6257,"id":"section:728a6021b1239dbed85b","kind":"subsection","labels":[],"line_end":119,"line_start":110,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/010-section-identity-catalogue-and-status-labels.tex","status_markers_as_written":[],"summary_excerpt":"Define the transfer function as with [formula in source] for modes well inside the horizon during the bounce and deviations confined to [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.3 Transfer Function","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16160,"byte_start":6593,"id":"section:a0085403b77c7da16d9d","kind":"subsection","labels":[],"line_end":394,"line_start":120,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/010-section-identity-catalogue-and-status-labels.tex","status_markers_as_written":[],"summary_excerpt":"Deterministic (given the bounce completion): The transfer-function shape [formula in source] (this appendix; implemented in bounce_perturbations). Given an explicit expansion-history budget, the mapping [formula in source] and the resulting [formula in source] curves are deterministic (implemented in k_calibration and boltzmann_transfer).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.4 The [formula in source] Gate (CMB Observability as Policy Interface)L.4 The k->ell Gate (CMB Observability as Policy Interface)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":379,"byte_start":0,"id":"section:0114fb5844cffc6acc5c","kind":"subsection","labels":[],"line_end":6,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/011-subsection-l-5-falsification-targets.tex","status_markers_as_written":[],"summary_excerpt":"Large-scale suppression or oscillatory features in [formula in source] are predicted at [formula in source] . Current CMB large-scale bounds constrain the allowable feature amplitude, providing a direct observational test of the bounce completion.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.5 Falsification Targets","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2450,"byte_start":379,"id":"section:548f1065cd7c5f4bbe4f","kind":"section","labels":["app:bh-dyonic"],"line_end":46,"line_start":7,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/011-subsection-l-5-falsification-targets.tex","status_markers_as_written":[],"summary_excerpt":"This appendix records a minimal dyonic toy solution showing the [formula in source] scaling of the axion profile and the induced polarization rotation. It is included as analytical support for the EHT intercept test (Sec.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"BH1 Dyonic Toy Solution and Polarization Rotation Scaling (Appendix)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10551,"byte_start":2450,"id":"section:0a3dab11f89158c7202c","kind":"section","labels":["tab:reference-ledger"],"line_end":116,"line_start":47,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/011-subsection-l-5-falsification-targets.tex","status_markers_as_written":[],"summary_excerpt":"round-mode=figures, round-precision=6 =0mu plus 1mu @> p0.20 > p0.12 > p0.10 > p0.10 > p0.12 > p0.28 @ Reference ledger used by the TFPT suite (auto-generated). Key & Value & [formula in source] & Units & Version & Source (stable key)\\\\ Key & Value & [formula in source] & Units & Version & Source (stable key)\\\\ 6r Continued on next page.\\\\ A_s_planck2018 & 2.0989031673e-09 & 2.938464434e-11 & dimensionless & Planck 2","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reference Ledger (Auto-Generated)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14793,"byte_start":10551,"id":"section:484182c7e6ea8509782d","kind":"section","labels":[],"line_end":241,"line_start":117,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv26"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv26/sections/011-subsection-l-5-falsification-targets.tex","status_markers_as_written":[],"summary_excerpt":"99 hehl1976 F. W. Hehl, P. von der Heyde, G. D. Kerlick, J. M. Nester, ``General Relativity with Spin and Torsion: Foundations and Prospects,'' Rev.\\ Mod.\\ Phys.\\ 48, 393 (1976).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"References","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":24201,"byte_start":0,"id":"section:7dcf2af04b559ebd7536","kind":"frontmatter","labels":["fig:alpha-k-sensitivity-suite","fig:bounce-transfer"],"line_end":616,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/preamble.tex","status_markers_as_written":[],"summary_excerpt":"compat=1.18 groupplots arrows.meta,positioning,decorations.markings,decorations.pathmorphing,calc,patterns,shapes.geometric","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Topological Fixed Point Theory (TFPT)\\\\[0.5em] A Parameter-Free Derivation of the Fine-Structure Constant\\\\ from Topology, Geometry, and Quantum Consistency","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2299,"byte_start":0,"id":"section:d8821c38bd47c49eefe6","kind":"frontmatter","labels":[],"line_end":26,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/001-section-kernel-and-discrete-grammar.tex","status_markers_as_written":[],"summary_excerpt":"We present the complete axiomatic foundation of Topological Fixed Point Theory (TFPT), which derives the fine-structure constant [formula in source] , within the declared scheme and renormalization condition, and other fundamental quantities from eight minimal assumptions rooted in topology, geometry, and quantum field theory. The theory rests on two fundamental invariants: the topological coupling [formula in source","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14000,"byte_start":2299,"id":"section:cde958b240632722da62","kind":"section","labels":["fig:compiler","fig:crosslink","tab:constant-factory"],"line_end":198,"line_start":27,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/001-section-kernel-and-discrete-grammar.tex","status_markers_as_written":[],"summary_excerpt":"Structural input (fixed, not fitted): the Standard Model abelian trace [formula in source] (determined by SM particle content and GUT normalization; not a TFPT knob).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kernel and Discrete Grammar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16477,"byte_start":14000,"id":"section:479071b597e817ab081e","kind":"section","labels":["fig:flow"],"line_end":246,"line_start":199,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/001-section-kernel-and-discrete-grammar.tex","status_markers_as_written":[],"summary_excerpt":"The Standard Model of particle physics contains approximately 19 free parameters that must be determined experimentally. Among these, the fine-structure constant [formula in source] stands out as a dimensionless number whose value has no explanation within conventional frameworks.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Introduction: The Problem of Parameters","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16896,"byte_start":16477,"id":"section:8279d0c21c6cf93f1ca3","kind":"section","labels":[],"line_end":254,"line_start":247,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/001-section-kernel-and-discrete-grammar.tex","status_markers_as_written":[],"summary_excerpt":"TFPT is built on eight axioms, organized into three categories: geometric structure, quantum field theory, and closure conditions. 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Reference data: CODATA 2022, PDG 2024. Metric signature: [formula in source] . Levi-Civita tensor: [formula in source] , [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Quantum Field Theory Axioms (A5–A6)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11339,"byte_start":4334,"id":"section:4e3eacfc8731e96d1d44","kind":"subsection","labels":["fig:b1-trace"],"line_end":223,"line_start":89,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/002-subsection-quantum-field-theory-axioms-a5-a6.tex","status_markers_as_written":[],"summary_excerpt":"Standard Model Hypercharge TraceSMT We adopt the convention [formula in source] and count left-handed Weyl fermions plus the Higgs scalar with their SU(2) and color multiplicities. 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TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Geometric Scale [formula in source] The Geometric Scale phi0","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10435,"byte_start":0,"id":"section:40512f111326204141b3","kind":"subsection","labels":["eq:CFE","fig:CFE","fig:alpha2-sensitivity","fig:cfe-unique-suite","fig:invariant_flow","fig:scheme-shift"],"line_end":269,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/003-subsection-the-cubic-fixed-point-equation-cfe.tex","status_markers_as_written":[],"summary_excerpt":"Effective Potential Parametersparams From the 11D Chern–Simons reduction (A5) and modulus-closure structure (A6): Notation: We use [formula in source] (calligraphic) for this CFE parameter to distinguish it from [formula in source] (gravitational coupling) and the contorsion tensor [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Cubic Fixed-Point Equation (CFE)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10570,"byte_start":10435,"id":"section:07eb3d726446d925370f","kind":"subsection","labels":[],"line_end":272,"line_start":270,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/003-subsection-the-cubic-fixed-point-equation-cfe.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Geometric Self-Consistency (Backreaction)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17563,"byte_start":10570,"id":"section:86896a2e8b3a19a4aa8c","kind":"subsubsection","labels":["eq:backreaction","tab:alpha"],"line_end":407,"line_start":273,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/003-subsection-the-cubic-fixed-point-equation-cfe.tex","status_markers_as_written":[],"summary_excerpt":"The response [formula in source] is the closed form consequence of defect sector reweighting on the orientable double cover. The linear form is the [formula in source] expansion, not a separate assumption.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Backreaction as Structural Response","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3265,"byte_start":0,"id":"section:83d4df99b10700189d94","kind":"subsubsection","labels":["fig:alpha-defect-z","sec:sensitivity"],"line_end":76,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/004-subsubsection-sensitivity-analysis.tex","status_markers_as_written":[],"summary_excerpt":"The sub-ppm precision of the [formula in source] prediction depends critically on the backreaction coefficient. We analyze the sensitivity to demonstrate this is not fine-tuning but a genuine geometric constraint.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Sensitivity Analysis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7122,"byte_start":3265,"id":"section:34d76b931306f01d909d","kind":"subsection","labels":["fig:error-ledger","fig:msbar-boundary","sec:comparison-policy"],"line_end":163,"line_start":77,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/004-subsubsection-sensitivity-analysis.tex","status_markers_as_written":[],"summary_excerpt":"( [formula in source] ), fonttitle= ] Why this matters: Precision electroweak fits and PDG summaries use the [formula in source] coupling at [formula in source] , [formula in source] , as the comparison observable. CODATA [formula in source] is an on-shell/IR reference and is therefore treated as secondary diagnostic once scheme and threshold bookkeeping is made explicit.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Comparison and Scheme Policy (No Hidden Knobs)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7324,"byte_start":7122,"id":"section:343ec2392783f03f0b47","kind":"section","labels":[],"line_end":167,"line_start":164,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/004-subsubsection-sensitivity-analysis.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"The Unified Field Equation (UFE)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8474,"byte_start":7324,"id":"section:a30c2996f37fc50b643c","kind":"subsection","labels":[],"line_end":196,"line_start":168,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/004-subsubsection-sensitivity-analysis.tex","status_markers_as_written":[],"summary_excerpt":"Quantum Vacuum TensorQVT Let Let [formula in source] denote the scalar invariant entering the coupling equation, Define the Quantum Vacuum Tensor","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Quantum Vacuum Tensor Packaging","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14675,"byte_start":8474,"id":"section:8a0bb682a3f728efbed9","kind":"subsection","labels":["eq:UFE","eq:bianchi","eq:maxwell"],"line_end":305,"line_start":197,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/004-subsubsection-sensitivity-analysis.tex","status_markers_as_written":[],"summary_excerpt":"UFE ActionUFEaction On a manifold [formula in source] with metric [formula in source] and torsionful connection [formula in source] , the action is: Here [formula in source] denotes the Ricci scalar constructed from the full torsionful connection [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Torsionful Geometric Action","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19247,"byte_start":14675,"id":"section:4cf7999e3c7d614edb7c","kind":"subsection","labels":["fig:torsion-bounds","sec:torsion-regimes"],"line_end":403,"line_start":306,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/004-subsubsection-sensitivity-analysis.tex","status_markers_as_written":[],"summary_excerpt":"TFPT distinguishes between cosmological torsion (which may be active in the early universe and drive a bounce) and local vacuum torsion (which is constrained by laboratory and astrophysical bounds on Lorentz violation). To avoid hidden assumptions, we treat ``torsion today'' as an explicit regime choice rather than a vague qualitative statement.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Present-Day Torsion Regimes and Local Tests","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3654,"byte_start":0,"id":"section:4d984c6f890a5b4ec051","kind":"subsubsection","labels":["fig:evpa_intercept","sec:eht-intercept"],"line_end":68,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/005-subsubsection-achromatic-polarization-rotation-around-co.tex","status_markers_as_written":[],"summary_excerpt":"Beyond the cosmic birefringence prediction (Theorem in the presence of a nonzero [formula in source] environment (see the companion note bhAchromaticRotationNote2025). EHT-style polarimetry provides the relevant data products for such an intercept test ehtm87pol2021. A simple dyonic toy model yields where [formula in source] is the emission radius and [formula in source] denote effective electromagnetic charges sourc","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Achromatic polarization rotation around compact objects (EHT intercept test)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5157,"byte_start":3654,"id":"section:c924623a20022181fa3a","kind":"subsection","labels":[],"line_end":103,"line_start":69,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/005-subsubsection-achromatic-polarization-rotation-around-co.tex","status_markers_as_written":[],"summary_excerpt":"Gravitational Coupling Consistencykappa The gravitational coupling [formula in source] (with dimension [formula in source] ) is constrained by consistency with the dimensionless ratio:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gravitational Coupling from Invariants","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5349,"byte_start":5157,"id":"section:cef345ba5055230e0651","kind":"section","labels":[],"line_end":107,"line_start":104,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/005-subsubsection-achromatic-polarization-rotation-around-co.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Observable Predictions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5816,"byte_start":5349,"id":"section:9233c2ba4bf961c0ffce","kind":"subsection","labels":[],"line_end":119,"line_start":108,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/005-subsubsection-achromatic-polarization-rotation-around-co.tex","status_markers_as_written":[],"summary_excerpt":"Axion–Photon Couplinggagg The CFE fixes the axion–photon vertex uniquely: This determines cosmic birefringence without free parameters.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Axion–Photon Coupling","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7553,"byte_start":5816,"id":"section:1739362fef52984a8697","kind":"subsection","labels":[],"line_end":153,"line_start":120,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/005-subsubsection-achromatic-polarization-rotation-around-co.tex","status_markers_as_written":[],"summary_excerpt":"Topological Excursion Quantizationtopoexcursion The topological axion excursion is quantized in discrete sector changes: with [formula in source] the minimal nontrivial class. The corresponding birefringence is [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cosmic Birefringence","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14702,"byte_start":7553,"id":"section:eb905ca431a31265d3e3","kind":"subsubsection","labels":["eq:shifted-axion-potential","fig:beta-tomography","fig:birefringence","sec:deltaa","tab:birefringence"],"line_end":316,"line_start":154,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/005-subsubsection-achromatic-polarization-rotation-around-co.tex","status_markers_as_written":[],"summary_excerpt":"Goal: Provide one minimal dynamical realization compatible with the topological quantization (Definition","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dynamical Completion of the Excursion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19144,"byte_start":14702,"id":"section:b74eba004cbc24ca75f6","kind":"subsection","labels":["fig:rg-two-loop-running"],"line_end":399,"line_start":317,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/005-subsubsection-achromatic-polarization-rotation-around-co.tex","status_markers_as_written":[],"summary_excerpt":"RG FingerprintsRGfingerprints The TFPT invariants leave signatures in the RG flow of gauge couplings: These values are obtained by two-loop RG running from PDG boundary conditions at [formula in source] using the declared PyR@TE model (checked by two_loop_rg_fingerprints in the verification suite; not direct measurements at the quoted scales). The crossing scale for [formula in source] is [formula in source] GeV.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Two-Loop RG Fingerprints","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":275,"byte_start":0,"id":"section:4f0fcd3491878c6837b6","kind":"section","labels":["sec:e8"],"line_end":5,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/006-section-texorpdfstring-the-e-8-cascade-and-block-constan.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"The E [formula in source] Cascade and Block ConstantsThe E8 Cascade and Block Constants","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2920,"byte_start":275,"id":"section:cf2cbe813bb2c8178219","kind":"subsection","labels":[],"line_end":54,"line_start":6,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/006-section-texorpdfstring-the-e-8-cascade-and-block-constan.tex","status_markers_as_written":[],"summary_excerpt":"E [formula in source] Orbit Graphorbitgraph Let [formula in source] denote the set of nilpotent orbits of the exceptional Lie algebra [formula in source] . For each orbit [formula in source] , define: [formula in source] : the dimension of the orbit as a variety [formula in source] : the ``centralizer dimension'' [formula in source] : the height (sum of coefficients in weighted Dynkin diagram) The orbit graph [formul","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nilpotent Orbit Structure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7494,"byte_start":2920,"id":"section:aef9ef63dea148a705fb","kind":"subsection","labels":["eq:ladder","fig:ladder"],"line_end":160,"line_start":55,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/006-section-texorpdfstring-the-e-8-cascade-and-block-constan.tex","status_markers_as_written":[],"summary_excerpt":"Holonomy degeneracy anchor for [formula in source] holonomydeg TFPT uses the SU(5) hypercharge holonomy data already fixed elsewhere in the construction. On the fundamental splitting, the holonomy spectrum separates into two eigenspaces of dimensions [formula in source] and [formula in source] , hence we define the discrete degeneracy count [formula in source] The minimal damping ratio compatible with a single additi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Log-Exact Ladder Formula","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12099,"byte_start":7494,"id":"section:439f12822f2579f80132","kind":"subsection","labels":["fig:blocks","tab:blocks"],"line_end":271,"line_start":161,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/006-section-texorpdfstring-the-e-8-cascade-and-block-constan.tex","status_markers_as_written":[],"summary_excerpt":"For a 6D Weyl fermion zero mode on a boundary cycle [formula in source] with flat [formula in source] connection (holonomy [formula in source] ), the variation of [formula in source] under the connection is proportional to the quadratic charge index: The proportionality constant is fixed by the topological normalization [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Block Constant Formula and Derivation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13520,"byte_start":12099,"id":"section:36629bedbcc001de416a","kind":"subsection","labels":[],"line_end":304,"line_start":272,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/006-section-texorpdfstring-the-e-8-cascade-and-block-constan.tex","status_markers_as_written":[],"summary_excerpt":"The neutrino block at [formula in source] provides concrete predictions for the seesaw mechanism.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neutrino Seesaw Predictions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13786,"byte_start":13520,"id":"section:0d486344a9daaccd772c","kind":"section","labels":[],"line_end":308,"line_start":305,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/006-section-texorpdfstring-the-e-8-cascade-and-block-constan.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Flavor Structure: The Z [formula in source] ArchitectureFlavor Structure: The Z3 Architecture","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16456,"byte_start":13786,"id":"section:1462f2f5a2feb0058d79","kind":"subsection","labels":[],"line_end":360,"line_start":309,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/006-section-texorpdfstring-the-e-8-cascade-and-block-constan.tex","status_markers_as_written":[],"summary_excerpt":"On a conformally flat boundary geometry, the unique projectively invariant quantity from four marked points is the cross-ratio. Any boundary monodromy acts as a PSL [formula in source] transformation. Therefore, relations depending only on boundary monodromies must be rational functions of a M\\\"obius map.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Universal Phase [formula in source] Universal Phase delta","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1404,"byte_start":0,"id":"section:c9a541433ed64cd2af72","kind":"subsection","labels":[],"line_end":32,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/007-subsection-m-obius-mass-relations.tex","status_markers_as_written":[],"summary_excerpt":"Mass Ratios from M\\\"obius Mapmassratios The M\\\"obius map [formula in source] evaluated at cusps [formula in source] yields mass ratios:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"M\\\"obius Mass Relations","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5189,"byte_start":1404,"id":"section:cb405c3e2f8067be8bd9","kind":"subsection","labels":[],"line_end":116,"line_start":33,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/007-subsection-m-obius-mass-relations.tex","status_markers_as_written":[],"summary_excerpt":"Cabibbo AngleCabibbo The Cabibbo parameter is fixed by the birefringence invariant [formula in source] : Compared to the PDG reference value, this is a sub-permille level deviation (status: solid).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cabibbo Angle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7822,"byte_start":5189,"id":"section:e682ab2773b3e8a15a70","kind":"subsubsection","labels":["fig:ckm-residuals"],"line_end":183,"line_start":117,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/007-subsection-m-obius-mass-relations.tex","status_markers_as_written":[],"summary_excerpt":"The shipped suite includes a deterministic CKM reconstruction pipeline with declared UV textures, two-loop RG dressing, and a reference-scale comparison at [formula in source] (module ckm_full_pipeline). The baseline benchmark gives a CKM matrix close to PDG at the level quantified by the reported [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Suite benchmark: RG-dressed CKM pipeline (explicit conventions)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11609,"byte_start":7822,"id":"section:944e425986cb68a1f806","kind":"subsubsection","labels":["fig:kaon_bar","fig:kaon_correlation","sec:rare-kaon"],"line_end":281,"line_start":184,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/007-subsection-m-obius-mass-relations.tex","status_markers_as_written":[],"summary_excerpt":"The ultra clean modes [formula in source] and [formula in source] provide a stringent test of the TFPT flavor architecture, because long-distance hadronic uncertainties are strongly suppressed (see the companion note rareKaonNote2025).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Rare Kaon Decays: [formula in source] as a clean flavor null testRare Kaon Decays: K to pi nu nu as a clean flavor null test","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15476,"byte_start":11609,"id":"section:bef235de7f89c0441859","kind":"subsection","labels":["fig:pmns-residuals"],"line_end":375,"line_start":282,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/007-subsection-m-obius-mass-relations.tex","status_markers_as_written":[],"summary_excerpt":"TFPT provides a closed prediction for [formula in source] via a single kernel identity plus the TM1 pattern. The remaining PMNS degrees of freedom [formula in source] are treated as an open interface requiring explicit Z [formula in source] -breaking and (eventually) correlated Yukawa/RG treatment; they must not be read as closed predictions at this stage.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"PMNS Neutrino Mixing: TM1 Pattern","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1782,"byte_start":0,"id":"section:f28e2c593e53e7d68e49","kind":"section","labels":["eq:As","eq:R2action","eq:ns","eq:r","tab:inflation"],"line_end":41,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/008-section-texorpdfstring-inflation-r-2-completion-starobin.tex","status_markers_as_written":[],"summary_excerpt":"The TFPT topological correction scale is set by [formula in source] (cf.\\ [formula in source] ). In effective gravity, the leading higher-curvature completion compatible with general covariance is an [formula in source] term.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Inflation: [formula in source] Completion (Starobinsky Limit)Inflation: R2 Completion (Starobinsky Limit)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3920,"byte_start":1782,"id":"section:5de1c91682ff22ca9e32","kind":"subsection","labels":["fig:r2-blocks","sec:r2derive"],"line_end":94,"line_start":42,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/008-section-texorpdfstring-inflation-r-2-completion-starobin.tex","status_markers_as_written":[],"summary_excerpt":"Relevant Torsion DegreesR2torsion Decompose torsion into irreducible parts [formula in source] (axial, trace, tensor). In the minimal UFE setting the dominant coupling is through axial torsion [formula in source] , and the torsion sector is treated at quadratic order so it can be integrated out in the one-loop effective action.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[formula in source] Term from the Torsionful Effective ActionR2 Term from the Torsionful Effective Action","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5762,"byte_start":3920,"id":"section:be9293a5cc770eafb7a9","kind":"subsection","labels":["eq:R2scale","fig:r2-scan"],"line_end":143,"line_start":95,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/008-section-texorpdfstring-inflation-r-2-completion-starobin.tex","status_markers_as_written":[],"summary_excerpt":"TFPT [formula in source] ScaleR2coeff Using the GR renormalization condition (A8) to fix the scheme, the coefficient of the [formula in source] term yields Here the square root applies only to [formula in source] , consistent with the numerical value above.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Coefficient Identification and GR Renormalization","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7392,"byte_start":5762,"id":"section:d150289ee4ec422d5b69","kind":"subsection","labels":["sec:bounce"],"line_end":180,"line_start":144,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/008-section-texorpdfstring-inflation-r-2-completion-starobin.tex","status_markers_as_written":[],"summary_excerpt":"Bounce-to-Inflation Backgroundbouncebg Assume a non-singular bounce driven by the torsion-induced [formula in source] term (Lemma above), followed by a transition into the [formula in source] inflationary phase. We take the CMB pivot scales to exit the horizon during the [formula in source] phase.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bounce + [formula in source] Perturbations and Transfer FunctionBounce + R2 Perturbations and Transfer Function","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7593,"byte_start":7392,"id":"section:a2dabfb0f715c857503d","kind":"section","labels":[],"line_end":184,"line_start":181,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/008-section-texorpdfstring-inflation-r-2-completion-starobin.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Axion Cosmology and Dark Matter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9770,"byte_start":7593,"id":"section:5797ca76ce224402af50","kind":"subsection","labels":[],"line_end":223,"line_start":185,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/008-section-texorpdfstring-inflation-r-2-completion-starobin.tex","status_markers_as_written":[],"summary_excerpt":"The TFPT axion sector is split into two distinct fields to avoid an internal contradiction (a single [formula in source] eV axion cannot remain quasi-static over Hubble times):","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Two-Field Structure: Topological vs.\\ QCD Axion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12923,"byte_start":9770,"id":"section:b12533c256cd711d1ed6","kind":"subsection","labels":[],"line_end":274,"line_start":224,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/008-section-texorpdfstring-inflation-r-2-completion-starobin.tex","status_markers_as_written":[],"summary_excerpt":"Axion Dark Matter ParametersaxionDM For the QCD axion field [formula in source] from the E [formula in source] cascade (PQ block at [formula in source] ):","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dark Matter Relic Density","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15004,"byte_start":12923,"id":"section:9032146512f66241ba07","kind":"subsection","labels":["sec:dark-energy"],"line_end":309,"line_start":275,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/008-section-texorpdfstring-inflation-r-2-completion-starobin.tex","status_markers_as_written":[],"summary_excerpt":"with no continuous knobs, fonttitle= ] We test the discrete defect-suppression candidate [formula in source] The two-defect sector uses [formula in source] and the corresponding [formula in source] (Sec.","summary_method":"opening prose excerpt; 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Domain & Quantity & Deviation & Status\\\\ Domain & Quantity & Deviation & Status\\\\ 4r Continued on next page.\\\\ 4l Structural (parameter-free)\\\\ CFE & [formula in source] & [formula in source] & green!60!black Derived (double cover + [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Summary of Claims and Status","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5862,"byte_start":5226,"id":"section:aa3f1a3a0bacb9c17972","kind":"section","labels":[],"line_end":77,"line_start":64,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/009-section-summary-of-claims-and-status.tex","status_markers_as_written":[],"summary_excerpt":"The following are not required: Slow-roll inflation (specific model) String landscape or anthropic selection Extra dimensions as free parameters Dark matter entirely from axions New particles beyond minimal axion sector Any fitted or adjusted parameters","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"What TFPT Does Not Assume","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7331,"byte_start":5862,"id":"section:d637193ea88af12d4735","kind":"section","labels":[],"line_end":103,"line_start":78,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/009-section-summary-of-claims-and-status.tex","status_markers_as_written":[],"summary_excerpt":"TFPT demonstrates that the fine-structure constant [formula in source] can be derived within an explicit set of eight minimal axioms rooted in topology, geometry, and quantum consistency. The key results are:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conclusions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7824,"byte_start":7331,"id":"section:56a96b24050a8e9ba10e","kind":"paragraph","labels":[],"line_end":111,"line_start":104,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/009-section-summary-of-claims-and-status.tex","status_markers_as_written":[],"summary_excerpt":"Two longer-range directions are sketched in internal notes and remain explicitly open: an asymptotic-safety UV completion for the torsionful gravity sector and a black-hole vortex/remnant picture with information-paradox implications. Both are framed as outlook items rather than closed predictions at this stage fiveProblemsNote2025,blackHolesBh1Note2025.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Outlook (open interfaces).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10716,"byte_start":7824,"id":"section:4b52f583eab925d61866","kind":"section","labels":["tab:constants"],"line_end":156,"line_start":112,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/009-section-summary-of-claims-and-status.tex","status_markers_as_written":[],"summary_excerpt":"@ll@ Quantity & Value\\\\ [formula in source] & \\\\ [formula in source] & \\\\ [formula in source] & \\\\ [formula in source] & \\\\ [formula in source] (self-consistent) & 0.053170209119023745\\\\ [formula in source] & \\\\ [formula in source] & [formula in source] \\\\ [formula in source] & \\\\ [formula in source] (E [formula in source] ) & [formula in source] \\\\ [formula in source] (E [formula in source] exponent) & 0.58723319078","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Numerical Constants (High Precision)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11533,"byte_start":10716,"id":"section:01f85e749fbbf21d1a51","kind":"section","labels":["app:gdiagnostic"],"line_end":169,"line_start":157,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/009-section-summary-of-claims-and-status.tex","status_markers_as_written":[],"summary_excerpt":"The suite records legacy diagnostic templates in which [formula in source] is varied away from the holonomy value [formula in source] (e.g.\\ the ordered-occupancy [formula in source] template). 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They are explicitly not used for parameter select","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Diagnostic [formula in source] Variants (Internal Sanity Checks)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12705,"byte_start":11533,"id":"section:412c3d103168c503b862","kind":"section","labels":["fig:rg-unification"],"line_end":200,"line_start":170,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/009-section-summary-of-claims-and-status.tex","status_markers_as_written":[],"summary_excerpt":"Gauge coupling convergence. Visualizes the unification gate scan used by the suite.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"RG Unification Overview (Supplementary)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20901,"byte_start":12705,"id":"section:5d8fca7936195d033a3d","kind":"section","labels":["eq:CFE-appendix","eq:potential","eq:stationarity"],"line_end":365,"line_start":201,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/009-section-summary-of-claims-and-status.tex","status_markers_as_written":[],"summary_excerpt":"This appendix records the coefficient bookkeeping used in the suite and provides a heuristic motivation for the CFE coefficient policy. It is not presented as a full background-field derivation. In the declared scheme, the one-loop effective potential for the electromagnetic coupling modulus is taken to have the form:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Coefficient Policy Sketch for the CFE","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1518,"byte_start":0,"id":"section:53286048df163fbd0d69","kind":"section","labels":[],"line_end":18,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"The TFPT verification suite turns paper claims into deterministic, assumption-explicit computations. All counts in this section are auto-generated from the suite artifacts (no hardcoded ``39 modules''): [formula in source] It ships: a conventional suite (registry-driven; core invariants, [formula in source] closure + policy bridge, RG/matching, flavor pipelines, cosmology/bounce wiring, torsion/birefringence, dashboa","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verification Suite Summary","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1898,"byte_start":1518,"id":"section:b27ab59790ce709c1023","kind":"subsection","labels":["sec:known-gaps"],"line_end":25,"line_start":19,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"For the PRL-facing manuscript we omit the auto-generated flagged/open inventory and list open interfaces only as conditional statements in the main text. The full suite manifest (with module-level status and plot inventories) is included in the replication bundle referenced in Appendix","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Known Gaps and Status (Summary)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9864,"byte_start":1898,"id":"section:4ff1f32db9fb8296e618","kind":"subsection","labels":["fig:likelihood-breakdown","sec:theoryv3-evidence"],"line_end":219,"line_start":26,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"The theoryv3 analysis branch is a compact ``evidence layer'' for the discrete kernel and crosslink logic. Current inventory (auto-generated from the replication bundle; theoryv3 is a baseline branch pinned to v2.5 by design): [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"theoryv3 Evidence Layer (Compressed, Auto-Generated)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10164,"byte_start":9864,"id":"section:4f3630da3717a884fd10","kind":"section","labels":["app:E8cert"],"line_end":226,"line_start":220,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"This appendix provides the complete verification data for the E [formula in source] chain uniqueness theorem (Theorem","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"E [formula in source] Chain CertificateE8 Chain Certificate","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10668,"byte_start":10164,"id":"section:bd7462e66c67ddbe98c1","kind":"subsection","labels":[],"line_end":236,"line_start":227,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"Each nilpotent orbit [formula in source] of [formula in source] is characterized by: Bala–Carter label: Standard notation (e.g., [formula in source] , [formula in source] , [formula in source] , ) Dimension: [formula in source] Centralizer dimension: [formula in source] Height: [formula in source] (sum of weighted Dynkin diagram coefficients)","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Orbit Data Structure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11344,"byte_start":10668,"id":"section:53cbc6fca0d1c65562e8","kind":"subsection","labels":[],"line_end":261,"line_start":237,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"The complete chain from [formula in source] to [formula in source] :","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Unique Chain (Excerpt)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12112,"byte_start":11344,"id":"section:6e6250ad96049af719bb","kind":"subsection","labels":[],"line_end":276,"line_start":262,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"The uniqueness is verified by: Constructing the complete Hasse diagram of [formula in source] from standard tables. Computing all cover relations with [formula in source] . Running dynamic programming to find all paths from [formula in source] to [formula in source] . Applying the cost function [formula in source] (second-difference smoothness). Verifying that the minimum-cost path is unique (cost gap to second-best ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verification Algorithm","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12352,"byte_start":12112,"id":"section:11969c29ee3b42b6632f","kind":"section","labels":["app:boundary"],"line_end":283,"line_start":277,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"This appendix derives the block index formula [formula in source] from the APS index theorem.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Boundary Trace Derivation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12743,"byte_start":12352,"id":"section:b3ff2a1e4d51010122b3","kind":"subsection","labels":[],"line_end":293,"line_start":284,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"Consider a 6D manifold [formula in source] with boundary [formula in source] . For a Weyl fermion coupled to a [formula in source] gauge field [formula in source] , the APS index theorem gives: where [formula in source] is the [formula in source] -invariant of the boundary Dirac operator.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13256,"byte_start":12743,"id":"section:1bd36948bb9da9f00e18","kind":"subsection","labels":[],"line_end":308,"line_start":294,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"On the orientable double cover [formula in source] , the boundary decomposes as: (two boundary cycles plus the twist seam).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Flat Connection on Boundary Cycles","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14773,"byte_start":13256,"id":"section:29c448f38d57644fe788","kind":"subsection","labels":[],"line_end":336,"line_start":309,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"The regulated determinant of the hypercharge-coupled Dirac operator contains a logarithmic term which we normalize as: We define the spectral index [formula in source] as the quadratic charge trace entering this term in our normalization; the overall prefactor is part of the declared coefficient policy (Appendix C) and differs by a fixed normalization from the conventional [formula in source] Seeley–DeWitt prefactor.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spectral Trace Coefficient and [formula in source] Spectral Trace Coefficient and b1","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15554,"byte_start":14773,"id":"section:8cd8896455122a43e846","kind":"subsection","labels":[],"line_end":356,"line_start":337,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"Step 1: Each boundary cycle contributes a factor proportional to [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of [formula in source] Derivation of kB","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15868,"byte_start":15554,"id":"section:971221617a233fea3320","kind":"section","labels":["app:seam"],"line_end":362,"line_start":357,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"This appendix provides the [formula in source] -invariant gluing derivation used in Axiom","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Seam Gluing and the [formula in source] -Invariant NormalizationSeam Gluing and the eta-Invariant Normalization","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16470,"byte_start":15868,"id":"section:87cb7afdff1482f22276","kind":"subsection","labels":[],"line_end":373,"line_start":363,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the orientable double cover of the M\\\"obius fiber and cut it along the seam [formula in source] to obtain a manifold-with-boundary [formula in source] with boundary components [formula in source] . Let [formula in source] be the Dirac operator on [formula in source] with APS boundary conditions on [formula in source] and a unitary matching operator [formula in source] identifying [formula i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cut Space and Operators","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":634,"byte_start":0,"id":"section:92ed0fc653e043b5f018","kind":"subsection","labels":[],"line_end":13,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"The APS gluing theorem expresses the [formula in source] -invariant of the glued manifold in terms of the cut manifold plus a discrete spectral-flow correction: where [formula in source] is the spectral flow of the matching operator. In TFPT bookkeeping this contributes a quantized seam term to the curvature normalization.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gluing Formula for the [formula in source] -InvariantGluing Formula for the eta-Invariant","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":918,"byte_start":634,"id":"section:945e3e6444cc95105130","kind":"subsection","labels":[],"line_end":20,"line_start":14,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"For the M\\\"obius [formula in source] identification, the matching satisfies [formula in source] . The minimal nontrivial class is modeled by the unitary phase","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"M\\\"obius Matching and the Minimal Gluing Class","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1584,"byte_start":918,"id":"section:f0b71c846c7db0c79564","kind":"subsection","labels":[],"line_end":37,"line_start":21,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"Interpolate boundary conditions by a phase [formula in source] , which gives the eigenvalues As [formula in source] runs from [formula in source] to [formula in source] , exactly one eigenvalue crosses zero, so [formula in source] and [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spectral Flow Computation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2122,"byte_start":1584,"id":"section:1de205195ff76c4a666a","kind":"subsection","labels":[],"line_end":47,"line_start":38,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"The two physical boundary cycles contribute [formula in source] , and the seam gluing adds [formula in source] , so the total curvature is [formula in source] . We treat [formula in source] as the dimensionless geometry modulus; the closure normalization [formula in source] fixes its scale and therefore yields","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Normalization of [formula in source] Normalization of phi_tree","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2628,"byte_start":2122,"id":"section:88b90d99849b1ef86895","kind":"section","labels":["app:48deriv"],"line_end":58,"line_start":48,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"This appendix explains the integer coefficient in [formula in source] . The key point is that the canonical quantity is and the appearance of ``48'' is simply the same number expressed in units of [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of the Coefficient 48 in [formula in source] Derivation of the Coefficient 48 in delta_top","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3352,"byte_start":2628,"id":"section:522bcc253273240fa154","kind":"subsection","labels":[],"line_end":71,"line_start":59,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"The topological correction [formula in source] arises from the leading gauge-invariant correction to the tree-level geometric scale [formula in source] . The requirements are: Gauge invariance: The correction must be built from [formula in source] only (no explicit [formula in source] dependence at this order). Dimensionlessness: Since [formula in source] is dimensionless, the correction must be a pure power [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Physical Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4157,"byte_start":3352,"id":"section:5fe6c348907a325f0434","kind":"subsection","labels":[],"line_end":88,"line_start":72,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"The effective action on the M\\\"obius fiber includes the Chern–Simons term [formula in source] . The leading topological correction comes from the one-loop determinant of the Dirac operator coupled to this background.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Power Counting: Why [formula in source] ?Power Counting: Why c3^4?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4552,"byte_start":4157,"id":"section:75b1f22c67b3db012d9a","kind":"subsection","labels":[],"line_end":98,"line_start":89,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"The non-orientable identification acts as a [formula in source] operation on the base, but in the spin bundle the same element lifts to order [formula in source] because a [formula in source] rotation acts as [formula in source] on spinors and only a [formula in source] rotation is trivial. This produces a universal deficit factor per minimal sector.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spin-Lifted Deficit Factor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5058,"byte_start":4552,"id":"section:5749ac5ce791e48c541a","kind":"subsection","labels":[],"line_end":108,"line_start":99,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"Cutting along [formula in source] yields boundary components [formula in source] . The four local corner patches [formula in source] , [formula in source] , [formula in source] , [formula in source] constitute the fundamental domain. Summing the spin-lifted deficit factor over these sectors yields In TFPT normalization this yields the canonical form [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Sector Count from Cut Geometry","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5412,"byte_start":5058,"id":"section:3e6c649931d61d401f61","kind":"subsection","labels":[],"line_end":118,"line_start":109,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"Using [formula in source] : so [formula in source] and [formula in source] are exactly equivalent.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conversion to the [formula in source] normalizationConversion to the c3 normalization","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5726,"byte_start":5412,"id":"section:f257455a4db592f237c6","kind":"subsection","labels":[],"line_end":124,"line_start":119,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"The spin-lift argument fixes the [formula in source] deficit factor robustly, and the sector count is fixed by seam symmetry. The seam normalization is provided by the [formula in source] -gluing derivation in Appendix","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Status note","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5959,"byte_start":5726,"id":"section:e8c84d6d6c1592fa74cd","kind":"section","labels":["app:flavor"],"line_end":130,"line_start":125,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"This appendix derives the M\\\"obius structure of flavor relations from boundary monodromy.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Flavor Monodromy and Cross-Ratio","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6741,"byte_start":5959,"id":"section:0f780ff69febdab56123","kind":"subsection","labels":[],"line_end":149,"line_start":131,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"On a conformally flat boundary, the metric is locally: Holomorphic automorphisms (Wilson lines of flat connections) act as M\\\"obius transformations:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Projective Invariance on Boundaries","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7175,"byte_start":6741,"id":"section:a50b2d500d879566331d","kind":"subsection","labels":[],"line_end":160,"line_start":150,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"Given four marked points [formula in source] on the boundary, the unique projective invariant is the cross-ratio:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cross-Ratio as Unique Invariant","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7713,"byte_start":7175,"id":"section:6e97d38a8623f19c546c","kind":"subsection","labels":[],"line_end":171,"line_start":161,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"The cusps [formula in source] arise from: Rationality: Quantized holonomies [formula in source] rational cusps. GUT compatibility: SU(5) hypercharge assignments give [formula in source] (quarks), [formula in source] (leptons), etc. Uniqueness: These are the only rational values that simultaneously separate the three SM sectors (up, down, lepton) and maintain GUT normalization.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cusp Selection","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8437,"byte_start":7713,"id":"section:d9abac6d0f31eeebf866","kind":"subsection","labels":[],"line_end":190,"line_start":172,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"Leading term: [formula in source] from the abelian trace (same as [formula in source] numerator divided by 41/10's denominator structure).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of [formula in source] Derivation of delta_star","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10105,"byte_start":8437,"id":"section:8449c833676b4c0bf34e","kind":"section","labels":["app:repro"],"line_end":222,"line_start":191,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":["relation:25d80331860e83f570c4","relation:5b08bcdce3f8c686bafb","relation:919aabb08381853b22ce","relation:b8f950d7c650c822b6f0"],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"Replication package: All numerical results can be reproduced using the TFPT verification suite (v5).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproducibility","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19140,"byte_start":10105,"id":"section:5c76fc1c4c5f1262aef7","kind":"section","labels":["app:prediction-ledger","tab:prediction-ledger"],"line_end":285,"line_start":223,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"Purpose: Provide a single, reviewer-friendly list of predictions and candidates that is tied to the same JSON sources used by the verification suite, to prevent number drift between Abstract, theorems, tables, and appendices.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Prediction Ledger and Falsification","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":21757,"byte_start":19140,"id":"section:ad9faa4d4f8f740c82db","kind":"section","labels":["app:identities"],"line_end":324,"line_start":286,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"This appendix labels frequently used equalities by logical status to prevent conflating definitions, algebraic rewrites, and genuine predictions.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Identity Catalogue and Status Labels","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":22655,"byte_start":21757,"id":"section:749f86b2a4b307883e75","kind":"section","labels":["app:r2"],"line_end":338,"line_start":325,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"K1: Field content and torsionful Lagrangian fixed by the minimal UFE sector. K2: Quadratic fluctuation operator is of Laplace type after background-field gauge fixing. K3: Heat-kernel coefficient [formula in source] captures the curvature-squared terms in [formula in source] . K4: Matching to [formula in source] after imposing the GR renormalization condition.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"One-Loop Effective Action in Riemann–Cartan and the [formula in source] CoefficientOne-Loop Effective Action in Riemann–Cartan and the R2 Coefficient","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":23013,"byte_start":22655,"id":"section:642bca9b0f8eacbbec94","kind":"subsection","labels":[],"line_end":344,"line_start":339,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"We evaluate the one-loop effective action in a Riemann–Cartan background with torsion decomposed into axial [formula in source] , trace [formula in source] , and tensor [formula in source] . The minimal UFE choice treats torsion at quadratic order, so integrating out torsion is Gaussian and parameter-free once [formula in source] fixes the normalization of the coupling.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.1 Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":23376,"byte_start":23013,"id":"section:4e32a8367966b059ff19","kind":"subsection","labels":[],"line_end":353,"line_start":345,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"After background-field gauge fixing, the quadratic operator for torsion fluctuations can be written in Laplace type, with [formula in source] built from curvature and torsion invariants. The contribution to [formula in source] is [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.2 Operator Form","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":23746,"byte_start":23376,"id":"section:79c74248a3cb831d4ca5","kind":"subsection","labels":[],"line_end":361,"line_start":354,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"The local part of [formula in source] is governed by the heat-kernel expansion where [formula in source] contains the curvature-squared terms. The torsion-dependent pieces combine into an effective [formula in source] operator in the low-energy action.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.3 Heat-Kernel Coefficients","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":23947,"byte_start":23746,"id":"section:5b4e323ccb7b6c3ab486","kind":"subsection","labels":[],"line_end":365,"line_start":362,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"The GR limit (A8) fixes the renormalization scheme by requiring that the [formula in source] limit reduces to the Einstein–Hilbert action with coefficient [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.4 Renormalization Condition","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":24312,"byte_start":23947,"id":"section:d143a83317611cd9f39c","kind":"subsection","labels":[],"line_end":374,"line_start":366,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"With the TFPT normalization of the torsion sector, the induced [formula in source] coefficient is fixed by [formula in source] , yielding which reproduces","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.5 TFPT Closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":476,"byte_start":0,"id":"section:3501abbab49f9be3242d","kind":"section","labels":["app:bounce"],"line_end":10,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/012-section-bounce-perturbations-and-the-transfer-function.tex","status_markers_as_written":[],"summary_excerpt":"This appendix provides a minimal outline; the full numerical transfer-function evaluation is implemented in the bounce_perturbations verification module (see replication bundle).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bounce Perturbations and the Transfer Function","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":790,"byte_start":476,"id":"section:9eb31e51b4eab5026c2b","kind":"subsection","labels":[],"line_end":15,"line_start":11,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/012-section-bounce-perturbations-and-the-transfer-function.tex","status_markers_as_written":[],"summary_excerpt":"The bounce background is modeled by a smooth scale factor [formula in source] where the torsion-induced [formula in source] term regularizes [formula in source] for scalar perturbations. The transition to the [formula in source] inflationary phase is implemented by matching [formula in source] and its derivatives at [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.1 Background Solution","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1083,"byte_start":790,"id":"section:0425f43355adff6685bf","kind":"subsection","labels":[],"line_end":20,"line_start":16,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/012-section-bounce-perturbations-and-the-transfer-function.tex","status_markers_as_written":[],"summary_excerpt":"Mode functions are initialized in an adiabatic vacuum well before the bounce and integrated through the bounce and into the [formula in source] era. The numerical scheme records the transfer function by comparing late-time solutions to the pure [formula in source] baseline.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.2 Numerical Integration Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1392,"byte_start":1083,"id":"section:e9e57a8b81d579dd9164","kind":"subsection","labels":[],"line_end":28,"line_start":21,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/012-section-bounce-perturbations-and-the-transfer-function.tex","status_markers_as_written":[],"summary_excerpt":"Define the transfer function as with [formula in source] for modes well inside the horizon during the bounce and deviations confined to [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.3 Transfer Function","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11019,"byte_start":1392,"id":"section:87ce05491d3c710edfbe","kind":"subsection","labels":[],"line_end":305,"line_start":29,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/012-section-bounce-perturbations-and-the-transfer-function.tex","status_markers_as_written":[],"summary_excerpt":"Deterministic (given the bounce completion): The transfer-function shape [formula in source] (this appendix; implemented in bounce_perturbations). Given an explicit expansion-history budget, the mapping [formula in source] and the resulting [formula in source] curves are deterministic (implemented in k_calibration and boltzmann_transfer).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.4 The [formula in source] Gate (CMB Observability as Policy Interface)L.4 The k->ell Gate (CMB Observability as Policy Interface)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11398,"byte_start":11019,"id":"section:ad2e198c96a8acdcae6e","kind":"subsection","labels":[],"line_end":311,"line_start":306,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/012-section-bounce-perturbations-and-the-transfer-function.tex","status_markers_as_written":[],"summary_excerpt":"Large-scale suppression or oscillatory features in [formula in source] are predicted at [formula in source] . Current CMB large-scale bounds constrain the allowable feature amplitude, providing a direct observational test of the bounce completion.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.5 Falsification Targets","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13469,"byte_start":11398,"id":"section:affe502115db1717bd7c","kind":"section","labels":["app:bh-dyonic"],"line_end":351,"line_start":312,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/012-section-bounce-perturbations-and-the-transfer-function.tex","status_markers_as_written":[],"summary_excerpt":"This appendix records a minimal dyonic toy solution showing the [formula in source] scaling of the axion profile and the induced polarization rotation. It is included as analytical support for the EHT intercept test (Sec.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"BH1 Dyonic Toy Solution and Polarization Rotation Scaling (Appendix)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8101,"byte_start":0,"id":"section:637d927670bfc8c840d3","kind":"section","labels":["tab:reference-ledger"],"line_end":70,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/013-section-reference-ledger-auto-generated.tex","status_markers_as_written":[],"summary_excerpt":"round-mode=figures, round-precision=6 =0mu plus 1mu @> p0.20 > p0.12 > p0.10 > p0.10 > p0.12 > p0.28 @ Reference ledger used by the TFPT suite (auto-generated). Key & Value & [formula in source] & Units & Version & Source (stable key)\\\\ Key & Value & [formula in source] & Units & Version & Source (stable key)\\\\ 6r Continued on next page.\\\\ A_s_planck2018 & 2.0989031673e-09 & 2.938464434e-11 & dimensionless & Planck 2","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reference Ledger (Auto-Generated)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12265,"byte_start":8101,"id":"section:3da7664dda4021b23bce","kind":"section","labels":[],"line_end":194,"line_start":71,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27-final"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/013-section-reference-ledger-auto-generated.tex","status_markers_as_written":[],"summary_excerpt":"99 hehl1976 F. W. Hehl, P. von der Heyde, G. D. Kerlick, J. M. Nester, ``General Relativity with Spin and Torsion: Foundations and Prospects,'' Rev.\\ Mod.\\ Phys.\\ 48, 393 (1976).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"References","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":23089,"byte_start":0,"id":"section:ac22d98f5d135ac165f2","kind":"frontmatter","labels":["fig:alpha-k-sensitivity-suite","fig:bounce-transfer"],"line_end":600,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/preamble.tex","status_markers_as_written":[],"summary_excerpt":"compat=1.18 groupplots arrows.meta,positioning,decorations.markings,decorations.pathmorphing,calc,patterns,shapes.geometric","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Topological Fixed Point Theory (TFPT)\\\\[0.5em] A Parameter-Free Derivation of the Fine-Structure Constant\\\\ from Topology, Geometry, and Quantum Consistency","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2240,"byte_start":0,"id":"section:7197172c202227126403","kind":"frontmatter","labels":[],"line_end":25,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/001-section-kernel-and-discrete-grammar.tex","status_markers_as_written":[],"summary_excerpt":"We present the complete axiomatic foundation of Topological Fixed Point Theory (TFPT), which derives the fine-structure constant [formula in source] , within the declared scheme and renormalization condition, and other fundamental quantities from eight minimal assumptions rooted in topology, geometry, and quantum field theory. The theory rests on two fundamental invariants: the topological coupling [formula in source","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13941,"byte_start":2240,"id":"section:ace0cdfc38e23080b9a2","kind":"section","labels":["fig:compiler","fig:crosslink","tab:constant-factory"],"line_end":197,"line_start":26,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/001-section-kernel-and-discrete-grammar.tex","status_markers_as_written":[],"summary_excerpt":"Structural input (fixed, not fitted): the Standard Model abelian trace [formula in source] (determined by SM particle content and GUT normalization; not a TFPT knob).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kernel and Discrete Grammar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16418,"byte_start":13941,"id":"section:2c0fafba6e2d5b1c149f","kind":"section","labels":["fig:flow"],"line_end":245,"line_start":198,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/001-section-kernel-and-discrete-grammar.tex","status_markers_as_written":[],"summary_excerpt":"The Standard Model of particle physics contains approximately 19 free parameters that must be determined experimentally. Among these, the fine-structure constant [formula in source] stands out as a dimensionless number whose value has no explanation within conventional frameworks.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Introduction: The Problem of Parameters","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16837,"byte_start":16418,"id":"section:a0ebac42476e539a4baf","kind":"section","labels":[],"line_end":253,"line_start":246,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/001-section-kernel-and-discrete-grammar.tex","status_markers_as_written":[],"summary_excerpt":"TFPT is built on eight axioms, organized into three categories: geometric structure, quantum field theory, and closure conditions. Each axiom is either derived from established physics or explicitly marked as a new postulate.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Axiomatic Foundation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":24410,"byte_start":16837,"id":"section:836641ffabb026e08664","kind":"subsection","labels":["fig:doublecover"],"line_end":414,"line_start":254,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/001-section-kernel-and-discrete-grammar.tex","status_markers_as_written":[],"summary_excerpt":"Riemann–Cartan GeometryRC The fundamental spacetime connection possesses torsion; the Levi-Civita connection is a limiting case when torsion vanishes.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Geometric Axioms (A1–A4)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4183,"byte_start":0,"id":"section:cef4167e3993ccc88951","kind":"subsection","labels":[],"line_end":87,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/002-subsection-quantum-field-theory-axioms-a5-a6.tex","status_markers_as_written":[],"summary_excerpt":"Units and constants: Natural units: [formula in source] ; energies in GeV, lengths in GeV [formula in source] . Reference data: CODATA 2022, PDG 2024. Metric signature: [formula in source] . Levi-Civita tensor: [formula in source] , [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Quantum Field Theory Axioms (A5–A6)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10842,"byte_start":4183,"id":"section:93c191847a65816a32a5","kind":"subsection","labels":["fig:b1-trace"],"line_end":220,"line_start":88,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/002-subsection-quantum-field-theory-axioms-a5-a6.tex","status_markers_as_written":[],"summary_excerpt":"Standard Model Hypercharge TraceSMT We adopt the convention [formula in source] and count left-handed Weyl fermions plus the Higgs scalar with their SU(2) and color multiplicities. Define the hypercharge trace Here [formula in source] is the SM-normalized trace coefficient and [formula in source] is the corresponding GUT-normalized coefficient used in the CFE. For the SM field content (three generations + one Higgs d","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Closure Axioms (A7–A8)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11047,"byte_start":10842,"id":"section:e379ca54e9a2e1fa467a","kind":"section","labels":[],"line_end":224,"line_start":221,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/002-subsection-quantum-field-theory-axioms-a5-a6.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Derivation of Fundamental Constants","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13305,"byte_start":11047,"id":"section:8c83bf00798eb2359c0d","kind":"subsection","labels":[],"line_end":275,"line_start":225,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/002-subsection-quantum-field-theory-axioms-a5-a6.tex","status_markers_as_written":[],"summary_excerpt":"Existence and Uniqueness of [formula in source] phi0 From Axioms A3 and A4, the geometric scale is uniquely determined:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Geometric Scale [formula in source] The Geometric Scale phi0","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10435,"byte_start":0,"id":"section:cff793a093e64eedab33","kind":"subsection","labels":["eq:CFE","fig:CFE","fig:alpha2-sensitivity","fig:cfe-unique-suite","fig:invariant_flow","fig:scheme-shift"],"line_end":269,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/003-subsection-the-cubic-fixed-point-equation-cfe.tex","status_markers_as_written":[],"summary_excerpt":"Effective Potential Parametersparams From the 11D Chern–Simons reduction (A5) and modulus-closure structure (A6): Notation: We use [formula in source] (calligraphic) for this CFE parameter to distinguish it from [formula in source] (gravitational coupling) and the contorsion tensor [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Cubic Fixed-Point Equation (CFE)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10570,"byte_start":10435,"id":"section:379959cf7d8f6e2d32a5","kind":"subsection","labels":[],"line_end":272,"line_start":270,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/003-subsection-the-cubic-fixed-point-equation-cfe.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Geometric Self-Consistency (Backreaction)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17356,"byte_start":10570,"id":"section:4ef6c1189bb41b274f03","kind":"subsubsection","labels":["eq:backreaction","tab:alpha"],"line_end":405,"line_start":273,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/003-subsection-the-cubic-fixed-point-equation-cfe.tex","status_markers_as_written":[],"summary_excerpt":"The response [formula in source] is the closed form consequence of defect sector reweighting on the orientable double cover. The linear form is the [formula in source] expansion, not a separate assumption.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Backreaction as Structural Response","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3265,"byte_start":0,"id":"section:f0c030bba2632f98ddf6","kind":"subsubsection","labels":["fig:alpha-defect-z","sec:sensitivity"],"line_end":76,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/004-subsubsection-sensitivity-analysis.tex","status_markers_as_written":[],"summary_excerpt":"The sub-ppm precision of the [formula in source] prediction depends critically on the backreaction coefficient. We analyze the sensitivity to demonstrate this is not fine-tuning but a genuine geometric constraint.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Sensitivity Analysis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6549,"byte_start":3265,"id":"section:94b586bbbc4a39626ff7","kind":"subsection","labels":["fig:msbar-boundary","sec:comparison-policy"],"line_end":142,"line_start":77,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/004-subsubsection-sensitivity-analysis.tex","status_markers_as_written":[],"summary_excerpt":"( [formula in source] ), fonttitle= ] Why this matters: Precision electroweak fits and PDG summaries use the [formula in source] coupling at [formula in source] , [formula in source] , as the comparison observable. CODATA [formula in source] is an on-shell/IR reference and is therefore treated as secondary diagnostic once scheme and threshold bookkeeping is made explicit.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Comparison and Scheme Policy (No Hidden Knobs)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6751,"byte_start":6549,"id":"section:8d8bbb30309359585cc7","kind":"section","labels":[],"line_end":146,"line_start":143,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/004-subsubsection-sensitivity-analysis.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"The Unified Field Equation (UFE)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7901,"byte_start":6751,"id":"section:2cbf64110e4e0f4fdc6b","kind":"subsection","labels":[],"line_end":175,"line_start":147,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/004-subsubsection-sensitivity-analysis.tex","status_markers_as_written":[],"summary_excerpt":"Quantum Vacuum TensorQVT Let Let [formula in source] denote the scalar invariant entering the coupling equation, Define the Quantum Vacuum Tensor","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Quantum Vacuum Tensor Packaging","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14102,"byte_start":7901,"id":"section:75f75dd7442146e5d048","kind":"subsection","labels":["eq:UFE","eq:bianchi","eq:maxwell"],"line_end":284,"line_start":176,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/004-subsubsection-sensitivity-analysis.tex","status_markers_as_written":[],"summary_excerpt":"UFE ActionUFEaction On a manifold [formula in source] with metric [formula in source] and torsionful connection [formula in source] , the action is: Here [formula in source] denotes the Ricci scalar constructed from the full torsionful connection [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Torsionful Geometric Action","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18674,"byte_start":14102,"id":"section:7ec6f196d079e1a3f5b3","kind":"subsection","labels":["fig:torsion-bounds","sec:torsion-regimes"],"line_end":382,"line_start":285,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/004-subsubsection-sensitivity-analysis.tex","status_markers_as_written":[],"summary_excerpt":"TFPT distinguishes between cosmological torsion (which may be active in the early universe and drive a bounce) and local vacuum torsion (which is constrained by laboratory and astrophysical bounds on Lorentz violation). To avoid hidden assumptions, we treat ``torsion today'' as an explicit regime choice rather than a vague qualitative statement.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Present-Day Torsion Regimes and Local Tests","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3654,"byte_start":0,"id":"section:ed492faa38a3a40a9e30","kind":"subsubsection","labels":["fig:evpa_intercept","sec:eht-intercept"],"line_end":68,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/005-subsubsection-achromatic-polarization-rotation-around-co.tex","status_markers_as_written":[],"summary_excerpt":"Beyond the cosmic birefringence prediction (Theorem in the presence of a nonzero [formula in source] environment (see the companion note bhAchromaticRotationNote2025). EHT-style polarimetry provides the relevant data products for such an intercept test ehtm87pol2021. A simple dyonic toy model yields where [formula in source] is the emission radius and [formula in source] denote effective electromagnetic charges sourc","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Achromatic polarization rotation around compact objects (EHT intercept test)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5157,"byte_start":3654,"id":"section:71f6e15100b34002b8cd","kind":"subsection","labels":[],"line_end":103,"line_start":69,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/005-subsubsection-achromatic-polarization-rotation-around-co.tex","status_markers_as_written":[],"summary_excerpt":"Gravitational Coupling Consistencykappa The gravitational coupling [formula in source] (with dimension [formula in source] ) is constrained by consistency with the dimensionless ratio:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gravitational Coupling from Invariants","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5349,"byte_start":5157,"id":"section:a749407931eccb4e4bb3","kind":"section","labels":[],"line_end":107,"line_start":104,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/005-subsubsection-achromatic-polarization-rotation-around-co.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Observable Predictions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5816,"byte_start":5349,"id":"section:180c031d1e57e5002d0d","kind":"subsection","labels":[],"line_end":119,"line_start":108,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/005-subsubsection-achromatic-polarization-rotation-around-co.tex","status_markers_as_written":[],"summary_excerpt":"Axion–Photon Couplinggagg The CFE fixes the axion–photon vertex uniquely: This determines cosmic birefringence without free parameters.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Axion–Photon Coupling","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7553,"byte_start":5816,"id":"section:5c13150ce51963da5a4e","kind":"subsection","labels":[],"line_end":153,"line_start":120,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/005-subsubsection-achromatic-polarization-rotation-around-co.tex","status_markers_as_written":[],"summary_excerpt":"Topological Excursion Quantizationtopoexcursion The topological axion excursion is quantized in discrete sector changes: with [formula in source] the minimal nontrivial class. The corresponding birefringence is [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cosmic Birefringence","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14702,"byte_start":7553,"id":"section:6a29aa87dbb6f1d893f2","kind":"subsubsection","labels":["eq:shifted-axion-potential","fig:beta-tomography","fig:birefringence","sec:deltaa","tab:birefringence"],"line_end":316,"line_start":154,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/005-subsubsection-achromatic-polarization-rotation-around-co.tex","status_markers_as_written":[],"summary_excerpt":"Goal: Provide one minimal dynamical realization compatible with the topological quantization (Definition","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dynamical Completion of the Excursion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19144,"byte_start":14702,"id":"section:2e20c8fb42523391ffd9","kind":"subsection","labels":["fig:rg-two-loop-running"],"line_end":399,"line_start":317,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/005-subsubsection-achromatic-polarization-rotation-around-co.tex","status_markers_as_written":[],"summary_excerpt":"RG FingerprintsRGfingerprints The TFPT invariants leave signatures in the RG flow of gauge couplings: These values are obtained by two-loop RG running from PDG boundary conditions at [formula in source] using the declared PyR@TE model (checked by two_loop_rg_fingerprints in the verification suite; not direct measurements at the quoted scales). The crossing scale for [formula in source] is [formula in source] GeV.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Two-Loop RG Fingerprints","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":275,"byte_start":0,"id":"section:f8b7d7b75775ee0241f9","kind":"section","labels":["sec:e8"],"line_end":5,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/006-section-texorpdfstring-the-e-8-cascade-and-block-constan.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"The E [formula in source] Cascade and Block ConstantsThe E8 Cascade and Block Constants","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2920,"byte_start":275,"id":"section:5eebd030081faabe9223","kind":"subsection","labels":[],"line_end":54,"line_start":6,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/006-section-texorpdfstring-the-e-8-cascade-and-block-constan.tex","status_markers_as_written":[],"summary_excerpt":"E [formula in source] Orbit Graphorbitgraph Let [formula in source] denote the set of nilpotent orbits of the exceptional Lie algebra [formula in source] . 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On the fundamental splitting, the holonomy spectrum separates into two eigenspaces of dimensions [formula in source] and [formula in source] , hence we define the discrete degeneracy count [formula in source] The minimal damping ratio compatible with a single additi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Log-Exact Ladder Formula","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12013,"byte_start":7494,"id":"section:95c50a8d7feb25d8e4da","kind":"subsection","labels":["fig:blocks","tab:blocks"],"line_end":271,"line_start":161,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/006-section-texorpdfstring-the-e-8-cascade-and-block-constan.tex","status_markers_as_written":[],"summary_excerpt":"For a 6D Weyl fermion zero mode on a boundary cycle [formula in source] with flat [formula in source] connection (holonomy [formula in source] ), the variation of [formula in source] under the connection is proportional to the quadratic charge index: The proportionality constant is fixed by the topological normalization [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Block Constant Formula and Derivation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13434,"byte_start":12013,"id":"section:9b20c48087cf8030f669","kind":"subsection","labels":[],"line_end":304,"line_start":272,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/006-section-texorpdfstring-the-e-8-cascade-and-block-constan.tex","status_markers_as_written":[],"summary_excerpt":"The neutrino block at [formula in source] provides concrete predictions for the seesaw mechanism.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neutrino Seesaw Predictions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13700,"byte_start":13434,"id":"section:b122f87946f5617c5557","kind":"section","labels":[],"line_end":308,"line_start":305,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/006-section-texorpdfstring-the-e-8-cascade-and-block-constan.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Flavor Structure: The Z [formula in source] ArchitectureFlavor Structure: The Z3 Architecture","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16370,"byte_start":13700,"id":"section:79ecd0ef33f89c701ace","kind":"subsection","labels":[],"line_end":360,"line_start":309,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/006-section-texorpdfstring-the-e-8-cascade-and-block-constan.tex","status_markers_as_written":[],"summary_excerpt":"On a conformally flat boundary geometry, the unique projectively invariant quantity from four marked points is the cross-ratio. Any boundary monodromy acts as a PSL [formula in source] transformation. Therefore, relations depending only on boundary monodromies must be rational functions of a M\\\"obius map.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Universal Phase [formula in source] Universal Phase delta","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1404,"byte_start":0,"id":"section:5d38042609c9e2aa66f5","kind":"subsection","labels":[],"line_end":32,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/007-subsection-m-obius-mass-relations.tex","status_markers_as_written":[],"summary_excerpt":"Mass Ratios from M\\\"obius Mapmassratios The M\\\"obius map [formula in source] evaluated at cusps [formula in source] yields mass ratios:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"M\\\"obius Mass Relations","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5189,"byte_start":1404,"id":"section:32ff3c5272cafefcb37e","kind":"subsection","labels":[],"line_end":116,"line_start":33,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/007-subsection-m-obius-mass-relations.tex","status_markers_as_written":[],"summary_excerpt":"Cabibbo AngleCabibbo The Cabibbo parameter is fixed by the birefringence invariant [formula in source] : Compared to the PDG reference value, this is a sub-permille level deviation (status: solid).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cabibbo Angle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7822,"byte_start":5189,"id":"section:0f2d04947c7c8e341e2d","kind":"subsubsection","labels":["fig:ckm-residuals"],"line_end":183,"line_start":117,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/007-subsection-m-obius-mass-relations.tex","status_markers_as_written":[],"summary_excerpt":"The shipped suite includes a deterministic CKM reconstruction pipeline with declared UV textures, two-loop RG dressing, and a reference-scale comparison at [formula in source] (module ckm_full_pipeline). The baseline benchmark gives a CKM matrix close to PDG at the level quantified by the reported [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Suite benchmark: RG-dressed CKM pipeline (explicit conventions)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11609,"byte_start":7822,"id":"section:e3230edd952da60a7be9","kind":"subsubsection","labels":["fig:kaon_bar","fig:kaon_correlation","sec:rare-kaon"],"line_end":281,"line_start":184,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/007-subsection-m-obius-mass-relations.tex","status_markers_as_written":[],"summary_excerpt":"The ultra clean modes [formula in source] and [formula in source] provide a stringent test of the TFPT flavor architecture, because long-distance hadronic uncertainties are strongly suppressed (see the companion note rareKaonNote2025).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Rare Kaon Decays: [formula in source] as a clean flavor null testRare Kaon Decays: K to pi nu nu as a clean flavor null test","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15476,"byte_start":11609,"id":"section:054256f6d3e6b1d9fedd","kind":"subsection","labels":["fig:pmns-residuals"],"line_end":375,"line_start":282,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/007-subsection-m-obius-mass-relations.tex","status_markers_as_written":[],"summary_excerpt":"TFPT provides a closed prediction for [formula in source] via a single kernel identity plus the TM1 pattern. The remaining PMNS degrees of freedom [formula in source] are treated as an open interface requiring explicit Z [formula in source] -breaking and (eventually) correlated Yukawa/RG treatment; they must not be read as closed predictions at this stage.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"PMNS Neutrino Mixing: TM1 Pattern","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1782,"byte_start":0,"id":"section:a03735557b9ac0c2c0bc","kind":"section","labels":["eq:As","eq:R2action","eq:ns","eq:r","tab:inflation"],"line_end":41,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/008-section-texorpdfstring-inflation-r-2-completion-starobin.tex","status_markers_as_written":[],"summary_excerpt":"The TFPT topological correction scale is set by [formula in source] (cf.\\ [formula in source] ). In effective gravity, the leading higher-curvature completion compatible with general covariance is an [formula in source] term.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Inflation: [formula in source] Completion (Starobinsky Limit)Inflation: R2 Completion (Starobinsky Limit)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3920,"byte_start":1782,"id":"section:f23634aa159657c635ec","kind":"subsection","labels":["fig:r2-blocks","sec:r2derive"],"line_end":94,"line_start":42,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/008-section-texorpdfstring-inflation-r-2-completion-starobin.tex","status_markers_as_written":[],"summary_excerpt":"Relevant Torsion DegreesR2torsion Decompose torsion into irreducible parts [formula in source] (axial, trace, tensor). In the minimal UFE setting the dominant coupling is through axial torsion [formula in source] , and the torsion sector is treated at quadratic order so it can be integrated out in the one-loop effective action.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[formula in source] Term from the Torsionful Effective ActionR2 Term from the Torsionful Effective Action","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5762,"byte_start":3920,"id":"section:2dcb2b0084765364ab4f","kind":"subsection","labels":["eq:R2scale","fig:r2-scan"],"line_end":143,"line_start":95,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/008-section-texorpdfstring-inflation-r-2-completion-starobin.tex","status_markers_as_written":[],"summary_excerpt":"TFPT [formula in source] ScaleR2coeff Using the GR renormalization condition (A8) to fix the scheme, the coefficient of the [formula in source] term yields Here the square root applies only to [formula in source] , consistent with the numerical value above.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Coefficient Identification and GR Renormalization","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7392,"byte_start":5762,"id":"section:068843d5c8c5c1068e89","kind":"subsection","labels":["sec:bounce"],"line_end":180,"line_start":144,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/008-section-texorpdfstring-inflation-r-2-completion-starobin.tex","status_markers_as_written":[],"summary_excerpt":"Bounce-to-Inflation Backgroundbouncebg Assume a non-singular bounce driven by the torsion-induced [formula in source] term (Lemma above), followed by a transition into the [formula in source] inflationary phase. We take the CMB pivot scales to exit the horizon during the [formula in source] phase.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bounce + [formula in source] Perturbations and Transfer FunctionBounce + R2 Perturbations and Transfer Function","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7593,"byte_start":7392,"id":"section:bd0b8da3d3df8972c2ba","kind":"section","labels":[],"line_end":184,"line_start":181,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/008-section-texorpdfstring-inflation-r-2-completion-starobin.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Axion Cosmology and Dark Matter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9770,"byte_start":7593,"id":"section:3d661652379ffff9837d","kind":"subsection","labels":[],"line_end":223,"line_start":185,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/008-section-texorpdfstring-inflation-r-2-completion-starobin.tex","status_markers_as_written":[],"summary_excerpt":"The TFPT axion sector is split into two distinct fields to avoid an internal contradiction (a single [formula in source] eV axion cannot remain quasi-static over Hubble times):","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Two-Field Structure: Topological vs.\\ QCD Axion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12923,"byte_start":9770,"id":"section:33fc259cfe25c644fb66","kind":"subsection","labels":[],"line_end":274,"line_start":224,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/008-section-texorpdfstring-inflation-r-2-completion-starobin.tex","status_markers_as_written":[],"summary_excerpt":"Axion Dark Matter ParametersaxionDM For the QCD axion field [formula in source] from the E [formula in source] cascade (PQ block at [formula in source] ):","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dark Matter Relic Density","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15004,"byte_start":12923,"id":"section:4b896af2998cdce300a8","kind":"subsection","labels":["sec:dark-energy"],"line_end":309,"line_start":275,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/008-section-texorpdfstring-inflation-r-2-completion-starobin.tex","status_markers_as_written":[],"summary_excerpt":"with no continuous knobs, fonttitle= ] We test the discrete defect-suppression candidate [formula in source] The two-defect sector uses [formula in source] and the corresponding [formula in source] (Sec.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dark Energy as a Defect-Suppressed Torsion Condensate (candidate)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16970,"byte_start":15004,"id":"section:54f8736e2526afa2bc06","kind":"section","labels":["tab:beta"],"line_end":340,"line_start":310,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/008-section-texorpdfstring-inflation-r-2-completion-starobin.tex","status_markers_as_written":[],"summary_excerpt":"The parameter [formula in source] provides a compact dictionary for expressing multiple quantities. Most equalities in this section are algebraic rewrites of earlier definitions rather than independent new inputs (see Appendix Inflation observables additionally depend on a dynamical completion (here: the conditional [formula in source] sector in Theorem","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[formula in source] -Centric Identity Summarybeta_rad-Centric Identity Summary","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5226,"byte_start":0,"id":"section:62b38ac9205092e5e972","kind":"section","labels":["tab:status"],"line_end":63,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/009-section-summary-of-claims-and-status.tex","status_markers_as_written":[],"summary_excerpt":"@p3cmp4cmp3cmp5.2cm@ TFPT status dashboard. ``Exact'': [formula in source] ; ``Solid'': [formula in source] ; ``Minor'': [formula in source] ; ``Moderate'': [formula in source] . Domain & Quantity & Deviation & Status\\\\ Domain & Quantity & Deviation & Status\\\\ 4r Continued on next page.\\\\ 4l Structural (parameter-free)\\\\ CFE & [formula in source] & [formula in source] & green!60!black Derived (double cover + [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Summary of Claims and Status","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5862,"byte_start":5226,"id":"section:835e1fdc2927b9d9cae5","kind":"section","labels":[],"line_end":77,"line_start":64,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/009-section-summary-of-claims-and-status.tex","status_markers_as_written":[],"summary_excerpt":"The following are not required: Slow-roll inflation (specific model) String landscape or anthropic selection Extra dimensions as free parameters Dark matter entirely from axions New particles beyond minimal axion sector Any fitted or adjusted parameters","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"What TFPT Does Not Assume","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7331,"byte_start":5862,"id":"section:d14379bf096b56b46d88","kind":"section","labels":[],"line_end":103,"line_start":78,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/009-section-summary-of-claims-and-status.tex","status_markers_as_written":[],"summary_excerpt":"TFPT demonstrates that the fine-structure constant [formula in source] can be derived within an explicit set of eight minimal axioms rooted in topology, geometry, and quantum consistency. The key results are:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conclusions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7824,"byte_start":7331,"id":"section:83d5ef69f9d85f51078c","kind":"paragraph","labels":[],"line_end":111,"line_start":104,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/009-section-summary-of-claims-and-status.tex","status_markers_as_written":[],"summary_excerpt":"Two longer-range directions are sketched in internal notes and remain explicitly open: an asymptotic-safety UV completion for the torsionful gravity sector and a black-hole vortex/remnant picture with information-paradox implications. Both are framed as outlook items rather than closed predictions at this stage fiveProblemsNote2025,blackHolesBh1Note2025.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Outlook (open interfaces).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10716,"byte_start":7824,"id":"section:02d5562e48d6024c2694","kind":"section","labels":["tab:constants"],"line_end":156,"line_start":112,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/009-section-summary-of-claims-and-status.tex","status_markers_as_written":[],"summary_excerpt":"@ll@ Quantity & Value\\\\ [formula in source] & \\\\ [formula in source] & \\\\ [formula in source] & \\\\ [formula in source] & \\\\ [formula in source] (self-consistent) & 0.053170209119023745\\\\ [formula in source] & \\\\ [formula in source] & [formula in source] \\\\ [formula in source] & \\\\ [formula in source] (E [formula in source] ) & [formula in source] \\\\ [formula in source] (E [formula in source] exponent) & 0.58723319078","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Numerical Constants (High Precision)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11533,"byte_start":10716,"id":"section:13f2d86700bd6bf872fa","kind":"section","labels":["app:gdiagnostic"],"line_end":169,"line_start":157,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/009-section-summary-of-claims-and-status.tex","status_markers_as_written":[],"summary_excerpt":"The suite records legacy diagnostic templates in which [formula in source] is varied away from the holonomy value [formula in source] (e.g.\\ the ordered-occupancy [formula in source] template). These runs are used only to verify that the defect-sector response is sensitive to discrete holonomy choices and to quantify the direction of the shift in [formula in source] . They are explicitly not used for parameter select","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Diagnostic [formula in source] Variants (Internal Sanity Checks)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12705,"byte_start":11533,"id":"section:48443a7144565b29ec83","kind":"section","labels":["fig:rg-unification"],"line_end":200,"line_start":170,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/009-section-summary-of-claims-and-status.tex","status_markers_as_written":[],"summary_excerpt":"Gauge coupling convergence. Visualizes the unification gate scan used by the suite.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"RG Unification Overview (Supplementary)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20847,"byte_start":12705,"id":"section:c839f12e00281969bcc5","kind":"section","labels":["eq:CFE-appendix","eq:potential","eq:stationarity"],"line_end":364,"line_start":201,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/009-section-summary-of-claims-and-status.tex","status_markers_as_written":[],"summary_excerpt":"This appendix records the coefficient bookkeeping used in the suite and provides a heuristic motivation for the CFE coefficient policy. It is not presented as a full background-field derivation. In the declared scheme, the one-loop effective potential for the electromagnetic coupling modulus is taken to have the form:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Coefficient Policy Sketch for the CFE","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1238,"byte_start":0,"id":"section:a25a1a5ec9c3854746fd","kind":"section","labels":[],"line_end":17,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"The TFPT verification suite turns paper claims into deterministic, assumption-explicit computations. All counts in this section are auto-generated from the suite artifacts (no hardcoded ``39 modules''): [formula in source] It ships: a conventional suite (registry-driven; core invariants, [formula in source] closure + policy bridge, RG/matching, flavor pipelines, cosmology/bounce wiring, torsion/birefringence, dashboa","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verification Suite Summary","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1618,"byte_start":1238,"id":"section:ffd4e29b1b7f08c11f14","kind":"subsection","labels":["sec:known-gaps"],"line_end":24,"line_start":18,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"For the PRL-facing manuscript we omit the auto-generated flagged/open inventory and list open interfaces only as conditional statements in the main text. The full suite manifest (with module-level status and plot inventories) is included in the replication bundle referenced in Appendix","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Known Gaps and Status (Summary)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9312,"byte_start":1618,"id":"section:0a55621df8ca813d76ee","kind":"subsection","labels":["fig:likelihood-breakdown","sec:theoryv3-evidence"],"line_end":216,"line_start":25,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"The theoryv3 analysis branch is a compact ``evidence layer'' for the discrete kernel and crosslink logic. Current inventory (auto-generated from the replication bundle; theoryv3 is a baseline branch pinned to v2.5 by design): [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"theoryv3 Evidence Layer (Compressed, Auto-Generated)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9612,"byte_start":9312,"id":"section:ac2bdda3c4cc75be28eb","kind":"section","labels":["app:E8cert"],"line_end":223,"line_start":217,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"This appendix provides the complete verification data for the E [formula in source] chain uniqueness theorem (Theorem","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"E [formula in source] Chain CertificateE8 Chain Certificate","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10116,"byte_start":9612,"id":"section:5db23094c78b14f0b5a3","kind":"subsection","labels":[],"line_end":233,"line_start":224,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"Each nilpotent orbit [formula in source] of [formula in source] is characterized by: Bala–Carter label: Standard notation (e.g., [formula in source] , [formula in source] , [formula in source] , ) Dimension: [formula in source] Centralizer dimension: [formula in source] Height: [formula in source] (sum of weighted Dynkin diagram coefficients)","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Orbit Data Structure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10792,"byte_start":10116,"id":"section:8cf3a0bfb29b3daee2a8","kind":"subsection","labels":[],"line_end":258,"line_start":234,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"The complete chain from [formula in source] to [formula in source] :","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Unique Chain (Excerpt)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11560,"byte_start":10792,"id":"section:5d2f324a6eed25813dfc","kind":"subsection","labels":[],"line_end":273,"line_start":259,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"The uniqueness is verified by: Constructing the complete Hasse diagram of [formula in source] from standard tables. Computing all cover relations with [formula in source] . Running dynamic programming to find all paths from [formula in source] to [formula in source] . Applying the cost function [formula in source] (second-difference smoothness). Verifying that the minimum-cost path is unique (cost gap to second-best ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verification Algorithm","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11800,"byte_start":11560,"id":"section:fdabf377b422ff0a4def","kind":"section","labels":["app:boundary"],"line_end":280,"line_start":274,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"This appendix derives the block index formula [formula in source] from the APS index theorem.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Boundary Trace Derivation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12191,"byte_start":11800,"id":"section:82a8613daf59424fe10a","kind":"subsection","labels":[],"line_end":290,"line_start":281,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"Consider a 6D manifold [formula in source] with boundary [formula in source] . For a Weyl fermion coupled to a [formula in source] gauge field [formula in source] , the APS index theorem gives: where [formula in source] is the [formula in source] -invariant of the boundary Dirac operator.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12704,"byte_start":12191,"id":"section:9d6b8cdf4dff3af06d24","kind":"subsection","labels":[],"line_end":305,"line_start":291,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"On the orientable double cover [formula in source] , the boundary decomposes as: (two boundary cycles plus the twist seam).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Flat Connection on Boundary Cycles","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14221,"byte_start":12704,"id":"section:681386ce9ef97188d6c0","kind":"subsection","labels":[],"line_end":333,"line_start":306,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"The regulated determinant of the hypercharge-coupled Dirac operator contains a logarithmic term which we normalize as: We define the spectral index [formula in source] as the quadratic charge trace entering this term in our normalization; the overall prefactor is part of the declared coefficient policy (Appendix C) and differs by a fixed normalization from the conventional [formula in source] Seeley–DeWitt prefactor.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spectral Trace Coefficient and [formula in source] Spectral Trace Coefficient and b1","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15002,"byte_start":14221,"id":"section:371877d1c851f7b108fa","kind":"subsection","labels":[],"line_end":353,"line_start":334,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"Step 1: Each boundary cycle contributes a factor proportional to [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of [formula in source] Derivation of kB","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15316,"byte_start":15002,"id":"section:ed5c156e99b099313749","kind":"section","labels":["app:seam"],"line_end":359,"line_start":354,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"This appendix provides the [formula in source] -invariant gluing derivation used in Axiom","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Seam Gluing and the [formula in source] -Invariant NormalizationSeam Gluing and the eta-Invariant Normalization","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15918,"byte_start":15316,"id":"section:a0694e1b0f74927951d8","kind":"subsection","labels":[],"line_end":370,"line_start":360,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/010-section-verification-suite-summary.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the orientable double cover of the M\\\"obius fiber and cut it along the seam [formula in source] to obtain a manifold-with-boundary [formula in source] with boundary components [formula in source] . Let [formula in source] be the Dirac operator on [formula in source] with APS boundary conditions on [formula in source] and a unitary matching operator [formula in source] identifying [formula i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cut Space and Operators","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":634,"byte_start":0,"id":"section:e28d5c2fe4c44208f1f8","kind":"subsection","labels":[],"line_end":13,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"The APS gluing theorem expresses the [formula in source] -invariant of the glued manifold in terms of the cut manifold plus a discrete spectral-flow correction: where [formula in source] is the spectral flow of the matching operator. In TFPT bookkeeping this contributes a quantized seam term to the curvature normalization.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gluing Formula for the [formula in source] -InvariantGluing Formula for the eta-Invariant","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":918,"byte_start":634,"id":"section:d3db3e0b0884957d5f51","kind":"subsection","labels":[],"line_end":20,"line_start":14,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"For the M\\\"obius [formula in source] identification, the matching satisfies [formula in source] . The minimal nontrivial class is modeled by the unitary phase","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"M\\\"obius Matching and the Minimal Gluing Class","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1584,"byte_start":918,"id":"section:ec850bab29c8725c90c2","kind":"subsection","labels":[],"line_end":37,"line_start":21,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"Interpolate boundary conditions by a phase [formula in source] , which gives the eigenvalues As [formula in source] runs from [formula in source] to [formula in source] , exactly one eigenvalue crosses zero, so [formula in source] and [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spectral Flow Computation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2122,"byte_start":1584,"id":"section:13484562d435757e59bc","kind":"subsection","labels":[],"line_end":47,"line_start":38,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"The two physical boundary cycles contribute [formula in source] , and the seam gluing adds [formula in source] , so the total curvature is [formula in source] . We treat [formula in source] as the dimensionless geometry modulus; the closure normalization [formula in source] fixes its scale and therefore yields","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Normalization of [formula in source] Normalization of phi_tree","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2628,"byte_start":2122,"id":"section:786db3ac30ee694bbe71","kind":"section","labels":["app:48deriv"],"line_end":58,"line_start":48,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"This appendix explains the integer coefficient in [formula in source] . The key point is that the canonical quantity is and the appearance of ``48'' is simply the same number expressed in units of [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of the Coefficient 48 in [formula in source] Derivation of the Coefficient 48 in delta_top","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3352,"byte_start":2628,"id":"section:02b71ca9cf021b57d2ad","kind":"subsection","labels":[],"line_end":71,"line_start":59,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"The topological correction [formula in source] arises from the leading gauge-invariant correction to the tree-level geometric scale [formula in source] . The requirements are: Gauge invariance: The correction must be built from [formula in source] only (no explicit [formula in source] dependence at this order). Dimensionlessness: Since [formula in source] is dimensionless, the correction must be a pure power [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Physical Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4157,"byte_start":3352,"id":"section:4b7cf0cd099fdf294d18","kind":"subsection","labels":[],"line_end":88,"line_start":72,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"The effective action on the M\\\"obius fiber includes the Chern–Simons term [formula in source] . The leading topological correction comes from the one-loop determinant of the Dirac operator coupled to this background.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Power Counting: Why [formula in source] ?Power Counting: Why c3^4?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4552,"byte_start":4157,"id":"section:7993c1c635b33839abf4","kind":"subsection","labels":[],"line_end":98,"line_start":89,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"The non-orientable identification acts as a [formula in source] operation on the base, but in the spin bundle the same element lifts to order [formula in source] because a [formula in source] rotation acts as [formula in source] on spinors and only a [formula in source] rotation is trivial. This produces a universal deficit factor per minimal sector.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spin-Lifted Deficit Factor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5058,"byte_start":4552,"id":"section:afcbc6d572c0d0c1bb93","kind":"subsection","labels":[],"line_end":108,"line_start":99,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"Cutting along [formula in source] yields boundary components [formula in source] . The four local corner patches [formula in source] , [formula in source] , [formula in source] , [formula in source] constitute the fundamental domain. Summing the spin-lifted deficit factor over these sectors yields In TFPT normalization this yields the canonical form [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Sector Count from Cut Geometry","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5412,"byte_start":5058,"id":"section:cfda3aafd48e7ae1fc3e","kind":"subsection","labels":[],"line_end":118,"line_start":109,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"Using [formula in source] : so [formula in source] and [formula in source] are exactly equivalent.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conversion to the [formula in source] normalizationConversion to the c3 normalization","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5726,"byte_start":5412,"id":"section:0e782f24a0a65181153c","kind":"subsection","labels":[],"line_end":124,"line_start":119,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"The spin-lift argument fixes the [formula in source] deficit factor robustly, and the sector count is fixed by seam symmetry. The seam normalization is provided by the [formula in source] -gluing derivation in Appendix","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Status note","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5959,"byte_start":5726,"id":"section:c04b5e821432d610339e","kind":"section","labels":["app:flavor"],"line_end":130,"line_start":125,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"This appendix derives the M\\\"obius structure of flavor relations from boundary monodromy.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Flavor Monodromy and Cross-Ratio","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6741,"byte_start":5959,"id":"section:528729217b1cde41a220","kind":"subsection","labels":[],"line_end":149,"line_start":131,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"On a conformally flat boundary, the metric is locally: Holomorphic automorphisms (Wilson lines of flat connections) act as M\\\"obius transformations:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Projective Invariance on Boundaries","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7175,"byte_start":6741,"id":"section:c571ec2996009072e763","kind":"subsection","labels":[],"line_end":160,"line_start":150,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"Given four marked points [formula in source] on the boundary, the unique projective invariant is the cross-ratio:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cross-Ratio as Unique Invariant","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7713,"byte_start":7175,"id":"section:6fc2af6815ed4ba5b233","kind":"subsection","labels":[],"line_end":171,"line_start":161,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"The cusps [formula in source] arise from: Rationality: Quantized holonomies [formula in source] rational cusps. GUT compatibility: SU(5) hypercharge assignments give [formula in source] (quarks), [formula in source] (leptons), etc. Uniqueness: These are the only rational values that simultaneously separate the three SM sectors (up, down, lepton) and maintain GUT normalization.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cusp Selection","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8437,"byte_start":7713,"id":"section:e5daa6cdfd838696ad44","kind":"subsection","labels":[],"line_end":190,"line_start":172,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"Leading term: [formula in source] from the abelian trace (same as [formula in source] numerator divided by 41/10's denominator structure).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of [formula in source] Derivation of delta_star","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10074,"byte_start":8437,"id":"section:8cc578495754b04789fa","kind":"section","labels":["app:repro"],"line_end":223,"line_start":191,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":["relation:097a0460891d9ffa2b5c","relation:49263ce33ddd5d397e2e","relation:d13e31f4a5e3bec9a21d"],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"Replication package: All numerical results can be reproduced using the TFPT verification suite (v5).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproducibility","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19109,"byte_start":10074,"id":"section:0a9d5f273b22f74682c7","kind":"section","labels":["app:prediction-ledger","tab:prediction-ledger"],"line_end":286,"line_start":224,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"Purpose: Provide a single, reviewer-friendly list of predictions and candidates that is tied to the same JSON sources used by the verification suite, to prevent number drift between Abstract, theorems, tables, and appendices.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Prediction Ledger and Falsification","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":21726,"byte_start":19109,"id":"section:cb945ec7855b09faf826","kind":"section","labels":["app:identities"],"line_end":325,"line_start":287,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"This appendix labels frequently used equalities by logical status to prevent conflating definitions, algebraic rewrites, and genuine predictions.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Identity Catalogue and Status Labels","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":22624,"byte_start":21726,"id":"section:bea0597f76aa8a6b0437","kind":"section","labels":["app:r2"],"line_end":339,"line_start":326,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"K1: Field content and torsionful Lagrangian fixed by the minimal UFE sector. K2: Quadratic fluctuation operator is of Laplace type after background-field gauge fixing. K3: Heat-kernel coefficient [formula in source] captures the curvature-squared terms in [formula in source] . K4: Matching to [formula in source] after imposing the GR renormalization condition.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"One-Loop Effective Action in Riemann–Cartan and the [formula in source] CoefficientOne-Loop Effective Action in Riemann–Cartan and the R2 Coefficient","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":22982,"byte_start":22624,"id":"section:1394a6984db2cdd0d721","kind":"subsection","labels":[],"line_end":345,"line_start":340,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"We evaluate the one-loop effective action in a Riemann–Cartan background with torsion decomposed into axial [formula in source] , trace [formula in source] , and tensor [formula in source] . The minimal UFE choice treats torsion at quadratic order, so integrating out torsion is Gaussian and parameter-free once [formula in source] fixes the normalization of the coupling.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.1 Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":23345,"byte_start":22982,"id":"section:ff94f81f9b5b15b5a6cc","kind":"subsection","labels":[],"line_end":354,"line_start":346,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"After background-field gauge fixing, the quadratic operator for torsion fluctuations can be written in Laplace type, with [formula in source] built from curvature and torsion invariants. The contribution to [formula in source] is [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.2 Operator Form","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":23715,"byte_start":23345,"id":"section:690b18e5ac9d1b11de76","kind":"subsection","labels":[],"line_end":362,"line_start":355,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"The local part of [formula in source] is governed by the heat-kernel expansion where [formula in source] contains the curvature-squared terms. The torsion-dependent pieces combine into an effective [formula in source] operator in the low-energy action.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.3 Heat-Kernel Coefficients","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":23916,"byte_start":23715,"id":"section:541a5d010655be3c6604","kind":"subsection","labels":[],"line_end":366,"line_start":363,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/011-subsection-texorpdfstring-gluing-formula-for-the-eta-inv.tex","status_markers_as_written":[],"summary_excerpt":"The GR limit (A8) fixes the renormalization scheme by requiring that the [formula in source] limit reduces to the Einstein–Hilbert action with coefficient [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.4 Renormalization Condition","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":365,"byte_start":0,"id":"section:ede9f3862e0e0c6f4281","kind":"subsection","labels":[],"line_end":9,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/012-subsection-k-5-tfpt-closure.tex","status_markers_as_written":[],"summary_excerpt":"With the TFPT normalization of the torsion sector, the induced [formula in source] coefficient is fixed by [formula in source] , yielding which reproduces","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.5 TFPT Closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":841,"byte_start":365,"id":"section:1a6a42a97afb4f9553a8","kind":"section","labels":["app:bounce"],"line_end":19,"line_start":10,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/012-subsection-k-5-tfpt-closure.tex","status_markers_as_written":[],"summary_excerpt":"This appendix provides a minimal outline; the full numerical transfer-function evaluation is implemented in the bounce_perturbations verification module (see replication bundle).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bounce Perturbations and the Transfer Function","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1155,"byte_start":841,"id":"section:783336cf505518771126","kind":"subsection","labels":[],"line_end":24,"line_start":20,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/012-subsection-k-5-tfpt-closure.tex","status_markers_as_written":[],"summary_excerpt":"The bounce background is modeled by a smooth scale factor [formula in source] where the torsion-induced [formula in source] term regularizes [formula in source] for scalar perturbations. The transition to the [formula in source] inflationary phase is implemented by matching [formula in source] and its derivatives at [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.1 Background Solution","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1448,"byte_start":1155,"id":"section:3988992daed690a31048","kind":"subsection","labels":[],"line_end":29,"line_start":25,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/012-subsection-k-5-tfpt-closure.tex","status_markers_as_written":[],"summary_excerpt":"Mode functions are initialized in an adiabatic vacuum well before the bounce and integrated through the bounce and into the [formula in source] era. The numerical scheme records the transfer function by comparing late-time solutions to the pure [formula in source] baseline.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.2 Numerical Integration Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1757,"byte_start":1448,"id":"section:5c6249c5e0da99225b7e","kind":"subsection","labels":[],"line_end":37,"line_start":30,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/012-subsection-k-5-tfpt-closure.tex","status_markers_as_written":[],"summary_excerpt":"Define the transfer function as with [formula in source] for modes well inside the horizon during the bounce and deviations confined to [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.3 Transfer Function","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11384,"byte_start":1757,"id":"section:b7348ec74cfe5467cd4f","kind":"subsection","labels":[],"line_end":314,"line_start":38,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/012-subsection-k-5-tfpt-closure.tex","status_markers_as_written":[],"summary_excerpt":"Deterministic (given the bounce completion): The transfer-function shape [formula in source] (this appendix; implemented in bounce_perturbations). Given an explicit expansion-history budget, the mapping [formula in source] and the resulting [formula in source] curves are deterministic (implemented in k_calibration and boltzmann_transfer).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.4 The [formula in source] Gate (CMB Observability as Policy Interface)L.4 The k->ell Gate (CMB Observability as Policy Interface)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11763,"byte_start":11384,"id":"section:36132632a8f7962616ce","kind":"subsection","labels":[],"line_end":320,"line_start":315,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/012-subsection-k-5-tfpt-closure.tex","status_markers_as_written":[],"summary_excerpt":"Large-scale suppression or oscillatory features in [formula in source] are predicted at [formula in source] . Current CMB large-scale bounds constrain the allowable feature amplitude, providing a direct observational test of the bounce completion.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.5 Falsification Targets","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13834,"byte_start":11763,"id":"section:62bbd076a104dcb63a4e","kind":"section","labels":["app:bh-dyonic"],"line_end":360,"line_start":321,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/012-subsection-k-5-tfpt-closure.tex","status_markers_as_written":[],"summary_excerpt":"This appendix records a minimal dyonic toy solution showing the [formula in source] scaling of the axion profile and the induced polarization rotation. It is included as analytical support for the EHT intercept test (Sec.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"BH1 Dyonic Toy Solution and Polarization Rotation Scaling (Appendix)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8101,"byte_start":0,"id":"section:9a97456d4692f0cc75a3","kind":"section","labels":["tab:reference-ledger"],"line_end":70,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/013-section-reference-ledger-auto-generated.tex","status_markers_as_written":[],"summary_excerpt":"round-mode=figures, round-precision=6 =0mu plus 1mu @> p0.20 > p0.12 > p0.10 > p0.10 > p0.12 > p0.28 @ Reference ledger used by the TFPT suite (auto-generated). Key & Value & [formula in source] & Units & Version & Source (stable key)\\\\ Key & Value & [formula in source] & Units & Version & Source (stable key)\\\\ 6r Continued on next page.\\\\ A_s_planck2018 & 2.0989031673e-09 & 2.938464434e-11 & dimensionless & Planck 2","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reference Ledger (Auto-Generated)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12265,"byte_start":8101,"id":"section:4cf94a60abf3f2fc060b","kind":"section","labels":[],"line_end":194,"line_start":71,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv27"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv27/sections/013-section-reference-ledger-auto-generated.tex","status_markers_as_written":[],"summary_excerpt":"99 hehl1976 F. W. Hehl, P. von der Heyde, G. D. Kerlick, J. M. Nester, ``General Relativity with Spin and Torsion: Foundations and Prospects,'' Rev.\\ Mod.\\ Phys.\\ 48, 393 (1976).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"References","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":24193,"byte_start":0,"id":"section:c78dfbb2a23470b4256c","kind":"frontmatter","labels":["fig:alpha-k-sensitivity-suite","fig:bounce-transfer"],"line_end":628,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/preamble.tex","status_markers_as_written":[],"summary_excerpt":"compat=1.18 groupplots arrows.meta,positioning,decorations.markings,decorations.pathmorphing,calc,patterns,shapes.geometric","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Topological Fixed Point Theory (TFPT)\\\\[0.5em] A Parameter-Free Derivation of the Fine-Structure Constant\\\\ from Topology, Geometry, and Quantum Consistency","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2299,"byte_start":0,"id":"section:87114bf7541b6b4da46a","kind":"frontmatter","labels":[],"line_end":26,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/001-section-kernel-and-discrete-grammar.tex","status_markers_as_written":[],"summary_excerpt":"We present the complete axiomatic foundation of Topological Fixed Point Theory (TFPT), which derives the fine-structure constant [formula in source] , within the declared scheme and renormalization condition, and other fundamental quantities from eight minimal assumptions rooted in topology, geometry, and quantum field theory. The theory rests on two fundamental invariants: the topological coupling [formula in source","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15029,"byte_start":2299,"id":"section:0300d9d030d730b2e68a","kind":"section","labels":["fig:compiler","fig:crosslink","tab:constant-factory"],"line_end":214,"line_start":27,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/001-section-kernel-and-discrete-grammar.tex","status_markers_as_written":[],"summary_excerpt":"Structural input (fixed, not fitted): the Standard Model abelian trace [formula in source] (determined by SM particle content and GUT normalization; not a TFPT knob).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kernel and Discrete Grammar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17506,"byte_start":15029,"id":"section:07f3e9ec96f55409f2af","kind":"section","labels":["fig:flow"],"line_end":262,"line_start":215,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/001-section-kernel-and-discrete-grammar.tex","status_markers_as_written":[],"summary_excerpt":"The Standard Model of particle physics contains approximately 19 free parameters that must be determined experimentally. Among these, the fine-structure constant [formula in source] stands out as a dimensionless number whose value has no explanation within conventional frameworks.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Introduction: The Problem of Parameters","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17925,"byte_start":17506,"id":"section:8d908f7f8627f7956306","kind":"section","labels":[],"line_end":270,"line_start":263,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/001-section-kernel-and-discrete-grammar.tex","status_markers_as_written":[],"summary_excerpt":"TFPT is built on eight axioms, organized into three categories: geometric structure, quantum field theory, and closure conditions. Each axiom is either derived from established physics or explicitly marked as a new postulate.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Axiomatic Foundation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7927,"byte_start":0,"id":"section:5f3412eeffde0fbaf870","kind":"subsection","labels":["fig:doublecover"],"line_end":168,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/002-subsection-geometric-axioms-a1-a4.tex","status_markers_as_written":[],"summary_excerpt":"Riemann–Cartan GeometryRC The fundamental spacetime connection possesses torsion; the Levi-Civita connection is a limiting case when torsion vanishes.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Geometric Axioms (A1–A4)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12261,"byte_start":7927,"id":"section:a2fa06eb2fe97c4f7bca","kind":"subsection","labels":[],"line_end":256,"line_start":169,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/002-subsection-geometric-axioms-a1-a4.tex","status_markers_as_written":[],"summary_excerpt":"Units and constants: Natural units: [formula in source] ; energies in GeV, lengths in GeV [formula in source] . Reference data: CODATA 2022, PDG 2024. Metric signature: [formula in source] . Levi-Civita tensor: [formula in source] , [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Quantum Field Theory Axioms (A5–A6)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19266,"byte_start":12261,"id":"section:f98790a721ccd02cbb1c","kind":"subsection","labels":["fig:b1-trace"],"line_end":391,"line_start":257,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/002-subsection-geometric-axioms-a1-a4.tex","status_markers_as_written":[],"summary_excerpt":"Standard Model Hypercharge TraceSMT We adopt the convention [formula in source] and count left-handed Weyl fermions plus the Higgs scalar with their SU(2) and color multiplicities. Define the hypercharge trace Here [formula in source] is the SM-normalized trace coefficient and [formula in source] is the corresponding GUT-normalized coefficient used in the CFE. For the SM field content (three generations + one Higgs d","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Closure Axioms (A7–A8)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":205,"byte_start":0,"id":"section:80b6ee6a76317ae2e189","kind":"section","labels":[],"line_end":4,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/003-section-derivation-of-fundamental-constants.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Derivation of Fundamental Constants","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2463,"byte_start":205,"id":"section:9dfc38aba0b40b6cf28e","kind":"subsection","labels":[],"line_end":55,"line_start":5,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/003-section-derivation-of-fundamental-constants.tex","status_markers_as_written":[],"summary_excerpt":"Existence and Uniqueness of [formula in source] phi0 From Axioms A3 and A4, the geometric scale is uniquely determined:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Geometric Scale [formula in source] The Geometric Scale phi0","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14777,"byte_start":2463,"id":"section:7b497dfdb6af2cb0c567","kind":"subsection","labels":["eq:CFE","fig:CFE","fig:alpha2-contract","fig:alpha2-sensitivity","fig:cfe-unique-suite","fig:invariant_flow","fig:scheme-shift"],"line_end":387,"line_start":56,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/003-section-derivation-of-fundamental-constants.tex","status_markers_as_written":[],"summary_excerpt":"Effective Potential Parametersparams From the 11D Chern–Simons reduction (A5) and modulus-closure structure (A6): Notation: We use [formula in source] (calligraphic) for this CFE parameter to distinguish it from [formula in source] (gravitational coupling) and the contorsion tensor [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Cubic Fixed-Point Equation (CFE)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":135,"byte_start":0,"id":"section:90b064fa49ead93c0bb0","kind":"subsection","labels":[],"line_end":3,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/004-subsection-geometric-self-consistency-backreaction.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Geometric Self-Consistency (Backreaction)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8828,"byte_start":135,"id":"section:1f15a1117b6af416140b","kind":"subsubsection","labels":["eq:backreaction","rem:two-defect-conventions","tab:alpha"],"line_end":166,"line_start":4,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/004-subsection-geometric-self-consistency-backreaction.tex","status_markers_as_written":[],"summary_excerpt":"The response [formula in source] is the closed form consequence of defect sector reweighting on the orientable double cover. The linear form is the [formula in source] expansion, not a separate assumption.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Backreaction as Structural Response","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12014,"byte_start":8828,"id":"section:bc1b46126f3c04b83f6d","kind":"subsubsection","labels":["fig:alpha-defect-z","sec:sensitivity"],"line_end":241,"line_start":167,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/004-subsection-geometric-self-consistency-backreaction.tex","status_markers_as_written":[],"summary_excerpt":"The sub-ppm precision of the [formula in source] prediction depends critically on the backreaction coefficient. We analyze the sensitivity to demonstrate this is not fine-tuning but a genuine geometric constraint.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Sensitivity Analysis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13973,"byte_start":12014,"id":"section:39833cf2f421bc9de506","kind":"paragraph","labels":["fig:tornado","tab:jacobian"],"line_end":298,"line_start":242,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/004-subsection-geometric-self-consistency-backreaction.tex","status_markers_as_written":[],"summary_excerpt":"The Jacobian [formula in source] evaluated at the self-consistent solution quantifies how each discrete or continuous input drives the headline value. Table","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Sensitivity hierarchy.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16498,"byte_start":13973,"id":"section:055a29c7e27cdb2c570b","kind":"subsection","labels":["fig:error-ledger","sec:comparison-policy"],"line_end":343,"line_start":299,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/004-subsection-geometric-self-consistency-backreaction.tex","status_markers_as_written":[],"summary_excerpt":"( [formula in source] ), fonttitle= ] Why this matters: Precision electroweak fits and PDG summaries use the [formula in source] coupling at [formula in source] , [formula in source] , as the comparison observable. CODATA [formula in source] is an on-shell/IR reference and is therefore treated as secondary diagnostic once scheme and threshold bookkeeping is made explicit.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Comparison and Scheme Policy (No Hidden Knobs)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18716,"byte_start":16498,"id":"section:e641c94f9c410b5d88c1","kind":"paragraph","labels":["fig:msbar-boundary"],"line_end":399,"line_start":344,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/004-subsection-geometric-self-consistency-backreaction.tex","status_markers_as_written":[],"summary_excerpt":"The running from [formula in source] to [formula in source] is computed by two independent implementations: Implementation A: step-by-step threshold matching (9 steps), yielding [formula in source] . Implementation B: single-step [formula in source] -based running, yielding [formula in source] . The double-implementation audit confirms exact numerical agreement (agreement_ppm\\,=\\,0.0). Systematic uncertainties in the","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bridge systematic uncertainty (double implementation).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":202,"byte_start":0,"id":"section:3af9e8ec4c5562033e19","kind":"section","labels":[],"line_end":4,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/005-section-the-unified-field-equation-ufe.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"The Unified Field Equation (UFE)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1352,"byte_start":202,"id":"section:eab30c6fb82550a4bdca","kind":"subsection","labels":[],"line_end":33,"line_start":5,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/005-section-the-unified-field-equation-ufe.tex","status_markers_as_written":[],"summary_excerpt":"Quantum Vacuum TensorQVT Let Let [formula in source] denote the scalar invariant entering the coupling equation, Define the Quantum Vacuum Tensor","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Quantum Vacuum Tensor Packaging","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7553,"byte_start":1352,"id":"section:ae289276690b57b9bb16","kind":"subsection","labels":["eq:UFE","eq:bianchi","eq:maxwell"],"line_end":142,"line_start":34,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/005-section-the-unified-field-equation-ufe.tex","status_markers_as_written":[],"summary_excerpt":"UFE ActionUFEaction On a manifold [formula in source] with metric [formula in source] and torsionful connection [formula in source] , the action is: Here [formula in source] denotes the Ricci scalar constructed from the full torsionful connection [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Torsionful Geometric Action","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12125,"byte_start":7553,"id":"section:275f91bb66e1c906f5ee","kind":"subsection","labels":["fig:torsion-bounds","sec:torsion-regimes"],"line_end":240,"line_start":143,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/005-section-the-unified-field-equation-ufe.tex","status_markers_as_written":[],"summary_excerpt":"TFPT distinguishes between cosmological torsion (which may be active in the early universe and drive a bounce) and local vacuum torsion (which is constrained by laboratory and astrophysical bounds on Lorentz violation). To avoid hidden assumptions, we treat ``torsion today'' as an explicit regime choice rather than a vague qualitative statement.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Present-Day Torsion Regimes and Local Tests","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15700,"byte_start":12125,"id":"section:4b3ca51a725c3ee2f9d3","kind":"subsubsection","labels":["fig:evpa_intercept","sec:eht-intercept"],"line_end":307,"line_start":241,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/005-section-the-unified-field-equation-ufe.tex","status_markers_as_written":[],"summary_excerpt":"Beyond the cosmic birefringence prediction (Theorem in the presence of a nonzero [formula in source] environment (see the companion note bhAchromaticRotationNote2025). EHT-style polarimetry provides the relevant data products for such an intercept test ehtm87pol2021. A simple dyonic toy model yields where [formula in source] is the emission radius and [formula in source] denote effective electromagnetic charges sourc","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Achromatic polarization rotation around compact objects (EHT intercept test)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17189,"byte_start":15700,"id":"section:479cfa5f6fa8a2e95987","kind":"paragraph","labels":["fig:eht-sensitivity"],"line_end":356,"line_start":308,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/005-section-the-unified-field-equation-ufe.tex","status_markers_as_written":[],"summary_excerpt":"A Monte Carlo forecast quantifies the noise and calibration requirements for EHT detection of the TFPT intercept signal [formula in source] mrad:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Sensitivity requirements.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1503,"byte_start":0,"id":"section:08dcbe233885fd200dce","kind":"subsection","labels":[],"line_end":35,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/006-subsection-gravitational-coupling-from-invariants.tex","status_markers_as_written":[],"summary_excerpt":"Gravitational Coupling Consistencykappa The gravitational coupling [formula in source] (with dimension [formula in source] ) is constrained by consistency with the dimensionless ratio:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gravitational Coupling from Invariants","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1695,"byte_start":1503,"id":"section:d6eec12212523c582fd4","kind":"section","labels":[],"line_end":39,"line_start":36,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/006-subsection-gravitational-coupling-from-invariants.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Observable Predictions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2162,"byte_start":1695,"id":"section:aeea5df4addc942b2d3e","kind":"subsection","labels":[],"line_end":51,"line_start":40,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/006-subsection-gravitational-coupling-from-invariants.tex","status_markers_as_written":[],"summary_excerpt":"Axion–Photon Couplinggagg The CFE fixes the axion–photon vertex uniquely: This determines cosmic birefringence without free parameters.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Axion–Photon Coupling","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4627,"byte_start":2162,"id":"section:b8be28f193f80e3ffe69","kind":"subsection","labels":[],"line_end":97,"line_start":52,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/006-subsection-gravitational-coupling-from-invariants.tex","status_markers_as_written":[],"summary_excerpt":"Topological Excursion Quantizationtopoexcursion The topological axion excursion is quantized in discrete sector changes: with [formula in source] the minimal nontrivial class. The corresponding birefringence is [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cosmic Birefringence","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11776,"byte_start":4627,"id":"section:03b2970b7ad1695c83cc","kind":"subsubsection","labels":["eq:shifted-axion-potential","fig:beta-tomography","fig:birefringence","sec:deltaa","tab:birefringence"],"line_end":260,"line_start":98,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/006-subsection-gravitational-coupling-from-invariants.tex","status_markers_as_written":[],"summary_excerpt":"Goal: Provide one minimal dynamical realization compatible with the topological quantization (Definition","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dynamical Completion of the Excursion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16218,"byte_start":11776,"id":"section:51711e9d740d6ac90261","kind":"subsection","labels":["fig:rg-two-loop-running"],"line_end":343,"line_start":261,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/006-subsection-gravitational-coupling-from-invariants.tex","status_markers_as_written":[],"summary_excerpt":"RG FingerprintsRGfingerprints The TFPT invariants leave signatures in the RG flow of gauge couplings: These values are obtained by two-loop RG running from PDG boundary conditions at [formula in source] using the declared PyR@TE model (checked by two_loop_rg_fingerprints in the verification suite; not direct measurements at the quoted scales). The crossing scale for [formula in source] is [formula in source] GeV.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Two-Loop RG Fingerprints","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16493,"byte_start":16218,"id":"section:c007dedeb680c1f8a03d","kind":"section","labels":["sec:e8"],"line_end":348,"line_start":344,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/006-subsection-gravitational-coupling-from-invariants.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"The E [formula in source] Cascade and Block ConstantsThe E8 Cascade and Block Constants","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2645,"byte_start":0,"id":"section:4ffc5485675c60f01096","kind":"subsection","labels":[],"line_end":49,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/007-subsection-nilpotent-orbit-structure.tex","status_markers_as_written":[],"summary_excerpt":"E [formula in source] Orbit Graphorbitgraph Let [formula in source] denote the set of nilpotent orbits of the exceptional Lie algebra [formula in source] . For each orbit [formula in source] , define: [formula in source] : the dimension of the orbit as a variety [formula in source] : the ``centralizer dimension'' [formula in source] : the height (sum of coefficients in weighted Dynkin diagram) The orbit graph [formul","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nilpotent Orbit Structure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7219,"byte_start":2645,"id":"section:f65a561432777892c1b6","kind":"subsection","labels":["eq:ladder","fig:ladder"],"line_end":155,"line_start":50,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/007-subsection-nilpotent-orbit-structure.tex","status_markers_as_written":[],"summary_excerpt":"Holonomy degeneracy anchor for [formula in source] holonomydeg TFPT uses the SU(5) hypercharge holonomy data already fixed elsewhere in the construction. On the fundamental splitting, the holonomy spectrum separates into two eigenspaces of dimensions [formula in source] and [formula in source] , hence we define the discrete degeneracy count [formula in source] The minimal damping ratio compatible with a single additi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Log-Exact Ladder Formula","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11824,"byte_start":7219,"id":"section:876e021c1345659e3588","kind":"subsection","labels":["fig:blocks","tab:blocks"],"line_end":266,"line_start":156,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/007-subsection-nilpotent-orbit-structure.tex","status_markers_as_written":[],"summary_excerpt":"For a 6D Weyl fermion zero mode on a boundary cycle [formula in source] with flat [formula in source] connection (holonomy [formula in source] ), the variation of [formula in source] under the connection is proportional to the quadratic charge index: The proportionality constant is fixed by the topological normalization [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Block Constant Formula and Derivation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13245,"byte_start":11824,"id":"section:76d584d1d843f962d483","kind":"subsection","labels":[],"line_end":299,"line_start":267,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/007-subsection-nilpotent-orbit-structure.tex","status_markers_as_written":[],"summary_excerpt":"The neutrino block at [formula in source] provides concrete predictions for the seesaw mechanism.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neutrino Seesaw Predictions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13511,"byte_start":13245,"id":"section:6becb48175a6c99e3277","kind":"section","labels":[],"line_end":303,"line_start":300,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/007-subsection-nilpotent-orbit-structure.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Flavor Structure: The Z [formula in source] ArchitectureFlavor Structure: The Z3 Architecture","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16181,"byte_start":13511,"id":"section:c4d3e285fba0ca639af0","kind":"subsection","labels":[],"line_end":355,"line_start":304,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/007-subsection-nilpotent-orbit-structure.tex","status_markers_as_written":[],"summary_excerpt":"On a conformally flat boundary geometry, the unique projectively invariant quantity from four marked points is the cross-ratio. Any boundary monodromy acts as a PSL [formula in source] transformation. Therefore, relations depending only on boundary monodromies must be rational functions of a M\\\"obius map.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Universal Phase [formula in source] Universal Phase delta","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1404,"byte_start":0,"id":"section:7c72cac5e9e79b62ea2b","kind":"subsection","labels":[],"line_end":32,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/008-subsection-m-obius-mass-relations.tex","status_markers_as_written":[],"summary_excerpt":"Mass Ratios from M\\\"obius Mapmassratios The M\\\"obius map [formula in source] evaluated at cusps [formula in source] yields mass ratios:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"M\\\"obius Mass Relations","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5189,"byte_start":1404,"id":"section:f0bc6d4cb60363cd9469","kind":"subsection","labels":[],"line_end":116,"line_start":33,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/008-subsection-m-obius-mass-relations.tex","status_markers_as_written":[],"summary_excerpt":"Cabibbo AngleCabibbo The Cabibbo parameter is fixed by the birefringence invariant [formula in source] : Compared to the PDG reference value, this is a sub-permille level deviation (status: solid).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cabibbo Angle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6725,"byte_start":5189,"id":"section:d7944b537d54e8fe600b","kind":"subsubsection","labels":[],"line_end":135,"line_start":117,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/008-subsection-m-obius-mass-relations.tex","status_markers_as_written":[],"summary_excerpt":"The shipped suite includes a deterministic CKM reconstruction pipeline with declared UV textures, two-loop RG dressing, and a reference-scale comparison at [formula in source] (module ckm_full_pipeline). The baseline benchmark gives a CKM matrix close to PDG at the level quantified by the reported [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Suite benchmark: RG-dressed CKM pipeline (explicit conventions)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9135,"byte_start":6725,"id":"section:28d48a8a8b9a57669ca6","kind":"subsubsection","labels":["fig:ckm-phase-bridge","fig:ckm-residuals"],"line_end":207,"line_start":136,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/008-subsection-m-obius-mass-relations.tex","status_markers_as_written":[],"summary_excerpt":"We treat phases as elements of an equivalence class under [formula in source] . Referee exit gates record both a representative value and its conjugate, and use a CP-odd sign to select the physical branch when magnitudes alone are insufficient.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Phase mapping law and equivalence classes (v2.8)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12922,"byte_start":9135,"id":"section:11e03f201972001a7c2b","kind":"subsubsection","labels":["fig:kaon_bar","fig:kaon_correlation","sec:rare-kaon"],"line_end":305,"line_start":208,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/008-subsection-m-obius-mass-relations.tex","status_markers_as_written":[],"summary_excerpt":"The ultra clean modes [formula in source] and [formula in source] provide a stringent test of the TFPT flavor architecture, because long-distance hadronic uncertainties are strongly suppressed (see the companion note rareKaonNote2025).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Rare Kaon Decays: [formula in source] as a clean flavor null testRare Kaon Decays: K to pi nu nu as a clean flavor null test","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16707,"byte_start":12922,"id":"section:c7852d7443423f10f7c1","kind":"subsection","labels":["fig:pmns-residuals"],"line_end":401,"line_start":306,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/008-subsection-m-obius-mass-relations.tex","status_markers_as_written":[],"summary_excerpt":"and [formula in source] , fonttitle= ] v2.8 closes all PMNS degrees of freedom. The kernel identity plus TM1 pattern provide [formula in source] , and a topology candidate family with a discrete [formula in source] shift now closes [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"PMNS Neutrino Mixing: TM1 Pattern","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1106,"byte_start":0,"id":"section:80ad77bdb9e944dfe9b8","kind":"subsection","labels":["sec:majorana"],"line_end":20,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/009-subsection-majorana-phases-and-neutrinoless-double-beta-.tex","status_markers_as_written":[],"summary_excerpt":"A discrete Majorana phase search ( majorana_phase_search_v28) yields a minimal effective mass for neutrinoless double beta decay: [formula in source] at phase representatives [formula in source] and [formula in source] (radians), modulo conjugation under [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Majorana phases and neutrinoless double beta decay (v2.8)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2888,"byte_start":1106,"id":"section:e04250082111badd6b71","kind":"section","labels":["eq:As","eq:R2action","eq:ns","eq:r","tab:inflation"],"line_end":61,"line_start":21,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/009-subsection-majorana-phases-and-neutrinoless-double-beta-.tex","status_markers_as_written":[],"summary_excerpt":"The TFPT topological correction scale is set by [formula in source] (cf.\\ [formula in source] ). In effective gravity, the leading higher-curvature completion compatible with general covariance is an [formula in source] term.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Inflation: [formula in source] Completion (Starobinsky Limit)Inflation: R2 Completion (Starobinsky Limit)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5026,"byte_start":2888,"id":"section:ab53b352ae69e023a9f7","kind":"subsection","labels":["fig:r2-blocks","sec:r2derive"],"line_end":114,"line_start":62,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/009-subsection-majorana-phases-and-neutrinoless-double-beta-.tex","status_markers_as_written":[],"summary_excerpt":"Relevant Torsion DegreesR2torsion Decompose torsion into irreducible parts [formula in source] (axial, trace, tensor). In the minimal UFE setting the dominant coupling is through axial torsion [formula in source] , and the torsion sector is treated at quadratic order so it can be integrated out in the one-loop effective action.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[formula in source] Term from the Torsionful Effective ActionR2 Term from the Torsionful Effective Action","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6868,"byte_start":5026,"id":"section:6fdfe0c2c55a03109c24","kind":"subsection","labels":["eq:R2scale","fig:r2-scan"],"line_end":163,"line_start":115,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/009-subsection-majorana-phases-and-neutrinoless-double-beta-.tex","status_markers_as_written":[],"summary_excerpt":"TFPT [formula in source] ScaleR2coeff Using the GR renormalization condition (A8) to fix the scheme, the coefficient of the [formula in source] term yields Here the square root applies only to [formula in source] , consistent with the numerical value above.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Coefficient Identification and GR Renormalization","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8498,"byte_start":6868,"id":"section:25025107fc192ca44648","kind":"subsection","labels":["sec:bounce"],"line_end":200,"line_start":164,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/009-subsection-majorana-phases-and-neutrinoless-double-beta-.tex","status_markers_as_written":[],"summary_excerpt":"Bounce-to-Inflation Backgroundbouncebg Assume a non-singular bounce driven by the torsion-induced [formula in source] term (Lemma above), followed by a transition into the [formula in source] inflationary phase. We take the CMB pivot scales to exit the horizon during the [formula in source] phase.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bounce + [formula in source] Perturbations and Transfer FunctionBounce + R2 Perturbations and Transfer Function","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8699,"byte_start":8498,"id":"section:bda88e7a2f92cc899a33","kind":"section","labels":[],"line_end":204,"line_start":201,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/009-subsection-majorana-phases-and-neutrinoless-double-beta-.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Axion Cosmology and Dark Matter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10880,"byte_start":8699,"id":"section:2b3b702ccb8a9196c64f","kind":"subsection","labels":[],"line_end":243,"line_start":205,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/009-subsection-majorana-phases-and-neutrinoless-double-beta-.tex","status_markers_as_written":[],"summary_excerpt":"The TFPT axion sector is split into two distinct fields to avoid an internal contradiction (a single [formula in source] eV axion cannot remain quasi-static over Hubble times):","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Two-Field Structure: Topological vs.\\ QCD Axion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12732,"byte_start":10880,"id":"section:2e4b61c1fc32104fc501","kind":"subsection","labels":["fig:phase-lattice","sec:phase-lattice"],"line_end":278,"line_start":244,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/009-subsection-majorana-phases-and-neutrinoless-double-beta-.tex","status_markers_as_written":[],"summary_excerpt":"Multiple independent gates project physical phases onto a [formula in source] lattice. In v2.8 this includes the CKM CP phase ( [formula in source] ), the PMNS Dirac phase ( [formula in source] ), and a Majorana phase representative ( [formula in source] ), each recorded with its conjugate under [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Phase lattice projection (v2.8)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15889,"byte_start":12732,"id":"section:ce5354f7102d353d0c4c","kind":"subsection","labels":[],"line_end":329,"line_start":279,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/009-subsection-majorana-phases-and-neutrinoless-double-beta-.tex","status_markers_as_written":[],"summary_excerpt":"Axion Dark Matter ParametersaxionDM For the QCD axion field [formula in source] from the E [formula in source] cascade (PQ block at [formula in source] ):","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dark Matter Relic Density","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18199,"byte_start":15889,"id":"section:7ccf03f262b66c595bb5","kind":"subsection","labels":["sec:dark-energy"],"line_end":374,"line_start":330,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/009-subsection-majorana-phases-and-neutrinoless-double-beta-.tex","status_markers_as_written":[],"summary_excerpt":"with no continuous knobs, fonttitle= ] We test the discrete defect-suppression candidate [formula in source] Here [formula in source] denotes the discrete normalization prefactor (not to be confused with the gap-equation integers below). The two-defect sector uses [formula in source] and the corresponding [formula in source] (Sec.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dark Energy as a Defect-Suppressed Torsion Condensate (v2.8 discrete gap closure)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2002,"byte_start":0,"id":"section:f42fe44e45fb5ddf8693","kind":"section","labels":["tab:beta"],"line_end":34,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/010-section-texorpdfstring-beta-text-rad-centric-identity-su.tex","status_markers_as_written":[],"summary_excerpt":"The parameter [formula in source] provides a compact dictionary for expressing multiple quantities. Most equalities in this section are algebraic rewrites of earlier definitions rather than independent new inputs (see Appendix Inflation observables additionally depend on a dynamical completion (here: the conditional [formula in source] sector in Theorem","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[formula in source] -Centric Identity Summarybeta_rad-Centric Identity Summary","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3997,"byte_start":2002,"id":"section:5d501657e2ffd119ad98","kind":"subsection","labels":["sec:constant-factory-v28","tab:constant-factory-v28"],"line_end":74,"line_start":35,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":["relation:d4efadb3addd28e33cc8"],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/010-section-texorpdfstring-beta-text-rad-centric-identity-su.tex","status_markers_as_written":[],"summary_excerpt":"A symbolic regression over the TFPT grammar produces a closed expression family for [formula in source] and lepton ratios with max log [formula in source] mismatches below [formula in source] on the declared targets.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Electroweak scale and lepton ladder (constant factory, v2.8)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9988,"byte_start":3997,"id":"section:f85f91d5236e161a822a","kind":"section","labels":["tab:status"],"line_end":140,"line_start":75,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/010-section-texorpdfstring-beta-text-rad-centric-identity-su.tex","status_markers_as_written":[],"summary_excerpt":"@p3cmp4cmp3cmp5.2cm@ TFPT status dashboard. ``Exact'': [formula in source] ; ``Solid'': [formula in source] ; ``Minor'': [formula in source] ; ``Moderate'': [formula in source] . Domain & Quantity & Deviation & Status\\\\ Domain & Quantity & Deviation & Status\\\\ 4r Continued on next page.\\\\ 4l Structural (parameter-free)\\\\ CFE & [formula in source] & [formula in source] & green!60!black Derived (double cover + [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Summary of Claims and Status","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10624,"byte_start":9988,"id":"section:3f9f2acf332dd37e3066","kind":"section","labels":[],"line_end":154,"line_start":141,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/010-section-texorpdfstring-beta-text-rad-centric-identity-su.tex","status_markers_as_written":[],"summary_excerpt":"The following are not required: Slow-roll inflation (specific model) String landscape or anthropic selection Extra dimensions as free parameters Dark matter entirely from axions New particles beyond minimal axion sector Any fitted or adjusted parameters","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"What TFPT Does Not Assume","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12093,"byte_start":10624,"id":"section:b11a7bada26efae7dd03","kind":"section","labels":[],"line_end":180,"line_start":155,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/010-section-texorpdfstring-beta-text-rad-centric-identity-su.tex","status_markers_as_written":[],"summary_excerpt":"TFPT demonstrates that the fine-structure constant [formula in source] can be derived within an explicit set of eight minimal axioms rooted in topology, geometry, and quantum consistency. The key results are:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conclusions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13251,"byte_start":12093,"id":"section:1d5829d7896cd91a02da","kind":"paragraph","labels":[],"line_end":190,"line_start":181,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":["relation:6997609ec7eb55134aff"],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/010-section-texorpdfstring-beta-text-rad-centric-identity-su.tex","status_markers_as_written":[],"summary_excerpt":"Where the kernel does not uniquely fix an observable (e.g.\\ CKM CP phase, PMNS full closure, [formula in source] , [formula in source] , Majorana phases), TFPT employs a uniform referee exit gate protocol: Finite candidate set: enumerate all topologically or algebraically admissible candidates (discrete, finite). Convention policy (filter only): rank candidates by a declared metric ( [formula in source] , [formula in","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Referee exit architecture (how TFPT closes open interfaces).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13744,"byte_start":13251,"id":"section:76612a913a9b092868eb","kind":"paragraph","labels":[],"line_end":198,"line_start":191,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/010-section-texorpdfstring-beta-text-rad-centric-identity-su.tex","status_markers_as_written":[],"summary_excerpt":"Two longer-range directions are sketched in internal notes and remain explicitly open: an asymptotic-safety UV completion for the torsionful gravity sector and a black-hole vortex/remnant picture with information-paradox implications. Both are framed as outlook items rather than closed predictions at this stage fiveProblemsNote2025,blackHolesBh1Note2025.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Outlook (open interfaces).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16636,"byte_start":13744,"id":"section:5a055f4a5dbe4be172ab","kind":"section","labels":["tab:constants"],"line_end":243,"line_start":199,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/010-section-texorpdfstring-beta-text-rad-centric-identity-su.tex","status_markers_as_written":[],"summary_excerpt":"@ll@ Quantity & Value\\\\ [formula in source] & \\\\ [formula in source] & \\\\ [formula in source] & \\\\ [formula in source] & \\\\ [formula in source] (self-consistent) & 0.053170209119023745\\\\ [formula in source] & \\\\ [formula in source] & [formula in source] \\\\ [formula in source] & \\\\ [formula in source] (E [formula in source] ) & [formula in source] \\\\ [formula in source] (E [formula in source] exponent) & 0.58723319078","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Numerical Constants (High Precision)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17473,"byte_start":16636,"id":"section:201bba2851d879c60273","kind":"section","labels":["app:gdiagnostic"],"line_end":256,"line_start":244,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/010-section-texorpdfstring-beta-text-rad-centric-identity-su.tex","status_markers_as_written":[],"summary_excerpt":"The suite records legacy diagnostic templates in which [formula in source] is varied away from the holonomy value [formula in source] (e.g.\\ the ordered-occupancy [formula in source] template). These runs are used only to verify that the defect-sector response is sensitive to discrete holonomy choices and to quantify the direction of the shift in [formula in source] . They are explicitly not used for parameter select","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Diagnostic [formula in source] g Variants (Internal Sanity Checks)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18645,"byte_start":17473,"id":"section:2e0e4a24dd75cc31eca9","kind":"section","labels":["fig:rg-unification"],"line_end":287,"line_start":257,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/010-section-texorpdfstring-beta-text-rad-centric-identity-su.tex","status_markers_as_written":[],"summary_excerpt":"Gauge coupling convergence. Visualizes the unification gate scan used by the suite.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"RG Unification Overview (Supplementary)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8117,"byte_start":0,"id":"section:4d1f701976d7a8e00c56","kind":"section","labels":["eq:CFE-appendix","eq:potential","eq:stationarity"],"line_end":164,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/011-section-coefficient-policy-sketch-for-the-cfe.tex","status_markers_as_written":[],"summary_excerpt":"This appendix records the coefficient bookkeeping used in the suite and provides a heuristic motivation for the CFE coefficient policy. It is not presented as a full background-field derivation. In the declared scheme, the one-loop effective potential for the electromagnetic coupling modulus is taken to have the form:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Coefficient Policy Sketch for the CFE","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9562,"byte_start":8117,"id":"section:88d16b55f4bf604217b2","kind":"subsection","labels":["sec:toy-bfg","tab:toy-bfg"],"line_end":196,"line_start":165,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/011-section-coefficient-policy-sketch-for-the-cfe.tex","status_markers_as_written":[],"summary_excerpt":"As a structural cross-check, we compute the one-loop effective action for an abelian gauge field coupled to a modulus [formula in source] with [formula in source] and an axionic [formula in source] term in background-field gauge. The resulting coefficient structure is:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Toy Background-Field Derivation (Term-Structure Check)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11999,"byte_start":9562,"id":"section:5f1b19931dba2fd8357e","kind":"section","labels":[],"line_end":229,"line_start":197,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":["relation:6400ad0830da200c9384"],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/011-section-coefficient-policy-sketch-for-the-cfe.tex","status_markers_as_written":[],"summary_excerpt":"The TFPT verification suite turns paper claims into deterministic, assumption-explicit computations. All counts in this section are auto-generated from the suite artifacts (no hardcoded ``39 modules''): [formula in source] Version breakdown: v2.5: 91, v2.7: 44, v2.8: 96, v2.8-t7: 4. Category breakdown: supplementary 107, kernel 64, policy 25, closed_interface 21, crosslink 12, dashboard 2, search_tool 2.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verification Suite Summary","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12379,"byte_start":11999,"id":"section:56a2ec6b29bbc7621648","kind":"subsection","labels":["sec:known-gaps"],"line_end":236,"line_start":230,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/011-section-coefficient-policy-sketch-for-the-cfe.tex","status_markers_as_written":[],"summary_excerpt":"For the PRL-facing manuscript we omit the auto-generated flagged/open inventory and list open interfaces only as conditional statements in the main text. The full suite manifest (with module-level status and plot inventories) is included in the replication bundle referenced in Appendix","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Known Gaps and Status (Summary)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6381,"byte_start":0,"id":"section:9e7ad02e457de1bdffb6","kind":"subsection","labels":["sec:theoryv3-evidence"],"line_end":125,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/012-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"The theoryv3 analysis branch is a compact ``evidence layer'' for the discrete kernel and crosslink logic. Current inventory (auto-generated from the replication bundle; theoryv3 is a baseline branch pinned to v2.5 by design): [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"theoryv3 Evidence Layer (Compressed, Auto-Generated)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9962,"byte_start":6381,"id":"section:642926e0ae6650eb954a","kind":"paragraph","labels":["fig:likelihood-breakdown"],"line_end":236,"line_start":126,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/012-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"The suite computes [formula in source] through 12 internal pathways (spread [formula in source] ). The authoritative value reported in the PRL claim surface is [formula in source] from module h0_diagnostic_closure_v28; all other [formula in source] pathways are classified as diagnostics. The suite contract ( h0_source_contract_audit_v1, PASS) enforces this hierarchy: only one module feeds [formula in source] into the","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[formula in source] consolidation policy.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10262,"byte_start":9962,"id":"section:1fb29c4b21777d0eff0f","kind":"section","labels":["app:E8cert"],"line_end":243,"line_start":237,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/012-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"This appendix provides the complete verification data for the E [formula in source] chain uniqueness theorem (Theorem","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"E [formula in source] Chain CertificateE8 Chain Certificate","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10766,"byte_start":10262,"id":"section:f806fc88a9070cb4c4a9","kind":"subsection","labels":[],"line_end":253,"line_start":244,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/012-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"Each nilpotent orbit [formula in source] of [formula in source] is characterized by: Bala–Carter label: Standard notation (e.g., [formula in source] , [formula in source] , [formula in source] , ) Dimension: [formula in source] Centralizer dimension: [formula in source] Height: [formula in source] (sum of weighted Dynkin diagram coefficients)","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Orbit Data Structure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11442,"byte_start":10766,"id":"section:e226e45f8e9759d92ac4","kind":"subsection","labels":[],"line_end":278,"line_start":254,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/012-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"The complete chain from [formula in source] to [formula in source] :","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Unique Chain (Excerpt)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12210,"byte_start":11442,"id":"section:7e8b73da2852b8d70b50","kind":"subsection","labels":[],"line_end":293,"line_start":279,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/012-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"The uniqueness is verified by: Constructing the complete Hasse diagram of [formula in source] from standard tables. Computing all cover relations with [formula in source] . Running dynamic programming to find all paths from [formula in source] to [formula in source] . Applying the cost function [formula in source] (second-difference smoothness). Verifying that the minimum-cost path is unique (cost gap to second-best ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verification Algorithm","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12450,"byte_start":12210,"id":"section:6b09bccceba39d70fbda","kind":"section","labels":["app:boundary"],"line_end":300,"line_start":294,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/012-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"This appendix derives the block index formula [formula in source] from the APS index theorem.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Boundary Trace Derivation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12841,"byte_start":12450,"id":"section:b3f6084709a748f58de8","kind":"subsection","labels":[],"line_end":310,"line_start":301,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/012-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"Consider a 6D manifold [formula in source] with boundary [formula in source] . For a Weyl fermion coupled to a [formula in source] gauge field [formula in source] , the APS index theorem gives: where [formula in source] is the [formula in source] -invariant of the boundary Dirac operator.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13354,"byte_start":12841,"id":"section:a7b5e5e9322b25a4f1e5","kind":"subsection","labels":[],"line_end":325,"line_start":311,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/012-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"On the orientable double cover [formula in source] , the boundary decomposes as: (two boundary cycles plus the twist seam).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Flat Connection on Boundary Cycles","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14871,"byte_start":13354,"id":"section:83ef82fbb72337191bd8","kind":"subsection","labels":[],"line_end":353,"line_start":326,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/012-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"The regulated determinant of the hypercharge-coupled Dirac operator contains a logarithmic term which we normalize as: We define the spectral index [formula in source] as the quadratic charge trace entering this term in our normalization; the overall prefactor is part of the declared coefficient policy (Appendix C) and differs by a fixed normalization from the conventional [formula in source] Seeley–DeWitt prefactor.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spectral Trace Coefficient and [formula in source] Spectral Trace Coefficient and b1","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15652,"byte_start":14871,"id":"section:7f347c70b325a9b2ae8f","kind":"subsection","labels":[],"line_end":373,"line_start":354,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/012-subsection-theoryv3-evidence-layer-compressed-auto-gener.tex","status_markers_as_written":[],"summary_excerpt":"Step 1: Each boundary cycle contributes a factor proportional to [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of [formula in source] Derivation of kB","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":314,"byte_start":0,"id":"section:4a590976d554bd14c337","kind":"section","labels":["app:seam"],"line_end":6,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/013-section-texorpdfstring-seam-gluing-and-the-eta-invariant.tex","status_markers_as_written":[],"summary_excerpt":"This appendix provides the [formula in source] -invariant gluing derivation used in Axiom","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Seam Gluing and the [formula in source] -Invariant NormalizationSeam Gluing and the eta-Invariant Normalization","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":916,"byte_start":314,"id":"section:d59495d3d8a086b057b1","kind":"subsection","labels":[],"line_end":17,"line_start":7,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/013-section-texorpdfstring-seam-gluing-and-the-eta-invariant.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the orientable double cover of the M\\\"obius fiber and cut it along the seam [formula in source] to obtain a manifold-with-boundary [formula in source] with boundary components [formula in source] . Let [formula in source] be the Dirac operator on [formula in source] with APS boundary conditions on [formula in source] and a unitary matching operator [formula in source] identifying [formula i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cut Space and Operators","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1550,"byte_start":916,"id":"section:0207910e80a48f1ca016","kind":"subsection","labels":[],"line_end":30,"line_start":18,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/013-section-texorpdfstring-seam-gluing-and-the-eta-invariant.tex","status_markers_as_written":[],"summary_excerpt":"The APS gluing theorem expresses the [formula in source] -invariant of the glued manifold in terms of the cut manifold plus a discrete spectral-flow correction: where [formula in source] is the spectral flow of the matching operator. In TFPT bookkeeping this contributes a quantized seam term to the curvature normalization.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gluing Formula for the [formula in source] -InvariantGluing Formula for the eta-Invariant","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1834,"byte_start":1550,"id":"section:744fbe89b0901979288f","kind":"subsection","labels":[],"line_end":37,"line_start":31,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/013-section-texorpdfstring-seam-gluing-and-the-eta-invariant.tex","status_markers_as_written":[],"summary_excerpt":"For the M\\\"obius [formula in source] identification, the matching satisfies [formula in source] . The minimal nontrivial class is modeled by the unitary phase","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"M\\\"obius Matching and the Minimal Gluing Class","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2500,"byte_start":1834,"id":"section:97e45f4c2f599f130ec8","kind":"subsection","labels":[],"line_end":54,"line_start":38,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/013-section-texorpdfstring-seam-gluing-and-the-eta-invariant.tex","status_markers_as_written":[],"summary_excerpt":"Interpolate boundary conditions by a phase [formula in source] , which gives the eigenvalues As [formula in source] runs from [formula in source] to [formula in source] , exactly one eigenvalue crosses zero, so [formula in source] and [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spectral Flow Computation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2959,"byte_start":2500,"id":"section:33563ecf04052bb7a123","kind":"subsection","labels":[],"line_end":63,"line_start":55,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/013-section-texorpdfstring-seam-gluing-and-the-eta-invariant.tex","status_markers_as_written":[],"summary_excerpt":"The two physical boundary cycles contribute [formula in source] , and the seam gluing adds [formula in source] , so the total curvature is [formula in source] . We treat [formula in source] as the dimensionless geometry modulus; the closure normalization [formula in source] fixes its scale and therefore yields","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Normalization of [formula in source] Normalization of phi_tree","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5042,"byte_start":2959,"id":"section:14c29b769d47bced54fd","kind":"subsection","labels":["fig:gluing-scan","sec:gluing-class-scan","tab:gluing-scan"],"line_end":122,"line_start":64,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/013-section-texorpdfstring-seam-gluing-and-the-eta-invariant.tex","status_markers_as_written":[],"summary_excerpt":"For general winding [formula in source] , the matching operator is [formula in source] with spectral flow [formula in source] , giving [formula in source] and [formula in source] . The resulting [formula in source] and self-consistent [formula in source] are discrete functions of [formula in source] :","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Family of Gluing Classes and Minimality","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5548,"byte_start":5042,"id":"section:6fc6de0593d35ef7a247","kind":"section","labels":["app:48deriv"],"line_end":133,"line_start":123,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/013-section-texorpdfstring-seam-gluing-and-the-eta-invariant.tex","status_markers_as_written":[],"summary_excerpt":"This appendix explains the integer coefficient in [formula in source] . The key point is that the canonical quantity is and the appearance of ``48'' is simply the same number expressed in units of [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of the Coefficient 48 in [formula in source] Derivation of the Coefficient 48 in delta_top","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6272,"byte_start":5548,"id":"section:80c49967979c7764c900","kind":"subsection","labels":[],"line_end":146,"line_start":134,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/013-section-texorpdfstring-seam-gluing-and-the-eta-invariant.tex","status_markers_as_written":[],"summary_excerpt":"The topological correction [formula in source] arises from the leading gauge-invariant correction to the tree-level geometric scale [formula in source] . The requirements are: Gauge invariance: The correction must be built from [formula in source] only (no explicit [formula in source] dependence at this order). Dimensionlessness: Since [formula in source] is dimensionless, the correction must be a pure power [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Physical Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7077,"byte_start":6272,"id":"section:9bf58788d22256f54603","kind":"subsection","labels":[],"line_end":163,"line_start":147,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/013-section-texorpdfstring-seam-gluing-and-the-eta-invariant.tex","status_markers_as_written":[],"summary_excerpt":"The effective action on the M\\\"obius fiber includes the Chern–Simons term [formula in source] . The leading topological correction comes from the one-loop determinant of the Dirac operator coupled to this background.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Power Counting: Why [formula in source] ?Power Counting: Why c3^4?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7472,"byte_start":7077,"id":"section:76530cf378367652d2f9","kind":"subsection","labels":[],"line_end":173,"line_start":164,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/013-section-texorpdfstring-seam-gluing-and-the-eta-invariant.tex","status_markers_as_written":[],"summary_excerpt":"The non-orientable identification acts as a [formula in source] operation on the base, but in the spin bundle the same element lifts to order [formula in source] because a [formula in source] rotation acts as [formula in source] on spinors and only a [formula in source] rotation is trivial. This produces a universal deficit factor per minimal sector.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spin-Lifted Deficit Factor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7978,"byte_start":7472,"id":"section:d40eeb1f2e2fe91569e6","kind":"subsection","labels":[],"line_end":183,"line_start":174,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/013-section-texorpdfstring-seam-gluing-and-the-eta-invariant.tex","status_markers_as_written":[],"summary_excerpt":"Cutting along [formula in source] yields boundary components [formula in source] . The four local corner patches [formula in source] , [formula in source] , [formula in source] , [formula in source] constitute the fundamental domain. Summing the spin-lifted deficit factor over these sectors yields In TFPT normalization this yields the canonical form [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Sector Count from Cut Geometry","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8332,"byte_start":7978,"id":"section:63171b8f3a709fd6ac65","kind":"subsection","labels":[],"line_end":193,"line_start":184,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/013-section-texorpdfstring-seam-gluing-and-the-eta-invariant.tex","status_markers_as_written":[],"summary_excerpt":"Using [formula in source] : so [formula in source] and [formula in source] are exactly equivalent.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conversion to the [formula in source] normalizationConversion to the c3 normalization","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8567,"byte_start":8332,"id":"section:4ea097f9b1fd871dc6c9","kind":"subsection","labels":[],"line_end":198,"line_start":194,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/013-section-texorpdfstring-seam-gluing-and-the-eta-invariant.tex","status_markers_as_written":[],"summary_excerpt":"The spin-lift argument fixes the [formula in source] deficit factor robustly, and the sector count is fixed by seam symmetry. The seam normalization is provided by the [formula in source] -gluing derivation in Appendix","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Status note","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9605,"byte_start":8567,"id":"section:85194fe40e6ec54030dd","kind":"subsection","labels":["sec:cut-invariance","tab:cut-invariance"],"line_end":225,"line_start":199,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/013-section-texorpdfstring-seam-gluing-and-the-eta-invariant.tex","status_markers_as_written":[],"summary_excerpt":"The patch count [formula in source] and hence [formula in source] is invariant under alternative cut descriptions of the fundamental domain. The following four cuts all yield identical [formula in source] :","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cut Invariance of [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9838,"byte_start":9605,"id":"section:5c06c3f82636ae24ae8c","kind":"section","labels":["app:flavor"],"line_end":231,"line_start":226,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/013-section-texorpdfstring-seam-gluing-and-the-eta-invariant.tex","status_markers_as_written":[],"summary_excerpt":"This appendix derives the M\\\"obius structure of flavor relations from boundary monodromy.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Flavor Monodromy and Cross-Ratio","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10620,"byte_start":9838,"id":"section:306d33b0416ad2821740","kind":"subsection","labels":[],"line_end":250,"line_start":232,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/013-section-texorpdfstring-seam-gluing-and-the-eta-invariant.tex","status_markers_as_written":[],"summary_excerpt":"On a conformally flat boundary, the metric is locally: Holomorphic automorphisms (Wilson lines of flat connections) act as M\\\"obius transformations:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Projective Invariance on Boundaries","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11054,"byte_start":10620,"id":"section:6cce62effca78e3a7bd0","kind":"subsection","labels":[],"line_end":261,"line_start":251,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/013-section-texorpdfstring-seam-gluing-and-the-eta-invariant.tex","status_markers_as_written":[],"summary_excerpt":"Given four marked points [formula in source] on the boundary, the unique projective invariant is the cross-ratio:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cross-Ratio as Unique Invariant","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11592,"byte_start":11054,"id":"section:6b338033097b5768f02b","kind":"subsection","labels":[],"line_end":272,"line_start":262,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/013-section-texorpdfstring-seam-gluing-and-the-eta-invariant.tex","status_markers_as_written":[],"summary_excerpt":"The cusps [formula in source] arise from: Rationality: Quantized holonomies [formula in source] rational cusps. GUT compatibility: SU(5) hypercharge assignments give [formula in source] (quarks), [formula in source] (leptons), etc. Uniqueness: These are the only rational values that simultaneously separate the three SM sectors (up, down, lepton) and maintain GUT normalization.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cusp Selection","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12316,"byte_start":11592,"id":"section:477f17713cf3dadb90ec","kind":"subsection","labels":[],"line_end":291,"line_start":273,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/013-section-texorpdfstring-seam-gluing-and-the-eta-invariant.tex","status_markers_as_written":[],"summary_excerpt":"Leading term: [formula in source] from the abelian trace (same as [formula in source] numerator divided by 41/10's denominator structure).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derivation of [formula in source] Derivation of delta_star","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15044,"byte_start":12316,"id":"section:133bbb3fdecc0149db2a","kind":"section","labels":["app:repro"],"line_end":348,"line_start":292,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":["relation:0a28a6d55448ff6622cc"],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/013-section-texorpdfstring-seam-gluing-and-the-eta-invariant.tex","status_markers_as_written":[],"summary_excerpt":"Replication package: All numerical results can be reproduced using the TFPT verification suite (v2.8).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproducibility","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15524,"byte_start":15044,"id":"section:8682b8e9897e94a66fb4","kind":"paragraph","labels":[],"line_end":356,"line_start":349,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/013-section-texorpdfstring-seam-gluing-and-the-eta-invariant.tex","status_markers_as_written":[],"summary_excerpt":"All external reference values (CODATA, PDG, lattice QCD, etc.)\\ used by the suite carry mandatory snapshot_date and source_version fields. A dedicated audit ( reference_snapshot_pin_audit) scans all data JSONs and fails if any reference-like entry lacks these fields. Status (v2.8): 42 missing pins out of 167 reference entries identified (audit PASS); resolution is tracked as an informational item.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reference snapshot pinning.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15902,"byte_start":15524,"id":"section:88efaf184d493417ae0f","kind":"paragraph","labels":[],"line_end":362,"line_start":357,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/013-section-texorpdfstring-seam-gluing-and-the-eta-invariant.tex","status_markers_as_written":[],"summary_excerpt":"A separate audit ( paper_table_number_sync_audit_v28) parses all \\ table values and compares against suite JSON outputs at rounding tolerance. Extracted 22 TFPT*Num commands; compared 8 quantities at 12-digit tolerance—all match.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Paper–suite number sync.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10266,"byte_start":0,"id":"section:b50789cf4459ce0a8c38","kind":"section","labels":["app:prediction-ledger","tab:prediction-ledger"],"line_end":68,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/014-section-prediction-ledger-and-falsification.tex","status_markers_as_written":[],"summary_excerpt":"Purpose: Provide a single, reviewer-friendly list of predictions and candidates that is tied to the same JSON sources used by the verification suite, to prevent number drift between Abstract, theorems, tables, and appendices.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Prediction Ledger and Falsification","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13662,"byte_start":10266,"id":"section:9e86c5ebb859da9a65e0","kind":"section","labels":["app:identities"],"line_end":112,"line_start":69,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/014-section-prediction-ledger-and-falsification.tex","status_markers_as_written":[],"summary_excerpt":"This appendix labels frequently used equalities by logical status to prevent conflating definitions, algebraic rewrites, and genuine predictions.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Identity Catalogue and Status Labels","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14560,"byte_start":13662,"id":"section:d37517cafc566fab505c","kind":"section","labels":["app:r2"],"line_end":126,"line_start":113,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/014-section-prediction-ledger-and-falsification.tex","status_markers_as_written":[],"summary_excerpt":"K1: Field content and torsionful Lagrangian fixed by the minimal UFE sector. K2: Quadratic fluctuation operator is of Laplace type after background-field gauge fixing. K3: Heat-kernel coefficient [formula in source] captures the curvature-squared terms in [formula in source] . K4: Matching to [formula in source] after imposing the GR renormalization condition.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"One-Loop Effective Action in Riemann–Cartan and the [formula in source] CoefficientOne-Loop Effective Action in Riemann–Cartan and the R2 Coefficient","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14918,"byte_start":14560,"id":"section:c3405563e2d865d60bdd","kind":"subsection","labels":[],"line_end":132,"line_start":127,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/014-section-prediction-ledger-and-falsification.tex","status_markers_as_written":[],"summary_excerpt":"We evaluate the one-loop effective action in a Riemann–Cartan background with torsion decomposed into axial [formula in source] , trace [formula in source] , and tensor [formula in source] . The minimal UFE choice treats torsion at quadratic order, so integrating out torsion is Gaussian and parameter-free once [formula in source] fixes the normalization of the coupling.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.1 Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15281,"byte_start":14918,"id":"section:fd4ae19cc07e7b0eab76","kind":"subsection","labels":[],"line_end":141,"line_start":133,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/014-section-prediction-ledger-and-falsification.tex","status_markers_as_written":[],"summary_excerpt":"After background-field gauge fixing, the quadratic operator for torsion fluctuations can be written in Laplace type, with [formula in source] built from curvature and torsion invariants. The contribution to [formula in source] is [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.2 Operator Form","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15651,"byte_start":15281,"id":"section:29e161c42ba84fe98d69","kind":"subsection","labels":[],"line_end":149,"line_start":142,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/014-section-prediction-ledger-and-falsification.tex","status_markers_as_written":[],"summary_excerpt":"The local part of [formula in source] is governed by the heat-kernel expansion where [formula in source] contains the curvature-squared terms. The torsion-dependent pieces combine into an effective [formula in source] operator in the low-energy action.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.3 Heat-Kernel Coefficients","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15852,"byte_start":15651,"id":"section:35445d2b62922b9bd87d","kind":"subsection","labels":[],"line_end":153,"line_start":150,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/014-section-prediction-ledger-and-falsification.tex","status_markers_as_written":[],"summary_excerpt":"The GR limit (A8) fixes the renormalization scheme by requiring that the [formula in source] limit reduces to the Einstein–Hilbert action with coefficient [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.4 Renormalization Condition","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16217,"byte_start":15852,"id":"section:64f8d7fff52e888f685c","kind":"subsection","labels":[],"line_end":162,"line_start":154,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/014-section-prediction-ledger-and-falsification.tex","status_markers_as_written":[],"summary_excerpt":"With the TFPT normalization of the torsion sector, the induced [formula in source] coefficient is fixed by [formula in source] , yielding which reproduces","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"K.5 TFPT Closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16693,"byte_start":16217,"id":"section:7807e515caaf85260363","kind":"section","labels":["app:bounce"],"line_end":172,"line_start":163,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/014-section-prediction-ledger-and-falsification.tex","status_markers_as_written":[],"summary_excerpt":"This appendix provides a minimal outline; the full numerical transfer-function evaluation is implemented in the bounce_perturbations verification module (see replication bundle).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bounce Perturbations and the Transfer Function","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17007,"byte_start":16693,"id":"section:b13c114938fb2c09d995","kind":"subsection","labels":[],"line_end":177,"line_start":173,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/014-section-prediction-ledger-and-falsification.tex","status_markers_as_written":[],"summary_excerpt":"The bounce background is modeled by a smooth scale factor [formula in source] where the torsion-induced [formula in source] term regularizes [formula in source] for scalar perturbations. The transition to the [formula in source] inflationary phase is implemented by matching [formula in source] and its derivatives at [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.1 Background Solution","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17300,"byte_start":17007,"id":"section:5df7c17b841324b93925","kind":"subsection","labels":[],"line_end":182,"line_start":178,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/014-section-prediction-ledger-and-falsification.tex","status_markers_as_written":[],"summary_excerpt":"Mode functions are initialized in an adiabatic vacuum well before the bounce and integrated through the bounce and into the [formula in source] era. The numerical scheme records the transfer function by comparing late-time solutions to the pure [formula in source] baseline.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.2 Numerical Integration Setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17609,"byte_start":17300,"id":"section:7a501231de6e8858e342","kind":"subsection","labels":[],"line_end":190,"line_start":183,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/014-section-prediction-ledger-and-falsification.tex","status_markers_as_written":[],"summary_excerpt":"Define the transfer function as with [formula in source] for modes well inside the horizon during the bounce and deviations confined to [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.3 Transfer Function","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9627,"byte_start":0,"id":"section:f3fa19b67f2f154f5cbd","kind":"subsection","labels":[],"line_end":277,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/015-subsection-texorpdfstring-l-4-the-k-to-ell-gate-cmb-obse.tex","status_markers_as_written":[],"summary_excerpt":"Deterministic (given the bounce completion): The transfer-function shape [formula in source] (this appendix; implemented in bounce_perturbations). Given an explicit expansion-history budget, the mapping [formula in source] and the resulting [formula in source] curves are deterministic (implemented in k_calibration and boltzmann_transfer).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.4 The [formula in source] Gate (CMB Observability as Policy Interface)L.4 The k->ell Gate (CMB Observability as Policy Interface)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10006,"byte_start":9627,"id":"section:99186b58fa651338355f","kind":"subsection","labels":[],"line_end":283,"line_start":278,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/015-subsection-texorpdfstring-l-4-the-k-to-ell-gate-cmb-obse.tex","status_markers_as_written":[],"summary_excerpt":"Large-scale suppression or oscillatory features in [formula in source] are predicted at [formula in source] . Current CMB large-scale bounds constrain the allowable feature amplitude, providing a direct observational test of the bounce completion.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"L.5 Falsification Targets","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12077,"byte_start":10006,"id":"section:c46e6b309c5f8a8d3c9e","kind":"section","labels":["app:bh-dyonic"],"line_end":323,"line_start":284,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/015-subsection-texorpdfstring-l-4-the-k-to-ell-gate-cmb-obse.tex","status_markers_as_written":[],"summary_excerpt":"This appendix records a minimal dyonic toy solution showing the [formula in source] scaling of the axion profile and the induced polarization rotation. It is included as analytical support for the EHT intercept test (Sec.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"BH1 Dyonic Toy Solution and Polarization Rotation Scaling (Appendix)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20129,"byte_start":12077,"id":"section:53d7ed66963432bf34f7","kind":"section","labels":["tab:reference-ledger"],"line_end":393,"line_start":324,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/015-subsection-texorpdfstring-l-4-the-k-to-ell-gate-cmb-obse.tex","status_markers_as_written":[],"summary_excerpt":"=0mu plus 1mu @> p0.22 > p0.14 > p0.08 > p0.10 > p0.12 > p0.24 @ Reference ledger used by the TFPT suite (auto-generated). Key & Value & [formula in source] & Units & Version & Source (stable key)\\\\ Key & Value & [formula in source] & Units & Version & Source (stable key)\\\\ 6r Continued on next page.\\\\ A_s_planck2018 & 2.09890e-9 & 0.02938e-9 & dimensionless & Planck 2018 & planck2018 Planck 2018 results VI (2020), b","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reference Ledger (Auto-Generated)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2591,"byte_start":0,"id":"section:6f1dc76a77b248010354","kind":"section","labels":["app:referee-exit-v28"],"line_end":37,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":["relation:0cb54c39753a22d00a9c"],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/016-section-referee-exit-snapshot-version-2-8.tex","status_markers_as_written":[],"summary_excerpt":"This appendix summarizes the closed gates and solver outcomes from the v2.8 referee exit snapshot (run date: 2026-02-08, git commit b9d26d4). All 235 modules achieved PASS status; 0 WARN, 0 FAIL.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Referee Exit Snapshot — Version 2.8","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7886,"byte_start":2591,"id":"section:7972e0e8abaebba6048f","kind":"paragraph","labels":[],"line_end":180,"line_start":38,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-theory-fullv28"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-theory-fullv28/sections/016-section-referee-exit-snapshot-version-2-8.tex","status_markers_as_written":[],"summary_excerpt":"All experimental reference values used by the verification suite are pinned to a specific publication date or data release. Where a DOI or arXiv identifier exists, it is recorded in the bibliography below and in the suite's sm_inputs_mz.json policy file. Online-only resources (NuFIT, PDG online tables) carry a snapshot date. This ensures that results are reproducible even if upstream databases update: the suite alway","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reference snapshot policy.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1675,"byte_start":0,"id":"section:03f1d6bd1f05e908244b","kind":"frontmatter","labels":[],"line_end":59,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/preamble.tex","status_markers_as_written":[],"summary_excerpt":"detect-all, round-mode = figures, round-precision = 10, exponent-mode = input, exponent-product = , group-separator = \\,, group-minimum-digits = 4","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TFPT v2.9: Admissible Vacua, Minimal Carrier, and Electromagnetic Stationarity\\\\[0.5em] A Carrier-First Primary Form","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2937,"byte_start":0,"id":"section:c1b312c4d39cc26db2e1","kind":"frontmatter","labels":[],"line_end":51,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/001-section-overview-and-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"This document rewrites TFPT v2.8 into a carrier-first primary form. The rigid core is the Minimal Carrier Theorem: admissibility on the orientable double cover together with the seam involution forces the minimal carrier [formula in source] . From this rigid package follow the global Standard Model group [formula in source] , one chiral family [formula in source] , the carrier norm [formula in source] , and the linea","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4862,"byte_start":2937,"id":"section:62b6d757977fd9fb8508","kind":"section","labels":[],"line_end":92,"line_start":52,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/001-section-overview-and-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"The v2.9 rewrite should be read from admissibility to carrier, from carrier to occupancy, and only then from occupancy to closure and phenomenology. The master line is therefore [formula in source] The main bridge branches are secondary to this line: [formula in source] The center of the architecture is therefore not the number [formula in source] by itself, but the rigid minimal carrier package that later induces [f","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Overview and Claim Map","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5189,"byte_start":4862,"id":"section:047654eb4505008d0a4a","kind":"section","labels":[],"line_end":100,"line_start":93,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/001-section-overview-and-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"The ambient v2.9 datum may be packaged as [formula in source] but the hard carrier core uses only [formula in source] . The field [formula in source] belongs to the absolute-scale and gravity channels discussed later in Section 8.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Admissibility and Seam Data","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6278,"byte_start":5189,"id":"section:2e1e43eb36c1351d7bda","kind":"subsection","labels":[],"line_end":121,"line_start":101,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/001-section-overview-and-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"The seam information needed by the carrier rewrite is already present in v2.8. In the minimal gluing class one has [formula in source] On the orientable double cover the distinguished cycles are [formula in source] where [formula in source] is the seam cycle in the glued description and corresponds to [formula in source] in the cut description. These data should appear near the front of the paper because Sections 3–6","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Seam data recalled from v2.8","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6317,"byte_start":6278,"id":"section:babe10e7c8aff0b3a756","kind":"section","labels":[],"line_end":123,"line_start":122,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/001-section-overview-and-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"The Minimal Carrier Theorem","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9180,"byte_start":6317,"id":"section:d4f656c700cf50720b1a","kind":"subsection","labels":[],"line_end":233,"line_start":124,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/001-section-overview-and-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be a split carrier with traceless diagonal generator [formula in source] If one simultaneously requires [formula in source] then necessarily [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Uniqueness of the [formula in source] 3+2 split","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; 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TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"One chiral family from the positive half-spinor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11805,"byte_start":10252,"id":"section:885f66331cadbddce146","kind":"subsection","labels":[],"line_end":356,"line_start":285,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/001-section-overview-and-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be a traceless diagonal generator on a rank- [formula in source] carrier [formula in source] . Then on the positive half-spinor [formula in source] one has [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Trace identities","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1042,"byte_start":0,"id":"section:46302812830ad8dbd8bf","kind":"subsection","labels":[],"line_end":35,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/002-subsection-general-abelian-index.tex","status_markers_as_written":[],"summary_excerpt":"For a branch with [formula in source] copies of the carrier family and [formula in source] light weak doublets from [formula in source] , one has [formula in source] For the minimal carrier this becomes [formula in source] Therefore [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"General abelian index","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1100,"byte_start":1042,"id":"section:93be441f9b64c1ccd1a3","kind":"section","labels":[],"line_end":37,"line_start":36,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/002-subsection-general-abelian-index.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Boundary Multiplicity and Admissible Occupancy","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1689,"byte_start":1100,"id":"section:90be177c6383c0cef52d","kind":"subsection","labels":[],"line_end":63,"line_start":38,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/002-subsection-general-abelian-index.tex","status_markers_as_written":[],"summary_excerpt":"Let each distinguished cycle [formula in source] carry an integer family index [formula in source] . Then the v2.8 block coefficient may be organized as [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Family-index bridge","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2381,"byte_start":1689,"id":"section:eecc0cdde15907015321","kind":"subsection","labels":[],"line_end":90,"line_start":64,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/002-subsection-general-abelian-index.tex","status_markers_as_written":[],"summary_excerpt":"On the canonical branch one therefore has [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Admissible occupancy and topological surcharge","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3252,"byte_start":2381,"id":"section:15709279023bc2823359","kind":"subsection","labels":[],"line_end":119,"line_start":91,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/002-subsection-general-abelian-index.tex","status_markers_as_written":[],"summary_excerpt":"The normalization of [formula in source] is best presented in two stages.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Seam descent normalization of [formula in source] c3","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3312,"byte_start":3252,"id":"section:a4e4e9d9e853f41635e1","kind":"section","labels":[],"line_end":121,"line_start":120,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/002-subsection-general-abelian-index.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Electromagnetic Stationarity and the Carrier CFE","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5304,"byte_start":3312,"id":"section:0d21bb68cc11f94c024d","kind":"subsection","labels":[],"line_end":205,"line_start":122,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/002-subsection-general-abelian-index.tex","status_markers_as_written":[],"summary_excerpt":"The electromagnetic closure channel should first be written on a general admissible branch. Define [formula in source] Then the carrier form of the CFE is [formula in source] This is the preferred v2.9 presentation because the coefficients are now grouped by carrier data rather than as parallel numerical motifs.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Carrier form of the stationary equation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5846,"byte_start":5304,"id":"section:aac655422d9a256161c6","kind":"subsection","labels":[],"line_end":220,"line_start":206,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/002-subsection-general-abelian-index.tex","status_markers_as_written":[],"summary_excerpt":"Evaluated on the stationary root of the canonical branch, several previously separate formulas become algebraic corollaries of the same carrier package: [formula in source] [formula in source] The structural gain is not that these quantities are numerically new, but that they are now visibly downstream of [formula in source] and the occupancy branch.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Algebraic corollaries of the carrier kernel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6461,"byte_start":5846,"id":"section:777b132dc9c066a2db10","kind":"subsection","labels":[],"line_end":239,"line_start":221,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/002-subsection-general-abelian-index.tex","status_markers_as_written":[],"summary_excerpt":"If the [formula in source] channel and the induced Einstein channel are successfully completed, then the inflationary block can be written as [formula in source] and therefore [formula in source] For [formula in source] this yields [formula in source] These results are kept separate from the hard carrier corollaries because they depend on the success of the relative- [formula in source] and gravity channels.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conditional [formula in source] chi-channel corollaries","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7938,"byte_start":6461,"id":"section:1d813809c603503d3eb3","kind":"section","labels":[],"line_end":261,"line_start":240,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/002-subsection-general-abelian-index.tex","status_markers_as_written":[],"summary_excerpt":"The carrier-centered rewrite is strongest when it excludes wrong branches, not when it celebrates an isolated number. The relevant deformations fall into three logical classes.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Discrete Exclusion Structure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8889,"byte_start":7938,"id":"section:786f37f2fb103efd150b","kind":"section","labels":[],"line_end":286,"line_start":262,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/002-subsection-general-abelian-index.tex","status_markers_as_written":[],"summary_excerpt":"The relative spectral action is the natural place to unify the [formula in source] -, [formula in source] -, and metric channels, but the heat-kernel completion is not yet theorem-hard. In v2.9 it should therefore appear as a completion target rather than as part of the rigid carrier packet.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Relative Spectral Completion Targets","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10458,"byte_start":8889,"id":"section:b9a006bf4d1393fceb17","kind":"subsection","labels":[],"line_end":333,"line_start":287,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/002-subsection-general-abelian-index.tex","status_markers_as_written":[],"summary_excerpt":"For a Dirac-type Laplace operator written as [formula in source] the local four-dimensional heat-kernel coefficient is [formula in source] For a Dirac-type curvature coupling one has [formula in source] , so the curvature part scales like [formula in source] After relative admissible-minus-reference subtraction and TFPT normalization, an Einstein-channel coefficient with denominator [formula in source] is therefore n","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Why the denominator 192 pi squared is plausible","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10541,"byte_start":10458,"id":"section:fb1db3161e3ef99f9b88","kind":"section","labels":[],"line_end":335,"line_start":334,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/002-subsection-general-abelian-index.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Downstream Reinterpretations: E [formula in source] E8, Higgs, Flavor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11031,"byte_start":10541,"id":"section:74dccaeb0256a16eb789","kind":"subsection","labels":[],"line_end":345,"line_start":336,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/002-subsection-general-abelian-index.tex","status_markers_as_written":[],"summary_excerpt":"The strongest E [formula in source] rereading to retain is [formula in source] The E [formula in source] sector is downstream of the carrier norm, not part of the hard minimal carrier core. One suggestive but non-rigid echo is [formula in source] . This identity is numerically suggestive, but not theorem-level and should remain secondary or appendix-level.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"E [formula in source] E8 as a downstream carrier rereading","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11525,"byte_start":11031,"id":"section:c61435255ddd3d0d5d0e","kind":"subsection","labels":[],"line_end":355,"line_start":346,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/002-subsection-general-abelian-index.tex","status_markers_as_written":[],"summary_excerpt":"If a light seam-even bosonic zero mode exists in [formula in source] , then the minimal carrier provides a natural Higgs candidate [formula in source] This is the correct representation-theoretic slot for a Standard Model Higgs doublet. The existence of the light mode itself remains part of the dynamical completion and should not be overstated as a theorem of the hard carrier core.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Higgs as a conditional seam-even mode in [formula in source] E2","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":878,"byte_start":0,"id":"section:d90cf3da524d8e5b8a95","kind":"subsection","labels":[],"line_end":30,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/003-subsection-flavor-and-the-phase-grammar.tex","status_markers_as_written":[],"summary_excerpt":"The hard group-theoretic statement is [formula in source] The separate, still dynamical question is whether the observed CKM, PMNS, and Majorana phases actually realize the associated discrete grammar.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Flavor and the phase grammar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1570,"byte_start":878,"id":"section:6ab01de63118baf92bbf","kind":"section","labels":[],"line_end":51,"line_start":31,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/003-subsection-flavor-and-the-phase-grammar.tex","status_markers_as_written":[],"summary_excerpt":"The rigid core of v2.9 is not a number but a theorem: [formula in source] [formula in source] From this follow the global Standard Model group, one chiral family, the carrier norm [formula in source] , and the general abelian index formula. Only on the canonical occupancy branch does the same rigid package produce [formula in source] The center is therefore the minimal carrier. The number [formula in source] is the f","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conclusion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2328,"byte_start":1570,"id":"section:61ecdd1ac1017d5eb517","kind":"section","labels":[],"line_end":70,"line_start":52,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/003-subsection-flavor-and-the-phase-grammar.tex","status_markers_as_written":[],"summary_excerpt":"@lX@ v2.8 language & v2.9 carrier reading \\\\ [formula in source] & [formula in source] together with [formula in source] on the minimal carrier packet \\\\ [formula in source] & [formula in source] on the canonical occupancy branch \\\\ [formula in source] & [formula in source] evaluated at [formula in source] \\\\ [formula in source] & [formula in source] with [formula in source] \\\\ [formula in source] in E [formula in so","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"v2.8 to v2.9 Dictionary","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2808,"byte_start":2328,"id":"section:d1515011efa17ff45bd0","kind":"section","labels":[],"line_end":86,"line_start":71,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/003-subsection-flavor-and-the-phase-grammar.tex","status_markers_as_written":[],"summary_excerpt":"The v2.8 block relation [formula in source] already shows that family multiplicity is tied to the three distinguished cycles of the orientable double cover. Writing [formula in source] makes the same factorization explicit and immediately yields [formula in source] The equal-one assignment is the minimal symmetric branch and is the natural source of [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Family-Index Bridge","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3162,"byte_start":2808,"id":"section:33e2995f99ec85a6d1be","kind":"section","labels":[],"line_end":101,"line_start":87,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/003-subsection-flavor-and-the-phase-grammar.tex","status_markers_as_written":[],"summary_excerpt":"The canonical bridge is [formula in source] With [formula in source] this gives [formula in source] This is the precise sense in which the topological surcharge is re-read as admissible occupancy transgression.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Occupancy Transgression","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3713,"byte_start":3162,"id":"section:7e569e1df9ad6a0aa85c","kind":"section","labels":[],"line_end":110,"line_start":102,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/003-subsection-flavor-and-the-phase-grammar.tex","status_markers_as_written":[],"summary_excerpt":"The seam descent logic is intentionally separated into two pieces: the spin-lifted seam loop closes only after [formula in source] , so [formula in source] and [formula in source] ; if the admissible carrier modulus is identified with the axionic angle variable, then [formula in source] and therefore [formula in source] . The first step is geometric. The second is the explicit carrier-to-axion identification.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Seam Descent Normalization","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4289,"byte_start":3713,"id":"section:43b6eb0be54f13f69d38","kind":"section","labels":[],"line_end":122,"line_start":111,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/003-subsection-flavor-and-the-phase-grammar.tex","status_markers_as_written":[],"summary_excerpt":"The relative Einstein target rests on the standard four-dimensional heat-kernel structure [formula in source] For Dirac-type curvature coupling [formula in source] , so curvature terms naturally carry a denominator of the form [formula in source] . The open step is not whether such a denominator is plausible, but which relative subtraction and sector trace produce the final canonical coefficient [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Relative [formula in source] a2 Sketch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5111,"byte_start":4289,"id":"section:c857c002ffa7ed94e137","kind":"section","labels":[],"line_end":142,"line_start":123,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v29"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v29/sections/003-subsection-flavor-and-the-phase-grammar.tex","status_markers_as_written":[],"summary_excerpt":"@> Xcccc@ Branch & [formula in source] & [formula in source] & [formula in source] & [formula in source] \\\\ canonical carrier branch & [formula in source] & [formula in source] & [formula in source] & 137.03599921615843 \\\\ boundary multiplicity deformation & [formula in source] & [formula in source] & [formula in source] & 156.094045457 \\\\ boundary multiplicity deformation & [formula in source] & [formula in source] ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Numerical Branch Table","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3670,"byte_start":0,"id":"section:1b65be961c617457d120","kind":"frontmatter","labels":[],"line_end":116,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/preamble.tex","status_markers_as_written":[],"summary_excerpt":"skins,breakable arrows.meta,positioning,calc,fit,backgrounds,matrix,decorations.pathmorphing compat=1.18","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TFPT: Carrier Algebra, Compression Identities, and Finite Completion\\\\[0.5em] An overdetermined rank-5 spectral theory on the oriented double cover","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3322,"byte_start":0,"id":"section:10ed59c4d51ebc81ad55","kind":"frontmatter","labels":[],"line_end":23,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/001-section-reading-guide-and-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"A minimal carrier [formula in source] on the oriented double cover is shown to be the unique rank-5 split satisfying [formula in source] and [formula in source] . This carrier already forces the global Standard Model group [formula in source] , one chiral family with [formula in source] from the positive half-spinor, the hypercharge–seam inversion [formula in source] , and a self-consistent electromagnetic closure eq","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9546,"byte_start":3322,"id":"section:5d2060d452f578617756","kind":"section","labels":["fig:dependency-map","tab:status-matrix"],"line_end":105,"line_start":24,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/001-section-reading-guide-and-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"The paper is organized in three reading layers: Big picture: one section explains what TFPT claims in plain language before the detailed datum and conventions begin. Detail: the main body then runs from primitive core and hard carrier kernel through kernel numerics, the two completion programs, the particle/mass compiler, and the benchmark interface. Proof sketches: the main text gives only the central proof sketches","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reading guide and claim map","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11061,"byte_start":9546,"id":"section:d186bb25882f48f69fbe","kind":"section","labels":["eq:compiler-chain"],"line_end":129,"line_start":106,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/001-section-reading-guide-and-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"TFPT is presented here as a carrier-first theory of admissible vacua on the oriented double cover. The seam involution enforces the minimal carrier [formula in source] . That carrier fixes the global Standard Model group, hypercharge, and one chiral family. The family count [formula in source] is then supported by two independent routes: a local patch-deficit count and a global monodromy argument. The monodromy space","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Big picture: what TFPT actually claims","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11111,"byte_start":11061,"id":"section:3ae9d515714efbe23280","kind":"section","labels":[],"line_end":131,"line_start":130,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/001-section-reading-guide-and-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Primitive core and hard carrier kernel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12479,"byte_start":11111,"id":"section:f2e3c62d4e138468e600","kind":"subsection","labels":[],"line_end":152,"line_start":132,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/001-section-reading-guide-and-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"We use natural units [formula in source] . Relative operators are formulated in Euclidean signature and compared through a declared Wick-rotation bridge when Lorentzian language is needed. Higgs fields are denoted by [formula in source] , Hamiltonians by [formula in source] , and the cosmological Hubble rate by [formula in source] ; this avoids overloading the letter [formula in source] . Newton's constant is always ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Primitive core and conventions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15622,"byte_start":12479,"id":"section:5e540e1c297938588428","kind":"subsection","labels":["eq:carrier-polynomial","eq:explicit-hypercharge","eq:hypercharge-seam-inversion","eq:minimal-carrier-conditions","sec:minimal-carrier-proof"],"line_end":275,"line_start":153,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/001-section-reading-guide-and-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be a split carrier with traceless diagonal generator [formula in source] If one simultaneously requires then necessarily [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Minimal carrier theorem","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18741,"byte_start":15622,"id":"section:851367271fcfc5a963a8","kind":"subsection","labels":["tab:one-family"],"line_end":349,"line_start":276,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/001-section-reading-guide-and-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"The determinant-preserving connected stabilizer of the minimal carrier split is [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Global gauge group and one-family packet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2074,"byte_start":0,"id":"section:2dc5ebc00f68735e5daa","kind":"subsection","labels":["eq:abelian-index","eq:family-character"],"line_end":71,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/002-subsection-character-trace-identities-and-the-abelian-in.tex","status_markers_as_written":[],"summary_excerpt":"For the present paragraph let [formula in source] Then Consequently, [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Character, trace identities, and the abelian index","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2514,"byte_start":2074,"id":"section:65662046925484a92d3b","kind":"section","labels":[],"line_end":75,"line_start":72,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/002-subsection-character-trace-identities-and-the-abelian-in.tex","status_markers_as_written":[],"summary_excerpt":"The carrier-first presentation should not leave the impression that TFPT is hard only at the level of group theory and representation bookkeeping. The numerical kernel already fixes a nontrivial output layer. Here that layer is pulled forward and read as the first established output package of the carrier/compiler architecture rather than as a later list of disconnected constants.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kernel numerics and electromagnetic closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3771,"byte_start":2514,"id":"section:7f952af87db76e36dfbc","kind":"subsection","labels":["eq:carrier-cfe","eq:hard-topological-kernel","eq:phi-opening"],"line_end":127,"line_start":76,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/002-subsection-character-trace-identities-and-the-abelian-in.tex","status_markers_as_written":[],"summary_excerpt":"On the retained hard branch the inherited topological corrections are Numerically, [formula in source] On a general admissible branch one writes The carrier form of the electromagnetic closure equation is then equation [formula in source] On the canonical family branch these hard coefficients admit the bridge reinterpretations [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Carrier form of the electromagnetic closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5939,"byte_start":3771,"id":"section:af3ff89dbd6bc8eaf36f","kind":"subsection","labels":["eq:hard-kernel-values","eq:kernel-benchmark-formulas"],"line_end":165,"line_start":128,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/002-subsection-character-trace-identities-and-the-abelian-in.tex","status_markers_as_written":[],"summary_excerpt":"The benchmark row for [formula in source] is defined by the positive self-consistent root of eq:carrier-cfe, not by freezing the opening at its retained seed value. 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The compression identities are not new theorems; they are exact algebraic consequences of the already established carrier data. The exclusion theorems are the sharpest available evidence that the carrier packet act","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Compression identities and carrier exclusion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9349,"byte_start":6450,"id":"section:b02ae0d3af8339690b37","kind":"subsection","labels":["eq:rank-lock","prop:rank-lock"],"line_end":236,"line_start":170,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/002-subsection-character-trace-identities-and-the-abelian-in.tex","status_markers_as_written":[],"summary_excerpt":"If the carrier identity [formula in source] , the canonical family data [formula in source] , and the optional occupancy compression [formula in source] are combined, then The unique integral solution is [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Rank lock and the [formula in source] - [formula in source] - [formula in source] 2-3-5 arithmetic","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10240,"byte_start":9349,"id":"section:7660f17fc132f2ecf884","kind":"subsection","labels":["eq:41-chain-main"],"line_end":255,"line_start":237,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/002-subsection-character-trace-identities-and-the-abelian-in.tex","status_markers_as_written":[],"summary_excerpt":"The integer [formula in source] is not an isolated numerical curiosity. Using the v2.8 block-index relation [formula in source] , the electroweak block trace and exponent are [formula in source] Then the unified chain reads Four different layers—electroweak block trace, E [formula in source] exponent, UV hypercharge trace, and carrier occupancy times norm plus one boson—collapse onto the same integer. The extra [form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The [formula in source] -chain identity","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11246,"byte_start":10240,"id":"section:fa5ff54df1264bf50156","kind":"subsection","labels":["eq:cabibbo-inversion","eq:lambda-c-master"],"line_end":273,"line_start":256,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/002-subsection-character-trace-identities-and-the-abelian-in.tex","status_markers_as_written":[],"summary_excerpt":"The bridge rows [formula in source] are not four independent hits but four projections of [formula in source] . The Cabibbo angle admits an explicit inversion back to the seed: From this all other bridge outputs become functions of [formula in source] alone: Thus on the canonical branch, Cabibbo alone pulls [formula in source] , [formula in source] , and [formula in source] . Conversely, [formula in source] pulls [fo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Single-seed compression and the Cabibbo inversion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13243,"byte_start":11246,"id":"section:011718d293d99c5af954","kind":"subsection","labels":["thm:carrier-exclusion"],"line_end":304,"line_start":274,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/002-subsection-character-trace-identities-and-the-abelian-in.tex","status_markers_as_written":[],"summary_excerpt":"The strongest argument that the carrier packet selects the physical world is not a further precision hit. It is that wrong discrete worlds fail brutally.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Carrier exclusion theorems","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13827,"byte_start":13243,"id":"section:aca1bb23558c3b68fc50","kind":"section","labels":[],"line_end":308,"line_start":305,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/002-subsection-character-trace-identities-and-the-abelian-in.tex","status_markers_as_written":[],"summary_excerpt":"This first completion block is the shortest route from the hard carrier packet to a broader Standard Model plus gravity compiler. It has three moves: the local patch-deficit count fixes the family number [formula in source] , while the monodromy space [formula in source] then explains nondegeneracy, phases, and mixing; a bosonic relative index is asked to select the unique light Higgs doublet; and the [formula in sou","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Completion program A: families, Higgs, and [formula in source] chi","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17490,"byte_start":13827,"id":"section:4dfd6d1d0ae54e107e2b","kind":"subsection","labels":["eq:family-patch-deficit","fig:family-triangle"],"line_end":364,"line_start":309,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/002-subsection-character-trace-identities-and-the-abelian-in.tex","status_markers_as_written":[],"summary_excerpt":"The simplest carrier-to-family bridge is to promote the three distinguished cycles into a monodromy space, [formula in source] so that [formula in source] . In this interpretation [formula in source] is neither an arbitrary flavor vector space nor a loose bookkeeping trick; it is a cycle space attached to the seam data. The geometric picture is shown in fig:family-triangle.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Family monodromy and occupancy","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1185,"byte_start":0,"id":"section:c62dd101b3fb5f44234f","kind":"subsection","labels":[],"line_end":13,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/003-subsection-occupancy-and-boundary-to-bulk-transgression.tex","status_markers_as_written":[],"summary_excerpt":"With the family bridge installed, the matter space becomes [formula in source] and the occupancy [formula in source] is already fixed by the preceding proposition. Here occupancy means the admissible chiral-state count after family lifting; it is not used as a primitive datum. The bridge point is not that family lifting creates a new numerical surcharge. Rather, the inherited hard kernel value [formula in source] adm","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Occupancy and boundary-to-bulk transgression","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1953,"byte_start":1185,"id":"section:0b2eff2c53632282a578","kind":"subsection","labels":[],"line_end":31,"line_start":14,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/003-subsection-occupancy-and-boundary-to-bulk-transgression.tex","status_markers_as_written":[],"summary_excerpt":"Once the carrier packet and family bridge are fixed, the focused main-text completion problem splits into a geometric program [formula in source] and a transport program [formula in source] . Record algebra is retained only as a conditional appendix layer in app:record.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"From bridge to geometric completion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2640,"byte_start":1953,"id":"section:abddd8b0a1c1d0ac1ab5","kind":"subsection","labels":[],"line_end":43,"line_start":32,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/003-subsection-occupancy-and-boundary-to-bulk-transgression.tex","status_markers_as_written":[],"summary_excerpt":"The geometric completion is formulated on a graded bundle [formula in source] with a declared reference pair [formula in source] and APS-type boundary conditions on the seam [formula in source] ; see Appendix [formula in source] This is a construction, not yet a theorem. Its value is to keep grading, reference subtraction, seam data, and the [formula in source] channel in one object from the start rather than mixing ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Relative APS and superconnection setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3558,"byte_start":2640,"id":"section:15b90d2c25e761fe7f36","kind":"subsection","labels":[],"line_end":73,"line_start":44,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/003-subsection-occupancy-and-boundary-to-bulk-transgression.tex","status_markers_as_written":[],"summary_excerpt":"The bosonic relative index satisfies [formula in source] Consequently the unique light seam-even bosonic zero mode lies in [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bosonic relative index and Higgs selection","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8692,"byte_start":3558,"id":"section:69c5091605b0ca192009","kind":"subsection","labels":["eq:carrier-dressed-v","eq:chi-effective-action","eq:induced-einstein","fig:chi-bifurcation","tab:heat-kernel-map"],"line_end":176,"line_start":74,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/003-subsection-occupancy-and-boundary-to-bulk-transgression.tex","status_markers_as_written":[],"summary_excerpt":"The local target action is written as The coefficient bookkeeping expected from the relative spectral expansion is summarized in tab:heat-kernel-map.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Heat-kernel coefficient map and [formula in source] chi bifurcation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9183,"byte_start":8692,"id":"section:40c61c33e8b926eb640b","kind":"section","labels":[],"line_end":180,"line_start":177,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/003-subsection-occupancy-and-boundary-to-bulk-transgression.tex","status_markers_as_written":[],"summary_excerpt":"The second completion block is the transport compiler. Its role is to turn the carrier packet and the family/occupancy bridge into actual masses, mixings, hadronic admissibility, and strong-CP control. The logic is again staged: first the discrete phase operator and the transport kernel, then path-length masses and mixing data, then confinement and strong CP as transport-side admissibility statements.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Completion program B: Yukawas, masses, flavor, confinement, and strong CP","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10698,"byte_start":9183,"id":"section:0a553cb8b9ad18370c39","kind":"subsection","labels":["fig:z6-circle"],"line_end":209,"line_start":181,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/003-subsection-occupancy-and-boundary-to-bulk-transgression.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] This makes the phase grammar concrete rather than rhetorical. The six admissible phases are shown in fig:z6-circle, and CP acts by inversion [formula in source] on this circle.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Discrete phase operator and transport grammar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15320,"byte_start":10698,"id":"section:17f5ff6729010d251df2","kind":"subsection","labels":["eq:mass-bridge","eq:minimal-word-lengths","eq:mobius-quotient","eq:path-length-yukawa","eq:transport-bridge-offset","eq:transport-spectrum","eq:yukawa-kernel","tab:transport-dictionary"],"line_end":305,"line_start":210,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/003-subsection-occupancy-and-boundary-to-bulk-transgression.tex","status_markers_as_written":[],"summary_excerpt":"Here is treated as a transport bridge parameter inherited from the cross-ratio and boundary-monodromy program, rather than as a proved hard-kernel identity. The full derivation is therefore deferred to the supplementary layer, while the regularized transport operator used here is and the singular limit [formula in source] is taken only in admissible sectors.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Regularized Yukawa kernels and path-length masses","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16363,"byte_start":15320,"id":"section:94948562d34b95ae29ea","kind":"subsection","labels":["eq:ckm-magnitudes","eq:ckm-phase","eq:neutrino-masses"],"line_end":340,"line_start":306,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/003-subsection-occupancy-and-boundary-to-bulk-transgression.tex","status_markers_as_written":[],"summary_excerpt":"The leading CKM magnitudes on the transport branch are The CKM phase receives a tri-familial dressing beyond the raw topological [formula in source] : so [formula in source] remains the base monodromy phase and [formula in source] is the leading family-transport correction.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"CKM and PMNS sharpening","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18293,"byte_start":16363,"id":"section:05bfa7920c557ec99f90","kind":"subsection","labels":["fig:admissible-words"],"line_end":379,"line_start":341,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/003-subsection-occupancy-and-boundary-to-bulk-transgression.tex","status_markers_as_written":[],"summary_excerpt":"For each carrier word [formula in source] , let [formula in source] be its color-center charge and let [formula in source] be its seam parity. Physical hadronic words satisfy [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Confinement as admissible word selection","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3059,"byte_start":0,"id":"section:c22ca8fb17494598c005","kind":"subsection","labels":["eq:strong-cp"],"line_end":62,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/004-subsection-strong-cp-closure-as-conditional-steps.tex","status_markers_as_written":[],"summary_excerpt":"Define The intended closure is decomposed into five conditional steps.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Strong CP closure as conditional steps","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3975,"byte_start":3059,"id":"section:8dfc6ca79b32627dc35f","kind":"section","labels":[],"line_end":72,"line_start":63,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/004-subsection-strong-cp-closure-as-conditional-steps.tex","status_markers_as_written":[],"summary_excerpt":"This section is the phenomenological heart of the manuscript. It is not meant to flatten all rows into one uniform notion of prediction. Instead it makes the compiler interface explicit: a declared RG map, a kernel-output map, and a mass ledger that separates genuinely derived quantities from solver-level candidates and anchor-dependent comparison rows. Accordingly this section is best read through three ledgers: a p","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Particle and mass compiler","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5629,"byte_start":3975,"id":"section:9a13546e4aab2cca7ac3","kind":"subsection","labels":[],"line_end":100,"line_start":73,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/004-subsection-strong-cp-closure-as-conditional-steps.tex","status_markers_as_written":[],"summary_excerpt":"The symbol [formula in source] denotes the declared comparison map from TFPT outputs to scheme-specified observables. Here it is the bookkeeping package [formula in source] and we write [formula in source] with the following restricted interpretation in the main text: [formula in source] is compared in the Thomson-limit on-shell convention, with the CODATA 2022 / NIST value taken as the normative low-energy reference","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"RG map for compiler outputs","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7029,"byte_start":5629,"id":"section:4d3bf5e59ff88703172e","kind":"subsection","labels":["tab:kernel-output-map"],"line_end":122,"line_start":101,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/004-subsection-strong-cp-closure-as-conditional-steps.tex","status_markers_as_written":[],"summary_excerpt":"The roles of [formula in source] and [formula in source] should not remain implicit. They are the central hard numeric quantities of the present main-text kernel. The downstream E [formula in source] parameter [formula in source] is isolated in the next section rather than folded back into the kernel center.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Central hard-kernel quantities","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10909,"byte_start":7029,"id":"section:bfbfa83f9c9d2c119922","kind":"subsection","labels":["tab:sm-mass-ledger-ew","tab:sm-mass-ledger-quarks"],"line_end":175,"line_start":123,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/004-subsection-strong-cp-closure-as-conditional-steps.tex","status_markers_as_written":[],"summary_excerpt":"For the mass surface itself the main text now uses only three row-level status words: derived, candidate, and anchor-dependent. The explicit candidate formulas, neutrino rows, and transport-ratio source data are moved to the appendix so that the main text shows a compact comparison-ready ledger rather than a mixed formula dump.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Mass-closure ledgers","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11351,"byte_start":10909,"id":"section:543460db4565fb1e4fba","kind":"section","labels":[],"line_end":182,"line_start":176,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/004-subsection-strong-cp-closure-as-conditional-steps.tex","status_markers_as_written":[],"summary_excerpt":"E [formula in source] is not part of the primitive carrier ontology and should not compete with the seam data, the carrier theorem, or the completion program for explanatory priority. In the present main-text form it plays one restricted role only: a downstream scale grammar attached to the already fixed carrier norm. [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"E [formula in source] E8 as downstream scale grammar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12399,"byte_start":11351,"id":"section:b950882a93fd4c1eb880","kind":"subsection","labels":["eq:e8-block-formula"],"line_end":200,"line_start":183,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/004-subsection-strong-cp-closure-as-conditional-steps.tex","status_markers_as_written":[],"summary_excerpt":"A physical E [formula in source] representation is not the stage label [formula in source] alone, but the full block triple [formula in source] . The compressed block formula is where [formula in source] is the unreduced Planck mass (not [formula in source] ), [formula in source] is the ladder stage with [formula in source] , [formula in source] is a mild block-multiplicity label ( [formula in source] ), and [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Block formula and reading discipline","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15097,"byte_start":12399,"id":"section:d506058b22c4c99b78b6","kind":"subsection","labels":["tab:e8-stage-atlas"],"line_end":234,"line_start":201,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/004-subsection-strong-cp-closure-as-conditional-steps.tex","status_markers_as_written":[],"summary_excerpt":"With the restrictive trace grammar [formula in source] the ladder produces a set of robust stage identifications. The main-text table shows only the robust nodes; the full real-domain atlas up to [formula in source] —including restricted-scan candidates and IR tail conjectures—is given in tab:e8-full-atlas in the appendix.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Restricted stage atlas","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16176,"byte_start":15097,"id":"section:98e0058e4c016e0089e0","kind":"subsection","labels":[],"line_end":260,"line_start":235,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/004-subsection-strong-cp-closure-as-conditional-steps.tex","status_markers_as_written":[],"summary_excerpt":"Two stages carry a particularly revealing double structure.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Split-node structure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18153,"byte_start":16176,"id":"section:fa38cdf61469ef638bf8","kind":"subsection","labels":["tab:e8-main-text"],"line_end":288,"line_start":261,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/004-subsection-strong-cp-closure-as-conditional-steps.tex","status_markers_as_written":[],"summary_excerpt":"] Under the restricted trace grammar, stages [formula in source] and [formula in source] have no unambiguous physical target. If [formula in source] is allowed to scan over all simple rationals, these stages can mimic almost any scale between [formula in source] and [formula in source] GeV. They mark the exact boundary where E [formula in source] without a derived block-trace theorem becomes too permissive. The open ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Permissiveness barrier and real-domain boundary","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":21659,"byte_start":18153,"id":"section:c32b199117df78dc771e","kind":"section","labels":["tab:benchmark"],"line_end":346,"line_start":289,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/004-subsection-strong-cp-closure-as-conditional-steps.tex","status_markers_as_written":[],"summary_excerpt":"The comparison values used in this section follow representative CODATA, PDG, NuFIT, Planck, and birefringence references codata2022,pdg2025,nufit2025,planck2018,minamiKomatsu2020,eskilt2023,sullivan2025. The main-text table is intentionally restricted to six rows whose comparison language is already reasonably convention-complete. The compact mass surface is given separately in tab:sm-mass-ledger-ew,tab:sm-mass-ledg","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Primary benchmark map and prediction ledger","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":23304,"byte_start":21659,"id":"section:e95b82b61b2b498c588f","kind":"subsection","labels":["tab:prediction-ledger"],"line_end":371,"line_start":347,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/004-subsection-strong-cp-closure-as-conditional-steps.tex","status_markers_as_written":[],"summary_excerpt":"The main benchmark table shows only a narrow comparison surface. To keep the compiler structure visible, tab:prediction-ledger summarizes which output packages belong to which layer of the paper.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Compact prediction ledger","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1931,"byte_start":0,"id":"section:63c14335e8912bb41c5a","kind":"subsection","labels":["fig:residual-plot"],"line_end":46,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/005-subsection-residual-map-and-principal-unresolved-compari.tex","status_markers_as_written":[],"summary_excerpt":"The residuals for the restricted six-row table are shown in fig:residual-plot. The carrier-linked electromagnetic, birefringence, and baryon-density channels all remain within the displayed few-sigma window. The CKM phase is not plotted here because it is better treated, at present, as the main unresolved transport-side comparison and is therefore moved to Appendix","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Residual map and principal unresolved comparisons","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3189,"byte_start":1931,"id":"section:230265151fe86b2efd87","kind":"subsection","labels":["tab:falsification"],"line_end":67,"line_start":47,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/005-subsection-residual-map-and-principal-unresolved-compari.tex","status_markers_as_written":[],"summary_excerpt":"@> p0.24 YY> p0.13 @ Statement & What would falsify it & Sector affected & Local or global failure \\\\ Minimal carrier [formula in source] & failure to recover the one-family packet or the global quotient from the carrier theorem & Hard & global \\\\ Family bridge and [formula in source] & no geometric monodromy interpretation of the three-cycle family space & Bridge & local-to-structural \\\\ Bosonic relative index selec","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Falsification matrix","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3256,"byte_start":3189,"id":"section:428218e29da53dacf38b","kind":"section","labels":[],"line_end":69,"line_start":68,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/005-subsection-residual-map-and-principal-unresolved-compari.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Conditional master theorem and finite proof obligations","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4012,"byte_start":3256,"id":"section:4b2358c66466d0ebf0a9","kind":"subsection","labels":["eq:conditional-compiler-chain"],"line_end":90,"line_start":70,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/005-subsection-residual-map-and-principal-unresolved-compari.tex","status_markers_as_written":[],"summary_excerpt":"Collecting the present hard, bridge, and completion layers, the intended compiler line is This line is not meant as a slogan. Each arrow is attached either to a hard theorem, a bridge construction, or one of the explicit completion interfaces listed in the proof-obligation table below.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Compiler chain","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5318,"byte_start":4012,"id":"section:f749a2d6a8938dd337e7","kind":"subsection","labels":[],"line_end":100,"line_start":91,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/005-subsection-residual-map-and-principal-unresolved-compari.tex","status_markers_as_written":[],"summary_excerpt":"Assume the hard carrier and kernel layers summarized in tab:status-matrix, together with the completion statements of the geometric and transport programs and the declared comparison map [formula in source] . Then every observable in the present main-text scope is the output of one carrier-first relative spectral compiler from primitive seam data to scheme-specified observables.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conditional master theorem","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6799,"byte_start":5318,"id":"section:3a3a9df38f284e056b4e","kind":"subsection","labels":["tab:proof-obligations"],"line_end":120,"line_start":101,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/005-subsection-residual-map-and-principal-unresolved-compari.tex","status_markers_as_written":[],"summary_excerpt":"@> p0.20 > p0.18 > p0.20 YY@ Target statement & Input data & Missing lemma & Minimal deliverable & Empirical consequence \\\\ Family space theorem & [formula in source] , [formula in source] , [formula in source] & monodromy-to-family theorem & derive [formula in source] from the seam cycle algebra & stabilizes the meaning of [formula in source] \\\\ Bosonic index closure & [formula in source] , [formula in source] & rel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Finite proof obligations","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8577,"byte_start":6799,"id":"section:70b254bd9df14d93caf8","kind":"section","labels":[],"line_end":128,"line_start":121,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/005-subsection-residual-map-and-principal-unresolved-compari.tex","status_markers_as_written":[],"summary_excerpt":"The present paper argues that a small carrier-first core already fixes nontrivial physics: the minimal [formula in source] carrier, the global Standard Model quotient, one chiral family, the carrier norm [formula in source] , the abelian index, the seam constant [formula in source] , the corrected opening [formula in source] , and the electromagnetic closure channel. The compression identities and exclusion theorems ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conclusion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8816,"byte_start":8577,"id":"section:8d620e206a2e26d76931","kind":"section","labels":["app:tech"],"line_end":133,"line_start":129,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/005-subsection-residual-map-and-principal-unresolved-compari.tex","status_markers_as_written":[],"summary_excerpt":"This appendix collects the technical bookkeeping that supports the carrier-first presentation but would slow the early main-text flow if placed before the carrier theorem.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Technical conventions and data layers","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9940,"byte_start":8816,"id":"section:e3c9f7fc71dc040c3715","kind":"subsection","labels":["tab:relative-objects"],"line_end":155,"line_start":134,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/005-subsection-residual-map-and-principal-unresolved-compari.tex","status_markers_as_written":[],"summary_excerpt":"The adjective relative is used in one fixed sense throughout the paper: every operator or action is compared to a declared reference object.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Relative objects","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12887,"byte_start":9940,"id":"section:d7639635d5d040781210","kind":"subsection","labels":["tab:layered-datum"],"line_end":220,"line_start":156,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/005-subsection-residual-map-and-principal-unresolved-compari.tex","status_markers_as_written":[],"summary_excerpt":"The technical bookkeeping behind the manuscript uses four levels: [formula in source] [formula in source] [formula in source] [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Layered datum and admissibility","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13102,"byte_start":12887,"id":"section:e4a561be1668c21e292d","kind":"section","labels":["app:constants"],"line_end":225,"line_start":221,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/005-subsection-residual-map-and-principal-unresolved-compari.tex","status_markers_as_written":[],"summary_excerpt":"This appendix collects material that is useful for internal compression but should not dominate the main-text scope of explicit claims.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Constants atlas and downstream scale grammar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18052,"byte_start":13102,"id":"section:85d00b0b6c3f339df248","kind":"subsection","labels":["fig:constant-cascade","tab:constants-atlas"],"line_end":309,"line_start":226,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/005-subsection-residual-map-and-principal-unresolved-compari.tex","status_markers_as_written":[],"summary_excerpt":"The seam loop is assumed to carry one unit of spectral flow, [formula in source] Because the spin lift closes only after [formula in source] , the normalized rotation modulus is [formula in source] The cascade in fig:constant-cascade is kept here as technical bookkeeping rather than as an early main-text dependency graphic.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Global rotation angle and constants atlas","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19464,"byte_start":18052,"id":"section:a1f907c06c0b841838e5","kind":"subsection","labels":[],"line_end":342,"line_start":310,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/005-subsection-residual-map-and-principal-unresolved-compari.tex","status_markers_as_written":[],"summary_excerpt":"In the present paper E [formula in source] is not used as a primitive cause. The retained parameter is [formula in source] On the retained branch this means [formula in source] The intended reading is a downstream scale grammar: the carrier packet fixes [formula in source] , [formula in source] then defines an optional ladder parameter, the ladder is allowed to organize scale spacing, but it does not replace the carr","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"E [formula in source] E8 as downstream scale grammar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":22173,"byte_start":19464,"id":"section:f5a00af96651681257ef","kind":"subsection","labels":["tab:e8-full-atlas"],"line_end":377,"line_start":343,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/005-subsection-residual-map-and-principal-unresolved-compari.tex","status_markers_as_written":[],"summary_excerpt":"The full real-domain atlas up to [formula in source] extends the main-text robust table with restricted-scan candidates and IR tail conjectures. Rows are classified as robust (restrictive grammar, unambiguous target), restricted-scan (plausible but less constrained), or tail conjecture (new trace class [formula in source] not yet derived from block structure).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Full stage atlas","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1827,"byte_start":0,"id":"section:a457097875facea4ad07","kind":"subsection","labels":["eq:41-chain"],"line_end":41,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/006-subsection-compression-identities-on-the-minimal-branch.tex","status_markers_as_written":[],"summary_excerpt":"The main-text compression identities are developed in the dedicated section on compression identities and carrier exclusion. This appendix subsection collects additional arithmetic continuations and the compression chain summary.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Compression identities on the minimal branch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5822,"byte_start":1827,"id":"section:a37d9807af25a8694888","kind":"subsection","labels":[],"line_end":168,"line_start":42,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/006-subsection-compression-identities-on-the-minimal-branch.tex","status_markers_as_written":[],"summary_excerpt":"The next relations mix the main-text carrier with optional appendix-level E [formula in source] , inflation, or geometric notation. They are useful compression patterns, but their interpretation should remain conditional or conjectural.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Optional arithmetic continuations","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7408,"byte_start":5822,"id":"section:f6b7f5c66f7a7bf901c9","kind":"subsection","labels":[],"line_end":234,"line_start":169,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/006-subsection-compression-identities-on-the-minimal-branch.tex","status_markers_as_written":[],"summary_excerpt":"The next package is stronger but also more conditional. It assumes that the carrier rank, family multiplicity, and seam normalization are all read as closed rather than only partially inherited.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conditional minimal-parameter picture","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8287,"byte_start":7408,"id":"section:a0ac73faa933af59552a","kind":"section","labels":["app:aps"],"line_end":247,"line_start":235,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/006-subsection-compression-identities-on-the-minimal-branch.tex","status_markers_as_written":[],"summary_excerpt":"The geometric completion uses APS-type relative data aps1975. In practice this means: one works with a declared pair [formula in source] rather than a single unanchored operator, boundary conditions on the seam [formula in source] are part of the definition of the relative index, the [formula in source] -term keeps track of the residual spectral asymmetry, the superconnection package is used in the same spirit as the","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Relative APS and superconnection setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9760,"byte_start":8287,"id":"section:ca4051523b744ecf2566","kind":"section","labels":["app:yukawa"],"line_end":281,"line_start":248,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/006-subsection-compression-identities-on-the-minimal-branch.tex","status_markers_as_written":[],"summary_excerpt":"The transport program is based on the regularized kernel [formula in source] Three remarks are important. The regulator [formula in source] is not optional: without it the kernel becomes ill-defined exactly where the admissibility question is most delicate. Positivity of the kernel is a transport-side selection principle, not yet a proved theorem of the hard kernel. Residual prefactors [formula in source] are bounded","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Yukawa kernels and positivity lemmas","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9990,"byte_start":9760,"id":"section:b764d8ae0b38cd19afa0","kind":"section","labels":["app:record"],"line_end":286,"line_start":282,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/006-subsection-compression-identities-on-the-minimal-branch.tex","status_markers_as_written":[],"summary_excerpt":"This appendix keeps the record-level constructions available without letting them dominate the scope of explicit claims in the main paper.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Optional record algebra, horizons, and prediction semantics","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10388,"byte_start":9990,"id":"section:a01a20ba779c25ae31f3","kind":"subsection","labels":[],"line_end":296,"line_start":287,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/006-subsection-compression-identities-on-the-minimal-branch.tex","status_markers_as_written":[],"summary_excerpt":"At finite volume or with a declared cutoff, an admissible vacuum candidate is written as [formula in source] provided the relative Hamiltonian is lower bounded on the admissible domain. In the absence of a full existence theorem this should be read as a minimizing-sequence statement, not as a solved cosmological theorem.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Minimal admissible vacuum","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10796,"byte_start":10388,"id":"section:7ae8374bd3f535250f39","kind":"subsection","labels":[],"line_end":310,"line_start":297,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/006-subsection-compression-identities-on-the-minimal-branch.tex","status_markers_as_written":[],"summary_excerpt":"The optional record algebra is [formula in source] As [formula in source] decreases, more stable channels open. 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This appendix intentionally avoids selling the factorization as exact fundamental structure.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Horizons as conjectural inner seams","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12103,"byte_start":11789,"id":"section:1e0974837d2b4f21b60d","kind":"subsection","labels":[],"line_end":348,"line_start":335,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/006-subsection-compression-identities-on-the-minimal-branch.tex","status_markers_as_written":[],"summary_excerpt":"The appendix-level prediction map is [formula in source] with [formula in source] This is kept only as an optional formal extension.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Prediction semantics","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12157,"byte_start":12103,"id":"section:07977edec461d993a656","kind":"section","labels":["app:benchmarks"],"line_end":351,"line_start":349,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/006-subsection-compression-identities-on-the-minimal-branch.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Extended benchmarks","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13380,"byte_start":12157,"id":"section:5f85cf9292b7ea5b05e1","kind":"subsection","labels":["tab:extended-benchmarks"],"line_end":372,"line_start":352,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/006-subsection-compression-identities-on-the-minimal-branch.tex","status_markers_as_written":[],"summary_excerpt":"@> p0.18 > p0.17 > p0.17 > p0.22 > p0.14 @ Observable & TFPT value & Reference value & Role & Status \\\\ [formula in source] & 1.198 rad & 1.196 rad & unresolved transport comparison & appendix comparison row \\\\ [formula in source] & 134.979 MeV & 134.977 MeV & hadronic out-of-sample check & appendix comparison row \\\\ [formula in source] & 0.0015 eV & [formula in source] eV & neutrinoless double-beta interface & appen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Extended comparison rows and supplementary checks","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4577,"byte_start":0,"id":"section:4026b8980d3f8fe48a93","kind":"subsection","labels":["tab:mass-source-supplement"],"line_end":89,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/paper-latex/tfpt-v30"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--paper-latex--tfpt-v30/sections/007-subsection-supplementary-mass-source-rows.tex","status_markers_as_written":[],"summary_excerpt":"The compact main-text mass ledgers intentionally suppress explicit formula detail. The source rows collected here retain that information without forcing the main text to read like a mixed formula notebook.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Supplementary mass-source rows","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":341,"byte_start":0,"id":"section:2d3587201870d8c81de9","kind":"frontmatter","labels":[],"line_end":8,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/00_orientation_note"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--00_orientation_note/preamble.tex","status_markers_as_written":[],"summary_excerpt":"tfptblue TFPT in One Map\\\\[0.4em] Boundary Polarization, Carrier Rigidity, and Observable Closure Stefan Hamann Alessandro Rizzo tfptgray Orientation Note for the TFPT 4.5 paper series –","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"tfptblue TFPT in One Map\\\\[0.4em] Boundary Polarization, Carrier Rigidity, and Observable Closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3564,"byte_start":0,"id":"section:a4db448b856ee20e27e4","kind":"frontmatter","labels":[],"line_end":80,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/00_orientation_note"],"relation_ids":["relation:1121851848e046a3774f"],"semantic_review":false,"source":"documents/archive--tfpt-45--00_orientation_note/sections/001-section-what-tfpt-claims.tex","status_markers_as_written":[],"summary_excerpt":"This note is the thin entry document for the TFPT 4.5 series. It does not attempt to prove the full theory. Its purpose is to state what TFPT claims, what it does not claim, how the closed branch is organized, and where each load-bearing argument is isolated in the paper sequence.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4272,"byte_start":3564,"id":"section:df72377a33dede842c24","kind":"section","labels":[],"line_end":107,"line_start":81,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/00_orientation_note"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--00_orientation_note/sections/001-section-what-tfpt-claims.tex","status_markers_as_written":[],"summary_excerpt":"TFPT is organized as a boundary-polarized spectral theory whose primitive input is a one-sided boundary datum [formula in source] The main theorem chain in the source draft is not a collection of unrelated numerological readouts. It is a staged reconstruction: [formula in source] The split series follows this burden of proof rather than the order in which a reader might find the numerics exciting.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"What TFPT Claims","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4670,"byte_start":4272,"id":"section:30e89d37033771ef4ad1","kind":"section","labels":[],"line_end":114,"line_start":108,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/00_orientation_note"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--00_orientation_note/sections/001-section-what-tfpt-claims.tex","status_markers_as_written":[],"summary_excerpt":"The orientation note does not certify every downstream comparison row as a theorem. In particular, the CMB interface, sky-map realization, horizon continuations, transient channels, and E8 scale grammar remain outside the primitive theorem chain. They are comparison and programmatic layers unless explicitly promoted by a later proof obligation.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"What TFPT Does Not Claim at This Level","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5143,"byte_start":4670,"id":"section:2d494898b376d99a3d21","kind":"section","labels":[],"line_end":128,"line_start":115,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/00_orientation_note"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--00_orientation_note/sections/001-section-what-tfpt-claims.tex","status_markers_as_written":[],"summary_excerpt":"The source manuscript condenses the closed branch through three decoders: [formula in source] This orientation is the reason the paper series separates the primitive kernel, the carrier packet, the precision readouts, the QFT closure layer, the metrology layer, and the cosmology interface.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Three Decoders","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9560,"byte_start":5143,"id":"section:9070e49b58a12ef7b1e8","kind":"section","labels":[],"line_end":232,"line_start":129,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/00_orientation_note"],"relation_ids":["relation:9900337cd0aa17c8206a"],"semantic_review":false,"source":"documents/archive--tfpt-45--00_orientation_note/sections/001-section-what-tfpt-claims.tex","status_markers_as_written":[],"summary_excerpt":"@p0.24 p0.08 p0.22 Y@ Layer & Tier & Lean-side target / reference & Notes / location \\\\ Boundary primitive kernel: algebraic shadow & L & BoundaryPolarization, BoundaryPolarization.ofCarrierInvolution & Algebraic equivalence between the polarisation picture and the involution picture is Lean-proved. Paper 1 + Lean note. \\\\ Boundary primitive kernel: analytic Paper-1 content & I & target type BoundaryPolarization & An","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Status Matrix","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11005,"byte_start":9560,"id":"section:74e461207c6ce033a883","kind":"section","labels":[],"line_end":258,"line_start":233,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/00_orientation_note"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--00_orientation_note/sections/001-section-what-tfpt-claims.tex","status_markers_as_written":[],"summary_excerpt":"Boundary Polarization and the Primitive Kernel of TFPT. Establishes [formula in source] and keeps all Standard-Model claims out. Carrier Rigidity, Hypercharge, and the Standard Model Packet from Boundary Polarization. Establishes the rigid [formula in source] carrier, hypercharge, [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] , and [formula in source] . El","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Series Map","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11322,"byte_start":11005,"id":"section:1a2546f9a2ac9572c026","kind":"section","labels":[],"line_end":264,"line_start":259,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/00_orientation_note"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--00_orientation_note/sections/001-section-what-tfpt-claims.tex","status_markers_as_written":[],"summary_excerpt":"The recommended public order is Paper 0, Paper 2, Paper 1, Paper 3, Paper 4, Paper 5, and finally Paper 6. The mathematical dependency order remains Paper 1 before Paper 2; the publication order uses Paper 2 as the clearest visible hook while Paper 0 explains the dependency discipline.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Publication Order","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11741,"byte_start":11322,"id":"section:7380db88a0ce2f695437","kind":"section","labels":[],"line_end":276,"line_start":265,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/00_orientation_note"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--00_orientation_note/sections/001-section-what-tfpt-claims.tex","status_markers_as_written":[],"summary_excerpt":"The orientation note draws especially from the abstract, the closed-architecture box, Sections 1 and 2, the canonical rigid-object discussion, the structural falsification map, and the conclusion. It intentionally does not import the extended empirical ledgers, E8 stage atlas, CMB figures, or mass tables.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Source Boundary","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12234,"byte_start":11741,"id":"section:269f4f814a11de4a62f4","kind":"section","labels":[],"line_end":288,"line_start":277,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/00_orientation_note"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--00_orientation_note/sections/001-section-what-tfpt-claims.tex","status_markers_as_written":[],"summary_excerpt":"This section contains the main technical development assigned to this paper by the TFPT 4.5 clean split. Cross-paper background is referenced through dependency and scope boxes; extended backend material is kept in the Technical Companion.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Main Technical Development","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":282,"byte_start":0,"id":"section:6a8ce74c5d3ba070bea7","kind":"frontmatter","labels":[],"line_end":7,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/01_boundary_kernel"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--01_boundary_kernel/preamble.tex","status_markers_as_written":[],"summary_excerpt":"tfptblue Boundary Polarization and the Primitive Kernel of TFPT Stefan Hamann Alessandro Rizzo tfptgray Paper 1 of the TFPT 4.5 series –","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"tfptblue Boundary Polarization and the Primitive Kernel of TFPT","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3440,"byte_start":0,"id":"section:6707621b12b5f3772c3d","kind":"frontmatter","labels":[],"line_end":89,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/01_boundary_kernel"],"relation_ids":["relation:ebc67fff8ac728476672"],"semantic_review":false,"source":"documents/archive--tfpt-45--01_boundary_kernel/sections/001-section-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"This paper isolates the primitive boundary kernel. Starting from the minimal operational seed and the one-sided boundary datum, it reconstructs the exact double, the deck involution, the Calderon polarization, the primitive admissibility complex, the primitive seam generator, the winding normalization [formula in source] , and the normalization [formula in source] . No Standard-Model, phenomenological, gravitational,","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4142,"byte_start":3440,"id":"section:f388f7f941baf59b7f2f","kind":"section","labels":[],"line_end":110,"line_start":90,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/01_boundary_kernel"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--01_boundary_kernel/sections/001-section-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"The paper proves the first load-bearing arrow of the TFPT series: [formula in source] All later discrete, physical, and numerical structures are treated as unavailable here. The purpose is to make the boundary primitive kernel auditable on its own.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Claim Map","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4526,"byte_start":4142,"id":"section:bc4b9e813b85171a99d2","kind":"section","labels":[],"line_end":120,"line_start":111,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/01_boundary_kernel"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--01_boundary_kernel/sections/001-section-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"The starting object is [formula in source] The paper should keep only the source manuscript material needed to explain one-sided admissible data, induced boundary spectral data, and the passage to a doubled closed datum. The proof burden is that the primitive boundary structure is not chosen by hand.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"One-Sided Boundary Datum","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4909,"byte_start":4526,"id":"section:7b3b47b77f66630b99e3","kind":"section","labels":[],"line_end":130,"line_start":121,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/01_boundary_kernel"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--01_boundary_kernel/sections/001-section-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"The exact double reconstructs [formula in source] with [formula in source] as deck involution and [formula in source] as the involution induced by the Calderon polarization. This section carries the analytic interface to Calderon projectors and the primitive relative spectral dynamics from the source draft.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Exact Double and Deck Involution","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5310,"byte_start":4909,"id":"section:c8971769ac838900b92e","kind":"section","labels":[],"line_end":140,"line_start":131,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/01_boundary_kernel"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--01_boundary_kernel/sections/001-section-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"The primitive selector is introduced before any color, determinant, family, or QFT sector: [formula in source] The section should include the primitive admissibility differential, the primitive Hodge form, and the selector upgrade logic only as far as it is needed to prove that a later full selector can factor through [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Primitive Admissibility Complex","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5662,"byte_start":5310,"id":"section:0a058b360956f9faa31f","kind":"section","labels":[],"line_end":151,"line_start":141,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/01_boundary_kernel"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--01_boundary_kernel/sections/001-section-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"The primitive seam generator records the two normalizations that are allowed to survive this paper: [formula in source] The winding class is a primitive boundary output. It is not yet a family-counting or flavor transport input; those interpretations are postponed to Papers 2 and 3.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Primitive Seam Generator","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7763,"byte_start":5662,"id":"section:6c04e27ea5f61161b8ac","kind":"section","labels":["rem:lean-target-paper1","thm:primitive-boundary-kernel"],"line_end":201,"line_start":152,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/01_boundary_kernel"],"relation_ids":["relation:3c8619683354bfab3ced"],"semantic_review":false,"source":"documents/archive--tfpt-45--01_boundary_kernel/sections/001-section-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"Under the one-sided boundary hypotheses and the primitive admissibility assumptions stated above, the minimal boundary datum canonically determines [formula in source] In particular, the Calderon polarization induces a direct-sum decomposition [formula in source] which (passed to the finite essential carrier [formula in source] ) inhabits the Lean-side target type BoundaryPolarization.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Boundary Primitive Kernel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8418,"byte_start":7763,"id":"section:6adae73f1df7ba8e0997","kind":"section","labels":[],"line_end":218,"line_start":202,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/01_boundary_kernel"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--01_boundary_kernel/sections/001-section-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"@p0.24 Y@ Audit item & Question \\\\ One-sided datum & Is every primitive object reconstructed from [formula in source] or from standard boundary spectral data? \\\\ Calderon interface & Are regularity and projection hypotheses explicit? \\\\ Primitive selector & Does [formula in source] precede the later singlet and determinant projections? \\\\ Winding class & Is [formula in source] fixed before any family or flavor interp","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Audit Protocol","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8752,"byte_start":8418,"id":"section:5aaaf13de56926aa7b0c","kind":"section","labels":[],"line_end":224,"line_start":219,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/01_boundary_kernel"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--01_boundary_kernel/sections/001-section-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"This section contains the main technical development assigned to this paper by the TFPT 4.5 clean split. Cross-paper background is referenced through dependency and scope boxes; extended backend material is kept in the Technical Companion.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Main Technical Development","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9826,"byte_start":8752,"id":"section:baa84683f82162539020","kind":"section","labels":[],"line_end":250,"line_start":225,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/01_boundary_kernel"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--01_boundary_kernel/sections/001-section-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"Use : Sections 1 and 2 only as a shortened claim map. Sections 3.1 and 3.2 for primitive core, one-sided boundary datum, doubling, deck involution, Calderon projector, and primitive admissibility complex. Section 4.1 only for the primitive seam generator, [formula in source] , and [formula in source] . Sections 8.1–8.4 only for primitive selector and upgrade logic. Sections 9.1–9.3 for operational seed, admissible bo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Source Extraction Map","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10172,"byte_start":9826,"id":"section:3e4f001b6b3b62132221","kind":"section","labels":[],"line_end":260,"line_start":251,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/01_boundary_kernel"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--01_boundary_kernel/sections/001-section-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"Carrier rigidity, the Standard-Model packet, exact electromagnetic closure, flavor transport, QFT reconstruction, gravity/metrology, cosmology, CMB targets, E8 grammar, horizons, and transient channels are not used as inputs in this paper.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Not Used Here","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":361,"byte_start":0,"id":"section:609a9f667334de63d8c3","kind":"frontmatter","labels":[],"line_end":8,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/02_carrier_rigidity_standard_model_packet"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--02_carrier_rigidity_standard_model_packet/preamble.tex","status_markers_as_written":[],"summary_excerpt":"tfptblue The [formula in source] Hypercharge Carrier Rigidity Theorem\\\\[0.35em] with Lean-Verified Algebraic Core and Standard-Model Packet Outlook Stefan Hamann Alessandro Rizzo tfptgray Paper 2 of the TFPT 4.5 series –","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"tfptblue The [formula in source] Hypercharge Carrier Rigidity Theorem\\\\[0.35em] with Lean-Verified Algebraic Core and Standard-Model Packet Outlook","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7788,"byte_start":0,"id":"section:e7c01a6c3406a761655d","kind":"frontmatter","labels":[],"line_end":157,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/02_carrier_rigidity_standard_model_packet"],"relation_ids":["relation:3ec4d7edc74ff8efa915"],"semantic_review":false,"source":"documents/archive--tfpt-45--02_carrier_rigidity_standard_model_packet/sections/001-section-formal-status-of-the-carrier-theorem.tex","status_markers_as_written":[],"summary_excerpt":"This paper proves the algebraic core of TFPT's carrier theorem and, separately, sketches its Standard-Model packet outlook. The carrier core takes four explicit interfaces — a carrier involution [formula in source] , a Higgs rank- [formula in source] interface [formula in source] , a Yukawa Stage-D trilinear interface [formula in source] with operational contraction predicates, and a primitive oriented determinant-pr","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9466,"byte_start":7788,"id":"section:0f984a39c60f6affc3f9","kind":"section","labels":["sec:formal-status"],"line_end":195,"line_start":158,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/02_carrier_rigidity_standard_model_packet"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--02_carrier_rigidity_standard_model_packet/sections/001-section-formal-status-of-the-carrier-theorem.tex","status_markers_as_written":[],"summary_excerpt":"This paper separates the carrier rigidity theorem (Status A, Lean verified) from the Standard-Model packet outlook (Status C, downstream).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Formal Status of the Carrier Theorem","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16454,"byte_start":9466,"id":"section:6bc4166c0d9d406c8109","kind":"section","labels":["rem:primitive-yukawa-naming","thm:carrier-rigidity"],"line_end":362,"line_start":196,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/02_carrier_rigidity_standard_model_packet"],"relation_ids":["relation:4c7683c1355abe4c5bcd"],"semantic_review":false,"source":"documents/archive--tfpt-45--02_carrier_rigidity_standard_model_packet/sections/001-section-formal-status-of-the-carrier-theorem.tex","status_markers_as_written":[],"summary_excerpt":"The paper does not begin by assuming [formula in source] It begins with the carrier involution induced by the boundary polarization: [formula in source] At this stage there is only a two-point algebra [formula in source] No [formula in source] split, hypercharge vector, Standard-Model packet, or electromagnetic number has been used.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Carrier Polynomial as a Corollary","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1705,"byte_start":0,"id":"section:88b221f684aadec7b605","kind":"section","labels":["sec:seam-winding"],"line_end":37,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/02_carrier_rigidity_standard_model_packet"],"relation_ids":["relation:fd0b1f56cf8f56f67ad2"],"semantic_review":false,"source":"documents/archive--tfpt-45--02_carrier_rigidity_standard_model_packet/sections/002-section-seam-winding-as-source-of-the-integer-conditions.tex","status_markers_as_written":[],"summary_excerpt":"The integer triple [formula in source] entering input (iii) of thm:carrier-rigidity is not assumed: it is the algebraic shadow of TFPT's seam class [formula in source] . The TFPT-side statement is the three-way obligation [formula in source] None of the three conjuncts is presented as a Lean theorem here; each is a Status-B obligation of TFPT's seam-class theory. Their joint Lean target is [formula in source] which i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Seam Winding as Source of the Integer Conditions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2925,"byte_start":1705,"id":"section:ce1f81ead18a4df70689","kind":"section","labels":["sec:gauge-outlook"],"line_end":71,"line_start":38,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/02_carrier_rigidity_standard_model_packet"],"relation_ids":["relation:2ed505382679d903b680"],"semantic_review":false,"source":"documents/archive--tfpt-45--02_carrier_rigidity_standard_model_packet/sections/002-section-seam-winding-as-source-of-the-integer-conditions.tex","status_markers_as_written":[],"summary_excerpt":"The remainder of this paper presents the Standard-Model packet outlook conditional on thm:carrier-rigidity. These sections are Status C (mathematical proposal): they are not part of the Lean-verified core and are not signature-locked in AuditContract.lean. The text below indicates this consistently.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Hypercharge and Gauge Quotient (Status C outlook)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3547,"byte_start":2925,"id":"section:2bce487ef88d07973605","kind":"section","labels":["sec:packet-outlook"],"line_end":87,"line_start":72,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/02_carrier_rigidity_standard_model_packet"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--02_carrier_rigidity_standard_model_packet/sections/002-section-seam-winding-as-source-of-the-integer-conditions.tex","status_markers_as_written":[],"summary_excerpt":"The spinor packet is conjectured to be [formula in source] This section sketches the one-family decomposition including the right-handed neutrino state. Character identities, trace identities, and the abelian index belong here. The expected Lean target is a DerivedSMRepresentations module bundling LinearMap.dualHypercharge, ExteriorPower.hypercharge, and TensorProduct.hypercharge; not yet present in the Lean note.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"One-Family Packet (Status C outlook)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4231,"byte_start":3547,"id":"section:b8e98635e3856fc5cb88","kind":"section","labels":[],"line_end":102,"line_start":88,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/02_carrier_rigidity_standard_model_packet"],"relation_ids":["relation:26a592af9df1d65ff0c9","relation:37d69af75921e51ed9ef","relation:4097917ffa006ab96b40","relation:4813a9aee73c9f838b14","relation:558297fdb5ecafefb835","relation:59d0e6d4edc373fbb24c","relation:5d63422c0e2c18ab069a","relation:5fbb1cb9de0f26f6dc00","relation:81b8a2629177011f975f","relation:a50ddcfc395e62c27195","relation:e8c614c53436f48168ab"],"semantic_review":false,"source":"documents/archive--tfpt-45--02_carrier_rigidity_standard_model_packet/sections/002-section-seam-winding-as-source-of-the-integer-conditions.tex","status_markers_as_written":[],"summary_excerpt":"The editorial risk is that [formula in source] look like disguised Standard-Model inputs. In v10/v11 of the Lean note this risk is mitigated: [formula in source] follows from [formula in source] via the Lean theorem exteriorPower.finrank_eq; and [formula in source] is the duality content of Yukawa Stage C ( PrimitiveIndecomposableYukawaCoupling), itself derived from Stage D under [formula in source] . 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It treats the electromagnetic fixed point, the transport pole of the cusp cubic, the retained seed decoder, and the flavor transport grammar yielding [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] , CKM, and PMNS reado","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4239,"byte_start":3876,"id":"section:a4e228cda3e7be6c28d2","kind":"section","labels":[],"line_end":97,"line_start":88,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/03_electromagnetic_closure_flavor_transport"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--03_electromagnetic_closure_flavor_transport/sections/001-section-electromagnetic-closure.tex","status_markers_as_written":[],"summary_excerpt":"The electromagnetic calculation is presented only after the carrier branch is fixed. The fixed point is read as a closed-branch output: [formula in source] The paper should include the carrier form of the electromagnetic closure and the compact audit of which structural quantities enter the fixed point.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Electromagnetic Closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4572,"byte_start":4239,"id":"section:b331e193d30d73b30d9e","kind":"section","labels":[],"line_end":108,"line_start":98,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/03_electromagnetic_closure_flavor_transport"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--03_electromagnetic_closure_flavor_transport/sections/001-section-electromagnetic-closure.tex","status_markers_as_written":[],"summary_excerpt":"The transport phase is governed by the cubic [formula in source] The lower critical point determines [formula in source] on the retained branch. 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Representative hard readouts include [formula in source] Large mass tables belong in the companion or a later empirical ledger, not in this paper.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Flavor Transport","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8921,"byte_start":7973,"id":"section:b4f215eea1ac180c1adf","kind":"section","labels":[],"line_end":202,"line_start":187,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/03_electromagnetic_closure_flavor_transport"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--03_electromagnetic_closure_flavor_transport/sections/001-section-electromagnetic-closure.tex","status_markers_as_written":[],"summary_excerpt":"@p0.18 p0.2 p0.18 p0.13 Y@ Constant & First appearance & Prior dependency & Before [formula in source] ? & Variation consequence \\\\ [formula in source] & Paper 2 carrier theorem & Paper 1 primitive kernel & Yes & Breaks [formula in source] , gauge quotient, and all downstream readouts. \\\\ [formula in source] & Paper 1 seam generator & Boundary primitive kernel & Yes & Breaks family counting and transport branch norma","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"No-Knobs Audit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9219,"byte_start":8921,"id":"section:6ca3fc0d9cf8ce339659","kind":"section","labels":[],"line_end":209,"line_start":203,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/03_electromagnetic_closure_flavor_transport"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--03_electromagnetic_closure_flavor_transport/sections/001-section-electromagnetic-closure.tex","status_markers_as_written":[],"summary_excerpt":"The alternative discrete worlds table is a falsification device. It should not be presented as decorative numerics. Each alternative must fail because it breaks a prior branch constraint, the fixed-point equation, or the simultaneous reuse audit.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Alternative Discrete Worlds","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9547,"byte_start":9219,"id":"section:bafb68a85151d35f3102","kind":"section","labels":[],"line_end":215,"line_start":210,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/03_electromagnetic_closure_flavor_transport"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--03_electromagnetic_closure_flavor_transport/sections/001-section-electromagnetic-closure.tex","status_markers_as_written":[],"summary_excerpt":"This section contains the main technical development assigned to this paper by the TFPT 4.5 clean split. Cross-paper background is referenced through dependency and scope boxes; extended backend material is kept in the Technical Companion.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Main Technical Development","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10674,"byte_start":9547,"id":"section:402bdac3fd09ce4bce51","kind":"section","labels":[],"line_end":240,"line_start":216,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/03_electromagnetic_closure_flavor_transport"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--03_electromagnetic_closure_flavor_transport/sections/001-section-electromagnetic-closure.tex","status_markers_as_written":[],"summary_excerpt":"Use : Sections 4.1 and 4.2 for electromagnetic closure. Sections 5.4 and 5.5 for UV seed shadow, Cabibbo inversion, and alternative discrete worlds. Sections 7.1–7.3 for the discrete phase operator, transport grammar, and Yukawa kernels. Sections 7.16–7.27 for CKM and PMNS closure. Appendix A only as a narrow operational prediction surface and compact prediction ledger. Add a dedicated [formula in source] audit appen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Source Extraction Map","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11017,"byte_start":10674,"id":"section:ac01d6f66ff8854f6dae","kind":"section","labels":[],"line_end":250,"line_start":241,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/03_electromagnetic_closure_flavor_transport"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--03_electromagnetic_closure_flavor_transport/sections/001-section-electromagnetic-closure.tex","status_markers_as_written":[],"summary_excerpt":"Strong-CP admissibility closure, OS/CAR reconstruction, local Minkowski nets, scattering, gravity/metrology proofs, CMB spectra, sky realization, E8 grammar, horizons, and large pole-mass tables are not used as proof inputs in this paper.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Not Used Here","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":323,"byte_start":0,"id":"section:c84e4a413e132341d695","kind":"frontmatter","labels":[],"line_end":8,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--04_admissibility_strong_cp_qft_closure/preamble.tex","status_markers_as_written":[],"summary_excerpt":"tfptblue Admissibility, Strong CP, and Nonperturbative QFT Closure\\\\[0.35em] on the TFPT Branch Stefan Hamann Alessandro Rizzo tfptgray Paper 4 of the TFPT 4.5 series –","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"tfptblue Admissibility, Strong CP, and Nonperturbative QFT Closure\\\\[0.35em] on the TFPT Branch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4033,"byte_start":0,"id":"section:47c3c9092ddf817cdf1b","kind":"frontmatter","labels":[],"line_end":86,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--04_admissibility_strong_cp_qft_closure/sections/001-section-selector-versus-dynamics.tex","status_markers_as_written":[],"summary_excerpt":"This paper isolates the analytic closure layer of TFPT. The selector [formula in source] is treated as a physical admissible-sector construction, while the dynamics is carried by [formula in source] , admissible Schwinger distributions, Osterwalder–Schrader reconstruction, the local Minkowski net, stable massive scattering, and the exact admissible RG flow.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4458,"byte_start":4033,"id":"section:c9780d5c35d84f98e55a","kind":"section","labels":[],"line_end":107,"line_start":87,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--04_admissibility_strong_cp_qft_closure/sections/001-section-selector-versus-dynamics.tex","status_markers_as_written":[],"summary_excerpt":"The central distinction is [formula in source] whereas dynamics is carried by [formula in source] This separation must be repeated in the introduction and conclusion because it is the main defense against overclaiming.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Selector Versus Dynamics","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4806,"byte_start":4458,"id":"section:51909432dd3e1149a474","kind":"section","labels":[],"line_end":117,"line_start":108,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--04_admissibility_strong_cp_qft_closure/sections/001-section-selector-versus-dynamics.tex","status_markers_as_written":[],"summary_excerpt":"After carrier and determinant data are fixed, the full selector is [formula in source] The paper should retain the two-stage upgrade from [formula in source] to [formula in source] , the Hodge projector description, and the exact role of the gap projection. Carrier material is summarized only as an input.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Full Admissibility Complex","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5171,"byte_start":4806,"id":"section:ffcba058206d2625906c","kind":"section","labels":[],"line_end":130,"line_start":118,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--04_admissibility_strong_cp_qft_closure/sections/001-section-selector-versus-dynamics.tex","status_markers_as_written":[],"summary_excerpt":"The strong-CP sector is stated as an admissibility result: [formula in source] The argument should connect hadronic singlet selection, determinant structure, [formula in source] -Hermiticity, and the sheet involution without importing phenomenological tuning.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Strong CP Closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5500,"byte_start":5171,"id":"section:eaf0d1935b534e4f5b24","kind":"section","labels":[],"line_end":136,"line_start":131,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--04_admissibility_strong_cp_qft_closure/sections/001-section-selector-versus-dynamics.tex","status_markers_as_written":[],"summary_excerpt":"The reflection-positivity block should state all assumptions on the admissible Schwinger functions, fermionic positivity, quotient form, and domain regularity. The OS theorem is used as a standard interface only after the admissible-sector positivity hypotheses are named.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reflection Positivity and OS Reconstruction","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5773,"byte_start":5500,"id":"section:e075f49e180aeaf4a160","kind":"section","labels":[],"line_end":142,"line_start":137,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--04_admissibility_strong_cp_qft_closure/sections/001-section-selector-versus-dynamics.tex","status_markers_as_written":[],"summary_excerpt":"The local Minkowski net, Haag–Ruelle/LSZ massive scattering, and dressed massless interface are treated as conditional closure outputs. The paper must distinguish stable massive scattering from low-curvature dressed massless behavior.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Local Net and Scattering","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6175,"byte_start":5773,"id":"section:20de188616827cd1449d","kind":"section","labels":[],"line_end":154,"line_start":143,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--04_admissibility_strong_cp_qft_closure/sections/001-section-selector-versus-dynamics.tex","status_markers_as_written":[],"summary_excerpt":"The exact admissible RG flow is the analytic continuation of the same sector: [formula in source] with the admissible projection included as part of the flow definition. The observable hierarchy is included only as far as it supports the QFT closure layer.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Exact Admissible Flow","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7728,"byte_start":6175,"id":"section:ef55cca101554d90da06","kind":"section","labels":[],"line_end":190,"line_start":155,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":["relation:200f1b25352dd77ba764","relation:501fb02aae20c871ce6f","relation:7675d5b6f599aa4b57c6","relation:927687bbb73792887429","relation:a238c5a3316cb16e5ef8","relation:de7396a6b1b676fbe3a1"],"semantic_review":false,"source":"documents/archive--tfpt-45--04_admissibility_strong_cp_qft_closure/sections/001-section-selector-versus-dynamics.tex","status_markers_as_written":[],"summary_excerpt":"This section contains the main technical development assigned to this paper by the TFPT 4.5 clean split. Cross-paper background is referenced through dependency and scope boxes; extended backend material is kept in the Technical Companion.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Main Technical Development","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8586,"byte_start":7728,"id":"section:dc2548243d0e4165fe45","kind":"section","labels":[],"line_end":209,"line_start":191,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--04_admissibility_strong_cp_qft_closure/sections/001-section-selector-versus-dynamics.tex","status_markers_as_written":[],"summary_excerpt":"Use : Sections 7.4 and 7.5 for hadronic admissibility and strong-CP ingredients. Section 8 as the main technical body, with carrier repetition removed. Sections 8.20–8.22 for topological positivity and strong-CP closure. Sections 8.23–8.41 for reflection positivity, OS closure, local net, and scattering. Section 13.2 for exact admissible RG flow, 1PI expansion, and observable hierarchy. Appendices E, F, and H as the ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Source Extraction Map","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8871,"byte_start":8586,"id":"section:228132cd22c2701bbf15","kind":"section","labels":[],"line_end":216,"line_start":210,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--04_admissibility_strong_cp_qft_closure/sections/001-section-selector-versus-dynamics.tex","status_markers_as_written":[],"summary_excerpt":"Exact electromagnetic benchmark derivations, CKM/PMNS prediction tables, gravity/metrology readouts, CMB spectra, sky realization, E8 grammar, full empirical ledgers, horizons, and transient channels are not used as proof inputs in this paper.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Not Used Here","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":328,"byte_start":0,"id":"section:501e611ed982c78e5d79","kind":"frontmatter","labels":[],"line_end":8,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--05_geometric_hodge_closure_dimensionless_metrology/preamble.tex","status_markers_as_written":[],"summary_excerpt":"tfptblue Geometric Hodge Closure and Dimensionless Metrology\\\\[0.35em] from the TFPT Boundary Branch Stefan Hamann Alessandro Rizzo tfptgray Paper 5 of the TFPT 4.5 series –","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"tfptblue Geometric Hodge Closure and Dimensionless Metrology\\\\[0.35em] from the TFPT Boundary Branch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3836,"byte_start":0,"id":"section:721911e8bd876db4d766","kind":"frontmatter","labels":[],"line_end":90,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--05_geometric_hodge_closure_dimensionless_metrology/sections/001-section-boundary-spectral-unit.tex","status_markers_as_written":[],"summary_excerpt":"This paper isolates the geometric and metrological branch of TFPT. The theory is not presented as predicting isolated SI numbers. Instead it constructs an internal dimensionless metrology from the boundary spectral unit [formula in source] , with gravity, Planck normalization, electroweak matching, and pole readouts expressed as boundary-normalized observables.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4129,"byte_start":3836,"id":"section:a7f46b9c5e07103cd4b0","kind":"section","labels":[],"line_end":99,"line_start":91,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--05_geometric_hodge_closure_dimensionless_metrology/sections/001-section-boundary-spectral-unit.tex","status_markers_as_written":[],"summary_excerpt":"The internal unit is [formula in source] All dimensionful-looking statements in this paper are rewritten as dimensionless quotients by powers of [formula in source] . This is the editorial rule that separates metrology from numerology.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Boundary Spectral Unit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4433,"byte_start":4129,"id":"section:a85b970c0ab5bf9c0f63","kind":"section","labels":[],"line_end":105,"line_start":100,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--05_geometric_hodge_closure_dimensionless_metrology/sections/001-section-boundary-spectral-unit.tex","status_markers_as_written":[],"summary_excerpt":"The geometric branch reconstructs a spectral Einstein functional and its Hodge closure. The paper should retain the source draft's geometric reconstruction, spectral Einstein functional, and Planck closure, but it should remove cosmological and horizon continuations.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Geometric Hodge Closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4780,"byte_start":4433,"id":"section:6f91b391bfcb41e42c2b","kind":"section","labels":[],"line_end":118,"line_start":106,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--05_geometric_hodge_closure_dimensionless_metrology/sections/001-section-boundary-spectral-unit.tex","status_markers_as_written":[],"summary_excerpt":"The Planck readout is internal: [formula in source] The question is not which SI value of [formula in source] is inserted, but which dimensionless branch quotient is fixed.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Planck Normalization","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7135,"byte_start":4780,"id":"section:88f7bb7763acd9ba04b2","kind":"subsection","labels":["eq:kappa-xi","ssec:einstein-limit-normalizer"],"line_end":162,"line_start":119,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--05_geometric_hodge_closure_dimensionless_metrology/sections/001-section-boundary-spectral-unit.tex","status_markers_as_written":[],"summary_excerpt":"Once the boundary spectral unit [formula in source] , the seam constant [formula in source] , and the retained seed [formula in source] are fixed, a single dimensionless quotient governs the transition between the UFE-normalized boundary functional and the Einstein–Hilbert presentation. Writing [formula in source] for the Einstein–Hilbert prefactor, the boundary-branch reduction yields a relation of the form The prod","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Einstein-limit normalizer [formula in source] xi = c3/phi0","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7488,"byte_start":7135,"id":"section:b30b9b028993b4c90136","kind":"section","labels":[],"line_end":173,"line_start":163,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--05_geometric_hodge_closure_dimensionless_metrology/sections/001-section-boundary-spectral-unit.tex","status_markers_as_written":[],"summary_excerpt":"The electroweak matching layer is included only as boundary-normalized metrology: [formula in source] is an internal dimensionless output. Pole matching may be included in compact form when it is expressed as a quotient by [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Electroweak Matching","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7919,"byte_start":7488,"id":"section:da0dcdd20924f9cd4558","kind":"section","labels":[],"line_end":189,"line_start":174,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--05_geometric_hodge_closure_dimensionless_metrology/sections/001-section-boundary-spectral-unit.tex","status_markers_as_written":[],"summary_excerpt":"The output layer is organized as [formula in source] Only the final projection chooses scheme or comparison conventions. The paper should keep this distinction visible whenever a physical readout is compared to an empirical row.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Observable Functor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8885,"byte_start":7919,"id":"section:70da2f72e0e0912c91df","kind":"section","labels":[],"line_end":210,"line_start":190,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--05_geometric_hodge_closure_dimensionless_metrology/sections/001-section-boundary-spectral-unit.tex","status_markers_as_written":[],"summary_excerpt":"This section contains the main technical development assigned to this paper by the TFPT 4.5 clean split. Cross-paper background is referenced through dependency and scope boxes; extended backend material is kept in the Technical Companion.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Main Technical Development","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9911,"byte_start":8885,"id":"section:8fca1a2211f07d612dd1","kind":"section","labels":[],"line_end":234,"line_start":211,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--05_geometric_hodge_closure_dimensionless_metrology/sections/001-section-boundary-spectral-unit.tex","status_markers_as_written":[],"summary_excerpt":"Use : Sections 6.4, 6.7, 6.8, and 6.9 for geometric reconstruction, spectral Einstein functional, and Planck closure. Sections 6.21–6.26 for electroweak matching and pole matching. Section 13.2 only for observable hierarchy parts not already used in Paper 4. Section 14 in full as the dimensionless metrology core. Appendix C only in shortened form and without making E8 prominent.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Source Extraction Map","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10135,"byte_start":9911,"id":"section:3989d5bf2e359ffa6552","kind":"section","labels":[],"line_end":240,"line_start":235,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--05_geometric_hodge_closure_dimensionless_metrology/sections/001-section-boundary-spectral-unit.tex","status_markers_as_written":[],"summary_excerpt":"Late-time [formula in source] , CMB spectra, sky realization, black holes, horizons, E8 stage atlas, transient channels, and cosmological comparison rows are not used as proof inputs in this paper.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Not Used Here","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":349,"byte_start":0,"id":"section:79180875bf2f0eb43208","kind":"frontmatter","labels":[],"line_end":8,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/06_cosmology_interfaces_downstream_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--06_cosmology_interfaces_downstream_closure/preamble.tex","status_markers_as_written":[],"summary_excerpt":"tfptblue Cosmology Interfaces of the TFPT Closed Branch\\\\[0.35em] Seam Transfer, Axion Sector, Reheating, and CMB Targets Stefan Hamann Alessandro Rizzo tfptgray Paper 6 of the TFPT 4.5 series –","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"tfptblue Cosmology Interfaces of the TFPT Closed Branch\\\\[0.35em] Seam Transfer, Axion Sector, Reheating, and CMB Targets","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3404,"byte_start":0,"id":"section:15a7d35d81ffae4245ac","kind":"frontmatter","labels":[],"line_end":81,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/06_cosmology_interfaces_downstream_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--06_cosmology_interfaces_downstream_closure/sections/001-section-cosmology-as-downstream-interface.tex","status_markers_as_written":[],"summary_excerpt":"This paper isolates the downstream cosmology interface of TFPT. Cosmology is not used as a primitive selector of the theory. It is read from the closed branch through seam transfer, determinant-line phase, scalaron sector, axion interface, reheating input, leptogenesis input, neutrino sector, CMB spectra, and conjectural sky-map realization targets.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3717,"byte_start":3404,"id":"section:8ee73443cb760ceae12f","kind":"section","labels":[],"line_end":93,"line_start":82,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/06_cosmology_interfaces_downstream_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--06_cosmology_interfaces_downstream_closure/sections/001-section-cosmology-as-downstream-interface.tex","status_markers_as_written":[],"summary_excerpt":"The closed branch is fixed before cosmology enters: [formula in source] This section should make the nonprimitive status of cosmology explicit.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Cosmology as Downstream Interface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4011,"byte_start":3717,"id":"section:6fb36890eae3b31ae8d5","kind":"section","labels":[],"line_end":104,"line_start":94,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/06_cosmology_interfaces_downstream_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--06_cosmology_interfaces_downstream_closure/sections/001-section-cosmology-as-downstream-interface.tex","status_markers_as_written":[],"summary_excerpt":"The seam-transfer expression is [formula in source] The text should state which part is theorem-level interface data and which part is an empirical comparison convention.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Seam Transfer and Infrared Determinant","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4322,"byte_start":4011,"id":"section:d0ca2a1debedf9301f14","kind":"section","labels":[],"line_end":117,"line_start":105,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/06_cosmology_interfaces_downstream_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--06_cosmology_interfaces_downstream_closure/sections/001-section-cosmology-as-downstream-interface.tex","status_markers_as_written":[],"summary_excerpt":"The axion sector is recorded as [formula in source] The axion interface belongs here because it depends on seam transfer and determinant-line phase, not on the primitive carrier proof.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Axion Interface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4586,"byte_start":4322,"id":"section:483b4d4658b6a3959f95","kind":"section","labels":[],"line_end":123,"line_start":118,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/06_cosmology_interfaces_downstream_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--06_cosmology_interfaces_downstream_closure/sections/001-section-cosmology-as-downstream-interface.tex","status_markers_as_written":[],"summary_excerpt":"Reheating and leptogenesis are stated as downstream inputs supplied by the closed branch. The paper should keep them status-coded and avoid turning the module into a hidden fit engine for later CMB targets.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reheating, Leptogenesis, and Neutrino Inputs","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4825,"byte_start":4586,"id":"section:d460ccf69df0e08ddf6a","kind":"section","labels":[],"line_end":129,"line_start":124,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/06_cosmology_interfaces_downstream_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--06_cosmology_interfaces_downstream_closure/sections/001-section-cosmology-as-downstream-interface.tex","status_markers_as_written":[],"summary_excerpt":"Stage 1 is the spectral target: transfer functions, angular spectra, and comparison rows. This stage may define falsification targets and benchmark rows, but it does not claim a unique sky-map realization.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"CMB Stage 1: Spectra","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5132,"byte_start":4825,"id":"section:f2fd860e7b6fc26700d5","kind":"section","labels":[],"line_end":135,"line_start":130,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/06_cosmology_interfaces_downstream_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--06_cosmology_interfaces_downstream_closure/sections/001-section-cosmology-as-downstream-interface.tex","status_markers_as_written":[],"summary_excerpt":"Stage 2 is a conjectural realization target. The source draft's distinction should remain explicit: a good CMB world is not automatically this CMB world. The map-realization layer therefore belongs in a programmatic or conditional section, not in the theorem stack.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"CMB Stage 2: Sky Realization","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5912,"byte_start":5132,"id":"section:f0e60a47149e6eefb905","kind":"section","labels":[],"line_end":152,"line_start":136,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/06_cosmology_interfaces_downstream_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--06_cosmology_interfaces_downstream_closure/sections/001-section-cosmology-as-downstream-interface.tex","status_markers_as_written":[],"summary_excerpt":"@p0.28 Y@ Module & Status in this paper \\\\ Stationary horizons and compact objects & Listed only as downstream programmatic obligations; technical material is in the Companion. \\\\ Code subspace, pointer dynamics, and record algebra & Not part of the cosmology-interface proof surface. \\\\ Transient event channels & Falsification and prediction semantics belong to the Companion. \\\\ Pole masses, Higgs readout, and full f","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Downstream Obligations Moved to the Companion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6848,"byte_start":5912,"id":"section:78dc731bfe3c36e77b3f","kind":"section","labels":[],"line_end":173,"line_start":153,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/06_cosmology_interfaces_downstream_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--06_cosmology_interfaces_downstream_closure/sections/001-section-cosmology-as-downstream-interface.tex","status_markers_as_written":[],"summary_excerpt":"This section contains the main technical development assigned to this paper by the TFPT 4.5 clean split. Cross-paper background is referenced through dependency and scope boxes; extended backend material is kept in the Technical Companion.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Main Technical Development","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7589,"byte_start":6848,"id":"section:7f8cc17f94ae4b0fb41a","kind":"section","labels":[],"line_end":191,"line_start":174,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/06_cosmology_interfaces_downstream_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--06_cosmology_interfaces_downstream_closure/sections/001-section-cosmology-as-downstream-interface.tex","status_markers_as_written":[],"summary_excerpt":"Use : Section 10 for FRW reduction, seam transfer, and scalaron branch. Sections 10.1 and 10.2 for falsification matrix and proof-obligation ledger. Appendix C.7, Appendix G, and the cosmology-interface proof material in Appendix J. Appendix N only for the axion-interface excerpt. Keep CMB Stage 1 and Stage 2 visibly separate.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Source Extraction Map","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7934,"byte_start":7589,"id":"section:2ae423d020a51a6197c7","kind":"section","labels":[],"line_end":201,"line_start":192,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/06_cosmology_interfaces_downstream_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--06_cosmology_interfaces_downstream_closure/sections/001-section-cosmology-as-downstream-interface.tex","status_markers_as_written":[],"summary_excerpt":"Carrier proofs, the full [formula in source] derivation, QFT closure proofs, Standard-Model packet proofs, and metrology proofs are not reproved or used as adjustable inputs in this paper. They enter only as fixed outputs of the earlier closed branch.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Not Used Here","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1599,"byte_start":0,"id":"section:a361b6ca86f19f4dd4d2","kind":"frontmatter","labels":[],"line_end":44,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/preamble.tex","status_markers_as_written":[],"summary_excerpt":"basicstyle= , backgroundcolor= tfptcodebg, frame=single, framerule=0.4pt, rulecolor= tfptblue!40, breaklines=true, showstringspaces=false, columns=fullflexible, xleftmargin=4pt, xrightmargin=4pt, aboveskip=6pt, belowskip=6pt,","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"tfptblue CMB Operational Closure and the\\\\ Planck Comparison Pipeline\\\\[0.35em] From the TFPT 4.6 Native Closure to a HEALPix Sky Realization,\\\\ the Lemma A–E Conjectures, Seven TFPT Bridge Theorems,\\\\ and the v4.6.8 Measurement Bridge Contract\\\\ (Five Artefact Validation Groups closing the Final Status Flip)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11304,"byte_start":0,"id":"section:6696018adf21f42f20da","kind":"frontmatter","labels":[],"line_end":226,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":["relation:712098e0c985c361814e","relation:cefe97b25fcab9ae5f81"],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/001-section-what-this-paper-does-and-does-not-do.tex","status_markers_as_written":[],"summary_excerpt":"This paper documents the v4.6 incarnation of the CMB operational closure between the TFPT 4.6 closed branch and the Planck PR3 component maps, including the v4.6.4 audit upgrade. We move beyond the v4.5 ``calibrated'' pipeline into a fully-strict, audit-disciplined comparison where every entry of the cosmological parameter vector [formula in source] is labelled derived_tfpt_candidate_v46 and traced back to one of fiv","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13672,"byte_start":11304,"id":"section:8a58c509d92464215d11","kind":"section","labels":["sec:what"],"line_end":277,"line_start":227,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":["relation:10aca2c7a51601c37443","relation:3ac0f2b12bc1ca8ef898"],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/001-section-what-this-paper-does-and-does-not-do.tex","status_markers_as_written":[],"summary_excerpt":"The downstream cosmology interface introduced in Paper 6 left two clean gaps for any honest CMB comparison: the seam-transfer determinant, the scalaron coefficient [formula in source] , and the leptogenesis Boltzmann were interfaces stated, not yet closed; Stage 2 — producing this sky — requires a boundary realisation operator [formula in source] whose existence was a programmatic target, not a theorem.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"What this paper does and does not do","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":473,"byte_start":0,"id":"section:c7d6c19cbd246f14fac2","kind":"section","labels":["sec:lemmas"],"line_end":15,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/002-section-the-five-lemmas-native-closure-conjecture-v4-6.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"The five lemmas: Native Closure Conjecture v4.6","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1631,"byte_start":473,"id":"section:79cfcc11c471d5bbf49d","kind":"paragraph","labels":["eq:lemmaA"],"line_end":38,"line_start":16,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/002-section-the-five-lemmas-native-closure-conjecture-v4-6.tex","status_markers_as_written":[],"summary_excerpt":"Proof skeleton. Read the determinant as a primitive admissible zeta determinant. The admissible trace [formula in source] admits a primitive-orbit decomposition; closed-branch selection plus [formula in source] plus [formula in source] leaves only the minimal seam class with multiplicity 2 (double sheet), area [formula in source] (primitive seam norm), and action [formula in source] (two oriented EM runs). The non-pr","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lemma A (Seam Determinant).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2581,"byte_start":1631,"id":"section:dfcd021c432501a11821","kind":"paragraph","labels":["eq:lemmaB"],"line_end":60,"line_start":39,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/002-section-the-five-lemmas-native-closure-conjecture-v4-6.tex","status_markers_as_written":[],"summary_excerpt":"Proof skeleton. Read [formula in source] as the inverse of the admissible curvature susceptibility [formula in source] in a constant-curvature family. The exponential is then a non-perturbative inverse-susceptibility effect, not a heat-kernel monomial.\\\\ Critical hook. Prove [formula in source] from the admissible path-integral structure.\\\\ Consequence. [formula in source] and the Starobinsky potential [formula in so","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lemma B (Curvature Residue).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3858,"byte_start":2581,"id":"section:c1704f9d83f0690b188c","kind":"paragraph","labels":["eq:lemmaC"],"line_end":89,"line_start":61,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/002-section-the-five-lemmas-native-closure-conjecture-v4-6.tex","status_markers_as_written":[],"summary_excerpt":"Four sub-claims, jointly: Proof skeletons. [formula in source] is a 4D radiation-density seam residue; [formula in source] is the QKE transport trace [formula in source] with three carrier families plus [formula in source] (weak-seam Ward) plus [formula in source] (EM holonomy); [formula in source] is the freeze-out occupancy [formula in source] with [formula in source] ; [formula in source] is the admissible line in","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lemma C (Thermal Transport).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4847,"byte_start":3858,"id":"section:87fc2b82b48a483e0d88","kind":"paragraph","labels":["eq:lemmaD"],"line_end":111,"line_start":90,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/002-section-the-five-lemmas-native-closure-conjecture-v4-6.tex","status_markers_as_written":[],"summary_excerpt":"Proof skeleton. [formula in source] is the antisymmetric two-form occupancy on [formula in source] ( [formula in source] since [formula in source] ); [formula in source] is the trace of the stable-neutral admissible projector times [formula in source] (quadratic seed intensity) and the flavour leakage [formula in source] ; [formula in source] is the Takagi trace of an admissible Majorana operator decomposed into orth","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lemma D (Matter Occupancy).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5957,"byte_start":4847,"id":"section:6322f7e4c6b01cc9fa93","kind":"paragraph","labels":["eq:lemmaE_alm","eq:lemmaE_phase"],"line_end":137,"line_start":112,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/002-section-the-five-lemmas-native-closure-conjecture-v4-6.tex","status_markers_as_written":[],"summary_excerpt":"where [formula in source] is the admissible primordial-curvature Hessian, [formula in source] is the primitive seam branch state with winding class [formula in source] , [formula in source] is the Calderon sheet involution (which enforces the reality constraint [formula in source] ), [formula in source] is the observer embedding (worldline + tetrad + orientation + last-scattering light cone), and [formula in source] ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lemma E (Branch Phase Selection).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8640,"byte_start":5957,"id":"section:0bf624212f6bc5ce352c","kind":"paragraph","labels":[],"line_end":195,"line_start":138,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/002-section-the-five-lemmas-native-closure-conjecture-v4-6.tex","status_markers_as_written":[],"summary_excerpt":"Stefan v4.6.3 review 6: Lemma E factors into five strictly weaker theorems, each carrying its own proof status. These are now formalised in tfpt_cmb.native_closure_v46.LEMMA_E_DECOMPOSITION and exposed by the Sprint-2A contract validator ( @p0.16 p0.36 Y@ ID & Statement & Status / hook \\\\ E1 Existence & [formula in source] is self-adjoint on [formula in source] with discrete bounded-below spectrum [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lemma E decomposition (E1–E5).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10286,"byte_start":8640,"id":"section:8301f1c88a5e5c8d3bef","kind":"section","labels":["sec:ledger"],"line_end":234,"line_start":196,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/002-section-the-five-lemmas-native-closure-conjecture-v4-6.tex","status_markers_as_written":[],"summary_excerpt":"@lll@ Symbol & Formula / origin & Numeric value \\\\ [formula in source] & [formula in source] & [formula in source] \\\\ [formula in source] & primitive seam winding class & [formula in source] \\\\ [formula in source] & [formula in source] & [formula in source] \\\\ [formula in source] & [formula in source] & [formula in source] \\\\ [formula in source] & [formula in source] & [formula in source] rad \\\\ [formula in source] &","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The TFPT primitives ledger and audit table","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10657,"byte_start":10286,"id":"section:6977d5718ecda58e5e57","kind":"paragraph","labels":[],"line_end":241,"line_start":235,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/002-section-the-five-lemmas-native-closure-conjecture-v4-6.tex","status_markers_as_written":[],"summary_excerpt":"The two [formula in source] values disagree at the [formula in source] relative level. The pipeline records this as an unresolved audit_mismatch and refuses to advertise any [formula in source] -dependent prediction without resolving which side — the formula or the text — is correct.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Audit flag.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13312,"byte_start":10657,"id":"section:81b85885d3610daba740","kind":"section","labels":["sec:cosmovec"],"line_end":281,"line_start":242,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/002-section-the-five-lemmas-native-closure-conjecture-v4-6.tex","status_markers_as_written":[],"summary_excerpt":"The full 26-parameter TFPTCosmology vector falls out of Lemmas A–D analytically. Computed values from output/native_closure_v46/cosmology_candidate.json (every field tagged derived_tfpt_candidate_v46, every formula sourced):","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The TFPT cosmology vector (Lemmas A–D outcome)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14010,"byte_start":13312,"id":"section:03d12a92284bdadf4dc5","kind":"paragraph","labels":[],"line_end":293,"line_start":282,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/002-section-the-five-lemmas-native-closure-conjecture-v4-6.tex","status_markers_as_written":[],"summary_excerpt":"This is a candidate 26-vector — not an extracted, fitted, or calibrated one. Each entry's provenance string in the JSON points at the lemma it descends from. No COBE, no FIRAS, no [formula in source] Standard-Model insertion, no [formula in source] BBN/CMB joint, no Planck [formula in source] . The agreement is the strongest single pre-test numerological consistency check TFPT has so far passed; it is not an out-of-s","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"What this is, what it isn't.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17158,"byte_start":14010,"id":"section:62b0b4d5c1d2440898ea","kind":"section","labels":["sec:closures"],"line_end":326,"line_start":294,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/002-section-the-five-lemmas-native-closure-conjecture-v4-6.tex","status_markers_as_written":[],"summary_excerpt":"The twelve closures [formula in source] survive verbatim; their status upgrades from operational_closure_v1 (v4.5) to derived_tfpt_candidate_v46 (v4.6) wherever the lemma chain backs them.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Operational closures, v4.6","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17442,"byte_start":17158,"id":"section:34aad1c1e9c631328569","kind":"paragraph","labels":[],"line_end":332,"line_start":327,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/002-section-the-five-lemmas-native-closure-conjecture-v4-6.tex","status_markers_as_written":[],"summary_excerpt":"The realisation operator [formula in source] of v4.5 becomes a concrete spectral construction in v4.6, see","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"New closure [formula in source] (Lemma E).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20079,"byte_start":17442,"id":"section:03ad70613846a3cdbeac","kind":"section","labels":["fig:Dl","sec:stage1"],"line_end":390,"line_start":333,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":["relation:6e078cb74ec4dc93ef88","relation:f8bdbc075097bf1b3d34"],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/002-section-the-five-lemmas-native-closure-conjecture-v4-6.tex","status_markers_as_written":[],"summary_excerpt":"The Stage-1 deliverable is the spectrum tuple [formula in source] computed by lensed CAMB with [formula in source] as input and the birefringence rotation [formula in source] applied analytically. The runner is tfpt_cmb.boltzmann.run_camb called from scripts/run_cmb_stage.py with –candidate-v46\\,–strict-map\\,–lens-potential-accuracy\\,4:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Stage 1: lensed CMB spectra","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":152,"byte_start":0,"id":"section:a464afa02abd563839ca","kind":"section","labels":["sec:stage2"],"line_end":4,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/003-section-stage-2-sky-realisation-four-modes-a-b-c-e.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Stage 2: sky realisation – four modes A, B, C, E","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":474,"byte_start":152,"id":"section:9c916ca64624edda84ff","kind":"paragraph","labels":[],"line_end":11,"line_start":5,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/003-section-stage-2-sky-realisation-four-modes-a-b-c-e.tex","status_markers_as_written":[],"summary_excerpt":"Sample [formula in source] coherently from the TFPT block-diagonal harmonic covariance and synthesise [formula in source] on HEALPix. This is one TFPT universe, not our universe. Run [formula in source] seeds and compare distribution-level statistics to Planck.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Mode A. Prediction.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":852,"byte_start":474,"id":"section:94e9d8a92bf20235ecc2","kind":"paragraph","labels":[],"line_end":19,"line_start":12,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/003-section-stage-2-sky-realisation-four-modes-a-b-c-e.tex","status_markers_as_written":[],"summary_excerpt":"Compute, in harmonic space, the Wiener filter [formula in source] with [formula in source] the TFPT spectrum, [formula in source] the Planck beam/mask operator, [formula in source] the Planck noise covariance, and [formula in source] the Planck map. The result is our sky reconstructed under the TFPT prior; not a prediction.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Mode B. Conditioned reconstruction.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1122,"byte_start":852,"id":"section:8ec724ed5a9debbfc84c","kind":"paragraph","labels":[],"line_end":25,"line_start":20,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/003-section-stage-2-sky-realisation-four-modes-a-b-c-e.tex","status_markers_as_written":[],"summary_excerpt":"Reuse Planck phases with TFPT amplitudes, [formula in source] . Diagnostic only; never reported as prediction.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Mode C. Phase-matched diagnostic.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1626,"byte_start":1122,"id":"section:8a13516d3c7282e5381d","kind":"paragraph","labels":["sec:modeE_def"],"line_end":35,"line_start":26,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/003-section-stage-2-sky-realisation-four-modes-a-b-c-e.tex","status_markers_as_written":[],"summary_excerpt":"The phases [formula in source] are constructed from [formula in source] via the canonical joint diagonalisation of the admissible primordial-curvature Hessian [formula in source] , with the spectral flag breaking degeneracies and the seam convention fixing the residual U(1). No Planck phase enters; no SMICA [formula in source] enters. See construction and acceptance results.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Mode E. Lemma-E branch phase selection (NEW in v4.6).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2793,"byte_start":1626,"id":"section:28b53a2ba4c1aa350abc","kind":"subsection","labels":["fig:mollweide","sec:final_maps"],"line_end":60,"line_start":36,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/003-section-stage-2-sky-realisation-four-modes-a-b-c-e.tex","status_markers_as_written":[],"summary_excerpt":"Figure SMICA, TFPT Mode A (random, lensed, [formula in source] ), TFPT Mode E (Lemma-E, candidate v4.6, [formula in source] ), and the Planck [formula in source] Mode-A residual.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Final maps: side-by-side","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3675,"byte_start":2793,"id":"section:06405cf37e3988baa942","kind":"subsection","labels":["fig:residhist"],"line_end":81,"line_start":61,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/003-section-stage-2-sky-realisation-four-modes-a-b-c-e.tex","status_markers_as_written":[],"summary_excerpt":"Figure distributes as [formula in source] with [formula in source] ; Mode E narrows to [formula in source] , a [formula in source] reduction relative to the same Mode-A run at the same [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Residual statistics","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3818,"byte_start":3675,"id":"section:f5c4c7fd82b05beae05a","kind":"section","labels":["sec:modeE"],"line_end":85,"line_start":82,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/003-section-stage-2-sky-realisation-four-modes-a-b-c-e.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Mode E in detail: Lemma E, candidate v4.6","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4321,"byte_start":3818,"id":"section:3cb85a1e3fb938d68d5d","kind":"subsection","labels":[],"line_end":101,"line_start":86,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/003-section-stage-2-sky-realisation-four-modes-a-b-c-e.tex","status_markers_as_written":[],"summary_excerpt":"The minimal native structure of Mode E (Stefan v4.6 brief 11) is i.e.\\ the admissible Hilbert space, the primordial-curvature Hessian, the primitive seam state, the Calderon involution, and the observer. Implementation: tfpt_cmb.branch_phase_selection.BranchOperatorBundle plus ObserverEmbedding.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Branch Operator Bundle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5384,"byte_start":4321,"id":"section:4427ed5d9336270018c6","kind":"subsection","labels":[],"line_end":124,"line_start":102,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/003-section-stage-2-sky-realisation-four-modes-a-b-c-e.tex","status_markers_as_written":[],"summary_excerpt":"In the absence of a real Sprint-2A boundary extraction, v4.6.3 ships a deterministic candidate bundle synthesised from the seven primitives: [formula in source] : Hermitian, eigenvalues [formula in source] on [formula in source] ; [formula in source] : seam-graded [formula in source] modulated by [formula in source] , normalised; [formula in source] : pairing involution [formula in source] ; spectral flag: c [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The candidate v4.6 bundle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6217,"byte_start":5384,"id":"section:100f0d23726b171e0ce3","kind":"subsection","labels":["fig:phij"],"line_end":144,"line_start":125,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/003-section-stage-2-sky-realisation-four-modes-a-b-c-e.tex","status_markers_as_written":[],"summary_excerpt":"Figure [formula in source] and the spectrum of [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Lemma-E phases","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6937,"byte_start":6217,"id":"section:eb52b201821685414080","kind":"subsection","labels":["fig:checks"],"line_end":162,"line_start":145,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/003-section-stage-2-sky-realisation-four-modes-a-b-c-e.tex","status_markers_as_written":[],"summary_excerpt":"Stefan v4.6 brief 10 lists nine acceptance checks Mode E must pass. Figure","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Acceptance checks","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7750,"byte_start":6937,"id":"section:5d13a1defc2c75194bab","kind":"subsection","labels":[],"line_end":177,"line_start":163,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/003-section-stage-2-sky-realisation-four-modes-a-b-c-e.tex","status_markers_as_written":[],"summary_excerpt":"The Mode-E residual RMS is [formula in source] , i.e.\\ [formula in source] below the Mode-A RMS [formula in source] at the same [formula in source] . We do not interpret this as evidence for Lemma E. In the candidate construction, the Lemma-E phases happen to inherit a deterministic structure that is not aligned with the Planck realisation by construction — the bundle is not extracted from the boundary data. The 13\\,","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The 13\\,\\% RMS reduction","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8920,"byte_start":7750,"id":"section:92b69d029df686a3d17e","kind":"section","labels":["sec:birefringence"],"line_end":199,"line_start":178,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/003-section-stage-2-sky-realisation-four-modes-a-b-c-e.tex","status_markers_as_written":[],"summary_excerpt":"The TFPT prediction [formula in source] sits well inside the Eskilt et al.\\ 2022 measurement [formula in source] and is consistent with the cosmological birefringence reported by recent re-analyses. The pipeline's own EB estimator on the SMICA component map yields [formula in source] — a factor [formula in source] smaller than the TFPT prediction.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Birefringence: TFPT vs Planck EB diagnostic","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10175,"byte_start":8920,"id":"section:63de841c254efaf3181e","kind":"section","labels":["sec:metrics"],"line_end":223,"line_start":200,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/003-section-stage-2-sky-realisation-four-modes-a-b-c-e.tex","status_markers_as_written":[],"summary_excerpt":"@p0.27 p0.16 p0.16 Y@ Quantity & TFPT v4.6.3 & Planck & Comment \\\\ [formula in source] & 6\\,546 & 6\\,202 & 5.6\\,\\% high; tracks [formula in source] excess. \\\\ [formula in source] & 0.722 & 0.758 & SMICA anafast \\\\ [formula in source] proxy (RMS T) & 44.85 & 42.21 & 6\\,\\% high \\\\ Cold-spot min. ( [formula in source] )& [formula in source] & [formula in source] & 5\\,\\% \\\\ Cold-spot max. ( [formula in source] )& [formul","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Comparison metrics and audit ledger","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10618,"byte_start":10175,"id":"section:3f6ab657a0e87ec1721f","kind":"paragraph","labels":[],"line_end":232,"line_start":224,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/003-section-stage-2-sky-realisation-four-modes-a-b-c-e.tex","status_markers_as_written":[],"summary_excerpt":"A diagonal-Gaussian [formula in source] using the Knox formula [formula in source] , binned in 25 logarithmic bins between [formula in source] and [formula in source] , broken out for TT, TE, EE, BB. TT diagnostic only; TE/EE/BB/TB/EB are explicitly tagged diagnostic only per v4.5 rules R [formula in source] and R [formula in source] , and the Knox numbers there are foreground/noise-dominated.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spectrum-shape [formula in source] .","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11071,"byte_start":10618,"id":"section:6855c6fbbe7a7d13c4de","kind":"paragraph","labels":[],"line_end":240,"line_start":233,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/003-section-stage-2-sky-realisation-four-modes-a-b-c-e.tex","status_markers_as_written":[],"summary_excerpt":"For each Mode-A seed we compute six summary statistics — [formula in source] , peak [formula in source] , [formula in source] -smoothed RMS, cold-spot extreme values, skewness, kurtosis — and ask where the Planck value falls in the TFPT distribution. Code: tfpt_cmb.compare.sky_statistics and planck_in_TFPT_distribution.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Realisation distribution.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12580,"byte_start":11071,"id":"section:2cd765c07ea2ebf520fd","kind":"section","labels":["sec:pipeline"],"line_end":280,"line_start":241,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":["relation:abd20e70464b39bbcc7c","relation:ec501f3a0fe4c119f793"],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/003-section-stage-2-sky-realisation-four-modes-a-b-c-e.tex","status_markers_as_written":[],"summary_excerpt":"The pipeline is implemented in tfpt_cmb with 358 passing tests; the v4.6.3 end-to-end run is reproduced by: cd full-plank/theory-work","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Pipeline","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13159,"byte_start":12580,"id":"section:251779a935bf6cfe780c","kind":"section","labels":["sec:sprint2a"],"line_end":292,"line_start":281,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/003-section-stage-2-sky-realisation-four-modes-a-b-c-e.tex","status_markers_as_written":[],"summary_excerpt":"Stefan's v4.6.3 review converges on a single sharp statement: the code is no longer the bottleneck; the data side and the proof side are. The next sensible step is therefore neither another plot nor another module — it is a formal, executable Branch Extraction Contract that any future Sprint-2A run must satisfy. This section defines that contract and reports what the v4.6.3 candidate bundle scores against it.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Sprint 2A Branch Extraction Contract","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14928,"byte_start":13159,"id":"section:ba4d7ea88722968045bc","kind":"subsection","labels":[],"line_end":336,"line_start":293,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/003-section-stage-2-sky-realisation-four-modes-a-b-c-e.tex","status_markers_as_written":[],"summary_excerpt":"Sprint 2A Branch Extraction Contract\\\\ Input. closed TFPT branch operators.\\\\ Output. [formula in source] \\,( npz), [formula in source] \\,( npz), [formula in source] \\,( npz), spectral_flag\\,( json+ npz), observer_embedding\\,( json), [formula in source] -grid\\,( npz), direction grid\\,( npz), shell-power validation\\,( json), branch origin\\,( json).\\\\ Hard checks. (1) [formula in source] Hermitian; (2) [formula in sour","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Contract specification","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16799,"byte_start":14928,"id":"section:60bce3ca3086efbef633","kind":"subsection","labels":[],"line_end":375,"line_start":337,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":["relation:1677a5b2255ce693d46b","relation:b0e769045618c216446f"],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/003-section-stage-2-sky-realisation-four-modes-a-b-c-e.tex","status_markers_as_written":[],"summary_excerpt":"We dump the candidate v4.6 synthetic bundle and run it through the validator: The result is exactly the audit Stefan asked for: [formula in source] hard checks pass; the six that fail are the v4.6.3 audit gap and they are the gap by design:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The candidate v4.6 bundle vs the contract","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1054,"byte_start":0,"id":"section:eb84aeaa1838454626cd","kind":"subsection","labels":[],"line_end":22,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/004-subsection-what-a-passing-sprint-2a-run-looks-like.tex","status_markers_as_written":[],"summary_excerpt":"The contract is not vapor. We additionally ship a hand-built compliant test bundle that PASSES every hard check (see tests/test_v464_sprint2a_contract.py::TestCompliantBundlePasses). The compliant bundle uses [formula in source] (real scalar so that [formula in source] holds trivially), an anti-diagonal Calderon involution, a uniform real [formula in source] with [formula in source] , a single canonical flag operator","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"What a passing Sprint 2A run looks like","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1164,"byte_start":1054,"id":"section:14e63f26725e17909913","kind":"subsection","labels":[],"line_end":26,"line_start":23,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/004-subsection-what-a-passing-sprint-2a-run-looks-like.tex","status_markers_as_written":[],"summary_excerpt":"The roadmap collapses to two engineering items and five theorem items:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The sole remaining work","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1516,"byte_start":1164,"id":"section:9b59602e5bee6ec454f7","kind":"paragraph","labels":[],"line_end":35,"line_start":27,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/004-subsection-what-a-passing-sprint-2a-run-looks-like.tex","status_markers_as_written":[],"summary_excerpt":"Sprint 2A boundary extraction yielding the seven contract files with [formula in source] and the canonical spectral flag (no Haar rotation). A real observer embedding: tetrad, [formula in source] , parity from a TFPT branch position computation.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Engineering.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1659,"byte_start":1516,"id":"section:145bd876aec2e3bc98fe","kind":"paragraph","labels":[],"line_end":39,"line_start":36,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/004-subsection-what-a-passing-sprint-2a-run-looks-like.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Theorems.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2434,"byte_start":1659,"id":"section:84e9714e24dfe155ac39","kind":"section","labels":["sec:discharge"],"line_end":55,"line_start":40,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/004-subsection-what-a-passing-sprint-2a-run-looks-like.tex","status_markers_as_written":[],"summary_excerpt":"Stefan's v4.6.5 review delivered an uncomfortable but accurate verdict: the proposed_solution fields of v4.6.5 were sketches, not discharges. v4.6.6 closes that gap. This section formalises the discharge of all 14 hooks: the full proof body, the boxed final form, the discharge taxonomy, the closure condition, and the new theorem (or data artifact) required to flip each hook to discharged.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The v4.6.6 Proof Discharge Package","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4633,"byte_start":2434,"id":"section:b983c04974ce44edef90","kind":"subsection","labels":[],"line_end":100,"line_start":56,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/004-subsection-what-a-passing-sprint-2a-run-looks-like.tex","status_markers_as_written":[],"summary_excerpt":"Every hook is tagged with one of 12 status classes. The taxonomy distinguishes convention adoption (no theorem needed) from theorem proof (paper-side work) from data extraction (engineering work) from numerical verification. This is the sharpening Stefan demanded:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Discharge taxonomy","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6363,"byte_start":4633,"id":"section:6b4819f05f57f2198a67","kind":"subsection","labels":[],"line_end":133,"line_start":101,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/004-subsection-what-a-passing-sprint-2a-run-looks-like.tex","status_markers_as_written":[],"summary_excerpt":"The seven steps are sequenced in tfpt_cmb.proof_discharge_v466.ROADMAP_V466. When all seven complete, every status flag in the pipeline flips from derived_tfpt_candidate_v46 to derived_tfpt without further code changes.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Critical-path roadmap (7 steps)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8461,"byte_start":6363,"id":"section:1d0c4c12c2eceefe20c8","kind":"subsection","labels":[],"line_end":176,"line_start":134,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/004-subsection-what-a-passing-sprint-2a-run-looks-like.tex","status_markers_as_written":[],"summary_excerpt":"The pipeline's flip predicate is tfpt_cmb.proof_discharge_v466.can_flip_to_derived_tfpt. It accepts the status flip iff the dictionary of discharge outcomes matches the 14 entries of REQUIRED_DISCHARGE_OUTCOMES, which are:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The single acceptance gate","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8980,"byte_start":8461,"id":"section:e5339d506f942a04e145","kind":"section","labels":["sec:closure467"],"line_end":187,"line_start":177,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/004-subsection-what-a-passing-sprint-2a-run-looks-like.tex","status_markers_as_written":[],"summary_excerpt":"Stefan's v4.6.6 review delivered the final acceptance test: theory-intern kann ich die verbleibenden Probleme schliessen, indem wir die fehlenden Brueckensaetze explizit als TFPT Theoreme formulieren und beweisen. v4.6.7 does this. Seven TFPT bridge theorems close all 14 hooks theory-internally; what remains is artefact validation, not theory.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The v4.6.7 Final Closure Proposal: Seven Bridge Theorems","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10692,"byte_start":8980,"id":"section:e1bc09da209713d5800c","kind":"subsection","labels":[],"line_end":226,"line_start":188,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/004-subsection-what-a-passing-sprint-2a-run-looks-like.tex","status_markers_as_written":[],"summary_excerpt":"The authoritative source is tfpt_cmb.closure_v467; this section is the human-readable summary. Each theorem is given by its ID, statement (verbatim), boxed final form, and the hooks it closes.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The seven bridge theorems","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11045,"byte_start":10692,"id":"section:6c98d3366398750777cf","kind":"paragraph","labels":[],"line_end":233,"line_start":227,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/004-subsection-what-a-passing-sprint-2a-run-looks-like.tex","status_markers_as_written":[],"summary_excerpt":"TFPT defines the physical vacuum-density determinant as the primitive admissible zeta determinant. Non-primitive admissible repetitions are not physical TFPT vacuum classes. This is a clean physical choice (the same role as the Selberg primitive-orbit decomposition on closed Riemannian manifolds), not a trick.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"BT1 (closes A.h1).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11486,"byte_start":11045,"id":"section:ec7f7040414e02e11d3b","kind":"paragraph","labels":[],"line_end":241,"line_start":234,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/004-subsection-what-a-passing-sprint-2a-run-looks-like.tex","status_markers_as_written":[],"summary_excerpt":"[formula in source] has a unique primitive curvature instanton with action [formula in source] and zero-mode norm [formula in source] ; saddle-point gives [formula in source] and inverting yields [formula in source] . Structurally analogous to Yang-Mills, BCS-gap, and Coleman-de\\,Luccia. Closes the inflation block [formula in source] without COBE.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"BT2 (closes B.h1).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11885,"byte_start":11486,"id":"section:739700c6043ccb8a3777","kind":"paragraph","labels":[],"line_end":248,"line_start":242,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/004-subsection-what-a-passing-sprint-2a-run-looks-like.tex","status_markers_as_written":[],"summary_excerpt":"Combines the dimensional radiation residue [formula in source] with the bosonic phase-space norm [formula in source] (giving [formula in source] ) and the QKE transport-trace decomposition with two Ward residues [formula in source] (weak seam) and [formula in source] (EM holonomy). The Stefan-Boltzmann inversion [formula in source] closes the metrology loop.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"BT3 (closes C1.h1, C2.h1).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12237,"byte_start":11885,"id":"section:7e1d43abe62c09825f7b","kind":"paragraph","labels":[],"line_end":255,"line_start":249,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/004-subsection-what-a-passing-sprint-2a-run-looks-like.tex","status_markers_as_written":[],"summary_excerpt":"The TFPT EM holonomy [formula in source] deforms the weak rate uniformly: [formula in source] . Linear freeze-out sensitivity [formula in source] gives [formula in source] and [formula in source] up to [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"BT4 (closes C3.h1).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13270,"byte_start":12237,"id":"section:0397745bedb9c017bcf7","kind":"paragraph","labels":[],"line_end":277,"line_start":256,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/004-subsection-what-a-passing-sprint-2a-run-looks-like.tex","status_markers_as_written":[],"summary_excerpt":"This is Stefan's main astrophysical achievement. Three sub-theorems combined collapse the line integral to two retained-state expectation values: C4a (Press-Schechter Source): [formula in source] with [formula in source] from [formula in source] (Lemma D2). C4b (Carrier IMF Photon Yield): [formula in source] . C4c (Admissible UV Escape): [formula in source] . The non-trivial content is not the integral arithmetic — t","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"BT5 (closes C4.h1, with sub-theorems C4a, C4b, C4c).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13700,"byte_start":13270,"id":"section:cd0e1d5ac876ac20c6d5","kind":"paragraph","labels":[],"line_end":286,"line_start":278,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/004-subsection-what-a-passing-sprint-2a-run-looks-like.tex","status_markers_as_written":[],"summary_excerpt":"Three claims unified: the carrier two-form trace [formula in source] ; the stable neutral completeness [formula in source] (with the leakage [formula in source] ); and the mass-metrology bridge [formula in source] that fixes the dimensionless Takagi trace as the eV unit.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"BT6 (closes D1.h1, D2.h1, D3.h1).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14129,"byte_start":13700,"id":"section:5dfa4e56e9be9f4f26b8","kind":"paragraph","labels":[],"line_end":294,"line_start":287,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/004-subsection-what-a-passing-sprint-2a-run-looks-like.tex","status_markers_as_written":[],"summary_excerpt":"The canonical branch phase theorem unifies the five E sub-theorems: existence ( [formula in source] self-adjoint on [formula in source] ), abelian flag algebra ( [formula in source] ), seam-state uniqueness, Calderon reality, and observer embedding [formula in source] for v5.0.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"BT7 (closes E1.h1–E5.h1).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15620,"byte_start":14129,"id":"section:bee5aa770bbee31451e0","kind":"subsection","labels":[],"line_end":327,"line_start":295,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/004-subsection-what-a-passing-sprint-2a-run-looks-like.tex","status_markers_as_written":[],"summary_excerpt":"@lll@ Hook & Bridge theorem & v4.6.7 outcome \\\\ A.h1 & BT1 & resolved_by_primitive_zeta_convention \\\\ B.h1 & BT2 & resolved_by_curvature_instanton_theorem \\\\ C1.h1 & BT3 & resolved_by_thermal_metrology \\\\ C2.h1 & BT3 & resolved_by_qke_ward_theorem \\\\ C3.h1 & BT4 & resolved_by_bbn_holonomy_sensitivity \\\\ C4.h1 & BT5 & resolved_by_reionization_transport_collapse \\\\ D1.h1 & BT6 & resolved_by_carrier_two_form_metrology \\","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The final hook resolution table","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16287,"byte_start":15620,"id":"section:5a933c86dc641fb7505f","kind":"subsection","labels":[],"line_end":348,"line_start":328,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/004-subsection-what-a-passing-sprint-2a-run-looks-like.tex","status_markers_as_written":[],"summary_excerpt":"@p0.32 Y@ Status & Meaning \\\\ derived_tfpt_candidate_v46 & v4.6 candidate; Lemmas A–E proposed, none discharged. \\\\ derived_tfpt_theory_complete_ pending_artifacts \\,( NEW v4.6.7) & All 14 hooks resolved theory-internally by 7 bridge theorems. Pending: artefact validation. \\\\ derived_tfpt & All artefact validations also passed. The pipeline becomes TFPT-derived in the strict sense. \\\\","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Status taxonomy after v4.6.7","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17775,"byte_start":16287,"id":"section:0420b633b1c0359383d9","kind":"subsection","labels":[],"line_end":380,"line_start":349,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/004-subsection-what-a-passing-sprint-2a-run-looks-like.tex","status_markers_as_written":[],"summary_excerpt":"ARTEFACT_VALIDATION_REQUIREMENTS contains five groups; each must independently pass for the final flip to derived_tfpt:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The five remaining artefact validation groups","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":415,"byte_start":0,"id":"section:ae5f315889777a358dc1","kind":"section","labels":["sec:measurement468"],"line_end":10,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/005-section-the-v4-6-8-measurement-bridge-contract.tex","status_markers_as_written":[],"summary_excerpt":"The v4.6.7 final closure proposal made the theory side complete; what remains is exactly five artefact-validation groups. v4.6.8 ships those five groups as an executable contract ( tfpt_cmb.measurement_bridge_v468) with a deterministic acceptance gate.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The v4.6.8 Measurement Bridge Contract","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1979,"byte_start":415,"id":"section:3241a199c704e798fada","kind":"subsection","labels":[],"line_end":49,"line_start":11,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/005-section-the-v4-6-8-measurement-bridge-contract.tex","status_markers_as_written":[],"summary_excerpt":"@p0.06 p0.18 p0.27 Y@ ID & Group & Acceptance criterion & Closes (artefact) \\\\ G1 & sprint_2a_branch_bundle (12 files) & [formula in source] AND 24/24 hard checks of sprint2a_contract.validate_sprint2a_branch pass. & E1, E2, E3, E4, E5 \\\\ G2 & sprint_2c_thermal_matter (7 files) & QKE Ward residues [formula in source] , [formula in source] numerically verified to [formula in source] ; BBN [formula in source] to [formu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The five validation groups","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3139,"byte_start":1979,"id":"section:046a88b0c9e3eb83133c","kind":"subsection","labels":[],"line_end":73,"line_start":50,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/005-section-the-v4-6-8-measurement-bridge-contract.tex","status_markers_as_written":[],"summary_excerpt":"ll File & Purpose \\\\ branch_metadata.json & metadata, must declare [formula in source] \\\\ B_sigma_adm.npz & boundary Dirac/seam operator \\\\ P_adm.npz & admissible projector [formula in source] \\\\ P_C.npz & Calderon polarisation projector \\\\ iota_C_adm.npz & Calderon sheet involution \\\\ Delta_prim_adm.npz & primitive Laplacian \\\\ Q_top_adm.npz & topological phase generator \\\\ K_zeta_adm.npz & primordial-curvature Hess","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The 12 G1 files","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3526,"byte_start":3139,"id":"section:e8ee4ba1723c19ce8c91","kind":"subsection","labels":[],"line_end":82,"line_start":74,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/005-section-the-v4-6-8-measurement-bridge-contract.tex","status_markers_as_written":[],"summary_excerpt":"Every group refuses any artefact whose filename matches planck_phase, planck_alm, *_phase (SMICA/NILC/SEVEM/Commander), haar_random_seed, or synthetic_v46. The contract is strict: even a single forbidden filename in a group's sub-tree fails that group, regardless of the numerical-check results.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Forbidden inputs","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4216,"byte_start":3526,"id":"section:815f55d708b4e3c4aaa9","kind":"subsection","labels":[],"line_end":101,"line_start":83,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/005-section-the-v4-6-8-measurement-bridge-contract.tex","status_markers_as_written":[],"summary_excerpt":"# Emit a documented skeleton tree (5 sub-directories with READMEs): python3 scripts/validate_measurement_bridge.py \\ –emit-skeleton input/measurement_bridge_v5","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Skeleton emitter and CLI","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4754,"byte_start":4216,"id":"section:d197cb32bfa6bafea7d5","kind":"subsection","labels":[],"line_end":118,"line_start":102,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/005-section-the-v4-6-8-measurement-bridge-contract.tex","status_markers_as_written":[],"summary_excerpt":"from tfpt_cmb.measurement_bridge_v468 import ( validate_measurement_bridge, can_flip_to_derived_tfpt, )","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The acceptance gate","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5962,"byte_start":4754,"id":"section:5ea787690e28cf9b9e50","kind":"subsection","labels":[],"line_end":148,"line_start":119,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/005-section-the-v4-6-8-measurement-bridge-contract.tex","status_markers_as_written":[],"summary_excerpt":"@p0.36 lY@ Status & Cycle & What flips \\\\ derived_tfpt_candidate_v46 & v4.6 & Initial candidate; lemmas A–E proposed, none discharged. \\\\ derived_tfpt_theory_complete_ pending_artifacts & v4.6.7 & can_flip_to_theory_complete(REQUIRED_DISCHARGE_OUTCOMES_V467) returns True. All 14 hooks resolved by 7 bridge theorems. \\\\ derived_tfpt & v4.6.8 (final) & can_flip_to_derived_tfpt(report) returns True. All 5 measurement-bri","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The complete status flow","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8249,"byte_start":5962,"id":"section:3404c2bf78c363ac3a22","kind":"section","labels":["sec:kills"],"line_end":178,"line_start":149,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":["relation:56fdee02a711ad74742e","relation:b9d898538d99993b4682"],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/005-section-the-v4-6-8-measurement-bridge-contract.tex","status_markers_as_written":[],"summary_excerpt":"@p0.26 Y@ Module & Kill condition \\\\ ledger & [formula in source] audit mismatch unresolved when used in production. \\\\ native_closure_v46 & Any of the seven primitives violated; any of Lemmas A–D falsified. \\\\ branch_phase_selection & [formula in source] not Hermitian; [formula in source] not an involution; any input matching planck_phase, planck_alm, smica_alm_as_phase_seed, nilc_phase, sevem_phase, commander_phase","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kill conditions and audit table","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10207,"byte_start":8249,"id":"section:157a7c50b2b0c5f60c40","kind":"section","labels":["sec:nonclaims"],"line_end":214,"line_start":179,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/005-section-the-v4-6-8-measurement-bridge-contract.tex","status_markers_as_written":[],"summary_excerpt":"No theorem-level lemmas. Lemmas A–E are conjectures with proof skeletons ( at TFPT v4.6. The pipeline runs in candidate mode only. No real Mode-E branch. The Mode-E run uses the candidate v4.6 synthetic bundle, not a real Sprint-2A extraction of [formula in source] , [formula in source] , [formula in source] from the boundary data. Real Mode E is a Sprint 2A–2D deliverable. No claim of pixel-level Planck agreement. M","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"What this pipeline does not claim","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11840,"byte_start":10207,"id":"section:9400f87be0e5ce310646","kind":"section","labels":["sec:roadmap"],"line_end":247,"line_start":215,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/005-section-the-v4-6-8-measurement-bridge-contract.tex","status_markers_as_written":[],"summary_excerpt":"The five outstanding theorem-level closures are Lemma A (Seam Determinant): rigorous definition of [formula in source] and proof that non-primitive admissible repetitions vanish. Lemma B (Curvature Residue): proof of [formula in source] from the admissible curvature path-integral. Lemma C: subdivide into C1–C4; C4 ( [formula in source] ) is the weakest link — needs SFR/ [formula in source] / [formula in source] to co","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Roadmap to a finished v5.0","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13911,"byte_start":11840,"id":"section:044bb626b205fc4a44dc","kind":"paragraph","labels":[],"line_end":290,"line_start":248,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/005-section-the-v4-6-8-measurement-bridge-contract.tex","status_markers_as_written":[],"summary_excerpt":"Even before the proofs land, the following are testable predictions of v4.6 and would either falsify the conjecture or sharpen the agreement: BAO scale (DESI Y3, eBOSS) at 0.5\\% precision; CMB lensing power spectrum (Planck PR4, ACT DR6, SPT-3G); [formula in source] tension (KiDS, DES, Euclid); Deuterium primordial abundance (high-resolution QSO absorption); Effective neutrino number from BBN (independent of CMB); Di","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Out-of-sample tests.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14614,"byte_start":13911,"id":"section:49689ab702d7c648da00","kind":"section","labels":["sec:v412"],"line_end":303,"line_start":291,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":["relation:2eb0782377e1441a8021","relation:d56c7c55820621aa42b4"],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/005-section-the-v4-6-8-measurement-bridge-contract.tex","status_markers_as_written":[],"summary_excerpt":"The v4.6 cycle delivered the candidate closure with five lemmas A–E and a 14-hook proof discharge. The next two sprints (v4.7, v4.8) narrowed the geometry to the Lens space [formula in source] on the spectral-action corridor, and v4.9's Fisher residual decomposition pinpointed the remaining [formula in source] gap to two parameters: [formula in source] and [formula in source] . Sprints v4.10–v4.12 closed this gap ope","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"v4.10–v4.12: Operator-Discharged Closure and the Planck Pass","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15978,"byte_start":14614,"id":"section:221d6c10c287d5eeeba5","kind":"subsection","labels":["fig:v412_sprint_history","sec:v412_history"],"line_end":332,"line_start":304,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/005-section-the-v4-6-8-measurement-bridge-contract.tex","status_markers_as_written":[],"summary_excerpt":"Figure [formula in source] value vs Planck 2018 [formula in source] CDM across all sprints between v4.6 and v4.12. The strict TFPT mode never refits parameters and always uses A_planck = 1.0 on the official Plik-lite native + lowl TT/EE likelihood (Cobaya). The drop from v4.9 ( [formula in source] ) to v4.10/v4.11/v4.12 ( [formula in source] / [formula in source] / [formula in source] ) is not a fit improvement — it ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Sprint history v4.6 [formula in source] v4.12","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18061,"byte_start":15978,"id":"section:7e72342b4f2a94622431","kind":"subsection","labels":["eq:ward_identity","sec:v412_ward"],"line_end":395,"line_start":333,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/005-section-the-v4-6-8-measurement-bridge-contract.tex","status_markers_as_written":[],"summary_excerpt":"Stefan v4.11 brief Section 3 introduced the central new theorem:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The visibility-amplitude Ward identity (v4.11)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1623,"byte_start":0,"id":"section:3e3fe5ac61532cf9aea4","kind":"subsection","labels":["sec:v412_bt2_discharge"],"line_end":36,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/006-subsection-the-bt2-operator-discharge-v4-11.tex","status_markers_as_written":[],"summary_excerpt":"Stefan v4.11 brief Section 4 demanded that the BT2 magnitude correction be derived from the full operator apparatus on the seam:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The BT2 operator discharge (v4.11)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2693,"byte_start":1623,"id":"section:fdc1169c1849c07bed49","kind":"subsection","labels":["sec:v412_provenance"],"line_end":63,"line_start":37,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/006-subsection-the-bt2-operator-discharge-v4-11.tex","status_markers_as_written":[],"summary_excerpt":"The numerical leakage scanner was replaced by a Provenance DAG that records, for every sensitive parameter, its full operator chain back to the seven primitives. Stefan v4.11 brief Section 5:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Provenance DAG (v4.11)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4688,"byte_start":2693,"id":"section:6e028adb7eddef8c968c","kind":"subsection","labels":["sec:v412_qcd"],"line_end":114,"line_start":64,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/006-subsection-the-bt2-operator-discharge-v4-11.tex","status_markers_as_written":[],"summary_excerpt":"Stefan v4.12 brief Section 5 demanded the same operator treatment for the baryonic weighted trace [formula in source] , with three required artefacts ( qcd_free_energy_tfpt.npz, bse_kernel_tfpt.npz, baryon_mass_operator_tfpt.npz) and the explicit prohibition of the doubled-occupancy form [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The QCD baryon-binding operator discharge (v4.12)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5397,"byte_start":4688,"id":"section:ba8e230280366555e124","kind":"subsection","labels":["fig:v412_gate","sec:v412_gate"],"line_end":134,"line_start":115,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/006-subsection-the-bt2-operator-discharge-v4-11.tex","status_markers_as_written":[],"summary_excerpt":"Combining the v4.11 BT2 / Ward / Provenance results with the v4.12 QCD discharge gives twelve final-gate checks that all pass:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The v4.12 final-gate matrix","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8416,"byte_start":5397,"id":"section:ff09d3c77e55a0457bbf","kind":"subsection","labels":["fig:v412_TT","fig:v412_mollweide","fig:v412_polspec","fig:v412_residual","sec:v412_camb"],"line_end":204,"line_start":135,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/006-subsection-the-bt2-operator-discharge-v4-11.tex","status_markers_as_written":[],"summary_excerpt":"The canonical v4.12 cosmology was emitted into a Boltzmann-runner JSON via scripts/build_v412_cosmology_json.py with all parameters tagged derived_tfpt_one_loop_v412 and the TFPT-native meta block recording [formula in source] , [formula in source] , [formula in source] , the BT2 / QCD operator-discharge flags, and the forbidden_form_excluded guard. CAMB at [formula in source] and lens-potential accuracy 2 yields [fo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Regenerated CAMB spectra and Mollweide comparison","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8496,"byte_start":8416,"id":"section:876ece3d3d9fbe51e28c","kind":"subsection","labels":["sec:v412_closure"],"line_end":207,"line_start":205,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/006-subsection-the-bt2-operator-discharge-v4-11.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"What is now closed and what remains open","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9407,"byte_start":8496,"id":"section:76589e951748a912ddaa","kind":"paragraph","labels":[],"line_end":227,"line_start":208,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/006-subsection-the-bt2-operator-discharge-v4-11.tex","status_markers_as_written":[],"summary_excerpt":"Every block of the CMB chain is now derived from native TFPT primitives via an explicit operator route: Inflation block: Lemma B [formula in source] + Starobinsky slow-roll at [formula in source] . Curvature stiffness: [formula in source] with [formula in source] operator-discharged on Lens [formula in source] . Cosmological constant: Lemma A. Recombination/Reionisation: Lemma C with [formula in source] (FROZEN at v4","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Operatorically discharged.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10112,"byte_start":9407,"id":"section:077d180c67f187c9d069","kind":"paragraph","labels":[],"line_end":242,"line_start":228,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/006-subsection-the-bt2-operator-discharge-v4-11.tex","status_markers_as_written":[],"summary_excerpt":"Stefan v4.12 brief Section 7 explicitly marks these as optional, NOT CMB-block blockers: Higher-order Spectral-Action coefficients [formula in source] could shift [formula in source] at [formula in source] — below any conceivable Planck sensitivity. Formal QFT proof of the [formula in source] residual in the visibility Ward identity (currently verified numerically: residual [formula in source] ). Multi-channel BSE (o","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Open items beyond v4.12.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10808,"byte_start":10112,"id":"section:aed5cc537ef538cebcce","kind":"paragraph","labels":[],"line_end":255,"line_start":243,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/006-subsection-the-bt2-operator-discharge-v4-11.tex","status_markers_as_written":[],"summary_excerpt":"The v4.12 closure is CMB-sector complete. Stefan's strict gate [formula in source] is passed with [formula in source] on the canonical curvature-gauge variant, with A_planck=1.0, no parameter refit, no Planck targets, no lattice-QCD targets, and an explicit Provenance DAG demonstrating that the apparent agreement with the Planck [formula in source] / [formula in source] values is emergent, not engineered. Items beyon","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Honest bound.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1166,"byte_start":0,"id":"section:4e5e7d0df9eb586da6b1","kind":"section","labels":["app:hooks"],"line_end":32,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/007-section-hook-solution-sketches-v4-6-5.tex","status_markers_as_written":[],"summary_excerpt":"This appendix is the v4.6.5 deliverable Stefan asked for in the v4.6.4 review: a full 1:1 transcription of every proof structure from full-plank/beschreibung.txt, plus a best-effort proposed solution for each of the [formula in source] open hooks. The authoritative machine-readable form is in tfpt_cmb.lemma_proof_outlines; this appendix gives the human-readable summary.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Hook Solution Sketches (v4.6.5)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1892,"byte_start":1166,"id":"section:3e04e51ccb89918e62d8","kind":"paragraph","labels":[],"line_end":46,"line_start":33,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/007-section-hook-solution-sketches-v4-6-5.tex","status_markers_as_written":[],"summary_excerpt":"Hook. TFPT must canonically identify [formula in source] , or prove that non-primitive admissible repetitions vanish.\\\\ Proposed solution. Adopt the primitive zeta determinant convention. The non-primitive contributions are bounded by [formula in source] in Planck units, 240 orders below any physical observable. The convention is mathematically consistent with Selberg-type primitive-orbit decompositions: the regulari","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lemma A.h1 (medium).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2692,"byte_start":1892,"id":"section:a95e9e8c90c77d844a96","kind":"paragraph","labels":[],"line_end":62,"line_start":47,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/007-section-hook-solution-sketches-v4-6-5.tex","status_markers_as_written":[],"summary_excerpt":"Hook. Prove [formula in source] from the admissible curvature path integral.\\\\ Proposed solution. The exponential is the signature of a non-perturbative instanton-class contribution. The admissible curvature path integral admits a tunneling configuration with Euclidean action [formula in source] . Saddle-point evaluation gives [formula in source] with [formula in source] the zero-mode normalisation. Structurally anal","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lemma B.h1 (hard).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3286,"byte_start":2692,"id":"section:562c665f3c970df11108","kind":"paragraph","labels":[],"line_end":72,"line_start":63,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/007-section-hook-solution-sketches-v4-6-5.tex","status_markers_as_written":[],"summary_excerpt":"Hook. Show that the dimensionless TFPT trace [formula in source] maps onto [formula in source] .\\\\ Proposed solution. The Stefan-Boltzmann inversion closes the loop in Planck units: [formula in source] with [formula in source] . Setting [formula in source] fixes [formula in source] . The acceptance criterion is a Paper-5 metrology theorem identifying [formula in source] with the Stefan-Boltzmann limit of the admissib","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lemma C1.h1 (easy).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4127,"byte_start":3286,"id":"section:660464d1fe573fcf997a","kind":"paragraph","labels":[],"line_end":88,"line_start":73,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/007-section-hook-solution-sketches-v4-6-5.tex","status_markers_as_written":[],"summary_excerpt":"Hook. Prove [formula in source] and [formula in source] from the explicit neutrino QKE.\\\\ Proposed solution. Both identities follow from the standard QKE [formula in source] with [formula in source] on the admissible neutrino subsector. The weak Hamiltonian couples through the primitive seam, so [formula in source] with the dimensionless seam Ward residue identified with [formula in source] . The EM identity is struc","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lemma C2.h1 (hard).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4963,"byte_start":4127,"id":"section:0e32b7565f5445fd8cc3","kind":"paragraph","labels":[],"line_end":102,"line_start":89,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/007-section-hook-solution-sketches-v4-6-5.tex","status_markers_as_written":[],"summary_excerpt":"Hook. Prove the BBN-network collapse onto [formula in source] .\\\\ Proposed solution. BBN is dominated by the freeze-out [formula in source] ratio. The TFPT EM holonomy [formula in source] shifts the weak rate uniformly: [formula in source] . Detailed-balance freeze-out then gives [formula in source] (the [formula in source] is the SM value at [formula in source] ). Other BBN reactions burn essentially all neutrons in","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lemma C3.h1 (hard).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5681,"byte_start":4963,"id":"section:041da2a709c47b380708","kind":"paragraph","labels":[],"line_end":116,"line_start":103,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/007-section-hook-solution-sketches-v4-6-5.tex","status_markers_as_written":[],"summary_excerpt":"Hook. Prove that the line integral of the admissible reionization transport collapses to [formula in source] without astrophysical fitting.\\\\ Proposed solution. C4 is the weakest sub-claim. The plausible path: derive [formula in source] from Press-Schechter with [formula in source] from D2; [formula in source] from the carrier-derived stellar IMF; [formula in source] from the admissible UV residue; substitute and ver","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lemma C4.h1 (hardest).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6203,"byte_start":5681,"id":"section:615a10f5d7b32bc730a2","kind":"paragraph","labels":[],"line_end":128,"line_start":117,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/007-section-hook-solution-sketches-v4-6-5.tex","status_markers_as_written":[],"summary_excerpt":"Hook. Prove [formula in source] .\\\\ Proposed solution. The Sheet Overlap eigenvalue [formula in source] is the geometric mean of the retained seed and its complement. The metrology bridge is [formula in source] , and this is exactly what the carrier trace evaluates to under Stefan-Boltzmann normalisation. Acceptance: a Paper-2 corollary establishing the carrier-metrology identity.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lemma D1.h1 (medium).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6810,"byte_start":6203,"id":"section:30f56d3e8cec86968141","kind":"paragraph","labels":[],"line_end":140,"line_start":129,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/007-section-hook-solution-sketches-v4-6-5.tex","status_markers_as_written":[],"summary_excerpt":"Hook. Prove that the stable neutral admissible sector is complete.\\\\ Proposed solution. Spectral completeness of [formula in source] follows from Paper 2's carrier classification combined with Paper 4's admissibility constraints. Strategy: enumerate every stable neutral spin-0/1/2 mode, verify [formula in source] , verify the [formula in source] leakage from [formula in source] . Acceptance: a Paper-2 corollary stati","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lemma D2.h1 (medium).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7593,"byte_start":6810,"id":"section:c93d60cc6e8e1a23d60e","kind":"paragraph","labels":[],"line_end":155,"line_start":141,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/007-section-hook-solution-sketches-v4-6-5.tex","status_markers_as_written":[],"summary_excerpt":"Hook. Mass-metrology bridge from dimensionless Takagi trace to eV.\\\\ Proposed solution. Paper 5 metrology defines [formula in source] (boundary spectral norm) and [formula in source] ; reduced Planck mass is [formula in source] . One eV in TFPT units is [formula in source] with [formula in source] . The conjecture [formula in source] interpreted in eV states that the TFPT seam phase has the energy scale of 1 eV. Nume","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lemma D3.h1 (hard).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8152,"byte_start":7593,"id":"section:9b453a5d07c5cca10999","kind":"paragraph","labels":[],"line_end":166,"line_start":156,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/007-section-hook-solution-sketches-v4-6-5.tex","status_markers_as_written":[],"summary_excerpt":"Hook. Sprint 2A boundary extraction.\\\\ Proposed solution. Sprint 2A must supply (i) the boundary Dirac [formula in source] (Paper 1 export), (ii) the admissible projector [formula in source] (Paper 4 selectors), (iii) the second functional derivative of [formula in source] at the cosmological vacuum, (iv) the projection. Acceptance: the Sprint-2A contract validator passes K_zeta_adm_hermitian on a real bundle with [f","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lemma E1.h1 (medium).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9117,"byte_start":8152,"id":"section:489cf8b41b3197563b9a","kind":"paragraph","labels":[],"line_end":184,"line_start":167,"numbered_or_version_tokens_as_written":["VIII.18"],"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/007-section-hook-solution-sketches-v4-6-5.tex","status_markers_as_written":[],"summary_excerpt":"Hook. Prove that the six flag operators [formula in source] pairwise commute on [formula in source] .\\\\ Proposed solution. Commutativity is a structural consequence of admissibility: (a) [formula in source] because the action is sheet-symmetric; (b) [formula in source] because both live on the boundary modes; (c) [formula in source] because [formula in source] is the closure of the carrier kinetic energy on which [fo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lemma E2.h1 (hardest).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9710,"byte_start":9117,"id":"section:44ec557c561eff372f4e","kind":"paragraph","labels":[],"line_end":195,"line_start":185,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/007-section-hook-solution-sketches-v4-6-5.tex","status_markers_as_written":[],"summary_excerpt":"Hook. Seam-orientation theorem.\\\\ Proposed solution. The closed Riemannian seam carries a canonical orientation form from its TFPT background metric (Paper 1). The primitive seam is a winding-class-1 closed loop in the boundary; its orientation is determined by the induced boundary orientation. [formula in source] is the unique (up to winding-1 isotopy) primitive-class generator consistent with this orientation. Acce","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lemma E3.h1 (medium).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10439,"byte_start":9710,"id":"section:7fc56d36ace0447c688d","kind":"paragraph","labels":[],"line_end":210,"line_start":196,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/007-section-hook-solution-sketches-v4-6-5.tex","status_markers_as_written":[],"summary_excerpt":"Hook. Prove [formula in source] for the real [formula in source] .\\\\ Proposed solution. [formula in source] is the second functional derivative of a real action and is therefore real-symmetric. When expressed in a real (sheet) basis, [formula in source] ; on a complex eigenbasis, [formula in source] implements complex conjugation modulo sheet swap, giving [formula in source] . The candidate v4.6 bundle fails because ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lemma E4.h1 (medium).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11787,"byte_start":10439,"id":"section:1808ee850d811cdf084e","kind":"paragraph","labels":[],"line_end":238,"line_start":211,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/007-section-hook-solution-sketches-v4-6-5.tex","status_markers_as_written":[],"summary_excerpt":"Hook. Derive the observer embedding [formula in source] from the TFPT branch.\\\\ Proposed solution. Two interpretations. Weak: [formula in source] is observational input; TFPT predicts a family of skies parametrised by [formula in source] and the observer matching is part of the experimental setup. Acceptance: a Paper-7-appendix specification fixing the Galactic frame as the standard observer, [formula in source] from","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lemma E5.h1 (hard).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12310,"byte_start":11787,"id":"section:5c4cc439c613f5bcc948","kind":"section","labels":["app:discharge"],"line_end":249,"line_start":239,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/007-section-hook-solution-sketches-v4-6-5.tex","status_markers_as_written":[],"summary_excerpt":"This appendix reproduces the full proof body of every v4.6.6 hook discharge. Each entry has (a) the formal claim, (b) the proof body verbatim from Stefan v4.6.6 brief, (c) the boxed final form that exhibits what closes the hook. The discharge status is given for each entry; the closure conditions are summarised in the master table of","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"v4.6.6 Proof Discharges (verbatim)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13292,"byte_start":12310,"id":"section:052f57fe3f4412c82339","kind":"subsection","labels":[],"line_end":270,"line_start":250,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/007-section-hook-solution-sketches-v4-6-5.tex","status_markers_as_written":[],"summary_excerpt":"Proof. Define the primitive admissible zeta determinant by [formula in source] . The primitive orbit formula on the closed seam geometry is [formula in source] . Closed-branch selection plus [formula in source] plus [formula in source] leaves only the minimal primitive seam class with [formula in source] (double sheet), [formula in source] (primitive seam norm), [formula in source] (two oriented EM runs). Hence [form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"A.h1 \\,—\\, Seam Determinant \\,( closed_pending_convention_adoption)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14165,"byte_start":13292,"id":"section:18a71b746fc4e4073a05","kind":"subsection","labels":[],"line_end":290,"line_start":271,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/007-section-hook-solution-sketches-v4-6-5.tex","status_markers_as_written":[],"summary_excerpt":"Proof. [formula in source] . TFPT defines the non-perturbative admissible curvature susceptibility as the saddle-point quantity [formula in source] with [formula in source] (retained-seed barrier) and [formula in source] (zero-mode norm). Inverting: [formula in source] . Then [formula in source] and the Starobinsky potential closes the inflation cascade. Curvature Instanton Theorem: [formula in source] has a unique r","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B.h1 \\,—\\, Curvature Residue \\,( closed_pending_curvature_instanton_theorem)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14675,"byte_start":14165,"id":"section:d79a2ccdced0ebe1036b","kind":"subsection","labels":[],"line_end":303,"line_start":291,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/007-section-hook-solution-sketches-v4-6-5.tex","status_markers_as_written":[],"summary_excerpt":"Proof. The lowest native four-dimensional radiation functional is [formula in source] ; the bosonic thermal phase-space norm gives the universal factor [formula in source] ; hence [formula in source] . Stefan-Boltzmann inversion gives [formula in source] in reduced Planck units. [formula in source] (Stefan-Boltzmann inversion)","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"C1.h1 \\,—\\, Photon Density \\,( closed_pending_paper5_metrology)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15386,"byte_start":14675,"id":"section:effb17ac700626e45b3f","kind":"subsection","labels":[],"line_end":318,"line_start":304,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/007-section-hook-solution-sketches-v4-6-5.tex","status_markers_as_written":[],"summary_excerpt":"Proof. [formula in source] with [formula in source] . Carrier rigidity: [formula in source] . Weak-seam Ward identity: [formula in source] . EM-holonomy Ward identity: [formula in source] . [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"C2.h1 \\,—\\, Effective Neutrino Number \\,( closed_pending_qke_collision_kernels)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16029,"byte_start":15386,"id":"section:4df1aaaa251d85018a31","kind":"subsection","labels":[],"line_end":334,"line_start":319,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/007-section-hook-solution-sketches-v4-6-5.tex","status_markers_as_written":[],"summary_excerpt":"Proof. The leading alpha channel binds four nucleons. In the symmetric freeze-out sector [formula in source] , [formula in source] . TFPT EM holonomy shifts the weak rate uniformly: [formula in source] . Linear sensitivity: [formula in source] . Hence [formula in source] and [formula in source] up to [formula in source] . [formula in source] under TFPT weak-rate deformation.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"C3.h1 \\,—\\, Helium Fraction \\,( closed_pending_bbn_verification)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16985,"byte_start":16029,"id":"section:65e2cf1dd148933e18b2","kind":"subsection","labels":[],"line_end":356,"line_start":335,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/007-section-hook-solution-sketches-v4-6-5.tex","status_markers_as_written":[],"summary_excerpt":"Proof skeleton. [formula in source] . Full discharge requires three sub-theorems: C4a Press-Schechter Source Theorem [formula in source] ; C4b Carrier IMF Photon Yield [formula in source] ; C4c Admissible UV Escape [formula in source] . Honest verdict (Stefan v4.6.6): not in reach without substantial additional TFPT structure; expect a separate dedicated TFPT companion paper.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"C4.h1 \\,—\\, Reionization Optical Depth \\,( open_hardest_no_full_discharge)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17537,"byte_start":16985,"id":"section:fea6c6b67d1a5c4308f3","kind":"subsection","labels":[],"line_end":370,"line_start":357,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/007-section-hook-solution-sketches-v4-6-5.tex","status_markers_as_written":[],"summary_excerpt":"Proof. Carrier rigidity [formula in source] . The baryonic occupancy is [formula in source] . Sheet Overlap eigenvalue gives [formula in source] . Hence [formula in source] . Stefan-Boltzmann normalised TFPT carrier metrology.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"D1.h1 \\,—\\, Baryon Density \\,( closed_pending_paper5_metrology)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":554,"byte_start":0,"id":"section:21189f754a84e03b0f8b","kind":"subsection","labels":[],"line_end":14,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/008-subsection-d2-h1-cold-dark-matter-density.tex","status_markers_as_written":[],"summary_excerpt":"Proof. [formula in source] (spectral completeness), [formula in source] (quadratic stable seed intensity), [formula in source] (Sheet-Overlap leakage). [formula in source] : spectral completeness theorem.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"D2.h1 \\,—\\, Cold Dark Matter Density \\,( closed_pending_neutral_enumeration)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1131,"byte_start":554,"id":"section:b65903fd9d86ddcdd67d","kind":"subsection","labels":[],"line_end":28,"line_start":15,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/008-subsection-d2-h1-cold-dark-matter-density.tex","status_markers_as_written":[],"summary_excerpt":"Proof. [formula in source] , Takagi-orthogonal. Then [formula in source] . The mass-metrology bridge [formula in source] sets the TFPT eV unit. Numerical: [formula in source] eV. [formula in source] as internal TFPT low-energy projection.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"D3.h1 \\,—\\, Sum of Neutrino Masses \\,( closed_pending_paper5_metrology)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1723,"byte_start":1131,"id":"section:0b78e24d6f5b9b42c90d","kind":"subsection","labels":[],"line_end":42,"line_start":29,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/008-subsection-d2-h1-cold-dark-matter-density.tex","status_markers_as_written":[],"summary_excerpt":"Claim. [formula in source] self-adjoint on [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"E1.h1 \\,—\\, Existence of branch operator \\,( closed_pending_sprint2a_extraction)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2361,"byte_start":1723,"id":"section:a49e100ba1f7febf0da2","kind":"subsection","labels":[],"line_end":56,"line_start":43,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/008-subsection-d2-h1-cold-dark-matter-density.tex","status_markers_as_written":[],"summary_excerpt":"Proof. [formula in source] (sheet symmetry); [formula in source] (boundary modes); [formula in source] (carrier kinetic); [formula in source] ( [formula in source] invariance); [formula in source] (Calderon polarisation). Joint spectral theorem: canonical lexicographic flag from joint eigenvalues; residual U(1) fixed by E3. [formula in source] abelian.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"E2.h1 \\,—\\, Canonical Spectral Flag \\,( closed_pending_six_commutators)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2798,"byte_start":2361,"id":"section:d60a7965c938fa10d156","kind":"subsection","labels":[],"line_end":66,"line_start":57,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/008-subsection-d2-h1-cold-dark-matter-density.tex","status_markers_as_written":[],"summary_excerpt":"Proof. Closed Riemannian seam carries canonical [formula in source] from TFPT metric; primitive seam is winding-class-1 closed loop; [formula in source] fixes the global phase. [formula in source] gauge-invariant.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"E3.h1 \\,—\\, Seam state uniqueness \\,( closed_pending_paper1_seam_orientation)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3373,"byte_start":2798,"id":"section:e78dc7c12b269a1eb7fa","kind":"subsection","labels":[],"line_end":81,"line_start":67,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/008-subsection-d2-h1-cold-dark-matter-density.tex","status_markers_as_written":[],"summary_excerpt":"Claim. [formula in source] and [formula in source] imply [formula in source] real.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"E4.h1 \\,—\\, Reality via Calderon involution \\,( closed_pending_sprint2a_real_basis)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5309,"byte_start":3373,"id":"section:a3099c8f59d953043054","kind":"subsection","labels":[],"line_end":123,"line_start":82,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--07_cmb_operational_closure_planck_pipeline/sections/008-subsection-d2-h1-cold-dark-matter-density.tex","status_markers_as_written":[],"summary_excerpt":"Claim. [formula in source] worldline, tetrad, orientation, [formula in source] , parity [formula in source] fixed.\\\\ Weak version (sufficient for v5.0): [formula in source] with conventional parity, [formula in source] from Friedmann, fixed tetrad.\\\\ Strong version: TFPT also derives Earth, Milky Way, satellite position from full universe microstate. Out of CMB-only scope. [formula in source] for v5.0.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"E5.h1 \\,—\\, Observer embedding \\,( weak_closed_strong_out_of_scope)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6539,"byte_start":0,"id":"section:2be3476aeaaa652270b0","kind":"frontmatter","labels":[],"line_end":205,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/00_orientation_note"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--00_orientation_source/sections/001-section-reading-guide-and-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"From the one-sided boundary datum [formula in source] the manuscript derives the Calder\\'on polarization [formula in source] , the boundary involution [formula in source] , the exact-double deck involution [formula in source] , and the doubled closed datum [formula in source] The hard core is now read through three decoders. First, the carrier decoder [formula in source] satisfies [formula in source] and in the primi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9520,"byte_start":6539,"id":"section:1ed9c2ee5dec43cf4b44","kind":"section","labels":[],"line_end":234,"line_start":206,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/00_orientation_note"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--00_orientation_source/sections/001-section-reading-guide-and-claim-map.tex","status_markers_as_written":[],"summary_excerpt":"The paper is organized in three reading layers: Big picture: one section explains what TFPT claims in plain language before the detailed datum and conventions begin. Detail: the main body then runs from boundary polarization and hard carrier rigidity through kernel numerics, the two closure-architecture sections, the closure theorem stack, the canonical rigid object, the seam-transfer cosmology block, and the interna","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reading guide and claim map","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":27216,"byte_start":9520,"id":"section:12bf5097766a9972f183","kind":"subsection","labels":["fig:dependency-map","tab:status-matrix"],"line_end":383,"line_start":235,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/00_orientation_note"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--00_orientation_source/sections/001-section-reading-guide-and-claim-map.tex","status_markers_as_written":["[P]"],"summary_excerpt":"The manuscript now contains a fully rigid algebraic core together with analytic closure blocks whose exact status is recorded theorem by theorem in the proof-obligation ledger. The remaining explicit standard-theorem interface is [formula in source] while the other former [formula in source] interfaces have now been pulled into the manuscript proof surface. The eight items below are therefore not a promise of later c","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Version 4.5 completion surface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11073,"byte_start":0,"id":"section:ecc6fa18b84127d2053b","kind":"section","labels":["eq:compiler-chain","eq:tfpt-master","eq:tfpt-selectors","fig:status-ladder","fig:tfpt-headline-claims","rem:selector-versus-dynamics"],"line_end":237,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/00_orientation_note"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--00_orientation_source/sections/002-section-big-picture-what-tfpt-actually-claims.tex","status_markers_as_written":[],"summary_excerpt":"TFPT is presented here as a boundary-polarized closed theory of admissible vacua on the oriented double cover. The formal theorem stack now starts from a thinner operational seed which functorially induces the one-sided boundary datum, and the manuscript also shows that within the induced boundary class no extra primitive discrete datum is needed. On the one-sided branch, the self-adjoint boundary operator [formula i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Big picture: what TFPT actually claims","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11135,"byte_start":11073,"id":"section:a95c8b6a1d951523521b","kind":"section","labels":[],"line_end":239,"line_start":238,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/00_orientation_note"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--00_orientation_source/sections/002-section-big-picture-what-tfpt-actually-claims.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Canonical rigid object and falsification interface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14019,"byte_start":11135,"id":"section:73e0b792da8201a1d9ae","kind":"subsection","labels":["eq:closed-output-chain"],"line_end":321,"line_start":240,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/00_orientation_note"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--00_orientation_source/sections/002-section-big-picture-what-tfpt-actually-claims.tex","status_markers_as_written":[],"summary_excerpt":"Collecting the operational-seed generation theorem, the minimal-packaging theorem for the induced boundary class, the boundary datum, the boundary primitive kernel, the joint discrete admissibility theorem, the derived selector, and the continuous closure theorems of sec:closure-theorems, the main-text reconstruction now takes the rigid two-stage form Here [formula in source] is the canonical rigid object of thm:no-a","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Canonical rigid object","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15517,"byte_start":14019,"id":"section:26972d57f1c0a2333f48","kind":"subsection","labels":["cor:canonical-rigid-object"],"line_end":348,"line_start":322,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/00_orientation_note"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--00_orientation_source/sections/002-section-big-picture-what-tfpt-actually-claims.tex","status_markers_as_written":[],"summary_excerpt":"By thm:intrinsic-closed-branch,thm:canonical-rigid-reconstruction-essential-injective,thm:spectral-completeness-rigid-tfpt, there exists a canonical rigid object [formula in source] in [formula in source] such that [formula in source] and every rigid closed admissible realization is uniquely unitarily equivalent to [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Canonical rigid-object corollary","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4106,"byte_start":0,"id":"section:2364dc5301838c28a046","kind":"subsection","labels":["sec:structural-falsification-map","tab:proof-obligations"],"line_end":44,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/00_orientation_note"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--00_orientation_source/sections/003-subsection-structural-falsification-map.tex","status_markers_as_written":[],"summary_excerpt":"The main text closes the theorem chain at [formula in source] and then attaches one structural side card, the falsification map [formula in source] This map reports which local or global structural failure mode would break each arrow of the reconstruction. It is hard-separated from the appendix-level empirical comparison map [formula in source] , which acts only after [formula in source] has been fixed and is collect","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Structural falsification map","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4128,"byte_start":4106,"id":"section:98ee9b117357241dce10","kind":"section","labels":[],"line_end":46,"line_start":45,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/00_orientation_note"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--00_orientation_source/sections/003-subsection-structural-falsification-map.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Conclusion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7069,"byte_start":4128,"id":"section:f55361310e5d255f06b6","kind":"subsection","labels":[],"line_end":137,"line_start":47,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/00_orientation_note"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--00_orientation_source/sections/003-subsection-structural-falsification-map.tex","status_markers_as_written":[],"summary_excerpt":"TFPT is organized around the one-sided boundary datum [formula in source] induced by the minimal operational seed, and reconstructs in a two-stage closure order [formula in source] This reconstruction first fixes the joint discrete datum and only afterwards the continuous Euler–Lagrange branch, thereby identifying the canonical rigid object of the boundary-polarized branch: [formula in source] The selector-to-dynamic","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Closed theorem stack and interface layers","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8238,"byte_start":7069,"id":"section:578930658f93d971b5e0","kind":"subsection","labels":[],"line_end":154,"line_start":138,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/00_orientation_note"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--00_orientation_source/sections/003-subsection-structural-falsification-map.tex","status_markers_as_written":[],"summary_excerpt":"From [formula in source] exactly two side maps are attached, both hard-separated from the theorem chain: Structural falsification map (main text). The map [formula in source] of sec:structural-falsification-map reports the structural failure mode that would break each arrow of the reconstruction. It uses no scheme conventions, no thresholds, and no comparison data. Empirical comparison map (appendix only). The map [f","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Two side maps from [formula in source] T-star","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10750,"byte_start":8238,"id":"section:39efd99c17f6a8960bc8","kind":"subsection","labels":["subsec:conditional-closure-status"],"line_end":221,"line_start":155,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/00_orientation_note"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--00_orientation_source/sections/003-subsection-structural-falsification-map.tex","status_markers_as_written":[],"summary_excerpt":"The closed-branch theorem stack is supplemented by a single, explicitly labeled conditional closure layer, organized so that every numerical readout can be promoted to a theorem as soon as a single named lift hypothesis is discharged. The four downstream readouts and their current status are [formula in source] The compressed integrated story is [formula in source] and in the matter sector [formula in source] The fou","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conditional closure layer and status of the four downstream readouts","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13522,"byte_start":10750,"id":"section:124e3d44910d64d30853","kind":"subsection","labels":[],"line_end":312,"line_start":222,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/00_orientation_note"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--00_orientation_source/sections/003-subsection-structural-falsification-map.tex","status_markers_as_written":[],"summary_excerpt":"A compressed decoder reading of the closed branch is [formula in source] [formula in source] In this condensed form, [formula in source] generates the carrier structure, the primitive winding class [formula in source] fixes the counting, and the retained seed [formula in source] decodes the bridge observables.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Main claim","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":211,"byte_start":0,"id":"section:40a0d2299455a89e2b23","kind":"frontmatter","labels":[],"line_end":4,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/01_boundary_kernel"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/001-section-primitive-core-and-carrier-interface-handoff.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":267,"byte_start":211,"id":"section:958fbf8e5ee3f4d6bd98","kind":"section","labels":[],"line_end":6,"line_start":5,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/01_boundary_kernel"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/001-section-primitive-core-and-carrier-interface-handoff.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Primitive core and carrier interface handoff","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3103,"byte_start":267,"id":"section:238b10aec16e96ddcb5a","kind":"subsection","labels":[],"line_end":57,"line_start":7,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/01_boundary_kernel"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/001-section-primitive-core-and-carrier-interface-handoff.tex","status_markers_as_written":[],"summary_excerpt":"We use natural units [formula in source] . Relative operators are formulated in Euclidean signature and compared through a declared Wick-rotation bridge when Lorentzian language is needed. Higgs fields are denoted by [formula in source] , Hamiltonians by [formula in source] , and the cosmological Hubble rate by [formula in source] ; this avoids overloading the letter [formula in source] . Newton's constant is always ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Primitive core and conventions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16056,"byte_start":3103,"id":"section:5453d74e18aa1a63bd2d","kind":"subsection","labels":["ass:almost-commutative-factorization","ass:bernstein-positivity","def:admissibility-complex","def:carrier-polarization-involution","def:physical-admissible-local-net","def:primitive-admissibility-complex","def:reduced-theorem-datum","lem:admissibility-nilpotency","lem:hodge-admissibility-projector","lem:primitive-admissibility-nilpotency","rem:forward-Padm","thm:primitive-datum-from-reduced-datum","thm:primitive-scaffold-from-reduced-datum","thm:primitive-selfadjoint-realization","thm:well-posed-primitive-dynamics"],"line_end":377,"line_start":58,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/01_boundary_kernel"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/001-section-primitive-core-and-carrier-interface-handoff.tex","status_markers_as_written":[],"summary_excerpt":"The carrier theorem is not intended to float above an unspecified microscopic dynamics. The starting point is therefore the one-sided boundary datum from which the primitive layer, the derived closed datum, and the canonical admissibility projector are reconstructed before the later closure theorems are invoked.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Primitive relative spectral dynamics","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4823,"byte_start":0,"id":"section:cd6f97115e845dbeadaf","kind":"frontmatter","labels":["fig:aps-split","rem:aps-roles"],"line_end":86,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/01_boundary_kernel"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/002-section-intrinsic-closed-branch-and-canonical-rigid-obje.tex","status_markers_as_written":[],"summary_excerpt":"The existence of self-adjoint [formula in source] -elliptic boundary conditions for formally self-adjoint Dirac-type operators is standard. In the zero-kernel case APS is already self-adjoint. If the adapted boundary operator has nontrivial kernel, one passes to a self-adjoint modified APS realization or, equivalently, to [formula in source] with [formula in source] chosen as in the normal form theorem for self-adjoi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5774,"byte_start":4823,"id":"section:0984253c39775ef719af","kind":"section","labels":["sec:rg-map-compiler-outputs"],"line_end":99,"line_start":87,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/01_boundary_kernel"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/002-section-intrinsic-closed-branch-and-canonical-rigid-obje.tex","status_markers_as_written":[],"summary_excerpt":"The closed branch is not selected by a comparison functional. At the top of the main-text theorem stack now stands a thinner operational seed layer: quasilocal Euclidean dynamics, reflection positivity, finite relative action, a nontrivial seam class, and one elliptic collar generator. That seed induces the one-sided admissible boundary datum. Once the induced datum is fixed, the remaining closure problem splits into","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Intrinsic closed branch and canonical rigid object","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12194,"byte_start":5774,"id":"section:da5a8d451e469c6cb1f5","kind":"subsection","labels":["ax:physical-operationality","cor:minimal-operational-seed","def:canonical-defect-filtration","def:operational-seed-category","def:operational-seed-complexity","sec:operational-seed-generation","thm:operational-collar-completion"],"line_end":249,"line_start":100,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/01_boundary_kernel"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/002-section-intrinsic-closed-branch-and-canonical-rigid-obje.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] denote the category whose objects are tuples [formula in source] satisfying: [formula in source] is a quasilocal Euclidean observable net with positive-time reflection [formula in source] ; [formula in source] is reflection positive and clustering on the admissible local algebra, with finite relative action with respect to the declared reference sector; [formula in source] is a nontrivial seam","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Operational seed and boundary generation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16542,"byte_start":12194,"id":"section:7f54fc651a1d27f17cf0","kind":"subsection","labels":["def:admissible-spectral-bordism-category","def:tfpt-core-class","thm:initial-admissible-bordism"],"line_end":334,"line_start":250,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/01_boundary_kernel"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/002-section-intrinsic-closed-branch-and-canonical-rigid-obje.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] denote the category whose objects are tuples such that: [formula in source] is an elliptic Dirac-type operator on a one-sided collar with reflection-regular boundary behavior; the retained Euclidean sector is reflection positive; the relative action with respect to the declared reference sector is finite; the seam class is nontrivial, equivalently [formula in source] . Morphisms are unitary in","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Initial admissible bordisms and induced boundary data","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17296,"byte_start":16542,"id":"section:db88205106dc439012fb","kind":"subsection","labels":["def:boundary-primitive-kernel","def:post-carrier-primitive-kernel"],"line_end":358,"line_start":335,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/01_boundary_kernel"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/002-section-intrinsic-closed-branch-and-canonical-rigid-obje.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the boundary primitive kernel attached to an admissible one-sided boundary datum. Here [formula in source] are fixed by the primitive seam generator theorem. No carrier split, no hypercharge operator, no family geometry, no determinant class, no transport pole, no effective strong angle, and no vacuum datum are part of this definition.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Primitive completion from the boundary kernel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17541,"byte_start":17296,"id":"section:32addd4ca5b8c6018639","kind":"section","labels":["app:tech"],"line_end":363,"line_start":359,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/01_boundary_kernel"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/002-section-intrinsic-closed-branch-and-canonical-rigid-obje.tex","status_markers_as_written":[],"summary_excerpt":"This appendix collects the technical bookkeeping that supports the boundary-to-carrier presentation but would slow the early main-text flow if placed before the carrier theorem.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Technical conventions and data layers","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1730,"byte_start":0,"id":"section:d99e299ca0fe44467cae","kind":"subsection","labels":["tab:relative-objects"],"line_end":25,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/01_boundary_kernel"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/003-subsection-relative-objects.tex","status_markers_as_written":[],"summary_excerpt":"The adjective relative is used in one fixed sense throughout the paper: every operator or action is compared to a declared reference object.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Relative objects","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5096,"byte_start":1730,"id":"section:49cc0c56c1033eba5582","kind":"subsection","labels":["tab:layered-datum"],"line_end":97,"line_start":26,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/01_boundary_kernel"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/003-subsection-relative-objects.tex","status_markers_as_written":[],"summary_excerpt":"The technical bookkeeping behind the manuscript uses five levels: [formula in source] [formula in source] [formula in source] [formula in source] [formula in source] Here [formula in source] is the primitive boundary kernel, while [formula in source] is the derived theorem-level post-carrier kernel reconstructed from the joint discrete datum and the full selector.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Layered datum and admissibility","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13551,"byte_start":5096,"id":"section:4d40facc7d8c3493f047","kind":"subsection","labels":["tab:symbol-guide","tab:symbol-guide-appendix","tab:symbol-guide-theorem"],"line_end":197,"line_start":98,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/01_boundary_kernel"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/003-subsection-relative-objects.tex","status_markers_as_written":[],"summary_excerpt":"The symbol guide is split into two tables to keep theorem-level objects lexically separate from appendix-only comparison and readout objects. tab:symbol-guide-theorem contains only symbols that participate in the main-text theorem chain; tab:symbol-guide-appendix contains only symbols that live in the appendix-level comparison and readout layer.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Symbol guide","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14524,"byte_start":13551,"id":"section:ffb75d29b50df527d442","kind":"section","labels":["app:aps"],"line_end":210,"line_start":198,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/01_boundary_kernel"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/003-subsection-relative-objects.tex","status_markers_as_written":[],"summary_excerpt":"The geometric completion uses APS-type relative data aps1975. In practice this means: one works with a declared pair [formula in source] rather than a single unanchored operator, boundary conditions on the seam [formula in source] are part of the definition of the relative index, the [formula in source] -term keeps track of the residual spectral asymmetry, the superconnection package is used in the same spirit as the","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Relative APS and superconnection setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":208,"byte_start":0,"id":"section:c1b5d420af7450ff4184","kind":"frontmatter","labels":[],"line_end":4,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/02_carrier_rigidity_standard_model_packet"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--02_carrier_source/sections/001-subsection-carrier-algebraic-normal-form.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10135,"byte_start":208,"id":"section:6f544a4b049875c25c42","kind":"subsection","labels":["eq:carrier-polynomial","eq:explicit-hypercharge","eq:hypercharge-seam-inversion","fig:minimal-carrier-glance","lem:primitive-trace-balanced-carrier","sec:minimal-carrier-proof","thm:carrier-minimality-k","thm:carrier-minimality-kpp"],"line_end":376,"line_start":5,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/02_carrier_rigidity_standard_model_packet"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--02_carrier_source/sections/001-subsection-carrier-algebraic-normal-form.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be a finite chiral carrier with two simple factors of ranks [formula in source] and let [formula in source] be the positive half-spinor packet. Let [formula in source] be a primitive integer two-point generator with [formula in source] Assume only [formula in source] Then necessarily [formula in source] Hence [formula in source] The even exterior algebra decomposes into exactly the six sectors","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Carrier algebraic normal form","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1978,"byte_start":0,"id":"section:d3c32988ecf314de1698","kind":"frontmatter","labels":["cor:minimal-carrier-compression","rem:carrier-discriminant"],"line_end":69,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/02_carrier_rigidity_standard_model_packet"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--02_carrier_source/sections/002-subsection-internal-carrier-stabilizer-and-one-family-pa.tex","status_markers_as_written":[],"summary_excerpt":"For a general split carrier [formula in source] with total rank [formula in source] and eigenvalues [formula in source] and [formula in source] , the carrier generator satisfies [formula in source] Its discriminant is [formula in source] Thus the square root of the carrier discriminant is the carrier rank itself. Moreover, [formula in source] On the minimal branch [formula in source] , this reduces to [formula in sou","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12880,"byte_start":1978,"id":"section:4308a8168b2dc758db07","kind":"subsection","labels":["fig:family-occupancy-map","prop:parity-code-family","tab:one-family","thm:global-sm-theorem","thm:physical-gauge-group","thm:physical-gauge-group-faithful"],"line_end":393,"line_start":70,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/02_carrier_rigidity_standard_model_packet"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--02_carrier_source/sections/002-subsection-internal-carrier-stabilizer-and-one-family-pa.tex","status_markers_as_written":[],"summary_excerpt":"The determinant-preserving connected stabilizer of the minimal carrier split is [formula in source] The corresponding Lie algebra factorization [formula in source] is only the differential, local form of the same statement; throughout the manuscript this quotient is intended as the internal carrier-stabilizer form whenever a group symbol is written, and the local algebra notation is used only when explicitly stated.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Internal carrier stabilizer and one-family packet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8083,"byte_start":0,"id":"section:8a5e534eb370e565034b","kind":"subsection","labels":["cor:family-degree-filters","cor:multiplicative-family-character","eq:abelian-index","eq:family-character","eq:family-x-polynomial","eq:multiplicative-family-character","eq:split-weight-enumerator","eq:x-mod-2","eq:x-mod-3","eq:x-mod-5","prop:family-hypercharge-compression","prop:split-weight-enumerator"],"line_end":246,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/02_carrier_rigidity_standard_model_packet"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--02_carrier_source/sections/003-subsection-character-trace-identities-and-the-abelian-in.tex","status_markers_as_written":[],"summary_excerpt":"For the present paragraph let [formula in source] Define also the split weight enumerator [formula in source] Then Moreover, Consequently, [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Character, trace identities, and the abelian index","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8764,"byte_start":8083,"id":"section:2441a4516b3e9773d840","kind":"section","labels":[],"line_end":255,"line_start":247,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/02_carrier_rigidity_standard_model_packet"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--02_carrier_source/sections/003-subsection-character-trace-identities-and-the-abelian-in.tex","status_markers_as_written":[],"summary_excerpt":"This section collects the algebraic compressions that turn the carrier packet and kernel numerics from a list of internally consistent outputs into an overdetermined structure. These compression identities are derived consistency statements on the retained branch: their formal derivation closes only once the bosonic-rank and branch-Yukawa carrier theorems have fixed the rigid [formula in source] split. By contrast, t","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Compression identities and numerical comparison of alternative discrete worlds","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5469,"byte_start":0,"id":"section:f2d4f33abc2df3027e84","kind":"subsection","labels":["cor:pythagorean-integrity-index","cor:rank-5-master-compression","eq:rank-lock","lem:universal-5-4-compression","prop:rank-lock"],"line_end":215,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/02_carrier_rigidity_standard_model_packet"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--02_carrier_source/sections/004-subsection-derived-texorpdfstring-48-4-cdot12-48-4-12-id.tex","status_markers_as_written":[],"summary_excerpt":"48=4·12 identity on the retained branch] On the retained branch, once the family multiplicity and carrier ranks have been fixed, one recovers [formula in source] with [formula in source] Equivalently, the former rank-lock formula is a derived consistency identity evaluated at the closed branch point:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derived [formula in source] 48=4·12 identity and the [formula in source] - [formula in source] - [formula in source] 2-3-5 arithmetic","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5506,"byte_start":0,"id":"section:f148432926e9b6fdccb9","kind":"subsection","labels":["cor:factorial-trace-delta2","cor:family-integrality-repair","prop:dual-root-generation"],"line_end":225,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/02_carrier_rigidity_standard_model_packet"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--02_carrier_source/sections/005-subsection-carrier-compressions-on-the-minimal-branch.tex","status_markers_as_written":[],"summary_excerpt":"and [formula in source] ] Let [formula in source] be the two distinct carrier eigenvalues singled out by the factorized carrier polynomial. Then [formula in source] Here [formula in source] is the unweighted Vieta sum of the two distinct carrier eigenvalues, not the trace on [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Carrier compressions on the minimal branch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5945,"byte_start":5506,"id":"section:a92ff0cf025c7bd01a99","kind":"subsection","labels":["eq:41-chain-main"],"line_end":239,"line_start":226,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/02_carrier_rigidity_standard_model_packet"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--02_carrier_source/sections/005-subsection-carrier-compressions-on-the-minimal-branch.tex","status_markers_as_written":[],"summary_excerpt":"The abelian coefficient is first carried only in the generic form The arithmetic specialization to [formula in source] is deferred until the family multiplicity and the Higgs sector have both been theorematically closed.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Generic abelian index identity","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6551,"byte_start":5945,"id":"section:48642a199186b58822e7","kind":"section","labels":[],"line_end":248,"line_start":240,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/02_carrier_rigidity_standard_model_packet"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--02_carrier_source/sections/005-subsection-carrier-compressions-on-the-minimal-branch.tex","status_markers_as_written":[],"summary_excerpt":"This first closure-architecture block is the shortest route from the hard carrier packet to the closed theorem body. It has three moves: primitive winding balance in the seam normal plane forces the four-corner structure of the fundamental section, that winding theorem globalizes into the family space [formula in source] , the determinant line selects the unique light Higgs doublet together with the compact seam phas","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Closure architecture A: families, Higgs, and local spectral scale","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9281,"byte_start":0,"id":"section:529a1099695fd9776d5a","kind":"subsection","labels":["cor:boundary-bulk-occupancy","cor:derived-occupancy-identity","fig:family-triangle","prop:family-holonomy-su3","prop:orbifold-aps-compatibility","thm:harmonic-family-modes","thm:topological-family-closure"],"line_end":238,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/02_carrier_rigidity_standard_model_packet"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--02_carrier_source/sections/006-subsection-family-monodromy-and-occupancy.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] denote the compact seam quotient with four [formula in source] corner points [formula in source] , and define the punctured family section [formula in source] Its rigid harmonic model is the Möbius class [formula in source] Set [formula in source] We use the distinguished cycle basis [formula in source] only as a concrete carrier-side basis of this family space; any later APS/Hodge realization","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Family monodromy and occupancy","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10539,"byte_start":9281,"id":"section:e18972a3bc46d3501db8","kind":"subsection","labels":[],"line_end":260,"line_start":239,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/02_carrier_rigidity_standard_model_packet"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--02_carrier_source/sections/006-subsection-family-monodromy-and-occupancy.tex","status_markers_as_written":[],"summary_excerpt":"With the family bridge installed, the matter space becomes [formula in source] and the occupancy [formula in source] is already fixed by the harmonic family-mode theorem and its bridge corollary. Here occupancy means the admissible chiral-state count after family lifting; it is not used as a primitive datum. The bridge point is not that family lifting creates a new numerical surcharge. Rather, the inherited hard kern","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Occupancy and boundary-to-bulk bridge","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11733,"byte_start":10539,"id":"section:664c3e0c0e3f89f47742","kind":"subsection","labels":[],"line_end":285,"line_start":261,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/02_carrier_rigidity_standard_model_packet"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--02_carrier_source/sections/006-subsection-family-monodromy-and-occupancy.tex","status_markers_as_written":[],"summary_excerpt":"Once the carrier packet and family closure architecture are fixed, the focused main-text closure problem splits into a geometric program [formula in source] and a transport program [formula in source] . Record algebra and prediction semantics are now tied directly to the admissible gap in the main theorem stack, while E [formula in source] scale grammar and horizon extrapolations are deferred to appendix-level contin","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"From bridge to geometric completion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16837,"byte_start":11733,"id":"section:2b0b46aa7c2361ea28c0","kind":"subsection","labels":["cor:constant-scale-reduction","def:canonical-residues","def:local-spectral-scale","thm:admissible-sector-on-reconstructed-geometry","thm:full-operator-reconstruction","thm:geometric-reconstruction-anchor","thm:geometric-reconstruction-from-Dgeo","thm:relative-geometric-reconstruction","thm:retained-branch-from-Padm"],"line_end":406,"line_start":286,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/02_carrier_rigidity_standard_model_packet"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--02_carrier_source/sections/006-subsection-family-monodromy-and-occupancy.tex","status_markers_as_written":[],"summary_excerpt":"The geometric completion is formulated on a graded bundle [formula in source] with the geometric Dirac anchor [formula in source] , the declared reference operator [formula in source] , and APS-type boundary conditions on the seam [formula in source] ; see Appendix app:aps. The geometric package is [formula in source] Here [formula in source] is the geometric Dirac anchor, while [formula in source] is the relative co","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Relative APS and superconnection setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13974,"byte_start":0,"id":"section:8b021a76ca81f512ce08","kind":"subsection","labels":["ass:remaining-closure-inputs","cor:bosonic-rank-two","def:relative-generating-functional","fig:admissibility-stack","lem:admissible-reflection-positivity","prop:master-closure-roadmap","thm:apsdom-upgrade","thm:callias-higgs-selection","thm:compact-determinant-higgs-index","thm:compact-higgs-unique","thm:determinant-class-higgs-selection","thm:determinant-clutching","thm:master-closure"],"line_end":394,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/02_carrier_rigidity_standard_model_packet"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--02_carrier_source/sections/007-subsection-bosonic-relative-index-and-higgs-selection.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] over the compactified oriented normal sphere [formula in source] . Then the primitive charge generator [formula in source] together with center neutrality and seam-evenness forces the clutching map [formula in source] for [formula in source] , while center neutrality forces [formula in source] for [formula in source] . Therefore [formula in source] This pair is the unique minimal nonnegative a","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bosonic relative index and Higgs selection","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13691,"byte_start":0,"id":"section:1df7697213ae2bf024ea","kind":"frontmatter","labels":["cor:yukawa-discharges-kpp","def:primitive-yukawa-generator","fig:carrier-closure-cut","lem:lowest-primitive-yukawa-generator","lem:unique-cubic-weak-invariant","thm:yukawa-forces-32"],"line_end":399,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/02_carrier_rigidity_standard_model_packet"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--02_carrier_source/sections/008-source.tex","status_markers_as_written":[],"summary_excerpt":"By definition, [formula in source] The denominator is a fixed positive normalizing constant, so the sign is determined entirely by the admissible numerator.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11067,"byte_start":0,"id":"section:c31408dd658bc23e8254","kind":"frontmatter","labels":["cor:derived-post-carrier-kernel","def:projected-modular-free-energy","lem:nontrivial-topological-support","lem:topological-sector-positivity","thm:discrete-sector-from-primitive-kernel","thm:joint-discrete-admissible-sector","thm:strong-cp-closure","thm:strong-cp-closure-positive"],"line_end":377,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/02_carrier_rigidity_standard_model_packet"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--02_carrier_source/sections/009-source.tex","status_markers_as_written":[],"summary_excerpt":"Center neutrality and seam-evenness are already the carrier-side admissibility rules for physical hadrons. Passing to the norm closure of the singlet admissible algebra acting on the vacuum gives the completed hadronic space, and no state with [formula in source] survives the selector.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8705,"byte_start":0,"id":"section:3f13c487d11f26bd5860","kind":"frontmatter","labels":["def:core-closure-functional","def:intrinsic-closure-map","def:sector-solution-sets","thm:canonical-rigid-reconstruction-essential-injective","thm:continuous-closure-from-master-functional","thm:internal-analytic-closure","thm:internal-analytic-closure-hard","thm:intrinsic-closed-branch","thm:observation-closure","thm:rigid-reconstruction-core","thm:singleton-fiber-product-branch"],"line_end":232,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/02_carrier_rigidity_standard_model_packet"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--02_carrier_source/sections/010-partial-alpha-gamma-u-1-alpha-0.tex","status_markers_as_written":[],"summary_excerpt":"On the retained admissible branch, the projected modular free energy factorizes as [formula in source] Its admissible critical points are therefore exactly the solutions of [formula in source] Equivalently, the continuous closure laws are [formula in source] In particular the continuous closure equations are derived from one primitive variational object rather than imposed as independent sector primitives. 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The numerical kernel already fixes a nontrivial output layer. Here that layer is pulled forward and read as the first established output package of the carrier/output architecture rather than as a later list of disconnected constants.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kernel numerics and electromagnetic closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12864,"byte_start":3791,"id":"section:8449f3a2f993af57960a","kind":"subsection","labels":["def:exact-seam-generating-function","eq:carrier-cfe","eq:phi-opening","fig:alpha-closure-flow","prop:carrier-susceptibility-exponent","prop:log-det-variation-u1","thm:alpha-canonical","thm:exact-electromagnetic-closure"],"line_end":338,"line_start":75,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/03_electromagnetic_closure_flavor_transport"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--03_em_flavor_source/sections/001-section-kernel-numerics-and-electromagnetic-closure.tex","status_markers_as_written":[],"summary_excerpt":"At this stage the electromagnetic closure is kept in generic closed form. The hard carrier data fix [formula in source] while the later family and Higgs theorems will specialize the abelian index coefficient and the topological bridge coefficient.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Carrier form of the electromagnetic closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15744,"byte_start":12864,"id":"section:c4e8bc1ef2f1d0603199","kind":"subsection","labels":["eq:hard-kernel-values","eq:kernel-benchmark-formulas"],"line_end":387,"line_start":339,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/03_electromagnetic_closure_flavor_transport"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--03_em_flavor_source/sections/001-section-kernel-numerics-and-electromagnetic-closure.tex","status_markers_as_written":[],"summary_excerpt":"The benchmark row for [formula in source] is defined by the positive self-consistent root of eq:carrier-cfe, not by freezing the opening at its retained seed value. 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The electromagnetic [formula in s","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kernel output package","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6052,"byte_start":0,"id":"section:4cc072651f082bf34cd6","kind":"subsection","labels":["cor:baryon-reactor-bridge-law","cor:ckm-pmns-bridge-law","cor:matter-radiation-quotient","cor:uv-half-circle","eq:cabibbo-inversion","eq:catalan-cabibbo","eq:lambda-c-master","eq:seed-budget-identity","prop:retained-seed-decoder"],"line_end":217,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/03_electromagnetic_closure_flavor_transport"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--03_em_flavor_source/sections/002-subsection-uv-seed-shadow-identities-and-the-cabibbo-inv.tex","status_markers_as_written":[],"summary_excerpt":"The retained scalar seed [formula in source] still satisfies exact UV identities. In the present version these identities are auxiliary kernel bookkeeping rather than the independence grammar of the physical observable layer. In particular, the Cabibbo angle admits an explicit inversion back to the UV seed: Setting [formula in source] the inversion formula becomes [formula in source] Hence where [formula in source] a","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"UV seed-shadow identities and the Cabibbo inversion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11319,"byte_start":6052,"id":"section:9cbbe111d650f4bacf78","kind":"subsection","labels":["fig:carrier-exclusion-matrix","thm:carrier-exclusion"],"line_end":328,"line_start":218,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/03_electromagnetic_closure_flavor_transport"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--03_em_flavor_source/sections/002-subsection-uv-seed-shadow-identities-and-the-cabibbo-inv.tex","status_markers_as_written":[],"summary_excerpt":"The strongest numerical pressure test on the carrier packet is not a further precision hit. It is that nearby wrong discrete worlds miss the electromagnetic closure decisively.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Carrier comparison of alternative discrete worlds","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11903,"byte_start":11319,"id":"section:6762cc666122ac246c2e","kind":"section","labels":[],"line_end":336,"line_start":329,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/03_electromagnetic_closure_flavor_transport"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--03_em_flavor_source/sections/002-subsection-uv-seed-shadow-identities-and-the-cabibbo-inv.tex","status_markers_as_written":[],"summary_excerpt":"The second closure-architecture block is the transport closure. Its role is to turn the carrier packet and the family/occupancy closure into actual masses, mixings, hadronic admissibility, and control of the strong-CP sector. The logic is again staged: first the discrete phase operator and the transport kernel, then residue and winding data, then matrix-factorized Yukawas, hadronic selection, determinant-line phase e","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Closure architecture B: Yukawas, masses, flavor, hadronic admissibility, and the strong-CP sector","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5045,"byte_start":0,"id":"section:184f2763f7510774968c","kind":"subsection","labels":["fig:holonomy-triangle","fig:z6-circle"],"line_end":87,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/03_electromagnetic_closure_flavor_transport"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--03_em_flavor_source/sections/003-subsection-discrete-phase-operator-and-transport-grammar.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] This makes the phase grammar concrete rather than rhetorical. The six admissible phases are shown as a finite hexagonal transport geometry in fig:z6-circle: the cusp values live on the same real axis as the positive-real phase, the admissible gap is visible directly, and the holonomy phase can be read as a triangle on the same discrete transport base.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Discrete phase operator and transport grammar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11586,"byte_start":5045,"id":"section:4f28881002e138056680","kind":"subsection","labels":["def:canonical-cycle-holonomy","def:structural-transport-kernel","eq:transport-bridge-offset","lem:regularized-transport-pole-stability","prop:closed-form-transport-pole","thm:algebraic-transport-pole","thm:transport-pole-algebraic"],"line_end":352,"line_start":88,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/03_electromagnetic_closure_flavor_transport"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--03_em_flavor_source/sections/003-subsection-discrete-phase-operator-and-transport-grammar.tex","status_markers_as_written":[],"summary_excerpt":"For each fermion sector define the structural positive transport kernel by [formula in source] whenever the inverse exists on [formula in source] . 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In particular, On the admissible cusp set [formula in source] the smallest singular value of the unregulated hexagon denominator is attained at [formula in source] and [formula in source] . Equivalently, [formula in source] Hence the finite admissible","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9803,"byte_start":0,"id":"section:129055b3f832dc887f27","kind":"frontmatter","labels":["cor:carrier-asymmetry-leptons","cor:charged-lepton-seed-decoder","cor:quark-source-ratios","cor:transport-length-sum-rule","prin:minimal-admissible-transport-packets","prop:transport-matrix-normal-form","tab:transport-dictionary","thm:charged-lepton-compression"],"line_end":360,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/03_electromagnetic_closure_flavor_transport"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--03_em_flavor_source/sections/006-source.tex","status_markers_as_written":[],"summary_excerpt":"transport triangle] Modulo full windings, the three diagonal packets define the residue sets [formula in source] [formula in source] Hence the up, down, and charged-lepton sectors lie on the same [formula in source] orbit of the base three-point subset [formula in source] . In each case the cyclic distance multiset is exactly [formula in source] So the exact structure here is a three-point circular distance system wi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3723,"byte_start":0,"id":"section:adeb4d9c05c9bbb7d89b","kind":"subsection","labels":["cor:cubic-vub-law","eq:ckm-magnitudes","eq:ckm-phase","prop:ckm-phase-asymptotic","thm:ckm-closure","thm:neutrino-closure"],"line_end":105,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/03_electromagnetic_closure_flavor_transport"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--03_em_flavor_source/sections/007-subsection-ckm-and-pmns-closure.tex","status_markers_as_written":[],"summary_excerpt":"On the canonical admissible branch the quark mixing matrix [formula in source] is a branch invariant fixed by the hard holonomy form of thm:exact-transport-closure. Its leading transport magnitudes are Its exact CP phase is [formula in source] on the canonical branch.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"CKM and PMNS closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10520,"byte_start":3723,"id":"section:6fdf2f907c680243bfc7","kind":"section","labels":["app:comparison","cor:retained-seed-factorization","sec:appendix-empirical-readout","tab:benchmark"],"line_end":222,"line_start":106,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/03_electromagnetic_closure_flavor_transport"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--03_em_flavor_source/sections/007-subsection-ckm-and-pmns-closure.tex","status_markers_as_written":[],"summary_excerpt":"This appendix does not define the theorem-level physical observable object itself. The canonical scheme-facing object is the orbit [formula in source] The tables below record only chosen representatives [formula in source] in declared scheme objects [formula in source] . The appendix is therefore the carrier of the comparison map [formula in source] and remains hard-separated from the theorem chain eq:closed-output-c","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Appendix-level empirical readout","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16778,"byte_start":10520,"id":"section:37f55f89510c77a79a9d","kind":"subsection","labels":["tab:operational-prediction-set"],"line_end":292,"line_start":223,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/03_electromagnetic_closure_flavor_transport"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--03_em_flavor_source/sections/007-subsection-ckm-and-pmns-closure.tex","status_markers_as_written":[],"summary_excerpt":"The narrow empirical readout table is not the whole experimental surface of the manuscript. tab:operational-prediction-set collects the rows that are operationally testable on near- to medium-term timescales, while keeping their status, next test, kill criterion, and dependency structure explicit. The point is not to flatten them into one truth class. Rather, the Status column now uses only the manuscript's final out","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Operational prediction set","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18985,"byte_start":16778,"id":"section:f22a5064eae6d0d27cc4","kind":"subsection","labels":["tab:basis-factorization"],"line_end":320,"line_start":293,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/03_electromagnetic_closure_flavor_transport"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--03_em_flavor_source/sections/007-subsection-ckm-and-pmns-closure.tex","status_markers_as_written":[],"summary_excerpt":"To make the renormalized / physical / scheme hierarchy explicit row by row, the visible appendix surface factors through the basis packages of [formula in source] as follows.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Basis factorization of readout rows","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":21923,"byte_start":18985,"id":"section:99e730f6ca596d7ed5b8","kind":"subsection","labels":["tab:prediction-ledger"],"line_end":352,"line_start":321,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/03_electromagnetic_closure_flavor_transport"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--03_em_flavor_source/sections/007-subsection-ckm-and-pmns-closure.tex","status_markers_as_written":[],"summary_excerpt":"The main empirical readout table shows only a narrow readout surface. To keep the output structure visible, tab:prediction-ledger summarizes which output packages belong to which layer of the paper.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Compact prediction ledger","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":205,"byte_start":0,"id":"section:306851babdac39e18091","kind":"frontmatter","labels":[],"line_end":4,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--04_qft_source/sections/001-subsection-hadronic-admissibility-as-singlet-selection.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2571,"byte_start":205,"id":"section:3fcf3866d66b7ac20561","kind":"subsection","labels":["fig:admissible-words"],"line_end":48,"line_start":5,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--04_qft_source/sections/001-subsection-hadronic-admissibility-as-singlet-selection.tex","status_markers_as_written":[],"summary_excerpt":"For each carrier word [formula in source] , let [formula in source] be its color-center charge and let [formula in source] be its seam parity. Physical hadronic words satisfy [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Hadronic admissibility as singlet selection","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8558,"byte_start":2571,"id":"section:2d503279c58503122138","kind":"subsection","labels":["cor:strong-cp-rg-stability","def:sheet-cp-symmetry","eq:strong-cp","lem:retained-gamma5-hermiticity","thm:sheet-cp-protection","thm:structural-strong-cp"],"line_end":207,"line_start":49,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--04_qft_source/sections/001-subsection-hadronic-admissibility-as-singlet-selection.tex","status_markers_as_written":[],"summary_excerpt":"Define Define the admissible sheet-CP operator by [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Transport-side ingredients for the strong-CP sector","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16220,"byte_start":0,"id":"section:dfd6ad94d3380e6b33e4","kind":"section","labels":["ass:remaining-closure-inputs","cor:factorized-admissibility-selector","def:full-admissibility-complex","def:relative-generating-functional","fig:admissibility-stack","lem:admissible-reflection-positivity","prop:master-closure-roadmap","sec:closure-theorems","thm:apsdom-upgrade","thm:master-closure","thm:padm-upgrade"],"line_end":397,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--04_qft_source/sections/002-section-closure-theorems-from-the-admissibility-complex.tex","status_markers_as_written":[],"summary_excerpt":"The preceding two sections introduced the carrier-compatible geometric and transport architecture. The primitive admissibility projector [formula in source] was already placed in the primitive section so that the proof direction runs from the boundary datum through the derived closed datum to [formula in source] , and only then to the later sector theorems. What remains in this section is therefore (i) the upgrade of","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Closure theorems from the admissibility complex","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12412,"byte_start":0,"id":"section:5c1910f055c3e2f71823","kind":"frontmatter","labels":["cor:yukawa-discharges-kpp","def:primitive-yukawa-generator","fig:carrier-closure-cut","lem:lowest-primitive-yukawa-generator","lem:nontrivial-topological-support","lem:topological-sector-positivity","lem:unique-cubic-weak-invariant","thm:strong-cp-closure","thm:strong-cp-closure-positive","thm:yukawa-forces-32"],"line_end":370,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--04_qft_source/sections/003-source.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the graded algebra of carrier-invariant Yukawa trilinears. A homogeneous nonzero invariant is called primitive if it is indecomposable, equivalently if it does not lie in the ideal generated by positive-degree invariants of strictly lower carrier degree.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17351,"byte_start":0,"id":"section:5248af93a50c00dd9d94","kind":"frontmatter","labels":["fig:gap-hardening-chain","lem:boundary-decoupling-admissible","lem:diagonal-weights-separate-basis","lem:parent-gap-from-transfer-block","thm:admissible-vacuum-existence","thm:admissible-vacuum-finite-volume","thm:cp-even-vacuum-uniqueness","thm:lorentzian-reconstruction","thm:reflection-positivity-admissible","thm:thermodynamic-limit","thm:uniform-parent-gap-injective"],"line_end":381,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--04_qft_source/sections/004-source.tex","status_markers_as_written":[],"summary_excerpt":"thm:sheet-cp-protection gives [formula in source] By lem:topological-sector-positivity, the admissible partition function admits a sector decomposition [formula in source] The antiunitary sheet symmetry of thm:sheet-cp-protection gives [formula in source] so the sector weights satisfy [formula in source] . Hence [formula in source] By lem:nontrivial-topological-support, one has [formula in source] . Therefore for eve","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5145,"byte_start":0,"id":"section:7a7755c65bfd436c721b","kind":"frontmatter","labels":["lem:norm-stable-gap-parent-path","rem:vacuum-honest-status","thm:eta-zero-parent-domination","thm:gap-stability-thermo-limit","thm:nonperturbative-admissible-qft"],"line_end":122,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--04_qft_source/sections/005-subsection-admissible-schwinger-functions-minkowski-loca.tex","status_markers_as_written":[],"summary_excerpt":"eta=0] Fix finite volume [formula in source] and let [formula in source] be the primitive blocked admissible transfer operator with Perron vector [formula in source] . Let [formula in source] be the blocked admissible parent Hamiltonian of lem:parent-gap-from-transfer-block, with [formula in source] Let the physical admissible Hamiltonian be written as [formula in source] where each added term is positive semidefinit","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17503,"byte_start":5145,"id":"section:58b3a771f93680088d7d","kind":"subsection","labels":["cor:master-closure-corollary","def:admissible-schwinger-functions","def:laboratory-scattering-sector","def:stable-record-algebra","fig:selector-versus-dynamics","rem:ir-dressed-massless-sectors","rem:resonant-states-admissible","thm:admissible-local-minkowski-net","thm:dressed-massless-interface","thm:full-admissible-os-closure","thm:lsz-stable-massive","thm:stable-massive-scattering"],"line_end":403,"line_start":123,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--04_qft_source/sections/005-subsection-admissible-schwinger-functions-minkowski-loca.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] denote a low-curvature branch region on which [formula in source] and [formula in source] All scattering statements below are formulated on [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Admissible Schwinger functions, Minkowski locality, and scattering closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":608,"byte_start":0,"id":"section:9643ca8ced2e76618571","kind":"section","labels":["sec:universality-operational"],"line_end":10,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--04_qft_source/sections/006-section-internal-reduction-theorem-and-renormalized-obse.tex","status_markers_as_written":[],"summary_excerpt":"Above the closed theorem stack ending at [formula in source] , the present version records one theorem-level input reduction and a stratified output-side observable chain. On the input side, the reduction is internal to a deliberately weakened ambient class. On the output side, the passage from [formula in source] to the renormalized low-energy package [formula in source] and then to the physical observable layer [fo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Internal reduction theorem and renormalized observable hierarchy","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16493,"byte_start":608,"id":"section:4cc52509e02e7fb2728e","kind":"subsection","labels":["def:physadm","def:rigid-closure-functor","def:universal-reduction","fig:internal-reduction-orbit","prop:universal-carrier-reduction","prop:universal-family-reduction","prop:universal-glueing","prop:universal-transport-reduction","thm:universality-tfpt"],"line_end":399,"line_start":11,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--04_qft_source/sections/006-section-internal-reduction-theorem-and-renormalized-obse.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] denote the category whose objects are tuples [formula in source] satisfying the following ambient admissibility axioms: Real even boundary datum: [formula in source] is an admissible real even one-sided boundary datum with reflection-regular collar. Quasilocal positive dynamics: [formula in source] is a quasilocal dynamics with reflection positivity and an admissible vacuum sector. Morphisms a","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Weakened ambient class","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13639,"byte_start":0,"id":"section:3e7cfda7c9252d871993","kind":"subsection","labels":["cor:em-ir-boundary-condition","cor:one-loop-shadow-exact-flow","def:admissible-effective-average-action","def:canonical-measurement-orbit","def:minimal-observable-basis","def:obs-category","def:physical-observable-category","def:renormalized-low-energy-package","def:scheme-groupoid","thm:admissible-1pi-graph-expansion","thm:exact-admissible-rg-flow","thm:operational-completeness"],"line_end":372,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--04_qft_source/sections/007-subsection-renormalized-physical-and-scheme-readout-laye.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be an admissible infrared regulator commuting with the structural sector selection. Define [formula in source] and set [formula in source] The renormalized admissible effective action is [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Renormalized, physical, and scheme readout layers","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5688,"byte_start":0,"id":"section:84c76a3dafcdc2baa222","kind":"frontmatter","labels":["cor:cosmology-axion-target","cor:no-double-counting","cor:response-birefringence-target","fig:admissible-rg-flow"],"line_end":139,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--04_qft_source/sections/008-section-relative-reflection-positivity-with-fermions.tex","status_markers_as_written":[],"summary_excerpt":"0.96 ! (hadm) at (-5.0,0.9) [formula in source] \\ sector; (wk) at (-1.6,0.9) [formula in source] \\ generator; (gk) at (1.8,0.9) [formula in source] \\ admissible flow; (gren) at (5.2,0.9) [formula in source] \\ 1PI action;","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5768,"byte_start":5688,"id":"section:9ac06ba4695ad4e6544a","kind":"section","labels":["app:os-fermions"],"line_end":142,"line_start":140,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--04_qft_source/sections/008-section-relative-reflection-positivity-with-fermions.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Relative reflection positivity with fermions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6255,"byte_start":5768,"id":"section:9ba4825482f7ea3785d0","kind":"subsection","labels":[],"line_end":152,"line_start":143,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--04_qft_source/sections/008-section-relative-reflection-positivity-with-fermions.tex","status_markers_as_written":[],"summary_excerpt":"The relative Euclidean theory used in the main closure section is not interpreted as a difference of measures. Instead it is organized as the normalized quotient [formula in source] Because the denominator is source independent on the admissible sector, the reference theory acts only as a fixed normalizer and does not interfere with reflection positivity.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Normalized quotient form","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7289,"byte_start":6255,"id":"section:adc712862a1f13cf0214","kind":"subsection","labels":[],"line_end":170,"line_start":153,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--04_qft_source/sections/008-section-relative-reflection-positivity-with-fermions.tex","status_markers_as_written":[],"summary_excerpt":"The commutation relations [formula in source] ensure that reflection preserves the admissible subspace. The bosonic part then follows the standard Markov / reflection-stable Osterwalder–Schrader argument on admissible observables. For fermions, the admissible CAR kernel may be written as a reflected quadratic form; equivalently one may express the same condition as positivity of the associated Pfaffian structure on t","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bosonic and fermionic positivity on [formula in source] Padm","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7702,"byte_start":7289,"id":"section:19059df087b765a037b9","kind":"section","labels":["app:os-scattering"],"line_end":178,"line_start":171,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--04_qft_source/sections/008-section-relative-reflection-positivity-with-fermions.tex","status_markers_as_written":[],"summary_excerpt":"This appendix upgrades the admissible Schwinger, reconstruction, and scattering block from a named standard interface to a manuscript-level proof package. 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Moreover, for every compact [formula in source] and every source monomial of total degree [formula in source] , its moments obey polynomial bounds determined by the same uniform heat-kernel estimates and finite local moments of the admissible constructive measure","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Tempered admissible Schwinger families","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12220,"byte_start":9833,"id":"section:591993c8c68b37136f0d","kind":"subsection","labels":["thm:tailored-os-car-reconstruction"],"line_end":255,"line_start":215,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--04_qft_source/sections/008-section-relative-reflection-positivity-with-fermions.tex","status_markers_as_written":[],"summary_excerpt":"Padm] Let [formula in source] be the admissible Schwinger family on the Euclidean continuation of [formula in source] . If reflection positivity, temperedness, graded Euclidean covariance, graded symmetry, and clustering hold on [formula in source] , then there exist: a Hilbert space [formula in source] with vacuum vector [formula in source] , a strongly continuous positive-energy semigroup [formula in source] with s","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"OS and CAR reconstruction on [formula in source] Padm","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14573,"byte_start":12220,"id":"section:cfa56a2cdb98159c5599","kind":"subsection","labels":["cor:lsz-admissible-massive","lem:one-particle-projectors-from-poles","thm:haag-ruelle-admissible-massive"],"line_end":300,"line_start":256,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--04_qft_source/sections/008-section-relative-reflection-positivity-with-fermions.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] have an isolated simple pole with positive residue at [formula in source] . Then the corresponding one-particle contribution defines a positive spectral projector on the admissible Hilbert space.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Stable massive Haag–Ruelle and LSZ closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15306,"byte_start":14573,"id":"section:3125dafc2086f760e4b4","kind":"subsection","labels":[],"line_end":317,"line_start":301,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--04_qft_source/sections/008-section-relative-reflection-positivity-with-fermions.tex","status_markers_as_written":[],"summary_excerpt":"The massless sector is not treated by bare Fock asymptotics in the present manuscript. The relevant object is the infrared-dressed interface package [formula in source] constructed from the soft charges of the admissible local net on the low-curvature region [formula in source] . This is exactly the interface package used in the main-text theorem thm:dressed-massless-interface.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dressed massless interface in the low-curvature region","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17276,"byte_start":15306,"id":"section:3af6d0fa08cdf2b14930","kind":"section","labels":["app:yukawa"],"line_end":355,"line_start":318,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/04_admissibility_strong_cp_qft_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--04_qft_source/sections/008-section-relative-reflection-positivity-with-fermions.tex","status_markers_as_written":[],"summary_excerpt":"This appendix is the proof motor for the transport positivity, determinant-phase suppression, and bounded-residual statements used in the main text. The transport program is based on the regularized kernel [formula in source] Three remarks are important. The regulator [formula in source] is not optional: without it the kernel becomes ill-defined exactly where the admissibility question is most delicate. 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This statement is kept in the appendix so that the main theorem surface doe","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Optional strong-coupling sharpening","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":219,"byte_start":0,"id":"section:9159fb725a00c14723ff","kind":"frontmatter","labels":[],"line_end":4,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/001-subsection-from-bridge-to-geometric-completion.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1413,"byte_start":219,"id":"section:a880f6c4757fad6fc643","kind":"subsection","labels":[],"line_end":29,"line_start":5,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/001-subsection-from-bridge-to-geometric-completion.tex","status_markers_as_written":[],"summary_excerpt":"Once the carrier packet and family closure architecture are fixed, the focused main-text closure problem splits into a geometric program [formula in source] and a transport program [formula in source] . Record algebra and prediction semantics are now tied directly to the admissible gap in the main theorem stack, while E [formula in source] scale grammar and horizon extrapolations are deferred to appendix-level contin","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"From bridge to geometric completion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6517,"byte_start":1413,"id":"section:c5e989620c1d94f86ecb","kind":"subsection","labels":["cor:constant-scale-reduction","def:canonical-residues","def:local-spectral-scale","thm:admissible-sector-on-reconstructed-geometry","thm:full-operator-reconstruction","thm:geometric-reconstruction-anchor","thm:geometric-reconstruction-from-Dgeo","thm:relative-geometric-reconstruction","thm:retained-branch-from-Padm"],"line_end":150,"line_start":30,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/001-subsection-from-bridge-to-geometric-completion.tex","status_markers_as_written":[],"summary_excerpt":"The geometric completion is formulated on a graded bundle [formula in source] with the geometric Dirac anchor [formula in source] , the declared reference operator [formula in source] , and APS-type boundary conditions on the seam [formula in source] ; see Appendix app:aps. The geometric package is [formula in source] Here [formula in source] is the geometric Dirac anchor, while [formula in source] is the relative co","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Relative APS and superconnection setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12994,"byte_start":6517,"id":"section:c5b105aee30ed726bcca","kind":"subsection","labels":["cor:bosonic-rank-two","thm:callias-higgs-selection","thm:compact-determinant-higgs-index","thm:compact-higgs-unique","thm:determinant-class-higgs-selection","thm:determinant-clutching"],"line_end":377,"line_start":151,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/001-subsection-from-bridge-to-geometric-completion.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] over the compactified oriented normal sphere [formula in source] . Then the primitive charge generator [formula in source] together with center neutrality and seam-evenness forces the clutching map [formula in source] for [formula in source] , while center neutrality forces [formula in source] for [formula in source] . Therefore [formula in source] This pair is the unique minimal nonnegative a","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bosonic relative index and Higgs selection","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1480,"byte_start":0,"id":"section:003cdf6248c0b3e54f08","kind":"subsection","labels":["eq:41-chain-specialized","fig:41-chain-strip"],"line_end":38,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/002-subsection-closed-texorpdfstring-41-41-chain-after-famil.tex","status_markers_as_written":[],"summary_excerpt":"Once the derived corner theorem and the Higgs uniqueness theorem are in place, the generic abelian-index identity eq:41-chain-main specializes to The extra [formula in source] is precisely the arithmetic contribution of the unique light seam-even Higgs doublet.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Closed [formula in source] 41 chain after family and Higgs closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14761,"byte_start":1480,"id":"section:c8d5c06b887f4073520d","kind":"subsection","labels":["cor:hierarchy-compression-vgeo","def:branch-source-masses","def:physical-ew-scale","eq:carrier-dressed-v","eq:chi-effective-action","eq:induced-einstein","eq:relative-bosonic-endomorphism","fig:chi-bifurcation","lem:two-sheet-zero-mode-normalization","prop:canonical-bosonic-normalization","tab:heat-kernel-map","thm:canonical-einstein-residue","thm:ew-geometric-to-physical-matching"],"line_end":391,"line_start":39,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/002-subsection-closed-texorpdfstring-41-41-chain-after-famil.tex","status_markers_as_written":[],"summary_excerpt":"The local target action is written as the low-curvature expansion of a canonical spectral Einstein functional: The relative bosonic endomorphism used below is and the resulting low-curvature residue decomposition is summarized in tab:heat-kernel-map.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Canonical spectral Einstein functional and geometric Hodge closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2161,"byte_start":0,"id":"section:31fceef207bb54a21eb1","kind":"frontmatter","labels":[],"line_end":71,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/003-subsection-native-charged-current-hard-matching-and-the-.tex","status_markers_as_written":[],"summary_excerpt":"From [formula in source] and [formula in source] one gets [formula in source] Substituting [formula in source] yields [formula in source] Solving for [formula in source] gives the displayed identity. Rewriting the result as [formula in source] one obtains [formula in source] . By thm:operational-completeness, the charged-current residue, the Higgs wave-function factor [formula in source] , the vacuum shift [formula i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12912,"byte_start":2161,"id":"section:9493c97c6a95a3400b9b","kind":"subsection","labels":["def:charged-ew2-seam-projector","eq:charged-ew2-seam-projector","eq:charged-seam-ew2-pullback","eq:tfpt-point-closed-deltar","lem:charged-seam-projector-ew2","thm:charged-current-point-closure","thm:dirac-pole-matching","thm:pole-level-readout"],"line_end":400,"line_start":72,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/003-subsection-native-charged-current-hard-matching-and-the-.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the primitive seam normalization constant and let [formula in source] be the admissible transport pole of thm:algebraic-transport-pole. The charged two-loop electroweak seam projector is Equivalently, using the canonical occupancy bridge [formula in source] , [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Native charged-current hard matching and the charged seam projector","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5872,"byte_start":0,"id":"section:d0943a01ef14269bd91b","kind":"frontmatter","labels":["fig:chi-bifurcation-clean","thm:gravity-cosmology-closure"],"line_end":170,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/004-subsection-absolute-spectral-planck-closure.tex","status_markers_as_written":[],"summary_excerpt":"(seed) at (0,0) primitive channel\\\\ [formula in source] ; (geoz) at (-3.2,-3.6) [formula in source] \\ / Higgs background; (qcd) at (3.2,-1.9) hadronic dressing\\\\ _ [formula in source] [formula in source] [formula in source] [formula in source] _ . This is the clean separation that prevents the Planck/Higgs/QCD scale clash.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12661,"byte_start":5872,"id":"section:46da828feec4ab1bf422","kind":"subsection","labels":["cor:computable-spectral-planck-root","cor:planck_normalization_stationary_branch","lem:strict-convexity-rho-planck","thm:absolute-spectral-planck-closure","thm:boundary-spectral-unit-rigidity","thm:stationary_geometric_scale_equation"],"line_end":391,"line_start":171,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/004-subsection-absolute-spectral-planck-closure.tex","status_markers_as_written":[],"summary_excerpt":"The stationary gravitational scale is no longer treated as a downstream completion block. It is read in boundary-normalized form directly on the main theorem surface.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Absolute spectral Planck closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10154,"byte_start":0,"id":"section:c22bd30db07eb34ac0f6","kind":"frontmatter","labels":["cor:schwarzschild_de_sitter_vacuum_branch","thm:constructive-geometric-measure","thm:geometric-uv-fixed-point","thm:sectorial-hamilton-decomposition","thm:spectral-uv-completion"],"line_end":267,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/005-section-absolute-dimensionless-metrology-from-the-bounda.tex","status_markers_as_written":[],"summary_excerpt":"On the stationary low-curvature vacuum branch the spherically symmetric exterior geometry is [formula in source] In particular the leading horizon radius is [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11015,"byte_start":10154,"id":"section:09632977166e5c21e3d5","kind":"section","labels":["sec:absolute-dimensionless-metrology"],"line_end":296,"line_start":268,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/005-section-absolute-dimensionless-metrology-from-the-bounda.tex","status_markers_as_written":[],"summary_excerpt":"The closed branch should not be read as a source of isolated SI numbers. Its hard content is an internal dimensionless metrology: the boundary datum carries its own spectral unit, the stationary geometric branch fixes the gravitational normalization relative to that unit, the renormalized 1PI action fixes physical electroweak and pole readouts, and only afterwards does one choose an external comparison scheme. In the","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Absolute dimensionless metrology from the boundary branch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11408,"byte_start":11015,"id":"section:57691c569a0485b3aee7","kind":"subsection","labels":["def:boundary-spectral-unit"],"line_end":308,"line_start":297,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/005-section-absolute-dimensionless-metrology-from-the-bounda.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the intrinsic boundary mass unit fixed by thm:boundary-spectral-unit-rigidity. For a physical quantity [formula in source] of mass dimension [formula in source] , define its boundary-normalized readout by [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Boundary spectral unit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13286,"byte_start":11408,"id":"section:64dcd40c0d2e38840998","kind":"subsection","labels":["cor:dimensionless-geometric-hierarchy","cor:dimensionless-planck-metrology","thm:unique-stationary-spectral-planck-root"],"line_end":381,"line_start":309,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/005-section-absolute-dimensionless-metrology-from-the-bounda.tex","status_markers_as_written":[],"summary_excerpt":"By thm:absolute-spectral-planck-closure, the admissible geometric branch carries the unique positive stationary root [formula in source] [formula in source] This root is the boundary-normalized Planck datum of the stationary branch.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Stationary spectral Planck root","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2036,"byte_start":0,"id":"section:f439b413f52df6383104","kind":"subsection","labels":["thm:carrier-exhausted-ir-seam-eigenvalue","thm:sector-dressed-spectral-scale-bifurcation"],"line_end":56,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/006-subsection-infrared-seam-and-sector-bifurcation.tex","status_markers_as_written":[],"summary_excerpt":"The primitive response [formula in source] bifurcates on the closed branch into distinct dressed spectral channels: [formula in source] Here [formula in source] is the stationary Einstein/Higgs background scale, while [formula in source] is the transport-dressed hadronic scale. They share one boundary origin but are not identified on the closed theorem surface.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Infrared seam and sector bifurcation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9065,"byte_start":2036,"id":"section:80fc19abb63f98581723","kind":"subsection","labels":["cor:dimensionless-gravitational-ew-metrology","cor:point-closed-planck-reconstruction","def:tfpt-metrology-functor","thm:dimensionless-ew-residue-matching","thm:dimensionless-pole-mass-readout","thm:dimensionless-tfpt-metrology"],"line_end":278,"line_start":57,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/006-subsection-infrared-seam-and-sector-bifurcation.tex","status_markers_as_written":[],"summary_excerpt":"On the renormalized branch, define [formula in source] Then the quantities [formula in source] are determined by [formula in source] . Consequently [formula in source] and hence [formula in source] is an internal readout of the closed branch.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Physical readout and metrology functor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10669,"byte_start":9065,"id":"section:7af001dbb7c995077871","kind":"subsection","labels":[],"line_end":344,"line_start":279,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/05_geometric_hodge_closure_dimensionless_metrology"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/006-subsection-infrared-seam-and-sector-bifurcation.tex","status_markers_as_written":[],"summary_excerpt":"The next package is stronger but also more conditional. It assumes that the carrier rank, family multiplicity, and seam normalization are all read as closed rather than only partially inherited.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conditional minimal-parameter picture","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":254,"byte_start":0,"id":"section:7682263021ff0db33c3a","kind":"frontmatter","labels":[],"line_end":4,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/06_cosmology_interfaces_downstream_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--06_cosmology_source/sections/001-section-frw-reduction-seam-transfer-and-the-scalaron-bra.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13855,"byte_start":254,"id":"section:045fa5ee1e2a674718cb","kind":"section","labels":["cor:ir-seam-transfer-bounds","fig:cosmology-output-flow","lem:automatic-seam-transfer-convergence","prop:seam-action-cosmology","sec:cosmology-closure","thm:axion-seam-phase","thm:boundary-winding-control","thm:cosmology-closure","thm:frw-cosmology-derivation","thm:leptogenesis-closure"],"line_end":389,"line_start":5,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/06_cosmology_interfaces_downstream_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--06_cosmology_source/sections/001-section-frw-reduction-seam-transfer-and-the-scalaron-bra.tex","status_markers_as_written":[],"summary_excerpt":"The trace-class seam transfer belongs to the main reconstruction surface. The cosmological constant and the reduced scalaron / determinant-line dynamics are therefore fixed directly on the closed branch. Axion, reheating, and leptogenesis quantities are read through explicit interface formulas built from the same theorem-level objects [formula in source] , [formula in source] , and the positive scalaron sector [formu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"FRW reduction, seam transfer, and the scalaron branch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3662,"byte_start":0,"id":"section:2d820500af07a5247cdd","kind":"subsection","labels":["tab:falsification"],"line_end":61,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/06_cosmology_interfaces_downstream_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--06_cosmology_source/sections/002-subsection-falsification-matrix.tex","status_markers_as_written":[],"summary_excerpt":"The present draft does not ask the reader to accept one undifferentiated output claim. Each main-text closure statement has a corresponding local or global failure mode, and those failure modes should be readable without first decoding the appendix tables.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Falsification matrix","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12645,"byte_start":3662,"id":"section:6ac286160fd9206948ae","kind":"subsection","labels":["tab:proof-obligation-ledger"],"line_end":130,"line_start":62,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/06_cosmology_interfaces_downstream_closure"],"relation_ids":["relation:404535c74b6674803cbc","relation:a7dc6cfc5589427aefcd","relation:ed05636733bed7e7dbc1"],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--06_cosmology_source/sections/002-subsection-falsification-matrix.tex","status_markers_as_written":[],"summary_excerpt":"To keep proof status, interface assumptions, and comparison-only layers visibly separated, we record the present audit path explicitly. We use five status classes: ] full proof in manuscript; ] full proof modulo an explicit standard theorem; ] proof sketch in main text with full proof deferred; ] readout or comparison only; ] programmatic closure target with a fixed mathematical statement but without a claimed proof ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Proof-obligation ledger","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16087,"byte_start":12645,"id":"section:27193bdda852d0217b0c","kind":"subsection","labels":["app:ir-seam-continuations","conj:ir-seam-car-continuation","conj:ir-seam-rec-continuation","cor:conditional-lambda-ir-readout"],"line_end":214,"line_start":131,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/06_cosmology_interfaces_downstream_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--06_cosmology_source/sections/002-subsection-falsification-matrix.tex","status_markers_as_written":[],"summary_excerpt":"Theorem thm:cosmology-closure and cor:ir-seam-transfer-bounds determine the theorem-level seam-transfer expression for [formula in source] and its determinant bounds. The numerical scales recorded below require one further infrared assumption and therefore are organized as a labeled conditional closure layer, separated from the theorem core. Each member of the layer is stated as a conjecture or as a corollary conditi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Infrared continuations of the seam transfer","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19871,"byte_start":16087,"id":"section:a9f7b87f0bddb729c73f","kind":"section","labels":["app:frw-interface-proofs","lem:determinant-line-axion-reduction","lem:minisuperspace-reduction-hodge-branch","lem:seam-transfer-vacuum-term","thm:full-frw-interface-theorem"],"line_end":297,"line_start":215,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/06_cosmology_interfaces_downstream_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--06_cosmology_source/sections/002-subsection-falsification-matrix.tex","status_markers_as_written":[],"summary_excerpt":"This appendix section upgrades the cosmology interface block from a proof sketch to a manuscript proof. The point is to keep the theorem-level content at the level of closed-branch interface data, while leaving late-time numerical continuation in the comparison layer.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"FRW reduction and cosmology interface proofs","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20719,"byte_start":19871,"id":"section:2b723594e455a5b956f0","kind":"subsection","labels":[],"line_end":324,"line_start":298,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/06_cosmology_interfaces_downstream_closure"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--06_cosmology_source/sections/002-subsection-falsification-matrix.tex","status_markers_as_written":[],"summary_excerpt":"The axion rows are cosmology readouts generated from the same determinant-line / seam-transfer / scalaron interface data that also fix reheating and the heavy-neutrino scale. On the closed cosmology branch, [formula in source] In standard haloscope units this gives [formula in source] so the practical scan prescription is a conservative window [formula in source] at the quoted coupled sensitivity. The present appendi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Axion interface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":206,"byte_start":0,"id":"section:43e8f3145de38237546d","kind":"frontmatter","labels":[],"line_end":4,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/001-section-downstream-closure-modules-from-the-closed-branc.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1166,"byte_start":206,"id":"section:1372a38f44e33d847460","kind":"section","labels":["sec:downstream_closure_modules"],"line_end":25,"line_start":5,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/001-section-downstream-closure-modules-from-the-closed-branc.tex","status_markers_as_written":["[P]"],"summary_excerpt":"The present section records the downstream closure modules that start from the already fixed branch object [formula in source] Nothing in this section changes the upstream theorem chain. The exact proof status of these downstream closures is recorded in the proof-obligation ledger, and each statement below is phrased only as far as it factors through already fixed branch data. The stationary geometric scale, boundary","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Downstream closure modules from the closed branch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3343,"byte_start":1166,"id":"section:1e7cb3e03bb094463fb0","kind":"subsection","labels":["cor:hawking_temperature_stationary_branch","prop:kerr_compact_object_corrections","prop:wald_entropy_scalaron_branch","thm:modular_horizon_thermality","thm:tensor_scalaron_wave_channel_closure"],"line_end":88,"line_start":26,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/001-section-downstream-closure-modules-from-the-closed-branc.tex","status_markers_as_written":["[P]"],"summary_excerpt":"Assume the split property and stationarity of the exterior wedge algebra on the vacuum branch. Then for the outside algebra one has [formula in source] where [formula in source] is the horizon modular generator. Hence the reduced outside state is KMS and the horizon temperature is [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[P] Stationary horizons, modular thermality, and compact objects","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16917,"byte_start":3343,"id":"section:13e455a1d3a6c1c21277","kind":"subsection","labels":["lem:decorrelation-weil-bound","rem:ergodic-vs-scalar","rem:finite-field-seam-mixer","rem:multiplicity-audit","rem:o20a-operator-level","thm:cmb_seam_phase_realization","thm:cmb_transfer_closure_closed_branch","thm:primordial_mode_closure_seam_state","thm:reheating_fixed_efolds"],"line_end":388,"line_start":89,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/001-section-downstream-closure-modules-from-the-closed-branc.tex","status_markers_as_written":["[P]"],"summary_excerpt":"The number of e folds on the closed branch is fixed by [formula in source] where the closed-branch reheating density [formula in source] is determined by the branch reheating scale [formula in source] , and the constant [formula in source] absorbs the standard pivot conversion [formula in source] at [formula in source] . 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The closed-branch determinant-line phase [formula in source] must be lifted to a determinate element of the spectral basis [formula in source] of [formula in source] on a finite-mode truncation, in","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1054,"byte_start":0,"id":"section:1271025c8f929c701189","kind":"subsection","labels":["cor:no_fuzzy_halo_regime","thm:axion_schrodinger_poisson_closure","thm:relative_admissible_vacuum_energy_finiteness"],"line_end":30,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/003-subsection-p-late-time-dark-sector-and-structure-growth.tex","status_markers_as_written":["[P]"],"summary_excerpt":"The late-time axion sector is governed by [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[P] Late time dark sector and structure growth","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5148,"byte_start":1054,"id":"section:71582daab73a540e5b13","kind":"subsection","labels":["def:scheme-fixed-yukawa-kernel","thm:closed_pole_mass_completion","thm:hadron_pole_masses_singlet_spectrum","thm:higgs_pole_readout_rg_branch"],"line_end":112,"line_start":31,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/003-subsection-p-late-time-dark-sector-and-structure-growth.tex","status_markers_as_written":["[P]"],"summary_excerpt":"Let [formula in source] and let [formula in source] denote the renormalized admissible flow. For every mass-independent renormalization scheme [formula in source] and every renormalization scale [formula in source] , the closed-branch quark mass readout is the scheme-and-scale-fixed map [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[P] Pole masses, Higgs readout, and full flavor output","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5662,"byte_start":5148,"id":"section:f3c733a0d9f99c529344","kind":"subsection","labels":["prop:global_admissible_code_subspace"],"line_end":126,"line_start":113,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/003-subsection-p-late-time-dark-sector-and-structure-growth.tex","status_markers_as_written":["[P]"],"summary_excerpt":"The physical sector is the global admissible code subspace [formula in source] and supports stable record algebras and pointer reductions of the form [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[P] Admissible code subspace, entanglement, and pointer dynamics","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6538,"byte_start":5662,"id":"section:862ecde5e84468525298","kind":"subsection","labels":["conj:topological_phase_slip_burst_channel"],"line_end":150,"line_start":127,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/003-subsection-p-late-time-dark-sector-and-structure-growth.tex","status_markers_as_written":["[P]"],"summary_excerpt":"Local determinant phase slips of the compact mode [formula in source] can source transient radio bursts with characteristic energy scale [formula in source] and photon conversion power [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[P] Topological transient channels and astrophysical bursts","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13335,"byte_start":6538,"id":"section:7c8de613acc23fb18738","kind":"section","labels":["app:comparison","cor:retained-seed-factorization","sec:appendix-empirical-readout","tab:benchmark"],"line_end":267,"line_start":151,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/003-subsection-p-late-time-dark-sector-and-structure-growth.tex","status_markers_as_written":[],"summary_excerpt":"This appendix does not define the theorem-level physical observable object itself. The canonical scheme-facing object is the orbit [formula in source] The tables below record only chosen representatives [formula in source] in declared scheme objects [formula in source] . The appendix is therefore the carrier of the comparison map [formula in source] and remains hard-separated from the theorem chain eq:closed-output-c","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Appendix-level empirical readout","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19593,"byte_start":13335,"id":"section:49a4732ecb6aaa77cb4f","kind":"subsection","labels":["tab:operational-prediction-set"],"line_end":337,"line_start":268,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/003-subsection-p-late-time-dark-sector-and-structure-growth.tex","status_markers_as_written":[],"summary_excerpt":"The narrow empirical readout table is not the whole experimental surface of the manuscript. tab:operational-prediction-set collects the rows that are operationally testable on near- to medium-term timescales, while keeping their status, next test, kill criterion, and dependency structure explicit. The point is not to flatten them into one truth class. Rather, the Status column now uses only the manuscript's final out","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Operational prediction set","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":21800,"byte_start":19593,"id":"section:6634b59abd1e5856a7b0","kind":"subsection","labels":["tab:basis-factorization"],"line_end":365,"line_start":338,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/003-subsection-p-late-time-dark-sector-and-structure-growth.tex","status_markers_as_written":[],"summary_excerpt":"To make the renormalized / physical / scheme hierarchy explicit row by row, the visible appendix surface factors through the basis packages of [formula in source] as follows.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Basis factorization of readout rows","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2938,"byte_start":0,"id":"section:dd4569858aa685fc786f","kind":"subsection","labels":["tab:prediction-ledger"],"line_end":32,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/004-subsection-compact-prediction-ledger.tex","status_markers_as_written":[],"summary_excerpt":"The main empirical readout table shows only a narrow readout surface. To keep the output structure visible, tab:prediction-ledger summarizes which output packages belong to which layer of the paper.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Compact prediction ledger","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3704,"byte_start":2938,"id":"section:4074cd83824ceb930858","kind":"subsection","labels":[],"line_end":43,"line_start":33,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/004-subsection-compact-prediction-ledger.tex","status_markers_as_written":[],"summary_excerpt":"The present main-text readout surface is no longer intentionally mixed. Its rows now use the manuscript's closed classes: theorem, physical observable, scheme projection, and appendix continuation. Carrier algebra and the exact [formula in source] row remain the sharpest numerically load-bearing entries, while the former seed-driven rows are now reorganized by sector rather than counted as one compressed shadow packa","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Empirical readout and kill-test logic","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5683,"byte_start":3704,"id":"section:2940f62e801e3f9c5344","kind":"subsection","labels":["fig:residual-plot"],"line_end":93,"line_start":44,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/004-subsection-compact-prediction-ledger.tex","status_markers_as_written":[],"summary_excerpt":"The residuals for the restricted six-row readout table are shown in fig:residual-plot. The carrier-linked electromagnetic, birefringence, and baryon-density channels all remain within the displayed few-sigma window. The CKM phase is not plotted here because it is better treated in the operational prediction set and Appendix app:benchmarks rather than inside the restricted six-row residual plot.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Residual readout and interface refinements","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5928,"byte_start":5683,"id":"section:3eba10f77107383cdc50","kind":"section","labels":["app:tech"],"line_end":98,"line_start":94,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/004-subsection-compact-prediction-ledger.tex","status_markers_as_written":[],"summary_excerpt":"This appendix collects the technical bookkeeping that supports the boundary-to-carrier presentation but would slow the early main-text flow if placed before the carrier theorem.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Technical conventions and data layers","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7658,"byte_start":5928,"id":"section:29cf0c90b46e29d07cfe","kind":"subsection","labels":["tab:relative-objects"],"line_end":123,"line_start":99,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/004-subsection-compact-prediction-ledger.tex","status_markers_as_written":[],"summary_excerpt":"The adjective relative is used in one fixed sense throughout the paper: every operator or action is compared to a declared reference object.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Relative objects","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11024,"byte_start":7658,"id":"section:56aeac129663ec15f98f","kind":"subsection","labels":["tab:layered-datum"],"line_end":195,"line_start":124,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/004-subsection-compact-prediction-ledger.tex","status_markers_as_written":[],"summary_excerpt":"The technical bookkeeping behind the manuscript uses five levels: [formula in source] [formula in source] [formula in source] [formula in source] [formula in source] Here [formula in source] is the primitive boundary kernel, while [formula in source] is the derived theorem-level post-carrier kernel reconstructed from the joint discrete datum and the full selector.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Layered datum and admissibility","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19401,"byte_start":11024,"id":"section:5c8c49a3dba7767a1392","kind":"subsection","labels":["tab:symbol-guide","tab:symbol-guide-appendix","tab:symbol-guide-theorem"],"line_end":293,"line_start":196,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/004-subsection-compact-prediction-ledger.tex","status_markers_as_written":[],"summary_excerpt":"The symbol guide is split into two tables to keep theorem-level objects lexically separate from appendix-only comparison and readout objects. tab:symbol-guide-theorem contains only symbols that participate in the main-text theorem chain; tab:symbol-guide-appendix contains only symbols that live in the appendix-level comparison and readout layer.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Symbol guide","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19616,"byte_start":19401,"id":"section:f9b8b8f5a95d9b4c2b47","kind":"section","labels":["app:constants"],"line_end":298,"line_start":294,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/004-subsection-compact-prediction-ledger.tex","status_markers_as_written":[],"summary_excerpt":"This appendix collects material that is useful for internal compression but should not dominate the main-text scope of explicit claims.","summary_method":"opening prose excerpt; 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TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Global rotation angle and constants atlas","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1570,"byte_start":0,"id":"section:1c914a18a77b1689724d","kind":"subsection","labels":[],"line_end":33,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/005-subsection-texorpdfstring-e-8-e8-as-downstream-scale-gra.tex","status_markers_as_written":[],"summary_excerpt":"In the present paper E [formula in source] is not used as a primitive cause. The retained parameter is [formula in source] On the retained branch this means [formula in source] The intended reading is a downstream scale grammar: the carrier packet fixes [formula in source] , [formula in source] then defines an optional ladder parameter, the ladder is allowed to organize scale spacing, but it does not replace the carr","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"E [formula in source] E8 as downstream scale grammar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4293,"byte_start":1570,"id":"section:baeb2e7a403904ee5599","kind":"subsection","labels":["tab:e8-full-atlas"],"line_end":68,"line_start":34,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/005-subsection-texorpdfstring-e-8-e8-as-downstream-scale-gra.tex","status_markers_as_written":[],"summary_excerpt":"The full real-domain atlas up to [formula in source] extends the main-text robust table with restricted-scan candidates and IR tail conjectures. Rows are classified as robust (restrictive grammar, unambiguous target), restricted-scan (plausible but less constrained), or tail conjecture (new trace class [formula in source] not yet derived from block structure).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Full stage atlas","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6440,"byte_start":4293,"id":"section:c9d32535641ba6dbd520","kind":"subsection","labels":["eq:41-chain"],"line_end":117,"line_start":69,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/005-subsection-texorpdfstring-e-8-e8-as-downstream-scale-gra.tex","status_markers_as_written":[],"summary_excerpt":"The main-text compression identities are developed in the dedicated section on compression identities and numerical comparison of alternative discrete worlds. This appendix subsection collects additional arithmetic continuations and the compression chain summary.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Compression identities on the minimal branch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11215,"byte_start":6440,"id":"section:6c4495375560cd846f4b","kind":"subsection","labels":["rem:defect-factorization-gcd-lcm"],"line_end":280,"line_start":118,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/005-subsection-texorpdfstring-e-8-e8-as-downstream-scale-gra.tex","status_markers_as_written":[],"summary_excerpt":"The next relations mix the main-text carrier with optional appendix-level E [formula in source] , inflation, or geometric notation. They are useful compression patterns, but their interpretation should remain conditional or conjectural.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Optional arithmetic continuations","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12819,"byte_start":11215,"id":"section:77b6ff177c8af9c8c5e6","kind":"subsection","labels":[],"line_end":346,"line_start":281,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/005-subsection-texorpdfstring-e-8-e8-as-downstream-scale-gra.tex","status_markers_as_written":[],"summary_excerpt":"The next package is stronger but also more conditional. It assumes that the carrier rank, family multiplicity, and seam normalization are all read as closed rather than only partially inherited.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conditional minimal-parameter picture","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3358,"byte_start":0,"id":"section:22cc51480536a5e53274","kind":"subsection","labels":["app:ir-seam-continuations","conj:ir-seam-car-continuation","conj:ir-seam-rec-continuation","cor:conditional-lambda-ir-readout"],"line_end":82,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/006-subsection-infrared-continuations-of-the-seam-transfer.tex","status_markers_as_written":[],"summary_excerpt":"Theorem thm:cosmology-closure and cor:ir-seam-transfer-bounds determine the theorem-level seam-transfer expression for [formula in source] and its determinant bounds. The numerical scales recorded below require one further infrared assumption and therefore are organized as a labeled conditional closure layer, separated from the theorem core. Each member of the layer is stated as a conjecture or as a corollary conditi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Infrared continuations of the seam transfer","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4331,"byte_start":3358,"id":"section:e528aa449e36702aba5a","kind":"section","labels":["app:aps"],"line_end":95,"line_start":83,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/006-subsection-infrared-continuations-of-the-seam-transfer.tex","status_markers_as_written":[],"summary_excerpt":"The geometric completion uses APS-type relative data aps1975. In practice this means: one works with a declared pair [formula in source] rather than a single unanchored operator, boundary conditions on the seam [formula in source] are part of the definition of the relative index, the [formula in source] -term keeps track of the residual spectral asymmetry, the superconnection package is used in the same spirit as the","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Relative APS and superconnection setup","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4411,"byte_start":4331,"id":"section:849a5ab4e7e29988291c","kind":"section","labels":["app:os-fermions"],"line_end":98,"line_start":96,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/006-subsection-infrared-continuations-of-the-seam-transfer.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Relative reflection positivity with fermions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4898,"byte_start":4411,"id":"section:6f97adf469554f5ab3a4","kind":"subsection","labels":[],"line_end":108,"line_start":99,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/006-subsection-infrared-continuations-of-the-seam-transfer.tex","status_markers_as_written":[],"summary_excerpt":"The relative Euclidean theory used in the main closure section is not interpreted as a difference of measures. Instead it is organized as the normalized quotient [formula in source] Because the denominator is source independent on the admissible sector, the reference theory acts only as a fixed normalizer and does not interfere with reflection positivity.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Normalized quotient form","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5932,"byte_start":4898,"id":"section:3e62027d730eadf67cd3","kind":"subsection","labels":[],"line_end":126,"line_start":109,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/006-subsection-infrared-continuations-of-the-seam-transfer.tex","status_markers_as_written":[],"summary_excerpt":"The commutation relations [formula in source] ensure that reflection preserves the admissible subspace. The bosonic part then follows the standard Markov / reflection-stable Osterwalder–Schrader argument on admissible observables. For fermions, the admissible CAR kernel may be written as a reflected quadratic form; equivalently one may express the same condition as positivity of the associated Pfaffian structure on t","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bosonic and fermionic positivity on [formula in source] Padm","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6345,"byte_start":5932,"id":"section:46aaa0c485552cb0fd29","kind":"section","labels":["app:os-scattering"],"line_end":134,"line_start":127,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/006-subsection-infrared-continuations-of-the-seam-transfer.tex","status_markers_as_written":[],"summary_excerpt":"This appendix upgrades the admissible Schwinger, reconstruction, and scattering block from a named standard interface to a manuscript-level proof package. The point is not to replace standard machinery by ad hoc notation, but to verify explicitly that the admissible branch satisfies the relevant hypotheses on [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Admissible OS reconstruction and asymptotic scattering","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8476,"byte_start":6345,"id":"section:db98896cc2bd07a555c8","kind":"subsection","labels":["lem:graded-euclidean-covariance-padm","lem:tempered-schwinger-bounds"],"line_end":170,"line_start":135,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/006-subsection-infrared-continuations-of-the-seam-transfer.tex","status_markers_as_written":[],"summary_excerpt":"On the Euclidean continuation of [formula in source] , each truncated admissible Schwinger distribution [formula in source] defines a tempered distribution. Moreover, for every compact [formula in source] and every source monomial of total degree [formula in source] , its moments obey polynomial bounds determined by the same uniform heat-kernel estimates and finite local moments of the admissible constructive measure","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Tempered admissible Schwinger families","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10863,"byte_start":8476,"id":"section:1e113de17835fcbe0cf8","kind":"subsection","labels":["thm:tailored-os-car-reconstruction"],"line_end":211,"line_start":171,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/006-subsection-infrared-continuations-of-the-seam-transfer.tex","status_markers_as_written":[],"summary_excerpt":"Padm] Let [formula in source] be the admissible Schwinger family on the Euclidean continuation of [formula in source] . If reflection positivity, temperedness, graded Euclidean covariance, graded symmetry, and clustering hold on [formula in source] , then there exist: a Hilbert space [formula in source] with vacuum vector [formula in source] , a strongly continuous positive-energy semigroup [formula in source] with s","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"OS and CAR reconstruction on [formula in source] Padm","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13216,"byte_start":10863,"id":"section:a793a2e5f9c55b10d109","kind":"subsection","labels":["cor:lsz-admissible-massive","lem:one-particle-projectors-from-poles","thm:haag-ruelle-admissible-massive"],"line_end":256,"line_start":212,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/006-subsection-infrared-continuations-of-the-seam-transfer.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] have an isolated simple pole with positive residue at [formula in source] . Then the corresponding one-particle contribution defines a positive spectral projector on the admissible Hilbert space.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Stable massive Haag–Ruelle and LSZ closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13873,"byte_start":13216,"id":"section:8179568fc4c8c5884599","kind":"subsection","labels":[],"line_end":271,"line_start":257,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/006-subsection-infrared-continuations-of-the-seam-transfer.tex","status_markers_as_written":[],"summary_excerpt":"The massless sector is not treated by bare Fock asymptotics in the present manuscript. The relevant object is the infrared-dressed interface package [formula in source] constructed from the soft charges of the admissible local net on the low-curvature region [formula in source] . This is exactly the interface package used in the main-text theorem thm:dressed-massless-interface.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dressed massless interface in the low-curvature region","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17594,"byte_start":13873,"id":"section:e1dd48d5555a9b0f5e6d","kind":"section","labels":["app:frw-interface-proofs","lem:determinant-line-axion-reduction","lem:minisuperspace-reduction-hodge-branch","lem:seam-transfer-vacuum-term","thm:full-frw-interface-theorem"],"line_end":352,"line_start":272,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/006-subsection-infrared-continuations-of-the-seam-transfer.tex","status_markers_as_written":[],"summary_excerpt":"This appendix section upgrades the cosmology interface block from a proof sketch to a manuscript proof. The point is to keep the theorem-level content at the level of closed-branch interface data, while leaving late-time numerical continuation in the comparison layer.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"FRW reduction and cosmology interface proofs","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1970,"byte_start":0,"id":"section:2334f2b3d13fcb70cd58","kind":"section","labels":["app:yukawa"],"line_end":38,"line_start":1,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/007-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"This appendix is the proof motor for the transport positivity, determinant-phase suppression, and bounded-residual statements used in the main text. The transport program is based on the regularized kernel [formula in source] Three remarks are important. The regulator [formula in source] is not optional: without it the kernel becomes ill-defined exactly where the admissibility question is most delicate. Positivity of","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Yukawa kernels and positivity lemmas","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2635,"byte_start":1970,"id":"section:26bf85fbb0c246d4fa02","kind":"subsection","labels":[],"line_end":54,"line_start":39,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/007-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"As an appendix-level dynamical sharpening of the hadronic admissibility theorem, one may further require the admissible center-neutral Wilson functional to obey strong-coupling dominance. On that optional route the relative Wilson loop satisfies [formula in source] and the physical Hilbert space contains no color-nonsinglet asymptotic states. This statement is kept in the appendix so that the main theorem surface doe","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Optional strong-coupling sharpening","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3077,"byte_start":2635,"id":"section:8a3d558aff0027052310","kind":"section","labels":["app:info-readings"],"line_end":62,"line_start":55,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/007-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"This appendix collects interpretive notes that help organize the algebraic structure of the boundary-polarized closed form. When a theorem-level statement appears below, it refers back to a main-text proposition; the appendix itself does not upgrade any status label beyond the declared theorem / derived-consequence / comparison / appendix discipline.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Information-theoretic and cut-and-project readings","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4271,"byte_start":3077,"id":"section:149909dc865f03cd1dd3","kind":"subsection","labels":["tab:checksum-41"],"line_end":88,"line_start":63,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/007-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"The canonical [formula in source] -chain admits a compact overdetermination reading:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[formula in source] 41-chain overdetermination of the canonical branch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5659,"byte_start":4271,"id":"section:d235520883fe98187cc3","kind":"subsection","labels":[],"line_end":120,"line_start":89,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/007-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"The bridge identities also admit a disciplined probabilistic reading. Since [formula in source] the Cabibbo scale is exactly the standard-deviation scale of a Bernoulli variable with success probability [formula in source] : [formula in source] Equivalently, the Fisher information of the Bernoulli family is [formula in source] so the Cabibbo bridge measures the inverse square-root Fisher scale of the retained seed. T","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Seed variance and surprisal readings","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8313,"byte_start":5659,"id":"section:e54150bab4029806cfd3","kind":"subsection","labels":[],"line_end":178,"line_start":121,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/007-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"The strongest information-theoretic statement is no longer a loose analogy. By prop:parity-code-family, the one-family packet is exactly the even-parity subspace on five occupation bits, [formula in source] so the carrier packet is kinematically the classical even-parity [formula in source] code. 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The stronger generative theorem path described in the conclusion would refine this object to the global admissible vacuum functional [formula in source] whose variations also select the transport branch. In this append","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Minimal admissible vacuum","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11812,"byte_start":11391,"id":"section:809be784f961d8ece0b0","kind":"subsection","labels":[],"line_end":267,"line_start":254,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/007-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"One useful coarse-grained record algebra is [formula in source] As [formula in source] decreases, more stable channels open. The intended arrow-of-time claim is therefore [formula in source] but only as a record-growth principle, not as a replacement for detailed nonequilibrium dynamics.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Record growth principle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12813,"byte_start":11812,"id":"section:74dd7cb9d9f61f22d69e","kind":"subsection","labels":["thm:born-pointer-algebra"],"line_end":296,"line_start":268,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/007-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"An observer is modeled as a stable pointer subalgebra [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Observer algebra and Born-type evaluation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13220,"byte_start":12813,"id":"section:725515bc8290a1e12fb1","kind":"section","labels":["app:horizons"],"line_end":304,"line_start":297,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/007-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"This appendix section records the horizon-side analytic input that supports the downstream modular thermality program. 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These items organize downstream interpretation, but they do not add new upstream theorem arrows to the rigid core.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Prediction semantics and transient event channels","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15174,"byte_start":14814,"id":"section:8aa39ee34ff0459a7794","kind":"subsection","labels":[],"line_end":360,"line_start":347,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/007-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"The main-text prediction map can be decorated by explicit experimental metadata as [formula in source] with [formula in source] This is kept only as an optional formal extension.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Prediction semantics","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15503,"byte_start":15174,"id":"section:6dc4af30cbb0c1ea9ae6","kind":"subsection","labels":[],"line_end":366,"line_start":361,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/007-section-yukawa-kernels-and-positivity-lemmas.tex","status_markers_as_written":[],"summary_excerpt":"The topological burst channel of conj:topological_phase_slip_burst_channel is kept at programmatic-target status. 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Derived consequences that still depend on internal branch formulas are excluded.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Empirical comparison surface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16262,"byte_start":15917,"id":"section:3fb1165fb73a951f577a","kind":"section","labels":["app:benchmarks"],"line_end":183,"line_start":179,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/008-section-closed-theoretical-outputs-and-empirical-compari.tex","status_markers_as_written":[],"summary_excerpt":"This appendix turns the broader prediction surface into explicit experimental bookkeeping. 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On the closed cosmology branch, [formula in source] In standard haloscope units this gives [formula in source] so the practical scan prescription is a conservative window [formula in source] at the quoted coupled sensitivity. The present appendi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Axion interface","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":29372,"byte_start":23733,"id":"section:57c2b014c34f4084e9c9","kind":"subsection","labels":["cor:charged-lepton-source-compression","tab:mass-source-supplement"],"line_end":351,"line_start":271,"occurrence":1,"owner_documents":["document:_archive/tfpt-45/technical_companion"],"relation_ids":[],"semantic_review":false,"source":"documents/archive--tfpt-45--source_extracts--technical_companion_source/sections/008-section-closed-theoretical-outputs-and-empirical-compari.tex","status_markers_as_written":[],"summary_excerpt":"The compact main-text mass ledgers intentionally suppress explicit formula detail. The source rows collected here retain that information without forcing the main text to read like a mixed formula notebook. 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The claim of novelty is not that these background ingredients are new in isolation, but that the minimal [formula in source] carrier packet, the compression identities, and the boundary-polarized closed architecture are organized into one tightly overdetermined program. Conver","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Novelty boundary and literature positioning","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1279,"byte_start":0,"id":"section:9a5dd1c78bb19be16661","kind":"frontmatter","labels":[],"line_end":45,"line_start":1,"occurrence":1,"owner_documents":["document:articles/2026-08-28/psi_lambda_convergence_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-28--psi_lambda_convergence_theorem_en/preamble.tex","status_markers_as_written":[],"summary_excerpt":"colorlinks=true, linkcolor=blue!55!black, citecolor=blue!55!black, urlcolor=blue!55!black","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[formula in source] Psi-lambda at the Quasi-Free Boundary:\\\\ Finite-Window Implementers, the [formula in source] Z4 Tower, and the Two-Edge Shale Obstruction","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":1473,"byte_start":0,"id":"section:5065e3400c5076398222","kind":"frontmatter","labels":[],"line_end":32,"line_start":1,"occurrence":1,"owner_documents":["document:articles/2026-08-28/psi_lambda_convergence_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-28--psi_lambda_convergence_theorem_en/sections/001-section-scope-frozen-input-and-the-necessary-correction.tex","status_markers_as_written":[],"summary_excerpt":"We prove the strongest statement presently justified by the frozen finite-collar data on the proposed field [formula in source] . On every fixed finite window, trace-norm convergence of the restricted covariances gives, after the canonical Araki–Wyss purification, canonical Bogoliubov implementers with an explicit Shale bound. Along every coherent subsequence these implementers converge, in fact in operator norm; the","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[]},{"byte_end":1534,"byte_start":1473,"id":"section:40a41b2194399cebbf35","kind":"section","labels":[],"line_end":34,"line_start":33,"occurrence":1,"owner_documents":["document:articles/2026-08-28/psi_lambda_convergence_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-28--psi_lambda_convergence_theorem_en/sections/001-section-scope-frozen-input-and-the-necessary-correction.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Scope, frozen input, and the necessary correction","topic_suggestions":[]},{"byte_end":3471,"byte_start":1534,"id":"section:b1ed2cc2005cadecb029","kind":"subsection","labels":[],"line_end":85,"line_start":35,"occurrence":1,"owner_documents":["document:articles/2026-08-28/psi_lambda_convergence_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-28--psi_lambda_convergence_theorem_en/sections/001-section-scope-frozen-input-and-the-necessary-correction.tex","status_markers_as_written":[],"summary_excerpt":"The one-particle lattice Hamiltonian used in the quantitative probes is the Qi–Wu–Zhang collar [formula in source] on a cylinder of circumference [formula in source] , open width [formula in source] , and boundary twist [formula in source] , [formula in source] . The topological and trivial controls are [formula in source] and [formula in source] , respectively. If [formula in source] denotes the finite one-particle ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The frozen input","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":3588,"byte_start":3471,"id":"section:22866ebd1bb6a6c4dd9f","kind":"subsection","labels":[],"line_end":89,"line_start":86,"occurrence":1,"owner_documents":["document:articles/2026-08-28/psi_lambda_convergence_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-28--psi_lambda_convergence_theorem_en/sections/001-section-scope-frozen-input-and-the-necessary-correction.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Why the originally proposed implication is false","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"}]},{"byte_end":4007,"byte_start":3588,"id":"section:5881aed8196c0715700a","kind":"paragraph","labels":[],"line_end":99,"line_start":90,"occurrence":1,"owner_documents":["document:articles/2026-08-28/psi_lambda_convergence_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-28--psi_lambda_convergence_theorem_en/sections/001-section-scope-frozen-input-and-the-necessary-correction.tex","status_markers_as_written":[],"summary_excerpt":"If [formula in source] is a proper window projection and [formula in source] is a global Fermi projection, then [formula in source] is generally a positive contraction, not a projection: [formula in source] Consequently, Shale–Stinespring cannot be applied to [formula in source] as though it were a Fock polarization. We repair this by the canonical Araki–Wyss purification in Section","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"A compressed covariance is not a polarization.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":4455,"byte_start":4007,"id":"section:464734c52bee24090d15","kind":"paragraph","labels":[],"line_end":107,"line_start":100,"occurrence":1,"owner_documents":["document:articles/2026-08-28/psi_lambda_convergence_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-28--psi_lambda_convergence_theorem_en/sections/001-section-scope-frozen-input-and-the-necessary-correction.tex","status_markers_as_written":[],"summary_excerpt":"Even in finite dimension, two mixed covariances [formula in source] and [formula in source] need not be unitarily conjugate: unitary conjugacy preserves the spectrum. Thus [formula in source] or [formula in source] does not by itself produce a Bogoliubov map on the original window CAR algebra. It does produce a canonical equivalence of the purified standard forms, which is the exact local result proved below.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Two covariances do not specify a sector automorphism.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":4867,"byte_start":4455,"id":"section:d6226513307cef2759f6","kind":"paragraph","labels":[],"line_end":114,"line_start":108,"occurrence":1,"owner_documents":["document:articles/2026-08-28/psi_lambda_convergence_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-28--psi_lambda_convergence_theorem_en/sections/001-section-scope-frozen-input-and-the-necessary-correction.tex","status_markers_as_written":[],"summary_excerpt":"A fit on [formula in source] cannot prove divergence as [formula in source] , and inequalities checked only for [formula in source] cannot prove an energy estimate for every [formula in source] . We therefore prove the logarithm exactly for the universal two-chiral-edge model and state the precise uniform-remainder hypothesis under which its coefficient transfers to a lattice collar.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Finite observations are not asymptotic theorems.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":7585,"byte_start":4867,"id":"section:621b005f0e4aa97fc0f2","kind":"section","labels":["thm:ps","thm:ss"],"line_end":186,"line_start":115,"occurrence":1,"owner_documents":["document:articles/2026-08-28/psi_lambda_convergence_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-28--psi_lambda_convergence_theorem_en/sections/001-section-scope-frozen-input-and-the-necessary-correction.tex","status_markers_as_written":[],"summary_excerpt":"Only two external analytic results are used in the proof. They are quoted here in the form needed below.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Classical theorems used, with full statements","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":7657,"byte_start":7585,"id":"section:9ca15eda535a5c9af5b8","kind":"section","labels":["sec:local"],"line_end":189,"line_start":187,"occurrence":1,"owner_documents":["document:articles/2026-08-28/psi_lambda_convergence_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-28--psi_lambda_convergence_theorem_en/sections/001-section-scope-frozen-input-and-the-necessary-correction.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Finite-window implementers and convergence","topic_suggestions":[]},{"byte_end":9411,"byte_start":7657,"id":"section:58de068d51a5df217528","kind":"subsection","labels":["eq:purification-bound","lem:purification"],"line_end":266,"line_start":190,"occurrence":1,"owner_documents":["document:articles/2026-08-28/psi_lambda_convergence_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-28--psi_lambda_convergence_theorem_en/sections/001-section-scope-frozen-input-and-the-necessary-correction.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the finite-dimensional one-particle space of a fixed window and let [formula in source] be a covariance, so [formula in source] . Put [formula in source] and define [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Canonical purification of a window covariance","topic_suggestions":[]},{"byte_end":8981,"byte_start":0,"id":"section:40997fa8df4a235e1a32","kind":"subsection","labels":["cor:measured","eq:angle","eq:direct-rotation","eq:field-bound","eq:implementer-norm","eq:intertwine-S","eq:local-shale","eq:nparticle","eq:shale-equality","eq:spin-bound","eq:trace-conv","lem:rotation","thm:local"],"line_end":286,"line_start":1,"occurrence":1,"owner_documents":["document:articles/2026-08-28/psi_lambda_convergence_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-28--psi_lambda_convergence_theorem_en/sections/002-subsection-the-direct-rotation.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be finite-rank orthogonal projections of equal rank and suppose [formula in source] . Set [formula in source] Then [formula in source] is unitary, [formula in source] , and [formula in source] depends continuously in operator norm on [formula in source] throughout the open set [formula in source] . In addition, [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The direct rotation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":6635,"byte_start":0,"id":"section:ac3bc77b2d4a37b12824","kind":"section","labels":["eq:average-expectation","eq:coefficient-expectation","eq:compatible-clock","eq:fusion","eq:limit-crossed","eq:naturality","eq:phi","sec:tower","thm:crossed"],"line_end":213,"line_start":1,"occurrence":1,"owner_documents":["document:articles/2026-08-28/psi_lambda_convergence_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-28--psi_lambda_convergence_theorem_en/sections/003-section-the-exact-texorpdfstring-mathbb-z-4-z4-tower.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be a unital inductive system of finite matrix algebras. Suppose [formula in source] is unitary, [formula in source] and let [formula in source] . Write [formula in source] for the canonical crossed-product unitary: [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The exact [formula in source] Z4 tower","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":6716,"byte_start":6635,"id":"section:0e68b7c0b5a826478097","kind":"section","labels":["sec:global"],"line_end":216,"line_start":214,"occurrence":1,"owner_documents":["document:articles/2026-08-28/psi_lambda_convergence_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-28--psi_lambda_convergence_theorem_en/sections/003-section-the-exact-texorpdfstring-mathbb-z-4-z4-tower.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"The quarter-twist logarithm and global obstruction","topic_suggestions":[]},{"byte_end":10488,"byte_start":6716,"id":"section:f339c82d64d93ca81452","kind":"subsection","labels":["eq:finite-sum","eq:harmonic","eq:multiplicity","eq:one-edge-log","eq:overlap","eq:projection-distance","eq:summand-expand","eq:tail","lem:overlap","thm:oneedge"],"line_end":354,"line_start":217,"occurrence":1,"owner_documents":["document:articles/2026-08-28/psi_lambda_convergence_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-28--psi_lambda_convergence_theorem_en/sections/003-section-the-exact-texorpdfstring-mathbb-z-4-z4-tower.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] . For [formula in source] and [formula in source] , define [formula in source] Both families are orthonormal bases. Let [formula in source] be the projection onto the closed span of [formula in source] and [formula in source] the projection onto the closed span of [formula in source] . The shift [formula in source] is exactly the momentum displacement [formula in source] relative to the spacin","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"One chiral edge","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":3839,"byte_start":0,"id":"section:5cad1e3e7c2a13d9114b","kind":"subsection","labels":["cor:twoedge","eq:quarter-coefficient","eq:remainder","eq:stable-log","eq:two-edge-log","lem:stability","thm:nonimpl"],"line_end":114,"line_start":1,"occurrence":1,"owner_documents":["document:articles/2026-08-28/psi_lambda_convergence_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-28--psi_lambda_convergence_theorem_en/sections/004-subsection-two-edges-and-comparison-with-the-qwz-measure.tex","status_markers_as_written":[],"summary_excerpt":"For two independent chiral edge branches, one at each boundary of a cylinder, the direct-sum polarizations satisfy [formula in source] For the adjacent [formula in source] sectors, [formula in source] , hence [formula in source] The difference from the measured slope [formula in source] is [formula in source] , or approximately [formula in source] of [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Two edges and comparison with the QWZ measurement","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":6586,"byte_start":3839,"id":"section:dd0bf1dd33c6b6abf274","kind":"section","labels":["thm:main"],"line_end":177,"line_start":115,"occurrence":1,"owner_documents":["document:articles/2026-08-28/psi_lambda_convergence_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-28--psi_lambda_convergence_theorem_en/sections/004-subsection-two-edges-and-comparison-with-the-qwz-measure.tex","status_markers_as_written":[],"summary_excerpt":"Consider a sequence of finite quadratic fermion systems with four [formula in source] -twisted sectors and a nested family of fixed finite windows. Assume the following precise hypotheses. On each fixed window, the restricted covariances [formula in source] converge in trace norm. For the adjacent sectors [formula in source] , their limiting Araki–Wyss projections have distance strictly less than one. In particular, ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Combined strongest theorem","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":6639,"byte_start":6586,"id":"section:d28c30435586af4ef9e4","kind":"section","labels":[],"line_end":179,"line_start":178,"occurrence":1,"owner_documents":["document:articles/2026-08-28/psi_lambda_convergence_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-28--psi_lambda_convergence_theorem_en/sections/004-subsection-two-edges-and-comparison-with-the-qwz-measure.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"What this theorem does and does not close","topic_suggestions":[]},{"byte_end":8306,"byte_start":6639,"id":"section:34871a67e03c377b97d2","kind":"subsection","labels":[],"line_end":216,"line_start":180,"occurrence":1,"owner_documents":["document:articles/2026-08-28/psi_lambda_convergence_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-28--psi_lambda_convergence_theorem_en/sections/004-subsection-two-edges-and-comparison-with-the-qwz-measure.tex","status_markers_as_written":[],"summary_excerpt":"Theorem fixed purified finite window. It does not prove convergence of a nontrivial charged intertwiner on one common infinite-volume edge Fock space. The measured inequalities with [formula in source] concern only [formula in source] and finite [formula in source] ; they do not imply [formula in source] Thus G1 remains open in its contract meaning.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Relation to G1–G4","topic_suggestions":[]},{"byte_end":9753,"byte_start":8306,"id":"section:6708abbb536bd1de838f","kind":"subsection","labels":[],"line_end":242,"line_start":217,"occurrence":1,"owner_documents":["document:articles/2026-08-28/psi_lambda_convergence_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-28--psi_lambda_convergence_theorem_en/sections/004-subsection-two-edges-and-comparison-with-the-qwz-measure.tex","status_markers_as_written":[],"summary_excerpt":"T. J. Osborne and A. Stottmeister, Conformal field theory from lattice fermions, Communications in Mathematical Physics 398 (2023), 219–283, https://arxiv.org/abs/2107.13834arXiv:2107.13834, prove strong convergence of the lattice fermion-bilinear currents on a finite-particle core (Theorem 5.1 for the displayed [formula in source] current, with the nonabelian bilinear extension by the Cauchy–Schwarz reduction around","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The MMST/Osborne–Stottmeister leg","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":10316,"byte_start":9753,"id":"section:cefe6e9e3ebe205d854e","kind":"subsection","labels":[],"line_end":256,"line_start":243,"occurrence":1,"owner_documents":["document:articles/2026-08-28/psi_lambda_convergence_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-28--psi_lambda_convergence_theorem_en/sections/004-subsection-two-edges-and-comparison-with-the-qwz-measure.tex","status_markers_as_written":[],"summary_excerpt":"The coefficient [formula in source] has a sharp analytic explanation: each chiral boundary contributes [formula in source] and the two boundaries contribute [formula in source] . The measured intercept [formula in source] is nonuniversal and receives bulk, ultraviolet, and finite-width contributions. To turn the coefficient match into a proof for the QWZ collar, one must establish the decomposition in the frozen prob","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Status of the measured QWZ logarithm","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":11938,"byte_start":10316,"id":"section:4889b76b941abf2a6f8d","kind":"section","labels":[],"line_end":299,"line_start":257,"occurrence":1,"owner_documents":["document:articles/2026-08-28/psi_lambda_convergence_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-28--psi_lambda_convergence_theorem_en/sections/004-subsection-two-edges-and-comparison-with-the-qwz-measure.tex","status_markers_as_written":[],"summary_excerpt":"red!65!blackred!3 0.91 Remaining gap (exact statement). For the [formula in source] , [formula in source] QWZ collar with quarter-twisted sectors, construct isometric embeddings of all finite-volume one-particle spaces into one edge Hilbert space and prove simultaneously: [formula in source] and there exist phase-coherent lattice intertwiners [formula in source] converging on one common finite-energy core to a nonzer","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Remaining gap","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"}]},{"byte_end":13473,"byte_start":11938,"id":"section:1ce7030a28aaa128aba2","kind":"section","labels":[],"line_end":342,"line_start":300,"occurrence":1,"owner_documents":["document:articles/2026-08-28/psi_lambda_convergence_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-28--psi_lambda_convergence_theorem_en/sections/004-subsection-two-edges-and-comparison-with-the-qwz-measure.tex","status_markers_as_written":[],"summary_excerpt":"The quasi-free conclusions that can be proved today are complete: finite-window standard-form implementers with an explicit Shale bound, their coherent strong convergence, the natural inner- [formula in source] crossed-product tower with correctly qualified unique expectations, and the universal two-edge quarter-twist obstruction with coefficient [formula in source] . The data strongly match this structure, but they ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conclusion","topic_suggestions":[]},{"byte_end":1365,"byte_start":0,"id":"section:0a1a88b1238b1ca5f08f","kind":"frontmatter","labels":[],"line_end":50,"line_start":1,"occurrence":1,"owner_documents":["document:articles/2026-08-29/holomorphic_kms_extension_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-29--holomorphic_kms_extension_en/preamble.tex","status_markers_as_written":[],"summary_excerpt":"colorlinks=true, linkcolor=blue!55!black, citecolor=blue!55!black, urlcolor=blue!55!black","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Holomorphic Rotational KMS Extension Theorem:\\\\ Index Four, the Canonical Expectation, and the TFPT Finite Shadow","topic_suggestions":[]},{"byte_end":1864,"byte_start":0,"id":"section:40019e04da209a36b2f2","kind":"frontmatter","labels":[],"line_end":40,"line_start":1,"occurrence":1,"owner_documents":["document:articles/2026-08-29/holomorphic_kms_extension_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-29--holomorphic_kms_extension_en/sections/001-section-setting-and-correction-of-terminology.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be an irreducible finite-index inclusion of conformal nets on [formula in source] , let [formula in source] for a proper gauge action commuting with rotations, and suppose that [formula in source] is holomorphic, with [formula in source] and central charge [formula in source] . We prove the strongest correct form of the proposed KMS extension statement. At angular inverse temperature [formula ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":1913,"byte_start":1864,"id":"section:102a07ad7c7e71df2b29","kind":"section","labels":[],"line_end":42,"line_start":41,"occurrence":1,"owner_documents":["document:articles/2026-08-29/holomorphic_kms_extension_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-29--holomorphic_kms_extension_en/sections/001-section-setting-and-correction-of-terminology.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Setting and correction of terminology","topic_suggestions":[]},{"byte_end":3030,"byte_start":1913,"id":"section:e79f960793232ca9a42a","kind":"subsection","labels":["eq:holomorphic","eq:local-inclusion"],"line_end":78,"line_start":43,"occurrence":1,"owner_documents":["document:articles/2026-08-29/holomorphic_kms_extension_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-29--holomorphic_kms_extension_en/sections/001-section-setting-and-correction-of-terminology.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be an irreducible local conformal net on [formula in source] in its vacuum representation [formula in source] . Let [formula in source] act properly by vacuum-preserving internal symmetries [formula in source] , meaning [formula in source] for every interval [formula in source] , every conformal transformation [formula in source] , and [formula in source] . Put [formula in source] We assume th","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conformal-net hypotheses","topic_suggestions":[]},{"byte_end":4505,"byte_start":3030,"id":"section:6ba6705516b9eeff9f25","kind":"subsection","labels":["def:geometric","eq:gibbs","eq:omega-def"],"line_end":117,"line_start":79,"occurrence":1,"owner_documents":["document:articles/2026-08-29/holomorphic_kms_extension_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-29--holomorphic_kms_extension_en/sections/001-section-setting-and-correction-of-terminology.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the conformal Hamiltonian and let [formula in source] be the rotation dynamics on the locally normal universal algebra [formula in source] . For [formula in source] put [formula in source] For a completely rational conformal net the character is finite, and the rotational KMS classification quoted below in fact recovers the trace-class property from any extremal KMS state. In the concrete [","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The rotational KMS state","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":4556,"byte_start":4505,"id":"section:ed332b01c8f86a4254a7","kind":"section","labels":[],"line_end":119,"line_start":118,"occurrence":1,"owner_documents":["document:articles/2026-08-29/holomorphic_kms_extension_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-29--holomorphic_kms_extension_en/sections/001-section-setting-and-correction-of-terminology.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Classical theorems used, stated in full","topic_suggestions":[]},{"byte_end":6023,"byte_start":4556,"id":"section:822cfcea14e75bfdc29e","kind":"subsection","labels":["eq:araki-cov","thm:araki"],"line_end":155,"line_start":120,"occurrence":1,"owner_documents":["document:articles/2026-08-29/holomorphic_kms_extension_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-29--holomorphic_kms_extension_en/sections/001-section-setting-and-correction-of-terminology.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be a complex Hilbert space, let [formula in source] be a possibly unbounded one-particle Hamiltonian, and let [formula in source] be the strongly continuous Bogoliubov dynamics on [formula in source] determined on generators by [formula in source] For every [formula in source] there is a gauge-invariant quasi-free state [formula in source] whose two-point function is [formula in source] and wh","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Araki's CAR KMS theorem","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":7339,"byte_start":6023,"id":"section:d8c85cafb513974c7139","kind":"subsection","labels":["eq:mod-restrict","eq:takesaki-intertwine","thm:takesaki"],"line_end":190,"line_start":156,"occurrence":1,"owner_documents":["document:articles/2026-08-29/holomorphic_kms_extension_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-29--holomorphic_kms_extension_en/sections/001-section-setting-and-correction-of-terminology.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be a von Neumann algebra, let [formula in source] be a faithful normal semifinite weight on [formula in source] , and let [formula in source] be a von Neumann subalgebra such that [formula in source] is semifinite. Write [formula in source] for the modular automorphism group of [formula in source] . The following are equivalent: [formula in source] is globally invariant under the modular group","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Takesaki's conditional-expectation theorem","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":10207,"byte_start":7339,"id":"section:6527ca0fcfd3647bfc3a","kind":"subsection","labels":["eq:group-average","eq:q-index","eq:rn-expectation","thm:qsystem"],"line_end":256,"line_start":191,"occurrence":1,"owner_documents":["document:articles/2026-08-29/holomorphic_kms_extension_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-29--holomorphic_kms_extension_en/sections/001-section-setting-and-correction-of-terminology.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be an inclusion of infinite factors with finite index and separable predual. There is a normal faithful conditional expectation [formula in source] of finite index. Fix one such expectation. Every other normal faithful conditional expectation [formula in source] is of the form [formula in source] for a positive invertible [formula in source] satisfying [formula in source] . Conversely every su","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Finite index, Radon–Nikodym uniqueness, and Q-systems","topic_suggestions":[]},{"byte_end":11938,"byte_start":10207,"id":"section:8024bd0d38360a739c5a","kind":"subsection","labels":["eq:mu-extension","eq:mu-sum","thm:klm"],"line_end":300,"line_start":257,"occurrence":1,"owner_documents":["document:articles/2026-08-29/holomorphic_kms_extension_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-29--holomorphic_kms_extension_en/sections/001-section-setting-and-correction-of-terminology.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be a local irreducible conformal net satisfying the split property and strong additivity, and suppose that its two-interval inclusion [formula in source] has finite index. Then [formula in source] is completely rational; it has finitely many inequivalent irreducible DHR sectors [formula in source] , all of finite statistical dimension, every locally normal representation is a direct sum of the","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The KLM [formula in source] -index theoremThe KLM mu-index theorem","topic_suggestions":[]},{"byte_end":13342,"byte_start":11938,"id":"section:6e9aebbd19f7ec7650a3","kind":"subsection","labels":["eq:sector-gibbs","eq:universal-sum","thm:lt"],"line_end":336,"line_start":301,"occurrence":1,"owner_documents":["document:articles/2026-08-29/holomorphic_kms_extension_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-29--holomorphic_kms_extension_en/sections/001-section-setting-and-correction-of-terminology.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be a completely rational conformal net and let [formula in source] be its locally normal universal [formula in source] -algebra. Then [formula in source] where the summands correspond bijectively to the inequivalent irreducible DHR representations [formula in source] . Every extremal rotational [formula in source] -KMS state is the Gibbs state in one irreducible representation: [formula in sou","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Rotational KMS classification","topic_suggestions":[]},{"byte_end":13384,"byte_start":13342,"id":"section:f2e7036ac3e83720cfec","kind":"section","labels":[],"line_end":338,"line_start":337,"occurrence":1,"owner_documents":["document:articles/2026-08-29/holomorphic_kms_extension_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-29--holomorphic_kms_extension_en/sections/001-section-setting-and-correction-of-terminology.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Verification of the hypotheses","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":14966,"byte_start":13384,"id":"section:992f64e38e1943a88315","kind":"subsection","labels":["eq:EI","eq:bimodule","eq:global-E","eq:regular-q","eq:tfpt-mu"],"line_end":384,"line_start":339,"occurrence":1,"owner_documents":["document:articles/2026-08-29/holomorphic_kms_extension_en"],"relation_ids":["relation:631a963cb5a8fc675e56"],"semantic_review":false,"source":"documents/articles--2026-08-29--holomorphic_kms_extension_en/sections/001-section-setting-and-correction-of-terminology.tex","status_markers_as_written":[],"summary_excerpt":"For each interval set [formula in source] and [formula in source] . Conformal-net local algebras are factors; and trivial relative commutant. Theorem applies. The group average is [formula in source] It is normal, unital, positive, faithful, idempotent, and [formula in source] -bimodular. For example, if [formula in source] , then [formula in source] Faithfulness follows because [formula in source] and [formula in so","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The index-four fixed-point Q-system","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":1757,"byte_start":0,"id":"section:fdea0ce6860d24d01db0","kind":"subsection","labels":["eq:collar-h","eq:frozen-C","eq:gibbs-weights"],"line_end":54,"line_start":1,"occurrence":1,"owner_documents":["document:articles/2026-08-29/holomorphic_kms_extension_en"],"relation_ids":["relation:94d82ddcb289aaecfc43"],"semantic_review":false,"source":"documents/articles--2026-08-29--holomorphic_kms_extension_en/sections/002-subsection-the-frozen-car-covariance.tex","status_markers_as_written":[],"summary_excerpt":"The finite collar used by v995 has eight complex fermion modes, hence [formula in source] In dimensionless modular units the one-particle Hamiltonian is [formula in source] and the script sets [formula in source] . Therefore [formula in source] This is exactly Araki's covariance [formula in source] , so the finite CAR representation is factorial and the density matrix is faithful. On the occupation basis [formula in ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The frozen CAR covariance","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":2212,"byte_start":1757,"id":"section:3d2d7b5378d5169e6dd3","kind":"subsection","labels":["eq:one-sector"],"line_end":67,"line_start":55,"occurrence":1,"owner_documents":["document:articles/2026-08-29/holomorphic_kms_extension_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-29--holomorphic_kms_extension_en/sections/002-subsection-the-frozen-car-covariance.tex","status_markers_as_written":[],"summary_excerpt":"By [formula in source] The vacuum already contributes one, so there can be no other irreducible DHR sector. Theorem state and no other extreme point. This verifies the analytic hypothesis needed for unconditional rotational KMS uniqueness.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Holomorphy and thermal classification","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":7685,"byte_start":2212,"id":"section:a40d55f336d04a48cbfe","kind":"section","labels":["eq:E-preserves","eq:gauge-invariance","eq:gibbs-kms","eq:inv-unique","eq:kms-modular","eq:main-extension","eq:modular-chain","thm:main"],"line_end":228,"line_start":68,"occurrence":1,"owner_documents":["document:articles/2026-08-29/holomorphic_kms_extension_en"],"relation_ids":["relation:04fd3e61f514b2b6f0ca","relation:24259801588819a27750"],"semantic_review":false,"source":"documents/articles--2026-08-29--holomorphic_kms_extension_en/sections/002-subsection-the-frozen-car-covariance.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] satisfy the hypotheses of Section 1: for every interval [formula in source] , [formula in source] is an irreducible index-four inclusion, [formula in source] for a proper internal gauge action commuting with rotations, and [formula in source] is a holomorphic conformal net with [formula in source] and [formula in source] . Let [formula in source] and let [formula in source] be the restriction ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The holomorphic KMS extension theorem","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":7729,"byte_start":7685,"id":"section:f40da98cb0f642563c7b","kind":"section","labels":[],"line_end":230,"line_start":229,"occurrence":1,"owner_documents":["document:articles/2026-08-29/holomorphic_kms_extension_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-29--holomorphic_kms_extension_en/sections/002-subsection-the-frozen-car-covariance.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Where the mixing directions went","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":8530,"byte_start":7729,"id":"section:d4b303822e65157368d4","kind":"subsection","labels":["eq:relative-commutant","eq:scalar-pert"],"line_end":257,"line_start":231,"occurrence":1,"owner_documents":["document:articles/2026-08-29/holomorphic_kms_extension_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-29--holomorphic_kms_extension_en/sections/002-subsection-the-frozen-car-covariance.tex","status_markers_as_written":[],"summary_excerpt":"Fix an interval and write [formula in source] , [formula in source] . An internal multiplicity mixer for the inclusion is an operator [formula in source] . By irreducibility, [formula in source] so [formula in source] . A normalized perturbation cannot use this scalar to create a new state direction. Explicitly, if [formula in source] and [formula in source] then carry the same scalar factor, and [formula in source] ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Relative-commutant mixing","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":9495,"byte_start":8530,"id":"section:f71d0f013b7815161275","kind":"subsection","labels":[],"line_end":286,"line_start":258,"occurrence":1,"owner_documents":["document:articles/2026-08-29/holomorphic_kms_extension_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-29--holomorphic_kms_extension_en/sections/002-subsection-the-frozen-car-covariance.tex","status_markers_as_written":[],"summary_excerpt":"A different possible mixing is a convex combination of thermal states in inequivalent irreducible representations. KLM gives the sector count through [formula in source] Holomorphy makes the sum equal one, so only [formula in source] remains. Longo–Tanimoto identifies the extreme rotational KMS states with the sector Gibbs states. Therefore there is no second thermal sector into which a state can mix.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Superselection-sector mixing","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":9540,"byte_start":9495,"id":"section:584fe4ac4fcf353a0b77","kind":"section","labels":[],"line_end":288,"line_start":287,"occurrence":1,"owner_documents":["document:articles/2026-08-29/holomorphic_kms_extension_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-29--holomorphic_kms_extension_en/sections/002-subsection-the-frozen-car-covariance.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"TFPT corollary and the P1 reading","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"}]},{"byte_end":11014,"byte_start":9540,"id":"section:9dd9abbebd5eb3848043","kind":"subsection","labels":["cor:v995"],"line_end":323,"line_start":289,"occurrence":1,"owner_documents":["document:articles/2026-08-29/holomorphic_kms_extension_en"],"relation_ids":["relation:e5f808dc31f9624d957e"],"semantic_review":false,"source":"documents/articles--2026-08-29--holomorphic_kms_extension_en/sections/002-subsection-the-frozen-car-covariance.tex","status_markers_as_written":[],"summary_excerpt":"Assume that the TFPT collar scaling limit realizes the net inclusion of Theorem the exact finite results of v995 are finite-dimensional shadows of the two uniqueness mechanisms: on [formula in source] , the KMS equations have rank [formula in source] on the state tangent and kernel zero; all [formula in source] selected same- [formula in source] -charge, unequal-modular-energy Hermitian directions fail stationarity a","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The finite matrix shadow","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":13935,"byte_start":11014,"id":"section:a90bfaafa3f1446fd499","kind":"subsection","labels":["cor:p1","eq:beta-angle","eq:p1","eq:quarter","eq:response-quarter","eq:transitive","lem:equidistribution"],"line_end":412,"line_start":324,"occurrence":1,"owner_documents":["document:articles/2026-08-29/holomorphic_kms_extension_en"],"relation_ids":["relation:004f91efc86156b76173","relation:aeb0eb0a235c95c40493","relation:dbdb1c69094a01ef4988"],"semantic_review":false,"source":"documents/articles--2026-08-29--holomorphic_kms_extension_en/sections/002-subsection-the-frozen-car-covariance.tex","status_markers_as_written":[],"summary_excerpt":"The exact statement needed for the P1 reading is elementary but has one hypothesis that must be visible.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Equidistribution over four deck channels","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":1453,"byte_start":0,"id":"section:fa0328aaea7476296880","kind":"section","labels":[],"line_end":31,"line_start":1,"occurrence":1,"owner_documents":["document:articles/2026-08-29/holomorphic_kms_extension_en"],"relation_ids":["relation:435058197ecb4b512c22","relation:4d8960595551d138fba9","relation:7d04dafd6c7919b240c4","relation:b3608883f54e990dd272"],"semantic_review":false,"source":"documents/articles--2026-08-29--holomorphic_kms_extension_en/sections/003-section-what-this-closes-and-does-not-close.tex","status_markers_as_written":[],"summary_excerpt":"For an abstract holomorphic conformal net satisfying the hypotheses, the rotational KMS extension theorem is complete: there is one extension, its expectation is canonical, and both local relative-commutant mixing and thermal-sector mixing are excluded. The finite v995 computation is exactly consistent with this result. Applying it to the TFPT collar remains conditional on the continuum-net identification in the box ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"What this closes and does not close","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":3081,"byte_start":1453,"id":"section:df7c31419ad580f2ce16","kind":"section","labels":[],"line_end":72,"line_start":32,"occurrence":1,"owner_documents":["document:articles/2026-08-29/holomorphic_kms_extension_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-29--holomorphic_kms_extension_en/sections/003-section-what-this-closes-and-does-not-close.tex","status_markers_as_written":[],"summary_excerpt":"red!65!blackred!3 0.91 Remaining gap (exact statement). For the TFPT [formula in source] QWZ collar with its four quarter-twisted deck labels, prove that the scaling-limit local von Neumann algebras are the hyperfinite type- [formula in source] factors of a conformal net and identify, as conformal nets with vacuum, common stress tensor, rotation dynamics, and [formula in source] action, the resulting concrete inclusi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Remaining gap","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":6366,"byte_start":3081,"id":"section:341c448635e2f91f2655","kind":"section","labels":[],"line_end":165,"line_start":73,"occurrence":1,"owner_documents":["document:articles/2026-08-29/holomorphic_kms_extension_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-29--holomorphic_kms_extension_en/sections/003-section-what-this-closes-and-does-not-close.tex","status_markers_as_written":[],"summary_excerpt":"The abstract operator-algebraic theorem is closed at its natural strength. Existence comes from the vacuum-sector rotational Gibbs state of the holomorphic extension. The index-four group average is the unique expectation by the finite-index Radon–Nikodym theorem and irreducibility. Takesaki's theorem gives the explicit modular restriction and intertwining chain. Gauge-invariant extension uniqueness is an elementary ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conclusion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":1287,"byte_start":0,"id":"section:154f4d2cc08ee9ec9729","kind":"frontmatter","labels":[],"line_end":46,"line_start":1,"occurrence":1,"owner_documents":["document:articles/2026-08-30/det16_mirror_gap_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--det16_mirror_gap_theorem_en/preamble.tex","status_markers_as_written":[],"summary_excerpt":"colorlinks=true, linkcolor=blue!55!black, citecolor=blue!55!black, urlcolor=blue!55!black","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Volume-Independent DET16 Mirror-Gap Theorem:\\\\ Exact Product Gap, Spin(10) Symmetry, and the Honest Stability Threshold","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":1753,"byte_start":0,"id":"section:b4a9b15bd2f0f6acbebd","kind":"frontmatter","labels":[],"line_end":39,"line_start":1,"occurrence":1,"owner_documents":["document:articles/2026-08-30/det16_mirror_gap_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--det16_mirror_gap_theorem_en/sections/001-section-concrete-model-and-frozen-finite-input.tex","status_markers_as_written":[],"summary_excerpt":"On every finite set of disjoint sixteen-mode clusters we prove exactly that the DET16 Hamiltonian [formula in source] has the unique product ground state [formula in source] , spectrum [formula in source] , and gap one independently of volume. The proof includes the graded-CAR argument: the determinant monomial has even degree sixteen, so local projectors on disjoint clusters commute without an ordering sign. We also","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":1803,"byte_start":1753,"id":"section:31287163df0de8efff6a","kind":"section","labels":[],"line_end":41,"line_start":40,"occurrence":1,"owner_documents":["document:articles/2026-08-30/det16_mirror_gap_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--det16_mirror_gap_theorem_en/sections/001-section-concrete-model-and-frozen-finite-input.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Concrete model and frozen finite input","topic_suggestions":[]},{"byte_end":2934,"byte_start":1803,"id":"section:8bcd1b39df69f2ce6417","kind":"subsection","labels":["eq:cluster","eq:frozen"],"line_end":78,"line_start":42,"occurrence":1,"owner_documents":["document:articles/2026-08-30/det16_mirror_gap_theorem_en"],"relation_ids":["relation:acc01e0d9a67f7a4c32b"],"semantic_review":false,"source":"documents/articles--2026-08-30--det16_mirror_gap_theorem_en/sections/001-section-concrete-model-and-frozen-finite-input.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] carry the positive-chirality spin representation [formula in source] of [formula in source] and let [formula in source] be its fermionic Fock space. For an ordered orthonormal basis [formula in source] , write [formula in source] and [formula in source] . Put [formula in source] The exact finite computation in verification/v1002_spin10_mirror_projector.py verifies [formula in source] and all f","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"One DET16 cluster","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":3989,"byte_start":2934,"id":"section:94a1d89c5cbe68b167b5","kind":"subsection","labels":["eq:H0","eq:commute","eq:gradedcommute","eq:gradedtensor"],"line_end":109,"line_start":79,"occurrence":1,"owner_documents":["document:articles/2026-08-30/det16_mirror_gap_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--det16_mirror_gap_theorem_en/sections/001-section-concrete-model-and-frozen-finite-input.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be any nonempty finite set of clusters. Fix an ordering only to identify the global Fock space with an ordinary tensor product, [formula in source] where the hat recalls that the intrinsic product is graded. Operators have fermion parity [formula in source] . If [formula in source] and [formula in source] are homogeneous and supported on disjoint clusters, the CAR give [formula in source] The ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Many disjoint clusters","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":6768,"byte_start":3989,"id":"section:9101dd6f85238ca87860","kind":"section","labels":["eq:gapone","eq:multiplicity","eq:productground","eq:spectrum","eq:syndrome","lem:order","thm:T1"],"line_end":188,"line_start":110,"occurrence":1,"owner_documents":["document:articles/2026-08-30/det16_mirror_gap_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--det16_mirror_gap_theorem_en/sections/001-section-concrete-model-and-frozen-finite-input.tex","status_markers_as_written":[],"summary_excerpt":"For any subset [formula in source] , the product [formula in source] is independent of the order chosen for its factors. Under any ordered tensor-product identification rank-one projectors on [formula in source] and the identity on [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Exact spectrum and the volume-independent unit gap","topic_suggestions":[]},{"byte_end":10345,"byte_start":6768,"id":"section:3fa841bc12f7ab2b5b1d","kind":"section","labels":["eq:detone","eq:gauss","lem:det","thm:T2"],"line_end":281,"line_start":189,"occurrence":1,"owner_documents":["document:articles/2026-08-30/det16_mirror_gap_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--det16_mirror_gap_theorem_en/sections/001-section-concrete-model-and-frozen-finite-input.tex","status_markers_as_written":[],"summary_excerpt":"The map [formula in source] is a continuous group character. Its differential at the identity is [formula in source] The trace vanishes on commutators. Since [formula in source] is semisimple, [formula in source] , so this linear functional vanishes identically. Thus [formula in source] is locally constant. The group [formula in source] is connected, and [formula in source] , hence [formula in source] for every [form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gauge, parity, translations, and degeneracy","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":10404,"byte_start":10345,"id":"section:76ee0d1ea1aed79b05b9","kind":"section","labels":[],"line_end":283,"line_start":282,"occurrence":1,"owner_documents":["document:articles/2026-08-30/det16_mirror_gap_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--det16_mirror_gap_theorem_en/sections/001-section-concrete-model-and-frozen-finite-input.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"The classical stability theorem, stated in full","topic_suggestions":[]},{"byte_end":14259,"byte_start":10404,"id":"section:35d1e874076a64a9f0a0","kind":"subsection","labels":["def:pert","eq:MZJ0","eq:MZLTQO","eq:MZc","eq:MZgap","eq:MZrelative","eq:exactLTQO","eq:interactionnorm","eq:localHB","eq:localgap","eq:pert","thm:MZ"],"line_end":400,"line_start":284,"occurrence":1,"owner_documents":["document:articles/2026-08-30/det16_mirror_gap_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--det16_mirror_gap_theorem_en/sections/001-section-concrete-model-and-frozen-finite-input.tex","status_markers_as_written":[],"summary_excerpt":"For a finite region [formula in source] , define [formula in source] As an operator on the full system, [formula in source] is the identity outside [formula in source] . If [formula in source] and [formula in source] is supported on [formula in source] , then [formula in source] Thus local ground states are exactly indistinguishable in the interior: the Local-TQO error function is identically zero. Theorem [formula i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Local-TQO and local gap","topic_suggestions":[]},{"byte_end":2123,"byte_start":0,"id":"section:d2e8b5390f14d8a13881","kind":"section","labels":["eq:stablehalf","thm:T3"],"line_end":47,"line_start":1,"occurrence":1,"owner_documents":["document:articles/2026-08-30/det16_mirror_gap_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--det16_mirror_gap_theorem_en/sections/002-section-volume-independent-perturbative-stability.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] range over finite subsets or tori of a fixed [formula in source] -dimensional bounded-degree lattice. Let [formula in source] be the DET16 Hamiltonian finite-range interaction satisfying Definition uniformly in volume. Then there exists [formula in source] , depending only on [formula in source] , the interaction range, and the local interaction-norm bound, but not on [formula in source] , suc","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Volume-independent perturbative stability","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":10864,"byte_start":2123,"id":"section:42c2beac40084e5dc2c7","kind":"section","labels":["eq:BDLeps","eq:BDLsymbolic","eq:FPK","eq:FPgap","eq:FPlocal","eq:FPscale","eq:FPwindow","eq:dynH0","eq:dynJ","eq:dyndelta","eq:dynhop","prop:BDLaudit","prop:FPaudit","sec:dynlinks","tab:FPaudit","thm:FP"],"line_end":276,"line_start":48,"occurrence":1,"owner_documents":["document:articles/2026-08-30/det16_mirror_gap_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--det16_mirror_gap_theorem_en/sections/002-section-volume-independent-perturbative-stability.tex","status_markers_as_written":[],"summary_excerpt":"Theorem not itself add fluctuating link Hilbert spaces. We therefore audit the finite-group dynamical-link extension first against the local Schrieffer–Wolff construction of Bravyi, DiVincenzo, and Loss BDL2011, and then against the gap theorem proved by Fröhlich and Pizzo FP2020.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dynamical finite gauge links: Lie–Schwinger gap theorem","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":13399,"byte_start":10864,"id":"section:0e3fe3476cf5c8d9f09e","kind":"subsection","labels":["eq:FPa","eq:FPgapcondition","eq:FPparametric","eq:FPwindows"],"line_end":345,"line_start":277,"occurrence":1,"owner_documents":["document:articles/2026-08-30/det16_mirror_gap_theorem_en"],"relation_ids":["relation:dee8a38c1decb3de6405"],"semantic_review":false,"source":"documents/articles--2026-08-30--det16_mirror_gap_theorem_en/sections/002-section-volume-independent-perturbative-stability.tex","status_markers_as_written":[],"summary_excerpt":"The Lie–Schwinger proof contains one explicit series constant: [formula in source] Appendix A of FP2020 uses the explicit convergence restriction [formula in source] Its local-gap estimate also has the explicit sufficient inequality [formula in source] whose positive boundary is [formula in source] . However, the induction closing Theorem 3.4 of FP2020 introduces unevaluated universal constants [formula in source] an","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"What is and is not explicit in the FP window","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":14601,"byte_start":13399,"id":"section:2112fb9d90d639af77c0","kind":"section","labels":["eq:block","eq:formbound","eq:linearbound","prop:relative"],"line_end":392,"line_start":346,"occurrence":1,"owner_documents":["document:articles/2026-08-30/det16_mirror_gap_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--det16_mirror_gap_theorem_en/sections/002-section-volume-independent-perturbative-stability.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] and [formula in source] . Suppose a self-adjoint perturbation [formula in source] satisfies [formula in source] and [formula in source] Then the ground vector remains [formula in source] , and [formula in source] In particular, the weaker displayed bound is positive for [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The proposed explicit count and why it is conditional","topic_suggestions":[]},{"byte_end":2337,"byte_start":0,"id":"section:b969269cec59b8c62a7b","kind":"subsection","labels":["eq:bondnorm","eq:count","eq:count3d","eq:hopping","eq:notblock"],"line_end":64,"line_start":1,"occurrence":1,"owner_documents":["document:articles/2026-08-30/det16_mirror_gap_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--det16_mirror_gap_theorem_en/sections/003-subsection-the-norm-count.tex","status_markers_as_written":[],"summary_excerpt":"For unit-amplitude nearest-neighbour hopping across one bond, [formula in source] with [formula in source] unitary, the one-particle bond matrix has sixteen eigenvalues [formula in source] and sixteen eigenvalues [formula in source] . Its fermionic second quantization therefore has [formula in source] If the lattice coordination is [formula in source] , at most [formula in source] such bonds touch one cluster. The ad","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The norm count","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":4389,"byte_start":2337,"id":"section:33d37547e51432bedff8","kind":"section","labels":["eq:margin","eq:mutants","eq:numeric","eq:scan"],"line_end":131,"line_start":65,"occurrence":1,"owner_documents":["document:articles/2026-08-30/det16_mirror_gap_theorem_en"],"relation_ids":["relation:18afaf4daa8129907432","relation:9309ccd59197fbe9b384"],"semantic_review":false,"source":"documents/articles--2026-08-30--det16_mirror_gap_theorem_en/sections/003-subsection-the-norm-count.tex","status_markers_as_written":[],"summary_excerpt":"The companion probe is [formula in source] It uses the exact four-mode determinant projectors and open-chain hopping machinery of the frozen v1002 route. All [formula in source] checks pass. The direct comparison is: [formula in source] Every entry lies above [formula in source] with [formula in source] for the two-cluster endpoint pair and [formula in source] for the three–four cluster chains. Except at the smallest","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Numeric twin","topic_suggestions":[]},{"byte_end":6559,"byte_start":4389,"id":"section:386078249ac31d7ffd5c","kind":"section","labels":["thm:main"],"line_end":177,"line_start":132,"occurrence":1,"owner_documents":["document:articles/2026-08-30/det16_mirror_gap_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--det16_mirror_gap_theorem_en/sections/003-subsection-the-norm-count.tex","status_markers_as_written":[],"summary_excerpt":"For the matter-only DET16 cluster model the projectors are mutually commuting even CAR operators; [formula in source] has exact spectrum [formula in source] , multiplicities [formula in source] is locally Spin(10)-Gauss invariant, parity invariant, and translation invariant for constant [formula in source] ; its unique product ground state has neither spontaneous symmetry breaking nor torus/topological degeneracy; ev","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Combined strongest theorem","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":6633,"byte_start":6559,"id":"section:fd0db8922a48238013e5","kind":"section","labels":["sec:boundary"],"line_end":180,"line_start":178,"occurrence":1,"owner_documents":["document:articles/2026-08-30/det16_mirror_gap_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--det16_mirror_gap_theorem_en/sections/003-subsection-the-norm-count.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Physical spectator and remaining boundary","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":9833,"byte_start":6633,"id":"section:cc5e83b2baf29bc6787b","kind":"subsection","labels":["eq:nomix","eq:spectator","eq:spectralsum"],"line_end":263,"line_start":181,"occurrence":1,"owner_documents":["document:articles/2026-08-30/det16_mirror_gap_theorem_en"],"relation_ids":["relation:712398ff6a637c1f4544"],"semantic_review":false,"source":"documents/articles--2026-08-30--det16_mirror_gap_theorem_en/sections/003-subsection-the-norm-count.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] carry a wall Hamiltonian [formula in source] and let [formula in source] carry [formula in source] . If the DET16 terms act as the identity on wall modes, then [formula in source] Hence [formula in source] The [formula in source] copy is exactly the original wall spectrum, with every multiplicity preserved.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Exact spectator statement","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"}]},{"byte_end":12169,"byte_start":9833,"id":"section:f00ab91bc062ae881454","kind":"section","labels":[],"line_end":319,"line_start":264,"occurrence":1,"owner_documents":["document:articles/2026-08-30/det16_mirror_gap_theorem_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--det16_mirror_gap_theorem_en/sections/003-subsection-the-norm-count.tex","status_markers_as_written":[],"summary_excerpt":"BHM2010 S. Bravyi, M. B. Hastings, and S. Michalakis, Topological quantum order: stability under local perturbations, J.\\ Math.\\ Phys.\\ 51 (2010), 093512, https://doi.org/10.1063/1.3490195 doi:10.1063/1.3490195.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conclusion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":1695,"byte_start":0,"id":"section:4183a7d19583b0408c74","kind":"frontmatter","labels":[],"line_end":60,"line_start":1,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":["relation:7b6be8bccc4750fc09d8"],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/preamble.tex","status_markers_as_written":["\\mP"],"summary_excerpt":"colorlinks=true, linkcolor=blue!55!black, citecolor=blue!55!black, urlcolor=blue!55!black","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Charged MMST Scaling-Limit Theorem:\\\\ A Complete In-House Proof Attempt for SEAM.MMST.TYPEIII.CHARGED.01","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":1952,"byte_start":0,"id":"section:b1247ef0938a179aa8e0","kind":"frontmatter","labels":[],"line_end":44,"line_start":1,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/001-section-verdict-and-logical-form.tex","status_markers_as_written":[],"summary_excerpt":"We attempt the complete scaling-limit theorem for the concrete order-four charged field [formula in source] The algebraic limit-exchange statement is proved in full for an arbitrary finite group: equivariant injective inductive limits commute isometrically with crossed products, coefficient and fixed-point expectations commute with the limit, and their Pimsner–Popa constants remain uniform. Assuming the charged field","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"}]},{"byte_end":4610,"byte_start":1952,"id":"section:6adc5de3cdbb8454fa22","kind":"section","labels":["eq:L1","thm:master"],"line_end":100,"line_start":45,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":["relation:cc49638a1b35e707f9c1"],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/001-section-verdict-and-logical-form.tex","status_markers_as_written":[],"summary_excerpt":"Let the finite collars, scaling maps, neutral current limit and charged operators be as in Section is exhausted by the neutral currents and the four charged grades as specified in (ALG-EXH) there. Then: For every [formula in source] there are [formula in source] and [formula in source] , independent of [formula in source] , such that on the finite-energy core [formula in source] After the canonical scaling identifica","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verdict and logical form","topic_suggestions":[]},{"byte_end":4686,"byte_start":4610,"id":"section:58ab7ae978cf29dd1bf3","kind":"section","labels":["sec:setup"],"line_end":103,"line_start":101,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/001-section-verdict-and-logical-form.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Setup: the frozen collar and charged generator","topic_suggestions":[]},{"byte_end":6351,"byte_start":4686,"id":"section:61d171f462ef0ef05e83","kind":"subsection","labels":["eq:bulkgap","eq:covariance","eq:momentum","eq:qwz","rem:gapcorrection"],"line_end":150,"line_start":104,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/001-section-verdict-and-logical-form.tex","status_markers_as_written":[],"summary_excerpt":"For circumference [formula in source] and fixed open width [formula in source] , the one-particle Qi–Wu–Zhang collar is [formula in source] The [formula in source] th deck sector, [formula in source] , has boundary phase [formula in source] , hence longitudinal momenta [formula in source] Sixteen Majorana copies produce the carrier central charge [formula in source] . We write [formula in source] for the one-particle","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The finite CAR collar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":7125,"byte_start":6351,"id":"section:c6799b25e02057cc4240","kind":"subsection","labels":["eq:census","eq:lambda","eq:lambda-norm","eq:lambda-order"],"line_end":182,"line_start":151,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/001-section-verdict-and-logical-form.tex","status_markers_as_written":[],"summary_excerpt":"In rational coordinates, [formula in source] The exact finite calculation gives [formula in source] and [formula in source] The norm-two vectors in [formula in source] , [formula in source] , have census [formula in source] so the four cosets contain [formula in source] roots and the two odd grades contain the full [formula in source] -dimensional spinor contribution.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The exact order-four vector","topic_suggestions":[]},{"byte_end":8919,"byte_start":7125,"id":"section:401fa19cef64d88b1ede","kind":"subsection","labels":["eq:chargedfield","eq:core","eq:graphconv","eq:latticesymbol"],"line_end":228,"line_start":183,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/001-section-verdict-and-logical-form.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the bosonic current obtained from the sixteen Majorana copies by edge-projected collar bosonization, with zero mode fixed by the [formula in source] charge sector. Each complex-fermion pair gives one boson. The longitudinal derivative uses the frozen lattice symbol [formula in source] The edge projection is the analytic top (or bottom) eigenbranch through the zero-energy crossing; massive b","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The finite charged field","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":14689,"byte_start":8919,"id":"section:61a4d83c2a6cb97ffd0f","kind":"section","labels":["eq:E8char","eq:KLMextension","eq:KLMsum","eq:modebound","eq:smearedbound","eq:traceclass","sec:classical","thm:CKLWenergy","thm:DM","thm:KLM","thm:OS","thm:Qsystems","thm:split"],"line_end":370,"line_start":229,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/001-section-verdict-and-logical-form.tex","status_markers_as_written":[],"summary_excerpt":"For the massless chiral lattice fermion systems constructed by operator-algebraic renormalization, with the regular scaling functions and compatible ground states specified in their construction, the renormalized Koo–Saleur approximants converge strongly on the finite-particle core to the corresponding Virasoro generators. The smeared approximants converge on that core, and the same argument applies to level-one Wess","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Classical inputs, quoted in the forms used","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":52,"byte_start":0,"id":"section:2ebb1b45ceb5dae7f0a5","kind":"section","labels":["sec:L1"],"line_end":3,"line_start":1,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/002-section-l1-uniform-energy-bounds.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"L1: uniform energy bounds","topic_suggestions":[]},{"byte_end":1383,"byte_start":52,"id":"section:c8c5be1ac1a1fb0892bf","kind":"subsection","labels":["eq:continuumEB","eq:currentmode","lem:continuumEB"],"line_end":42,"line_start":4,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/002-section-l1-uniform-energy-bounds.tex","status_markers_as_written":[],"summary_excerpt":"In the level-one lattice VOA of the glued rank-eight lattice, the norm-two vector [formula in source] is a weight-one affine current. For every [formula in source] there is a constant [formula in source] such that [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The continuum estimate is complete","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":10505,"byte_start":1383,"id":"section:0b98bdbf75c1bdb48084","kind":"subsection","labels":["eq:Cf","eq:KG","eq:NSmomenta","eq:Schur","eq:SobolevUGF","eq:UGFhere","eq:chiralgreen","eq:epsilonN","eq:greenform","eq:greenmultiplier","eq:modeUGF","eq:pointwisegreen","eq:resolventidentity","eq:sinecomparison","eq:structurefactor","lem:Schur","lem:edgedoublet","lem:resolvent","lem:sine","thm:L1reduction","thm:UGF"],"line_end":294,"line_start":43,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/002-section-l1-uniform-energy-bounds.tex","status_markers_as_written":[],"summary_excerpt":"We now define and estimate the concrete [formula in source] used by the collar bosonization. It is important that this is a definition from the frozen QWZ edge band, not a continuum ansatz.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The edge-projected lattice Green form","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":10953,"byte_start":10505,"id":"section:1140c8b5234792a8864a","kind":"paragraph","labels":[],"line_end":304,"line_start":295,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":["relation:449205103537368b588c"],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/002-section-l1-uniform-energy-bounds.tex","status_markers_as_written":[],"summary_excerpt":"The companion probe experiments/tfpt-discovery/mmst_ugf_bound_probe.py checks every displayed inequality at [formula in source] . It finds [formula in source] , verifies [formula in source] and the unit edge slope, and rejects both a gapless transverse mutant (whose ratio grows from [formula in source] to [formula in source] ) and the false symbol constant [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Finite audit (numerical support, not proof).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":11021,"byte_start":10953,"id":"section:dd08d9ae5a6148835372","kind":"section","labels":["sec:L2"],"line_end":307,"line_start":305,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/002-section-l1-uniform-energy-bounds.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"L2: strong convergence and local algebras","topic_suggestions":[]},{"byte_end":11981,"byte_start":11021,"id":"section:a4b92576e5ec1bf5a0d6","kind":"subsection","labels":["eq:Fockisometry","eq:modecompat","eq:modeisometry","eq:oneparticleboson"],"line_end":339,"line_start":308,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/002-section-l1-uniform-energy-bounds.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] with the single Nyquist representative convention of [formula in source] . Define [formula in source] Thus [formula in source] is the zero-extension/Shannon embedding of the old Fourier modes into the refined lattice. 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Theorem","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The multiplier rate extracted from UGF","topic_suggestions":[]},{"byte_end":6436,"byte_start":5550,"id":"section:88e790a15d18040fcd87","kind":"paragraph","labels":[],"line_end":189,"line_start":172,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":["relation:458a4b1cc2bfc92947a4"],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/003-subsection-the-multiplier-rate-extracted-from-ugf.tex","status_markers_as_written":[],"summary_excerpt":"The companion probe experiments/tfpt-discovery/mmst_tel_probe.py checks [formula in source] . The Gram and compatibility errors are exactly zero, the measured coefficient envelope is [formula in source] , and a smooth-test Wick seminorm fits [formula in source] . A wrong-rate [formula in source] mutant and a non-isometric embedding mutant are both rejected.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Finite audit (numerical support, not proof).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10715,"byte_start":6436,"id":"section:bd6d1336259ad1689a45","kind":"subsection","labels":["eq:Hankeltarget","eq:PellerHS","eq:allN211","eq:hardylog","eq:measured211","eq:regularizedsymbol","eq:tworemainder","prop:HankelReduction"],"line_end":306,"line_start":190,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":["relation:06186a0cf0f808331616","relation:54d4fd1a64f8e0adb112","relation:56bc39ed4c5a6cb27631"],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/003-subsection-the-multiplier-rate-extracted-from-ugf.tex","status_markers_as_written":[],"summary_excerpt":"The exact Hardy model gives the quarter-twist coefficient [formula in source] For the frozen QWZ exhaustion, the computed decomposition is [formula in source] with [formula in source] A [formula in source] fit predicts [formula in source] , with maximum fit residual [formula in source] . These values support boundedness of [formula in source] but do not prove either [formula in source] for the full-CAR remainder.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TEL-b: the two-edge full-CAR remainder","topic_suggestions":[]},{"byte_end":14300,"byte_start":10715,"id":"section:c772ab6fb9c9caa09f5c","kind":"subsection","labels":["eq:Rdefecttable","eq:Rdyadicbound","eq:Rnormtail","eq:Rscalarresidue","eq:Rtailproposed","prop:tailfailure"],"line_end":404,"line_start":307,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/003-subsection-the-multiplier-rate-extracted-from-ugf.tex","status_markers_as_written":[],"summary_excerpt":"There are two natural full-CAR one-particle embeddings from circumference [formula in source] to [formula in source] . The low-energy embedding [formula in source] preserves the integer Fourier label [formula in source] , while the physical-momentum dilation [formula in source] sends [formula in source] . The proposed tail mechanism would require, for one of them, [formula in source] with one explicit [formula in sou","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Third angle: certified finite part plus a dyadic tail","topic_suggestions":[]},{"byte_end":14661,"byte_start":14300,"id":"section:cc93617532a2b2466455","kind":"paragraph","labels":[],"line_end":411,"line_start":405,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":["relation:d0d1c00dd21f2a480201"],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/003-subsection-the-multiplier-rate-extracted-from-ugf.tex","status_markers_as_written":[],"summary_excerpt":"experiments/tfpt-discovery/mmst_telb_tail_probe.py reproduces all six established finite norms, evaluates both embeddings through [formula in source] , verifies the reverse-triangle inequality, and rejects an [formula in source] mutant as an [formula in source] tail. Its verdict is TAIL-TELESCOPING-FAILS; all diagnostic and honesty guards pass.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Third-angle audit.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":1529,"byte_start":0,"id":"section:d2abf380018ca8dae043","kind":"subsection","labels":["eq:integralpairing","thm:relativeLocality"],"line_end":42,"line_start":1,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/004-subsection-relative-locality-of-the-charged-and-neutral-.tex","status_markers_as_written":[],"summary_excerpt":"The limiting edge-projected charged field is relatively local with respect to the neutral [formula in source] current net.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Relative locality of the charged and neutral fields","topic_suggestions":[]},{"byte_end":3120,"byte_start":1529,"id":"section:b97bc8122d0311e44b14","kind":"subsection","labels":["eq:canonicalendo","eq:irreducibleinclusion","thm:outerness"],"line_end":82,"line_start":43,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/004-subsection-relative-locality-of-the-charged-and-neutral-.tex","status_markers_as_written":[],"summary_excerpt":"On every limiting local factor generated by the neutral algebra and the four charged grades, every nonidentity element of the [formula in source] gauge action is outer.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Outerness of the limiting four-grade action","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":8855,"byte_start":3120,"id":"section:ca091ab682b2d3ecd50b","kind":"subsection","labels":["eq:EXHsharp","eq:algconv","eq:generatedfinite","lem:algconv","prop:BVexhaustion","thm:L2reduction"],"line_end":212,"line_start":83,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":["relation:f48ab230a49ca4fce05e"],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/004-subsection-relative-locality-of-the-charged-and-neutral-.tex","status_markers_as_written":[],"summary_excerpt":"For an interval [formula in source] , define the field-generated finite algebra [formula in source] Define [formula in source] similarly from the limiting fields.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"From fields to local algebras","topic_suggestions":[]},{"byte_end":9019,"byte_start":8855,"id":"section:e44895688f64a3faf583","kind":"section","labels":["sec:L3"],"line_end":215,"line_start":213,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/004-subsection-relative-locality-of-the-charged-and-neutral-.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"L3: finite-group [formula in source] crossed products commute with the limitL3: finite-group crossed products commute with the limit","topic_suggestions":[]},{"byte_end":12301,"byte_start":9019,"id":"section:2a389e0ac3144ae52c80","kind":"subsection","labels":["eq:PP","eq:coeffE","eq:crossediso","eq:crossmap","eq:equivariance","eq:fixedE","thm:crossedlimit"],"line_end":307,"line_start":216,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/004-subsection-relative-locality-of-the-charged-and-neutral-.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be finite and let [formula in source] be an inductive system of unital [formula in source] -algebras with injective maps. Suppose [formula in source] are actions and [formula in source] Let [formula in source] and [formula in source] . Then the canonical map is a [formula in source] -isomorphism [formula in source] For the coefficient expectations [formula in source] and fixed-point expectatio","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The [formula in source] -inductive theoremThe C-star inductive theorem","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":14261,"byte_start":12301,"id":"section:9e7f5173a15931603ba6","kind":"subsection","labels":["cor:Z4","cor:stateE","eq:grades","eq:quarterE"],"line_end":366,"line_start":308,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/004-subsection-relative-locality-of-the-charged-and-neutral-.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be compatible [formula in source] -invariant states. Then [formula in source] , the limit state [formula in source] satisfies [formula in source] , and the GNS extensions of [formula in source] converge on the dense inductive union to the GNS extension of [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"State preservation and the charged grades","topic_suggestions":[]},{"byte_end":14365,"byte_start":14261,"id":"section:33afecedbcedc2a8fa2f","kind":"section","labels":["sec:L4"],"line_end":369,"line_start":367,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/004-subsection-relative-locality-of-the-charged-and-neutral-.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"L4: holomorphy and identification with [formula in source] E8 level 1","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"}]},{"byte_end":4244,"byte_start":0,"id":"section:a4ec880324ba47c0530f","kind":"subsection","labels":["cor:typeIII","eq:basenet","eq:c8","eq:character","eq:gluedlattice","eq:mu16","eq:muone","eq:thetaE4","eq:unimodular","thm:identification"],"line_end":114,"line_start":1,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/005-subsection-the-neutral-net-and-its-index.tex","status_markers_as_written":[],"summary_excerpt":"The intended neutral current net is [formula in source] Its central charge is [formula in source] The discriminant groups of [formula in source] and [formula in source] each have order four, so the product lattice net has [formula in source] The isotropic diagonal subgroup generated by [formula in source] has order four. The exact lattice identities verify integer spin, evenness and unimodularity of the extension lat","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The neutral net and its index","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6623,"byte_start":4244,"id":"section:a16cba036190d6383a82","kind":"section","labels":["eq:P1"],"line_end":175,"line_start":115,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/005-subsection-the-neutral-net-and-its-index.tex","status_markers_as_written":[],"summary_excerpt":"convergence] If the final gap box is discharged, the field [formula in source] converges on the finite-energy core, is relatively local, has order-four fusion, and generates the missing odd [formula in source] weight-one states. The conditional statement in [formula in source] at the Quasi-Free Boundary becomes unconditional for this collar.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Downstream corollary cascade","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":9893,"byte_start":6623,"id":"section:2fb6cd875276a150402c","kind":"section","labels":[],"line_end":257,"line_start":176,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":["relation:0671db0b46b63ca5d14a","relation:5ade9503cedff24e7d87","relation:e5d7989b8fddab555dbe"],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/005-subsection-the-neutral-net-and-its-index.tex","status_markers_as_written":["\\mP"],"summary_excerpt":"@p0.13 p0.24 p0.16 p0.39 @ Item & Statement & Status & Reason\\\\ S0 & Frozen generator arithmetic: [formula in source] , [formula in source] , order four, census [formula in source] & & Exact rational lattice calculation; rechecked 10/10.\\\\ S1 & Neutral bilinear currents and stress tensor have a scaling limit & & Osborne–Stottmeister Theorems 4.11, 4.16 and 5.1; the frozen neutral objects are in the bilinear class.\\\\ ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Per-lemma status","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":13129,"byte_start":9893,"id":"section:263c5e01a142571bcd11","kind":"section","labels":[],"line_end":330,"line_start":258,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":["relation:b02a4afe031887dd8137","relation:b7e503b1ce95132e1aa8"],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/005-subsection-the-neutral-net-and-its-index.tex","status_markers_as_written":[],"summary_excerpt":"red!65!blackred!3 0.92 Remaining microscopic-exhaustion gaps (status 2026-09-05).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The remaining analytic gap","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":14366,"byte_start":13129,"id":"section:bd6cf08b9bb07e5a84ac","kind":"paragraph","labels":[],"line_end":350,"line_start":331,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":["relation:1ec13db4f436aecbe007","relation:8bab9c2162026e7fd576"],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/005-subsection-the-neutral-net-and-its-index.tex","status_markers_as_written":[],"summary_excerpt":"The repository checker v1033_charged_disorder.py constructs order-four charged corners in the actual QWZ matter Fock space only after adding a local four-level flux register to the seam Hamiltonian. An onsite scalar matter gauge transformation alone cannot change its Wilson holonomy. The eight-channel quarter twist has charge [formula in source] , hence [formula in source] , not the required [formula in source] . Eve","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Round-7 microscopic twist boundary (2026-09-05).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":4218,"byte_start":0,"id":"section:f10d7756aa987f8fe028","kind":"section","labels":[],"line_end":107,"line_start":1,"occurrence":1,"owner_documents":["document:articles/2026-08-30/mmst_charged_scaling_limit_en"],"relation_ids":["relation:13c247dcbfb9c0f75911","relation:bb4e3fd7bd303d1701cd","relation:e7d24a311ccd7ebc9389"],"semantic_review":false,"source":"documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/006-section-conclusion.tex","status_markers_as_written":[],"summary_excerpt":"The order-four arithmetic and the finite-group operator algebra are not the obstruction. The edge-projected Green form is now uniformly dominated for every [formula in source] with [formula in source] , and it converges to the chiral Green form in local [formula in source] quadratic-form norm. Exact compatible dyadic edge-mode isometries now give the charged graph-defect rate [formula in source] for fields and adjoin","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conclusion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":1150,"byte_start":0,"id":"section:b0fa4b0dcd35f08f5957","kind":"frontmatter","labels":[],"line_end":43,"line_start":1,"occurrence":1,"owner_documents":["document:articles/2026-08-30/tfpt_thermodynamic_dynamics_en"],"relation_ids":["relation:7d849e4323ca55125e8e"],"semantic_review":false,"source":"documents/articles--2026-08-30--tfpt_thermodynamic_dynamics_en/preamble.tex","status_markers_as_written":[],"summary_excerpt":"colorlinks=true, linkcolor=blue!55!black, citecolor=blue!55!black, urlcolor=blue!55!black","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Thermodynamic Dynamics for the TFPT Finite-Range\\\\ Master-Hamiltonian Class","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":1265,"byte_start":0,"id":"section:665d1fce3f7c4d6f2241","kind":"frontmatter","labels":[],"line_end":28,"line_start":1,"occurrence":1,"owner_documents":["document:articles/2026-08-30/tfpt_thermodynamic_dynamics_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--tfpt_thermodynamic_dynamics_en/sections/001-section-the-concrete-uniformly-local-class.tex","status_markers_as_written":[],"summary_excerpt":"We isolate the uniformly finite-dimensional, finite-range Hamiltonian class actually assembled by the TFPT [formula in source] - and [formula in source] -dimensional probes: electric and plaquette gauge terms, gauge-dressed fermion hopping, the DET16 mirror projector, and the seam clock and charge terms. At the frozen [formula in source] -dimensional coefficients the interaction has range [formula in source] , larges","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":1311,"byte_start":1265,"id":"section:ca221ce847445e4b4967","kind":"section","labels":[],"line_end":30,"line_start":29,"occurrence":1,"owner_documents":["document:articles/2026-08-30/tfpt_thermodynamic_dynamics_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--tfpt_thermodynamic_dynamics_en/sections/001-section-the-concrete-uniformly-local-class.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"The concrete uniformly local class","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":4230,"byte_start":1311,"id":"section:db01ea1aa320dae5cd00","kind":"subsection","labels":["eq:H","eq:ambient","eq:localdim","eq:quasilocal","tab:terms"],"line_end":111,"line_start":31,"occurrence":1,"owner_documents":["document:articles/2026-08-30/tfpt_thermodynamic_dynamics_en"],"relation_ids":["relation:06dbe6188fdfb95368ad"],"semantic_review":false,"source":"documents/articles--2026-08-30--tfpt_thermodynamic_dynamics_en/sections/001-section-the-concrete-uniformly-local-class.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] with graph distance [formula in source] and coordination [formula in source] . For a finite [formula in source] , put [formula in source] One cell contains the four representative physical edge modes, a mirror Fock factor, the two positively oriented outgoing finite-group gauge links, and a four-state seam clock. Thus [formula in source] The DET4 numerical analogue has dimension [formula in so","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ambient tensor-product algebra","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":5033,"byte_start":4230,"id":"section:4eb86e473c472c9b53e6","kind":"subsection","labels":["eq:constants","eq:kappa"],"line_end":139,"line_start":112,"occurrence":1,"owner_documents":["document:articles/2026-08-30/tfpt_thermodynamic_dynamics_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--tfpt_thermodynamic_dynamics_en/sections/001-section-the-concrete-uniformly-local-class.tex","status_markers_as_written":[],"summary_excerpt":"Define the finite-range interaction moment [formula in source] There are two assigned electric links, four plaquettes, and four bonds incident on a square-lattice cell. Consequently [formula in source] These bounds are independent of [formula in source] . More generally, bounded degree, finite [formula in source] , finite local dimension and finite [formula in source] are the class hypotheses; the displayed numbers a","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Uniform constants","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":8038,"byte_start":5033,"id":"section:5890da8efe52b8feadb2","kind":"section","labels":["eq:LR","eq:LRhyp","eq:TFPTvelocity","eq:iteration","eq:pathweight","eq:poissontail","eq:vLR","thm:LRclassical"],"line_end":224,"line_start":140,"occurrence":1,"owner_documents":["document:articles/2026-08-30/tfpt_thermodynamic_dynamics_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--tfpt_thermodynamic_dynamics_en/sections/001-section-the-concrete-uniformly-local-class.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be a graph, let every local Hilbert space be finite dimensional with a uniform dimension bound, and let a self-adjoint interaction satisfy [formula in source] For every finite [formula in source] , define [formula in source] . If [formula in source] , [formula in source] , and [formula in source] , then, uniformly in [formula in source] , [formula in source] Thus an admissible Lieb–Robinson ve","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Lieb–Robinson theorem and explicit TFPT velocity","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":10979,"byte_start":8038,"id":"section:a83819dcff945ddb5996","kind":"section","labels":["eq:convergence","eq:duhamel","eq:limit","eq:shell","thm:dynamics"],"line_end":300,"line_start":225,"occurrence":1,"owner_documents":["document:articles/2026-08-30/tfpt_thermodynamic_dynamics_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--tfpt_thermodynamic_dynamics_en/sections/001-section-the-concrete-uniformly-local-class.tex","status_markers_as_written":[],"summary_excerpt":"For every [formula in source] , the net [formula in source] exists in norm, uniformly for [formula in source] in compact real intervals and independently of the exhausting sequence. It extends uniquely to a strongly continuous one-parameter group of [formula in source] -automorphisms of [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Norm thermodynamic limit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":13669,"byte_start":10979,"id":"section:30db4349cae910dc7034","kind":"section","labels":["eq:fixed","eq:gaugecov","eq:projectorcompat","prop:gauss"],"line_end":363,"line_start":301,"occurrence":1,"owner_documents":["document:articles/2026-08-30/tfpt_thermodynamic_dynamics_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--tfpt_thermodynamic_dynamics_en/sections/001-section-the-concrete-uniformly-local-class.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the group of finitely supported local gauge transformations on the ambient field algebra, and let [formula in source] denote its action. Define [formula in source] The electric and plaquette terms are gauge invariant; the hopping contains its parallel transporter; the determinant projector is a Spin(10) singlet; and the seam charge is neutral as assembled. Thus [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gauss law and the correct consistent family","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":2531,"byte_start":0,"id":"section:0e46a5a279dce3de4926","kind":"section","labels":["eq:finiteKMS","eq:gibbs","eq:groundineq","eq:smear","thm:states"],"line_end":61,"line_start":1,"occurrence":1,"owner_documents":["document:articles/2026-08-30/tfpt_thermodynamic_dynamics_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--tfpt_thermodynamic_dynamics_en/sections/002-section-existence-of-equilibrium-states.tex","status_markers_as_written":[],"summary_excerpt":"The infinite-volume system [formula in source] , and its invariant subalgebra [formula in source] , have at least one ground state. For every [formula in source] , they have at least one [formula in source] -KMS state.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Existence of equilibrium states","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":4057,"byte_start":2531,"id":"section:f31237f5fb1b89d8d1a6","kind":"section","labels":["eq:numericconvergence","eq:numericvelocity"],"line_end":106,"line_start":62,"occurrence":1,"owner_documents":["document:articles/2026-08-30/tfpt_thermodynamic_dynamics_en"],"relation_ids":["relation:ed0a1ab157fb376cfa00"],"semantic_review":false,"source":"documents/articles--2026-08-30--tfpt_thermodynamic_dynamics_en/sections/002-section-existence-of-equilibrium-states.tex","status_markers_as_written":[],"summary_excerpt":"The companion [formula in source] uses the exact nearest-neighbour physical-edge sector of the assembled model while comparing it against the complete class constant earlier IR-universality witness. It reports: [formula in source] For the one-site projector, [formula in source] , and nested open volumes, the specialization of [formula in source] The zeros are numerical precision statements, not analytic finite-speed ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Numeric twin","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":6285,"byte_start":4057,"id":"section:b26762fa76b33b384e1a","kind":"section","labels":["thm:combined"],"line_end":156,"line_start":107,"occurrence":1,"owner_documents":["document:articles/2026-08-30/tfpt_thermodynamic_dynamics_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--tfpt_thermodynamic_dynamics_en/sections/002-section-existence-of-equilibrium-states.tex","status_markers_as_written":[],"summary_excerpt":"For the TFPT master-Hamiltonian class finite-dimensional local factors and coefficients of Table the finite-volume dynamics satisfy the uniform Lieb–Robinson bound [formula in source] ; the thermodynamic-limit dynamics exist in norm on all local observables and define a strongly continuous automorphism group; the group restricts consistently to the Gauss-invariant quasilocal algebra, with projector compatibility in t","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Combined theorem and exact boundary","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":8274,"byte_start":6285,"id":"section:f1269209928f923042c2","kind":"section","labels":[],"line_end":212,"line_start":157,"occurrence":1,"owner_documents":["document:articles/2026-08-30/tfpt_thermodynamic_dynamics_en"],"relation_ids":[],"semantic_review":false,"source":"documents/articles--2026-08-30--tfpt_thermodynamic_dynamics_en/sections/002-section-existence-of-equilibrium-states.tex","status_markers_as_written":[],"summary_excerpt":"The amended contract makes the continuum limit optional but the thermodynamic limit mandatory. The latter is now proved at the Hamiltonian-class level for the concrete finite-group, finite-local-space TFPT assembly. The proof is insensitive to finite-volume boundary shape and does not infer thermodynamics from a finite scan. Its explicit velocity is conservative, while the numerical witness checks the expected cone, ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conclusion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":2992,"byte_start":0,"id":"section:d85367316428383efbf7","kind":"frontmatter","labels":[],"line_end":57,"line_start":1,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:6c376c55a7c1fe3e8322"],"semantic_review":false,"source":"documents/changelog/preamble.tex","status_markers_as_written":["[C]","[E]","[O]","[X]","\\mC","\\mE","\\mO","\\mX"],"summary_excerpt":"TFPT — Changelog\\\\[1mm] All changes and new results, by date Stefan Hamann Alessandro Rizzo This file is the canonical, dated record of every change to the TFPT theory development: new verification modules ( vN), status changes, editorial passes and infrastructure. It is maintained in the same change as the work it records, and it is also imported at the end of the introduction document. Module numbers vN refer to ve","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TFPT — Changelog\\\\[1mm] All changes and new results, by date","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3261,"byte_start":2992,"id":"section:2fca84369c4a253cec63","kind":"section","labels":[],"line_end":63,"line_start":58,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":[],"semantic_review":false,"source":"documents/changelog/preamble.tex","status_markers_as_written":[],"summary_excerpt":"tocsectionAppendix: changelog The dated record of every change (canonical source: changelog.tex, also compiled standalone). Module numbers vN refer to verification/vN_*.py.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Appendix: changelog","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7743,"byte_start":0,"id":"section:f091de1c3533bab48372","kind":"subsection","labels":[],"line_end":102,"line_start":1,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:00f5493d33e75f892576","relation:043d78928940265f8692","relation:07e316733f3eb854ee06","relation:0c7b4c73a919b4e9d94b","relation:0cfdce5bf31ee21e2f28","relation:0f871930d110222e0a42","relation:0fac897c3114ea6f1871","relation:10caf32875d0df0f126f","relation:125d8e314c68479e975b","relation:150c7294419b39cc3cee","relation:154ffc4783552f0f52f8","relation:1674735db675d85343a2","relation:1681c8f67c1c780ab4ad","relation:16f3ae1f598f65afac47","relation:17693ae5dee69276fc96","relation:1816d89678249b54a4f2","relation:18509a95677a0914dfac","relation:1969a4f7a20188980502","relation:1979228a6315715aab09","relation:1b5b51acaa1645a5f84a","relation:1bf63b2f630825e454f4","relation:2374346baf3cc5897b8b","relation:245d0bec3091b1259a7e","relation:25097a4c3c8f8ce018f2","relation:25164bd2b1b4964f6d08","relation:2554bcf90f503bf1f422","relation:28e154b506ae24d89af1","relation:2a5422e63cf853c7270e","relation:2f785fd782cb9394bdf7","relation:361aac49a1921b4c5cb6","relation:3a00c45795b116e79085","relation:487fe4b63a324a35a949","relation:48a923c4142d0423f999","relation:48edc7eaea65e8016a4f","relation:4f120cb082318cb62bfe","relation:4ff547d0f1d9b90bb9ef","relation:5390cec264623cea21c9","relation:59d2cd2112b3074ba775","relation:5a23aa03cdaa364a870b","relation:5c926da738f167b92993","relation:5e83144c816b058d9adb","relation:5f320ebf403a89bbc61d","relation:5fc404f49446f30154fa","relation:607df365b2406ea15e4f","relation:6b0f59e3246a2721cb4a","relation:6babaf7fa747f662a326","relation:6f3861cef1559f868e8e","relation:72330963066c5bd04eda","relation:76810a8efb5342152ff2","relation:7bf3b3ed373c25732706","relation:7cb4a34989f422ffcf59","relation:7f416ff6069163176816","relation:8156e377a58648aebe4b","relation:82583abda4f1df435c31","relation:83488fb0448811c8ce9f","relation:838f992a91822c39edea","relation:841354da103d31744e02","relation:8a4a2ca9ecc27943e58b","relation:8e5888bae510b3a59175","relation:8e6aa14e28d12f6795c3","relation:95fabe348319de408f61","relation:9834c793a9a67233b4e8","relation:9f7ceea8f6f9b7e9ba18","relation:9fb92c71fb94e2912a98","relation:a3317b3f652356894272","relation:a41d8581bbed490fc552","relation:a46b36fbe23b0167c770","relation:a5691612800635bc614c","relation:aa425f903a730c89642b","relation:abd9b53793c22fc69063","relation:abfc49e36565637dc0b7","relation:b61df5fde77c514747ea","relation:b90280d4319c586cc053","relation:bd4af038b85cd4494daa","relation:bdf273abc9b07fb92436","relation:be104993f191859b0d97","relation:c0e2ec3c310287fbc7ac","relation:c0fd7481f0f86990009e","relation:c25188a95106226772d8","relation:c4dfc30463fbd10bed38","relation:c63417dc9e1a4617c6b2","relation:c6765c85282c5d253610","relation:cbc93ac5e49364fe78f6","relation:d1fd78504b27505013b4","relation:d7c10f74cd666cb24c52","relation:d91080af690e754ed17f","relation:d97b96d57982adc5d591","relation:dad939845329b463753d","relation:dfabde82442a25ccd710","relation:e31644587a8df76d249e","relation:e786a803473be4e1592f","relation:eb8f309b352f59825293","relation:eb9686bd56fe135c11e7","relation:ef497e33d2ec9ddfb60e","relation:ef6ca09fad14041167af","relation:f27c748da7e966b9b44b","relation:f3b4bca475f3790f6462","relation:f4b422e299651fac5042","relation:f7bc2f7b7854c894f4d1","relation:fcf49d364166c3e41233"],"semantic_review":false,"source":"documents/changelog/sections/001-source.tex","status_markers_as_written":[],"summary_excerpt":"The combined publication history was separated by research ownership. Complete original dated entries remain byte-preserved in the independent archive, including mixed entries that also recorded physical work. The following existing TFPT modules retain their original identifiers and their currently scoped physical, compiler or verification roles. This entry records ownership and preserves history navigation; it does ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-10-18: Project separation and retained physics history","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9010,"byte_start":7743,"id":"section:c6a235002defa9df2d26","kind":"subsection","labels":[],"line_end":121,"line_start":103,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":[],"semantic_review":false,"source":"documents/changelog/sections/001-source.tex","status_markers_as_written":[],"summary_excerpt":"The new tfpt_explorer package connects the origin principles, algebraic compiler, geometric and topological structures, physical readouts, and their evidence in an executable process with a guided graphical tour. It includes source browsing, verification and experiment discovery, and a Lean bridge that preserves the distinction between formal statements and executable numerical checks. Six recent source documents and","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-09-29 (CLXIII): Executable TFPT explorer and consolidated session synthesis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10954,"byte_start":9010,"id":"section:117cbc6545f0d479f930","kind":"subsection","labels":[],"line_end":151,"line_start":122,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":[],"semantic_review":false,"source":"documents/changelog/sections/001-source.tex","status_markers_as_written":[],"summary_excerpt":"The post-Round 27 research archive, including Rounds 28–50 and subsequent named branches, is integrated without rewriting source-pinned historical records. 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Neutral four-point collision ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-09-09 (CLXII): Source fields, full lattice dynamics and Clock/E8 bridge consolidated","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13052,"byte_start":10954,"id":"section:04b5cf8557bf29474e32","kind":"subsection","labels":[],"line_end":183,"line_start":152,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:1a6166422eb5e78ce976"],"semantic_review":false,"source":"documents/changelog/sections/001-source.tex","status_markers_as_written":[],"summary_excerpt":"The previously local theory-contract archive is shipped with its proofs, source-pinned checkers and immutable per-round validation snapshots. The intervening geometry, positive-parent, constraint-domain and charge transport branches retain their distinct hypotheses and additional off-shell inputs; they are not combined into a claimed microscopic TOE. The contracts paper now includes the full-reference argument for th","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-09-07 (CLXI): Non-RH research through Round 27 integrated into repository, papers and website","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14728,"byte_start":13052,"id":"section:b1a00da71a3c4d3df9e9","kind":"subsection","labels":[],"line_end":208,"line_start":184,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:cb005341aba2394a342c","relation:e1af34e820b0d290ee35"],"semantic_review":false,"source":"documents/changelog/sections/001-source.tex","status_markers_as_written":[],"summary_excerpt":"Linux reproduction exposed an eigensolver-dependent choice of a pure zero-mode vacuum in v1033_charged_disorder.py. The numerical diagnostic now uses the basis-independent fixed-particle ground-space mixture and computes variational energy bounds over every pure zero-space filling. At [formula in source] the smooth [formula in source] -scaled mixture excess is [formula in source] , with full ground-space interval [fo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-09-06 (CLX): QWZ zero-mode portability correction and a free 3D matter contract","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16632,"byte_start":14728,"id":"section:cfb240e07819e5428824","kind":"subsection","labels":[],"line_end":236,"line_start":209,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:06006194d680e8facd15","relation:0ab0ed567892224c1010","relation:4e937db6b683b611c64a","relation:559b16894e148850fdfb","relation:5e33f0c5e4296dd1796b","relation:626ef5da757810de6f22","relation:7e1a0616be3e85c81db6","relation:a2f8765da2a68972f67e","relation:d190713b491e874a03ad","relation:d7aa6b7d1f9b3cc55592","relation:e7ff40ebe35b4eceaf22","relation:e9256adb4f219d582b54"],"semantic_review":false,"source":"documents/changelog/sections/001-source.tex","status_markers_as_written":[],"summary_excerpt":"Five modules v1031– v1035 add [formula in source] typed checks (183 exact, 13 source-contract, 37 floating) to the registered suite ( [formula in source] modules), including the round-6 quantum prerequisite. v1031_quantum_tensor_curvature.py ( [formula in source] ) constructs the zero-mean Weyl/Fock target and its distribution limit; v1032_covariant_curvature.py ( [formula in source] ) supplies exact identities for t","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-09-05 (CLIX): non-RH round 7 — free quantum curvature, charged twists and interaction boundaries","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19708,"byte_start":16632,"id":"section:a25026597f4b790eb050","kind":"subsection","labels":[],"line_end":279,"line_start":237,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:02faf880da2802df210a","relation:09ff4407d56f2c931133","relation:1c29144c3d0a43fff92f","relation:34d1e8818c0d7e215bee","relation:4fdba9f9104792aebdb7","relation:52faac0f0c012c84e384","relation:603978b3b568d94e32e8","relation:61f72449c1b1c70cf81f","relation:6f2c474be69234ee3d98","relation:c4c95cabe5c073584ffb","relation:cddf1c324589b3bcbcb8","relation:da6182e8038dcfcc3752","relation:f10b25dcfdc1cce8f650","relation:fa0d2db1b19bd8d499ab","relation:fb75dbc2e36d59e03f1a"],"semantic_review":false,"source":"documents/changelog/sections/001-source.tex","status_markers_as_written":[],"summary_excerpt":"Five modules graduate as v1026– v1030; the suite grows from 1018 to 1023 modules. Their standalone checks pass [formula in source] . v1026_ telb_ round4_ closure.py ( [formula in source] , native python-flint 0.9.0) executes CF, DG, one-sided CROSS, 512 validated Acb eigensystems, sixteen Fourier modes, all infinite aliases and 154 numerical regressions. With v1022/v1025 inputs it proves [formula in source] at fixed ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-09-05 (CLVIII): non-RH round 4 — uniform TEL-B norm and explicit T1–T8 boundaries","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":22810,"byte_start":19708,"id":"section:17757402db902787518b","kind":"subsection","labels":[],"line_end":280,"line_start":280,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:32190f234088a48c4748","relation:74a019ac223651545635","relation:80d52922952437b7b5f1","relation:ab0f858b64ed0c91f371","relation:cbdfc794d9f9acaae5d4","relation:d03dcf4afb625761f090","relation:e95039bfe733897cf483","relation:eb1ff3f83480a4ea1d48"],"semantic_review":false,"source":"documents/changelog/sections/001-source.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"=150 2026-09-05 (CLVII) (non-RH T1–T8 Round 3 graduates as v1022– v1025; suite [formula in source] , ledger rows [formula in source] through six narrow subcontracts; [formula in source] module checks; NO marker move; TFPT.TOE.COMPLETE.01 and every T1–T8 gate remain ). v1022_ telb_ round3_ certificates.py ( [formula in source] ; native python-flint==0.9.0, 256-bit Arb/Acb) replaces the float/Richardson TEL-B input by 5812 rational cells and the exact cut jump, proving [formula in source] and [formula in source] . Together with the stated analytic digamma/midpoint lemmas, its executable Arb arithmetic gives [formula in source] , [formula in source] and [formula in source] ; full C2b remains open exactly at CF [formula in source] and DG [formula in source] . Its exact one-mode [formula in source] countermodel refutes the former ALG2 Vandermonde-to-generated-algebra implication: FE-GEN or an exact gauge/code-projected microscopic-algebra theorem is still required, and ALG1 remains conditional on the generated projection. v1025_ telb_ c1_ c2a_ certificates.py ( [formula in source] ; native 100-bit Arb/Acb) executes the existing analytic C1/C2a proofs: [formula in source] and [formula in source] for every even [formula in source] . v1023_ derivative_ filtered_ wall.py ( [formula in source] ) proves only the finite quasi-free singular-value block: the high continuation branch is separated, but the bare [formula in source] subspace is not invariant, the low branch has [formula in source] rather than a Weyl cone, and no DET16/DET32, interacting-parent, measure/anomaly/index or [formula in source] D theorem follows. v1024_ parent_ internal_ boundaries.py ( [formula in source] ) supplies finite parent-internal T6–T8 witnesses and no-gos: a positive seam/neutrino-pair intertwiner with projective full-Fock [formula in source] lift but no mass texture; the uniform-gap and direct-TT locality obstructions but no graviton; and a gapped internal [formula in source] cap that is chosen, [formula in source] -breaking and complement-trivial, hence no global [formula in source] . T1 retains only finite axiom-core/W-bridge support while unconditional provenance and the dimension selector remain open; T3 remains at Hamiltonian-class level; T5 retains finite IR witnesses and the v1020 spectator obstruction while prime completion, OS reconstruction, confinement and scattering remain open. The common missing object is still one shared [formula in source] D parent satisfying T3–T8. Native-only handling is explicit in the website reproducer; v1022/v1025 are not represented as Pyodide certificates. NO RH CLAIM. Surfaces: tfpt_research_contracts, tfpt_4_frontier, introduction, tfpt_2_standard_model, the MMST article/PDF, ledger, generated verification maps/index, website paper/DAG/gap/FAQ mirrors and changelog.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":24115,"byte_start":22810,"id":"section:aa4a70b2117802d4bb85","kind":"subsection","labels":[],"line_end":281,"line_start":281,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:175a8ca567e9e8ce525f","relation:a41bebc0d45bffd7ced1","relation:aa4f1b88749f09c77ca5","relation:c6fed7c783e9b45f352a","relation:fa71fc03c391122cee71"],"semantic_review":false,"source":"documents/changelog/sections/001-source.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"=150 2026-09-04 (CLIV) (TEL-B reduction absorbed into the SEAM.MMST.TYPEIII.CHARGED.01 contract text and ledger row; NO marker move, status stays ). The standalone note articles/2026-09-04/telb_bound_b_sketch.tex is superseded and removed: the contract is now the single home. Cover identity [formula in source] sawtooth split [formula in source] ; bound (A) certified numerically for all [formula in source] ( [formula in source] , all-mode BV, one float64 TV constant); bound (B) reduced to [formula in source] (measured [formula in source] ), open items C1/C2a/C2b. Residual restated as TEL-B-EXTERNAL (2026-09-04 reduction); the [formula in source] dyadic-increment route is superseded (measured [formula in source] at r645, no longer the route). Numerically [formula in source] , conditional analytic [formula in source] ; analytically open. Evidence (experiments, not veri-citable): mmst_telb_trace_decomposition_probe.py, mmst_telb_cover_split_probe.py, mmst_telb_bound_a_probe.py ( [formula in source] ), mmst_telb_bound_b_probe.py ( [formula in source] , G18–G20 open by design). Surfaces: tfpt_research_contracts (new TEL-B reduction subsection); ledger row claim text only; website changelog.ts regenerated.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":26289,"byte_start":24115,"id":"section:8c44b477c1ab034d5ccf","kind":"subsection","labels":[],"line_end":283,"line_start":282,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0368851a5509b026e014","relation:171c569aae3953742a27","relation:3d459424c28bcf9ad248","relation:6491599b68548cc6932f","relation:7b37d4ffa844d63405cf","relation:7ceec1581f47d7bb7a90","relation:7fc7ccd8093766fb22b0","relation:b37d0663a4ac833ad6f1","relation:d5c13add0a0304a07ae2","relation:e917e5daaf0a7e04bacf","relation:f463f2ae2b6883af63ff"],"semantic_review":false,"source":"documents/changelog/sections/001-source.tex","status_markers_as_written":["\\mC","\\mO"],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"=150 2026-08-31 (CXLIX) (Monday-morning harvest — axiom-core closure [formula in source] state/gap batteries graduate as v1015– v1016; suite [formula in source] , ledger [formula in source] no new rows, existing contract rows updated, NO status-marker upgrades; Python-only / Wolfram mirror deferred as for v974–v1014, engine still DEFERRED_NO_ENGINE). (1) v1015_ axiom_ core_ closure.py ( [formula in source] ): character-blind P-dem response DERIVED — [formula in source] exactly at collar sizes [formula in source] and [formula in source] , democracy residual [formula in source] ; mutants split [formula in source] and [formula in source] . Together with P-anch (v1014) BOTH W-bridge premises are derived at finite level; the axiom-core remainder is ZERO modulo the externalized MMST identification. AX.P2.01 stays an axiom (finite shadows; continuum identification is the same external leg). T1 note on TFPT.TOE.COMPLETE.01: the structure-postulate route is now fully premise-supported at finite level. (2) v1016_ state_ gap_ batteries.py ( [formula in source] ): [formula in source] seam-modular cap is the unique finite-level non-entropic selector ( [formula in source] , SK RMS [formula in source] , [formula in source] saddle preserved; finite-proxy caveat; FTRANSFER.SK.RHO0.01 stays ). TEL-B certified-tail BLOCKED ( [formula in source] [formula in source] , UV-supported remainder); strictly smaller external target [formula in source] with factor- [formula in source] measured headroom; [formula in source] -uniform CAR nuclearity PROVED ( [formula in source] ) as ALG specialist input; ALG-EXH unchanged ( SEAM.MMST.TYPEIII.CHARGED.01 stays ). DFP volume-uniform gap cited-verified for [formula in source] open chains ( [formula in source] , [formula in source] ); dynamical-link leg closed at that level; remaining rotor/wall/ [formula in source] D ( CHIRAL4D.MIRROR.DET16.01 stays ). Surfaces: tfpt_research_contracts executed-update paragraphs (five items [formula in source] L1 nuclearity note); tfpt_4_frontier [formula in source] introduction Monday-morning note; MMST handoff HTML update-2026-08-31 block; website papers.ts / VerificationDag.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":28700,"byte_start":26289,"id":"section:62b5d88e8412144c1f8b","kind":"subsection","labels":[],"line_end":285,"line_start":284,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:10df0ed023c15028a074","relation:169e154e5447c2582b81","relation:2e470c5743bfd9c5e651","relation:7017b3e14bec27a972b0","relation:784aa1c47d101a001823","relation:be41536ed4a549107bb4","relation:d59698ecf85bc6612217","relation:d5a989ab059ba24f2803","relation:f1b3528f67a12d5be600"],"semantic_review":false,"source":"documents/changelog/sections/001-source.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"=150 2026-08-30 (CXLVIII) (late-evening harvest — thermodynamic-dynamics theorem [formula in source] detline/W-bridge refinements graduate as v1013– v1014; suite [formula in source] , ledger [formula in source] no new rows, existing contract rows updated, NO status-marker upgrades; Python-only / Wolfram mirror deferred as for v974–v1012, engine still DEFERRED_NO_ENGINE). (1) v1013_ thermodynamic_ dynamics.py ( [formula in source] ): the mandatory-dynamics leg of QFT4D.LATTICE.FUNDAMENTAL.01 is CLOSED at Hamiltonian-class level. Cited articles/ 2026-08-30/ tfpt_ thermodynamic_ dynamics_ en.tex/ .pdf: uniform Lieb–Robinson bound [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] ; norm-convergent [formula in source] ; gauge-invariant quasilocal [formula in source] (Gauss caveat resolved on the invariant subalgebra); existence of ground and [formula in source] -KMS states. Numeric twin: measured [formula in source] proved bound; analytic finite-volume bound dominates nested differences at buffers [formula in source] ; [formula in source] mutant ratio [formula in source] ; Gauss-positive control commutes, violating embedding has commutator norm [formula in source] . Remaining: phase uniqueness, limit gap, IR universality. Decision typing UNCHANGED. (2) v1014_ bridge_ refinements.py ( [formula in source] ): finite detline restriction isomorphism VERIFIED ( [formula in source] constancy [formula in source] , conjugation covariance exact, [formula in source] / mirror [formula in source] ); orientation fixes only the conjugate branch ( [formula in source] ); the residual constant [formula in source] is the [formula in source] reference normalization — recorded on ALPHA.QUILLEN.EXACT.01. W-bridge: P-anch DERIVED ( [formula in source] via the winding lock); P-dem PARTIAL (the [formula in source] average annihilates the nontrivial character space); missing object [formula in source] the character-blind determinant-response map — the same MMST/Quillen externalized leg as TEL-B/ALG-EXH/P1. AX.P2.01 stays an axiom. Convergence: every remaining axiom-core and continuum gap now runs through ONE externalized theorem. Surfaces: tfpt_research_contracts executed-update paragraphs; tfpt_4_frontier [formula in source] introduction late-evening note; website papers.ts / VerificationDag.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":30892,"byte_start":28700,"id":"section:a1b31833986dad8762ee","kind":"subsection","labels":[],"line_end":287,"line_start":286,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:38189c1c4927ec190be9","relation:422b9785110739a99688","relation:5105755e7499176bfb96","relation:561d0503106cc7833c2a","relation:a6fcc4293ad82c748c6f","relation:d9c8bb710cec1d5f31ca","relation:ee04e0ab0720f1bd124f","relation:fc2c29ed0a2d911fb806"],"semantic_review":false,"source":"documents/changelog/sections/001-source.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"=150 2026-08-30 (CXLVII) (evening TOE-gate wave — four executed witnesses graduate as v1012; suite [formula in source] , ledger [formula in source] no new rows, existing contract rows updated, NO status-marker upgrades; Python-only / Wolfram mirror deferred as for v974–v1011). v1012_ toe_ gate_ witnesses.py ( [formula in source] ): T5 IR universality on the physical QWZ edge — [formula in source] (limit [formula in source] ), clustering dichotomy [formula in source] vs power-law exponent [formula in source] , Lieb–Robinson cone [formula in source] with leakage [formula in source] , cubic curvature [formula in source] with volume; TYPED SPLIT: gauge holonomy [formula in source] seam clock are not propagating modes, so the common- [formula in source] test needs dynamical gauge excitations. T8 [formula in source] eight-candidate table ALL unique; hard sectors kill the SK response ( [formula in source] ); every response-alive set is exactly [formula in source] even without [formula in source] — entropic-proximity selection is VACUOUS at finite level; verdict NO_SET_WORKS with the double diagnosis; binding requirement [formula in source] a non-entropic principle (Euclidean-cap / orientation-branch). T6 [formula in source] six-fold NULL: six pre-declared D4-odd candidates, all parity-checked, all NULL (five at [formula in source] ; [formula in source] is [formula in source] too large); the [formula in source] cancellation requires the true [formula in source] D functional — third and final scaffold-level nu-mechanism bound this week. T7 interacting TT: conserved interaction-complete lattice stress [formula in source] , TT spectral positivity exact, sum rules [formula in source] , dominant positive- [formula in source] pole persists under [formula in source] (gapped); [formula in source] trend [formula in source] suppressed [formula in source] / [formula in source] enhanced [formula in source] ; free analytic match. Missing: TFPT content, [formula in source] volume scaling, Ward identities. Ledger notes only on TFPT.TOE.COMPLETE.01, FTRANSFER.SK.RHO0.01, FLAV.NU.TEXTURE.MECHANISM.01, GRAV.SPIN2.EMERGENCE.01 (all stay ). Surfaces: tfpt_research_contracts executed-update paragraphs; tfpt_4_frontier [formula in source] introduction evening-wave note; website papers.ts / VerificationDag.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":33690,"byte_start":30892,"id":"section:86d6234f384db2b3c770","kind":"subsection","labels":[],"line_end":289,"line_start":288,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:5553c2289c02c202831c","relation:55a52cfb50fc5b3d3612","relation:6664530add0d4730b4c1","relation:6b702ca79f4335728a48","relation:86f79b8d8e3f350cb1f9","relation:9953fd2be3ab6a63c723","relation:9b42c8fb1e59135c4f1f","relation:ac9ea0d91b5598160232","relation:ad046deed4842ec50944","relation:c4e5884743b28a99038d","relation:d5555aa03aeeb8261a9c","relation:ff652b93d9074b5c1ef4"],"semantic_review":false,"source":"documents/changelog/sections/001-source.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"=150 2026-08-30 (CXLVI) (afternoon harvest — simplicity campaign [formula in source] [formula in source] D ladder graduate as v1010– v1011; suite [formula in source] , ledger [formula in source] no new rows, existing contract rows updated, NO status-marker upgrades; Python-only / Wolfram mirror deferred as for v974–v1009). (1) v1010_ simplicity_ bridge_ census.py ( [formula in source] ): derivation matrix over four frozen seeds, unique remainder min [formula in source] ; anchor [formula in source] is not among the three declared Milnor maps; [formula in source] four novel candidates NULL. Bridge [formula in source] CANONICAL — the bit-selector ladder forces [formula in source] and family [formula in source] forces [formula in source] column sums [formula in source] ; [formula in source] 's carrier-looking [formula in source] is inherited from [formula in source] column [formula in source] , not inserted (the v1005 circularity flag is corrected as forced provenance). Bridge [formula in source] CHOICE-but-conditionally-unique: spectrum [formula in source] alone has [formula in source] solutions; democratic-image [formula in source] carrier-anchor kernel leave exactly the corpus shift (count [formula in source] ); remaining obligation [formula in source] seam-geometric derivation of those two directional premises. Milnor strong all-structure bridge NONEXISTENT at [formula in source] (clock [formula in source] vs [formula in source] , CP rank [formula in source] vs [formula in source] ) and at every upstairs home ( [formula in source] , Gaussian [formula in source] , affine); only the coarse [formula in source] -module [formula in source] pairing bridge exists (witness constructed; [formula in source] , [formula in source] ). Ring-internal identities of v1004 (rank clock, socle CP, self-clock) unaffected. SEAM.MILNOR.LOCALRING.01 stays \\ (canonical status SHARPENED); AX.P2.01 stays an axiom (pencil rehabilitated, W premises remain). (2) v1011_ 3p1d_ ladder_ battery.py ( [formula in source] ): B6–B9 compressed — minimal [formula in source] D viable (exact Gauss [formula in source] , confinement [formula in source] vs [formula in source] , exact in-face isotropy, [formula in source] ); exact tree-fixing [formula in source] with tree-independence [formula in source] ; DET survives coupling; back-reaction; periodicity restores holonomy [formula in source] ; charged channels [formula in source] at weak [formula in source] ; charge- [formula in source] control matches B8 to [formula in source] ; [formula in source] collapses above [formula in source] . BINDING: the matching point of the coupling functional must sit in the deconfined/weak regime. QFT4D.LATTICE.FUNDAMENTAL.01 Decision typing UNCHANGED (Kronecker limitation removed); GAUGE.DETLINE.FIXPOINT.01 stays \\ with the matching-scale constraint recorded. Surfaces: tfpt_research_contracts executed-update paragraphs (MILNOR sharpening, P2 rehabilitation, QFT4D ladder, DETLINE matching-scale); tfpt_4_frontier [formula in source] introduction afternoon note; website papers.ts / VerificationDag.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":36848,"byte_start":33690,"id":"section:710760dba8520599a644","kind":"subsection","labels":[],"line_end":291,"line_start":290,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:00809843194747b405a6","relation:149b0eded01eff37f1c4","relation:369165f658e52a431769","relation:4419defee34e717be644","relation:57c638ad5eb49a55fa83","relation:6382c8e9768f9bba7400","relation:6d95f0b0e23f915167e0","relation:86a65e5f60776e03eb10","relation:9c0dd69b9159b7e16ec4","relation:a2ac0e6f415b3c9aee76","relation:a2fdad68fe913fd5c2a5","relation:d13c47025cf071b22387","relation:deae54018b6943097808","relation:ea2650f6618d6dfda029","relation:f662ae2843ab33cafe75","relation:f924378b08cbcab2bb35"],"semantic_review":false,"source":"documents/changelog/sections/001-source.tex","status_markers_as_written":["\\mC","\\mO"],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"=150 2026-08-30 (CXLV) (review wave 7 — four exploration strands graduate as v1006– v1009: the MMST lemma battery, the DET16 stability battery, the [formula in source] D master-object assembly scaffold, and the [formula in source] constrained minimizer; suite [formula in source] , ledger [formula in source] no new rows, existing contract rows updated, NO status-marker upgrades; Python-only / Wolfram mirror deferred as for v974–v1005). (1) v1006_ mmst_ lemma_ battery.py ( [formula in source] ): five lemmas in-house on SEAM.MMST.TYPEIII.CHARGED.01 \\ — L3 crossed-product; UGF [formula in source] (measured plateau [formula in source] , max measured [formula in source] [formula in source] at [formula in source] ); TEL-a [formula in source] with exact isometries ( [formula in source] , measured envelope [formula in source] ); integer D5+A3 pairings; [formula in source] outerness in the limit [formula in source] finite-inner correction. Residual boxed: TEL-B-EXTERNAL (Hankel [formula in source] ; HS remainder sourced from the paper max [formula in source] / fit [formula in source] / v998 bound [formula in source] , not recomputed) [formula in source] ALG-EXH (two Buchholz–Verch estimates). Display stays . Cited articles/2026-08-30/mmst_charged_scaling_limit_en.tex ( [formula in source] pp) [formula in source] externalization_mmst_handoff_v2_en.html. (2) v1007_ det16_ stability_ battery.py ( [formula in source] ): T1/T2 proved (v1002); T3 Michalakis–Zwolak cited-verified (LTQO, [formula in source] , gap [formula in source] ). Counting line [formula in source] ; [formula in source] closing scan through [formula in source] ; dynamical [formula in source] uniquely gapped (full-probe min [formula in source] pinned; compressed suite). SW [formula in source] ; [formula in source] bounded. [formula in source] boxed (ordinary hopping not block-diagonal); BDL boxed (no volume-uniform gap remainder). CHIRAL4D.MIRROR.DET16.01 stays ; CHIRAL4D.NOMIRROR.01 unmoved. Cited articles/2026-08-30/det16_mirror_gap_theorem_en.tex. (3) v1008_ master_ assembly_ scaffold.py ( [formula in source] ): [formula in source] D master-object scaffold-coherent — combinatorial [formula in source] ; frozen-link [formula in source] , [formula in source] ; unique-contractive [formula in source] ; QWZ wall slope [formula in source] , DET gap [formula in source] through [formula in source] ; assembly [formula in source] [formula in source] , clock [formula in source] . [formula in source] spaces [formula in source] / [formula in source] out of suite. Decision QFT4D.LATTICE.FUNDAMENTAL.01 and GAUGE.DETLINE.FIXPOINT.01 \\ unmoved. (4) v1009_ rho0_ minimizer.py ( [formula in source] ): finite uniqueness of the KMS compression (Klein); Hessian strictly positive; centre dim [formula in source] ; identity [formula in source] . TYPED: V1000_CONSEQUENCE_MISMATCH (compression kills the SK response vs frozen contrast [formula in source] ) [formula in source] CENTER_FLATNESS_PREMISE_FALSE. Canonical formula needs a weaker admissible set. FTRANSFER.SK.RHO0.01 stays . Surfaces: tfpt_research_contracts executed-update paragraphs; tfpt_4_frontier wave-7 paragraph; introduction status card; website papers.ts / VerificationDag.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":41401,"byte_start":36848,"id":"section:89a96ea40df8ee1ce3c8","kind":"subsection","labels":[],"line_end":293,"line_start":292,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:004b483901ae7ef6dd1e","relation:2975d14e860a0959a9ac","relation:3e4fd0e3ee3e0653a5dd","relation:3e98f2842d60174cdee9","relation:46f093fe8982d1d7b505","relation:62e6b0a2a74f4a667fef","relation:6a63f21494491e1fe9c8","relation:6b5eff7a11960dfcfc1d","relation:6da543119477d8cdbb95","relation:7134df5c38e273a9e689","relation:74c29519a210ef350604","relation:9789d65fe2e8490abeee","relation:ae1502eef8650d571523","relation:b148dc6de565651872ab","relation:bab189654ef29a753762","relation:c0887501133e1d1ad331","relation:c484e05574a3a51c7a6d","relation:d4021ded36496549620c","relation:da3789875802bfa2eacf","relation:dc36fd822d2d220d1da5","relation:e026074afcd4281f1bb8","relation:fa80b279d0e0c818864b","relation:fb5ff098670e7e899f28","relation:fde0b0f1a723c4ba590b"],"semantic_review":false,"source":"documents/changelog/sections/001-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"=150 2026-08-30 (CXLIV) (review wave 6 — two exploration probes graduate as v1004– v1005 plus two registrations and display corrections: the Milnor–Frobenius–Gray finite algebra, the circularity-flagged relative pencil, the local-ring identification contract, the Weinberg–Witten spin-2 firewall, and honest rest/SM/gravity wording; suite [formula in source] , ledger [formula in source] : two new rows, existing contract rows updated, NO status-marker upgrades; Python-only / Wolfram mirror deferred as for v974–v1003). (1) v1004_ milnor_ frobenius_ gray.py ( [formula in source] ): CLASSICAL (cite, no claim) — Milnor algebra of [formula in source] dimension [formula in source] , spectral numbers [formula in source] [formula in source] exponents [formula in source] . NEW-IN-CORPUS EXACT -finite: rank clock [formula in source] table-sum [formula in source] ; [formula in source] ; self-clock iff [formula in source] ; [formula in source] unique among ordered spherical triples; Galois–Gray [formula in source] (binary Gray order [formula in source] ); CP [formula in source] socle/Frobenius; integral dual-number bridge [formula in source] free rank [formula in source] over [formula in source] , basis-dependent. INTERPRETIVE : [formula in source] . Mutants: [formula in source] [formula in source] ; [formula in source] self-clock survives but exponents fail; wrong socle rank [formula in source] . NEW ledger row SEAM.MILNOR.LOCALRING.01 : required canonical geometric/mechanical identification of the raw seam collar / [formula in source] transition bus with [formula in source] preserving dual-number action, Frobenius pairing, Gray torsor, deck action and CP (rank clock and socle-CP as outputs); kill [formula in source] second inequivalent identification or [formula in source] -equivariance failure; currently \\ because Milnor algebra [formula in source] exponents are classical and the corpus map is unproven. (2) v1005_ relative_ pencil_ bridges.py ( [formula in source] ): EXACT -finite Hankel [formula in source] [formula in source] Jacobi spec [formula in source] diag [formula in source] (v106/v119) and winding spec [formula in source] [formula in source] fixed plane (v4). EXACT BUT CIRCULARITY-FLAGGED : unique [formula in source] , [formula in source] , factorisation [formula in source] , CM [formula in source] , dual number mod [formula in source] , index [formula in source] SNF [formula in source] — BUT carrier [formula in source] already sits in the column sums of [formula in source] and [formula in source] : NOT a P2 selector until [formula in source] , [formula in source] , [formula in source] are derived from seam geometry independently; AX.P2.01 typing UNCHANGED. INTERPRETIVE : Klein-four SNF [formula in source] only after [formula in source] (side-blind nulls v521, not a theorem). Mutants: [formula in source] fails; perturbed [formula in source] breaks factorisation; [formula in source] breaks Hankel. (3) registrations (no marker moves). NEW GRAV.WEINBERG.WITTEN.01 : binding firewall BEFORE any spin-2 marker move — the microscopic Hamiltonian family must NOT possess a fundamental Lorentz-covariant local conserved [formula in source] ; Lorentz, diffeomorphism Ward identities and the spin-2 mode must emerge in the SAME IR limit; acceptance [formula in source] positive TT density, two helicities, massless pole, emergent diff Ward, universal soft coupling, named evaded Weinberg–Witten premise; kill [formula in source] microscopic covariant local [formula in source] together with a massless composite spin-2 claim; child of T7, cross-link GRAV.SPIN2.EMERGENCE.01 (not back). (4) display corrections (honest wording, no claim changes). Status-at-a-glance: compiler rest [formula in source] now sits NEXT TO the strict-physical-TOE rest (ten-component [formula in source] / eight TFPT.TOE.COMPLETE.01 gates, one line). SM completeness retyped: the discrete Standard-Model structure (charges, families, flavor operators) is derived under the axioms; [formula in source] D existence, chiral measure, mirror gap, couplings and neutrino dynamics are open. Gravity display: ``parameter-free'' headlines replaced by ``the classical covariant field equation carries no free dimensionless Newton coupling under the named QFT/entanglement premises ''. Surfaces: tfpt_research_contracts (new sections MILNOR.LOCALRING, WEINBERG.WITTEN; SPIN2 firewall note; T7 child; v358/v359 keybox titles); tfpt_4_frontier wave-6 paragraph; introduction status card [formula in source] SM/gravity lines; tfpt_2 gravity heading [formula in source] conclusion; website StatusMatrix / WhatTfptClaims / ClaimStack / GravityEmergence / OpenGates / VerificationDag.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":46010,"byte_start":41401,"id":"section:5a8078e84394b902d12b","kind":"subsection","labels":[],"line_end":295,"line_start":294,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:14acc922b1042bef305b","relation:197499992fced946ff30","relation:278cb97e38a98fec6c05","relation:63f81e8ad02a47d90aca","relation:76a356961b7b3b0ead9f","relation:81acf5bfa93d71cdc5e9","relation:8a8f718fc08c8e53798f","relation:8ac701bbb8e7849f0604","relation:98bf498776ff4f47588e","relation:a4626300588a291a1b83","relation:ba7f30c913fbf918ea86","relation:caa81e58124e99d47df3","relation:d2a8372dd2e3ce9795f7","relation:d4bbb077e7cb97f3e654","relation:ece19ed6399c9c25b06e","relation:fa1b872145498be1d14f"],"semantic_review":false,"source":"documents/changelog/sections/001-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO","\\mX"],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"=150 2026-08-29 (CXLIII) (review wave 5 — two exploration probes graduate as v1002– v1003 plus three registrations: the DET16 finite-cluster hit, the two neutrino-texture structural nulls, the master scaling-limit theorem SEAM.MMST.TYPEIII.CHARGED.01, the gauge-stiffness step-scaling divergence, and the holomorphic-KMS document; suite [formula in source] , ledger [formula in source] : three new rows, existing contract rows updated, NO status-marker upgrades; Python-only / Wolfram mirror deferred as for v974–v1001). (1) v1002_ spin10_ mirror_ projector.py ( [formula in source] ): DET16 rank-one projector on the full [formula in source] cluster — [formula in source] , [formula in source] , defect [formula in source] ; [formula in source] hermitian idempotent [formula in source] , rank [formula in source] ; [formula in source] spectrum [formula in source] , gap exactly [formula in source] ; all [formula in source] [formula in source] Fock commutators [formula in source] ( [formula in source] ); parity commutator [formula in source] ; [formula in source] and [formula in source] singlets. Hopping stability on the [formula in source] -mode analogue: gap [formula in source] ( [formula in source] clusters) / [formula in source] ( [formula in source] clusters) at [formula in source] ; spectators untouched. NEW ledger row CHIRAL4D.MIRROR.DET16.01 Candidate \\ (exact finite-cluster gapping; open: dynamical gauge fields, domain-wall geometry, [formula in source] D volume theorem). (2) the Casimir kill, permanent. Number-preserving Casimir projector uniqueness fails at every cluster size: one [formula in source] (none at [formula in source] ); [formula in source] half-filling multiplicity [formula in source] ; [formula in source] (exact Weyl alternation, [formula in source] ). Ledger note on CHIRAL4D.NOMIRROR.01: number-preserving Casimir projector route excluded; display stays . (3) v1003_ nu_ structural_ nulls.py ( [formula in source] ): charged-sector data [formula in source] , [formula in source] ; Schur-texture NULL — all [formula in source] preregistered [formula in source] fail, D4 reflection forces [formula in source] , hierarchy [formula in source] structurally unreachable from D4-even seam data, required [formula in source] matches none of [formula in source] comparators; orientation-doubling structure theorem — [formula in source] odd sector generically lifts the degeneracy (exact rational witness); scale NULL — [formula in source] fail, required cancellation [formula in source] not supplied, [formula in source] -branches isospectral. NEW ledger row FLAV.NU.TEXTURE.MECHANISM.01 : both nulls are binding constraints (mechanism must be D4-odd AND supply a [formula in source] even-odd cancellation; pure seam data excluded -typed). FLAV.NUSCALE.05/ .06 notes only; candidates unmoved. (4) registrations (no marker moves). NEW SEAM.MMST.TYPEIII.CHARGED.01 : ONE scaling-limit theorem [formula in source] strongly on the finite-energy core [formula in source] crossed-product continuity, from which [formula in source] , [formula in source] , type III [formula in source] , unique rotational KMS, unique CE, deck equidistribution and modular invariance follow as corollaries; children SEAM.SIMPLECURRENT.GENERATOR.01, SEAM.STATE.RPMIXING.01 continuum, ALPHA.QUILLEN.EXACT.01 rigidity, AX.P1.01 reading (listed on the parent, not back). Cited document articles/2026-08-29/holomorphic_kms_extension_en.tex ( [formula in source] pp): unconditional rotational-KMS uniqueness via KLM [formula in source] Longo–Tanimoto GIVEN the identification; P1 [formula in source] theorem-conditional on seam identification [formula in source] [formula in source] ; axiom typing UNCHANGED. GAUGE.DETLINE.FIXPOINT.01: mechanism executed at fixed volume (unique fixed point, contraction [formula in source] , exact [formula in source] and [formula in source] Dynkin ratio [formula in source] ) BUT the preregistered thermodynamic step-scaling [formula in source] is DIVERGENT ( [formula in source] oscillates [formula in source] , [formula in source] at [formula in source] ); typed hurdle: the [formula in source] D toy has no plaquette self-interaction, the real contract needs [formula in source] D; display stays . [formula in source] boundary note: unit choice closed; dimensionless hierarchies [formula in source] remain predictive obligations. Surfaces: tfpt_research_contracts (new sections MIRROR.DET16, TYPEIII.CHARGED, NU.TEXTURE.MECHANISM; DETLINE stiffness update; NOMIRROR Casimir kill); tfpt_4_frontier wave-5 paragraph; tfpt_2 (texture-mechanism note); introduction status card [formula in source] hierarchy sentence.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":50829,"byte_start":46010,"id":"section:970b604e67143eb148a6","kind":"subsection","labels":[],"line_end":298,"line_start":296,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:019631a453d6e047b558","relation:057d5bc3d3dbc2bb13ca","relation:067c54a93a807f56152a","relation:097012d1925e430d70fd","relation:17f770d69ccd3520a3c8","relation:1d8f7927e651c15cd4cf","relation:2966bfda7753ef1ca4f5","relation:300355ae006b697edc4a","relation:30e17e241e687b4f8403","relation:31a4c55818def8d45ae5","relation:320e9d5aa49cb4573bb9","relation:360e1d52d1641780a74a","relation:3a8db0228387315b2a67","relation:5221c7aadaf49c6486fb","relation:62af26b33c0a30fb2149","relation:658016f27446058e955a","relation:6e755c6ff8fb3c0c9386","relation:7055282f7ffe8cc32228","relation:7b5b93405b474f363993","relation:a24171e26b2bdfceccf8","relation:b89f01c1d311abb14e37","relation:c94f4197eba2769d41e2","relation:cb2f838fc221b70fbeb0","relation:cd580bccaf2446e3cfa1","relation:d013d1c2ee830660e148","relation:d14aebd109e7031d68ef","relation:d54217c9278973aff2e9","relation:dc95dc9bf97076200356","relation:f1d04921fc1946efe56e"],"semantic_review":false,"source":"documents/changelog/sections/001-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"=150 2026-08-29 (CXLII) (review wave 4 — four exploration probes graduate as v998– v1001 plus the lattice-fundamental quasilocal-family amendment, the [formula in source] closed-metrology retype, the ALPHA.QUILLEN relative-determinant note, and the master contract TFPT.TOE.COMPLETE.01; suite [formula in source] , ledger [formula in source] : two new rows, existing contract rows updated, NO status-marker upgrades; Python-only / Wolfram mirror deferred as for v974–v997). (1) v998_ seam_ modular_ closure.py ( [formula in source] ): two-edge HS remainder bounded by [formula in source] on the frozen plateau [formula in source] ; lattice character [formula in source] EXACT four orders [formula in source] ; [formula in source] as Eisenstein series, [formula in source] -expansion match to [formula in source] orders exact (Jacobi identity; the reviewer's C7 sharpening); [formula in source] numeric transform at [formula in source] digits with [formula in source] -weight bookkeeping. Ledger notes on SEAM.EQUIV.MMST.01 and SEAM.SIMPLECURRENT.GENERATOR.01: C7 arithmetic shadow now exact; net-level C7 stays cited/open. (2) v999_ weak_ collision_ hp.py ( [formula in source] ): the continuous-time dilation leg — generator extraction Richardson [formula in source] ; [formula in source] symbolic; [formula in source] exact; GNS splitting defect [formula in source] ; locality [formula in source] ; strong-collision singularity contrast rank [formula in source] . DYN.UNITARY.DILATION.01: the finite ladder is now COMPLETE (discrete/kernel/field-free/interacting-classical/quantum-coupled/continuous-time); open [formula in source] the thermodynamic field limit only; contract stays . (3) v1000_ spin2_ sk_ witnesses.py ( [formula in source] ): lattice graviton — positivity exact, [formula in source] TT helicities at all [formula in source] momenta ( [formula in source] ), [formula in source] exact; SK — KMS/FDT [formula in source] , [formula in source] -dependence contrast [formula in source] vs static [formula in source] , saddle [formula in source] -fold degenerate with [formula in source] unique in the [formula in source] lift . GRAV.SPIN2.EMERGENCE.01 quadratic Hamiltonian half executed; FTRANSFER.SK.RHO0.01 mechanism executed; both contracts stay . (4) v1001_ nu_ pentagon_ chain.py ( [formula in source] ): [formula in source] inventory theorem; misalignment [formula in source] ; pentagon double hit [formula in source] frozen, all three measured angles [formula in source] (honest max pull [formula in source] ) at [formula in source] , unique LEE survivor [formula in source] ; v3 chain SHA-16 a4c28732fa687620 with [formula in source] eV, [formula in source] meV, [formula in source] meV, [formula in source] ; v270– [formula in source] tension [formula in source] TYPED; census null [formula in source] . NEW ledger row FLAV.NUSCALE.06 Candidate \\ (pentagon-class misalignment; mechanism [formula in source] the [formula in source] -to-flavor operator ; kills DESI/DUNE [formula in source] vs [formula in source] /JUNO). NO seesaw closure; FLAV.NUSCALE.05 unmoved. (5) Amendments (typed; no marker moves). QFT4D.LATTICE.FUNDAMENTAL.01: a single finite box is not a world — the fundamental object is the quasilocal consistent family [formula in source] with [formula in source] ; continuum ( [formula in source] ) optional, thermodynamic limit and controlled IR universality mandatory (dated 2026-08-29). ANCHOR.VGEO.01/ .02: display retyped from open-physics/primitive phrasing to CLOSED METROLOGY STRUCTURE ( [formula in source] unit torsor; one dimensionful calibration necessary by dimensional analysis — No-Unit v153/ v725); display stays , no physical . ALPHA.QUILLEN.EXACT.01: the correct object is the relative determinant [formula in source] ; BFK [formula in source] is [formula in source] -independent at fixed cut number so [formula in source] — no physical compensation (consistent with COMPENSATION_INTERNAL). NEW master contract TFPT.TOE.COMPLETE.01 : eight gates T1–T8 with the binding separation [formula in source] vs [formula in source] AND independent holdouts; every existing [formula in source] D/dilation/detline/SK/flavor/gravity contract is a child of one gate. Surfaces: tfpt_research_contracts (executed-update paragraphs at MMST/SIMPLECURRENT, DILATION, GRAV.SPIN2, SK.RHO0; new sections TOE.COMPLETE and NUSCALE.06; lattice-fundamental amendment; ALPHA relative-det note); tfpt_4_frontier [formula in source] introduction status card / [formula in source] row; tfpt_2 (NUSCALE.06 candidate paragraph).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":54316,"byte_start":50829,"id":"section:ccd38232c9f484cdbcb7","kind":"subsection","labels":[],"line_end":300,"line_start":299,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:002d2a0dc142499ab783","relation:18156a86901ed016d176","relation:2b3ff5831e8350b38d8b","relation:3e00827e1172faceefb2","relation:4123895e2a15225ab5bd","relation:4629f2a6863adba0c17a","relation:4b9a47368abeb61cbd6c","relation:6caa1f0edfb78636b671","relation:7145e2bbfdcda561c591","relation:7eaac11b9464c573cffb","relation:7ff1f586d43ca5eef511","relation:80bc48de984002c93c3e","relation:875351355749d4a27d13","relation:9317ecfa1a4ebbede288","relation:9e45fb08783555d54d82","relation:a9708086379276419e83","relation:c37645d29620d1eaab51","relation:d8ea0c3bc813c518f7ef","relation:e863e8b73b85292ccf83","relation:fbd03683ac6aad2409b5"],"semantic_review":false,"source":"documents/changelog/sections/001-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"=150 2026-08-28 (CXLI) (the completeness wave — four exploration probes graduate as v994– v997 (suite [formula in source] , ledger [formula in source] : eight contract rows updated, NO status-marker upgrades; Python-only / Wolfram mirror deferred as for v974–v993). (1) v994_ mmst_ criteria_ battery.py ( [formula in source] ): [formula in source] of [formula in source] MMST identification criteria executed -measured — measured [formula in source] (16 Majorana copies), conformal edge spectrum [formula in source] , current normalisation [formula in source] , sector collapse [formula in source] , and the flagship: [formula in source] /GSO-projected lattice character sums reproduce the [formula in source] vacuum character [formula in source] three orders deep; C6 is now written out in articles/2026-08-28/psi_lambda_convergence_theorem_en.tex (analytic log coefficient [formula in source] vs measured [formula in source] , [formula in source] ); C7 modular invariance stays cited/open. Ledger notes on SEAM.EQUIV.MMST.01 (stays ) and SEAM.SIMPLECURRENT.GENERATOR.01 (stays ; open rest [formula in source] C7 [formula in source] net G2/G3/G4). (2) v995_ kms_ subnet_ rigidity.py ( [formula in source] ): all [formula in source] v972 mixing directions killed by KMS alone on finite [formula in source] ; covariance provably redundant; unique [formula in source] -invariant crossed-product extension [formula in source] . SEAM.STATE.RPMIXING.01 finite KMS rigidity ; type-III/continuum stays . (3) v996_ gauge_ grammar_ kill.py ( [formula in source] ): H0 structural kill — negative [formula in source] flip the stationary-root signs ( [formula in source] inverse [formula in source] , [formula in source] [formula in source] ); [formula in source] conventions [formula in source] hits; [formula in source] control [formula in source] survives all mutants; detline curvature [formula in source] exponentially with rate [formula in source] (numerical Bismut–Freed shadow). GAUGE.DETLINE.FIXPOINT.01 naive grammar excluded ; genuinely nonabelian structure required — typed; [formula in source] remains an external input; contract stays . (4) v997_ spin2_ smg_ witnesses.py ( [formula in source] ): Barnes–Rivers quadratic decomposition — [formula in source] clean (one massless TT pole, two helicities, scalaron at [formula in source] exact); the local [formula in source] Weyl [formula in source] truncation necessarily carries an opposite-residue spin-2 ghost — typed; FK SMG toy: [formula in source] unique [formula in source] -singlet ground state, Schmidt rank [formula in source] , volume-independent gap [formula in source] at [formula in source] ; [formula in source] contrast [formula in source] -degenerate; physical chiral edge keeps [formula in source] exactly. GRAV.SPIN2.EMERGENCE.01 quadratic witnesses , content pinned on the untruncated form factor; CHIRAL4D.NOMIRROR.01 SMG toy-proved , [formula in source] D [formula in source] stays ; both contracts stay . Canonical note (not a module) on FLAV.NUSCALE.05: NU_TEXTURE_CENSUS_NULL [formula in source] — frozen [formula in source] inventory provably insufficient; mechanism \\ sharpened. Surfaces: tfpt_research_contracts (executed-update paragraphs at MMST/SIMPLECURRENT, RPMIXING, GAUGE.DETLINE.FIXPOINT.01, GRAV.SPIN2.EMERGENCE.01, CHIRAL4D.NOMIRROR.01, ALPHA.QUILLEN rigidity/ln-2 notes); tfpt_2 (census-null note); tfpt_4_frontier [formula in source] introduction card addendum. Exploration record: articles/2026-08-28/big_picture_simplicity_first_en.md.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":57242,"byte_start":54316,"id":"section:c86ec693b903bfd2aa01","kind":"subsection","labels":[],"line_end":303,"line_start":301,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:33b4bf32bbd4525d2459","relation:3fb446aac683c0e0ad57","relation:40b6ee3a79d6d4227482","relation:47e37ffb5964e358da72","relation:6e6d679b58f81ba9ad1f","relation:75c023c7eac4375c96ba","relation:79333de8ae040c537169","relation:8ea97e8957bda38bed13","relation:961834cb76963192c815","relation:a8def3b9d1333c9799c6","relation:af652e094ca21007004b","relation:b6b0c1c5c899d9f4993f","relation:c7fcde2a33c4234136a2","relation:cbceb840857b752cd1f8","relation:ce1b77250b79793253f6","relation:e5b03f2ce6122ef1ed43","relation:faed2559c390b8ccc12d","relation:fda990922628e9652d68"],"semantic_review":false,"source":"documents/changelog/sections/001-source.tex","status_markers_as_written":["\\mC","\\mO"],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"=150 2026-08-28 (CXL) (review wave 3 — the third external bird's-eye review adjudicated and integrated: ONE new module v993 plus THREE new \\ contracts plus a v986 motivation retype plus the dual-rest formula; suite [formula in source] , ledger [formula in source] ; NO status-marker upgrades; Python-only / Wolfram mirror deferred as for v974–v992). (1) v993_ minimal_ defect_ selector.py ( [formula in source] ): the FULL rank-8 ADE census (SNF of Cartan) with cyclic [formula in source] glue on BOTH factors selects [formula in source] uniquely ( [formula in source] aliases collapsed) — the [formula in source] architecture of v624 is an OUTPUT of (rank 8 [formula in source] cyclic [formula in source] ), not an INPUT; kill tests [formula in source] / [formula in source] (product 16, fail cyclicity) and the [formula in source] control [formula in source] ; [formula in source] exact (lattice shadow of [formula in source] ); the [formula in source] average is the UNIQUE trace-preserving finite conditional expectation (uniqueness needs the module property; kernel dim [formula in source] without it). Ledger notes on AX.P1.01/ AX.P2.01: axiom typing UNCHANGED; the equidistribution identification stays the open \\ of v813; cited-not-proved remain [formula in source] and holomorphic uniqueness of [formula in source] . SEAM.SIMPLECURRENT.GENERATOR.01 canonical status grows the [formula in source] parity-shadow line. (2) Three new research contracts, all , no scripts: GAUGE.DETLINE.FIXPOINT.01 (all three gauge couplings as unique stationary points of one nonabelian zeta-det/inflow functional; generalizes ALPHA.QUILLEN.EXACT.01; honest: [formula in source] is currently an external input); GRAV.SPIN2.EMERGENCE.01 (massless transversal spin-2 pole from the same spectral determinant; Einstein equation stays downstream/conditional; GRAV.NONCIRCULAR.01 binding); FTRANSFER.SK.RHO0.01 (cosmological transfers need [formula in source] , not [formula in source] alone; typed candidate [formula in source] , [formula in source] orientation picks [formula in source] ; FTRANSFER.GENERATING.01 covers equilibrium only). (3) v986 docstring retype: the [formula in source] motivation is loose ( [formula in source] ); the operator reading is the [formula in source] eigenvalue route [formula in source] ; texture data-constrains-texture; check logic and pass/fail UNCHANGED. (4) Dual rest: introduction status card (and the research-contracts keybox, with a brief frontier mirror) now carries [formula in source] (compiler) beside [formula in source] (strict-physical-TOE accounting of the 2026-08-27/28 contract wave); nothing in the second formula is claimed closed. Exploration not promoted: the wave-3 Quillen zero-mode Gram identity is a reformulation ( [formula in source] ), not a Quillen-metric object.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":60888,"byte_start":57242,"id":"section:64a9e573649942dd32e9","kind":"subsection","labels":[],"line_end":306,"line_start":304,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:1c5ada9249b3dc5f81ab","relation:2bfa8ec25dc8e68cdb46","relation:496ec4fb38b4c65a4f5b","relation:4fbeafce046f60fd2a80","relation:6b35cc21022af9a1368d","relation:848a1413c17adfdf419e","relation:8970e82128c61c0d4d08","relation:8adba9c5b7d49c5532d4","relation:9e189922242bf010eac9","relation:9fcf94a52cf4a2560875","relation:a5a33676a25e369b1dd2","relation:b7a8b4d32cbd719cc060","relation:d183e9b74a46e5c4bc7b","relation:da7a704584dcd9d26ad6","relation:dae689c1dc52a7fd5c82","relation:fd7a48f80bfc456c8bcd"],"semantic_review":false,"source":"documents/changelog/sections/001-source.tex","status_markers_as_written":["[C]","[N]","\\mO"],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"=150 2026-08-28 (CXXXVIII) (the master-object wave, part 2 — the second external bird's-eye review (``one 4D lattice [formula in source] one seam simple current [formula in source] one unitary dilation [formula in source] one determinant line [formula in source] one [formula in source] '') adjudicated: its four machine-checkable candidate results verified and integrated as FOUR new modules (suite [formula in source] , ledger [formula in source] : one new row FLAV.NUSCALE.05; three contract rows updated, NO status-marker moves). (1) v983_ simple_ current_ generator.py: the SEAM.SIMPLECURRENT.GENERATOR.01 generator is identified — the glue vector [formula in source] with [formula in source] , [formula in source] , order 4 in the discriminant group [formula in source] of [formula in source] ; isotropic glue [formula in source] even unimodular rank-8 overlattice ( [formula in source] ); coset root census [formula in source] — the odd fusion powers of the ONE class carry the full [formula in source] spinor sector; kill tests (vector-class / mismatched glue) fire; holomorphy shadow [formula in source] vs [formula in source] at the lattice level; the analytic half (G1–G4) stays . (2) v984_ markov_ qca_ dilation.py: the DISCRETE leg of DYN.UNITARY.DILATION.01 realized constructively — the collision step [formula in source] is exactly unitary, the Stinespring identity [formula in source] holds symbolically, [formula in source] and six fresh ancillas give [formula in source] exactly (radius-1 collision band); must-fail fires ( [formula in source] ); typed remark AGAINST the review text: a reused mod-3 adder ancilla still reproduces the populations exactly; the continuous Hamiltonian/OS legs stay . (3) v985_ quillen_ channel_ swap.py: the v974 CHANNEL-SWAP face of ALPHA.QUILLEN.EXACT.01 resolved at the finite level by [formula in source] -character grading — the deck swap [formula in source] maps the jump spectrum [formula in source] onto the mark pattern [formula in source] exactly (odd swap fails), the graded [formula in source] difference is [formula in source] -free [formula in source] , the channelwise unit ratio is uniform [formula in source] ; continuum Bismut–Freed, KMS rigidity and the [formula in source] compensation stay . (4) v986_ nu_ scalaron_ rung.py: the SCALARON-TRACE RUNG [formula in source] GeV — a structured point INSIDE the v481 window, [formula in source] from the 1-loop requirement (the review claimed [formula in source] 1\\%; the honest value is 1.8), [formula in source] sharper than the declined integer rung; exact ladder position [formula in source] , [formula in source] from the closed [formula in source] Clebsch door — adjacency TYPED, not consumed (v488 killed the Clebsch mechanism; the generation-blind scalaron trace is a different class, itself ); kill test [formula in source] eV; new row FLAV.NUSCALE.05 [C]/[N], no seesaw closure. The remaining review content is typed, not consumed: the axion line ( [formula in source] , [formula in source] ) and the Riemann–Roch carrier ARE the existing v185/v211/v189; the 4D action, chiral measure, OS package, bulk dictionary, determinant-line unification, [formula in source] , transduction matrix and joint likelihood stay open contracts exactly as registered on 2026-08-27. Paper surfaces: tfpt_research_contracts (three executed-update paragraphs), tfpt_2_standard_model (scalaron-trace rung paragraph).)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":66073,"byte_start":60888,"id":"section:edc607bc9be0dce5ac62","kind":"subsection","labels":[],"line_end":308,"line_start":307,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:19d74595daff709c9ba3","relation:1e639dce2f25057bb787","relation:22b059fac5577f6bb479","relation:2bcb37212b4965a2136a","relation:465f3f3ed975a690c40f","relation:4e0db6441ab7133bd009","relation:65b8d1a8918b856a0b22","relation:941bae4d8588ae2506d3","relation:94f38f07d1064cc73aab","relation:d149a2d6a332c1ccdca4","relation:e83a7f881f1ecad159c7","relation:e989d3a3c97dfdbfe99f","relation:ed127f537c807920dab9"],"semantic_review":false,"source":"documents/changelog/sections/001-source.tex","status_markers_as_written":["[C]","[E]","[O]"],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"=150 2026-08-27 (CXXXVI) (the transport-lift wave — the two external-review rounds on the quantum structure of the seam transport graduate from the experiments tree into the load-bearing suite as v976_seam_lift_birkhoff.py and v977_transfer_unistochastic_wilson.py (suite [formula in source] , ledger [formula in source] : new rows TRANSFER.HIDDEN.CIRCULATION.01 and TRANSFER.COHERENT.WILSON.01, both ``executed half [E] / selection open [O]''; the exploration probes transfer_ birkhoff_ circulation_ probe.py 42/42 and transfer_ coherent_ wilson_ probe.py 28/28 stay in experiments/tfpt-discovery/ as the discovery record). (1) v976 — the Birkhoff fibre and the entanglement-breaking no-go. The Birkhoff (random-permutation) fibre of the seam single step [formula in source] (exact sixth root of the v221 kernel, [formula in source] bit-exact) is exactly a one-parameter line [formula in source] ; the hidden coordinate is the sign-character Fourier coefficient [formula in source] , populations are exactly [formula in source] -free, and no fibre member is chiral ( [formula in source] forced). The one-step coherence spectrum is [formula in source] and the triangle loop current is an exact eigen-observable [formula in source] — one step plus one current readout measures [formula in source] without an ancilla. On the contrast qubit the Choi partial transpose has spectrum [formula in source] : the deployed sixth-root spectrum sits exactly on the entanglement-breaking boundary because [formula in source] (mutated spectra miss by [formula in source] ); at the full three-level the family stays NPT at every tested iteration with [formula in source] , [formula in source] -independent. The no-go that sharpens DYN.UNITARY.DILATION.01: the deployed Kraus dilation [formula in source] is measure-and-prepare, hence entanglement breaking with quantum capacity [formula in source] and [formula in source] exactly — any dilation closing that contract must be a genuinely different object. Shannon KKT certificates: [formula in source] is exactly capacity-achieving for both [formula in source] and [formula in source] ( [formula in source] bit, [formula in source] bit, ratio [formula in source] ) — the surviving classical message is binary on every scale. The defect–Birkhoff value coincidence (weights [formula in source] vs the v652 ladder [formula in source] ) is recorded typed [C] with its honest multiplicity audit; the forcing functor is the named open contract TRANSFER.DEFECT.BIRKHOFF.01. (2) v977 — the unistochastic [formula in source] lift and the 5-12-13 Wilson code. [formula in source] is unistochastic: an exact [formula in source] with [formula in source] entrywise, angles forced by [formula in source] ( [formula in source] , [formula in source] , [formula in source] ), [formula in source] unique, lift set [formula in source] up to rephasing; Jarlskog [formula in source] exactly, and the real part of every Wilson plaquette is fixed by [formula in source] through unitarity — the full rephasing-invariant Wilson data is classical up to the [formula in source] orientation bit [formula in source] . The main plaquette is [formula in source] , normalized [formula in source] with [formula in source] (atoms: [formula in source] , [formula in source] , [formula in source] ); all nine plaquettes close on four Gaussian phase types with norms exclusively [formula in source] . The center bridge: [formula in source] for the v530 atom matrix, [formula in source] , and the v530 sibling quotients fail the identity — the bridge selects the atom quotient. Rationality selection: [formula in source] is rational only at [formula in source] (the deployed step hits [formula in source] exactly, so [formula in source] ); census over 238 valid family points: exactly one full-code point [formula in source] the deployed [formula in source] ( [formula in source] the preregistered [formula in source] kill). No fixed microstep: [formula in source] and a Dirichlet recurrence witness ( [formula in source] ) shows no single closed unitary generates the relaxing sequence — repeated steps require dephasing between steps, the six-step macro-gate [formula in source] (the coherent sharpening of clock-vs-walk). The PMNS near-miss stays a negative control ( [formula in source] vs [formula in source] ; [formula in source] ; no PMNS derivation). Surfaces. Research-contracts document: the DYN.UNITARY.DILATION.01 section gains the executed lift-structure sharpening, the CCC reduced-channel prose and the two former ``exploration-only'' citations of rounds DCXCVI/DCXCVII are upgraded to veri citations; origin_theory gains the honest ``what the classical transport does not determine'' paragraph next to the v221 recoverability code; tfpt_2 gains the [formula in source] bridge corollary in the v530 center-quotient block. No status marker moves; both contracts stay open; no PMNS/CP/flavor claim.)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":71809,"byte_start":66073,"id":"section:01c88746fb95cc0958d7","kind":"subsection","labels":[],"line_end":310,"line_start":309,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:09d0bd54e5c489819ac6","relation:0a186a3b6bead73e94e9","relation:23253a3dbe29fdc89d79","relation:2cdc667a90f1b77d92e1","relation:2cf08d29fd31a110c80f","relation:2de4432870ac536743ec","relation:3c93ac2a3bff1c145ed7","relation:414a05316cf04e6b955b","relation:52085d90396b914e6fe1","relation:53ebb689f1f8a5243f9b","relation:63ff1f55d4dc18a991b1","relation:648c6bed82478d8fa0cb","relation:688ed0fb5b5d17a57ca8","relation:69b58d00926e16c3d6f2","relation:805aae012f0734e3bcef","relation:897020b97f0dbb305b86","relation:90c5b3bd5f20dd4d045c","relation:91b049279c33950216b3","relation:984170f91406ff6657ca","relation:9c3a0d6bb57e2c770ffa","relation:9e7144b0fdab4364fa07","relation:a57a4d5f3df60ef419c1","relation:a5c5e735c8c2d7590c68","relation:a6076bb5819679a61380","relation:d6e8fb84a307da2efb22","relation:dbb4d304260522d7981e","relation:e5a5839ca3a50a186a6a","relation:e7815144fab512ae79ee","relation:e8f3b98c52f34ca393d2"],"semantic_review":false,"source":"documents/changelog/sections/001-source.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"=150 2026-08-27 (CXXXI) (the external deep-review round — dimension / dynamics / gravity firewalls and the 4D construction ladder: the review diagnosis ``chiral [formula in source] D seam net [formula in source] local, interacting [formula in source] D quantum world'' is implemented as eight new contract IDs in tfpt_research_contracts plus one new load-bearing module. (1) DIMENSION.UPLIFT.FIREWALL.01 (standing rule, in force): no [formula in source] D theorem closes a [formula in source] D claim; every contract closure states the spacetime dimension of hypotheses AND conclusion; audit census recorded (SEAM.EQUIV.01 is [formula in source] D in and out — even fully proved it is a boundary building block, not the 4D theory; the v957 kinematic uplift does not close it; the anomaly-inflow bulk is invertible/topological, never to be silently equated with physical spacetime); the realistic route ordering (seam as boundary module [formula in source] genuine 4D Euclidean lattice [formula in source] OS package [formula in source] chirality/no-mirror [formula in source] only then BW/CHM [formula in source] entanglement gravity [formula in source] bulk–seam equivalence) is registered as the programme skeleton. (2) SEAM.BULK4D.RECON.01 : the previously implicit seam [formula in source] bulk theorem made explicit (4D local algebras/Schwinger functions; locality/microlocality, Poincar\\'e covariance [formula in source] spectrum condition, spin-statistics [formula in source] CPT, both helicities, clustering, nontrivial S-matrix, unique operator dictionary). (3) the dynamics split DYN.MARKOV.EMBED.01 / DYN.UNITARY.DILATION.01 (``three meanings of dynamics'': relaxation [formula in source] / dissipative semigroup [formula in source] / unitary [formula in source] ): the finite kernel half of MARKOV.EMBED is executed \\ as v971_markov_embedding_generator.py ( [formula in source] , sympy-exact) — [formula in source] of the v221 seam kernel is an EXACT classical Markov generator: [formula in source] by spectral calculus, row sums symbolically zero, off-diagonals exactly [formula in source] (the reviewer's independently verified numbers), uniformization certificate [formula in source] entrywise [formula in source] [formula in source] positivity-preserving doubly stochastic for all [formula in source] , [formula in source] (gap [formula in source] ), negative control: second eigenvalue [formula in source] gives [formula in source] — provably NOT embeddable; the field level and the local size-consistent unitary dilation (Stinespring [formula in source] Lieb–Robinson [formula in source] OS continuation) stay ; binding precision: the shared F_transfer relaxation shape is a universal CONTRACTION CLASS, not one physical clock (v723/v724/v777). (4) QFT4D.OS.RECON.01 \\ (the genuine 4D Euclidean lattice OS package) with the binding phrasing rule: the v381 all-orders leg is a local perturbative construction under the stated EG/BRST hypotheses (Duch weak adiabatic limit cited, hypotheses unverified for the concrete model; no confinement / mass gap / asymptotic charged states / nonperturbative Higgs vacuum / full S-matrix follows) — tfpt_2 and tfpt_5 phrasing restricted accordingly. (5) CHIRAL4D.NOMIRROR.01 \\ (explicit GW/overlap chiral lattice operator; local gauge-invariant measure, perturbative [formula in source] global anomaly freedom, no Witten [formula in source] anomaly, no mirrors, correct index/charges, stable continuum limit; Mastropietro arXiv:2303.02790 as calibration). (6) GRAV.NONCIRCULAR.01 (standing rule, in force): BW is a theorem WITHIN a local Poincar\\'e-covariant QFT (Mund/Morinelli counterexample landscape cited), never a generator of Lorentz spacetime from a modular flow; every BW/CHM use declares assumption-vs-result; audit census: the entanglement-equilibrium Einstein derivation (v323/v358/v359) is typed ASSUMPTION (conditional on the 4D package, never citable as evidence for it), QG.AMB.01 correctly declared, the seam KMS [formula in source] chain dimension-typed, the intrinsic-BW programme the honest result-direction attempt. (7) OBS.TRANSDUCTION.01: the transduction principle (internal eigenvalue [formula in source] nonvanishing projection [formula in source] [formula in source] physical coupling [formula in source] observable signature; without the middle arrow neither non-observation falsifies nor observation confirms; minimal model machine-checked at exploration level in fo01, uniform functional blind to [formula in source] , character channel recovers [formula in source] to [formula in source] ; the ACT [formula in source] Planck birefringence proximity typed coincidence-level pending the shared-action proof). (8) PRED.JOINTLIKELIHOOD.01 : evidence reorganized from hit-counting into overdetermined relation bundles (flavor sum rule; [formula in source] , [formula in source] ; one normalized axion action; character-resolved transfer) with the statistical demand (joint likelihood, atom-induced covariance, effective dof, prespecified null [formula in source] formula grammar, real holdout); the v100 ``13/13, [formula in source] '' statement retyped as a look-elsewhere quantifier under its declared null — the 2026-06-09 freeze protects FUTURE measurements, it does not retroactively make historically known data blind. Docs corrected in the same change: docs/OPEN_PROBLEMS.md (the Einstein-derivation overstatement rewritten to the conditional Jacobson-route typing with the explicit does-NOT-follow list; ``zero open internal mechanisms'' fixed to match the contract scope fence — ledger wins; the all-orders phrasing restricted) and docs/FALSIFICATION.md (the null-model section retitled and rescoped, freeze and kill tests unchanged). Ledger [formula in source] rows; suite [formula in source] modules; bash build.sh audit and the manifest regeneration are the joint exit gate)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":79444,"byte_start":71809,"id":"section:84ec2c9d7a3c77ec2664","kind":"subsection","labels":[],"line_end":312,"line_start":311,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:227317645d0ecb9e4bf5","relation:2bccbd2fb667865c864f","relation:2f9502b4853fe08154fd","relation:34481218f037014d0f67","relation:3fa6101e153e69147e0e","relation:42b440807cf7b42d11e5","relation:448d3a2d243b5b1cec7d","relation:4c2e9f7f63504d092a80","relation:66e46646d6d1ec937bf9","relation:71b202e9da84fcdfdc50","relation:7cd4e48b75390bc5cb69","relation:7d9225e3b91d8be077cf","relation:7e85ed42161379686686","relation:87c2d903cb6a1fb18da8","relation:b59765aeb05570c020d3","relation:b7549e999281a55d62c1","relation:c64ca69653c94441cfe5","relation:cdd924d0d503d7ae35d3","relation:d611d33929ce7d5f5ab0","relation:dcd92e49ed629d74ff32","relation:ec18c9b9d3bfad909001","relation:f229f954ad04580db336","relation:f47210577b32e5d81e8b","relation:f72ef699f800fe774604","relation:fe05dcba9408185912d9"],"semantic_review":false,"source":"documents/changelog/sections/001-source.tex","status_markers_as_written":["[E]","[O]","\\mC","\\mO"],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"=150 2026-08-24 (CXVIII) (the CCC-crossover promotion — the kinematics dictionary of the conformal-cyclic crossover graduates from the experiments tree into the load-bearing suite as v957_ccc_crossover_kinematics.py (suite [formula in source] ; six discovery probes of rounds DL–DLV re-run GREEN AS TYPED at promotion and embedded BYTE-EXACT with pinned SHA-256 hashes: ccc_crossover_gates_probe.py [formula in source] , ccc_uplift_4d_probe.py [formula in source] , ccc_fork_kms_holonomy_probe.py [formula in source] , ccc_kernel_gamma_kms_probe.py [formula in source] , ccc_transfer_selector_probe.py [formula in source] , ccc_kappa_freeze_probe.py [formula in source] ): (1) Penrose's reciprocal gauge [formula in source] is the element [formula in source] of the PROVEN [formula in source] M\\\"obius stabiliser [formula in source] — [formula in source] reverses the clock ( [formula in source] the [formula in source] sheet parity), swaps the aeon poles [formula in source] , and the crossover locus [formula in source] is the unit circle carrying ALL FOUR marks; (2) conformal-factor rigidity: on the 2D seam the clock alone leaves exactly ONE constant-curvature modulus (Liouville-exact dilation family) and the reciprocal [formula in source] kills it (unique zero at [formula in source] ); on the 3D crossover the deck ALONE kills all conformal moduli (the [formula in source] deck-commutant is [formula in source] -dimensional [formula in source] , ALL Killing, boost content [formula in source] ; global uniqueness on the explicit Obata boost family, 200-axis scan bounded below by [formula in source] ) — TFPT's candidate answer to CCC's open unique-conformal-factor problem, [formula in source] staying pure unit calibration; (3) the entropy reset of the cyclic \\ reading is a REDUCED CHANNEL: the v221 transport is CPTP not unitary ( [formula in source] ), its Stinespring isometry explicit ( [formula in source] exact), [formula in source] EXACTLY, the global overlap invariant and the environment retaining the full distinguishability — ``unitarity [formula in source] rank-1 attractor'' is isometry [formula in source] partial trace; (4) the kinematic [formula in source] uplift from corpus objects only: stereographic(Hopf [formula in source] ) [formula in source] EXACTLY (the seam sphere IS the Hopf base), the v492 deck [formula in source] acts freely so the crossover [formula in source] is the smooth lens boundary of the corpus [formula in source] ALE [formula in source] , clock [formula in source] and the reciprocal lift [formula in source] normalise the deck and descend ( [formula in source] to [formula in source] , inverting the clock), the four marks lift to four Hopf fibre circles paired by the deck into the TWO [formula in source] sheet orbits with Gauss linking number [formula in source] , the 4D bridge is the cone [formula in source] with the inversion [formula in source] a conformal involution (pullback [formula in source] symbolic) fixing the unit lens POINTWISE and swapping the aeon ends, and the Lorentzian shadow [formula in source] is Einstein [formula in source] (symbolic Ricci) with a SPACELIKE round- [formula in source] crossover and [formula in source] vanishing to first order; (5) the KMS/modular closure of discrete [formula in source] dynamics at the free level: detailed balance EXACT, [formula in source] EXACTLY (the seam gap IS a modular energy), [formula in source] (one clock tick [formula in source] one unit of KMS time at [formula in source] ), OS Gram PSD, and the v526 normalisation [formula in source] replicated exactly [formula in source] the Gibbons–Hawking normalisation on the crossover fibre; (6) the holonomy dictionary: the two clock-pole circles descend to the lens core geodesics with the full [formula in source] monodromy [formula in source] while EVERY seam string carries exactly the 2-torsion [formula in source] , and [formula in source] is trivial on the base while flipping the spinor coordinates — the v522 statement ``gaugeable datum [formula in source] the 2-torsion [formula in source] ; full wrap [formula in source] fermion parity'' in geometric form (typed \\ correspondence); (7) the selector necessity (the [formula in source] -facing theorem): the admissible OS reflections of the v512 mark family [formula in source] form the pair-exchanging [formula in source] for every [formula in source] and close to [formula in source] EXACTLY at [formula in source] (the order-4 clock factorises into admissible reflections, [formula in source] , iff [formula in source] ), and at Majorana operator level on the [formula in source] seam ring with fermionic reordering signs kept the free parent is [formula in source] -real on ALL 16 axes (v521 side-blindness replicated) while the interacting family is [formula in source] -real on exactly [formula in source] axes and the clock-axis cuts ONLY at [formula in source] , asymmetric couplings breaking reality — the UNIQUENESS half of the v534 straddle selector ( [formula in source] , symmetric couplings) is thereby DERIVED as a [formula in source] -reality necessity (the survival half and the coupling sign stay v534's nonperturbative toy facts, cited; reality is sign-blind, checked); (8) the frozen Gate-6 kernel: exactly two decay modes [formula in source] and [formula in source] (ratio [formula in source] ), the frozen defect-class overlap table [formula in source] / [formula in source] with the sheet-parity sign rule, disc radius [formula in source] , and [formula in source] DERIVED from the v526 KMS normalisation up to a declared convention band — [formula in source] ticks across the whole band, relic contrast [formula in source] : the template degenerates ROBUSTLY to the sharp causal top-hat disc; three freeze hashes pinned and recomputed in-run. NEW LEDGER ROWS: CCC.SEAM.KINEMATICS.01 [E] (the certified dictionary) and CCC.SEAM.CROSSOVER.01 [O] (the dynamical-crossover research contract: D1 interacting algebra on the crossover [formula in source] WOIT [formula in source] in the crossover geometry, D2 field-level Stinespring, D3 the cosmology fork decision — Starobinsky [formula in source] priced decidable by [formula in source] experiments —, D4 the executed disc search; kill criteria frozen incl.\\ the forbidden mark/Hawking-point count identification); new contract section in tfpt_research_contracts; the origin-theory Penrose-CCC bullet SHARPENED (asymptotic de Sitter does NOT imply conformal flatness — [formula in source] for Schwarzschild–de Sitter, machine-checked; the CCC smoothness/Weyl conditions are additional crossover data) and pointed at the certified kinematics; PREREGISTERED SEARCH scaffolded at experiments/ccc-crossover-disc/ (frozen hypotheses ccc_disc_v1.yaml with kill criteria K1–K6, null battery and BH- [formula in source] [formula in source] replication decision rule; freeze-check CLI 3/3 hashes intact; 5/5 guard tests; catalog entry 7b.9 of the experiments README) — verdict slot data_limited (preregistered); the Planck PR3 SMICA data pass executed separately at experiments level (first data contact logged in the project README). FENCES CARRIED EVERYWHERE: the cyclic/CCC reading stays \\ and is NOT upgraded by the promotion; WOIT.OS.TWISTOR.01 stays \\ with all kill tests live (the module certifies kinematics [formula in source] free level [formula in source] the necessity direction ONLY); the deck fork is decided only CONDITIONALLY on the v522 wrap identification; a null disc search damages nothing in the compiler core. Research notes DL–DLV appended to experiments/next.txt; FULL run_all.py ALL CHECKS PASSED at 950 modules; bash build.sh release green; bash build.sh audit [formula in source] AUDIT OK; manifests regenerated LAST. No omega closed beyond the two new rows; NO claim that CCC follows from TFPT)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; 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support/formula-only content is not paraphrased","title":"=150 2026-08-20 (CXI) (the externalization contracts — the two open non-RH kind-(A) external-math targets SEAM.EQUIV.01 and ALPHA.QUILLEN.EXACT.01 packaged as short, self-contained EXTERNALIZATION CONTRACTS for outside specialist mathematicians (conformal nets/VOA/AQFT for the seam; determinant lines/ [formula in source] -invariants/index theory for alpha), added as two new sections at the end of tfpt_research_contracts (before ``Certifiability and recommended order''), plus a one-sentence pointer in the head keybox; DOCUMENTATION ONLY — no module touched, no number changed, no status marker moved, no gate closed or narrowed, NO RH claim: (1) the SEAM.EQUIV.01 contract states the minimal theorem (the scaling limit of the gapped [formula in source] -equivariant CAR collar exists in local-net topology; the index-4 simple-current extension functor commutes with the limit; the OS reconstruction is the holomorphic [formula in source] lattice net) broken into the four review-named lemmata L1 (uniform energy/nuclearity bounds — honestly typed: NO uniform nuclearity estimate exists in the corpus), L2 (convergence of local algebras, the cited Osborne–Stottmeister scaling-limit theorem with the [formula in source] -equivariant structure retained), L3 (crossed product commutes with the limit; the finite index-4 Q-system is explicit, v125/ v154/ v469) and L4 (uniqueness of the holomorphic [formula in source] reconstruction; [formula in source] vs the same- [formula in source] rival [formula in source] ), with the complete typed hypothesis list (12 PROVEN-FINITE rows citing v302/ v113/ v155/ v160/ v356/ v366/ v367/ v368/ v461/ v376/ v377/ v378/ v379/ v125/ v154/ v216/ v286, 5 CITED-CLASSICAL rows, 1 OPEN target), the runnable finite models, the HONEST Lean axiom surface ( SeamScalingLimit.lean kernel-proves only the arithmetic hypotheses by decide; the analytic content is named cited axioms over opaque Props; no sorry; explicitly flagged: L1–L4 have ZERO Lean content beyond the composition audit), five must-fail controls (MF-S1: [formula in source] alone must NOT suffice — the red-team point; MF-S2: index-2 glue must yield [formula in source] ; MF-S3: the trivial [formula in source] collar must give no chiral limit; MF-S4: non-order-4 clock breaks the marks; MF-S5: the v286 import firewall) and four acceptance tests; (2) the ALPHA.QUILLEN.EXACT.01 contract states the two-step theorem T1 (gap-stable continuum limit [formula in source] under norm-resolvent convergence with the Fermi gap uniformly open over the twist torus — the Dai–Freed section has no zero; finite side computed, v472) and T2 ( [formula in source] [formula in source] Bismut–Freed curvature [formula in source] inflow response with the exact corpus coefficients [formula in source] , [formula in source] , [formula in source] , [formula in source] , exponent [formula in source] ), the two named open faces (the analytic diagonal- [formula in source] /multiplicity face v484/ v485 and the topological EM1 lemma v48/ v435), the typed hypothesis list (10 PROVEN-FINITE rows citing v3/ v48/ v341/ v382/ v434/ v470/ v435/ v342/ v367/ v472/ v484/ v485/ v391/ v433, 5 CITED-CLASSICAL rows, 1 OPEN target), the runnable finite models, the HONEST Lean statement (there is NO Lean formalisation of this target — stated plainly), four must-fail controls (MF-A1: no experimental [formula in source] anywhere in the construction; MF-A2: deck/carrier/Chern-level ablations must destroy the CODATA match; MF-A3: [formula in source] , [formula in source] ; MF-A4: the [formula in source] [formula in source] -power/metric-independence partition) and the review's three acceptance tests verbatim (no experimental [formula in source] input; unique physical fixed point [formula in source] ; ablations destroy the hit) plus one structural test; (3) the website paper mirror of tfpt_research_contracts ( papers.ts) gains one section entry covering both contracts; tfpt_research_contracts.pdf and changelog.pdf recompiled and mirrored via bash build.sh website; maps and changelog.ts regenerated via bash build.sh gen; bash build.sh audit [formula in source] AUDIT OK; manifests regenerated LAST. Both targets stay [O]; NO RH claim anywhere)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":89054,"byte_start":84355,"id":"section:b07b7756eee0700cde9a","kind":"subsection","labels":[],"line_end":323,"line_start":315,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:d272b81ac2620985adae","relation:f26b3d62ee6930aaff47"],"semantic_review":false,"source":"documents/changelog/sections/001-source.tex","status_markers_as_written":["\\mC","\\mE","\\mX"],"summary_excerpt":"Scorecard (regenerated). [formula in source] row: JUNO [formula in source] -day value [formula in source] ( [formula in source] ; supersedes the [formula in source] -day [formula in source] ). [formula in source] row: CMB-SPA [formula in source] added, status consistent [formula in source] tension [formula in source] watch-flag (central value above the [formula in source] band edge). Flat-budget row: CMB-SPA [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-08-04 (LVIII) (the news round: a pure data-refresh against the August-2026 literature — no new analysis of our own, honest in both directions. CONFIRMING: JUNO's Neutrino-2026 update ( [formula in source] days) lands at [formula in source] — the sharpest single measurement of the solar angle, [formula in source] from the frozen prediction [formula in source] , central value moving toward it from the [formula in source] -day run; ICARUS's first standalone result (no [formula in source] disappearance, new [formula in source] exclusions at [formula in source] CL) adds another sterile null exactly as [formula in source] requires; the sequentially-valid DESI reanalysis localises the evolving-dark-energy signal almost entirely in the LRG2 bin (without it the evidence collapses, mildly pro- [formula in source] CDM — the dissolution trend the [formula in source] watchdog predicts); two new independent birefringence analyses ( [formula in source] constant-model-preferred; PR4 field-level [formula in source] ) stay consistent with the [formula in source] seed; CMB-SPA [formula in source] lands [formula in source] from the parameter-free budget [formula in source] (correlated legs, never a new independent hit). WEAKENING, equally prominent: CMB-SPA (SPT-3G D1 [formula in source] ACT [formula in source] Planck) gives [formula in source] — the central value sits above the TFPT band edge [formula in source] for the first time (edge at [formula in source] , preferred branch [formula in source] at [formula in source] ; not yet the dated kill ``robustly [formula in source] '', typed an honest mild weakening, scorecard row tension [formula in source] watch-flag); the DESI DR2 effective-mass posterior keeps the [formula in source] \\,eV floor under [formula in source] model-dependent pressure (unchanged, on record). ONE BRIDGE DIES: the muon [formula in source] seam-vertex bridge's dated kill condition (2026-07-02) has FIRED — WP25 (Phys.\\ Rep.\\ 2025) adopts the lattice HVP as the SM baseline and the BMW hybrid evaluation (Nature 2026) confirms it, experiment [formula in source] SM [formula in source] , so the converged [formula in source] lies outside [formula in source] : the vertex identification is excluded in its present form, the scorecard row is typed kill_channel, ledger FR.MUONG2.01 carries the dated kill note, and tfpt_4_frontier gets the dated update paragraph [formula in source] summary-table move [formula in source] \\ on the bridge — the exact compiler number [formula in source] and the compiler core are untouched (no core marker moves): the watchdog delivered exactly what it was built for. OPERATIONAL: the Vela GO-programme preregistration is FROZEN as experiments/p9-forecast/hypotheses/p9_go_programmes_v1.yaml ahead of the expected 2026/27 giant-glitch window (no glitch since 2024-04-29; long-component decision rule and the [formula in source] -TOAs/day cadence requirement inside; draft SHA recorded as provenance); CHIME/FRB Catalog-2 [formula in source] RepCat4 data-availability notes recorded in repeater-cascade and frb-ontology. Scorecard [formula in source] typed rows (consistent [formula in source] , null [formula in source] , parked [formula in source] , kill_channel [formula in source] ); predictions.ts mirrors the JUNO/ [formula in source] / [formula in source] status; no verification module touched, no core marker moves)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":90695,"byte_start":89054,"id":"section:003e725a1fda16978fec","kind":"subsection","labels":[],"line_end":338,"line_start":324,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:253c2ba52f6c114a5a60","relation:7a7625d44798d64add3b","relation:8dbeb229f86174b86b8e","relation:cc9a9854cd86d3371bd3","relation:f2c30b7563343d91226f"],"semantic_review":false,"source":"documents/changelog/sections/001-source.tex","status_markers_as_written":[],"summary_excerpt":"v623_covered_seam.py ( QGEO.COVERSEAM.01, [formula in source] checks; probe 9/9, COVERED-SEAM-SKELETON). Connectivity census ( [formula in source] : one circle; trivial and alternating: [formula in source] components); the explicit 48-walk (three base turns, [formula in source] crossings); [formula in source] deck and [formula in source] id on all [formula in source] points with proper order [formula in source] ; the","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-08-01 (XXXVI) (the covered seam lands ( v623 promoted) — the lattice skeleton of the covering-level identification: the seam lifted to the [formula in source] -cover is ONE 48-site NS circle for the uniform weights (the alternating pair DISCONNECTS it — a new independent kill), the lifted clock has EXACT ORDER 12 with [formula in source] deck ( [formula in source] as lattice combinatorics), the v622 kernel identity generalizes verbatim to [formula in source] , and the deck-character mode grid is the 12-grid ( [formula in source] ) with the untwisted sector equal to the base seam VERBATIM and the twisted pair carrying [formula in source] on bilinears (the [formula in source] sheets); the fermionic deck lift satisfies [formula in source] (the spin double))","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":92376,"byte_start":90695,"id":"section:f1286299e54bfa3f1866","kind":"subsection","labels":[],"line_end":352,"line_start":339,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:16a135dac45b40da9bf3","relation:25ec1c8b53735c28d2a9","relation:28bbd167fe33f5d74b64","relation:3669b153d34489ec2f97","relation:3d13f7db9e2d80d2f58f","relation:471ad79f70b3a478639b","relation:54eea1b5daf0faaff990","relation:6dbc386a308bd4bff971","relation:8889decf3214defd3792","relation:ab02fc0638f68a5b618e","relation:adc7b25ecf5de4166a83","relation:dc9e36d7e563d4e79a15","relation:e56de8e0ab7ce1fa7eca"],"semantic_review":false,"source":"documents/changelog/sections/001-source.tex","status_markers_as_written":[],"summary_excerpt":"v622_seam_identification.py ( QGEO.SEAMID.01, [formula in source] checks; probe 10/10, SEAM-IDENTIFIED). Mode-sum identity for all [formula in source] with the closed form [formula in source] ; Ramond must-fail; mark midpoints [formula in source] exact; reflection axes [formula in source] with cuts [formula in source] ; through-mark axes [formula in source] the straddled cuts [formula in source] ; v617's bond reflect","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-08-01 (XXXV) (the seam identification lands ( v622 promoted) — THE PHYSICAL SEAM IS THE CONFORMAL SEAM: the v519 chiral seam kernel is EXACTLY the discrete NS (antiperiodic) chiral mode sum on the 16-site circle, including the even-distance zeros (the flat band IS the NS spectrum; the Ramond sum fails as must-fail control); the four mark-bond midpoints sit EXACTLY at [formula in source] under the site map [formula in source] (no site touches a mark — the v519 ``marks at bond midpoints'' becomes literal geometry); the group dictionary is exact (clock [formula in source] , RP reflections [formula in source] diameter reflections); and the v534 STRADDLE LAW becomes geometry — straddled cuts [formula in source] exactly the through-mark axes; the second v617 bedrock residue closes at the kernel [formula in source] dictionary level, leaving the covering-level identification)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":94230,"byte_start":92376,"id":"section:b4f8dafdea7dae9c5e81","kind":"subsection","labels":[],"line_end":368,"line_start":353,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:03d24a683199cda39757","relation:17a92485245c0843e0ef","relation:3d38fd19d8863772c501","relation:5090a7222c75c8a7ad66","relation:5a76dc896bfc5b2a0a88","relation:88fd9282f2e25f7f7eb8","relation:b4f3417161d884828277","relation:cc34f011076d18ba9a2f","relation:e3bfa2f847045a46a8a9"],"semantic_review":false,"source":"documents/changelog/sections/001-source.tex","status_markers_as_written":[],"summary_excerpt":"v615_gamma_toy_interacting.py ( WOIT.GAMMA.TOY.01, [formula in source] checks; probe 11/11, GAMMA-TOY-LANDED). Chiral/mirror parents ( [formula in source] , gap [formula in source] ); v534 survivor anchor reproduced; sector-exact mirror flip (even [formula in source] PD, odd [formula in source] ND, max odd eigenvalue [formula in source] ); [formula in source] convention control; mark transport [formula in source] exa","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-08-01 (XXXII) (the interacting gamma slice lands at toy level ( v615 promoted): the gamma battery executed ON the RP-surviving interaction class (the alignment bit [formula in source] , positive coupling, v534) — THE INTERACTING MIRROR FLIP: at the forced twist [formula in source] the mirror state's odd sector is STRICTLY NEGATIVE DEFINITE on every cut and every coupling [formula in source] (bounded away from zero: kill test (3) cannot fire on the surviving class — v608 upgraded from [formula in source] to the full grid); the mark transport exists interacting (kill test (7) does not fire); the odd transfer spectrum stays multiplicity-free; and the dead member has no RP home — the dynamical bit selection and the chirality data CO-LOCATE on the same member)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1633,"byte_start":0,"id":"section:4ddc9b76dd9cd0f415e9","kind":"subsection","labels":[],"line_end":15,"line_start":1,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:332d907c47409bb4e75f","relation:734572c5af5c18e737d1","relation:74fa19fa6cbc7745fc92","relation:7a61d306f368f76572f4","relation:a51654f31b81600d281d"],"semantic_review":false,"source":"documents/changelog/sections/002-source.tex","status_markers_as_written":[],"summary_excerpt":"v614_transport_deck.py ( QGEO.TRANSPORT.01, [formula in source] checks; probe 12/12, TRANSPORT-CANONICAL). Exact rotation substitution identity; uniform deck [formula in source] across all three omega-sheet rows (must-fail: [formula in source] , [formula in source] ); [formula in source] exact; 25-digit branch-tracked certificates at [formula in source] (dps [formula in source] , max [formula in source] ; [formula in","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-08-01 (XXXI) (the Gauss–Manin transport round lands ( v614 promoted) — THE DECK STEP IS THE BOUNDARY MONODROMY: transporting the segment cycles along the rigid quarter-rotation loop, the discriminant [formula in source] winds ONCE around [formula in source] and the transported periods factorize EXACTLY, [formula in source] ; at [formula in source] the deck factor is [formula in source] on EVERY sheet (the exponent [formula in source] forced by the puncture count); the canonical transport matrix in the segment basis is EXACTLY [formula in source] — the v613 dictionary [formula in source] is CANONICAL, no conjugator freedom left, and [formula in source] re-derives [formula in source] ; v613's residue F1 closed at the transport level)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3459,"byte_start":1633,"id":"section:1b7258ac6e85e7a30697","kind":"subsection","labels":[],"line_end":31,"line_start":16,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:24890e57ce7ac6e26b73","relation:28d57680ae0560d2fe2d","relation:35bcf6a7ea3c6bb9bbad","relation:5096ae7cbbf7de5ad02e","relation:a75f53a3233757a5325b","relation:da11c864fa0562376227"],"semantic_review":false,"source":"documents/changelog/sections/002-source.tex","status_markers_as_written":[],"summary_excerpt":"v613_canonical_periods.py ( QGEO.PERNORM.01, [formula in source] checks; probe 19/19, PERIOD-NORMALIZED). Deck-free rotation on segments (40-digit certificates) with the must-fail control (raw period rows are NOT [formula in source] -eigenvectors, residual [formula in source] — the naive ansatz falsified before the honest construction); [formula in source] exact with explicit conjugator [formula in source] ; characte","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-08-01 (XXX) (the canonical period normalization lands ( v613 promoted) — THE ANALYTIC BRIDGE CLOSES: the quarter rotation acts DECK-FREE on the four branch segments (all [formula in source] wrap factors exactly [formula in source] ), and the exact dictionary is [formula in source] — [formula in source] EXACTLY, explaining [formula in source] structurally, with the deck power unique; the period rows (hol [formula in source] , hol [formula in source] , antihol [formula in source] ) realize the rotation eigenframe; the Hodge weights are explicit Gamma monomials ( [formula in source] , complex Beta formula); and [formula in source] PER CHARACTER: the compiler polarization is MINUS the analytic Hodge form — Riemann–Hodge positivity realized, v612's named step B5 executed)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4604,"byte_start":3459,"id":"section:447deb795673a2406b44","kind":"subsection","labels":[],"line_end":42,"line_start":32,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:06a2b573e98e610a5b71","relation:282c94b4a814a582ae4a","relation:bca7065a08efce6c008f","relation:f162624b8089635b8f9c"],"semantic_review":false,"source":"documents/changelog/sections/002-source.tex","status_markers_as_written":[],"summary_excerpt":"v612_polarization_frame.py ( QGEO.POLFRAME.01, [formula in source] checks; probe 9/9, POLARIZATION-FRAMED). Simple spectrum, [formula in source] ; exact diagonalization (honest typing: diagonality follows from J-unitarity, the content is the values and the signature distribution); product of diagonal values [formula in source] exactly. Sync. Ledger row + note on QGEO.PERIODS.01; tfpt_3 (audit block); diary; suite [fo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-08-01 (XXIX) (the polarization frame lands ( v612 promoted): the braid rotation has three simple eigenvalues [formula in source] , the polarization [formula in source] diagonalizes EXACTLY in the rotation eigenbasis (values [formula in source] , [formula in source] , [formula in source] ), and THE UNIQUE POSITIVE (HODGE) DIRECTION IS THE PRIMITIVE [formula in source] EIGENSPACE — the analytic Hodge structure and the finite rotation agree on where positivity lives; the canonical period normalization (Beta weights) is the named next step)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5752,"byte_start":4604,"id":"section:757aa7c70d8acd2d7063","kind":"subsection","labels":[],"line_end":53,"line_start":43,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0dd01d825ad0cabf1f8a","relation:3b1346287f8a1bc3e255","relation:a5267daa07f7102e9426","relation:a742705c3e3ab82b50ad","relation:ad13ccd22dac60badcdf"],"semantic_review":false,"source":"documents/changelog/sections/002-source.tex","status_markers_as_written":[],"summary_excerpt":"v611_periods.py ( QGEO.PERIODS.01, [formula in source] checks; probe 6/6, PERIODS-CLASSICAL). Five symbolic Beta identities; three 40-digit rotation-character certificates; the classical [formula in source] -CM period; the PSLQ-null cross-factor consistency; the period dictionary named as the Hodge/RP resource. Sync. Ledger row + note on QGEO.LANDSCAPE.01; tfpt_3 (audit block); diary; suite [formula in source] script","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-08-01 (XXVIII) (the periods round lands ( v611 promoted): the analytic layer of the cover is CLASSICAL — all five basic period integrals are exact Beta values with Gamma denominators on the [formula in source] grid ( [formula in source] ); the [formula in source] rotation acts on periods with the exact characters [formula in source] ; [formula in source] exactly; and the cross-factor period ratio admits no low-degree integer relation (PSLQ null) — the two CM factors are period-independent, as the v610 splitting demands)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7129,"byte_start":5752,"id":"section:afc592079e9bb0b61bda","kind":"subsection","labels":[],"line_end":65,"line_start":54,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:07fb14a08a3a8134d249","relation:1226b442fd453700c3ac","relation:19979e1f455ec56aee01","relation:1b53ef1f74bc75cf6758","relation:5dd443ea7a3d3d751787","relation:632a0ee0cdce4de3983a","relation:68ff691ab1da0ca82f64","relation:e85bcc044f6a3922a7e9"],"semantic_review":false,"source":"documents/changelog/sections/002-source.tex","status_markers_as_written":[],"summary_excerpt":"v610_curve_landscape.py ( QGEO.LANDSCAPE.01, [formula in source] checks; probe 9/9, LANDSCAPE-MAPPED). Differential characters [formula in source] ; splitting confirmed at [formula in source] primes (ten exact zero-differences; surface traces [formula in source] at [formula in source] mod [formula in source] ); [formula in source] for [formula in source] mod [formula in source] ; census: anchor class [formula in sour","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-08-01 (XXVII) (the curve landscape lands ( v610 promoted): the Jacobian SPLITS into a [formula in source] -CM abelian surface — the field of deck AND marks together — times the [formula in source] -CM elliptic quotient [formula in source] , point-count-confirmed ( [formula in source] exactly for all ten tested [formula in source] mod [formula in source] ); the integer-spectrum census honestly relativizes single-char hits (7894 integer entries — single spectra are cheap; the anchor class is the most frequent nontrivial family at [formula in source] ; the compiler's distinction is the joint structure); two new canonical period resources named)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8481,"byte_start":7129,"id":"section:0b80dc1625937c6d13eb","kind":"subsection","labels":[],"line_end":78,"line_start":66,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:27682342cd28e3a498ac","relation:2ae9d1334413b196bff3","relation:3676acaa4299c5b2aaf2","relation:56ed7f165b7dd34eb9d0","relation:59068e09ab0118ede663","relation:8821eddcf72e511b1de0","relation:b143d8afb7ea7a5b7e60","relation:bda065d155ac020162e6","relation:cdb7d1afbeee59e408df"],"semantic_review":false,"source":"documents/changelog/sections/002-source.tex","status_markers_as_written":[],"summary_excerpt":"v609_translator_factorization.py ( QGEO.CFACTOR.01, [formula in source] checks; probe 8/8, C-FACTORIZATION-LANDED). Intertwiner space 1-dim; [formula in source] ; [formula in source] ; [formula in source] ; [formula in source] exact ( [formula in source] ); [formula in source] reproduces [formula in source] on the pair; honest scope: [formula in source] carries the corpus datum by definition; the v606 arithmetic nega","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-08-01 (XXVI) (the translator factorization lands ( v609 promoted): the geometric identity of [formula in source] is CLOSED — the mirror intertwiner [formula in source] ( [formula in source] ) is unique, unimodular ( [formula in source] ), [formula in source] -integral and [formula in source] -involutive ( [formula in source] exactly), and the v605 element factorizes exactly as [formula in source] with [formula in source] : [formula in source] — all three v605 residuals are now resolved (seam reversal v603, zero-mode rule v607, [formula in source] -identity v609))","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9997,"byte_start":8481,"id":"section:d139efd67906ac278dc5","kind":"subsection","labels":[],"line_end":93,"line_start":79,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:6ee7ab3aed87c6f1a4e5","relation:76f50199dcce25d07f31","relation:8e9dff935760dbae1944","relation:b04507450a4aee47abf5","relation:b27611dabff627a9f681","relation:c7c9b023329beb18791d","relation:f479434526c5634ec8e3"],"semantic_review":false,"source":"documents/changelog/sections/002-source.tex","status_markers_as_written":[],"summary_excerpt":"v608_gamma_free_slice.py ( WOIT.GAMMA.FREE.01, [formula in source] checks; probe 9/9, GAMMA-FREE-SLICE-LANDED; the v524 machinery imported read-only). Chiral [formula in source] ; anti-chiral [formula in source] with even [formula in source] PD and odd [formula in source] strictly ND; clock spectrum [formula in source] multiplicity-free on the fermion domain; mark algebras PD [formula in source] with [formula in sour","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-08-01 (XXV) (the free gamma slice lands ( v608 promoted) — the first executed step of the WOIT [formula in source] milestone: mirror modes are STRICTLY OS-negative sector-exactly (every mirror fermion vector has negative OS norm — no mirror survives reconstruction, kill test (3) cannot fire at the free level), the chiral generation is multiplicity-free (clock spectrum exactly [formula in source] ), and the mark transport exists ( [formula in source] is the mark-A [formula in source] B transport, PD — kill test (7) does not fire free); [formula in source] itself stays open on [formula in source] ; side finding: [formula in source] is unipotent mod [formula in source] )","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11334,"byte_start":9997,"id":"section:602529c0cb84730e96ee","kind":"subsection","labels":[],"line_end":106,"line_start":94,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:311009963746ff82b7c4","relation:6211f537d6d4b6ff6ca2","relation:68696fe0433d879a5593","relation:83f88ad6a0b206f6549f","relation:84cfcfa464901256cde6","relation:a9dc312879a6f4446d56","relation:cca4ecbf79ac53949373"],"semantic_review":false,"source":"documents/changelog/sections/002-source.tex","status_markers_as_written":[],"summary_excerpt":"v607_selection_rule.py ( QGEO.SELRULE.01, [formula in source] checks; probe 10/10, SELECTION-RULE-LANDED). [formula in source] -multiplication acts as the identity on the torsion; the induced [formula in source] -action is [formula in source] mod [formula in source] with only fixed class [formula in source] ; [formula in source] irreducible over [formula in source] gives structural uniqueness of the eigenline ( [form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-08-01 (XXIV) (the selection rule lands ( v607 promoted): the infinity torsion is a genuine [formula in source] space, the deck rotation acts with char [formula in source] mod [formula in source] — EXACTLY ONE projective eigenline, and it IS the top mode; the three modes carry mutually exclusive canonical labels (seam [formula in source] [formula in source] -real, top [formula in source] deck-eigen, zero [formula in source] the only unlabeled) and [formula in source] flips exactly the labeled pair: BOTH v590 demands expressed through cover structure (typed reading; the gate residual is the continuum derivation))","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13067,"byte_start":11334,"id":"section:66dbe925f5d84de3e49b","kind":"subsection","labels":[],"line_end":124,"line_start":107,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:16dddd0a949ce49f4236","relation:1b2f2f30081057106cb8","relation:1f95867b039cc141ef19","relation:2e9c205b2fb3fe4b4905","relation:6d49e4dcc96ee713857f","relation:76efe84d41f7335b96f3","relation:8e228843954d79d2e9af","relation:b2b3fee862d7de5f2cc0","relation:b54239c989b1b5415b9e","relation:d217d0b73243497ec6a6","relation:e1971b2f049d86fb482b","relation:ff3cd87aa2b8873f8fba"],"semantic_review":false,"source":"documents/changelog/sections/002-source.tex","status_markers_as_written":[],"summary_excerpt":"v605_translator.py ( QGEO.TRANSLATOR.01, [formula in source] checks; probe 11/11, TRANSLATOR-LANDED). [formula in source] exact (1-dim intertwiner space, [formula in source] invertible); [formula in source] [formula in source] -integral (denominator [formula in source] ); seam lift zero in the free part, [formula in source] in the torsion of [formula in source] ; order chain [formula in source] with indices [formula ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-08-01 (XXI) (the translator round lands ( v605 promoted): the corpus RP anti-automorphism IS the J-adjoint twisted by an explicit inner element [formula in source] ( [formula in source] is inner, [formula in source] unique up to scale, [formula in source] integral over [formula in source] — the single-sheet negatives resolved, the [formula in source] detour unnecessary); the seam is a NONZERO pure 3-torsion class at infinity (torsion coordinates [formula in source] ); the [formula in source] survives frame-joining as the saturation defect (chain indices [formula in source] , [formula in source] ); the [formula in source] duality certified with a Lean addendum)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14687,"byte_start":13067,"id":"section:2cfba076381b50ca717c","kind":"subsection","labels":[],"line_end":139,"line_start":125,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:40569f16c204c6ace17f","relation:5182d7a73d1061935081","relation:753cb3e47f1cfbb81ffb","relation:860615c3a13357f4a582","relation:97e78947a9d491190067","relation:ac458956c9c9d793058d","relation:f3c9074a3db15f7df23e"],"semantic_review":false,"source":"documents/changelog/sections/002-source.tex","status_markers_as_written":[],"summary_excerpt":"v604_equivariant_order.py ( QGEO.EQORDER.01, [formula in source] checks; probe 12/12, EQUIVARIANT-ORDER-LANDED). Anti-isometry exact; [formula in source] ; all [formula in source] rotated words [formula in source] -integral, joint lattice full rank [formula in source] , Smith divisors [formula in source] ; [formula in source] divisors [formula in source] ; each finite cusp twist torsion-free; three objects share [for","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-08-01 (XX) (the equivariant-order round lands ( v604 promoted): [formula in source] IS an anti-isometry of the polarization ( [formula in source] exact — correcting a diary side remark), [formula in source] restricts to the integer form [formula in source] with [formula in source] ; the four mark frames generate a FULL order of index [formula in source] in [formula in source] ; and the 3-torsion localizes at infinity ( [formula in source] , finite cusps torsion-free): [formula in source] at the marks, [formula in source] at infinity — the integral infinity/order-torsion bridge; translator negatives extended (the [formula in source] -sheet named))","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16038,"byte_start":14687,"id":"section:bec26de23262d380efe5","kind":"subsection","labels":[],"line_end":153,"line_start":140,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:3b8620d93c7f5c485edd","relation:6d5ff31e113fc22dd097","relation:6f79e6b1b9c1f20d4a24","relation:7f4223d4d4bf6823dd0d","relation:99ba1146c654501a6be9","relation:a4682a3a5d03d087fdd6","relation:cb4ce15f8dbf93a366bc"],"semantic_review":false,"source":"documents/changelog/sections/002-source.tex","status_markers_as_written":[],"summary_excerpt":"v603_seam_marks.py ( QGEO.SEAMMARKS.01, [formula in source] checks; probe 15/15, SEAM-REAL-LANDED). Seam: [formula in source] , [formula in source] unique, [formula in source] , [formula in source] , [formula in source] ; infinity: unreduced Burau braid relations, invariant column [formula in source] , full twist eigenvalues [formula in source] ; marks: [formula in source] integer restriction, in the word algebra wit","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-08-01 (XIX) (the seam-and-marks round lands ( v603 promoted): the seam line is a REAL line of the cover (unique common eigenline, [formula in source] -fixed) and [formula in source] reverses it — the v590 seam-reversal demand holds geometrically; the infinity cusp separates in the unreduced Burau module; the first per-mark [formula in source] witness lands ( [formula in source] , class order [formula in source] in the word-order cokernel); the corpus-transpose translator negatives are quantified)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17797,"byte_start":16038,"id":"section:25dcbc4eda230593c159","kind":"subsection","labels":[],"line_end":171,"line_start":154,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:09b4c79ba95fc266765c","relation:27cf07ce3b0f43eb7f9d","relation:4f9973d749546dd7d755","relation:68c4147c2efa9417fc05","relation:93ee86d4a6b8e25e2a6a","relation:b354c9a90a37a7309497","relation:b9b6dd28d3aecdd8d9e2","relation:dee8ef37d8ab2aa2da1d","relation:f1df214e26cd577da8af"],"semantic_review":false,"source":"documents/changelog/sections/002-source.tex","status_markers_as_written":[],"summary_excerpt":"v602_duality_forms.py ( QGEO.DUALFORMS.01, [formula in source] checks; probe 17/17, DUALITY-FORMS-LANDED). [formula in source] J-self-adjoint, [formula in source] the exact product reversal, [formula in source] conjugate to the compiler pair; [formula in source] , [formula in source] , [formula in source] , ladder all exact in the J-projector language; Weil-twisted form positive definite ( [formula in source] ); hone","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-08-01 (XVIII) (the duality-and-forms round lands ( v602 promoted): the J-adjoint exchanges the two parabolic types exactly ( [formula in source] compiler pair); the dictionary completes in the J-projector language (the corpus anchor formula [formula in source] holds verbatim on the curve); Weil positivity holds exactly (the Riemann bilinear relations on the [formula in source] -sheet); the canonical bilinear form [formula in source] is symmetric with [formula in source] ; the v600 integer core is Lean-certified ( FORM.QGEO.04); the contracts paper gains the [formula in source] -cover model paragraph)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19186,"byte_start":17797,"id":"section:e515cdbbc400349f3d3b","kind":"subsection","labels":[],"line_end":185,"line_start":172,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:138a18724c0a635f3067","relation:361e59ec2702a63c216f","relation:70d879db77fd081ff36a","relation:78ae141e0bc9de99d3ce","relation:7c9b24ab9901e2b6bfff","relation:daf48fc1422d397ec21a"],"semantic_review":false,"source":"documents/changelog/sections/002-source.tex","status_markers_as_written":[],"summary_excerpt":"v601_equivariant_dual.py ( QGEO.CANON.01, [formula in source] checks; probe 14/14, EQUIVARIANT-DUAL-LANDED). [formula in source] idempotent rank-1 J-projectors rotating exactly under [formula in source] ; pair family [formula in source] , [formula in source] : [formula in source] -integral, compiler-exact, equivariant by construction; duality: conjugate to [formula in source] exactly (must-fail to [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-08-01 (XVII) (the canonicity round lands ( v601 promoted): the J-adapted cusp projectors give a manifestly [formula in source] -equivariant presentation of the pair (mark choice [formula in source] winding choice), which realizes the DUAL parabolic exactly (conjugate to the transposed compiler pair; the direct intertwiner is singular); the v590 Klein four-group lives integrally on the curve; the Weil-twisted RP comparison and the seam identification stay open)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20832,"byte_start":19186,"id":"section:97886ff8881b257d4648","kind":"subsection","labels":[],"line_end":203,"line_start":186,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:27be7e0e9574d6376de6","relation:46169a8c6dc995b7d43a","relation:61697c8675221f26da3b","relation:68a67059c3b94ef1b72b","relation:85b889533ce140a3ecb4","relation:9e627eba062f0535ae0e","relation:af49e17afbbe36e74103","relation:b86ffc8b666456fe0617","relation:f2e7fc39dc7acae2c62c"],"semantic_review":false,"source":"documents/changelog/sections/002-source.tex","status_markers_as_written":[],"summary_excerpt":"v600_joint_embedding.py ( QGEO.EMBED.01, [formula in source] checks; probe 15/15, JOINT-EMBEDDING-LANDED). The pair [formula in source] , [formula in source] : chars and joint traces compiler-exact ( [formula in source] , [formula in source] , [formula in source] ); seven words independent; explicit invertible [formula in source] with [formula in source] , [formula in source] ; the real structure integer on [formula ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-08-01 (XVI) (the joint embedding lands ( v600 promoted): the compiler pair [formula in source] is REALIZED on the [formula in source] -cover — a [formula in source] -even degree-2 pair, [formula in source] -integral, seven-word rank [formula in source] , simultaneous conjugation to the compiler pair solved exactly, integer restrictions on the saturated [formula in source] lattice, and saturation index [formula in source] with the exact v566 divisor pattern; canonicity typed open, the gate does not move)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":22551,"byte_start":20832,"id":"section:95268c80786bff7e280f","kind":"subsection","labels":[],"line_end":221,"line_start":204,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:1b95ae30cfc41c3db7e7","relation:2942dc9775f927f2e7d4","relation:305a7f57270022b68819","relation:4ad7210d5ded89944e30","relation:a9139fef3c1346ac81e6","relation:ddb4c58c3f09d29c0af3"],"semantic_review":false,"source":"documents/changelog/sections/002-source.tex","status_markers_as_written":[],"summary_excerpt":"v599_real_structure.py ( QGEO.REAL.01, [formula in source] checks; probe 18/18, REAL-STRUCTURE-LANDED). Existence and uniqueness of [formula in source] (1-dimensional intertwiner space, [formula in source] exact, four twist intertwinings [formula in source] ); the grading functor [formula in source] locates [formula in source] , [formula in source] (the anchor spectrum) and [formula in source] exactly at char level; ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-08-01 (XV) (the real structure lands ( v599 promoted): the anti-holomorphic [formula in source] reflection on the [formula in source] -cover exists and is unique up to scale with [formula in source] ; its grading functor closes all three dictionary gaps at char level ( [formula in source] , [formula in source] with the anchor spectrum [formula in source] , [formula in source] ); the [formula in source] -decomposition carries [formula in source] , [formula in source] , [formula in source] ; the joint algebra embedding stays open (quantified negative); and the invariant form has [formula in source] — a sheet-diamond determinant-list member — with Lorentz signature [formula in source] )","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":23669,"byte_start":22551,"id":"section:dfb873484a0e4a888733","kind":"subsection","labels":[],"line_end":234,"line_start":222,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:36486d6202b2dbb3a92d","relation:5f69f4cfd240f56d6b73","relation:9e8611b7103dc311edb6","relation:e441145c1f45959305f4"],"semantic_review":false,"source":"documents/changelog/sections/002-source.tex","status_markers_as_written":[],"summary_excerpt":"v598_cover_dictionary.py ( QGEO.DICT.01, [formula in source] checks; probe 4/4, DICT-THREE-ENTRIES). All three entries exact (numeric prefilter, symbolic confirmation); supporting structure: opposite-twist products nilpotent, [formula in source] ; negatives quantified ( [formula in source] combinations, [formula in source] matches for [formula in source] / [formula in source] / [formula in source] / [formula in sourc","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-08-01 (XIII) (the cover dictionary reaches THREE exact entries ( v598 promoted): [formula in source] , [formula in source] — the [formula in source] sheet coupling is the diamond-diagonal Gram difference — and the binary AnchorLadder [formula in source] ; the grading half is absent from [formula in source] canonical combinations, with the real structure as the named suspect)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":24690,"byte_start":23669,"id":"section:6f0c3fead8d18c268fdb","kind":"subsection","labels":[],"line_end":246,"line_start":235,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:56add128bf8281bf5671"],"semantic_review":false,"source":"documents/changelog/sections/002-source.tex","status_markers_as_written":[],"summary_excerpt":"The hit. The cusp Gram [formula in source] has characteristic polynomial [formula in source] exactly — the rank-one winding operator (trace [formula in source] ) as a Gram of a [formula in source] -conjugate cusp twist: the fifth fingerprint. Additional exact structure: opposite-twist products [formula in source] are nilpotent ( [formula in source] ), [formula in source] has spectrum [formula in source] . Honest nega","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-08-01 (XI) (the dictionary's first entry: U IS LOCATED — the winding operator appears as a cusp Gram on the [formula in source] -cover; exploration round, documented as a note on QGEO.COVER.01)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":26268,"byte_start":24690,"id":"section:3e4a71dc12f0870304d4","kind":"subsection","labels":[],"line_end":263,"line_start":247,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:2d35ed1bbbf203d6aad6","relation:4b616324d6b223141d85","relation:4e7b9f39551fe22a2043","relation:5264aa8a90e10ff6a6a7","relation:a38bf429e6b9c720b3b7","relation:d0562530dee40ba1abd1"],"semantic_review":false,"source":"documents/changelog/sections/002-source.tex","status_markers_as_written":[],"summary_excerpt":"v597_mu4_cover_model.py ( QGEO.COVER.01, [formula in source] checks; probe 6/6, FINGERPRINTS-HIT). Genus [formula in source] , five cusps ( [formula in source] ), Chevalley–Weil [formula in source] ; Burau at [formula in source] with verified braid relations, [formula in source] , [formula in source] ; cusp classes [formula in source] , order [formula in source] with the per-mark [formula in source] mechanism ( [form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-08-01 (X) (Strategy I/II executed: the [formula in source] -cover [formula in source] hits FOUR compiler fingerprints ( v597 promoted) — rank-3 Eisenstein [formula in source] , projective [formula in source] via the deck, cusp-class group [formula in source] of order [formula in source] , and the unique invariant hermitian form of LORENTZ signature [formula in source] matching Paper II's polarization: the first geometric candidate that could close GATE.QGEO and the RP slot with one construction)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":27634,"byte_start":26268,"id":"section:61e2b6b2694744d301be","kind":"subsection","labels":[],"line_end":277,"line_start":264,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:099533283b1e0c496780","relation:47aeb929594b20ba302c","relation:800e0d14ed43081f40cc","relation:8a8e3c870f02adbb94b1","relation:9704bfbb1cbde7eeabd0","relation:99280af7891d5744fd93","relation:fa84287f9d9e9f4287f3"],"semantic_review":false,"source":"documents/changelog/sections/002-source.tex","status_markers_as_written":[],"summary_excerpt":"v590_involution_existence.py ( QGEO.INVOL.01, [formula in source] checks; probe 7/7, EXISTENCE-UNCONDITIONAL). All eight spectral sign choices on [formula in source] 's eigenspaces are integer, involutive and order-stabilizing on both twins; narrowing [formula in source] : the trace [formula in source] half dies by the v574 rank theorem, [formula in source] and [formula in source] on [formula in source] single out [f","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-08-01 (IV) (the sheet involution exists unconditionally ( v590 promoted): the integral [formula in source] -commuting involutions are exactly [formula in source] (rigidity, both twins); the v574 type theorem [formula in source] seam reversal [formula in source] zero-mode fixing single out the explicit [formula in source] with exact [formula in source] -signature uniquely — GATE.QGEO.01's involution-existence input relocates to DERIVED)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":29458,"byte_start":27634,"id":"section:ad7223db244d878602d3","kind":"subsection","labels":[],"line_end":297,"line_start":278,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:190132525678501e4221","relation:26fa77ee63cd4de89cf0","relation:50e48bc0488cfbccb37e","relation:8d9912bcda93cbc3502f","relation:8f430876bae0c8bc158c","relation:b34cd7188f818db49895","relation:dfb993f14d92128648e5"],"semantic_review":false,"source":"documents/changelog/sections/002-source.tex","status_markers_as_written":[],"summary_excerpt":"v584_ext_source_response.py ( DIAMOND.BIT.EXTSOURCE.01, [formula in source] checks; probe 8/8, UNIT-BOX-SEPARATED). The interacting kernel [formula in source] ( [formula in source] from the shared Ext arrows [formula in source] ) has exact thresholds [formula in source] : compiler [formula in source] and [formula in source] , alt [formula in source] and [formula in source] — numerators exactly the v572 pencil factors","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-07-31 (XVII) (the interacting RP route of the alignment bit, executed: EXT-SOURCE COUPLING SEPARATES THE 81-TWINS DIRECTIONALLY IN THE UNIT BOX ( v584 promoted) — exact rational flip thresholds with the v572 pencil factors as numerators; positive coupling [formula in source] heals exactly the compiler twin, the alt twin is rigid; response pole on the golden polynomial)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":30963,"byte_start":29458,"id":"section:fb925495ff0f316b1a06","kind":"subsection","labels":[],"line_end":315,"line_start":298,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:2bedd0a189a64083cc2f","relation:38275a3dbb9a8904732c","relation:3a9de0df63fe637d1b4b","relation:52bc98e6e08fe17e8d39","relation:9095486604f94230f2ae","relation:bbd4de92dbb60c5f1e46","relation:cf1054c8ece0417d4f2b","relation:f2b5e088bee50864eb88","relation:f700e9a5feb0e9737ae3"],"semantic_review":false,"source":"documents/changelog/sections/002-source.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"v575_cr_continuous_uniflow.py ( FTR.CRCONT.01, [formula in source] checks; probe [formula in source] , UNIFLOW-DEGENERATE). The frozen protocol exports, recomputed from primitives (F_pole [formula in source] via the v99 generator; F_Boltzmann the SAME contraction by the v425 single-flow theorem; F_QCD [formula in source] ; F_relic adiabatic [formula in source] ), form the quadruple [formula in source] with a forced r","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-07-31 (XI) (the continuous half of the cross-ratio check executed and closed: UNIFLOW-DEGENERATE ( v575 promoted) — the native exports are forced degenerate by the single-flow theorem, so the continuous half closes onto v425; both halves of the preregistered check are now executed)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":32312,"byte_start":30963,"id":"section:fad05632a3d0b323783d","kind":"subsection","labels":[],"line_end":331,"line_start":316,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0e198f17a57d30363c0a","relation:199919053b74c7d68754","relation:509bf33e06b620d3bd89","relation:a992188cc5d43757125f"],"semantic_review":false,"source":"documents/changelog/sections/002-source.tex","status_markers_as_written":[],"summary_excerpt":"v574 extended (probe [formula in source] ). Dropping the winding demand entirely (arbitrary first column), the self-code package leaves the four-column family [formula in source] — exactly one uniform: the compiler. The winding demand is the uniformity choice ( [formula in source] of [formula in source] ). Final declared list of the reconstruction: involution existence, column uniformity, [formula in source] (E8-glue","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-07-31 (X) (closing the round: the winding form's content located exactly ( v574 [formula in source] checks — without it a four-column family survives, exactly one uniform: the compiler), and the half-sided RP restrictions shown blind ( v572 [formula in source] — the interacting construction is the one remaining RP route))","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":34451,"byte_start":32312,"id":"section:1bc03b42708092f8463b","kind":"subsection","labels":[],"line_end":355,"line_start":332,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:1f5856966706c6867430","relation:2e3feb6b79b75eafeec4","relation:2f52d4a28b7544c18e4a","relation:529e25b7c964e1a68718","relation:877b3198653d9d89eda4"],"semantic_review":false,"source":"documents/changelog/sections/002-source.tex","status_markers_as_written":[],"summary_excerpt":"v572 extended (probe [formula in source] ). Along the Gibbs family [formula in source] of the v566 anchor operator [formula in source] , the pencil determinant factors exactly differently on the twins — compiler [formula in source] , alternative [formula in source] ( [formula in source] ) — and only the compiler's extra factor has a root inside the physical Gibbs range: the compiler twin's RP kernel degenerates at a ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-07-31 (VIII) (two decisive deepenings: the anchor-Hamiltonian Gibbs pencil delivers the first DYNAMICAL distinction of the reconstruction bit ( v572 [formula in source] checks: the compiler twin is Gibbs-critical at [formula in source] , the alternative never), and the redundancy ablation shrinks the reconstruction inputs to three ( v574 [formula in source] checks: [formula in source] and [formula in source] fall relative to the self-code demands))","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2813,"byte_start":0,"id":"section:86289022df2156d0b3e5","kind":"subsection","labels":[],"line_end":32,"line_start":1,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:03a34af391c038ca5283","relation:1a4c587557840bcb9e43","relation:2ac7ad6e82e557fddc52","relation:46746fb1b5e0d034befb","relation:52d13ca17034526427a9","relation:61b68b6f63b585929af4","relation:6a121a4269feae407458","relation:951c5ffe6da059782539","relation:a904cee9fba9c948e537","relation:ac1c4444f008e83a3ba9","relation:c81daaaaa48a0737cada","relation:dabeb5667e6b922b3cac","relation:e4aff8a048dcf89c40b9","relation:f8981f26604a0c7d214e"],"semantic_review":false,"source":"documents/changelog/sections/003-source.tex","status_markers_as_written":[],"summary_excerpt":"Probe bit_selector_probe.py ( [formula in source] , verdict SELECTOR-FOUND). Priorities 2+3 of the self-code review, fused with the v567 residual bit. The bit is integrally visible: the two [formula in source] -twins ( [formula in source] vs [formula in source] ) generate different integral orders (equal index, equal Smith divisors, different lattices). The selector: the dominant mode of the sheet direction is [formu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-07-31 (III) (the residual reconstruction bit located and given a canonical witness: the ladder self-consistency selects the compiler [formula in source] uniquely (SELECTOR-FOUND); the split geometry excluded; Priority 2 sharpened + v568 promoted + ledger/paper/diary/website sync)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5472,"byte_start":2813,"id":"section:abb53343f07d4a85f8f9","kind":"subsection","labels":[],"line_end":62,"line_start":33,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:095c24cd905b2192339b","relation:1ea5f00a6049b6371700","relation:1f84c2ba5f2927c8cf1b","relation:2f47ed00245c6c029899","relation:38069fa9cbc4d4b4be80","relation:4d19d2adda09a5b929b5","relation:5aeb641c1fcf8cf2fca7","relation:61166b27e00579a29733","relation:66116b50428277db6345","relation:74dbc120d7f61a074c4b","relation:7d3142725d62fa008b08","relation:8088cdf184a1d2237893","relation:839a39a710e4919964b0","relation:9fdac2692e5418e556a9","relation:a357dcb036d3e3aec751","relation:ae1a860f5ebc6079b28f","relation:ae4eb7505d7510bc1af1","relation:aeb675123dd11a1eca85","relation:b20755bc83adf56c9646","relation:ccfc187df21bc9d48d68"],"semantic_review":false,"source":"documents/changelog/sections/003-source.tex","status_markers_as_written":[],"summary_excerpt":"Audit probe carrier_free_q_reconstruction_probe.py ( [formula in source] , verdict RECONSTRUCTS-TO-FAMILY). Priority 1 of the self-code review executed. The circularity located: v11's uniqueness certificate for [formula in source] uses row sums [formula in source] , column sums [formula in source] and [formula in source] — the [formula in source] in the budgets and in [formula in source] ; all of it forbidden in the ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-07-31 (II) (the No-Carrier-Reconstruction audit, Stage A: the anchor self-code is carrier-free, and [formula in source] reconstructs up to ONE binary sheet-coupling choice (RECONSTRUCTS-TO-FAMILY) + v567 promoted + ledger/paper/diary/website sync)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9330,"byte_start":5472,"id":"section:a7b499839afbb3b8e6af","kind":"subsection","labels":[],"line_end":106,"line_start":63,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:31231207c3a7aac6860c","relation:3f4f7d13d32abc3f8071","relation:8c9a6fdaf9322983a4b9","relation:9976e0b8463e47312585","relation:ae5cddf8e04101cff87d","relation:d847ff0706fc97de1d9e","relation:f5cf9a6bb230c7c69ede","relation:fb581bace58a8fbc7889"],"semantic_review":false,"source":"documents/changelog/sections/003-source.tex","status_markers_as_written":[],"summary_excerpt":"Discovery probe woit_os_beta3_pt_dual_probe.py ( [formula in source] , [formula in source] \\,s, verdict SUCCESS per the frozen preregistration; contract wording verbatim: success [formula in source] Woit's Minkowski conjugation identified with the family-D conjugation on the quotient, kill [formula in source] the duality forces a clock-centralising (family A) structure). The class (block theorem): a [formula in sourc","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-07-30 (II) (WOIT [formula in source] executed: the [formula in source] duality typed against [formula in source] — the OS cut and the [formula in source] signature forced, the kill branch empty by algebra, the induced member [formula in source] the [formula in source] carrier (SUCCESS) + v565 promoted + contract/paper/diary/website sync)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13536,"byte_start":9330,"id":"section:708d06b08bf9729fd162","kind":"subsection","labels":[],"line_end":148,"line_start":107,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:043077ada3283846215c","relation:156ebd2fc9ef78de38cc","relation:44ffed84b44f016c415c","relation:451f53729898f7e2f7a7","relation:4ec1c99b1fb7a7f244bf","relation:649885fb372cf64bbcfb","relation:782303188d0448445519","relation:8b3d5ebaf82a7e2ffa39","relation:9647646b291a7689633c","relation:a862f9ec1a2a23e5866b","relation:b712095c792fca80a95f","relation:e551e6a762f9b2e7effc","relation:f3a955cf45106312cbcf","relation:f8b8683aafd94b9e25af"],"semantic_review":false,"source":"documents/changelog/sections/003-source.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"New module v534 ( SEAM.STRADDLE.CONE.01). The 2026-07-23 review-round contract (recorded ``not promoted'' in entry (X)) is executed, double-verdicted. V2 [formula in source] ERFOLG — the selection law (the central datum): with independent couplings [formula in source] on the four mark quartets of [formula in source] and the equivariant (uniform) direction, reflection positivity holds on every admissible cut over the ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-07-24 (I) ( v534 — the straddle cone executed: THE FIRST DYNAMICAL SELECTION OF THE ALIGNMENT BIT — reflection positivity keeps exactly ONE member of the interacting mark family alive, [formula in source] with positive coupling; the literal leading-order cone formalization dies; NO marker moves)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18623,"byte_start":13536,"id":"section:bc972235a8e75d6dcfea","kind":"subsection","labels":[],"line_end":201,"line_start":149,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:1b6fbfcb7a2f7332297a","relation:291068d2d59012e51cc0","relation:2b5f12fd8ace3f0f1b19","relation:2e7dd37e96966321fe39","relation:4239aa9374f64c3aa6e3","relation:56a0affd4748cbced8a5","relation:7080fa9632bcc9a01a05","relation:7d5fdafd73cb2537ffb4","relation:7dac80bb27d6677df45e","relation:8c300b35ece1ad1ee182","relation:920235a1aab5ea5f2277","relation:9670929e2432316715eb","relation:9a630b29bd98c594fb3a","relation:ae3493b4ae946aef95e2","relation:b2a25ee5981624a2729e","relation:bc3ffc96679ebd160522","relation:c92b1cc2bf1f7d4d7741","relation:e25a23dc86d3e4906562","relation:f6287736cb9dc09ed12f"],"semantic_review":false,"source":"documents/changelog/sections/003-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"New module v530 ( DIAMOND.CENTER.QUOTIENT.01). The Sheet-Diamond center [formula in source] carries the fixed primitive line [formula in source] ( [formula in source] ), and the induced operator on [formula in source] is exactly the atom matrix [formula in source] \\ with [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] . The center self-","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-07-23 (X) ( v530– v533 — the external review round promoted: center quotient compiler, Coxeter Stage A tensor clock, dual-degree modular checksum [formula in source] , sheet-transfer disc [formula in source] norm line; every identity machine-confirmed exactly before promotion (probe [formula in source] ); NO marker moves)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20318,"byte_start":18623,"id":"section:d7de69fc09310845215e","kind":"subsection","labels":[],"line_end":208,"line_start":202,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0bdb1ff1291103a0e68a","relation:8e6a0debe5a134d8d2cd"],"semantic_review":false,"source":"documents/changelog/sections/003-source.tex","status_markers_as_written":[],"summary_excerpt":"Website home. Slim one-viewport hero (proof strip: 523 machine-checked modules [formula in source] Wolfram mirror [formula in source] Lean carrier [formula in source] 0 external replications yet; copyable python run_all.py [formula in source] ALL CHECKS PASSED; CTA trio film / browser check / kill board). Narrative order: Hero [formula in source] IntroVideo ( \\#intro-video kept) [formula in source] In one breath [for","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-07-23 (IX) (website entry redesign: narrative home, honesty band, proof strip, guided-tour route — editorial only, NO new modules, NO marker moves)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":23602,"byte_start":20318,"id":"section:8b84d2fb55ac4a48656b","kind":"subsection","labels":[],"line_end":230,"line_start":209,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:00b491e26cf28c50890e","relation:0b3c1d8d3ed2de4b6cb3","relation:12b4f5abd9d55456e371","relation:1e1eba8414928fa24e15","relation:278b86437dcdd0f7ff1c","relation:3468037d04e1e33f8751","relation:41367de6702cbf485b4f","relation:4b54dbd7ec908606d29b","relation:524951113dbcdbff5133","relation:5ae857d23a2cd76493a4","relation:67dab7e2a6f648cba99f","relation:6c25fd0bb1651d02af9d","relation:6f1728107efff07e208c","relation:84d851535ed5253af241","relation:8f49be644118246c773c","relation:975d53720861b9f8e559","relation:9fc0a0d52d3982219177","relation:a05a94022bbb06b28aa5","relation:a47f50bc9dc4422affd2","relation:ae0cb60107f83cec3ec5","relation:afbde00a0d13d05e6285","relation:b8e9b7066eb0d2f7ccc0","relation:ba20630a619f7210b9c7","relation:d446a6faeb61c7c77bf6","relation:e56917b69dd2e0e9b2ed","relation:ed3b5a3c91bb132bcaa7"],"semantic_review":false,"source":"documents/changelog/sections/003-source.tex","status_markers_as_written":[],"summary_excerpt":"Papers. tfpt_5_redteam (Target G [formula in source] method/outcome/title honesty pass); tfpt_1, tfpt_2 and origin_theory (bit-reduction statements [formula in source] ten tests [formula in source] twist-class definition); origin_theory (thermal-seam keybox, horizon chapter); tfpt_horizon_readouts (head keybox third leg); tfpt_3 (title [formula in source] keybox: thirty-step story, measure chain derived); tfpt_resear","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-07-23 (VIII) (prominence pass — the v519–v529 breakthroughs lifted into the FRAME texts of the papers and the website data layer; purely editorial, NO new modules, NO marker moves — (1) tfpt_5_redteam gains the seam round Target G: the ten-test side-blind scoreboard on the alignment bit ( v512/ v521/ v525/ v529) and the first firing kill test of the programme — the interacting straddle law ( v529), documented as a named threat AND the first hard selection principle for [formula in source] , fenced at toy level; (2) the bit-reduction statements in tfpt_1, tfpt_2 and origin_theory extended from the v512 state to the current state (ten side-blind tests, the twist-class definition with gauge-robust order parameter, ``in principle interferometrically readable'', v528 — the bit stays formal input); (3) the thermal seam lifted into the origin_theory horizon chapter (new keybox: [formula in source] measured, temperature the third leg of [formula in source] , v526) and into the tfpt_horizon_readouts head keybox; (4) tfpt_3 title/keybox now carry the thirty-step story and ``the measure chain is derived'' ( v520/ v523) prominently; (5) tfpt_research_contracts title/intro keybox now show the executed stages of CELEST.SEAM.01 (M1–M3, [formula in source] -chains decided, [formula in source] derived) and WOIT.OS.TWISTOR.01 ( [formula in source] executed, [formula in source] next under the straddle constraint); both contracts stay Open)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":25931,"byte_start":23602,"id":"section:e4833e93d562514547a4","kind":"subsection","labels":[],"line_end":244,"line_start":231,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:084fe98263269c2b5f3b","relation:0e861ae7871e021018f8","relation:1d15c78d70b57e51ade4","relation:37ccd6cf3c932c8dd09d","relation:3e7c87aa575c5a87ef0a","relation:5d4f371c29423b439cad","relation:9d6cd9fdf4f03e6257b4","relation:ad9af755cb24bfac05a0","relation:bc4b633501eab4bde14e"],"semantic_review":false,"source":"documents/changelog/sections/003-source.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"Suite. New module v529_seam_interacting_toy_fk.py ( [formula in source] checks, [formula in source] s); registered in run_all.py [formula in source] script_registry.csv; suite [formula in source] modules green. Ledger. New row SEAM.INT.FKTOY.01; WOIT.OS.TWISTOR.01 text-precised (Kill-Test-2 toy shadow [formula in source] straddle law); scoreboard rows text-precised ( [formula in source] ); no status moves. Papers. tf","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-07-23 (VII) ( v529 — the interacting Fidkowski–Kitaev seam toy promoted as the ledger row SEAM.INT.FKTOY.01: the FIRST firing Kill-Test-2 shadow — triple verdict F1 [formula in source] KILL / F2 [formula in source] KILL / F3 [formula in source] ERFOLG; the celestial/twistor story in tfpt_3 gains Step 30 and the header goes twenty-six [formula in source] thirty steps — (1) F1 [formula in source] KILL : [formula in source] exists exactly on the interacting model ( [formula in source] , [formula in source] , clock-tower inversion, [formula in source] ) so Kill-Test 1 does not fire; but Kill-Test 2 fires at toy level: RP breaks for every [formula in source] — inertia ladder [formula in source] ; Gibbs [formula in source] same ladder; mechanism [formula in source] interference; STRADDLE LAW ( [formula in source] ); \\ fence one toy / one interaction class / flat-band parent — narrows the Woit route, does not close it; WOIT.OS.TWISTOR.01 stays Open with the toy shadow documented as a named Kill-Test-2 threat; (2) F2 [formula in source] KILL : the TENTH side-blind test ( [formula in source] ) — [formula in source] maps [formula in source] EXACTLY despite [formula in source] -seeing spectra; (3) F3 [formula in source] ERFOLG : grading [formula in source] [formula in source] tower [formula in source] FK anchor [formula in source] constructive OS quotient at [formula in source] ; Wolfram extension [formula in source] (verified engine run); suite [formula in source] ; NO marker moves)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":27435,"byte_start":25931,"id":"section:1dfae3ea2125bff27c23","kind":"subsection","labels":[],"line_end":254,"line_start":245,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:1f3a1bd24f1133127581","relation:2695c07f676bcce2bc90","relation:5a792c305bf5b9258d72","relation:86f04c7b2b3cc02fd10c","relation:a54c23cecd2be994409f","relation:c6734e9f435c32db34ca","relation:e6fbab74f233c57079d2","relation:e9c978885a23451b0ddc"],"semantic_review":false,"source":"documents/changelog/sections/003-source.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"Suite. New module v528_seam_bit_twist_class_definition.py ( [formula in source] checks, [formula in source] s). Ledger. New row SEAM.BIT.TWISTCLASS.01; SEAM.TAU.FLAG.01 text-precised (web [formula in source] ); no status moves. Papers. tfpt_3 Step 29; contracts [formula in source] introduction (``symmetry-lift bit'' now also ``the twist-class choice, in principle interferometrically readable''). Wolfram. Three exact ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-07-23 (VI) ( v528 — the alignment bit as an exact measurable TWIST-CLASS choice promoted as the ledger row SEAM.BIT.TWISTCLASS.01: the physical definition — verdict SUCCESS; the celestial/twistor story in tfpt_3 gains Step 29 — (1) Facets \\#14 ( [formula in source] -flip [formula in source] ) and \\#15 (twist-frustration [formula in source] ) both directions exact (cardinality lemma [formula in source] ; [formula in source] -class census [formula in source] axes: flip class exactly at [formula in source] ); (2) order parameter [formula in source] at [formula in source] else [formula in source] , gauge-robust; (3) unification \\#14=\\#15=flag-transitivity [formula in source] ONE [formula in source] invariant ( v512 web [formula in source] ); Kramers [formula in source] POSITION half (derived), twist class [formula in source] MODULUS half (the input); (4) \\ measurement sketch (interferometric in principle); the bit remains formal input; NO marker moves)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":28775,"byte_start":27435,"id":"section:408ed5c27f7477e3c981","kind":"subsection","labels":[],"line_end":262,"line_start":255,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:1eb3d97ebce4be3ca52a","relation:43014c77667db0ae33d7","relation:4d7f1559ba674121b113","relation:adcee0b59f3cd563d8fc","relation:dddea6354fb379fdbefc","relation:f517e1c5ed050b2a007d"],"semantic_review":false,"source":"documents/changelog/sections/003-source.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"Suite. New module v527_seam_clock_silver_spectrum.py ( [formula in source] checks, [formula in source] s). Ledger. New row SEAM.CLOCK.SILVER.01; no status moves. Papers. tfpt_3 Step 28; contracts thermal/silver follow-on. Wolfram. Three exact mirrors ( [formula in source] pencil; [formula in source] -scaling witness; gap [formula in source] ).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-07-23 (V) ( v527 — the silver clock eigenvalue EXPLAINED and DEMYSTIFIED, promoted as the ledger row SEAM.CLOCK.SILVER.01: double verdict STRUCTURE [formula in source] SUCCESS / CONNECTION [formula in source] KILL (anti-numerology style); the celestial/twistor story in tfpt_3 gains Step 28 — (1) STRUCTURE SUCCESS : [formula in source] closed via diagonal Hankel pencil at [formula in source] , [formula in source] , doubling [formula in source] exact second quantisation, carrier [formula in source] silver-midpoint axes, gap [formula in source] ; [formula in source] -scaling [formula in source] pure [formula in source] lattice datum (not continuum); positive clock only for [formula in source] ; (2) CONNECTION KILL : preregistered [formula in source] -candidate census over [formula in source] frozen numbers: [formula in source] hits above null; placebos comparable; (3) cross-link v526: [formula in source] [formula in source] thermal kernel ratio; NO marker moves)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":30411,"byte_start":28775,"id":"section:d9dfc4ce2d7febed0290","kind":"subsection","labels":[],"line_end":271,"line_start":263,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:1b8a8267c538912aa309","relation:3d5201768eef7ca3d5fd","relation:48921e8a47506e3e0acf","relation:5a6ba47a0c7b98e69442","relation:5f76fd5a6145151f2cc1","relation:7d27514b056e7cd48854","relation:878daf98d9fd3f0add25","relation:cd991782c80973250c83","relation:dca65899313e3e7c3e5d"],"semantic_review":false,"source":"documents/changelog/sections/003-source.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"Suite. New module v526_seam_thermal_kms_nariai_bridge.py ( [formula in source] checks, [formula in source] s). Ledger. New row SEAM.THERMAL.KMS.01; no status moves. Papers. tfpt_3 Step 27; tfpt_horizon_readouts (third leg of [formula in source] ); tfpt_research_contracts (thermal follow-on); introduction. Wolfram. Three exact mirrors (Q-polynomial/ [formula in source] measurement; [formula in source] chain; [formula ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-07-23 (IV) ( v526 — the thermal seam promoted as the ledger row SEAM.THERMAL.KMS.01: KMS of the reconstructed free OS quotient CLOSED onto the Nariai/BH temperature chain — the THIRD LEG of [formula in source] ; verdict SUCCESS; the celestial/twistor story in tfpt_3 gains Step 27 — (1) [formula in source] MEASURED [formula in source] at both levels ( [formula in source] : [formula in source] , [formula in source] ; [formula in source] : pairing exponent [formula in source] ; wrong [formula in source] excluded); (2) [formula in source] EXACT [formula in source] , [formula in source] [formula in source] Bisognano–Wichmann/Hawking normalisation ( v208) ; (3) modular Hamiltonian closed ( [formula in source] , [formula in source] ; Tomita KMS- [formula in source] on all [formula in source] pairs); (4) [formula in source] third-leg class- [formula in source] selection / (Hawking/Nariai chain; v104 cross-link); (5) entropy [formula in source] , [formula in source] , horizon fractions do NOT transfer ; (6) -5 silver [formula in source] thermal kernel ratio; non-compact [formula in source] ; NO marker moves)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":35126,"byte_start":30411,"id":"section:0e7ddbc8b9cd02f418a6","kind":"subsection","labels":[],"line_end":293,"line_start":272,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:1330ffc4ffa2c1660822","relation:214b070822ef868c6213","relation:28ff378a58d421798cb9","relation:3d252ff4b2f62a5e831c","relation:447b5961829c4bc57e22","relation:4501d5c49d4ef0df8b7d","relation:4e65d8d8e25b2e2f578e","relation:522ad6bca29f15ff5ffe","relation:76cb9e28071b4cf27114","relation:7a94f674d37656f2a046","relation:8fe03ab26df0e03f2fbf","relation:938ae5cad821b7f460a3","relation:94361270e44002a8fdea","relation:afa001a623a077cd96c0","relation:b4a32773d6c3658d6f81","relation:b8f4e32dc6dfc8f125eb","relation:d5810c131c278bc88008","relation:debb6f7aa74ce5abfbc5","relation:e513ff6b9c8aa6cd68ac","relation:f33d49d794a20a2a8446","relation:f8f85fb1272ed2808cd0","relation:f90a202b77d7f593338f","relation:fe95ad84976b01a3478f","relation:ff338625cae7c032b29d"],"semantic_review":false,"source":"documents/changelog/sections/003-source.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"Suite. New module v525_seam_bit_twist_blind.py ( [formula in source] checks, [formula in source] s; Pfaffian-exact insertion machinery cross-validated three ways, [formula in source] -digit certificates); registered in run_all.py [formula in source] script_registry.csv; suite [formula in source] modules green. Ledger. New row SEAM.BIT.TWISTBLIND.01 (KILL, honest negative, preregistered); SEAM.BIT.RPBLIND.01 and SEAM.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-07-23 (III) ( v525 — the twist-state attack on the alignment bit DECIDED and promoted as the ledger row SEAM.BIT.TWISTBLIND.01: ``mark-decorated states do not see [formula in source] '' — an honest, decided NEGATIVE result (v508 style), the NINTH side-blind test on the v512 scoreboard ( [formula in source] ); the free-plus-twist class (everything Wick-computable) is EXHAUSTED; the celestial/twistor story in tfpt_3 gains Step 26 and the header goes twenty-three [formula in source] twenty-six steps — (1) ALL LIFTINGS WELL-DEFINED AND BLIND : (a) the [formula in source] -gauge arc decoration ( [formula in source] ) satisfies [formula in source] on the swap axes [formula in source] the twisted Gram is a diagonal unitary congruence [formula in source] , spectra IDENTICAL to untwisted (dev [formula in source] ); (b) the Kadanoff–Ceva [formula in source] -twist insertion [formula in source] is well-defined on the [formula in source] ladder ( [formula in source] real nonzero; the [formula in source] odd- [formula in source] degeneration is the [formula in source] checkerboard artifact) and its RP SPECTRA are the FIRST free-class data of the programme that depend on [formula in source] (pairwise up to [formula in source] ) — yet the INERTIA is [formula in source] PD with the same [formula in source] for EVERY [formula in source] : the decoration sees [formula in source] , positivity does not; (c) the [formula in source] twist at [formula in source] is pure plane gauge; (c [formula in source] ) the genuine Bogoliubov defect at [formula in source] : [formula in source] -compatibility selects exactly [formula in source] of [formula in source] sign patterns (NS-wrap-forced), the winner genuinely non-monomial — still PD, spectra identical; STRUCTURE THEOREM (mechanism exact): the defect planes never straddle a cut bond, so every [formula in source] -compatible quasi-free mark decoration is RP-spectrally INVISIBLE; (2) SUB-RESULTS : the defect energy [formula in source] for EVERY [formula in source] (spread [formula in source] ) — [formula in source] -blind; the [formula in source] -twist Casimir [formula in source] measures [formula in source] ( [formula in source] ) but exactly mirror-symmetric under [formula in source] — a family gauge, never a side selector; Kramers [formula in source] for every [formula in source] ; (3) the HARVEST : two bit-presupposing [formula in source] structures (the [formula in source] flip [formula in source] on the mark-fixing axes via [formula in source] ; the twist frustration of the mark-fixing mirror, [formula in source] indefinite for both [formula in source] — the lattice shadow of the Ising twist field's mirror-oddness) — both formulable only on the fixing axes existing iff [formula in source] (the v512 facet class); (4) NEGATIVE CONTROLS : the twist-free limit [formula in source] v519/v521 exactly; the site cut keeps failing; the v512 counterwitness is arc-equivalent at [formula in source] to the blind member [formula in source] — no state selector can exclude it; a single twist has [formula in source] identically; : the door narrows to a genuinely INTERACTING [formula in source] whose OS data are NOT Pfaffian-reducible to the chiral vacuum; Wolfram extension (with v523/v524) [formula in source] (verified engine run 2026-07-23, [formula in source] + base [formula in source] ); suite [formula in source] modules; NO marker moves — the alignment bit remains genuine discrete input)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":39585,"byte_start":35126,"id":"section:f1cafbf24805c6c09d79","kind":"subsection","labels":[],"line_end":314,"line_start":294,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:010e213011123b8118bf","relation:0730bf27099f8d63014d","relation:14361c6ec195a0eccf65","relation:3a1411fe9028c805c868","relation:43963d1a40a5c923d0d5","relation:44249411e4aa43143205","relation:4d05e3573e8effa84606","relation:5f82fc335c18a25c9203","relation:985e96f9e4ecdebadcd6","relation:a5d8167512e4e72e144d","relation:a6569630c3e46e8ef618"],"semantic_review":false,"source":"documents/changelog/sections/003-source.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"Suite. New module v524_woit_beta2_os_quotient.py ( [formula in source] checks, [formula in source] s; exact sympy [formula in source] Pfaffian-Wick [formula in source] [formula in source] -digit inertia certificates); registered in run_all.py [formula in source] script_registry.csv. Ledger. New row WOIT.BETA2.OS.01 (SUCCESS, -typed per precision (iii)); WOIT.OS.TWISTOR.01 claim/canonical status extended ( [formula in","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-07-23 (II) ( v524 — the WOIT- [formula in source] milestone of the OS twistor bridge WOIT.OS.TWISTOR.01 executed and promoted as the ledger row WOIT.BETA2.OS.01: ``the OS quotient of the free system made explicit'' — verdict SUCCESS per the frozen preregistration, -typed per contract precision (iii); the celestial/twistor story in tfpt_3 gains Step 25 — (1) [formula in source] EXPLICIT : [formula in source] ( [formula in source] ): the [formula in source] bond-cut OS Gram exactly Hermitian, parity-block-diagonal, inertia [formula in source] PD (min eigenvalue [formula in source] at [formula in source] digits), null space [formula in source] , [formula in source] ; [formula in source] (complete half algebra): [formula in source] PD (min [formula in source] ), [formula in source] — compact euclidean time reconstructs a THERMAL (KMS) representation; exact certificate [formula in source] ; (2) the TRANSFER SEMIGROUP (Klein–Landau) : [formula in source] exactly Hermitian on all domains ( [formula in source] , dims [formula in source] ), chain identities exact, vacuum fixed; the positivity pattern [formula in source] the site/bond dichotomy: even [formula in source] PSD via the exact square identity [formula in source] ( [formula in source] ), odd [formula in source] indefinite ( [formula in source] ) — the one-step transfer is NOT positive (the chirality datum, kill-3 shadow sharpened), its even powers are; (3) THE CLOCK [formula in source] : [formula in source] : [formula in source] PD [formula in source] (min [formula in source] ), compressed spectrum [formula in source] , vacuum eigenvalue exactly [formula in source] , spectral projections [formula in source] ; [formula in source] : spectrum EXACTLY [formula in source] in both parity sectors — the silver axes of the v519 torsor return as the clock eigenvalue; the reconstructed rotation group [formula in source] unitary with the group law; (4) the v522 RESOLUTION : the census [formula in source] reproduced; EVERY anti-matching entry is a wrap overlap, every overlap-free entry matches — the pre-quotient non-Hermiticity is EXACTLY the domain/wrap artifact; on the quotient the clock has spectral calculus; pre-registered KMS deviation: no contraction on the compact circle ( [formula in source] exactly, [formula in source] ); (5) GSO/ [formula in source] : the grading survives; the perpendicular torsor mirror descends anti-unitarily ( [formula in source] ), [formula in source] on every sector (Kramers-free), [formula in source] exactly; (6) CONTROLS : site cut [formula in source] — the kill branch fires there; family A [formula in source] ; anti-chiral [formula in source] no quotient; wrong direction non-Hermitian (all mismatches wrap-overlap); KILL TESTS: (1)/(2) strengthened, (3) shadow sharpened, none fires, all seven stay live on [formula in source] ; TRANSPARENCY: run 1 [formula in source] (a sympy simplify failure on a TRUE [formula in source] product formula, fixed by a Laurent-polynomial certificate; no criterion changed); NO marker moves — WOIT.OS.TWISTOR.01 stays Open, [formula in source] is next)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":44195,"byte_start":39585,"id":"section:26516787d04ebc9e58b3","kind":"subsection","labels":[],"line_end":336,"line_start":315,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:15fadd62d454ffb347e7","relation:2b73e87ea8d88af43b38","relation:3cda24a54d8e3fb4ac6a","relation:4a51369cedba1203ce8a","relation:560933a862c6662670f8","relation:6197b27c3762856e996a","relation:710c439f0dc12a3fc009","relation:79115085def9bcf0d4bc","relation:7f8a254566cfc0de4cd2","relation:bc85bcb887d5c82b7424","relation:cd5b2ae464b738aad00f","relation:d5e5be24629dc08d36d4","relation:deb6d706e6194dce9d8e","relation:f36a9a1f23c3d79cb8d4"],"semantic_review":false,"source":"documents/changelog/sections/003-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Suite. New module v523_celestial_wp5e_wm_derived.py ( [formula in source] checks, [formula in source] s; exact [formula in source] / [formula in source] /cyclotomic arithmetic [formula in source] [formula in source] -digit Hurwitz/block certificates); registered in run_all.py [formula in source] script_registry.csv. Ledger. New row CELEST.WP5E.WM.01 (ERFOLG); the v516 row CELEST.WP5E.M2.01 and the v520 row CELEST.WP5","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-07-23 (I) ( v523 — the constructive [formula in source] derivation executed and promoted as the ledger row CELEST.WP5E.WM.01: `` [formula in source] is the Atiyah–Bott / zeta-determinant fixed-point factor, COMPUTED from three independent sources'' — verdict ERFOLG per the frozen preregistration; the residual \\ of v516/ v520 is closed at the fibre-zero-mode level and narrows to the GLOBAL BCOV integral on [formula in source] beyond the fibre zero-mode factor; the celestial/twistor story in tfpt_3 gains Step 24 — (1) ATIYAH–BOTT (route i) : the equivariant mode ledger of the fibre [formula in source] equals the closed form [formula in source] exactly in [formula in source] for all [formula in source] ; REGULAR at [formula in source] with Abel value [formula in source] , [formula in source] ; [formula in source] Ces\\`aro convergence in exact arithmetic; fixed-point splitting at EVERY truncation level [formula in source] for the phased (skeleton) AND the v520-forced unphased (completion) trace — the Abel-limit [formula in source] is the v516 contact vector COMPUTED, not declared; (2) ZETA/QUILLEN (routes ii/iii) : [formula in source] of the [formula in source] -twisted circle Laplacian [formula in source] EXACTLY (Lerch [formula in source] reflection formula symbolically, Hurwitz certificates [formula in source] ); Quillen split [formula in source] , [formula in source] , the real positive holomorphic section UNIQUE via the [formula in source] conjugation pairing; the [formula in source] [formula in source] block at the [formula in source] nodes carries the exact constant term [formula in source] (deviations [formula in source] ); (3) the CONSISTENCY CHAIN : [formula in source] ; [formula in source] at every scale; [formula in source] ; the [formula in source] budget [formula in source] forces [formula in source] uniquely (leftovers [formula in source] ); per-sector Okubo squares [formula in source] ; total [formula in source] ; [formula in source] , [formula in source] ; [formula in source] , [formula in source] ; (4) NEGATIVE CONTROLS : [formula in source] gives [formula in source] , leftovers [formula in source] , Quillen contradiction; [formula in source] gives [formula in source] ; the [formula in source] /Eguchi–Hanson anchor PASSES with the same derivation ( [formula in source] , [formula in source] , [formula in source] , [formula in source] ); the [formula in source] KILL fires; [formula in source] breaks the zeta [formula in source] AB identity itself; [formula in source] : [formula in source] — the weights wander correctly, only [formula in source] carries the [formula in source] chain; TYPED PREMISES \\ (the mandatory fence): TP-REG (Abel/Ces\\`aro/zeta regularisation [formula in source] the definition of the equivariant character), TP-Q (Quillen structure of BCOV [formula in source] [formula in source] v520 TP-4), TP-NUM (unphased numerator [formula in source] v520 ERFOLG-A), TP-CH (insertion channel [formula in source] ); : the global BCOV integral beyond the fibre zero-mode factor, the resolved-ALE route not built, SEAM.EQUIV.TWISTOR.01 stays Open; NO marker moves)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":46809,"byte_start":44195,"id":"section:64f2a1b29cd0df071dd4","kind":"subsection","labels":[],"line_end":351,"line_start":337,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:00c9b2cd6bf9fd37f126","relation:28f0f8b01b038c7bbf97","relation:83cab43ef9d5faaaffe0","relation:935bb320c4f9d5eb3bee","relation:c1fd7e5b1fd85899c930"],"semantic_review":false,"source":"documents/changelog/sections/003-source.tex","status_markers_as_written":[],"summary_excerpt":"Scorecard. New row ``BH HFQPO third-tooth extension on non-RXTE archives'' (NICER/MAXI J1820+070 plus AstroSat/LAXPC; hfqpo-ladder extension) in the generator experiments/build_evidence_scorecard.py (status null, stage search_target, signature S1e); OVERRIDES give both HFQPO rows the shared independence_group hfqpo_ladder_tooth; generator re-run: evidence_scorecard.json [formula in source] rows, README stats block re","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-07-22 (XIII) (HFQPO scorecard extension — the NICER/MAXI J1820+070 third-tooth null and the AstroSat/LAXPC block integrated as a new evidence-scorecard row (search target, never a claim): the preregistered single-QPO extension of the H3 ladder discriminator (frozen hypotheses/hfqpo_ext_v1.yaml BEFORE any photon download) ran on [formula in source] NICER ObsIDs ( [formula in source] GB, [formula in source] s [formula in source] ks stack at [formula in source] kc/s) — sanity gate PASS (the published [formula in source] Hz anchor reproduced at [formula in source] Hz, [formula in source] rms, [formula in source] ), injection calibration PASS ( [formula in source] recovery at [formula in source] rms), the geometric tooth at [formula in source] Hz NOT detected ( [formula in source] single-trial; [formula in source] upper limit [formula in source] rms BELOW the detected anchor strength [formula in source] null_with_sensitivity), the integer line at [formula in source] Hz at [formula in source] after trials — BELOW the preregistered [formula in source] threshold, documented as a sub-threshold excess consistent with the weak second harmonic of ATel \\#11951, NOT a hit; AstroSat/LAXPC (GRS 1915+105, scientifically the strongest channel) infrastructure_blocked (ISSDC login-gated); the RXTE [formula in source] NICER nulls now cover five sources on two instruments — the tooth channel is recommended DORMANT; anti-double-counting: the parent RXTE row and the new extension row share independence_group hfqpo_ladder_tooth (one hypothesis, two instruments, never two independent nulls); scorecard regenerated ( [formula in source] rows), predictions.txt HFQPO row extended (``Kanal ruhend''); experiment-only integration — no verification claim, no marker moves)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":52409,"byte_start":46809,"id":"section:e8fb60dc4323384272d7","kind":"subsection","labels":[],"line_end":382,"line_start":352,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:33da9ed7338dedad60ab","relation:3db12096a92894548c14","relation:3fa09e6335c6bbdff497","relation:82a36d78209e4d58389f","relation:831f293ed6db247267ea","relation:9f3e20200edb6658ba1b","relation:a58ee6ed08f976a23937","relation:b8912eb0c1a5dc93da4c","relation:ba6c9ed1ab92924cb7f9","relation:d70c84803823d707f251","relation:d8dbdf2e5ae75a4c156a","relation:df496394e7f7bc9bdb68","relation:f4ec2d5bd3305e74a243","relation:fcda195b67c3b693cf1a"],"semantic_review":false,"source":"documents/changelog/sections/003-source.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"v522_woit_beta1_gso_gauge.py ( WOIT.BETA1.GSO.01, 16 checks, [formula in source] 5 s; exact sympy Pfaffian–Wick [formula in source] exact [formula in source] Fractions; definiteness via [formula in source] -digit spectra, tolerance [formula in source] ; deterministic). G1 the gauge datum (Z8/NS tower, Ramond control, invariant dimensions [formula in source] ); G2 [formula in source] normalises the tower and restricts","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-07-22 (XII) ( v522 — the WOIT- [formula in source] milestone of the OS twistor bridge WOIT.OS.TWISTOR.01 executed and promoted as the ledger row WOIT.BETA1.GSO.01: ``the clock is time-like, GSO is the gauge datum'' — a TYPED result (verdict UNDECIDED per the frozen preregistration, the mechanism identified exactly, gauge-fixed RP established under the corrected typing; the celestial/twistor story in tfpt_3 gains Step 23) — (1) the HERMITICITY WITNESS : the [formula in source] clock average violates Hermiticity EXACTLY (the one-step insertion [formula in source] has entry [formula in source] where the conjugate transpose demands [formula in source] ; entrywise census [formula in source] Hermitian-matching, [formula in source] ANTI-matching, [formula in source] violations — the pairing is complex-SYMMETRIC, strictly weaker than Hermitian: ``positivity after gauge fixing'' is not well-posed for the clock reading); (2) TIME-LIKE TYPING : ALL [formula in source] dihedral reflection axes of the NS seam circle invert the clock lift ( [formula in source] ), NONE commutes — the [formula in source] clock IS Woit's euclidean rotation; the gaugeable ( [formula in source] -compatible) part of the [formula in source] Fock tower is EXACTLY its [formula in source] -torsion [formula in source] [formula in source] the GSO/fermion-parity [formula in source] (Hermiticity census over all powers; [formula in source] the full wrap [formula in source] the [formula in source] rotation of the seam [formula in source] fermion parity); (3) the POSITIVE PART : GSO-fixed RP holds EXACTLY — [formula in source] even [formula in source] parity-projected bond-cut Gram [formula in source] PD (min eigenvalue [formula in source] at [formula in source] digits), [formula in source] complete half algebra: all odd rows/columns killed exactly, even block [formula in source] PD ( [formula in source] ), no degree truncation; the site-cut defect SURVIVES gauge fixing ( [formula in source] — the bond placement is gauge-invariant information); family A keeps failing ( [formula in source] indefinite vs family D's [formula in source] ); Kramers: [formula in source] on [formula in source] , [formula in source] restricts with [formula in source] ; Ramond control: the wrap [formula in source] ``true [formula in source] '' lift fails state invariance — the NS/ [formula in source] tower is forced; (4) KILL-TEST BOOKKEEPING: kill test (2)'s free shadow does NOT fire (no legitimate Hermitian gauge-fixed form has a negative direction), kill test (1) stays discharged also gauge-invariantly; both stay formally live on [formula in source] ; (5) TRANSPARENCY: the first frozen run scored [formula in source] (the clock-reading checks failed exactly as the mechanism predicts) and the preregistered deg-2 invariant dimension [formula in source] was a combinatorial error (correct census [formula in source] ) — documented in full, the verdict by the frozen [C-3] logic (Hermiticity failure [formula in source] UNDECIDED); CONTRACT PRECISION (iii) (prose, no marker): ``gauge-invariant subalgebra'' at the free level means the GSO/fermion-parity [formula in source] — the only [formula in source] -compatible part of the [formula in source] tower; the clock is the euclidean rotation itself (timelike), its equivariant statement moves to [formula in source] (OS quotient first, then the clock as reconstructed transfer operator); Wolfram extension (with v520/v521) [formula in source] (verified engine run); NO marker moves — WOIT.OS.TWISTOR.01 stays Open, [formula in source] proper re-routed via [formula in source] )","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; 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exact sympy solvesets [formula in source] exact Gram entries [formula in source] exact [formula in source] Fractions; inertia via [formula in source] -digit spectra, tolerance [formula in source] ; deterministic). S the anti-linear census (family D/A, counterwitness, face \\#13 closure, cut incidence, side conditions); L the lattice ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-07-22 (XI) ( v521 — the RP/ [formula in source] attack on the alignment bit DECIDED and promoted as the ledger row SEAM.BIT.RPBLIND.01: ``free OS positivity does NOT see [formula in source] '' — an honest, decided NEGATIVE result in the v508 style (the celestial/twistor story in tfpt_3 gains Step 22): does free reflection positivity ( v519) or anti-linear [formula in source] existence break for [formula in source] on the deformed mark family [formula in source] — which would DERIVE the v512 alignment bit from OS positivity? NO — (1) the CENSUS \\ (exact solvesets, symbolic [formula in source] ): for EVERY [formula in source] exactly the two mark-SWAPPING reflections [formula in source] exist (axes [formula in source] , [formula in source] ; all [formula in source] cut/mark incidence solvesets EMPTY); mark-FIXING reflections exist exactly at [formula in source] (solveset [formula in source] , lost immediately at [formula in source] ); the v510/ v512 counterwitness [formula in source] carries the swap pair exactly; (2) RP IS [formula in source] -BLIND : bond-cut Gram inertias [formula in source] PD for all tested [formula in source] with the full sorted spectra IDENTICAL to [formula in source] digits (deviation [formula in source] ) — the ENTIRE free-RP spectral datum carries ZERO [formula in source] information; the [formula in source] odd- [formula in source] failure (site axes, [formula in source] , [formula in source] ) is a lattice-PLACEMENT artifact: at [formula in source] ALL [formula in source] have mark-compatible BOND axes with PD inertia [formula in source] ; continuum: the OS kernel in axis-adapted coordinates is EXACTLY [formula in source] — the axis position drops out identically (Cauchy–Stieltjes PD); the counterwitness PASSES free RP ( [formula in source] -point Gram [formula in source] ); (3) [formula in source] EXISTENCE IS [formula in source] -BLIND : [formula in source] , deck normalisation and Fock implementability ( [formula in source] , exact [formula in source] ) for every [formula in source] ; the ONLY [formula in source] -sensitive v519 clause ( [formula in source] ) is for [formula in source] not violated but NOT FORMULABLE (a mark-compatible order- [formula in source] rotation exists iff [formula in source] ) — it PRESUPPOSES the bit; same for the clock-tower clause; (4) the battery HAS TEETH at every [formula in source] : family A/antipode fails RP structurally (zero diagonal, [formula in source] ), the chirality– [formula in source] pinning persists ( [formula in source] ND) — RP separates the two real-structure FAMILIES, never the SIDES; (5) precondition controls: hexagonal (marks not concyclic — no seam circle), silver (deck not free), lifting audit (B [formula in source] index relabelling, [formula in source] -blind by construction; B' fails the [formula in source] negative control — discarded); \\ FACE \\#13 of the v512 equivalence web: the group generated by the admissible OS reflections is [formula in source] for every [formula in source] and closes to [formula in source] exactly at [formula in source] ( [formula in source] the clock) — [formula in source] faces, a typed REFORMULATION of the bit, not a derivation; \\ the honest gap: marks decorating the STATE (defect/twist insertions, interacting [formula in source] ) [formula in source] exactly v519's \\ scope; VERDICT: KILL exactly as preregistered — the free RP/ [formula in source] battery is the EIGHTH side-blind test on the v512 scoreboard ( [formula in source] ); the alignment bit is NOT derivable from OS positivity and remains genuine discrete input; NO marker moves — the bit stays the one \\ carrier input)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; 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exact [formula in source] /Fraction/sympy rational nullspaces [formula in source] 1/960-grid phase arithmetic [formula in source] mpmath 30-digit kernels [formula in source] numpy double SVD, deterministic). S0 exact foundations (roots, ledgers, A-core [formula in source] [formula in source] -anchor targets, Weil re","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-07-22 (X) ( v520 — the WP5e BCOV measure question DECIDED at probe level and promoted as the ledger row CELEST.WP5E.MEASURE.01: ``single-valuedness is derived, the completion reading wins'' — the [formula in source] consolidation in the v518 style, ERFOLG-A on the preregistered decision layer (the celestial/twistor story in tfpt_3 gains Step 21): which of the two exact, contradictory measures on [formula in source] is the true BCOV measure — (A) the DECLARED completion reading ( v516) or (B) the DERIVED chiral measure ( v518)? — (1) the INVARIANT SUBSPACE : [formula in source] in the dressed [formula in source] -component Weil system (exact rational nullspace); EVERY kernel vector lies in the [formula in source] -span of [formula in source] — the two Lagrangian gluings, both theta [formula in source] , level-1 quartic [formula in source] the UNPHASED trace; strict trivial-character solutions at physical weight [formula in source] : ZERO for every dressing ( [formula in source] combinations); (2) SOURCE 1 — the F-LEMMA : the only strict chiral families are [formula in source] (dims [formula in source] ) and [formula in source] (dims [formula in source] ), both with nontrivial [formula in source] -character EXACTLY; the canonical column-matched member obeys [formula in source] pointwise (certificate [formula in source] , [formula in source] ); EXACT change of variables [formula in source] fundamental-domain independence forces [formula in source] for EVERY chiral integrand: the v518 route was never a well-defined nonvanishing moduli integral (the kill is SHARPENED — its unfolded values are convention bookkeeping); (3) SOURCE 2 — the QUILLEN PAIRING : [formula in source] on all [formula in source] pairs and both generators; [formula in source] exactly vs one-sided [formula in source] ( [formula in source] -fixed: [formula in source] , [formula in source] defective); the doubled [formula in source] -dim hol [formula in source] antihol system closes STRICTLY at trivial character and physical weight (nullspaces [formula in source] ), contains the unphased diagonal ( [formula in source] ) AND the physical columns [formula in source] ( [formula in source] [formula in source] ); negative control hol [formula in source] hol: EMPTY nullspace [formula in source] ; (4) the CONSISTENCY CLOSURE : the forced unphased numerator in the v518 scaffold reproduces [formula in source] EXACTLY on every level [formula in source] ; [formula in source] -weighted spreads [formula in source] , [formula in source] , zero negative cells; [formula in source] — the [formula in source] -weighted mirror image of [formula in source] / [formula in source] ; linearity [formula in source] : the circle to v516 is CLOSED; (5) D3 — the [formula in source] /EH ANCHOR : only the declared reading hits ( [formula in source] , [formula in source] , scale tooth [formula in source] ); all three derived instantiations fail (spreads [formula in source] , [formula in source] sign wrong); (6) D1 — COLUMN CANONICALISATION : the physical AB column [formula in source] is contained EXACTLY in the [formula in source] family ( [formula in source] [formula in source] , one scalar per orbit — canonicalising [formula in source] ); the canonical member STILL fails every tester; NEGATIVE CONTROLS: [formula in source] ( [formula in source] / [formula in source] exact, [formula in source] -only), wrong form ( [formula in source] ), wrong weight (dev [formula in source] ), shuffle ( [formula in source] / [formula in source] ), planted family detected ( [formula in source] ), hol [formula in source] hol empty; \\ TYPED PREMISES (the mandatory fence): TP-1 (F-independent moduli integral), TP-2 (nonvanishing — must source [formula in source] ), TP-3 ( v518 kernel convention), TP-4 (Quillen structure of BCOV [formula in source] ); \\ the constructive BCOV derivation of the [formula in source] normalisation itself; WIRKUNG (text only, no marker moves): the v516 fence and the v518 tension now read ``decided at probe level for the declared reading under TP-1..TP-4 (v520)''; SEAM.EQUIV.TWISTOR.01 stays Open; VERDICT ERFOLG-A per the preregistered criteria — both constructive sources fire independently, the consistency closure carries)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; 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exact sympy [formula in source] exact [formula in source] Fractions; RP definiteness via [formula in source] -digit spectra of exact Hermitian matrices, tolerance [formula in source] ; deterministic). Part W: W-S1 the two-family classification (symbolic solve); W-S2 family D (relations, Kramers-free, mark pinning, seam action, torso","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-07-22 (IX) ( v519 — the WOIT- [formula in source] milestone of the OS twistor bridge WOIT.OS.TWISTOR.01 executed and promoted as the ledger row WOIT.THETA.FREE.01: ``the real structure exists — and free reflection positivity picks the same family''; the celestial/twistor story in tfpt_3 is now TWENTY steps — (1) THETA CLASSIFICATION COMPLETE : exactly TWO families of anti-linear structures on [formula in source] normalise the clock [formula in source] — family D ( [formula in source] , [formula in source] ): [formula in source] EXACTLY at matrix level, [formula in source] ( [formula in source] IMPOSSIBLE: [formula in source] — Kramers-free), inverts the deck, fixed set [formula in source] the great circle through the deck poles; family A ( [formula in source] ): centralises the clock projectively (NEVER inverts it), [formula in source] per [formula in source] , fixed set [formula in source] resp.\\ empty; ROLE SEPARATION: family A DEFINES the euclidean section (Woit's [formula in source] side: [formula in source] , no real points — replicated exactly on [formula in source] ), family D REFLECTS it (the OS conjugation, [formula in source] conjugation with real points [formula in source] ); (2) MARK PINNING : [formula in source] preserves the [formula in source] marks iff [formula in source] — a [formula in source] -element [formula in source] -TORSOR ( [formula in source] mark axes, [formula in source] silver-midpoint axes), clock conjugation [formula in source] [formula in source] [formula in source] clock orbits; (3) SPIN/FOCK : the [formula in source] plane has no phase leaks ( [formula in source] ); exact [formula in source] : [formula in source] with [formula in source] (normalised [formula in source] ), inverts the clock tower ( [formula in source] ) and normalises the deck; the KRAMERS DICHOTOMY: the deck-induced candidate [formula in source] has [formula in source] — the v510 split/nonsplit dichotomy IS the [formula in source] vs [formula in source] dichotomy; the deck does NOT furnish [formula in source] , the seam-circle REFLECTION does; (4) KILL TEST 1 (free level) : does NOT fire — [formula in source] exists with [formula in source] AND [formula in source] and satisfies all three side conditions simultaneously (marks, deck normalisation, spin/Fock); (5) FREE RP : the NS vacuum [formula in source] has [formula in source] exactly; preconditions exact ( [formula in source] , [formula in source] , [formula in source] ; the deck FAILS anti-invariance); BOND CUT: one-particle Gram [formula in source] PD (min eigenvalue [formula in source] , [formula in source] digits), even [formula in source] sector [formula in source] PD, [formula in source] complete half-sided algebra PD (even [formula in source] odd each [formula in source] ) — RP with NO degree truncation; twist [formula in source] FORCED ( [formula in source] non-Hermitian); CONTROLS: the site cut fails exactly ( [formula in source] , inertia [formula in source] ; continuum control: Cauchy–Stieltjes strictly positive — a lattice-PLACEMENT artifact, RP selects the site placement relative to the marks); the clock-CENTRALISING family-A structure fails RP structurally ( [formula in source] ) — RP and [formula in source] select the SAME family; bonus: the anti-chiral state flips the odd sector to [formula in source] ND (the free shadow of kill test 3); / \\ NOT shown: the interacting algebra [formula in source] (kill test 1 stays live there), gauge-fixed RP (kill test 2), OS reconstruction, chirality without mirrors (kill tests 3/6), [formula in source] incidence (kill test 7) — the WOIT- [formula in source] / [formula in source] roadmap named ( [formula in source] [formula in source] on the gauge-invariant subalgebra [formula in source] gauge-fixed RP on the equivariant SDYM [formula in source] sector; [formula in source] the OS quotient of the free system explicit; [formula in source] the [formula in source] duality vs [formula in source] typed; [formula in source] the chirality theorem [formula in source] the mark incidence); TWO CONTRACT PRECISIONS (prose, no marker): (i) `` [formula in source] induced by the seam reflection'' means the seam-circle REFLECTION, not the deck — the deck furnishes the [formula in source] Kramers class (the v510 bridge); (ii) the marks sit RP-side on the BOND MIDPOINTS of the [formula in source] -Majorana circle; Wolfram extension [formula in source] (verified engine run); NO marker moves — WOIT.OS.TWISTOR.01 stays Open: kill test 1 is discharged on the FREE level only and stays formally live on the interacting algebra)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":30304,"byte_start":21421,"id":"section:6ddf4757acde55521050","kind":"subsection","labels":[],"line_end":174,"line_start":124,"numbered_or_version_tokens_as_written":["E1.5"],"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:05dc9a0e803fefc05e00","relation:082737b9b02f571abd44","relation:0c8122bc2cd84ce6adbc","relation:12e015b5f63356a01d21","relation:34d2c9036784848319b7","relation:38d80b8a8916347dd7b2","relation:52c188b487a75270142c","relation:5d5329bd2d4cc2272df4","relation:61fbf4c5679a7e9185d3","relation:70c211538b396f19cb64","relation:78443d0a8bb27bb621dc","relation:83c7b05eb1afbaffc5b0","relation:85ffd60e08c37ef24c97","relation:895e61f034687a755dac","relation:a3d10a9f9df046705c1a","relation:a6aa829827558d5feda1","relation:a796b4e6c86b0948c737","relation:b82fa68bc5e3e6e70ae1","relation:be3f0efa7b780be1c400","relation:c44c698e71af82f1bf28","relation:d5c33fba19ea5c41c3ea","relation:d7e54985ec7f1239e1eb","relation:e1ade465ced85fd3394c","relation:e6e25f6cd7391b1fbdd9","relation:f50d61f4ee1d4a52a04a","relation:f871095370494735fe5c","relation:fda184df716cde454897"],"semantic_review":false,"source":"documents/changelog/sections/004-source.tex","status_markers_as_written":["[O]","\\mC","\\mO"],"summary_excerpt":"v518_celestial_wp5e_delta1_derived_kill.py ( CELEST.WP5E.DELTA1.01, 30 checks, [formula in source] 20 s; exact [formula in source] /Fraction/1-960-grid phase arithmetic [formula in source] mpmath 30-digit kernels [formula in source] numpy double SVD, deterministic). S0 conventions [formula in source] 16-class ledgers [formula in source] targets; S1 the 16-component Weil system (exact) [formula in source] the E1.5 clo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"=150 2026-07-22 (VIII) ( v518 — the WP5e [formula in source] chain ( [formula in source] ) DECIDED and promoted as the ledger row CELEST.WP5E.DELTA1.01: ``the derived chiral measure kills the [formula in source] route'' — an honest, decided NEGATIVE result in the v508 style, with the v516 tension stated: does the Harvey–Moore/BCOV fundamental-domain integral on [formula in source] , evaluated under a measure DERIVED from blockwise [formula in source] covariance of the dressed [formula in source] -component Weil system (solved for — not declared, not scanned), deliver the twisted contact vector [formula in source] or the [formula in source] slice? NO — (1) the 16-COMPONENT WEIL COMPLETION ( [formula in source] ): the discriminant module of [formula in source] is [formula in source] with [formula in source] , Gauss sums [formula in source] (signature [formula in source] rank [formula in source] ), the Weil relations hold EXACTLY in [formula in source] ( [formula in source] , [formula in source] , [formula in source] , [formula in source] , tensor split [formula in source] ), the diagonal [formula in source] and anti-diagonal [formula in source] are the two invariant Lagrangians (both counts [formula in source] : two [formula in source] gluings), [formula in source] with [formula in source] of every [formula in source] -image weight on the [formula in source] shifted classes, and the [formula in source] -vector theta [formula in source] -covariance CLOSES: the [formula in source] E1.5 residual [formula in source] (naive [formula in source] -character rule) drops to [formula in source] ; (2) the OBSTRUCTION IS A FINITE [formula in source] CHARACTER, IDENTIFIED ( [formula in source] ): the dressed gauge blocks [formula in source] carry constant transport [formula in source] ( [formula in source] + digits, recognised as exact [formula in source] -grid phases at [formula in source] ), the [formula in source] -fixed pairs [formula in source] carry [formula in source] EXACTLY (the naked level-matching defect), the transport-groupoid loops land in [formula in source] resp.\\ [formula in source] with joint holonomy eigenspaces dim [formula in source] resp.\\ [formula in source] and every eigen-phase of order [formula in source] ; the KOBOUNDARY TEST: the [formula in source] relation defects [formula in source] , [formula in source] , [formula in source] are [formula in source] EXACTLY on all [formula in source] pairs — the multiplier system is a CHARACTER of the orbit stabilisers, NOT a genuine 2-cocycle, and on [formula in source] it is [formula in source] ; (3) the CANCELLATION EXISTS AND IS THE TWISTED FIBRE BLOCK [formula in source] , NOT THE THREE SPHERE AXIONS: [formula in source] is an exact identity ( [formula in source] + digits; the axion [formula in source] -phases are v502 vacuum-energy data), the T-fix mechanism is one line of exact phase arithmetic — [formula in source] at every [formula in source] -fixed node — and the exact CANCELLATION TABLE reads: none [formula in source] residual order [formula in source] , [formula in source] (the three sphere axions) [formula in source] , [formula in source] , [formula in source] (hol AND anti), wrong weights [formula in source] ; the strict solutions are exactly [formula in source] (dims [formula in source] ) and [formula in source] (dims [formula in source] ) at [formula in source] , certified on the dressed functions at a fresh [formula in source] ( [formula in source] , NO residual multiplier); (4) the DECISION — ALL THREE PREREGISTERED TESTERS FAIL: under both derived solutions the integral ( [formula in source] -digit kernels, negative-exponent cell audit, cut-6 vs cut-8 scan) fails [formula in source] (fractions [formula in source] / [formula in source] ), fails [formula in source] ( [formula in source] ), fails [formula in source] (spreads [formula in source] / [formula in source] ) and the [formula in source] slice, and the honest [formula in source] orbit rebalance rescues nothing in the positive cone ( [formula in source] : [formula in source] only at [formula in source] ; [formula in source] : only at [formula in source] ) — a GENUINE KILL on the derived surface; (5) NEGATIVE CONTROLS: [formula in source] /Eguchi–Hanson (gauge-only residual order [formula in source] — the [formula in source] defect is [formula in source] -specific — and the SAME fibre dressing cancels it to [formula in source] ), [formula in source] (only even sectors, all axion [formula in source] -characters in [formula in source] : the order-4 supply structurally absent), wrong form [formula in source] ( [formula in source] , its [formula in source] -rule fails at [formula in source] ), wrong signature ( [formula in source] exactly); \\ the [formula in source] KS-weight identification (deck weights [formula in source] the twistor fibre weights forced by the v514 incidence ledger — exact match, NOT a complete BCOV derivation) [formula in source] the kernel-family convention [formula in source] the discrete [formula in source] choice (both evaluated, both fail); the MANDATORY TENSION FENCE: the DECLARED completion reading ( v516/M2) delivers the [formula in source] slice and cancels [formula in source] ; the DERIVED chiral measure (this module) fails all three testers — both are exact; the sharp open question is which of the two is the true BCOV measure — neither result is hidden behind the other; \\ the BCOV-integral derivation on [formula in source] that decides between the two measures; Wolfram extension [formula in source] (verified engine run); NO marker moves — the [formula in source] route is decided negative under the derived measure, the cubic-GS question stays dissolved, SEAM.EQUIV.TWISTOR.01 stays Open, SEAM.EQUIV.01 untouched)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":37145,"byte_start":30304,"id":"section:e992bd516774ac42110f","kind":"subsection","labels":[],"line_end":211,"line_start":175,"numbered_or_version_tokens_as_written":["S6.3","S8.3"],"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:15fa2a46a5d052e33671","relation:2f7ea11a5496428c43d4","relation:39e0cf84a8c3edc00393","relation:3df11f366df8dc6f9c9c","relation:4462602278741bdc685c","relation:4ecc7152d6de366f7ae1","relation:511950a60cdd1049b8c5","relation:56756e12e35c1eac0e27","relation:5696bef9d0e4ba9cc22f","relation:8309d128bc33dc822081","relation:83d0d0434702e8400951","relation:8b4497924fd633121176","relation:90bb02c8130728b55482","relation:9134427c6dbd3130e1ba","relation:9835fd9485fca53d74b5","relation:9e2979b904cdd0969107","relation:b1ee95b396023247ac96","relation:b691d23ab0efdc34b19b","relation:b836d2c8766795f2b999","relation:ba0ef50bec2dffb49b8d","relation:dd602049ff84e4e00964","relation:e35889b004ebf7f1b6fa","relation:eef53ce3636e3624c6ed"],"semantic_review":false,"source":"documents/changelog/sections/004-source.tex","status_markers_as_written":["\\mC","\\mO"],"summary_excerpt":"v517_celestial_wp5e_m3_a0_uplift.py ( CELEST.WP5E.M3.01, 23 checks, [formula in source] 7 s; exact sympy, no floats; deterministic). S0 replication (GH multipole ledger [formula in source] the twistor family at general orbit phase, v515 slice); S1 the kernel bridge (null coordinate, residue [formula in source] -ledger identity, source flux); S2 the uplift (asymptotic log [formula in source] , seam-fibre correction [f","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-22 (VII) ( v517 — WP5e back-reaction milestone M3 ``the [formula in source] uplift'' executed (SUCCESS on the preregistered v514 S8.3 criterion), promoted as the ledger row CELEST.WP5E.M3.01: the [formula in source] GH multipole ( [formula in source] the [formula in source] direction) is uplifted to the twistor-potential kernel [formula in source] — the LOG of the v515 family polynomial — and the induced K\\\"ahler-potential correction is a log-type correction COUPLED TO THE CENTRE COUNT ON FOUR SCALES — (1) the KERNEL BRIDGE: the [formula in source] section is a NULL coordinate ( [formula in source] identically for an ARBITRARY kernel [formula in source] : the uplift is well-typed), the RESIDUE IDENTITY [formula in source] holds EXACTLY (residue [formula in source] ), so the GH potential [formula in source] IS the [formula in source] -derivative of the contour transform of [formula in source] ; flux [formula in source] per centre, source charge [formula in source] (the [formula in source] -ledger matched); (2) the ASYMPTOTIC KERNEL LOG: [formula in source] with LOG COEFFICIENT [formula in source] centre count (the CPS `` [formula in source] '' analogue at kernel level); at the clock-fixed seam fibre [formula in source] the [formula in source] slot closes and the first correction is EXACTLY [formula in source] the [formula in source] multipole in kernel clothes; exact [formula in source] -grading ( [formula in source] pieces PURE [formula in source] , [formula in source] piece [formula in source] [formula in source] -free: the [formula in source] breaking sits exclusively in the [formula in source] pieces); NO [formula in source] power terms (the v514 honest zero preserved — the [formula in source] correction is power-law at infinity); the once-integrated GLT tower [formula in source] with [formula in source] unless [formula in source] and [formula in source] : EVERY correction carries the prefactor [formula in source] centre count; (3) the EXCEPTIONAL-LOCUS LOG: [formula in source] ( [formula in source] -coefficient [formula in source] , clock phase [formula in source] ); the modulus response [formula in source] equals [formula in source] AT the exceptional locus and falls off as [formula in source] at infinity (no constant, no log): the [formula in source] -log lives at the exceptional locus, exactly as v514 S6.3 demanded; (4) the PERIOD RESPONSE: [formula in source] is LINEAR in [formula in source] (uniform first-order shift: lockstep [formula in source] phase ratios [formula in source] preserved exactly), [formula in source] uniformly, and the integrated shift around the [formula in source] circle is the monodromy [formula in source] ONE Coxeter clock step (the v493 monodromy REPRODUCED from perturbation theory; the finite monodromy is the cyclic centre permutation [formula in source] ); the node [formula in source] -support is [formula in source] -FREE (the [formula in source] seam bridge is [formula in source] -rigid), all [formula in source] pair discriminants [formula in source] ( [formula in source] connectivity: the forced uniform flux vector persists), the BM kernel is modulus-free with [formula in source] (the quantised fluxes cannot move); (5) NEGATIVE CONTROLS: the [formula in source] multipole is [formula in source] -independent in [formula in source] AND in the kernel (clock-invariant, breaks nothing); the [formula in source] /Eguchi–Hanson analogue reads [formula in source] on EVERY dial ( [formula in source] amplitude [formula in source] , kernel log [formula in source] , exceptional log [formula in source] , response [formula in source] , monodromy [formula in source] ); wrong centre counts [formula in source] : kernel log coefficient [formula in source] , modulus slot [formula in source] — the observable MOVES with the centre count; forbidden family [formula in source] : [formula in source] (selection rule broken), [formula in source] (no [formula in source] -log) — fails BOTH uplift dials; \\ the GLT dictionary ( [formula in source] the GH K\\\"ahler-potential kernel, Lindstr\\\"om–Ro cek / Ivanov–Ro cek); \\ the full nonlinear K\\\"ahler potential of the resolved [formula in source] ALE; with v516 the v514 fence M1–M3 is FULLY WORKED OFF; Wolfram extension [formula in source] (verified engine run); NO marker moves — the KILL (decoupling from the centre count) does NOT fire, SEAM.EQUIV.TWISTOR.01 stays Open (preparation, not construction), SEAM.EQUIV.01 untouched)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":43676,"byte_start":37145,"id":"section:e01862309e920e04fb7f","kind":"subsection","labels":[],"line_end":244,"line_start":212,"numbered_or_version_tokens_as_written":["S3.8","S4.3","S8.2"],"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0701a0c564ba840bd852","relation:26890da24a68bd9764df","relation:293d4f20adbc7e68b011","relation:2f47d079018df353e968","relation:317c751a747f13f17db4","relation:386f9e417e08a56d8ef1","relation:39e2c9f45c16e1bbb879","relation:3f83df784a1001e76238","relation:438397e99c7b60b86d1a","relation:4b0f89ea7c2b32154f1a","relation:4daa4e68f3b02a29bb6c","relation:570cb032c67c718327cd","relation:5fbeccd9d711bc6d3473","relation:6e5fa2e818b1d05ffc5f","relation:72fc36c565b60a35ea56","relation:76de2b0ac7c81d133a4b","relation:7a183b3af31255add553","relation:837428e59b5dc1ac9fdf","relation:93ca6808cd05566abe62","relation:93d30cdbd1b0304a6ebc","relation:9d2fcfaf68938b193615","relation:a2a29ab704a654994221","relation:a4060ed923d72616410b","relation:ba952556398928d62821","relation:d5214d75a2d6f50a0560","relation:ddfdf7ead21e06466156","relation:e3df17c6c8a0c9b5a9e3","relation:f43eeb782b2b0afe5396"],"semantic_review":false,"source":"documents/changelog/sections/004-source.tex","status_markers_as_written":["\\mC","\\mO"],"summary_excerpt":"v516_celestial_wp5e_m2_twisted_ks_measure.py ( CELEST.WP5E.M2.01, 23 checks, [formula in source] 1 s; exact sympy/Fraction, no floats; deterministic). S0 replication (roots, class quartics, [formula in source] two routes, bulk Okubo); S1 the index bridge [formula in source] the completion weights (no free scale, parameter-free locks); S2 the contact term (two forms, genuine-contact certificate); S3 the success table ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-22 (VI) ( v516 — WP5e back-reaction milestone M2 ``the twisted Kodaira–Spencer measure'' executed (SUCCESS on the preregistered v514 S8.2 criterion, ON THE DECLARED COMPLETION MEASURE — verdict B), promoted as the ledger row CELEST.WP5E.M2.01: the one-loop box coefficient per sector on [formula in source] under the completion contact term [formula in source] — the twisted-sector LOOP contributes the UNPHASED sector trace with the [formula in source] zero-mode normalisation [formula in source] , of which the Atiyah–Bott skeleton kept only the phase-weighted insertion part — (1) the COMPLETION-WEIGHT IDENTITY (the centrepiece): per glue class [formula in source] EXACTLY ( [formula in source] the v502 sector Casimir energies, [formula in source] the McKay/Kronheimer charges, v505 S4.3 index bridge): THE THREE SPHERE AXIONS PAIR THROUGH THEIR OWN ch [formula in source] CHARGES — an exact identity, NO free scale, no fit; (2) PARAMETER-FREE LOCKS: [formula in source] for ANY scale [formula in source] (the ch [formula in source] pattern alone kills [formula in source] ); ratio [formula in source] the [formula in source] -forced leading ratio (REPRODUCED, not fitted); the [formula in source] budget fixes [formula in source] uniquely (leading system det [formula in source] , unique weights [formula in source] ); (3) the SUCCESS TABLE: [formula in source] — a PERFECT Okubo square ( [formula in source] , [formula in source] in EVERY twisted channel: [formula in source] ); total [formula in source] Dedekind [formula in source] Okubo [formula in source] the UNIQUE quartic-free weighting of v505 S3.8 (the rigidity theorem is exactly what the measure lands on); both v508 certificates KILLED ( [formula in source] , [formula in source] ); the v511 slice [formula in source] SUPPLIED EXACTLY ( [formula in source] ) — NO cubic [formula in source] -channel needed ( [formula in source] free [formula in source] ); remainder inside the exchange span ( [formula in source] , [formula in source] ): the BULK axion cancels every channel with the SAME [formula in source] , the twisted propagator carrying the AB zero-mode factor [formula in source] ; the v514 measure chain stays [formula in source] -blind; (4) NEGATIVE CONTROLS: wrong scale [formula in source] leaves [formula in source] — only [formula in source] clears the budget; the [formula in source] shuffle breaks [formula in source] AND [formula in source] ; [formula in source] glue keeps [formula in source] / [formula in source] — the KILL branch FIRES there (Okubo failure inherited: [formula in source] doubly special); [formula in source] degenerates to the [formula in source] target and breaks the conjugation pairing [formula in source] the index bridge; the [formula in source] /Eguchi–Hanson anchor PASSES with the same mechanism ( [formula in source] , coupling scale [formula in source] centre count); (5) the MULTIPLIER NOTE (cross-reference to the parallel [formula in source] strand): the contact weights [formula in source] are REAL RATIONALS with no multiplier system of their own; the [formula in source] residual phases are the SQUARES of the [formula in source] discriminant [formula in source] -phases [formula in source] — orders [formula in source] squaring to [formula in source] , a finite [formula in source] system; Gauss sums [formula in source] , [formula in source] , full Weil sum [formula in source] ; \\ the MANDATORY FENCE: the completion reading (the loop of twisted states carries the UNPHASED sector trace with the same zero-mode normalisation) is DECLARED, supported by the [formula in source] modular-completion finding, NOT derived from the BCOV integral; \\ the BCOV-integral derivation ( [formula in source] territory); Wolfram extension [formula in source] (verified engine run); NO marker moves — the KILL (leftover independent quartic in ANY sector) does NOT fire, the completion reading stays -declared, SEAM.EQUIV.TWISTOR.01 stays Open, SEAM.EQUIV.01 untouched)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":50009,"byte_start":43676,"id":"section:77b944418033334668b5","kind":"subsection","labels":[],"line_end":283,"line_start":245,"numbered_or_version_tokens_as_written":["S8.1"],"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0e4930df2aeb0d8e0e10","relation:2dc63a494823fffaa2be","relation:2de8de878ef6bdc4757e","relation:4293d1046a3d0be59be8","relation:4e2531a99b51feb7f05a","relation:503c0ac20ec6c0fd8d9c","relation:5138b495139d2c5bd0ab","relation:59d5f3c3fe748e9fadd5","relation:5eb1ccf0cb7149fa3fef","relation:6cec84d92e0276a24ef3","relation:761a8f649255df06459b","relation:931911d688810a3fb643","relation:99e48207ddf539afc2a7","relation:adadaaffb40f172b7f54","relation:b16ac8a5dbde4748c280","relation:b9e4884de15360081fea","relation:c7eaa9a1756ad380ae6e","relation:cfbb5798fb5efe348eb5","relation:e78804aaebd9412240e2","relation:ebdc0484ca903913384a","relation:faaa32a67aa767df3d81","relation:fe8f0f7d5102cbeb3a37"],"semantic_review":false,"source":"documents/changelog/sections/004-source.tex","status_markers_as_written":["\\mC","\\mO"],"summary_excerpt":"v515_celestial_wp5e_m1_omega_n.py ( CELEST.WP5E.M1.01, 30 checks, [formula in source] 1 s; exact sympy, no floats; deterministic). S1 the residue form (three routes, cover factor [formula in source] , weight ledger, EH anchor, wrong-weight control); S2 the twistor family (closed form, [formula in source] reality, clock lift, section-level dichotomy); S3 periods (generic reduction, lockstep, covariance, collision ledg","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-22 (V) ( v515 — WP5e back-reaction milestone M1 ``the [formula in source] [formula in source] '' executed (SUCCESS on the preregistered v514 S8.1 criterion), promoted as the ledger row CELEST.WP5E.M1.01: the back-reacted holomorphic [formula in source] -form [formula in source] is CLOSED FORM on the [formula in source] twistor family, every [formula in source] period is [formula in source] -integral with the lockstep flux vector, and the lens geometry FORCES the source charge [formula in source] — (1) the RESIDUE FORM DERIVED: on [formula in source] all three ambient representatives satisfy [formula in source] exactly and pull back to [formula in source] (Poincar\\'e residue, derived not assumed); orbifold-cover pullback at [formula in source] : [formula in source] (flat form) — the residue normalisation CARRIES the source charge [formula in source] ; clock [formula in source] ( v492 S5 replicated); weight ledger [formula in source] , [formula in source] ; (2) the TWISTOR FAMILY CLOSED: from the four [formula in source] centre sections [formula in source] exactly [formula in source] ( [formula in source] identically; [formula in source] gives exactly the v493 family; [formula in source] opens only off-seam), CY-compatible clock lift [formula in source] , [formula in source] , [formula in source] ; (3) [formula in source] CLOSED [formula in source] PERIOD TABLE: [formula in source] with CPS/Bochner–Martinelli kernels on the centre twistor lines, [formula in source] off-source; boundary [formula in source] at the orbifold point [formula in source] (minimal invariant charge [formula in source] — the lens fundamental domain FORCES [formula in source] ), deformed phase [formula in source] , linking [formula in source] uniformly [formula in source] , per-sphere flux vector [formula in source] (forced uniform: clock orbit [formula in source] [formula in source] connectivity), seam-fibre phase vector [formula in source] ; [formula in source] carries ZERO [formula in source] -flux (all flux sourced); [formula in source] fibre residue [formula in source] transversal residue (density [formula in source] ); (4) CLOCK COVARIANCE: [formula in source] for ALL [formula in source] ; the [formula in source] collision nodes sit exactly on the [formula in source] eighth roots of unity ( [formula in source] , the [formula in source] bridge), clock orbits [formula in source] , honest conifold points (Hessian det [formula in source] , quadric rank [formula in source] ); (5) the HONEST KILL PROBE: forbidden family [formula in source] : [formula in source] lockstep (vs [formula in source] ), [formula in source] -support [formula in source] twelfth roots [formula in source] , no antipodal pairing — BUT the [formula in source] quantisation holds there TOO: integrality alone is NOT the discriminator, the discriminator is the lockstep phase structure [formula in source] the clock forcing; the v509 dial survives; (6) ANCHORS [formula in source] CONTROLS: EH/ [formula in source] (charge [formula in source] forced), CPS original (every integer [formula in source] allowed), [formula in source] ( [formula in source] , collapse at step zero), fractional charges [formula in source] excluded; \\ global kernel patching / Hitchin small resolution / CPS brane dictionary; \\ M2 (twisted KS measure), M3 ( [formula in source] uplift), the quantised BCOV coefficient; Wolfram extension [formula in source] (verified engine run); NO marker moves — M2/M3 and BCOV stay , SEAM.EQUIV.TWISTOR.01 stays Open ( v515 is preparation, not construction), SEAM.EQUIV.01 untouched)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":57282,"byte_start":50009,"id":"section:70380cf4813f5dcd47e6","kind":"subsection","labels":[],"line_end":362,"line_start":284,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:01fefe6b9f374490d78d","relation:0398aaf29f39a30fdbbc","relation:168ce7361a6843247ada","relation:1ce1a2166390c36ae246","relation:24c9e3b70f8691ca2f91","relation:2c31d886ecce6c15570d","relation:3af083a781d0a616fdc1","relation:483a865adffbff481ea2","relation:4f27c6d63f03ad816505","relation:596f7ca3777d35b2d0ed","relation:5d024ec697013f1a051d","relation:721d026227bb860f5915","relation:7e9a66ffec4ec77b2643","relation:8cdadb0cd98a56cffb1c","relation:94859ad91a46c62c958e","relation:9c8aa325fe902f296178","relation:a4e1e4018df1e5fa3595","relation:a50c0da843b4a669821b","relation:a870886a8adb457df30c","relation:ad44c53f946aee42d417","relation:afd3ab727d0d7453c18d","relation:b0893824f7b6e6408fa6","relation:b7ef0e1c1c3d39d955ac","relation:bb34ad4b42ae2f284687","relation:d03aa0403ce251133d09","relation:dd293cb6f90bfe2c2439","relation:e877f995332859290d31","relation:ea223abc3dfb7209abf7","relation:efc9d56822a12cda8b91","relation:f4f4c6a7ea06c7a2a3a6","relation:f6ec8eb639a888af30f5","relation:fbb516dcd4a4cf382705","relation:fe9126b60e28be203059"],"semantic_review":false,"source":"documents/changelog/sections/004-source.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"An external expert review of the celestial/twistor branch confirmed the substance and asked for semantic precision — role separation, status clarity, and the exact naming of what is missing. Six changes plus one new central research contract, all editorial/structural: (\\\"A1) Route renamed [formula in source] the Woit bridge. The tfpt_3 celestial section and the contract heading are now ``The celestial and twistor con","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-22 (IV) (external review integrated: route renamed, object diagram, group-extension definition, SEAM.EQUIV route split (MMST/TWISTOR ids, no status change), [formula in source] role table, WOIT.OS.TWISTOR.01 contract — a pure structure/text integration, NO new physics claims, NO marker moves, suite unchanged at [formula in source] )","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5980,"byte_start":0,"id":"section:21c9669befc5eafd6176","kind":"subsection","labels":[],"line_end":36,"line_start":1,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0585a5f097bdca5c3d55","relation:1060d3129d5664463ba5","relation:2b024c2f030e2e14907d","relation:337a28c2decc320bca30","relation:33fc6fbad7c775f49d39","relation:541726594f4df0402202","relation:569fad60ca0a1add978e","relation:5a49c667a55bb40ef877","relation:6ca854b3c56118a0a861","relation:7b50d2d919c841ff214c","relation:86e114e8155b22f5fe41","relation:8b3540efed7eb70a6826","relation:a77521c74dba275b17d0","relation:aa8305ddc876ad59d746","relation:b166117970ef61ced907","relation:b2eb7204baafa507b51a","relation:d8fa61c84861a2a20784","relation:db83e7896a3c8a05fe08","relation:dc62b6bcd6a506998804","relation:e7e86f41a7446a1d830e"],"semantic_review":false,"source":"documents/changelog/sections/005-source.tex","status_markers_as_written":["\\mC","\\mO"],"summary_excerpt":"v514_celestial_wp5e_eps1_axion_slot.py ( CELEST.WP5E.EPS1.01, 34 checks, [formula in source] 4 s; exact sympy/Fraction, no floats; deterministic). S1 Penrose accounting; S2 equivariant ledger [formula in source] character series [formula in source] Molien [formula in source] E3 sharpening [formula in source] graviton control; S3 the [formula in source] residue (Okubo / measure / flux) with honest gaps; S4–S5 GH centr","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-22 (III) ( v514 — WP5e- [formula in source] ``the [formula in source] bulk-axion slot'' executed (verdict B), promoted as the ledger row CELEST.WP5E.EPS1.01: the [formula in source] tower field of the celestial route is now a CONSTRUCTION, [formula in source] is pinned three ways, and the first honest back-reaction step is taken in Gibbons–Hawking form — (1) the EQUIVARIANT [formula in source] SLOT: the pushforward ledger [formula in source] on [formula in source] gives per degree [formula in source] exactly [formula in source] classes [formula in source] the exact wave-operator nullspaces ( [formula in source] for [formula in source] ), the v492 action on the fibre coordinates [formula in source] with incidence-forced column weights [formula in source] closes the equivariant bookkeeping BLOCK BY BLOCK (all [formula in source] , all [formula in source] characters); character series [formula in source] , [formula in source] , [formula in source] ; the [formula in source] slot has multiplicity [formula in source] — THE BULK AXION SURVIVES THE PROJECTION; Molien invariant ring [formula in source] — [formula in source] , [formula in source] , relation degree [formula in source] the [formula in source] weight ( v492/ v493 bridge); E3 bijection sharpened (twisted minimal content [formula in source] [formula in source] the Coxeter eigenvalues, [formula in source] ); graviton control: [formula in source] invariant only from fibre degree [formula in source] with multiplicity [formula in source] ; (2) [formula in source] TRIPLY PINNED: Okubo [formula in source] on the [formula in source] glue roots ( [formula in source] , [formula in source] ); the measure chain cancels [formula in source] EXACTLY (vertex [formula in source] [formula in source] , propagator [formula in source] , anomaly [formula in source] ; [formula in source] for arbitrary [formula in source] ; wrong bookings EXCLUDED: anomaly-only [formula in source] , missing propagator renormalisation [formula in source] ); flux (minimal CPS quantum [formula in source] , single channel iff [formula in source] , [formula in source] exact); (3) the GH/ [formula in source] BACK-REACTION STEP: invariant [formula in source] -centre configurations [formula in source] exactly [formula in source] branches, the free orbit re-derives the v493 family ( [formula in source] , [formula in source] , monodromy [formula in source] one clock step), the charge- [formula in source] GH point is exactly [formula in source] ( [formula in source] : seam boundary [formula in source] ), periods [formula in source] LOCKSTEP ( v509 counter-check), Coxeter clock from geometry ( [formula in source] ), source charge [formula in source] , EH asymptotic log coefficient EXACTLY [formula in source] (the CPS log is an exceptional-locus statement; Burns contrast [formula in source] ), multipole rule [formula in source] with [formula in source] carrying [formula in source] ; controls [formula in source] ( [formula in source] irrational, squares only [formula in source] ), [formula in source] (Veronese), [formula in source] (three channels); \\ conditional on Costello's flat- [formula in source] matching; \\ the quantised BCOV coefficient and the twisted channels ( [formula in source] ) — M1–M3 preregistered (the [formula in source] [formula in source] / the twisted KS measure / the [formula in source] uplift, each with success [formula in source] kill); Wolfram extension [formula in source] (verified engine run); NO marker moves — WP5e stays , SEAM.EQUIV.01 untouched, CELEST.SEAM.01 stays Open)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10855,"byte_start":5980,"id":"section:37056704285dbc4b9f42","kind":"subsection","labels":[],"line_end":68,"line_start":37,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:054e29f4db5721c789cf","relation:1155c1b766749383ba96","relation:1fc80fb7b924cd1a955e","relation:2877143d7b9467472267","relation:2925baa5236bc04b09ed","relation:6daaf68e987f03dc425a","relation:6eeb266e21494ac576bf","relation:762076d0bc6ac51f256b","relation:79aecc880099485068a7","relation:938e3530242dcd3b7453","relation:b6ba89599d4e6ebcda1e","relation:cda8fab53e970fcc52f2","relation:d40f8434d835293a6875","relation:d6105887f4267fc9e188","relation:e6aa92a2a0e3897aed8a"],"semantic_review":false,"source":"documents/changelog/sections/005-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v513_celestial_dterm_nonderivation.py ( CELEST.DTERM.NONDERIV.01, 24 checks, [formula in source] 2 s; exact sympy/Fraction, no floats; deterministic). N0 baseline ( [formula in source] roots [formula in source] , [formula in source] , [formula in source] two routes, [formula in source] pinned by the [formula in source] slot alone); N1 convention table [formula in source] the stable factorisation [formula in source] ;","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-22 (II) ( v513 — the [formula in source] negative certificate, promoted as the ledger row CELEST.DTERM.NONDERIV.01 (anti-numerology certificate in the v508 style, honest rigid NEGATIVE result): can geometry derive [formula in source] ? NO — the v511 \\ fence `` [formula in source] '' does NOT survive the honest four-route battery with its PRE-DECLARED look-elsewhere ledger: (1) the CONVENTION TABLE gives [formula in source] across five normalisations (probe tr-fund/ [formula in source] -Killing; Gell-Mann; [formula in source] -Killing; plain trace; ch [formula in source] -normalised [formula in source] ) — only [formula in source] of [formula in source] hits [formula in source] , while the convention-STABLE content is the factorisation [formula in source] , both factors \\ (Killing propagator [formula in source] from [formula in source] over the actual roots; [formula in source] -slot fixing via [formula in source] ); (2) K1 DEAD: the charge-legal flux pairings [formula in source] give [formula in source] — they BRACKET [formula in source] and both MISS; the only flux hit [formula in source] is the FORBIDDEN [formula in source] pairing (charge [formula in source] , v511 innerness); look-elsewhere: [formula in source] expressions from [formula in source] \\ numbers, [formula in source] hits on [formula in source] , controls [formula in source] , [formula in source] , [formula in source] ; (3) K2: quantisation delivers only lattices ( [formula in source] with [formula in source] the [formula in source] nd multiple, no minimality; strict ch [formula in source] units [formula in source] EXCLUDE [formula in source] ); the cubic quantum is lattice-dependent ( [formula in source] on coroots, [formula in source] on weights), the integer [formula in source] has [formula in source] factorisations; (4) K3 PROVENANCE CLASH (the death blow): cubic indices [formula in source] with [formula in source] numerically [formula in source] — but the quartic class decomposition [formula in source] comes from classes [formula in source] vs the cubic [formula in source] from classes [formula in source] : same number, disjoint mechanism [formula in source] coincidence; the Weyl side is WRONG ( [formula in source] -channel is [formula in source] , [formula in source] ; [formula in source] has no cubic; [formula in source] a second accidental [formula in source] ); (5) K4 controls ( [formula in source] , [formula in source] doubling [formula in source] , false [formula in source] with six cubics, [formula in source] ) separate consistently; VERDICT: NUMEROLOGY as a derivation claim — the v511 \\ fence stays a fence, now typed look-elsewhere-loaded; the honest \\ core is [formula in source] ; Wolfram extension [formula in source] (verified engine run); NO marker moves — the fence stays , the physical generation of the [formula in source] stays , CELEST.SEAM.01 stays Open)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16347,"byte_start":10855,"id":"section:4fee06b8389287124647","kind":"subsection","labels":[],"line_end":104,"line_start":69,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0fa3fed6ba230d0ad5a0","relation:1577ba0a0908bbcfa833","relation:190eb8b7b4ee5ab8e010","relation:48bd32a6a2e998c48702","relation:4b490b3b3d744849a365","relation:53329d611ce55180bf7a","relation:5a4cc31ae1aa39766adb","relation:5f35eae26068e57dcd41","relation:6fb33e0516239c2915a5","relation:7756bac2968fc0fbbe2f","relation:797b5a8ce84862904a43","relation:8bd47c69fe3bbcff93ce","relation:92b4d4cc240a244e905b","relation:97fc6e3c7fb7a715da0c","relation:9cdb72d52c95293acc02","relation:a0f51f076c04afaa7883","relation:a16d86730e975e16deeb","relation:d71aa2930be46add84bf","relation:dab718d1f2c03061ce23","relation:e7c3191ef80d0027c3c4","relation:ed67faac0086da4560fe","relation:f6ac0312a299a0c1ec33","relation:fcf831c43c8d1b6b0988"],"semantic_review":false,"source":"documents/changelog/sections/005-source.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"v512_seam_tau_flag.py ( SEAM.TAU.FLAG.01, 29 checks, [formula in source] 6 s; sympy-exact [formula in source] mpmath 30 digits [formula in source] one numpy lattice commutator; deterministic). S0 family frame (counterwitness inside the family: [formula in source] , [formula in source] , cross-ratio [formula in source] ); H1 complete symmetry census (census basis, rotation solvesets, stabiliser jump, flag/arc orbits, ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-22 (I) ( v512 — the flag-transitivity equivalence web promoted as SEAM.TAU.FLAG.01: the [formula in source] attack executed on the free RP seam circle — BARE MARK-TRANSITIVITY IS FALSIFIED as a selector (on the test family [formula in source] , [formula in source] , the symmetry group is the pair-exchanging [formula in source] for EVERY [formula in source] , simply transitive on the four marks; complete census: deck-commuting M\\\"obius maps are diagonal/antidiagonal; hardening: ALL undirected per-mark data are identical for every [formula in source] — no local jet sees the bit), and THE SHARP SELECTOR is FLAG transitivity (marks AND their two sides indistinguishable) [formula in source] the clock — stabiliser jump [formula in source] , flag/arc orbits [formula in source] , order- [formula in source] rotation ( [formula in source] solveset [formula in source] ), mark mirror [formula in source] ; welded into a [formula in source] -FOLD EQUIVALENCE WEB (every link exact): clock rotation, [formula in source] , mark mirror, flag transitivity, three spectral degeneracies (odd-doublet split [formula in source] , zero only at [formula in source] — counterwitness exactly [formula in source] ; arc-Laplacian degeneracy [formula in source] ; the v215-K3 indicator in CLOSED FORM [formula in source] — the v503 lattice curve analytically), [formula in source] -twist existence ( [formula in source] ; Atiyah–Bott rationality [formula in source] -BLIND — [formula in source] for all [formula in source] , [formula in source] rational non-CM: rationality selects NOTHING), cusp- [formula in source] -cycle implementability (H4 rigidity: [formula in source] with orders [formula in source] cannot induce it; centraliser scalar, [formula in source] nonscalar [formula in source] no projective involution — projective order exactly [formula in source] , [formula in source] -shadow consistent v510), harmonic, [formula in source] ; NEGATIVE CONTROLS: hexagonal (not concyclic, fails preconditions), silver (harmonic but topologically dead), [formula in source] marks (impossible on the free circle: [formula in source] vs [formula in source] invariant subsets; bare [formula in source] transitivity already forces equal spacing — `` [formula in source] counts''); \\ THE REST: the last input reduces from a continuous modulus to ONE discrete symmetry-lift bit ( [formula in source] : side-indistinguishability of the four equally-decorated marks), v216 local equality does NOT deliver it, its negation is now concretely measurable; scoreboard: the counterwitness passes all [formula in source] established unsided tests, fails all [formula in source] clock-equivalent ones; Wolfram extension [formula in source] (verified engine run); NO marker moves — the bit stays , QGEO.REALIZE.01 and P2.TYPING.01/ AX.P2.01 text-precised only, SEAM.BIT.FREEDOM.01 cross-referenced)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; 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integer-scaled weight multisets [formula in source] Kostant/Weyl alternating sums [formula in source] sympy/Fraction, no floats; deterministic). D0/D1 structure: [formula in source] roots, class split [formula in source] ; [formula in source] SEMISIMPLE without [formula in source] ( [formula in source] class- [for","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-21 (XXIII) ( v511 — WP5e- [formula in source] of CELEST.SEAM.01 ``the full-tensor ledger'' promoted as CELEST.WP5E.DELTA2.01 (intermediate verdict, exact): the named escape route of the v508 exchange no-go executed on the FULL adjoint tensor structure of [formula in source] — the COLLAPSE IS CONFIRMED full-tensorially AND arity-crossing (the INNERNESS THEOREM: [formula in source] semisimple with NO [formula in source] (class- [formula in source] roots [formula in source] , root span rank [formula in source] ), [formula in source] in the Cartan OF [formula in source] [formula in source] every invariant tensor carries total charge [formula in source] : the bilinear Hom table is nonzero ONLY at [formula in source] (dims [formula in source] ) and ALL [formula in source] non-neutral trilinear sector triples have [formula in source] ), BUT ONE CUBIC DOOR OPENS: of the neutral trilinears ( [formula in source] sym [formula in source] antisym, [formula in source] , [formula in source] , [formula in source] , [formula in source] ; all cross-sector ones pure brackets) the UNIQUE totally symmetric survivor is the [formula in source] [formula in source] -symbol ( [formula in source] has no cubic Casimir, [formula in source] protects [formula in source] ), whose exchange quartic [formula in source] (TWO independent routes, Killing propagator [formula in source] from the roots) has [formula in source] — the v508 master kill (product theorem) does NOT extend to cubic vertices; the pairing stays OBSTRUCTED in the charge reading with the genuinely WEAKER certificate [formula in source] , [formula in source] ( [formula in source] rank [formula in source] , augmented [formula in source] ), and becomes EXACTLY solvable relaxed: [formula in source] (residual [formula in source] ); \\ fences [formula in source] , [formula in source] ; controls: [formula in source] has NO symmetric cubic and no [formula in source] block ( [formula in source] doubly special), false [formula in source] /sector assignments separate; the [formula in source] burden SHARPENED to the [formula in source] slice or the selection-rule relaxation — and the [formula in source] exploration run itself stands UNDECIDED at exploration level (strict holomorphic [formula in source] reading REFUTED at the [formula in source] /Eguchi–Hanson anchor [formula in source] method boundary, not a kill; contact term [formula in source] the MODULAR COMPLETION of the AB data, a Harvey–Moore [formula in source] -integral with forced leading [formula in source] ratio [formula in source] ; massive coset levels [formula in source] mandatory); Wolfram extension [formula in source] (verified engine run); NO marker moves — WP5e proper stays , SEAM.EQUIV.01 stays )","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":26171,"byte_start":23496,"id":"section:3721516595f24fd66f4c","kind":"subsection","labels":[],"line_end":185,"line_start":161,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0a2bf6c6c155698aee41","relation:0b9c3e697173dcc177f2","relation:6d6904281f48c2043369","relation:94b3d94e534a9f97e473","relation:97569c49f6f101a02abe","relation:ab07840de73041e0f969","relation:b37184884ade7ce32823","relation:b4fadc565440f317fe24","relation:c309484c312e584da5be","relation:cee672489573a4e02686","relation:d0d7bb459f19ce4dfefb","relation:d22c020a75802f2be031","relation:d583d2b358d3cde287f6","relation:ebbab897269290af5477","relation:ef760fea27c2edd51717","relation:f45f1442ecfa66949123"],"semantic_review":false,"source":"documents/changelog/sections/005-source.tex","status_markers_as_written":["\\mC","\\mO"],"summary_excerpt":"What is consolidated (and why now). The P2 state of affairs was spread over five module rounds: the partition corollary ( v491: [formula in source] unique [formula in source] ), the weight typing ( v499: Deligne [formula in source] Birkhoff–Grothendieck [formula in source] Mehta–Seshadri force [formula in source] , residuals R1/R2 ), the residual convergence ( v503: QGEO-R1 [formula in source] P2-R1), the clock rigid","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-21 (XXII) (P2 consolidation — the axiomatics reduction state written as ONE coherent statement across the papers (editorial, NO new claims, NO marker moves): the compiler's dimensionless inputs reduce to four marks (derived from P1-side topology, v216), ONE square-modulus datum ( [formula in source] — equivalently: the clock / the CM-fixed half-period / the non-split extension class on the free seam circle; v491/ v499/ v506/ v507/ v510) and [formula in source] , plus the \\ identifications R1/R2 of v499; AX.P2.01 stays a DECLARED axiom and QGEO.REALIZE.01 stays / \\ — the consolidation describes the reduction state, not an abolition)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":33027,"byte_start":26171,"id":"section:c31c8db87fec4e08752e","kind":"subsection","labels":[],"line_end":242,"line_start":186,"numbered_or_version_tokens_as_written":["F1.1"],"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:1344297f9ff135acff1b","relation:15dd544f81e632ad6d52","relation:2a870390ed0a76a363ce","relation:337962c96188c9de9272","relation:3a2f3cacef44b4c23990","relation:41de866e857b467f6913","relation:47b29318d9473f6869ba","relation:4da662f8fcefdc2d8681","relation:54ad6c44b15a34542117","relation:589bfb6f4a0a2f516a2e","relation:5ac450e65dbd2c52f982","relation:6f02fb23efa695eac943","relation:7590449aa3f7ffa5cb51","relation:7ad89a30bb9af5b7ff99","relation:83d7e3336e7cda5f29d1","relation:87116b88604568f09df7","relation:926a236a947f6fbf8e23","relation:9733f51971cd49c5b260","relation:acb3aa320bda50bab5af","relation:b87de5ff3c86828518e3","relation:b9026e8be291ff2652c9","relation:c5bdf490860cd00ddf17","relation:cecbb9e61803d6f35f06","relation:d0a9fbbbb2150273fcf1","relation:d760c732536439eb7edf","relation:e9e93aea18dcc13f10ff","relation:feb163d624a066d7b349"],"semantic_review":false,"source":"documents/changelog/sections/005-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v510_seam_bit_freedom.py ( SEAM.BIT.FREEDOM.01, 30 checks, [formula in source] s; sympy [formula in source] exact [formula in source] Fractions, no floats; deterministic). Part A (dihedral/fermionic): the involution census in [formula in source] on the refined [formula in source] -point seam circle ( [formula in source] : [formula in source] involutions, EXACTLY ONE free [formula in source] the antipodal shift by [fo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-21 (XXI) ( v510 — the freedom attack on the v506/ v507 alignment bit promoted as SEAM.BIT.FREEDOM.01: the POSITION half of the bit is TOPOLOGY — the collar deck is a covering deck (the [formula in source] seam of the M\\\"obius double), and covering decks act FREELY; the DIHEDRAL THEOREM (on the seam circle the free involution is UNIQUE [formula in source] the antipode: [formula in source] involutions in [formula in source] , exactly [formula in source] free; [formula in source] complete census, brute force [formula in source] at [formula in source] ; quotient topology circle/antipode [formula in source] CIRCLE [formula in source] vs circle/reflection [formula in source] INTERVAL [formula in source] — the [formula in source] Gauss–Bonnet budget needs closed circles, so freeness IS the established P1 datum); NONSPLIT [formula in source] FREE over the complete [formula in source] -involution census in exact [formula in source] (free [formula in source] nonsplit with [formula in source] roots [formula in source] the [formula in source] tower; ALL [formula in source] reflections [formula in source] scalar [formula in source] , split, [formula in source] roots); the REAL-STRUCTURE classification (deck-commuting families [formula in source] exactly two; [formula in source] equatorial, deck FREE; silver [formula in source] real axis THROUGH the deck poles, NOT free — the edge class is the restriction of the BRANCHED pillowcase involution; hexagonal [formula in source] NO mark-fixing real structure, RP-incompatible); HARMONIC [formula in source] FREE [formula in source] exactly ( [formula in source] ); honest counterwitnesses (``nonsplit [formula in source] clock'' is FALSE: [formula in source] and [formula in source] with [formula in source] ); the alignment bit REDUCES from ``harmonic AND central'' to the square-modulus datum [formula in source] alone; Wolfram extension [formula in source] (verified engine run); NO marker moves — QGEO.REALIZE.01 stays / , AX.P2.01 stays an axiom, P2-R1 halved)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":40406,"byte_start":33027,"id":"section:469263059c1e8cf1fd20","kind":"subsection","labels":[],"line_end":305,"line_start":243,"numbered_or_version_tokens_as_written":["S4.10","S4.8"],"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:2c0f47c5a01da6d7d168","relation:3c787449a4f1ed409de2","relation:4afe6f9a4f625da07cbb","relation:6d383381bdcf6ccaefc7","relation:6f29acfe4f6e1b569e0f","relation:a80c58ae2a1b28421deb","relation:be25e034b4d6adad9cee","relation:cdde80f5a84bd462e5f8","relation:d0d2fc319d4c4a12e515","relation:dc9d2bdf43f204b2ea84","relation:e1be9de924808ddb1114","relation:e46556ce41f4139d9bf6"],"semantic_review":false,"source":"documents/changelog/sections/005-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v509_celestial_wp5e_eps2_level_from_flux.py ( CELEST.WP5E.EPS2.01, 28 checks, [formula in source] s; sympy/Fraction exact, no floats; deterministic). Target: derive the boundary level [formula in source] from flux quantisation on the lockstep spheres, following the Costello–Paquette–Sharma Burns-holography mechanism (PRL 130, 061602; arXiv:2306.00940). CPS skeleton replicated exactly: the [formula in source] period o","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-21 (XX) ( v509 — WP5e- [formula in source] of CELEST.SEAM.01 ``the CPS level-from-flux dial'' promoted as CELEST.WP5E.EPS2.01, verdict B: the Costello–Paquette–Sharma Burns-holography mechanism (``level [formula in source] flux quantum [formula in source] Dynkin index'') executed on the lockstep spheres — the CPS SKELETON exact ( [formula in source] period [formula in source] with pullback density [formula in source] , exceptional-sphere K\\\"ahler flux [formula in source] , boundary level magnitude [formula in source] by the symplectic-boson contraction, [formula in source] ); the PAIRING MATRIX pinned, not postulated ( [formula in source] ledger [formula in source] integrality [formula in source] unimodularity [formula in source] effectivity [formula in source] [formula in source] by complete enumeration: rows [formula in source] , [formula in source] unimodular, exactly [formula in source] effective [formula in source] identity [formula in source] diagram flip), fluxes [formula in source] with uniformly ONE quantum per charged current; ``level [formula in source] total flux'' KILLED by the lockstep test itself ( [formula in source] unequal [formula in source] flavour multiplicity), the per-current reading [formula in source] anchored by the lattice current count [formula in source] and embedding index [formula in source] ; ord- [formula in source] -vs-level- [formula in source] RESOLVED (the clock order counts fractional flux sectors: [formula in source] , Lagrangian [formula in source] glue, KLM [formula in source] ) with the NEW sector-counter dial [formula in source] for [formula in source] — exactly ONE sector iff [formula in source] ; the LOCKSTEP THEOREM lifts the v505 ``one scale [formula in source] one level'' to a THEOREM of clock invariance ( [formula in source] equal, monodromy [formula in source] pure phase [formula in source] , [formula in source] : no invariant flux vector; NEW falsifier [formula in source] : [formula in source] orderings lockstep); honest limit: uniform doubling keeps the lockstep (equality, not the value); controls [formula in source] / [formula in source] / [formula in source] separate honestly; Wolfram extension [formula in source] (verified engine run); NO marker moves — WP5e stays \\ (the CPS dictionary on [formula in source] typed , the type-I B-model back-reaction ), SEAM.EQUIV.01 stays )","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":43851,"byte_start":40406,"id":"section:708e832b50ab71d1e9e7","kind":"subsection","labels":[],"line_end":339,"line_start":306,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:19123e7c48de0ab001f2","relation:4e3c299a5a077785c252","relation:4e590bd0d975feb49aec","relation:50a4163d9e7dbfda18aa","relation:6210309636dae0febfb9","relation:7e63e24ad1afd05477d0","relation:870eb8c8c241aca44682","relation:a84f2e6b429ea4a6364b","relation:fc8e657bbf0553209466","relation:feabea97d116afbf768d"],"semantic_review":false,"source":"documents/changelog/sections/005-source.tex","status_markers_as_written":[],"summary_excerpt":"experiments/e8-ladder-bed v2 (2DCS): amendment preregistered, run, and killed by its own controls. Trigger: arXiv:2512.16829 (Watanabe, Trebst, Hickey) — a THEORY-only paper (four-kink/ED localized-limit spectra at [formula in source] – [formula in source] \\,T, not the E8 point; no measurements); as of 2026-07-21 no experimental 2DCS measurement of CoNb [formula in source] O [formula in source] exists anywhere (web-c","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-21 (XIX) ( e8-ladder-bed v2 — the 2DCS extension executed with an honest preregistered kill_2d verdict at the DETECTOR level: the known-answer map recovers [formula in source] rungs incl.\\ [formula in source] via F3 difference coordinates (MC [formula in source] ), but the 2D control battery breaks (scramble [formula in source] , jitter [formula in source] at the destructive [formula in source] level) — the v1 1D results (BCVO [formula in source] , CoNb [formula in source] O [formula in source] [formula in source] ) are untouched; scorecard row updated, status/stage unchanged; experiments level only — no verification module, no gate closes, no marker moves)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":50047,"byte_start":43851,"id":"section:31d9a188bf3ec46b9310","kind":"subsection","labels":[],"line_end":392,"line_start":340,"numbered_or_version_tokens_as_written":["S3.7","S3.9","S5.8"],"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:33312e139be5c5d19e43","relation:3d2dfdb10162fc3cd341","relation:419ae50d893d071c323d","relation:571765f0119fb5f003a3","relation:60b56ec3b21ee82a1331","relation:60bb317e80057fd533de","relation:af7f8576fda25e5585dd","relation:cad67028b03644c50ca6","relation:fe1606837a2590e5f415"],"semantic_review":false,"source":"documents/changelog/sections/005-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v508_celestial_wp5e_gamma_pairing.py ( CELEST.WP5E.GAMMA.01, 27 checks, [formula in source] 4 s; sympy/Fraction exact, no floats; deterministic). Question: can the three twisted sphere axions [formula in source] (Coxeter eigencharacters [formula in source] on [formula in source] , v505 S5.8) cancel the rigid [formula in source] residual of the Atiyah–Bott ledger ( [formula in source] , v505 S3.7) by Green–Schwarz-typ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-21 (XVIII) ( v508 — WP5e- [formula in source] of CELEST.SEAM.01 ``the sphere-axion pairing check'' promoted as CELEST.WP5E.GAMMA.01, an honest rigid NEGATIVE result: the VERTEX-SPACE THEOREM — the [formula in source] -invariant quadratics on the [formula in source] -dim glue Cartan are EXACTLY [formula in source] (dim [formula in source] ) and the quartics EXACTLY [formula in source] (dim [formula in source] ), with the PRODUCT THEOREM as the master kill (any two invariant quadratics multiply into [formula in source] — zero [formula in source] content, so [formula in source] annihilates EVERY exchange image while [formula in source] ); the strict two-index [formula in source] rule COLLAPSES (the sphere axions have no invariant bilinear Cartan vertex at all), the twist-insertion channels give a rank- [formula in source] exchange matrix with [formula in source] and the annihilator certificate [formula in source] ; side discovery [formula in source] ; naturalness DISSOLVES (ch [formula in source] -natural and AB-weight couplings both certify [formula in source] vs required [formula in source] — scale-independent); controls: [formula in source] has no sphere partners AND uncancelled [formula in source] , [formula in source] no [formula in source] structure; the O-fence is SHARPENED: the exchange sub-branch is dead, the [formula in source] residual MUST be carried by twisted BCOV contact terms ( [formula in source] binary: coefficient exactly [formula in source] , computed not fitted; escape [formula in source] : the full-tensor ledger); Wolfram extension [formula in source] (verified engine run); NO marker moves — CELEST.SEAM.01 stays Open, the slot bijection untouched, the preregistered level-kill still does not fire, SEAM.EQUIV.01 stays )","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7214,"byte_start":0,"id":"section:cdda6bb5746f6a6a897d","kind":"subsection","labels":[],"line_end":65,"line_start":1,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:21e8c36ae4bb02bb7d9b","relation:2251a9c2ce2f3c169d74","relation:3173c2119aebe91d4a59","relation:36968b35ee4c902e1cc7","relation:45f62db9fac2c5848b6c","relation:4d5eba34abbafda3f096","relation:6bb7c7998d753eee4cbc","relation:6f2f1e62b41a98e1771d","relation:6f8c7d124171aaf23797","relation:72b89510a3d146cc71e6","relation:7ca1deee18b42a979e76","relation:7d631e8ab1f2e2fe89c6","relation:8a8fc9a32ef040085cb4","relation:964345b192be9ed4aef5","relation:b6b2556cdc4f53c08f1d","relation:bb2df5b6821fa5f1851c","relation:d9f8b8da543a53fe9849","relation:dc5b957b722626d82662","relation:e80c209e254b4df67c33","relation:f6bc53d7ae5ac756ab48"],"semantic_review":false,"source":"documents/changelog/sections/006-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v507_seam_bit_origin.py ( SEAM.BIT.ORIGIN.01, 26 checks, [formula in source] 2.6 s; Part A sympy-exact torus/M\\\"obius arithmetic [formula in source] Part B exact [formula in source] Fractions; deterministic). Conjecture under attack: marks and deck both descend from the SAME torus structure (the seam double [formula in source] , v214/ v260), so the common origin would force the central alignment automatically and the","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-21 (XVII) ( v507 — the tautology attack on the v506 alignment bit, executed and refuted, promoted as SEAM.BIT.ORIGIN.01: the ORIGIN THEOREM — marks [formula in source] fixed points of the hyperelliptic involution [formula in source] the [formula in source] half-periods [formula in source] of the seam double, and EVERY mark-free collar deck IS a half-period translation (in all three stabiliser types [formula in source] the free involutions are exactly the three [formula in source] : the CLASS of the deck is forced, its POSITION is not); the CORE SOLVE (symbolic [formula in source] ): a marks-preserving root of [formula in source] exists [formula in source] (one per [formula in source] ; intrinsic: the deck pairs separate harmonically), union [formula in source] the harmonic orbit [formula in source] ; the EQUIVALENCE TETRAD ``Uhr existiert [formula in source] ( [formula in source] AND deck [formula in source] CM-fixed half-period) [formula in source] (Stab [formula in source] AND deck central) [formula in source] deck pairs harmonic [formula in source] NS Fock lift NONSPLIT''; the FERMION DICHOTOMY (the new physical face): central [formula in source] nonsplit vs edge [formula in source] SPLIT ( [formula in source] vs [formula in source] roots — the bit IS a Fidkowski–Kitaev-type extension class, distinguished but not derived); the silver set [formula in source] the in-family misalignment witness; Wolfram extension [formula in source] (verified engine run); NO marker moves — the bit stays , SEAM.CLOCK.RIGIDITY.01/ QGEO.REALIZE.01/ P2.TYPING.01 text precised only)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13624,"byte_start":7214,"id":"section:cdd3ea07b0ec5995036b","kind":"subsection","labels":[],"line_end":122,"line_start":66,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:16dbcbafa2d96878cf4b","relation:1d3773be34a772f99409","relation:5c4861d31a695704660f","relation:64138193f5c2282fe4e8","relation:797c30226721d015cf53","relation:918e80e3e6a87a2555a3","relation:9999dd3cd8237c81e061","relation:9ad5c858aa9635592b2b","relation:b0e50841ed561e372c3d","relation:b694c372c5b02809f3f9","relation:b8391884e2e1f01d7596","relation:ba6eed0b4c20402e1b3f","relation:d610620bd7984fed5c4b","relation:d9e56ed3af03f8514eff","relation:dc6822cdf61397ceaac7","relation:e467fc1b68c488694155"],"semantic_review":false,"source":"documents/changelog/sections/006-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v506_seam_clock_rigidity.py ( SEAM.CLOCK.RIGIDITY.01, 34 checks, [formula in source] 3.5 s; Part A sympy-exact M\\\"obius/divisor arithmetic [formula in source] Part B exact [formula in source] Fractions; deterministic). v503 localised the one remaining identification input (``why does the raw seam carry the order- [formula in source] clock'', QGEO-R1 [formula in source] P2-R1); v506 reduces it. Theorem A (M\\\"obius sid","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-21 (XVI) ( v506 — seam clock rigidity, Route B of the v503 classification, promoted as SEAM.CLOCK.RIGIDITY.01: TWO exact theorems reduce the order- [formula in source] clock input to ONE alignment bit — Theorem A (M\\\"obius): the deck [formula in source] has EXACTLY TWO square roots [formula in source] in [formula in source] , both automatically order [formula in source] , and a marks-preserving root exists [formula in source] the deck is the CENTRAL involution of the mark- [formula in source] (counterexample [formula in source] : harmonic with full [formula in source] but deck non-central [formula in source] [formula in source] roots — harmonicity alone insufficient); Theorem B (Fock, the core): the NS deck implementation is FORCED to order [formula in source] — [formula in source] , i.e.\\ [formula in source] EXACTLY, a nonsplit [formula in source] , with the [formula in source] tower [formula in source] , [formula in source] ( [formula in source] fermionically explained) and the R-sector control split ( [formula in source] ); the one \\ rest: ``the collar deck is the central involution of the mark- [formula in source] '' — the fermionic [formula in source] forces the ORDER, not the spatial alignment; Wolfram extension [formula in source] (verified engine run); NO marker moves — QGEO.REALIZE.01 stays / \\ (text precised), P2.TYPING.01 R1 mapped onto the same bit)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19220,"byte_start":13624,"id":"section:3e3e7c41b2e8190a5e2f","kind":"subsection","labels":[],"line_end":173,"line_start":123,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:079dda60726f0d83dd05","relation:135af2afa0f864dd23c8","relation:1c59a6c57c0362755af0","relation:265676d84d89a3f846e1","relation:2e0f6fb00084a79f21d4","relation:3d64f9dfd3b1a498088e","relation:585567225197c148d904","relation:5b016f57ff450d5f1d5e","relation:5b9ffa7345676c19337f","relation:9ebbb87a7c4ab41b17c6","relation:a416bd78166d04107d71","relation:a604b62d628b2c19fa00","relation:a8917486340564954e08","relation:bbea005ea611146718bc","relation:bdc91380ea3c133bcfeb","relation:c074ee0459802517db2a","relation:c494984dbc952eb39496","relation:cfaa2d6e071ebc53b9f0","relation:f77d9c1f4fa3b5bbd940","relation:fda76da5da7e2fa8e7ec"],"semantic_review":false,"source":"documents/changelog/sections/006-source.tex","status_markers_as_written":["\\mC","\\mO"],"summary_excerpt":"v505_celestial_wp5e_beta_equivariant_ledger.py ( CELEST.WP5E.BETA.01, 47 checks, [formula in source] 1.3 s; sympy/Fraction exact, no floats; deterministic). The twistor side of WP5e pushed as far as exact arithmetic reaches: the Atiyah–Bott/Lefschetz skeleton of the one-loop box anomaly (Costello; Bittleston–Sharma–Skinner) on [formula in source] with the [formula in source] [formula in source] -glue monodromy. AB le","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-21 (XV) ( v505 — WP5e- [formula in source] of CELEST.SEAM.01 ``the equivariant anomaly ledger on twistor space'' promoted as CELEST.WP5E.BETA.01: the Atiyah–Bott/Lefschetz fixed-point skeleton of the one-loop twistor inflow is EXACT — denominators [formula in source] with Dedekind sum [formula in source] , equivariant characters [formula in source] by two routes, invariant Okubo [formula in source] with the twisted sectors NOT reducing and the AB sum leaving the RIGID residual [formula in source] , the index bridge [formula in source] exact with glue defect [formula in source] both routes, the level dials [formula in source] geometric (current count [formula in source] ), and the honest E3 REFUTATION: [formula in source] fills the GRAVITON slot [formula in source] , NOT the axion slot [formula in source] — the three sphere classes fill the three twisted axion slots instead; the preregistered kill (``inflow demands a level [formula in source] '') does NOT fire on the equivariant skeleton; WP5e: [formula in source] (CFT side, v502) [formula in source] [formula in source] (equivariant twistor skeleton, v505) executed, the global BCOV quantisation stays ; Wolfram extension [formula in source] (verified engine run); SEAM.EQUIV.01 stays , no marker moves)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":25724,"byte_start":19220,"id":"section:f7d73358ce212e71ac18","kind":"subsection","labels":[],"line_end":231,"line_start":174,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:074953bb3d552d4ae3cc","relation:3d65fdc69264c456e850","relation:450da8732caf2f12a9b4","relation:4f203c52cbec3917f6af","relation:a0b6a708af0aeebd9423","relation:dedf8f40d77e1048d8d5","relation:ee767a3ade8255f77bae","relation:faba2058c24a47c5a917"],"semantic_review":false,"source":"documents/changelog/sections/006-source.tex","status_markers_as_written":["\\mC","\\mO"],"summary_excerpt":"v504_celestial_wp5d_klm_completeness.py ( CELEST.WP5DB.01, 37 checks, [formula in source] 12 s; numpy/scipy Gaussian machinery ED-validated [formula in source] exact GF2/integer algebra; deterministic). Complete rationality (Kawahigashi–Longo–M\\\"uger) [formula in source] split [formula in source] strong additivity [formula in source] finite two-interval [formula in source] -index; v501 (WP5d- [formula in source] ) wi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-21 (XIV) ( v504 — WP5d- [formula in source] of CELEST.SEAM.01 ``split [formula in source] strong additivity from the lattice'' promoted as CELEST.WP5DB.01: the two remaining KLM legs of complete rationality witnessed for the orbifold prescription — strong additivity ALGEBRAICALLY EXACT with the shared boundary Majorana ( [formula in source] , GF2 spans full, rank [formula in source] ; disjoint exactly index [formula in source] [formula in source] the v501 [formula in source] bit), the entropic touching defect BOUNDED [formula in source] with the Ising [formula in source] -exponent approach ( [formula in source] ) while the preregistered [formula in source] /Dirac control DIVERGES (Klich–Levitov pinned, infinite index), the split property at the elliptic-nome rate [formula in source] ( [formula in source] – [formula in source] ) with EXACT orbifold inheritance ( [formula in source] [formula in source] the [formula in source] compound — Longo heredity), and Pimsner–Popa [formula in source] identically ( [formula in source] , [formula in source] , [formula in source] — two independent index routes); with v501 ALL THREE KLM ingredients carry lattice witnesses; the continuum uplift stays \\ — ``finite-group orbifolds of completely rational nets are completely rational'' is XU'S THEOREM, cited not claimed; Wolfram extension [formula in source] (verified engine run); SEAM.EQUIV.01 stays , CELEST.SEAM.01 stays Open, no marker moves)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":30629,"byte_start":25724,"id":"section:a036d63765e830eb593f","kind":"subsection","labels":[],"line_end":279,"line_start":232,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:11077c02234ce173b0a3","relation:19a18d09aecad4791461","relation:23f6c818485ad20cd1a0","relation:2b20020c48e6c93b2f19","relation:3bbd59461df1c6933a7b","relation:74636267ad23a7047cf8","relation:764027fb417e1c8246bd","relation:98db44354641b1c02a28","relation:9dcd6e096cfb28cfb24e","relation:a9ec4abb44f34a99466f","relation:aa3d65d7a4f79fb26d40","relation:b0f8046e626744cf8f59","relation:b4562af2386de919630b","relation:bdf921d94be2443e9601","relation:c753785a0f80457e221a","relation:d076057fe58d3d212a62","relation:d2f8034cf63dc2172820","relation:dae7569ed591fda1c717","relation:dc28f0e8d57b5e07feea","relation:f8ff72d9935735a12b4e","relation:f9b3ac16c262b07f7a34","relation:fc310ab40cd4ab441ab8","relation:fe3daad41857eb3b7fa1"],"semantic_review":false,"source":"documents/changelog/sections/006-source.tex","status_markers_as_written":["\\mC","\\mO"],"summary_excerpt":"v503_qgeo_emergence_light.py ( QGEO.EMERGE.LIGHT.01, 17 checks; mpmath [formula in source] digits [formula in source] v280-style lattice DtN [formula in source] sympy exact). The v215 lever 7 (``the decisive kill is deferred: compute the raw seam-collar DtN without inputting the marks and check whether four square marks emerge'') executed in its first honest light version. No dynamical selection: [formula in source] ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-21 (XIII) ( v503 — the v215 deferred emergence test (lever 7) executed light and promoted as QGEO.EMERGE.LIGHT.01: NO dynamical selection of the square modulus — the free field's global [formula in source] winner is the hexagonal torus, [formula in source] is a saddle, criticality at the square is Palais symmetry; the square is pinned by rigidity alone (the raw DtN is mod- [formula in source] block-diagonal iff [formula in source] , an isolated zero); and the residual converges: QGEO-R1 [formula in source] P2-R1 [formula in source] one common rest, ``why does the raw seam carry the order- [formula in source] clock''; Wolfram extension [formula in source] (verified engine run); NO marker moves — QGEO.REALIZE.01 stays / , AX.P2.01 stays a declared axiom)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":35959,"byte_start":30629,"id":"section:8abc3c61baefc9b60bc8","kind":"subsection","labels":[],"line_end":330,"line_start":280,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0738fcb4768ac6b7e6fa","relation:25cb996fbab42eef51f8","relation:457b63df5bc8c2641e5d","relation:608383d26ffeae2f653f","relation:962ffa555750e5316ba4","relation:98b2f29e01a075d0b9ce","relation:9a1be910c72c27530a3c","relation:9cb0bb20c335ddda3daf","relation:ae7a42a546b860c834f6","relation:b5f7bb8b2bea9e860084","relation:bb4202c83e0e57aeb3d8","relation:d0596b18b877b85596b9","relation:e9f9a4d9c5fd57c4f0bd"],"semantic_review":false,"source":"documents/changelog/sections/006-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v502_celestial_wp5e_prefactor_level.py ( CELEST.WP5E.ALPHA.01, 33 checks, exact sympy/Fraction, no floats). The two exactly computable consistency anchors of the WP5e twistor uplift established. Part A — the prefactor: Hurwitz- [formula in source] exact ( [formula in source] ; [formula in source] ; Ising shift [formula in source] per Majorana); the clock is inner ( [formula in source] and [formula in source] both rea","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-21 (XII) ( v502 — WP5e- [formula in source] of CELEST.SEAM.01 ``prefactor and level bookkeeping'' promoted as CELEST.WP5E.ALPHA.01: the [formula in source] prefactor of [formula in source] IS exact [formula in source] vacuum-energy bookkeeping (the clock is inner [formula in source] shift orbifold [formula in source] , common [formula in source] ; discriminant form [formula in source] Casimir via spectral flow AND [formula in source] -Majorana free fermions), and [formula in source] is forced THREE independent ways (current condition; conformal embedding; central charge [formula in source] the prefactor itself; plus the WP5b singular-vector dial [formula in source] ); honest sharpening: glue- [formula in source] integrality holds for ALL [formula in source] and fixes nothing; the BCOV/Costello–Li twistor inflow stays \\ — WP5e is subdivided ( [formula in source] done, WP5e proper open); Wolfram extension [formula in source] (verified engine run); SEAM.EQUIV.01 stays , no marker moves)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":40546,"byte_start":35959,"id":"section:b18b388084f449438cbb","kind":"subsection","labels":[],"line_end":374,"line_start":331,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0ba5035ebde56e544169","relation:10f898681512d084515d","relation:1391a2f3f9c05cec9037","relation:16c3cb80ea5871b2cb9d","relation:189679c8ea3d1ae111f2","relation:1b2cadbc9145bad0a8f4","relation:1b6c3dc3dc167b32ed2a","relation:500ecd6406dbce06b108","relation:7255b0ece29701fc217e","relation:8578dfc37ba3c7470cfa","relation:86fa67191639fc38ef6a","relation:924d7005669d739a5d0a","relation:93dec7c47ae3a10ec89f","relation:a43553bbd09b64102602","relation:bbe099175bb305db9fe0","relation:c20daab9dc91911ade2a","relation:d9c2042d604149fc1a9c","relation:f06a05a06060a2007a5f","relation:f4d7f673546ce3711594"],"semantic_review":false,"source":"documents/changelog/sections/006-source.tex","status_markers_as_written":["\\mC","\\mO"],"summary_excerpt":"v501_celestial_wp5d_two_interval_index.py ( CELEST.WP5D.01, 39 checks, numpy/scipy Gaussian machinery [formula in source] exact Fractions). The WP5d roadmap discriminator — [formula in source] (Haag-dual two-interval net, one sector) vs [formula in source] — executed at the [formula in source] (lattice-index) stage on the v367 seam edge ( [formula in source] critical Majorana layers, [formula in source] , v450-style ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-21 (XI) ( v501 — WP5d- [formula in source] of CELEST.SEAM.01 ``the two-interval index from the lattice'' promoted as CELEST.WP5D.01: the KLM Haag-duality discriminator measured entropically on the seam edge — the [formula in source] -layer carrier saturates the [formula in source] offset at machine precision, [formula in source] the v490 census, and the condensation arithmetic [formula in source] closes with [formula in source] ; the preregistered KILL (`` [formula in source] -offset [formula in source] after condensation'') does NOT fire; contract now ``WP1–WP5d executed; WP5e the single remaining milestone''; Wolfram extension [formula in source] (verified engine run); SEAM.EQUIV.01 stays , no marker moves)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4795,"byte_start":0,"id":"section:82c47adfed4340093cda","kind":"subsection","labels":[],"line_end":46,"line_start":1,"numbered_or_version_tokens_as_written":["S4.10"],"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:07374d379f24b3d54981","relation:1443a2e610fa8bfaffd8","relation:2878ec596151a1e430c7","relation:446909b8f2bd125443f2","relation:475363596382ea1e8934","relation:4f97b39971878d18b510","relation:a59b50c2d64e82fe94ba","relation:a9203f100b5c8b7bd3ec","relation:cc0327fc442c8be3b170","relation:ed7e3351e87111099ac5"],"semantic_review":false,"source":"documents/changelog/sections/007-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v500_celestial_wp5c_gns_limit_state.py ( CELEST.WP5C.01, 35 checks, exact integer/Fraction, no floats, deterministic). WP5a ( v497) made the boundary limit precise, WP5b ( v498) built the deleting operator; WP5c constructs the state. [formula in source] is quasi-free: loop sector [formula in source] the affine [formula in source] vacuum [formula in source] -point functions via the machine-determined compact anti-invo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-21 (X) ( v500 — WP5c of CELEST.SEAM.01 ``the GNS limit state'' promoted as CELEST.WP5C.01: the quasi-free family [formula in source] exists, is positive, stabilises exactly at the WP5a threshold, and its limit carries the null ideal in its GNS kernel — the full [formula in source] -block exact level-2 Gram has rank [formula in source] exactly with kernel [formula in source] weight by weight; [formula in source] IS the GNS zero vector (the WP5b S4.10 tension resolved at the state level); a CCR obstruction proves the family formulation necessary; preregistered SUCCESS criterion met, KILL not triggered; Wolfram extension [formula in source] (verified engine run); SEAM.EQUIV.01 stays , no marker moves)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9640,"byte_start":4795,"id":"section:749d598aa0815d32790b","kind":"subsection","labels":[],"line_end":94,"line_start":47,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0954203839038438cc7e","relation:1034c588c46e2b107c26","relation:2500fb406758bc9e7bea","relation:2b7754abebdb892cec62","relation:2c0523759ddd37d7926f","relation:3ab7ccd1a5a587326123","relation:4bd8678217563b10b5fb","relation:4da1b40db0a93a8928ca","relation:509df4cad018a646575b","relation:50c9c136eeedd0e47451","relation:59e57b5e3e7edbf2af48","relation:5de87ee5d894d18e1744","relation:6b77e3ac21fb62b12b4f","relation:7aad19eac1ebe53553bb","relation:7ac9bbb770cf90afcdea","relation:7b7feeda970ac12fb697","relation:922d82edb7dd0fe795f5","relation:9e2827763665ae7e8680","relation:ac1ad455810f5942ba6b","relation:adee9469e8efd4c1e1bb","relation:b9b660efe758aa873148","relation:d00bc56be46f1df03469","relation:d15f1aa543fdd905cc19","relation:d355ca08822d12242a14","relation:f2449640bd231d1b5422","relation:f7daab7faeea69f85a06"],"semantic_review":false,"source":"documents/changelog/sections/007-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v499_p2_weights_deligne_bg.py ( P2.TYPING.01, 23 checks, sympy exact, no floats). v491 reduced P2 to `` [formula in source] positive integers summing to [formula in source] ''; its residual was the typing (why integers, why positive, why sum [formula in source] ). Now typed: given the \\ anchors ( [formula in source] marks, v216; rank [formula in source] , v137/ v228; cusp-class local monodromy [formula in source] and","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-21 (IX) ( v499 — the P2 weight-typing postulate HARDENED: the anchor [formula in source] typed as the Birkhoff–Grothendieck splitting exponents of the Deligne canonical extension, so integrality/positivity/sum- [formula in source] become theorems given the \\ anchors; the v491 check-9 residual sharpened, the tfpt_2 ``balanced'' selection typed as stability; Wolfram extension [formula in source] (verified engine run); no gate closes, no marker moves — AX.P2.01 stays a declared axiom, QGEO.SYM stays )","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12643,"byte_start":9640,"id":"section:891953ab4ad2ba19100f","kind":"subsection","labels":[],"line_end":125,"line_start":95,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:1020d26ca78b439daca9","relation:1a2f1766f7ce09c31f1d","relation:2c507d38769f3e28f646","relation:34b0e99b3dd43e904174","relation:43e42fc5013ec66321e0","relation:4e770b407c5a063625ac","relation:5924615548f0fa01e818","relation:7b75c93d37f35b2f6d4d","relation:8143cfc37bd34e1ea3d8","relation:85367933f36aab176c19","relation:85b8e99f06fc4d06fbcf","relation:a821899aab43031a9423","relation:b63ad803ab646f09afe8","relation:c132e710a4128f4f16d7","relation:d4878617456acfb43cc8","relation:da5a687c1fc63d542cfb","relation:fd27e7a29d2d15551d12"],"semantic_review":false,"source":"documents/changelog/sections/007-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"tfpt_3_e8_audit_bootstrap: new section ``The celestial route: from the [formula in source] clock to the [formula in source] boundary shadow''. 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Success on the preregistered WP5b criterion: the deleting object exists and is explicit. Construction: [formula in source] (weight [formula in source] , level [formula in source] quarter units [formula in source] , an integer level) in a machine-built Chevalley/Frenkel–Kac basis — bimultiplicative [f","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-21 (VII) (CELEST.SEAM.01 WP5b executed and promoted: v498 — ``the singular vector as an operator'', the deleting object of the v497 null ideal constructed explicitly and machine-verified singular; contract now WP1–WP4 [formula in source] WP5a [formula in source] WP5b done, WP5c–e \\ (roadmap); Wolfram extension [formula in source] (verified engine run); no gate closes, no marker moves, SEAM.EQUIV.01 untouched)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":22130,"byte_start":17672,"id":"section:6ac9a89a114dc5f7b30d","kind":"subsection","labels":[],"line_end":221,"line_start":177,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0101b7018d5b1cc86ad4","relation:124f0087b45354e33ce2","relation:3162c65ededc7fc0e6b7","relation:331e81c9554bab03c6e2","relation:5e971446aa38bbb2f581","relation:9657f979adb9f9b84a4e","relation:bb44300abf5ee9fdc7f5","relation:d365697cf75a01e95e95","relation:df64c6c1fbbc78a1785d","relation:e58863525f37b2cff942","relation:e8015f2e6583181abf40","relation:ecadce1957b685570359","relation:fe8d58f468b562a41a58"],"semantic_review":false,"source":"documents/changelog/sections/007-source.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"v497_celestial_wp5a_null_ideal.py ( CELEST.WP5A.01, 34 checks, exact integer/Fraction, no floats). Three results make the WP4 limit reading precise. 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The pre-registered WP3 ``alignment test only'': the Okubo coefficient [formula in source] is derived as an exact polynomial identity for all 8 algebras on Costello's list (sl [formula in source] , sl [formula in source] , g [formula in source] , so [formula in source] , f [formula in source] , e [formula in source] , e [formula in s","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-21 (III) (CELEST.SEAM.01 WP3 [formula in source] WP4 executed and promoted: v495 Green–Schwarz alignment (verdict B, honestly non-selective) [formula in source] v496 character-vs-S-algebra type mismatch (verdict B(ii), boundary-limit shadow); contract now WP1–WP4 done, WP5 ; no gate closes, no marker moves, SEAM.EQUIV.01 untouched)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":33724,"byte_start":30473,"id":"section:e2d9ada460279647968e","kind":"subsection","labels":[],"line_end":342,"line_start":310,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:639172a5ee53613d30c3","relation:8ddd7ff8c0806f46d20e","relation:f0df0a6d61f777eb9637"],"semantic_review":false,"source":"documents/changelog/sections/007-source.tex","status_markers_as_written":[],"summary_excerpt":"experiments/pulsar-glitch-recovery PG.06b FULL executed ( tfpt-pulsar vela-full). 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This module shows the shared rule is NOT a new unknown: \\ the unit chain [formula in source] — one bare boundary insertion divided by ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-14 (III) ( v484 — the two open analytic targets MERGE: the shared `` [formula in source] per boundary insertion'' rule of ALPHA.QUILLEN.EXACT.01 and HYP.PHI0.PUNCTURE.01 is the KMS seam unit [formula in source] with [formula in source] , derived on the seam circle for the finite cycle sector — no gate closes, no marker moves)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6074,"byte_start":2559,"id":"section:db9b59159ab5489cccfa","kind":"subsection","labels":[],"line_end":61,"line_start":27,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:1453c3f4427af137ab7b","relation:3383afc42d3300973530","relation:3a2ce46fd47f32484429","relation:3d1d62a7534d5a2c2a54","relation:42f35307d9fae3ac8397","relation:4b3e1ff7df1bdadae7d4","relation:4b6b6a464ecc9d10cf88","relation:4c63343db614761b4121","relation:702238dcc45e1711d865","relation:7b7a5c2a746686dd3157","relation:847c5b740ca09da11d3d","relation:9f36de774bd750714df5","relation:a8d2c1c46b92a7632905","relation:bd90cff8e038b3f2df10","relation:cc901b6e9c99d2cc1f7c","relation:faa391515353062ab091"],"semantic_review":false,"source":"documents/changelog/sections/009-source.tex","status_markers_as_written":["\\mC","\\mO"],"summary_excerpt":"v482_seesaw_rung_decision.py ( FLAV.NUSCALE.03). The decision computation NAMED by v481 is EXECUTED in bracketed (assumption-robust) form: the integer rung [formula in source] needs a rescue factor [formula in source] in [formula in source] ( [formula in source] vs [formula in source] eV), while [formula in source] GeV ( [formula in source] ), [formula in source] ( [formula in source] ), a [formula in source] band on","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-14 (II) ( v482– v483 — the deep-dive round: the [formula in source] -scale decision computation EXECUTED (the integer [formula in source] -rung excluded unstructured, the [formula in source] -proximate structure escape recorded and declined) and the [formula in source] puncture target HALVED (the geometric side proven exact: all twisted pillowcase heat traces are [formula in source] -independent rationals, so the [formula in source] must sit in the per-mark coupling weight) — no gate closes, no marker moves)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11940,"byte_start":6074,"id":"section:fe85126d1b3e41ef8954","kind":"subsection","labels":[],"line_end":130,"line_start":62,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:02d9693f1efb0b30121e","relation:1a61ca1ad37d62cc5165","relation:2726e325095d452cf605","relation:2a16e3435ccd2189d204","relation:39a0b887e6ca6d94d49d","relation:3c6ad21111459f7a4708","relation:4bd56c49bd7d8bd5db13","relation:6aa1d02b0dd013c84bab","relation:6c41860932ac5e7aa6b3","relation:72234f118663a554907c","relation:82894b90dc802cbd9dae","relation:87017ab5f43d29090766","relation:936ee2bb0855290ad315","relation:97c4eeaddb02f26ab230","relation:9c2506fb8e6e1bb83706","relation:a0b528348ea60bc05492","relation:a684f99d71bbb9122b45","relation:aa43b1e04bbc6d0c81b2","relation:acad4131a26eaebe1fb1","relation:ce5dec1c675170ccaa8e","relation:cecfce28dfab84891ad5","relation:cff745d76dc7ddeaaa68","relation:d25fdaa91664f5aef433","relation:d3a10e6220938b8cacc0","relation:d42c99080c4fbd5312ac","relation:f8f74a82721757a0cfdf"],"semantic_review":false,"source":"documents/changelog/sections/009-source.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"Website /verification: live journey views. The static script_timeline.png and residual_chain.png images (stale at the v303– v407 figure state, with alt text and captions still describing the old eleven-phase/ v237 state) are replaced by two interactive components, SuiteTimeline.tsx (17 phases, v1– v481) and ResidualChain.tsx (the reduction chain through the certification round to the bedrock): every phase/step lists ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-14 (website + figure refresh — the /verification journey views become live HTML (the stale timeline/residual-chain images replaced by interactive components wired to the in-browser reproducer), the prediction surface's empirical-audit wall of text restructured into dated, expandable rounds, and the generated timeline/residual-chain figures extended to the current suite — presentation only, no content or marker moves)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18190,"byte_start":11940,"id":"section:e99d6098550f62e277de","kind":"subsection","labels":[],"line_end":192,"line_start":131,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0a853ced78323ff6e636","relation:0f1e23e7009e261789eb","relation:2bbb9010690ecc312d30","relation:2ea4615e8084b82ed237","relation:32d54bd9f87f4b7b11d3","relation:3e83bb0fa7831905345d","relation:3fe265ec87d41f467d8d","relation:55db3e0078d3a5698cee","relation:597183e053f02f2821b7","relation:5c695f4a3760c3997cbc","relation:669ed5d47ce014866333","relation:68ce380fee3566abdcc2","relation:6e250e01c82ceac8a6fc","relation:6fd63dbbac5e09a9518e","relation:702c33525ac6f8e89538","relation:71953effe2a23e89d5b9","relation:744e4570e2103eee68e5","relation:7512502868dbcc9cbce1","relation:7e957ca78f496024cfa5","relation:84483139af541b1fb459","relation:85eafcaac49a698b6ae6","relation:9e6342df46e491663fad","relation:a00b8221f8fcf9c2fc4b","relation:b3a03112c9bd8193b811","relation:ba6e5e7a2bf5d6b8258f","relation:be084d8ce4d1eb5eac94","relation:c2b8a79b127a03602eeb","relation:cb3ddc9890601294ca1f","relation:cb97bbf37a7ab93a10cb","relation:cd0f59f573af918b933f","relation:dd047934b72ab429c556","relation:e8f04c7a790310188c6e","relation:ebc2d2ef7b64a88f74e9","relation:ec13eade1d56cac76bd3","relation:fb3dd554eee1b83ba0d9"],"semantic_review":false,"source":"documents/changelog/sections/009-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO","\\mX"],"summary_excerpt":"v479_kronheimer_quiver_bridge.py ( SEAM.KRONHEIMER.01). The R3 residual of the [formula in source] keystone ( v344: ``the rewrite attractor graph IS the du Val singularity'') is an ESTABLISHED THEOREM — Kronheimer's ALE hyper-K\\\"ahler quotient construction [formula in source] Torelli classification (J. Diff. Geom. 29 (1989) 665 and 685) — with all finite input data already compiler outputs, machine-checked : the Kac ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-14 ( v479– v481 — the bird's-eye ``overlooked tools'' round: R3's graph [formula in source] geometry bridge discharged to Kronheimer 1989; the four [formula in source] marks realised as the exactly solvable four-interval multilocal modular geometry with [formula in source] manifest; and the absolute [formula in source] -scale collapsed to a one-parameter, PS-window-bracketed candidate under the carrier normalisation [formula in source] — no gate closes, no marker moves)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20632,"byte_start":18190,"id":"section:671808877239add5f598","kind":"subsection","labels":[],"line_end":215,"line_start":193,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0abf1aee91bb417a2f1d","relation:1cc6f8d732952bc46eb2","relation:20ab05be9b0b23ad3ecf","relation:289f644cd93db9f700dc","relation:5212d01d1dc2ce5e0204","relation:71e99c7027677c223eee","relation:720f4f2803e28d23998e","relation:816326d99c9e1198d19d","relation:8b1bffd41c2a37a1b7a7","relation:8c1fee53b068913bdc4b","relation:951f1fb5ab408f5a93be","relation:9578069696743b6e4d67","relation:95f10aecd98b5c0de1a6","relation:a484e060b86e96a5c2cd","relation:b5e8ed494ff16f63d4cd","relation:b8d7075c65f845212946","relation:c2eedb34adecde4fa62e","relation:cb51f75dc3800e99b788","relation:d74f01e483d3d3d92acc","relation:d797c165f6aa6049feeb","relation:e49bc2bec6c1c16e44a6","relation:f06dcacb0af3ff6986d5"],"semantic_review":false,"source":"documents/changelog/sections/009-source.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"v478_entropic_continuum_legs.py ( GRAV.ENTROPIC.LEGS.01). Leg A (AP2 continuum, exhibited): on the exactly solvable critical chain (infinite-volume sinc kernel, [formula in source] -digit precision) the compressed interval state has [formula in source] with [formula in source] (monotone [formula in source] the Dirac [formula in source] , the v450 reading; gapped control [formula in source] , area law); the Peschel mo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-13 ( v478 — first computable steps on the two remaining legs of the entropic-action bridge: the state-side modular data flows to the CHM/Bisognano–Wichmann geometric form (Calabrese–Cardy [formula in source] , CHM parabola, even bands exactly zero) — the bridge's modular side meets TFPT's Einstein-derivation input; and the measure condition reduced to one exact KMS time [formula in source] with the [formula in source] near-miss explicitly declined; both legs stay , no status moves)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":22969,"byte_start":20632,"id":"section:8f73277edff787de34d0","kind":"subsection","labels":[],"line_end":238,"line_start":216,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:101924f381aa2984652b","relation:16020e694fe2ca792702","relation:196b770d63431affe8a0","relation:20186576ccb963b20641","relation:35cbbed1af66618a59fd","relation:4ec373052e3cb1dc5821","relation:52660e0bab2260a7cf68","relation:554c03b5f958ed1a028b","relation:5eedde062812e2878ebb","relation:be2748b7b012dde5e095","relation:e94918d42df1625848b1","relation:fdd6e28b2d49ad6190d1"],"semantic_review":false,"source":"documents/changelog/sections/009-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v477_entropic_scaleflow.py ( GRAV.ENTROPIC.SCALEFLOW.01). \\ The Frullani identity upgrades to a scale-flow representation: [formula in source] (symbolic [formula in source] [formula in source] quadrature) — Bianconi's log action IS the flat scale-integral of relative heat-kernel actions, while TFPT's [formula in source] evaluates one KMS scale with a weight: the bridge between the two action principles is a choice of","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-13 ( v477 — the scale-flow representation of the entropic action: the surviving [formula in source] route typed as one moment condition [formula in source] with the exact closure [formula in source] — the kill-test gap is a scale-measure datum, satisfied by the same KMS moment TFPT already fixes ( v36); zero new dials, no status moves)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":25377,"byte_start":22969,"id":"section:67117a94f5952e2ebab9","kind":"subsection","labels":[],"line_end":262,"line_start":239,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:05907f0324a0b57522ba","relation:0ad687c8075b199f9613","relation:1a07d244442a7f05f08b","relation:2e37fd239670079e51c9","relation:45fad200c12d0e4ec7fb","relation:4fcc56a1a8e6ca1cc695","relation:66111ed7b0bf286c0721","relation:7400c2fc8dd77005c90b","relation:771bd052c1654077841b","relation:7e88a920492e4e68c953","relation:a70f3e57fff73ee95061","relation:b80e8eb41ae6c781c5ea","relation:dbc7b543feb801d84ce9","relation:e87f5c6182a0f157e86a","relation:ff651368f8b2d23b6668"],"semantic_review":false,"source":"documents/changelog/sections/009-source.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"v476_entropic_compression_toy.py ( GRAV.ENTROPIC.COMPRESS.01). The last open work package of the v473 round, exercised on a gapped staggered-mass chain ( [formula in source] ). The seam situation is reproduced (pure bulk: the ground-state covariance is a projection to [formula in source] ; thermal boundary: [formula in source] , Peschel [formula in source] finite, [formula in source] — v155 in the bridge context). Th","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-13 ( v476 — the AP2 compression conjecture of the entropic-action bridge made well-posed on an exactly solvable model: the literal operator-side reading is ill-posed on a pure bulk, the state-side reading is forced, the mismatch is exactly quadratic in the cross-cut correlations and gap-suppressed; AP2 stays , no status moves)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":27836,"byte_start":25377,"id":"section:b4b55c039ea31bf60d78","kind":"subsection","labels":[],"line_end":287,"line_start":263,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:06909981b5eb4aa8f9b1","relation:09b81f4aad29fad8cb42","relation:0d2aee81e504fa439ea8","relation:1a02e3d82f4ff72d6d4c","relation:689000c8a191b58153cd","relation:76cd8fabab94a18c925c","relation:7ee5a212da19480dec90","relation:cd8f51d0b9c8ffaacef4","relation:f3dd7377d4e3d0c2001b","relation:fa60bfaa33446277b028","relation:fa77a6ad86ca3705ba21"],"semantic_review":false,"source":"documents/changelog/sections/009-source.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"v475_entropic_scalaron_gate.py ( GRAV.ENTROPIC.SCALARON.01). Work package 5 of the v473 bridge. \\ On a maximally symmetric background the relative curvature operator [formula in source] has eigenvalues exactly [formula in source] (Bianconi's Appendix-B flattening verified symbolically, incl.\\ the [formula in source] two-form block), giving the exact vacuum action [formula in source] — the [formula in source] re-deriv","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-13 ( v475 — the [formula in source] kill test of the entropic-action bridge, executed: exact tensorial factors on the maximally symmetric background, raw entropic scalaron [formula in source] ( [formula in source] , trans-Planckian) [formula in source] the light-trace-mode reading is dead, KMS renormalisation the only surviving [formula in source] route; plus the explicit Lorentzian-positivity witness; no status moves)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":30778,"byte_start":27836,"id":"section:a8fda6d5b1c48ce7d8c8","kind":"subsection","labels":[],"line_end":316,"line_start":288,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:29c5ac14ddf857a418f9","relation:2b2d06fbba338f49aa61","relation:3089c7fe2ee066272183","relation:45d3e370fca207353c9d","relation:4882e48b1ff286963519","relation:5c77a46b8b537cdfa1d1","relation:6761829ac443623f87a4","relation:854f29ba59fe6451b5fa","relation:86dd0535199bf45aecc4","relation:a245db5489942775ae63","relation:c0d8451fff4dd8112c98","relation:c43c90ef18127eb1a1e7","relation:cd6093acca4a2cac384a","relation:f7d43ef491566cbc8278","relation:f80b54441f007a23b02d","relation:f9bf7b32402fe84a8a50"],"semantic_review":false,"source":"documents/changelog/sections/009-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v474_entropic_hodge_carrier.py ( GRAV.ENTROPIC.HODGE.01). Work packages 1 and 4-algebra of the v473 bridge, machine-checked on the finite carrier Fock space [formula in source] ( [formula in source] ). \\ CAR [formula in source] Clifford: the ten [formula in source] 's from [formula in source] satisfy [formula in source] exactly (all [formula in source] pairs, integer matrices); the [formula in source] bilinears [form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-13 ( v474 — the operator level of the entropic-action bridge: the [formula in source] Clifford/spinor structure exhibited on the carrier Fock space, the Hodge fold identified as the [formula in source] conjugation, and the v473 [formula in source] -target decided — supports exactly [formula in source] , the naive pair-block reading killed; no status moves)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":33746,"byte_start":30778,"id":"section:7df526709d9eeccd2491","kind":"subsection","labels":[],"line_end":345,"line_start":317,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0dd4e949764023648749","relation:276c76ed4463b3162be0","relation:2f36bcddff368056f46a","relation:4393fe9363ebe5fa9858","relation:50648d35f6c26c1d1afd","relation:6820ef62b4cfd4c963eb","relation:70000477d9092fede46f","relation:7406a9f5e67b9e35be9d","relation:7ad305f7ef5e7cf81443","relation:85df4110ed98f63d38eb","relation:8895da1620f1f0a64e65","relation:ad601c51c6f5e6de2847","relation:e679d308f99b5929f888"],"semantic_review":false,"source":"documents/changelog/sections/009-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v473_entropic_action_bridge.py ( GRAV.ENTROPIC.ACTION.01). TFPT's classical field equation [formula in source] is derived thermodynamically ( v358/ v359) and honestly typed ``equation of state, not a from-action quantisation'' . Bianconi's entropic action [formula in source] (the quantum relative entropy between the spacetime metric and the matter-induced metric, Araki-related via [formula in source] ) is a local cov","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-13 ( v473 — the entropic-action bridge: Bianconi's Gravity from entropy (Phys.\\ Rev.\\ D 111, 066001 (2025); arXiv:2408.14391) quantified as an external candidate for the missing action level of the parameter-free Einstein equation; her free constant pinned [formula in source] , the [formula in source] gap [formula in source] pre-registered as kill test; no status moves, the v359 equation-of-state typing stays )","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":36321,"byte_start":33746,"id":"section:1d709d6b4fbbfe522d4a","kind":"subsection","labels":[],"line_end":371,"line_start":346,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:03e20848bd0f31b4c53c","relation:0df1af74a6f9d0f6e21c","relation:64694deceb8433d25d69","relation:cb207f130fec0c8c3d1c"],"semantic_review":false,"source":"documents/changelog/sections/009-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Uniqueness scan follow-up (no new results — presentation only). A structure scan for ``what does TFPT predict that nobody else pins?'' found three concrete, falsifiable readouts that were fully computed and ledgered but missing from the public prediction surfaces; they are now surfaced, with their existing typing unchanged. 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Plus: the GW ringdown-echo channel hardened — 10 loudest events incl.\\ GW250114, redshift-corrected templates, stacked search and a 12-variant signature battery, all null)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10807,"byte_start":9694,"id":"section:90bdf395a7242e67386f","kind":"subsection","labels":[],"line_end":107,"line_start":95,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:01153772c9af9ea716e5","relation:039a18d8967cfbcd3c68","relation:4117e79b27741fce7906","relation:7fdd124120e39044fb85","relation:8f59f6315bc5f7920244","relation:be216b2917b3739387d4","relation:c492afa3ad707fdd50d0","relation:e3c67198eaeadda48f12"],"semantic_review":false,"source":"documents/changelog/sections/010-source.tex","status_markers_as_written":[],"summary_excerpt":"v295_flataway_a2_exact.py ( FLATAWAY.A2.01). 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The [formula in source] -spinor extension leg of SEAM.EQUIV.01 no longer rests on 2024/2025 preprints: \\ the [formula in source] spinor has [formula in source] , so its statistics phase is [formula in source] — exactly the Longo–Rehren locality criterion — and the [formula in source] simple-current crossed product [formula in source] is a local index-","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-07-02 ( v469/ v470 — the closure-route round on the two named targets: the SEAM.EQUIV.01 extension leg re-founded on 1995–2001 peer-reviewed crossed-product theorems [formula in source] the realisation axiom reduced to invariant level; the [formula in source] level [formula in source] the computed bulk Chern invariant [formula in source] the seam [formula in source] -normalisation [formula in source] the embedding index [formula in source] ; both targets stay )","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":21315,"byte_start":17057,"id":"section:3317d161dfba545d677a","kind":"subsection","labels":[],"line_end":218,"line_start":176,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:04969efc309430386cab","relation:07d2eed7f55bd3d5352b","relation:2158ee06069d362b0562","relation:25c5309010e8ebaadd31","relation:330f16a3955a77017453","relation:3da1f9c226ea19df14a3","relation:475f4dca8bd8c01abb93","relation:5b1217b82654eca25ddd","relation:722124376f260cbce4eb","relation:77b8e6705251f57ef69a","relation:8f20b456691cc0bbc033","relation:93dae5fe035897ba382b","relation:94fe6072fd4cff2b63fa","relation:998cccb2c55333170b3a","relation:babaedd8ecf30c809efd","relation:ca6ac1c9b661f96129cb","relation:cab2b9002f9b28cb2391","relation:d359bf3f8bae2a33ab5a","relation:d6b26f5d5d9bd4b09291","relation:e6bb7151cbfcabef132f","relation:f1e9a924ec01d54240ec","relation:f218b973472078540411","relation:f3e9d5a43abd2beaf578"],"semantic_review":false,"source":"documents/changelog/sections/010-source.tex","status_markers_as_written":["[C]","[E]","[N]","[O]","[X]","\\mO"],"summary_excerpt":"v467_thirdgen_mixing_pattern.py ( FLAV.THIRDGEN.PATTERN.01). 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The recent G-block modules all sharpened the target of the scaling limit; this round attacks the two halves that actually remain. 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Sharpens v460's verdict from a cited statement to an exhibited topological obstruction on the same v367 [formula in source] collar. \\ CHERN INTEGER: the FHS Chern is [formula in source] (chiral [formula in source] ), [formula in source] (trivial [formula in source] ), [formula in source] (opposite mass). \\ WILSON-LOOP / WANNIER-CENTRE WINDING [formula in source] CH","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-30 ( v461/ v462 + Lean axiom merge — the strict-locality obstruction made explicit, the 128-spinor extension exhibited at character level, and the SEAM.EQUIV.01 residual reduced to ONE realisation axiom [formula in source] ONE combined cited theorem)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":36744,"byte_start":34215,"id":"section:586aafa793fa108ed39d","kind":"subsection","labels":[],"line_end":371,"line_start":348,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0ea3167d64813ecf7336","relation:1092277afa8133f54db5","relation:1f4e73cf809884d707fe","relation:6da59f82201021f38f97","relation:96e38c9f217a548254d1","relation:a30f6e239346b3b85713","relation:b2a754112b8a586f1a53","relation:bade67fe02bfdd8bc697","relation:bccfa86613546a4f6caf","relation:c1262568c64a0d1ccac4","relation:c40b6125a1f187da234f","relation:cf0b580a39754fb27a65","relation:d27e7ab4d1843bd985d1","relation:edaa4097640ecc63f53c","relation:fb93e73bf23ab64670c1","relation:ffb84f5fdd5732e6d023"],"semantic_review":false,"source":"documents/changelog/sections/010-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v460_seam_s3_lto.py ( SEAM.S3.LTO.01). NPW26 ( arXiv:2605.10693) prove the intrinsic Bisognano–Wichmann lemma for commuting-projector (local-topological-order) models with a [formula in source] reflection; v424 reduced the keystone BW residual to that theorem modulo two open sub-steps, of which (ii) was settled by v426 and the continuum lift of BW by the uniform-in- [formula in source] tower v455. This module attacks","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-30 ( v460 — the explicit flat-band commuting-projector (LTO) realisation of the S3 input: advancing the SEAM.EQUIV.01 sub-step (i) from abstract existence to an explicit gap-protected quasi-local projector net carrying the [formula in source] reflection and the [formula in source] clock)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5444,"byte_start":0,"id":"section:7ca01292e7152e165e80","kind":"subsection","labels":[],"line_end":52,"line_start":1,"numbered_or_version_tokens_as_written":["P1.01"],"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:009825bec1a7b6470b8f","relation:06e551d1c09dd0d1820e","relation:08a6ed39fd95f650c1b0","relation:09d9af4fd34b3e24a357","relation:183ce54818f8329445d4","relation:27baa56cc7ebf9138857","relation:308d0824670f0225dde8","relation:3dc6b2a21107344c3df2","relation:48d342fe335da4519813","relation:4e697b54949e29c1854c","relation:55431890ade1f6f1b1a4","relation:5a499963b17699a37460","relation:602396eef9d12640ea41","relation:66c7f68a5f0a0b13f0c6","relation:74b26df8203eb6bf4696","relation:7e4ed6fc9d35bb7f0b59","relation:86aa1349dc4a8a0528fd","relation:86ada28faeda3600a5c9","relation:90e092b974d2f4d89dde","relation:91c01de74bbc10f6e1e7","relation:a0b350ee436e96cc0658","relation:a110495bb9d9231b73c4","relation:a6949079a687af664947","relation:ac88b3583c38bc940984","relation:bbae8951d51e8993f4d5","relation:bf1cf24d2f52eb3410a3","relation:f06c8762e7046184f93a","relation:f39acc9cfde94f115de1"],"semantic_review":false,"source":"documents/changelog/sections/011-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO","\\mX"],"summary_excerpt":"v454_seam_edge_virasoro.py ( SEAM.EQUIV.EDGE.VIRASORO.01). Tests the cited MMST ``Koo–Saleur lattice generators [formula in source] continuum Virasoro with the correct [formula in source] '' fact on our own free-fermion edge (G2). \\ the Affleck–Cardy Casimir energy fits [formula in source] ( [formula in source] per Majorana, [formula in source] ); \\ the lattice [formula in source] current closes its affine level exac","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-30 ( v454– v459 + Lean + Wolfram — the post-F ``G-block'': the lattice Sugawara current algebra, a uniform-in- [formula in source] Tomita–Takesaki tower, chirality forced by [formula in source] , an [formula in source] character kill test, the exact MMST citation audit and the complementary lattice-VOA route)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10806,"byte_start":5444,"id":"section:12f49e008971e532539c","kind":"subsection","labels":[],"line_end":104,"line_start":53,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:032091f62dcf83ec3648","relation:03ad92144f4e33eb0398","relation:07c2f6d56e65f2bee1d8","relation:1a8b12888cb5638753fd","relation:1cc37dacc32de1e66da6","relation:1eba9bfb47e33953eaeb","relation:1fcdb28634c42832899f","relation:28576a4194f6cd702bc8","relation:2a6b1911f311edda87ed","relation:35d54dd15ce55056b0b1","relation:36cee0e40a6e2fd565fc","relation:3ae6699ba9aa8a99c5b9","relation:3c3836d11b49d20999d0","relation:3e244beab3f937eabef8","relation:3fed4058530ee3fde3f8","relation:430e7bbed3dd78493331","relation:473997232f9cd585620f","relation:4bc8e5023d9b3f128189","relation:5282638fe63eba946753","relation:57e1f56243dbb1def558","relation:5a964032c8169b063a06","relation:64b71d42914f108557a1","relation:69b205c1170ef626ed52","relation:78ff63c2e00eaf09f21e","relation:8622c3d504fbe35fe48c","relation:86eb814d4fa6a55f2057","relation:8d9641abea6a7751fe61","relation:9a5c64f54828540d2385","relation:9bf641fb18a6ab91c848","relation:a3c00ce7d651af3472e7","relation:a52637fc848a1af6eb4a","relation:a88180e42c48d57191d9","relation:a8e7f5390b77e973dba1","relation:aad9f8a05954e948e766","relation:b0a0df58e99ec0ddc1e8","relation:b20deadfff251f491f74","relation:b6ad61398e7112fc8b60","relation:c3366e9b56a4cb8a328c","relation:c9e7fa38c9068f9962b3","relation:d0df122b438d8086783a","relation:d3163c018e557b59202f","relation:d32003231c701b7175ab","relation:d5c5f472dfaa4d0ca631","relation:e3bb293a7cca57a6aa03","relation:e51fd5bfc14108622c4e","relation:ecc94e6e24ecd0e4e69c","relation:f798731f2267e4c7293c","relation:ff893d7307f23abf57b6"],"semantic_review":false,"source":"documents/changelog/sections/011-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v449_seam_mmst_uniform.py ( SEAM.EQUIV.MMST.UNIFORM.01). Strengthens the cited MMST hypothesis from convergence at a single cross-ratio ( v444/ v448) to the uniformity the theorem actually asserts, on the same v367/ v368 collar. \\ cross-ratio A [formula in source] , the deviation shrinking monotonically; \\ an independent cross-ratio B [formula in source] its own value [formula in source] , so convergence is not a tun","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-30 ( v449– v453 + Lean + Wolfram — the edge CFT named end-to-end: uniform-in- [formula in source] convergence, three independent reads of [formula in source] , the Ising operator tower, the [formula in source] modular data, and [formula in source] -symmetry derived from the four marks)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15375,"byte_start":10806,"id":"section:e41d583f251c87e99261","kind":"subsection","labels":[],"line_end":149,"line_start":105,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:1bdf3e41ddf36b05aa4d","relation:214d46118c62ca6b5123","relation:2698e199528e1c418db6","relation:28c8840eb3bee03a6bbc","relation:30fbc9dd6e4537f1f488","relation:30ff3ca7c51591339563","relation:3b87846c540d4b39265e","relation:45168bdc97f9ffa3d99b","relation:581320f4758b206d700b","relation:5e9faa16ae5bf42e7b03","relation:615df65c21a55a02fb7a","relation:66a417f6f5d57ec322a4","relation:66b539de02f007826b22","relation:6abaf526fa758000c62f","relation:7599f169fa028e1e5094","relation:7b232ea9dbf8217e3c39","relation:7d1c37d7d70fcc6a41f2","relation:7f8f91f2fe5d8b16a2eb","relation:8203c38294d88b0617d7","relation:89bf8c56e36944581cb2","relation:8a34222fde07444368b9","relation:8afb23c4ae292344bfde","relation:95a894336dd3378ba31b","relation:a1f8a7301777562f5770","relation:aaffd9ad2ef9b9c6486b","relation:bd81888bc6e1f7faf956","relation:c65d17236da9e7c653e1","relation:d202d891b10b3a925770","relation:db323d23be412422cba4","relation:fdb7e181e2188ee07b18","relation:fe903bd8837e78595ae7","relation:fff126519174a73bfe9e"],"semantic_review":false,"source":"documents/changelog/sections/011-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v446_seam_clock_invariance.py ( SEAM.RIGIDITY.CLOCKINV.01). Closes v445's single residual one notch further: the operator condition [formula in source] (clock-invariance) is shown to be a consequence of a structural symmetry, not an independent assumption. \\ the OS canonical transfer [formula in source] (fixed by RP [formula in source] reflection, v54) of a [formula in source] -invariant RP covariance satisfies [form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-30 ( v446/ v447/ v448 + Lean + Wolfram — deriving clock-invariance from [formula in source] -symmetry, an independent topological reading of the edge [formula in source] , and pinning the one external MMST fact at four-point order)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17839,"byte_start":15375,"id":"section:04b7cfb5801c917940c7","kind":"subsection","labels":[],"line_end":174,"line_start":150,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:03eb42c66656edccb260","relation:1c5f03883b481f7723f6","relation:1caac04c8551123aace8","relation:2ce56e45eaf2538e3efe","relation:2edf0e7182dcf61ce577","relation:3543badb7fb314fb99c6","relation:3a8914e669e99ee57a9c","relation:3c0ee7abb89b722c682a","relation:4080e450d940ba483e5a","relation:4b3e0221adff17ae753e","relation:4ca47a8092a531cc4a5f","relation:518b0f83f23e351db7b6","relation:5da9700b2f42f694cd98","relation:689fe48e92698f782168","relation:712763170bedfe2f8f5b","relation:77003bba79eea31898a7","relation:77762c8e7db3155a6538","relation:7e918a512af038d4731d","relation:8a0f89d7c0f416231c2f","relation:97ccf722442d569ecb22","relation:9d7aa75a530f85bd6c48","relation:ab909be959ea973ac783","relation:bb5d148d5570bc6f584d","relation:c111c00bcca1d3f1db99","relation:c42502ab2d69ce26a4cb","relation:c598677eec0b1f3babd3","relation:c85bce880ac434b7360d","relation:cfdee70a994dfbdf8c98","relation:d41075c72b809d9fe4e5","relation:d7778993dc9b0d44603e","relation:daad685a1f94f25d6df7","relation:ecd34a4edcf639ba9cdf","relation:ed655a3b54fab6ab0c8f","relation:f5e024b7cfea00124767","relation:fc218238e53a804e7435","relation:ffbbd571697e42312704"],"semantic_review":false,"source":"documents/changelog/sections/011-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v445_seam_rigidity_forcing.py ( SEAM.RIGIDITY.FORCING.01). The rigidity route ( v398/ v442) showed a [formula in source] -block-diagonal [formula in source] commutes with the order- [formula in source] clock [formula in source] . This module proves the converse and the exact structure, isolating the single remaining physical premise. \\ FORCING (entrywise iff): [formula in source] iff [formula in source] whenever [for","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-30 ( v445 — the rigidity FORCING converse: commuting with the order- [formula in source] clock is exactly [formula in source] -block-diagonality, upgrading the rigidity step from ``permit'' to ``force'')","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20522,"byte_start":17839,"id":"section:fcc9c4aa50365441ef12","kind":"subsection","labels":[],"line_end":202,"line_start":175,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:113eb67dd87955613da4","relation:18e8fa9a7263af1c369e","relation:3b60e8916b40fc109125","relation:41567769a68b55b34f1c","relation:56b16af4ad2af3759e60","relation:5cbee181b3e8b364fac8","relation:7288c0b5a2bdad7c8e0a","relation:7d808544d54bd79fcc52","relation:954d12a61976a54d4401","relation:9920bf1c0a796089dfdd","relation:9e5871d942b3d63edee8","relation:9f82acb96779956ead0a","relation:a03aaeea30039a2228b8","relation:a224592d205ce3d261e8","relation:a536944447f85fd60eba","relation:af772ea4467ff917a09b","relation:ba97657c2317136fa581","relation:cbbd8d9b99919fd4fe0b","relation:cdaa3bd256e5bc721905","relation:e02e12d1e4c7bcc399e2","relation:e4486e979fe03ea5724d"],"semantic_review":false,"source":"documents/changelog/sections/011-source.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"Context. Two of the seven convergent attacks on the keystone residual are turned from numerical witnesses into kernel-checked facts, in the audit-contract style of SeamScalingLimit.lean / BWKeystone.lean: the load-bearing algebra/bookkeeping is proved by the Lean kernel, while the cited theorems and the one open continuum input remain named axioms. lake build OK; \\#print axioms clean. Tracked as two new FORM.* ledger","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-30 (Lean kernel-hardening of two of the seven SEAM.EQUIV.01 routes — the Borchers/Wiesbrock standard-pair relations and the applicability-ledger count, machine-verified with clean axioms; rigor without new mathematics)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; 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TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-30 (the chiral-edge scaling motor v444 — the edge half of the one SEAM.EQUIV.01 continuum residual: the lattice edge already carries the conformal data of a chiral [formula in source] Majorana CFT and converges under refinement, grounding the EDGE the way v439 grounded the BULK; the keystone stays )","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; 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The keystone SEAM.EQUIV.01 is ``closed modulo a cited theorem'': its one open input is the continuum existence of the seam's chiral massless scaling limit. Six new modules attack that residual from independent directions; each is honest about not closing it. 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On the exported tfpt5_shadow.zip the independent surfaces reproduced ( build.sh notes [formula in source] 11 ok; Wolfram base/extension; Red Team; Lean transcript), but the package layer did not: make_manifest.py –check reported a stale verification/website_map.csv and build.sh audit crashed because it unconditionally required website/lib/release.ts, which the shadow subset del","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-30 (shadow-export coherence — the tfpt5-shadow mirror is now reproducible as shipped: the audit is shadow-aware, the content maps are non-destructive on the website-free subset, and an export gate blocks any incoherent mirror)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":34037,"byte_start":30369,"id":"section:44fb2c4f56d2211a1e7f","kind":"subsection","labels":[],"line_end":342,"line_start":299,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:200052168760988b0047","relation:27f3c64590808454ba79","relation:2eca72e96b420f6b508a","relation:35be6e2d868c6e432125","relation:3c675cac8d61eba8877d","relation:4e7df0a9792bbb4ca380","relation:60fdaaac0e1b10cfb734","relation:66e452bcd7f311cf7734","relation:698674644e8d74e899c8","relation:725788f96fabc235d1f2","relation:827454024c3066940458","relation:85a2ca06f157e0c4c60b","relation:919e7a3dfb2020f9a352","relation:a3e172661325ec3788fc","relation:ac471ed1c455f645affd","relation:be73be9dd84b16d33c16","relation:c7691ac1b24f67b5cac6","relation:cb0e3c45624ee8d309b9","relation:d5760dde8acd02e881e1","relation:e3b135445b396bfa683b","relation:eb588fb627a874911cb7","relation:f7b4056e09bad6f38dd4"],"semantic_review":false,"source":"documents/changelog/sections/011-source.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"New /llms.txt context file for AI / answer engines (ChatGPT, Perplexity, Claude, Gemini), generated at build time from the same data layer as the site ( papers.ts, predictions.ts, version.ts) so it never drifts. 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The target ALPHA.QUILLEN.EXACT.01 ( v382) stays ; [formula in source] stays . \\ [formula in source] -power / metric-independence test. The three EM-closure coefficients carry [formula in source] -powers exactly [formu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-29 ( v435 — a fourth honest step on the [formula in source] Quillen target: a [formula in source] -power test isolates the cubic [formula in source] as the unique metric-independent (topological) rung, and types its coefficient as a conditional integer level)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5730,"byte_start":2564,"id":"section:314c7c0b2567b3598a9c","kind":"subsection","labels":[],"line_end":65,"line_start":31,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:01a0b3adcbb28e5f16b9","relation:041c06a53dc4323091bb","relation:0ecdeb820ad85ea7f4ff","relation:26ca4c1cd9c97a5795c8","relation:37748137ffe676ff706b","relation:3db58805f9a57d9f6dbb","relation:5a552cb83078997ec764","relation:5bb2980f2fd5ffe9def2","relation:982a2ff2b1f891992885","relation:b462a2680cf06c5da548","relation:bdad52c6767bf8abc679","relation:d155864c57df107036fa","relation:dc7b91df06aa531b254b","relation:e2365d2a502e1909ae09","relation:e6a0af31ddc55b94be98","relation:fdc8af72114e90592834"],"semantic_review":false,"source":"documents/changelog/sections/012-source.tex","status_markers_as_written":["[C]","[O]","\\mC","\\mE","\\mO"],"summary_excerpt":"New module v434 ( ALPHA.QUILLEN.PROGRESS.03) — it settles the status of the three residuals named after v433 and shows they are not three independent open problems. The target ALPHA.QUILLEN.EXACT.01 ( v382) stays ; [formula in source] stays . \\ [formula in source] is the [formula in source] [formula in source] heat-kernel coefficient (the [formula in source] theorem). The one-loop [formula in source] function of a ga","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-28 ( v434 — a third honest step on the [formula in source] Quillen target: [formula in source] is the [formula in source] heat-kernel coefficient, and the three residuals collapse to one [formula in source] [formula in source] one [formula in source] )","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8507,"byte_start":5730,"id":"section:1bdc1e997517317b5cc9","kind":"subsection","labels":[],"line_end":96,"line_start":66,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:25bfb3f13384a4125ec0","relation:275b34262db56f656d45","relation:2dc136d8afc7f5da70b8","relation:3722f27c7875a20f8a4a","relation:566af3baa040fec557b6","relation:6b302e1b326f6669b1d1","relation:6b66f384dd79870e7023","relation:8493ddfb1adcd5071b82","relation:9acf05d433f4b379e4ea","relation:c22734a52612e268e096","relation:c87ed8fbdf0eb3d2d384"],"semantic_review":false,"source":"documents/changelog/sections/012-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"New module v433 ( ALPHA.QUILLEN.PROGRESS.02) — a second honest step on the external target ALPHA.QUILLEN.EXACT.01 ( v382); it grounds and connects, it does not close it. 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The seam [formula in source] is the SAME cyclic [formula in source] as the [formula in source] simple-current glue — not a mere order- [formula in source] coincidence — bridging the Galois gearbox of v419 to [formula in source] / SEAM.EQUIV.01. \\ [formula in source] (one Smith invariant factor [formula in source] [formula in source] cyclic, [formula in source] ); [formula in sou","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-25 (The Galois [formula in source] Net bridge: v422)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1607,"byte_start":0,"id":"section:8ac4310a6a4cf6c449f1","kind":"subsection","labels":[],"line_end":19,"line_start":1,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:114b05cbb9fed28e0a0a","relation:1e3fce1b9c7fd3edabff","relation:3b66ee6219173ff40e6b","relation:4aa6f64b33a6a73c5ac6","relation:52bf56037e4a794f1248","relation:7f0193799add68ded9d9","relation:8e4c45dbf0e645b27598","relation:ac13b2e79668445fe7ec","relation:cda1832e8f96de36f33a","relation:d85024660b66f0141e5d","relation:ea9a40dd608a8e0848c5","relation:ed118c12429cb718e3de","relation:f63b497ea1d71497b255","relation:f82d8648f8a3f7b59e60","relation:fe146dccde611ec9820a"],"semantic_review":false,"source":"documents/changelog/sections/013-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"New module v420 ( FR.POLE.QED.01). 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A positive resolution of the cyclic/Galois asymmetry ( v409, RES.COXETER.SYMMETRY.01): why the seam [formula in source] sits on the Galois side, not on the cyclic [formula in source] dial. \\ [formula in source] is squarefree, so [formula in source] has element orders [formula in source] — no order [formula in source] , so the seam [formula in source] cannot be a rotation hand and is","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-25 (The seam [formula in source] is the carrier's Galois group: v419 [formula in source] figure)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5714,"byte_start":3678,"id":"section:4061f274c55499fb2ed1","kind":"subsection","labels":[],"line_end":67,"line_start":45,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0181306daad1d87c844e","relation:044d6b0203931c7f311d","relation:0b0a51b56c60b9bd6ab8","relation:0f0e42e51958a4e26fc5","relation:17c1b5b2c73ce06c9c57","relation:1f306c5f726293487c56","relation:1fb7a863edea3ccdb006","relation:3bcc94b25549c17d7a82","relation:3f862178e578a3b1e0f6","relation:41b2f57d3558e6bcfd18","relation:568a2624bb433297154e","relation:5d3163b7e48e74937809","relation:65b0d49957bad350b692","relation:695af5069aee58f98b87","relation:6ef2e401f0ebf669ffc3","relation:7f61e2c1fb8b249ed28b","relation:8c6e5564354bd3953da3","relation:9e9952640aa6e9d8fdf7","relation:cab32d6331f2cf900e1d","relation:cb48f9782e8da7885af6","relation:cd048dcb96a8b2bdf463","relation:ced87135b014cb26c975","relation:d166ed2212af6f33f0f9","relation:d7c8a96d40d9de7da0b1","relation:e1fe93cd8fb56db40783","relation:f5136b3b90d55fad7376","relation:f893265c5d96a2617f01","relation:fbfd9b0312c6e4fc20df"],"semantic_review":false,"source":"documents/changelog/sections/013-source.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"New module v418 ( ARITH.NORMTRIPLE.01). The carrier split [formula in source] read in the three atom-rings gives [formula in source] (scalaron, [formula in source] , quark numerator), and the carrier- [formula in source] clock missing from v417 is found as the [formula in source] [formula in source] -companion [formula in source] . \\ [formula in source] , [formula in source] , [formula in source] (the four primitive ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-25 (The cyclotomic norm triple [formula in source] the carrier-5 clock: v418)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7712,"byte_start":5714,"id":"section:b3159de77fcabb12cc0c","kind":"subsection","labels":[],"line_end":90,"line_start":68,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:045c8b87bae93edd859b","relation:101728a733aff3c97460","relation:2c1487e0a3ce923e74b4","relation:33d859a712f99024f300","relation:34dc5a76a8de0d271932","relation:39a530ea73633739a0ec","relation:3c4074f76c59f1da9d9c","relation:44991e218e2ace000568","relation:602f39df8e47ef804f5e","relation:6ad5d1bb37ef0b2be093","relation:70258858f113d2793ed1","relation:7849c871aa4470e676a9","relation:88bf6482771d1a7c76ee","relation:8a12a63b0005d41540a8","relation:9aa7ec5e8d7778612b00","relation:ab582da4b80e305ed2cb","relation:aca623811cb764f02b1c","relation:bd1cde21e7636a07a2e7","relation:d5fd794fc03c8fd60986","relation:d62077734d12dba879ab","relation:d86a1d75006143dc9e99","relation:f17b19999c904d98639f","relation:f8e35a34e0bd695199a3","relation:fc2e08fe5a2c4a8ae49a"],"semantic_review":false,"source":"documents/changelog/sections/013-source.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"New module v417 ( DIAMOND.EISEN.01). The hexagonal dual of v415: the [formula in source] flavor side put on operators and unified with the seam into one order- [formula in source] Coxeter clock. \\ the family rotation [formula in source] is the order- [formula in source] Eisenstein deck ( [formula in source] , so [formula in source] on the plane [formula in source] ), the order- [formula in source] dual of [formula in","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-25 (The Eisenstein/CP operator [formula in source] the order-30 clock: v417)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10409,"byte_start":7712,"id":"section:bb2a02a767e560376342","kind":"subsection","labels":[],"line_end":121,"line_start":91,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0fbe8184f12be9f08687","relation:25e8ba49e74151dd4652","relation:342eb76247df61f133e1","relation:36923250c696c112b91f","relation:3876e4c2c00e95ff2b63","relation:389be017a0c4e6f5c88a","relation:4f423e4864ca3f82f9f5","relation:549e77053e47e75ea5a7","relation:6151e787cdf2c5f19c8a","relation:62d33f44d6b8071fbb09","relation:63fd6a032d35752741d6","relation:6e8e26e959a005ead1d6","relation:7818ca5aa1666944af49","relation:79f0834d3e46d210e370","relation:9e14623f5d4577606c12","relation:9fdc3c862eb68fd730d4","relation:a036f068dddbca1644dd","relation:bec6d17f977e49e9687e","relation:c0858aea5a3c1ab9abf1","relation:ca3c667d1e8890667a76","relation:cbae3679dcd2f6c1ca25","relation:cc7c67bbf5206dfd0554","relation:cd5ea60850f8334f921f","relation:d24964b89fb23d2afd28","relation:dccb1261f508fccc892d","relation:defc7ae9f2e128f03fc0","relation:dfd4f75c3a47e8371d5a","relation:e0634246ceadbcd0dee2","relation:ea1f409de53027f3ce6f"],"semantic_review":false,"source":"documents/changelog/sections/013-source.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"New module v415 ( DIAMOND.GAUSS.01). The square CM-norm dictionary of v222/ v230 is operator-realised, and the [formula in source] deck becomes an intrinsic diamond object. \\ the integer commutator [formula in source] has [formula in source] , [formula in source] on the rank- [formula in source] image and [formula in source] — a [formula in source] quarter-turn born from the binary [formula in source] and ternary [fo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-25 (The Gaussian operator [formula in source] the atom trichotomy: v415, v416)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14064,"byte_start":10409,"id":"section:2ff762f6d6932ac2b2c5","kind":"subsection","labels":[],"line_end":158,"line_start":122,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0014a21295390cecdbdf","relation:061a46a46d2f7519d9d5","relation:23332d53f42eba1bdde7","relation:2bbfac82fc954e5fc05a","relation:332157f9227b7fd059bd","relation:4105835cc623baee67b4","relation:6637efb93d77c585e013","relation:68543e2e2663b734fcfa","relation:6b4e4054545f2359a8fa","relation:7121974b1ceb5eb3f112","relation:7365f8aa39742165158d","relation:7c4632741e718a03065d","relation:82bfd48e58fd35e5e91e","relation:86fed9953fcc017efbb9","relation:872f63ad8b5c74d01298","relation:87b87f3346e93e705636","relation:aa2b7ea8187a78ba1c57","relation:bbd95fc94a909d70d73b","relation:cb6ba0e53a4a53743dc9","relation:d1b41753fed90185ad99","relation:e0b601869b02ffd0da53","relation:e64d9b19391ec74d6975","relation:e84ba31cf46fa11399f5","relation:eaa3e9e45dc347633913","relation:f388e8c0a601ca7abcb3","relation:fb8a7274669d73bcb737"],"semantic_review":false,"source":"documents/changelog/sections/013-source.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"New module v410 ( SHEET.GEN.BINARY.01). The rank- [formula in source] sheet axis [formula in source] of the centered cross ( v95/ v218) is a binary internal compiler: its powers print the carrier spine. \\ the closed form [formula in source] (proved by the inductive step [formula in source] ), so [formula in source] ; \\ the four bilinear families [formula in source] , [formula in source] , [formula in source] , [formu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-24 (The sheet generator [formula in source] as a binary internal compiler: v410– v414)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17394,"byte_start":14064,"id":"section:cb81efd922f7b6f4776f","kind":"subsection","labels":[],"line_end":192,"line_start":159,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:030b657a128ea6031ff0","relation:245cb2d386d3823670bb","relation:42ebc7fe2bff845b7fce","relation:5a64f82d8fc26335f034","relation:651d497de46d1f8138c9","relation:686ef5f5e31d7939d218","relation:887fde20574f15149bea","relation:8a646754c2248a69b5fb","relation:94ab288073faf162d15c","relation:98dd33c7de545646d00c","relation:9b62e0f336badffde4b3","relation:a5fec95328d61ee0564e","relation:b2e30dbcacb19104b8fe","relation:b6261fc0ac8191fb0670","relation:e72edbbcfa19cac7bd6b"],"semantic_review":false,"source":"documents/changelog/sections/013-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"New module v408 ( HYP.PHI0.PUNCTURE.01). Names the [formula in source] puncture term [formula in source] as the order- [formula in source] local boundary heat-kernel (Seeley–DeWitt) contact term of the [formula in source] puncture divisor, summed over [formula in source] admissible states — the analytic complement of the icosahedral tree term ( v396). \\ the exact split [formula in source] , the puncture count, the cl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-24 (Two new tracked targets + axion-branch consistency: v408, v409)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20347,"byte_start":17394,"id":"section:3c0ef7a887cebe028f40","kind":"subsection","labels":[],"line_end":201,"line_start":193,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0a6548c8597c58c594f0","relation:3d1505c5eeddd1d49193","relation:43d43d3ad58103df4843","relation:630a5cc37c192b44d621","relation:6e791d2ea28120d52a43","relation:76716ea8434545166879","relation:8ba304008b9dcde5de65","relation:9105294fec23a91fa105","relation:9309af1fea7660e04257","relation:951380de05e837b13647","relation:a35dfe6a18c8d40c0de2","relation:cebae25efc7d16277c53","relation:d450ef2cf8b170541ea7","relation:d5323b9dc42322710288","relation:dc19f6623763c12def3a","relation:dc7af68f2eaf6a6cd145","relation:e4f7f7c996ef82121859","relation:e54dedfe44c39fb5bb05","relation:eaafa75b3b73c561c833","relation:ee9c1bc54b5d953e1d37"],"semantic_review":false,"source":"documents/changelog/sections/013-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Ledger hygiene. Resolved a duplicate active claim_id: GATE.UWALL.06–09 was carried by two distinct chains. It is an ID collision (not a supersede): the monodromy/residue chain v114– v117 keeps .06–.09 (as asserted by v123_inventory_update.py and run_all.py); the older exterior-leg chain v42– v45 is renumbered to GATE.UWALL.15–.18 (internal depends_on carried along). No claim content changed. 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A named contract (genre of v286/ v398), NOT a closure. \\ [formula in source] (the family CM point degenerates [formula in source] ) vs [for","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-24 (The [formula in source] dual keystone + the flavor residuals it homes: v405– v407)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":25939,"byte_start":23369,"id":"section:8e3e6d08d3c102a09298","kind":"subsection","labels":[],"line_end":214,"line_start":209,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:08052f9420732899b400","relation:12c56ebf2a0b97a34122","relation:12cb2472481070b94d75","relation:13670aa92d94fb4a5f24","relation:19359538d4aeedd7a3a4","relation:1d18b1b1674c48ae3431","relation:3dc9753cd6d49ba33ebe","relation:453234919573b7865506","relation:70b7cfed2ce00bb41292","relation:759be4522d559d4ec542","relation:81a6cbae54fb51185c21","relation:882f7e137104fe33b03e","relation:9e566f0af3ae7ff1b9e8","relation:a9bc95ee68931556ea09","relation:cc086a942f240602e6fe","relation:f43a1756210517a1ee65","relation:ffea1721c3e25538ec26"],"semantic_review":false,"source":"documents/changelog/sections/013-source.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"/ \\ v403_facet_compositum.py ( ARITH.HULL.01): the three single-prime number-field facets of the order- [formula in source] clock ( v390/ v394, used so far only one at a time) compose to one field [formula in source] . \\ the squarefree parts [formula in source] are independent in [formula in source] , so [formula in source] with Galois group [formula in source] (order [formula in source] ); 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The Calabrese–Cardy finite-size entanglement-entropy scaling of the critical free-fermion content gives [formula in source] per complex mode (Peschel correlation-matrix EE; the [formula in source] sizes avoid the half-filling zero-mode), so the 16-Majorana ( [formula in source] complex) collar has [formula in source] , chiral ( [formula in source] , v367/ v368). Numerical [formula in","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-23 (S3 closure stack — the target of the seam scaling limit pinned at EVERY computable level: central charge [formula in source] from the lattice ( v376), the [formula in source] character ( v377), the genus-1 torus count [formula in source] ( v378), and reflection positivity ( v379); only the abstract continuum existence (cited MMST) stays external)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19829,"byte_start":18802,"id":"section:2ad2ac4126620b31f007","kind":"subsection","labels":[],"line_end":204,"line_start":193,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:39b970488e7e1df4bc5e","relation:6a4ae8f4583bab541b7b","relation:942ac9a059d6e19de184"],"semantic_review":false,"source":"documents/changelog/sections/014-source.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"v375 ( OBSERVATORY.REGISTRY.01). A CI over freeze_file.csv: \\ every prediction carries a kill criterion (falsifiability complete, no orphan claims); \\ the headline values re-derive from [formula in source] ( [formula in source] , [formula in source] , [formula in source] ); \\ a live scorecard records [formula in source] vs the JUNO first run ( [formula in source] , compatible), [formula in source] vs NuFIT 6.0 NO ( [","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-23 (Track 4 — the prediction OBSERVATORY: a status-typed CI over the frozen prediction registry that makes the falsifiability surface machine-checkable, with a live data scorecard ( v375))","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":21675,"byte_start":19829,"id":"section:2692631f31aef19d9368","kind":"subsection","labels":[],"line_end":223,"line_start":205,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0c90788dd9d8b7c0bb8f","relation:191fc767e17819183866","relation:242d3b8903b34d9e6b31","relation:28418debcf78dc86420c","relation:30893ca6c791b50bad22","relation:3e8ad9d0b93199b0603f","relation:48970caaccd9d5573017","relation:63139db432b8ed6ac56b","relation:677ca90909e061b99d9a","relation:8c85435b0f956c960587","relation:94711a0267f2b61ba54f","relation:9fab164ed93ba9cbf17b","relation:bd823ae077f114a5d687","relation:c15a4721d525b13fc928","relation:e6353038ec2f82bc0b9b","relation:eb7c4601c23053dda1e5","relation:f735266743a74373b5cf"],"semantic_review":false,"source":"documents/changelog/sections/014-source.tex","status_markers_as_written":["\\mC","\\mE","\\mX"],"summary_excerpt":"v371 ( FR.POLE.SOLVE.01). A clean negative: standard QED/EW running cannot be the Koide source [formula in source] pole transfer (it pushes [formula in source] above [formula in source] ; the required [formula in source] is negative while QED's is positive), so the transfer is the non-QED [formula in source] operator / [formula in source] Moebius generator ( v183/ v82). , plain running excluded as the kill. Python (n","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-23 (Track 3 — the [formula in source] functor promoted from contracts to TYPED runnable solvers with kill tests: Koide source [formula in source] pole ( v371), [formula in source] Boltzmann ( v372), axion finite- [formula in source] relic ( v373), [formula in source] uncertainty budget ( v374))","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":23473,"byte_start":21675,"id":"section:1a6d16256ec9d6226d97","kind":"subsection","labels":[],"line_end":242,"line_start":224,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:24c23f8b12d99ebacef0","relation:2ab2ee3e9f57e764ebcf","relation:3756b3ee475a4244ac65","relation:40d70afde9334a9cc62a","relation:4644315fb2a6a09741f7","relation:567642cc3bb1fe1f2e8a","relation:5c81c524a360b8108721","relation:621cfea6973dec2613b9","relation:69af5d85ddff88fe150e","relation:920364fcb03255f33deb","relation:a4ee46a9c193e15dae56","relation:b90e6ac4855fea3c71c1","relation:bc1744ea23818dabae5f","relation:c05396161259b351d8f5","relation:cd77c667de345c58e8f9","relation:d6229364588cbd82aa8f","relation:e6b585a2e8c1e78bb859"],"semantic_review":false,"source":"documents/changelog/sections/014-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v367 ( SEAM.S3.LATTICE.01) — Track 1. 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Extends v304 (the scalar [formula in source] pole algebra) to the actual tensor spin structure. \\ the Barnes–Rivers projectors are complete ( [formula in source] , [formula in source] , [formula in source] sum to [formula in source] ; [formula in source] split [formula in source] ), the EH propagator is [formula in source] , and the Stelle ghost is a spin-2 state. \\ the enti","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-23 (Track 2 — perturbative graviton unitarity sector-by-sector: the Barnes–Rivers spin decomposition localises the Stelle ghost in the spin-2 sector, cured by the entire KMS form factor; the spin-0 mode by the GHP contour ( v370))","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":27232,"byte_start":24913,"id":"section:4a157afd200102fcaaee","kind":"subsection","labels":[],"line_end":280,"line_start":258,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:03a92ab7f70647f8305d","relation:09d383290d1d24a0d681","relation:1dbfad7a7115aeccdca2","relation:262e4eeb215ea9526a7a","relation:2d9f5d2df270c1b0faa1","relation:2f3163469930687dea84","relation:31511f200536987b13d7","relation:359dea06cb7026a79e61","relation:35f4577518b3474b2cef","relation:3851be427bd64fa20954","relation:42266d0e08c854dccfb5","relation:525eb0368927b2dc200a","relation:5d6b7d12d6ed9efca86d","relation:61512a1266bddb73e4fc","relation:66c9a82f06766f6bf919","relation:6b249c542d5d4479d270","relation:74b9d05c49287ecde105","relation:779046fbd6b84bff0542","relation:77983d34db50af3d33c5","relation:797e41f85621e941b539","relation:7d4e0c16c6054c20809f","relation:b1631bee916898486243","relation:bb122de6102bc8d19c21","relation:d3601a1034b5aa1c46e6","relation:d42ceae24d8942feeaca","relation:d5f4f4698e612205d320","relation:e96c9c45eb71e9b7b53d","relation:fe6bd592985ef5b0b3f4"],"semantic_review":false,"source":"documents/changelog/sections/014-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v365 ( QGAMB.SADDLE.01) — Direction 3. 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The No-Unit Theorem ( v153) already made [formula in source] a forced metrology primitive. \\ The SHARPENING after the parameter-free gravity ( v358/ v359/ v361): the Einstein coefficient [formula in source] and the [formula in source] prefactor [formula in source] are dimensionless, so [formula in source] and [formula in source] reduce to [formula in source] times atoms — the gr","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-23 (Direction 6, [formula in source] sharpened: after the parameter-free gravity, the gravity sector adds NO new dimensionful input either, so [formula in source] is the SINGLE dimensionful input of the complete theory — final tally [formula in source] , ZERO dimensionless dials: v364)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":32237,"byte_start":30692,"id":"section:b0eabbf91a1894618a3d","kind":"subsection","labels":[],"line_end":330,"line_start":317,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:3ae592e97e53ae301736","relation:416c9c9207867ea1eaef","relation:5502f9eae46c55957f9c","relation:589e2ff0647f8431dc7c","relation:632fad97477ad981b61f","relation:72c6758ac25e60859f0a","relation:73e7419af95a4ed3dfc4","relation:782b095e678a1c03e19e","relation:8881d5a12b3e908f345e","relation:9186f3a45e544152c31a","relation:9ba17f22b8c4560541ff","relation:a4d10757db4c798a6304","relation:aaf8c78b6eb5e088ed34","relation:b27548d9d8aa0b637542","relation:c87085d4afaca925d5a8","relation:e2c106906b70a38e662e","relation:ee21fc4d57b60fff0562"],"semantic_review":false,"source":"documents/changelog/sections/014-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v361 ( GRAV.BACKREACT.01) — Direction 5. With the parameter-free equation ( v359) and the explicit J3 flux ( v358), the backreaction of TFPT's carrier matter is computed. \\ the carrier's gravitational anomaly is forced: [formula in source] (the chiral central charge of the [formula in source] -Majorana content). \\ the backreaction is FINITE [formula in source] from [formula in source] : the matter vacuum energy throu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-23 (Direction 5, the matter–gravity backreaction: the carrier's gravitational anomaly is forced [formula in source] , and the matter vacuum-energy backreaction is finite ( [formula in source] the forced [formula in source] from [formula in source] , not [formula in source] ) — the loop closes; no new SM-quantum-number read-out (declined): v361)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":33934,"byte_start":32237,"id":"section:b9e3cb43b2bc303303e6","kind":"subsection","labels":[],"line_end":347,"line_start":331,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:04d92785b56c17ffb2de","relation:1476dc4576a286c87cbf","relation:1ea5597f3fd701c6b76f","relation:264dc43766cc0a18cbe7","relation:37000bc4a548f0823b47","relation:396bc176e460747dd821","relation:50cc221ac17f6c75b1e1","relation:5f7299a58a3307fcbd12","relation:80adc667b8e78f79d526","relation:8761b9cd00d0a613a9f9","relation:8ca8e811b51c3e9f67ef","relation:cfcedaffd39e1c7bddb8","relation:d48b3a0c01ce76741551","relation:ee4521550e91c6b663a5"],"semantic_review":false,"source":"documents/changelog/sections/014-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v360 ( GRAV.GAPCORR.01) — Direction 2, run honestly. 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TFPT's forward discipline ( v305) is one-directional: every physical READOUT must map onto an [formula in source] structure (anti-fitting). The sharp adversarial question runs the OTHER way — how much [formula in source] structure maps onto NOTHING, and is the recurring golden ratio numerology? \\ THE REVERSE AUDIT: of [formula in source] 's eight Casimir i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-22 (the REVERSE numerology audit, and what the golden ratio means: of [formula in source] 's 8 Casimir invariants only [formula in source] feed a primary readout and [formula in source] are hull overhead; the golden ratio is UNMAPPED structure, so it cannot be numerology: v354)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10798,"byte_start":9281,"id":"section:dcc46f2343a1ce26d935","kind":"subsection","labels":[],"line_end":99,"line_start":85,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:182333751d003523c48e","relation:2bab79f043addca727d5","relation:52bc8c13b45cd67fd7d2","relation:5742fdc77431958c6fe1","relation:6b0f3cf78609ab041fc5","relation:7b96b3c43508557101d1","relation:7e84d5fb2a377899bb8c","relation:889468e4347425a3fe56","relation:8e5a2da398b2f5210501","relation:951237f5daac7009057f","relation:a1e1d43d277606379eb7","relation:a303a829ae42c65f4838","relation:c4df0dfe85f1e1edf633","relation:ccce2300ce38e5993457","relation:cd36bf4c3e8954a32ee8"],"semantic_review":false,"source":"documents/changelog/sections/015-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v353 ( TFPT.SELFLOOP.01) — refining v352. 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A direct, honest answer to ``is there any other way to fully solve the one open arrow L2?''. \\ the precise locus: the seam gives the flat pillowcase base [formula in source] ( [formula in source] , v216) while the [formula in source] structure is the Seifert base over the spherical [formula in source] ( [formula in source] ), so L2 bridges two geometric types – why it needs the carrier ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-22 (can the one open arrow be fully solved? the closure-mode classification: the flat [formula in source] spherical base locus, four modes, no free theorem – only rigidity or axiom [formula in source] : v347)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20465,"byte_start":18970,"id":"section:00c96659d1c56ecb746e","kind":"subsection","labels":[],"line_end":197,"line_start":183,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0fe8ca20b8c953d86233","relation:2c6aaa6c7c20a246d927","relation:517cfd7d40b04e35fd55","relation:5a40637d1cc6dc98befd","relation:77d8c7e28b1aee63321d","relation:7ea133f65a7e2afbd24a","relation:8a2ab1e54c0470a5f5fa","relation:8cb02a536a7adfa4848c","relation:8e138dbc13a1abeb1118","relation:9bb6eed4577a8ad667b1","relation:aefc7fed94e83838832f","relation:ea2113ee21d4a3637920"],"semantic_review":false,"source":"documents/changelog/sections/015-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v346 ( SEAM.EQUIV.GEOM.01). 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Carries out the combinatorial core of the hypergraph-homotopy route (R3, the most promising fresh angle from v344) as far as it computably goes. 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The carrier's second-order topological defect [formula in source] projected through the seam-loop phase gives [formula in source] ( [formula in source] vs the dispersive [formula in source] ; [formula in source] vs lattice/CMD-3). The value is exact ; the vertex identification is the \\ bridge. Ledger FR.MUONG2.01; Wolfram-mirrored. An ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-15 (archive integration \\#5: six dormant results revived from the old papers)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9098,"byte_start":8159,"id":"section:954c40e55830e15dd43b","kind":"subsection","labels":[],"line_end":110,"line_start":99,"numbered_or_version_tokens_as_written":["S1.2"],"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:e20a9a0f75555f8c4403"],"semantic_review":false,"source":"documents/changelog/sections/020-source.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"The M\\\"obius seam is the boundary Lorentz structure ( tfpt_3, ). Added a paragraph to the ``M\\\"obius origin of [formula in source] '' section: [formula in source] (Penrose \\& Rindler, Spinors and Space-time, Vol. 1, 1.2–1.4), the celestial sphere of null directions via stereographic projection. This gives the self-consistency loop a spacetime meaning — the carrier clock [formula in source] is an elliptic [formula in ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-15 (archive integration \\#4: M\\\"obius [formula in source] Lorentz foundation citation)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10101,"byte_start":9098,"id":"section:fc9d294f005b7ca60e26","kind":"subsection","labels":[],"line_end":122,"line_start":111,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:7ab98bcec22c69342561"],"semantic_review":false,"source":"documents/changelog/sections/020-source.tex","status_markers_as_written":["\\mC"],"summary_excerpt":"Haloscope coupling tied to [formula in source] ( tfpt_4_frontier, ). Made explicit: in the determinant-line normalization the axion–photon anomaly coefficient is [formula in source] ( [formula in source] ), so the haloscope [formula in source] coupling is set by the same [formula in source] that fixes [formula in source] and [formula in source] — a \\ structural relation (the coefficient, not a parameter-free physical","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-15 (archive integration \\#3: axion coupling [formula in source] + retired small-angle reading)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11470,"byte_start":10101,"id":"section:e60c8c7dc2298081bbd9","kind":"subsection","labels":[],"line_end":139,"line_start":123,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:090b9091ed80395ed548","relation:38d9780af8173049511f","relation:4a18660e57555ddf52bf","relation:57fc5812c9d5ca09ee01","relation:5b761b25454680e3eab5","relation:5eece3dbaff123f7bddd","relation:9d728ea094bc824f3d54","relation:c28ac914e5c30da45f8b","relation:f38e13cfc9a95d24d394","relation:f4c78086a1abac11601b"],"semantic_review":false,"source":"documents/changelog/sections/020-source.tex","status_markers_as_written":["\\mC","\\mE","\\mX"],"summary_excerpt":"HOR.EHT.01 ( v203, / / ). The surviving core of the old UFE/black-hole notes ( not the RN-type metric — superseded by the Nariai/seam [formula in source] horizon readouts v101– v104/ v190; only the polarization signature survives): a local achromatic polarization-rotation intercept around a horizon-scale black hole, [formula in source] . 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The closed TFPT CKM point ( [formula in source] , [formula in source] , [formula in source] , [formula in source] rad; v18/ v88, no flavor fit) feeds the cleanest FCNC probe. 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The v199 bedrock residual — ``the bounded sub-principal symbol of the raw seam DtN has no off-character (mod 4) matrix elements'' — is reduced one genuine step further: block-diagonality is not an independent postulate. Writing the DtN as [formula in source] with [formula in source] the bounded sub-principal piece [formula in source] multiplication by a curvature [formula in source] (stan","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-15 (bedrock: the [formula in source] residual reduced once more — v201)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16526,"byte_start":14445,"id":"section:208cd3e2a794336cad9d","kind":"subsection","labels":[],"line_end":198,"line_start":175,"numbered_or_version_tokens_as_written":["S6.2"],"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:7646c88b5adbeb002596","relation:84181a12d26580d39c18","relation:f7cba8122b2c92dceecf"],"semantic_review":false,"source":"documents/changelog/sections/020-source.tex","status_markers_as_written":["\\mC"],"summary_excerpt":"Axion relic solver ( experiments/ftransfer/axion_relic/relic_solver.py, ). 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Honest finding: at the predicted [formula in source] the estimate over-produces dark matter, [formula in source] – [formula in source] (robustly [","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-15 (F_transfer workshop: the axion relic solver — an honest over-production tension)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18595,"byte_start":16526,"id":"section:4d42f8071e36f9952644","kind":"subsection","labels":[],"line_end":221,"line_start":199,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:2f1b53d4b1304fd0f3e3","relation:4d72cf0cbc8582c2842d","relation:566df7e1453213296611","relation:597b9ba487a81e7eb0fa","relation:7c4c9efd6f8749653bbd","relation:b5c636620b7e0744dd9b","relation:c6b4e8e10a346ba6ebad","relation:cb223bef4154844b94a1","relation:d39aada3d9b3b43523db"],"semantic_review":false,"source":"documents/changelog/sections/020-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v199_seam_state_invariance.py / \\ (claim QGEO.STATE.01, work package A). Attacking [formula in source] directly on the raw seam. (1) \\ the setup is non-circular: [formula in source] is the Coxeter element of [formula in source] ( [formula in source] , v117), an automorphism of the raw CAR algebra (16 Majoranas) — both carrier-side, no seam geometry. (2) \\ for a quasi-free RP state [formula in source] , so [formula in","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-14 (work packages A+B: attacking [formula in source] + the variational scan — v199, v200)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20348,"byte_start":18595,"id":"section:b56f3a2e55f262711774","kind":"subsection","labels":[],"line_end":241,"line_start":222,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:048fa00365e7cb07a413","relation:0c99b554ef01937958b8","relation:1340a3d349dba2a3766e","relation:35fb5e45d85579bc0f88","relation:539353defd6eceda013f","relation:65873c6b040256932b9e","relation:667a39be5b9157fb9d2b","relation:7db7824338809c1f58f0","relation:99d33db56d157b34336e","relation:a56e8ec24086608c228b","relation:abde57d644b5c7cfce42","relation:ef851002385decdbd5b3"],"semantic_review":false,"source":"documents/changelog/sections/020-source.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"v198_modular_commutator_reduction.py \\ (claim QGEO.MODULAR.01). 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(2) \\ by Tomita–Takesa","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-14 (cracking the bedrock to a state-invariance: principal symbol [formula in source] Tomita–Takesaki — v198)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":22614,"byte_start":20348,"id":"section:c926c39e5cf2b4b2f828","kind":"subsection","labels":[],"line_end":266,"line_start":242,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0636817743a4632980fa","relation:0d56cf490091bf30c0ac","relation:1145350dba5bb77a1940","relation:3a31921c0c5faa7bddd4","relation:83af1e67bfd333d0e0a8","relation:900785e6f042e57bb7fd","relation:b46856e4aa33f34dc912","relation:b51acf2112bfa5b84fd7","relation:bf75bab9736891f7cc06","relation:bfbd68021e5237b562eb","relation:c46cb9b4f115bc697b54","relation:cd1bb3d7d1caf4ba06fa","relation:d0a29e43bdd4078472c0","relation:d0ff775503af084ed515","relation:e8fd75f79fbf44c9a9d6"],"semantic_review":false,"source":"documents/changelog/sections/020-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v195_marks_lefschetz_character.py / \\ (claim QGEO.MARKS.02). 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So Mark","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-14 (three review levers: Marks-via-Lefschetz, E_fail functional, RR [formula in source] D5 — v195–v197)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":23978,"byte_start":22614,"id":"section:113a50c68f53872c39d4","kind":"subsection","labels":[],"line_end":283,"line_start":267,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0617ef4c2b2f0971fbab","relation:081be54a9ffd9b2ce03e","relation:1f5a6b72b1c19884bfc0","relation:579a28618f5b572d0bf1","relation:5fe0b4a38974f193c218","relation:65b7f0419bf7cf3a5ee7","relation:761b105a78e9a64aabbf","relation:841714d0a33fb0ae91d6","relation:884786c192b1e75b5bf2","relation:97e3e7438608ed94b05b","relation:9c60a27716b4bdff04bc","relation:a87a232af0f3c1063445","relation:b46a274f987f77a75f50","relation:c0d4754d44bf78ab9b8a","relation:fa0f0b5af23e121cab13"],"semantic_review":false,"source":"documents/changelog/sections/020-source.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"v194_raw_seam_dtn_rp.py \\ (claim QGEO.DTN.01). The next hard lever — ``is the raw RP-seam DtN definable from RP data alone?'' (sub-claim 2 of QGEO.ENERGY.02) — was tackled, and the honest result is a reduction, not a closure. (1) \\ the commutator [formula in source] closes on the finite cohomology [formula in source] ( [formula in source] , distinct [formula in source] characters; v177). (2) \\ the hinge is met: the D","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-14 (subclaim 2 of ENERGY.02 tackled: raw-seam-DtN RP-definability — v194)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":25661,"byte_start":23978,"id":"section:6151ea351f3cf66e9630","kind":"subsection","labels":[],"line_end":303,"line_start":284,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0e75972d6ac871e7eeed","relation:1680eed18577ff8edcaa","relation:9be145c23c29b68e84d8","relation:9d1646c926d895e11404","relation:9e6fdabee9e6aae5c198","relation:9f724b9d65665030c5ac","relation:aef5691ee65b7c2c075b","relation:cfe062e6a17cd27f0e8d","relation:d293ef7e845d3fa340f3","relation:e2e7d9de384e8ac76708","relation:fa4d66cd1318b75684d0"],"semantic_review":false,"source":"documents/changelog/sections/020-source.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"v193_qgeo_energy_commutator.py \\ (claim QGEO.ENERGY.02). The non-circular sharpening of QGEO.ENERGY.01: the energy commutator [formula in source] on the rank- [formula in source] Calder\\'on polarisation, with three sub-claims — (1) \\ [formula in source] is carrier-defined (Coxeter of [formula in source] , v117), not imported from the seam; (2) \\ the non-circularity hinge: [formula in source] must be the raw RP-seam D","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-14 (QGEO.ENERGY.02 energy-commutator + QFT-wording hardening — v193)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":28076,"byte_start":25661,"id":"section:fe43532db2385fecd956","kind":"subsection","labels":[],"line_end":331,"line_start":304,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0081cd3a7017a7600cf9","relation:03444ffdf69bf4e20814","relation:173e4308f407f02ca84a","relation:36eb0662aee5e444b845","relation:4cb432c2f1319ed1f619","relation:4f7c5ca40c8efeb3eb65","relation:8056daa7eaeb7e81d998","relation:ba424fb6961834f9ddbc","relation:ca5827ec217285562f38","relation:cd468dffd248556e66a7","relation:ee76cd182c016de6c1d7","relation:f99fb07383560f5712bf","relation:fc3f629c38e20146e2a6","relation:ff632c4d5fe3bb9adf17"],"semantic_review":false,"source":"documents/changelog/sections/020-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v189_riemann_roch_carrier.py / \\ (claim ARCH.RRCAR.01). The pair [formula in source] are the two canonical invariants of one object, the four-point seam divisor [formula in source] on [formula in source] : the cycle side [formula in source] (already QGEO.COHOM.01) and the function side [formula in source] , matched by [formula in source] . 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Version 5.1 (rev 120) of the ten-PDF document set was published as a new version of the TFPT deposit — record 20687564, DOI 10.5281/zenodo.20687564. This version carries the F_transfer-firewall round ( v184– v188): the honest [formula in source] anchored-Boltzmann test (sharper scenario, not a closure), the axion hilltop-relic typing, the ledger v187 and prose v188 guards, and the Route B/Koide/d","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-14 (Zenodo release 5.1 (rev 120) — F_transfer firewall, v184–v188)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":32680,"byte_start":29003,"id":"section:b559ae6d59524fc410e4","kind":"subsection","labels":[],"line_end":385,"line_start":345,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0025791bdf86fc20cd1f","relation:0236a72f4e309451c580","relation:12b648d46fce4ea8a4ed","relation:16a4d92cc10ec2d0b06b","relation:196138fa4f69bdef0f0d","relation:362f625a8e0000ba1705","relation:3bc2636ca5b311399964","relation:416dc832b8b5162e9bf3","relation:4c5b4b2a05ae800ef352","relation:52891a6837758385dc1b","relation:8514d55b8f0439a4701d","relation:863f78fae7afdf38086e","relation:bccaeeb3a0e0d946de57","relation:cdcd3e28af6bad9cedda","relation:d72bf2a7e58d405dbae9","relation:f9db2b48dbad270465d1"],"semantic_review":false,"source":"documents/changelog/sections/020-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v184_etaB_anchored_boltzmann.py \\ (claim FR.ETAB.03). An honest test of the external-review [formula in source] proposal ( [formula in source] , [formula in source] ). Firewall verdict: sharper scenario, not a closure. The washout anchors plausibly ( [formula in source] meV, [formula in source] atom, in the strong-washout window) ; but [formula in source] does not — [formula in source] is the seesaw scale [formula in","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-14 (F_transfer round: eta_B honest test v184, axion relic v185, discipline guard v187)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1759,"byte_start":0,"id":"section:c1ba016bb9366edd1984","kind":"subsection","labels":[],"line_end":21,"line_start":1,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:009aa3500c2e544d03f2","relation:01eab2231a5c7652270d","relation:44e64ab13215f12ff771","relation:518fed398336a8ffd786","relation:65cc339146b3644d5dc9","relation:6653941bd859b4226227","relation:cc7bcfeb7849247c17c7","relation:d9aa71811a484732c7b9","relation:e6c425199678fc59d4aa","relation:fac21ddeb43459ee016d"],"semantic_review":false,"source":"documents/changelog/sections/021-source.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"v183_koide_f_corner_transfer.py / \\ (claim FR.KOIDE.07). An external-review proposal, validated exactly: the Koide source [formula in source] pole factor [formula in source] is not a bare arithmetic guess but an operator identity on the carrier, [formula in source] . Here [formula in source] is the [formula in source] cubic family block ( [formula in source] ) and [formula in source] , where [formula in source] is th","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-14 (operator origin of the Koide 53/54 factor: the missing Sheet-Diamond corner, v183)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4101,"byte_start":1759,"id":"section:05aaf35318c9e1bb8204","kind":"subsection","labels":[],"line_end":49,"line_start":22,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:1fbeb4f5598ffaabc760","relation:2af1881a56c39a1a2916","relation:2dbfc102efbbe4eec9b4","relation:4bdca9de3aa5f9315303","relation:8f9383d167f21bd2a4b3","relation:98a5de41bc04ffd9365e","relation:dbfd08717e552069f15d","relation:e456ee0655fb93932c93"],"semantic_review":false,"source":"documents/changelog/sections/021-source.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"v182_reviewer_residual_map.py / \\ (claim REVIEW.MAP.01). A careful external review raised four concerns (A mapping [formula in source] , B UV-gravity abstractness, C grammar-tuning/meta-look-elsewhere, D Koide M\\\"obius flow). This module shows three of them reduce, by the same discipline as v175– v181, onto the two already-named residuals [formula in source] : A (Pl\\\"ucker- [formula in source] [formula in source] QBL","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-14 (review recommendations 1/3/4 + the four concerns A–D mapped to the named residuals)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6394,"byte_start":4101,"id":"section:f7f27b7893f1db12bbb4","kind":"subsection","labels":[],"line_end":76,"line_start":50,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:17feb52cead506d863c7","relation:22d2e7d01d939628920d","relation:2e123ae45933a2121a4f","relation:7b91c614252345b8a78f","relation:91e6252525f1b3d3fe8f","relation:ca5977af0decacaed0b7","relation:d780a3efc9695e2e5abb"],"semantic_review":false,"source":"documents/changelog/sections/021-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO","\\mX"],"summary_excerpt":"Ledger CSV bug fixed + guarded. Three rows ( AX.P1.01, AX.P2.01, QGEO.ISO.01) had unquoted commas in a status/external field (e.g.\\ ``a=(1,1,2)'', ``PSL(2,C)''), so a strict CSV parser read 11–12 columns instead of 10 — a real machine-readability defect in the single source of truth. All offending fields are now quoted (every row parses to exactly 10 columns), and audit_sync.py gained a check_csv_wellformed guard (le","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-14 (external-review response: CSV fix, G_net 3-level, QGEO.SYM.01 page, claim detox)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7245,"byte_start":6394,"id":"section:56260a726c20b0e2fff7","kind":"subsection","labels":[],"line_end":88,"line_start":77,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:45c2426651ddf025ae46","relation:548e67598a9e528738bf","relation:df8aba0eb06b2623f9ee","relation:f397e387eaccc80a8817"],"semantic_review":false,"source":"documents/changelog/sections/021-source.tex","status_markers_as_written":[],"summary_excerpt":"Published to Zenodo. Version 5.1 (rev 114) of the ten-PDF document set was published as a new version of the TFPT deposit — record 20686284, DOI 10.5281/zenodo.20686284. This version carries the AQFT-closure-to-bedrock chain ( v175– v181, the structural residual reduced to the single definitional premise QGEO.SYM.01), the two overview figures ( residual_chain, script_timeline), and the P1/P2 anchor-reduction provenan","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-14 (Zenodo release 5.1 (rev 114) — v175–v181 bedrock + figures + P1/P2)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9145,"byte_start":7245,"id":"section:e2c33aad84858bc51b9d","kind":"subsection","labels":[],"line_end":110,"line_start":89,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:11e7a3309a048de98dd1","relation:1a7363cf22a7be7f65b1","relation:2ca3a20fd0f515658f6b","relation:341a58003d6832e0fa2f","relation:3cc41142ecb5f27bd278","relation:5b314498237489fa734e","relation:61ca4168d564ef970c5b","relation:6c9046deac98d2573781","relation:78b454650fbd8e77f6c4","relation:89dd97e33040dfc58e84","relation:9910efc3f8597d13eeb7","relation:9c4154e846b25d3ddac0","relation:aab6c0864244c2bbe1cc","relation:e0884dca3c64077946f8","relation:e878ef13935b5aba059f","relation:ef19ca867f62d1a04ff1","relation:fc055918f43bb5395df3","relation:fdab1c10fc53d26f0ee9"],"semantic_review":false,"source":"documents/changelog/sections/021-source.tex","status_markers_as_written":[],"summary_excerpt":"Two overview figures ( make_figures.py; PDF [formula in source] website PNG). (i) residual_chain — the structural-residual reduction chain v175– v181 as a descending staircase from ``build a quantum-gravity measure'' to the single definitional bedrock QGEO.SYM.01; embedded in tfpt_research_contracts. (ii) script_timeline — the eight-phase journey of the [formula in source] 181 scripts (foundations [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-14 (overview figures + P1/P2 reduction reflected on the axiom surfaces)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":11128,"byte_start":9145,"id":"section:4ff2bf714d7cbf97df82","kind":"subsection","labels":[],"line_end":133,"line_start":111,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:3b7416b99ef4a92264fa","relation:4e00a2b5c76aa0fff2ee","relation:594c1beaf3be5581ae2c","relation:61e89d62aa4d738e5deb","relation:6e45293fca19dfe06872","relation:878d32408552b57c6e10","relation:c85eac5c0cfea1bde9fa","relation:d4be4e5b36a1b67d441c","relation:f598c6dacf898459c7b8"],"semantic_review":false,"source":"documents/changelog/sections/021-source.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"v181_clock_is_conformal_symmetry.py / \\ (claim QGEO.SYM.01). The isometry premise QGEO.ISO.01 ( v180) is weakened one more genuine step — to a conformal- symmetry premise — via equivariant uniformisation (Nielsen realisation; for cyclic groups Ker\\'ekj\\'art\\'o [formula in source] uniformisation): a conformal automorphism (strictly weaker than an isometry — every isometry is conformal, conformal allows any positive sc","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-14 (the final reduction to bedrock v181 + full non-changelog status sweep)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12956,"byte_start":11128,"id":"section:10f005ddcd31b0102625","kind":"subsection","labels":[],"line_end":155,"line_start":134,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0c14e742b9d8cf348c5d","relation:529c45b02370ea6d2d7e","relation:8643b3fd22231a329197","relation:c2bcbeb6f850fc2fa718","relation:ca53d2a38d4aa7d56a59"],"semantic_review":false,"source":"documents/changelog/sections/021-source.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"v180_clock_is_mobius.py / \\ (claim QGEO.ISO.01). Cracks QGEO.CONF.01 one level further: the conformal-realisation premise is replaced, via three classical theorems, by a strictly milder, non-circular premise. (1) Uniformisation (Poincar\\'e–Koebe): a genus- [formula in source] Riemann surface is conformally [formula in source] , so the genus- [formula in source] seam double (P1, v179) with its RP-metric conformal stru","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-14 (the conformal premise reduces to a milder isometry premise v180)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14596,"byte_start":12956,"id":"section:359527c60ffa08a51bf0","kind":"subsection","labels":[],"line_end":175,"line_start":156,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0dbf6f36d3a6058e3bbb","relation:1c4e2b72dd516393aa5f","relation:24333253d764e0ccaf89","relation:2a40b586d30f2886e81f","relation:2c61beda44c798bd2626","relation:2d1232374f85e0dc6a8a","relation:3088f39c723ab0e74370","relation:38ddfdda890344f0c76f","relation:3cdc18a16a5a5a1304e5","relation:4cff06e3642c5176689b","relation:598dd3599a9261730e78","relation:5d290c018a4cc872403f","relation:613ae34e7105b818d72f","relation:704b5bb569e1d87fb67a","relation:a096c502816a567d9369","relation:a3a3bec971bdeb8c0c14","relation:a5bf210b6b4dd805d392","relation:a99bd9c7b047b551bd4a","relation:c6e28236008fd07f69ef"],"semantic_review":false,"source":"documents/changelog/sections/021-source.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"v179_conformal_realisation.py / \\ (claim QGEO.CONF.01). Investigating the two residual premises left by v178 shows they are not independent — they collapse onto a single geometric premise (honest unification; the premise itself stays ). Marks's residual is not three independent assumptions: (1) genus- [formula in source] is P1 — the one-sided Gauss–Bonnet [formula in source] uses [formula in source] and [formula in s","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-14 (the two obligations collapse to ONE geometric premise v179)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16494,"byte_start":14596,"id":"section:c99473f27f0afd476930","kind":"subsection","labels":[],"line_end":197,"line_start":176,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:17861b995e4a2bac36e8","relation:3a7177d23c75e303245f","relation:5789c9d9b4db2bb38573","relation:6e88dfbb7bca043188d2","relation:75696c7ab23fca282693","relation:84f210fdef60574ade3e","relation:8d1c0dbb8b2becb13291","relation:b2f0f3aab1aea1bfa9fa","relation:bb25c3ed8405f0acf34b","relation:d23d6202858f16b7418a","relation:d7d9fddd4fd443642cd6","relation:e7da2bea13d2335709a9","relation:ef02ffbe760718ac46b2","relation:f820399f74c423653c1a","relation:fcdc4c94b13847dae993"],"semantic_review":false,"source":"documents/changelog/sections/021-source.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"v178_marks_kernel_attempt.py / \\ (claim QGEO.REDUCE.01). An honest attempt at QGEO.MARKS.01 and QGEO.KERNEL.01. These are genuine constructive-geometry/AQFT statements, not finite computations — neither is closed. What the module does is push each as far as computation allows: it closes the finite \\ core of each and reduces each to one sharper premise. Marks core : given a genus- [formula in source] double with an or","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-14 (an honest attempt at the two obligations v178 — deeper reduction, not closure)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18534,"byte_start":16494,"id":"section:2f06593b8d87effdfab6","kind":"subsection","labels":[],"line_end":222,"line_start":198,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0f0862a6aeb06a75166e","relation:2866a22308bf8c8961b5","relation:34f271eab1b9dbd526ab","relation:39a453e0cf462c255b85","relation:404dd3d2d9e90b72f965","relation:43be11a5f0245662c526","relation:525bb89f3d0f088320c5","relation:548d99a5d39f07937d79","relation:56bae3bab1b4fa268a23","relation:638e0af2318d79b6d52b","relation:7e43a49c001634ff2a41","relation:902783727cfada42cb3e","relation:90e66a139c77be1eb3a7","relation:a58ba5d1b79777798f6d","relation:cb358daa172858c011f7","relation:dc10112cfa6d2f4f6079","relation:e580cd9c44a309687dd3","relation:e8dc9ceca1c202ed2626","relation:f50621c0c8831ec1eba2","relation:f5631ed4b7292e2838e3"],"semantic_review":false,"source":"documents/changelog/sections/021-source.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"v177_seam_marking_kernel.py / \\ (claims QGEO.TREE.01, QGEO.MARKS.01, QGEO.KERNEL.01). A second external residual-class audit pointed out that the v176 statement takes the marks/ [formula in source] as a hypothesis — a near-circular trap. This module factors the central theorem honestly as [formula in source] and closes four nodes constructively (all validated symbolically before adoption): Uniform \\ — an order- [form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-14 (QGEO proof tree v177 — the residual sharpened into two named obligations)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20684,"byte_start":18534,"id":"section:83cee7585db61c131b9a","kind":"subsection","labels":[],"line_end":247,"line_start":223,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:20ffd3f44ca6763686ab","relation:26b55241a837ee0799b3","relation:293743b9599be53e7165","relation:3500d552e130f57de959","relation:46d69b801d2d068f6ace","relation:57c47f3e9cc1d2201b89","relation:63b3ed5e30591f1efc71","relation:87398dce2f95261a1e65","relation:9bfd4c41ce892db04c55","relation:9e19152f4ca4f8d9da6a","relation:a2ad269ab59740669580","relation:a43441b0e96aad600a4e","relation:ad6c8d7c0f6dbffcbd5c","relation:b678e0f6ae1c8fd2f899","relation:cc03210a46dd0ced42f4","relation:e8b6ed29d6714b03c007","relation:ec7db06ca233e938519b","relation:f260e3cd6b5c89709b65","relation:f3dfd2c094431cb90cc9"],"semantic_review":false,"source":"documents/changelog/sections/021-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v176_seam_collar_realisation.py / \\ (claim QGEO.REALIZE.02). Following an external residual-class audit, the single remaining structural item is formulated as one central theorem and certified as a reduction (not a fabricated proof). Theorem: given an oriented one-sided RP seam collar with a sheet-odd Calder\\'on involution, faithful [formula in source] marks, four parabolic marks with [formula in source] decompositio","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-13 (Seam Collar Realisation Theorem v176 — the one central proof obligation)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":21523,"byte_start":20684,"id":"section:63da5b8be1d09edb111a","kind":"subsection","labels":[],"line_end":259,"line_start":248,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:7862d5ec13c49615238e","relation:88fcf6a7cb38f62d7e9e","relation:8a58a9a8939107fff819","relation:8e9954f449aa66a26df4","relation:a0349b5f5445824f8780","relation:c7bbbfa96201f6c8416f"],"semantic_review":false,"source":"documents/changelog/sections/021-source.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"Published to Zenodo. Version 5.1 (rev 105) of the ten-PDF document set (introduction, origin_theory, tfpt_1–5, horizon, research_contracts, changelog) was published as a new version of the TFPT deposit — record 20681451, DOI 10.5281/zenodo.20681451. This version carries the AQFT closure round (v170–v175): the seam Fock-space readings and the heavy-artillery discharge of net existence [formula in source] full-cone ref","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-13 (Zenodo release 5.1 (rev 105) — v174 + v175 + doc refresh)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":23883,"byte_start":21523,"id":"section:e16d657ff22e85d37e54","kind":"subsection","labels":[],"line_end":287,"line_start":260,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:1076c92691608054e2e4","relation:58352a8f64dfeee38dcf","relation:7f57ca1b054dd4c87bce","relation:91ffd56267aac0327225","relation:9585783ae3a7dd47d839","relation:9b3de29efc84db0a5936","relation:a227d890256f85e2ac00","relation:a295a530fe1cd89771ce","relation:a446621899abff24935d","relation:c6a0419b0a99112c0ebe","relation:c7e6c27ee61abbc665d5","relation:c91d86668ddd80a122f0","relation:ca740ed02a0fa6f2673a","relation:d520e738ce5f2d112288","relation:d9d2af4fdfeea20a274f","relation:e75a7baca25fd008f3a8"],"semantic_review":false,"source":"documents/changelog/sections/021-source.tex","status_markers_as_written":["[E]","\\mE","\\mO"],"summary_excerpt":"v175_net_existence_full_cone.py / \\ (claim QFT.NETRP.01). The two structural residuals that the premise-(A) chain had relocated to already-open items — [formula in source] net existence and full-cone reflection positivity — are now discharged to a theorem, leaving the seam realisation as the single irreducible open premise (nothing fabricated). (1) Full-cone RP for all [formula in source] : the CAR second-quantisatio","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-13 (the heavy artillery v175: net existence + full-cone RP discharged to [E])","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":25134,"byte_start":23883,"id":"section:190cc30037d75411e25f","kind":"subsection","labels":[],"line_end":303,"line_start":288,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:2fc58e362bf953fa1eaa","relation:4863d3f03d9d1d10626d","relation:a5499152d74791a61321","relation:ade7ef15cc68948c3575","relation:b60bf52813c7e6e286dd","relation:b95d61db0fe8dbb668c2","relation:c31ddec693f598d4f432","relation:d9c1031441e9e0b901f8","relation:daac46d06a963cb3bf33"],"semantic_review":false,"source":"documents/changelog/sections/021-source.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"v174_seam_fock_readings.py \\ (claim QFT.FOCK.01). Three more exact audit bridges from the same source note. (1) CAR cone compression: the even CAR algebra of the 16 seam Majoranas has [formula in source] directions, but a quasi-free Bogoliubov transport reduces the whole cone to a [formula in source] -dim one-particle problem ( [formula in source] ) — the explicit count behind v161. (2) Witten index [formula in sourc","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-13 (seam Fock-space readings v174: CAR cone, Witten index, g-theorem)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":27570,"byte_start":25134,"id":"section:e36b11d50051a79291df","kind":"subsection","labels":[],"line_end":333,"line_start":304,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:25808e7c077d62c6f4c1","relation:2c7ce24c1bd72cdab63d","relation:2deb4c9a80ec888f5d86","relation:394d1aea0f4299ca4d5e","relation:4af26f0751736d6e48d0","relation:5a438fa83d8372a5079a","relation:65e93de713fdbabb272d","relation:6ea752912176de006bda","relation:a64be87779f01cb4e648","relation:c6fd36a35051ba9ebadf","relation:c833dc35c595e4b8f141","relation:fca5e55f1f1017e40f10","relation:fceddbc2408945eed095","relation:fe518d4890674d581530"],"semantic_review":false,"source":"documents/changelog/sections/021-source.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"v170_diamond_slice_compression.py \\ (claim E8.SLICE.01). E8 Slice Compression Lemma: the seven [formula in source] audit slices are one projection of two alphabets — anchor power sums [formula in source] ( [formula in source] ) and Sheet-Diamond determinants [formula in source] summing to [formula in source] . All seven [formula in source] -slices, the [formula in source] edge graph, and the row-budget cross [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-13 (CFT/QFT bridges: slice compression v170, OS moment v171, trace-anomaly seed v172, Pfaffian CP v173)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":28161,"byte_start":27570,"id":"section:e7ac5f2397b1b7d72c99","kind":"subsection","labels":[],"line_end":343,"line_start":334,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":[],"semantic_review":false,"source":"documents/changelog/sections/021-source.tex","status_markers_as_written":[],"summary_excerpt":"Published to Zenodo. Version 5.1 (rev 97) of the ten-PDF document set (introduction, origin_theory, tfpt_1–5, horizon, research_contracts, changelog) was published as a new version of the TFPT deposit — record 20678568, DOI 10.5281/zenodo.20678568. The uploader's DEFAULT_RECORD_ID was advanced to the new record for the next release. Also fixed build.sh zenodo on macOS bash 3.2 (empty-array expansion under set -u).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-13 (Zenodo release 5.1 (rev 97))","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":30284,"byte_start":28161,"id":"section:b3882fb1623949f1d1b5","kind":"subsection","labels":[],"line_end":369,"line_start":344,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:1bd4c322f029309c05de","relation:4389d60cdb97b6159a46","relation:478c5c2778b06803c2a7","relation:5f5e41d0e573b26e8923","relation:75e5c43f6e41a5c4a3b3","relation:9e76c5fc35c4ef8cf190","relation:a2d389ea5026ababf895","relation:c4e0b03b1fa49ee54b20","relation:de8690e0f19fac8f3249","relation:efe1600ef1fd45fa93c6"],"semantic_review":false,"source":"documents/changelog/sections/021-source.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"v168_qgeo_rigidity.py / (claims QGEO.RIGID.01, QGEO.REALIZE.01). Hardens the finite half of the one remaining Tier-1 hinge GATE.QGEO (the seam [formula in source] flavour [formula in source] horizon identification). Exact, machine-checked: [formula in source] has cross-ratio [formula in source] and a faithful M\\\"obius stabiliser of order [formula in source] ; [formula in source] has rank [formula in source] ; and the","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-13 (QGEO rigidity theorem v168 + [formula in source] leptogenesis interface v169)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1542,"byte_start":0,"id":"section:b0bd96461774b2724095","kind":"subsection","labels":[],"line_end":21,"line_start":1,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:1f944592d8c74e0115f2","relation:48206abdd1e268de9aa6","relation:6ae77875971cc02df471","relation:6bdb526e2cea5f76bf0f","relation:c5bc12a323f011fd1896","relation:f276238888bc27662423"],"semantic_review":false,"source":"documents/changelog/sections/022-source.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"v166_higgs_free_seam.py / (claim HIGGS.FREESEAM.01). A new prediction tying the Higgs mass to premise (A). The seam UV is the free chiral [formula in source] fixed point (v158, Gaussian, no relevant/marginal interactions), so the one marginal SM scalar coupling vanishes there: [formula in source] and [formula in source] — the Shaposhnikov–Wetterich double-criticality, here derived from the free seam, not assumed. Int","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-13 (Higgs quartic from the free seam: SM near-criticality explained, v166)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3304,"byte_start":1542,"id":"section:593d2f8d7dd5d5b3f6dd","kind":"subsection","labels":[],"line_end":46,"line_start":22,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:135c3bcfba42aa1854c9","relation:4b2c5cca7c6ac52ddfa3","relation:7690b143d7501b159cfc","relation:7694094052e087e7fe3e","relation:81fec4ad11881d7b16f6","relation:8ef04b429971deb80d2b","relation:93e93559bed6867a7585","relation:943dae99300a9f8074db","relation:e8035755448557896838"],"semantic_review":false,"source":"documents/changelog/sections/022-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"v163_rg_stability_flavor.py / (claim FLAV.RGSTAB.01). Scale-tagging of the flavor sector. The lepton-mixing seeds ( [formula in source] , [formula in source] ) are RG-stable: the PMNS running is [formula in source] -suppressed (the only mixing-rotating Yukawa term is [formula in source] , PyR@TE SM RGEs), so [formula in source] and [formula in source] — two to three orders below precision. Seam value [formula in sour","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-13 (PyR@TE [formula in source] follow-ups: flavor scale-tagging v163, QCD scale v164)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5188,"byte_start":3304,"id":"section:d1579fbe47c96d49e4e0","kind":"subsection","labels":[],"line_end":71,"line_start":47,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:02c6af2ed47d3f25217c","relation:33520b9e88ba0b430be6","relation:7c0755cfb323ba529993","relation:902cde7e05c645a8c15a","relation:d1c5ce9260e854b1252c"],"semantic_review":false,"source":"documents/changelog/sections/022-source.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"New module v159_pyrate_gauge_crosscheck.py / (claim EM.BUDGET.02). The one-loop gauge coefficients used by the transfer functor are confirmed by an independent third-party RGE generator. Feeding the carrier / Standard-Model field content into the textbook one-loop formula (GUT normalisation) gives [formula in source] , and PyR@TE\\,3 ( arXiv:2007.12700, github.com/LSartore/pyrate) writes [formula in source] , [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-13 (PyR@TE external cross-check of the [formula in source] gauge inputs — v159)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6891,"byte_start":5188,"id":"section:a3835ef2388efb1a54cd","kind":"subsection","labels":[],"line_end":90,"line_start":72,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:186ad96a41772eee552c","relation:1dc6890d8a318ca58c8d","relation:1ef63a7d823d3c9b01cf","relation:28dde2388813f946384d","relation:29f463ca6ac710556e68","relation:2cb4969abc1294f2bc30","relation:2d55a2b15b22394009f3","relation:4d392aa9df4b7351927e","relation:4ea19529f54e84f01566","relation:70c2725eb397a4ea805a","relation:7f1f43ba3310a8cc6c41","relation:a0418995960e4cdea472","relation:a11a50616f9c5e0a3e3e","relation:c88b9f803b8bd3dbea65","relation:e3d4d40ffbee323dd663"],"semantic_review":false,"source":"documents/changelog/sections/022-source.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"New module v167_inventory_post_closure.py / . The terminal residual inventory (line v105 [formula in source] v123 [formula in source] v167), re-pinned after the (A)-chain. With (A) discharged ( GATE.METRIC.16–19) the v123 five structural classes collapse: the seam clock (R1), the index- [formula in source] net (R2) and the [formula in source] -realisation (R5) all merge into one Tier-1 hinge — the seam [formula in so","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-13 (terminal residual inventory: (A) no longer a structural class; one hinge + F_transfer + irreducible core, v167)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8823,"byte_start":6891,"id":"section:55b733511958e907bad8","kind":"subsection","labels":[],"line_end":112,"line_start":91,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:020f225cab1ee5db885f","relation:0e41788adb361fec50ae","relation:27aaf01c23417299117b","relation:28adda3177b35e7d88ad","relation:321ebf31411991e9902b","relation:3b18407ba966596736c6","relation:407cd84c39d2fd727313","relation:527c400122cd1899761a","relation:553a007958bd8cb92e08","relation:580e4c30d0a96e2e96be","relation:635d14f934c84854ae27","relation:6932b3d46451bf75e38e","relation:72c2c891a94aabd33cb9","relation:79137d0771ca9cd865e3","relation:826382e1fdebfa32e519","relation:92f1dac79e4eecf7503f","relation:a502be3d0f2b7277ccc7","relation:bc5a95ffe5f60b9b6050","relation:becdec9f4614e421c4bd","relation:e18d311e9a2d7c88a380","relation:e36bb62bfab1a5511038"],"semantic_review":false,"source":"documents/changelog/sections/022-source.tex","status_markers_as_written":["\\mC","\\mO"],"summary_excerpt":"New module v165_premise_a_closure.py / . Pins the two residual gates of the v160– v162 (A)-chain to their floor. [formula in source] (net existence) closes by assembly of established mathematics : the [formula in source] free Majoranas give a free-fermion conformal net (Buchholz–Mack–Todorov), the holomorphic [formula in source] lattice net is [formula in source] (Frenkel–Kac–Segal / Dong–Xu / Kawahigashi–Longo), the","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-13 (premise A maximal honest closure: A2 by assembly, R1 = GATE.QGEO, zero independent open gates, v165)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10710,"byte_start":8823,"id":"section:cc5f650209aae2bdc4e6","kind":"subsection","labels":[],"line_end":133,"line_start":113,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0cf32247dc3001f27b60","relation:24aecd07802405ec4b1e","relation:531495251fe7d01ed399","relation:5483c332ce1b22d73c7a","relation:57250d55014572b6420f","relation:6a414ed38193628c2737","relation:88b40f80e6de4a655b34","relation:900fb3cc354352ab4b9c","relation:9b2b797610d9eb0e8b34","relation:9f84ba2ea82c776a03a2","relation:abb33c72adc8fe9b1873","relation:d26d55b0d5fc95348b37","relation:e5a2bcf5c48494c7692b","relation:eb2f91fb346927366617","relation:f2e17b397a35f863a1cc"],"semantic_review":false,"source":"documents/changelog/sections/022-source.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"New module v162_seam_transport_identification.py / . Pushes the v161 residual as far as it rigorously goes and shows it carries no new open content. The one-particle symbol splits into a gap value [formula in source] and a fixed space [formula in source] . [formula in source] is forced: a [formula in source] -equivariant generator is diagonal in the cusp basis (the deck average is the diagonal projection, [formula in","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-13 (the final identification: premise A factors into the already-open A2 + R1, no new open content, v162)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12736,"byte_start":10710,"id":"section:901199b7ffce4a10a268","kind":"subsection","labels":[],"line_end":155,"line_start":134,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0c15f26278823e0747e8","relation:16c9325aa25f4847daf8","relation:1a67ade98f745475e763","relation:2f2e4c8cb9a6df13fd1a","relation:50d52e314360657c2cc1","relation:6f133583dc779b4a716b","relation:9eebe41b09d12cc6aa6b","relation:b52f5c9c28fb9cc5ac27","relation:d5064ea517dd73600da6","relation:f3c00ffbe7f998e553a1"],"semantic_review":false,"source":"documents/changelog/sections/022-source.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"New module v161_one_particle_reduction.py / . Discharges the scope premise of v160 (``the transport is gapped on the full Schwinger cone'') via Bogoliubov second quantisation. A quasi-free transport is [formula in source] , the second quantisation of a one-particle contraction [formula in source] on the [formula in source] -dim Majorana space; [formula in source] acts on the degree- [formula in source] correlator sec","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-13 (the cone reduces to one particle: premise A's scope premise discharged to a 16-dim statement, v161)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14754,"byte_start":12736,"id":"section:c39fabd7834a6c050a87","kind":"subsection","labels":[],"line_end":178,"line_start":156,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:1325d70fca27ca5237e1","relation:26202413f246b43efabe","relation:2c0a6a13a577a2369045","relation:62ff97e30992150c49bc","relation:75fa45f90ebf6b514452","relation:8c742de9326a5bb293c3","relation:bbee77f4435a8965874b","relation:c0331de6cef574309958","relation:c87fcdf14cb8d3721f4d","relation:ec028ec99f10f08c942b"],"semantic_review":false,"source":"documents/changelog/sections/022-source.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"New module v160_seam_gaussianity_from_pf.py / . Formalises the proposed closure of premise (A) (``the seam bulk is a reflection-positive free field'') as a fixed-point theorem and types it honestly. The exact parts: (1) a quasi-free state has all higher connected cumulants [formula in source] — verified by the signed set-partition/Pfaffian moment [formula in source] cumulant inversion on a concrete pure Majorana cova","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-13 (premise A as a conditional fixed-point theorem; the load relocates to one scope premise, v160)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15327,"byte_start":14754,"id":"section:841d8f1544a52bd38c3f","kind":"subsection","labels":[],"line_end":188,"line_start":179,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:a550793229d0912d3537"],"semantic_review":false,"source":"documents/changelog/sections/022-source.tex","status_markers_as_written":[],"summary_excerpt":"Changelog sort enforced. audit_sync.py now checks that every dated subsection\\*\\YYYY-MM-DD...\\ block in this file is non-increasing (newest first; range titles such as 2026-06-07 / 2026-06-08 sort by the later date). A manual prepend had left five 2026-06-12 entries above seven 2026-06-13 blocks — reordered; future mis-sorts fail build.sh audit as [B.changelog].","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-13 (changelog date-order audit + reorder pass)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16556,"byte_start":15327,"id":"section:3683cb3ca5b3f7afe565","kind":"subsection","labels":[],"line_end":203,"line_start":189,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:0cca5275727fb147db41","relation:128dd4f33b937ebe3c1f","relation:597983d87b5617c39c98","relation:690b270df8a72d46e750","relation:87523a37207889f7441c","relation:e472a95006d777fee68f"],"semantic_review":false,"source":"documents/changelog/sections/022-source.tex","status_markers_as_written":[],"summary_excerpt":"The free chiral [formula in source] fixed point is provably stable ( v158, exact dimension count). The finite core of (A)'s ``reaches-the-fixed-point'' residual: the chiral Majorana has [formula in source] , the bilinear current [formula in source] , the quartic [formula in source] . The relevant window [formula in source] for bosonic deformations is empty, the [formula in source] currents are chiral ( v157, not [for","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-13 (premise A: the destination fixed point is provably stable, v158)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17895,"byte_start":16556,"id":"section:dd21f4d89cdafe68cd70","kind":"subsection","labels":[],"line_end":220,"line_start":204,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:52f90d9a067cf54b90f5","relation:5c25bb1d906695058038","relation:6cf701f439ade41bb9d2","relation:92f7108b8f34b84e1da5","relation:adf541d7bf80822f2578"],"semantic_review":false,"source":"documents/changelog/sections/022-source.tex","status_markers_as_written":[],"summary_excerpt":"The free-bulk premise becomes a fixed-point property ( v157, simplicity-first). Instead of postulating Gaussianity, three facts click: (i) the DtN/Calder\\'on symbol is universally [formula in source] (Lee–Uhlmann — order- [formula in source] [formula in source] DO, principal symbol [formula in source] ; interactions live in the irrelevant lower-order symbol), so the free dispersion is bulk-detail-independent; (ii) a ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-13 (premise A reframed: freeness is a rigid boundary fixed point, v157)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19392,"byte_start":17895,"id":"section:fc84e3c0ee4eb2d211d7","kind":"subsection","labels":[],"line_end":238,"line_start":221,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:155951ee1fff7000313b","relation:1f15d409c06c7c10a210","relation:2ed2da424789e6694618","relation:73272bad40797d7abba0","relation:740c267393bb55f0fcb6","relation:841ee6c34f65aedc993a","relation:a0fab5e196cab6605d45"],"semantic_review":false,"source":"documents/changelog/sections/022-source.tex","status_markers_as_written":[],"summary_excerpt":"The constructive route carried to its exact endpoint ( v156). `` [formula in source] '' is no longer an assertion: the chiral seam net is built explicitly and the identification checked. (a) The Dirichlet-to-Neumann (Calder\\'on) operator of the [formula in source] d Laplacian is the free chiral dispersion [formula in source] (harmonic extension [formula in source] ); (b) [formula in source] free Majoranas give [formu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-13 (Route 3: the seam net constructed and [formula in source] verified, v156)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20856,"byte_start":19392,"id":"section:4b70b6153a1845cabead","kind":"subsection","labels":[],"line_end":257,"line_start":239,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:2a560cf3a231a7ae3a1d","relation:2fd87b66a45a06bfef2d","relation:3fb477ed9b28a2494cda","relation:41638232b679982b7c92","relation:6a3a4942b18f666c6c83","relation:70be6a3c996da990a272","relation:81407f5826748e7bf40a","relation:aa72ffb7fd3398a7ebf4","relation:ae1ee008147d5ab652a9","relation:b7bdf21887712da9256a","relation:c5f4ac648709d71f447f","relation:c93a2e61bfaaeeb0f4cc","relation:e5304c14643f4f859a3d","relation:fb5d1d0cf2cc44800662"],"semantic_review":false,"source":"documents/changelog/sections/022-source.tex","status_markers_as_written":[],"summary_excerpt":"[formula in source] 's last premise reduces to a single shared physical premise ( v155, Python-only). The seam-side identification of the Simple-Current Extension Theorem ( v154) splits ( v110) into (a) ``the Calder\\'on involution is sheet-odd'' (the double-cover deck, structural) and (b) ``the seam [formula in source] -point kernel is quasi-free''. Part (b) is not independent: the boundary marginal of a reflection-p","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-13 (the seam-side identification reduced to one shared premise, v155)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":23130,"byte_start":20856,"id":"section:65e6ea58d3d1fb647f95","kind":"subsection","labels":[],"line_end":284,"line_start":258,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:00983c4620e64217642c","relation:04fc78e320fcf09e5687","relation:2d9c8e18376113de09cb","relation:2e3898c890217e672a48","relation:3287fe60c8d936933463","relation:432b8c757c49cad3c8e5","relation:5755ee2925d550c018d3","relation:898b7f324fd4464d3f50","relation:93b7288fd015f0bc51d2","relation:980a3b82258035afe280","relation:a03f795386be0c252b3e","relation:a7f8e6b1e3ffedc110ac","relation:ace01174947da1740825","relation:ba3df883aa2defff743c","relation:c577567a3be26e82f70b","relation:cb562d3ee82d7cf3b0c6","relation:d131e948dd7c4bcfca28","relation:d7f3db3dc480329d547d","relation:d920b1c86068b6e5fee4","relation:dcb55099640174ebd189","relation:ddd7778d7e49a1b4c1bf","relation:e4137820e7ba9d3e8f50","relation:e90068a991d520205a9e","relation:fa71378e1f0e4837c0d3"],"semantic_review":false,"source":"documents/changelog/sections/022-source.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"[formula in source] re-typed: the No-Unit Theorem ( v153). Every load-bearing compiler datum is mass-dimension [formula in source] and invariant under a unit rescaling [formula in source] , whereas a mass / [formula in source] is not — so a dimensionless boundary compiler provably cannot select an absolute scale. [formula in source] is therefore an irreducible metrology primitive, not an open gap, and the three appar","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-13 (external review formalised: No-Unit Theorem + Simple-Current Extension Theorem, v153– v154)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":24301,"byte_start":23130,"id":"section:7510d6c9f8fef452a8a6","kind":"subsection","labels":[],"line_end":301,"line_start":285,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":[],"semantic_review":false,"source":"documents/changelog/sections/022-source.tex","status_markers_as_written":[],"summary_excerpt":"No old-version framing left in the active docs. A consistency sweep found a residual layer of old-series ``Paper N'' attributions and removed them: four literal ``Paper 6'' references ( tfpt_4_frontier leptogenesis/axion, tfpt_2 seam determinant), the old ``Paper 4'' (OS/admissibility) and ``Paper 5'' (APS/Hodge) references in tfpt_2, the old ``Paper 3'' transport-kernel attributions in tfpt_2, and the internal ``Pap","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-13 (currency sweep: remaining old-series ``Paper N'' cross-references removed)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":25442,"byte_start":24301,"id":"section:1a45d75b719beb596c5e","kind":"subsection","labels":[],"line_end":317,"line_start":302,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:1caa76cb2c0f354572ac","relation:4af26757f2721f05bf65","relation:7b83e86bd286a538d9f4","relation:7c2b272132406ef950a0","relation:9b2703461eb28ed3cb0e","relation:a513b6cf79d76e800de9","relation:b0b8905ee1774f7c6fb7","relation:ba9397a8d5bed87226ef","relation:cac8dc3df7e04834c227","relation:fc93593ccb38c1764278"],"semantic_review":false,"source":"documents/changelog/sections/022-source.tex","status_markers_as_written":[],"summary_excerpt":"R3: the [formula in source] normalisation merges into the one anchor ( v152). 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So [formula in s","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-13 (fifth round: the R3 normalisation is the dimensionful anchor, v152)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":25992,"byte_start":25442,"id":"section:96bab9fe7e8297dfe11c","kind":"subsection","labels":[],"line_end":326,"line_start":318,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:fdccfd49d5fc863bdcc7"],"semantic_review":false,"source":"documents/changelog/sections/022-source.tex","status_markers_as_written":[],"summary_excerpt":"Release version string. build.sh now writes tex-artefacts/release-version.txt as \\TFPTversion\\ (rev \\git count\\) (matches TFPTdatestamp without the date). scripts/zenodo_upload.py and build.sh zenodo/ zenodo-publish use this label on Zenodo; cursor rules extended for when zenodo_description.html must move with deposit-facing changes.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-12 (Zenodo version label: semantic + git rev)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":26569,"byte_start":25992,"id":"section:2f507dd11e908355b7f4","kind":"subsection","labels":[],"line_end":335,"line_start":327,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:cffb2da23216159699ff"],"semantic_review":false,"source":"documents/changelog/sections/022-source.tex","status_markers_as_written":[],"summary_excerpt":"Automated Zenodo versioning. 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New single source tex-artefacts/version.tex defines TFPTauthors (Stefan Hamann, Alessandro Rizzo), a curated TFPTversion, and a title/footer date stamp ( today [formula in source] version [formula in source] revision). build.sh writes the auto build revision (git commit count) into the gitignored tex-artefacts/version-auto.tex, so every document's title page and pag","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-12 (version system, predictions/K5, readability pass B3)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":25120,"byte_start":22799,"id":"section:826ddf772de04049b71a","kind":"subsection","labels":[],"line_end":330,"line_start":303,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:7d2ec6932f4f29680a81","relation:d1246313cb8330afa3a6"],"semantic_review":false,"source":"documents/changelog/sections/023-source.tex","status_markers_as_written":[],"summary_excerpt":"Shared imports moved to tex-artefacts/. The shared, imported-only TeX fragments ( tfpt_style.tex, tfpt_figures.tex, tfpt_docset.tex, tfpt_status.tex) now live in a dedicated tex-artefacts/ folder; all nine active documents input them via tex-artefacts/<name> (and tfpt_style loads tex-artefacts/tfpt_figures). changelog.tex stays at the repo root because it is also a standalone build.sh notes deliverable. 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The [formula in source] non-load-bearing aside boxes (audit / recorded / interpretation: auditbox/ audbox/ intbox/ resbox/ roadbox) across tfpt_1, tfpt_2, tfpt_3 and origin_theory are converted to inline bold run-in paragraphs — the reviewer's prescription that an audit fingerprint must not carry the same visual volume as a theorem. 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The introduction's one-sentence claim is softened from ``derives all constants'' to ``constructs a discrete compiler; physical readouts run through named, status-typed bridges''; the ledger zombie in FLAV.QRATIO.01 is removed (the statement no longer says ``stays [P]'' — ratios are \\ closed on the derived stratum, only the absolute scale stays , with an explicit forbidden-wording not","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-12 (review pass on list.txt)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":746,"byte_start":0,"id":"section:e2e448f834c8b18c1b82","kind":"subsection","labels":[],"line_end":11,"line_start":1,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":[],"semantic_review":false,"source":"documents/changelog/sections/024-source.tex","status_markers_as_written":[],"summary_excerpt":"Shared style and central status artifact. 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The established frozen selectors ( [formula in source] annihilator [formula in source] , [formula in source] , [formula in source] ) pin [formula in source] uniquely among hexagon matrices ( [formula in source] ); the atom margins become theorems — H2 introduces no new residual class. Inventory update (v123). Residual table re-pinned post v110–v122: exactly five structural classes (R1 clock, R2","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-12","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8294,"byte_start":5875,"id":"section:9575cef792be9f73f7ff","kind":"subsection","labels":[],"line_end":108,"line_start":76,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:1103d6555a9f7d13892f","relation:13a06bc14f38e407c1d1","relation:258cc858065464fcd8f8","relation:2e624b783f94333c64aa","relation:2f418380ed730b307c66","relation:4baa4ffebe56dea87fdf","relation:5ddc85d09f5bc2c8e015","relation:60cb574dd439e87fa8cf","relation:6b4d87003543501f5761","relation:7003c2abf96d7c70d720","relation:7bf6e1f191570772aa62","relation:7c7ccc93aafaf3c87b35","relation:7f46d2449b4acb3eece6","relation:870fd8209d584badb28c","relation:8b7683b4b928c2bd31ca","relation:8bf96cf2c9cc73552a1b","relation:9106fada14f19f6f57e9","relation:a2a0f03ab93b7f5896fc","relation:ab750767eb0a9b1977cd","relation:b6d51956aa5c7f315aaf","relation:ca3d2584e11f73c92c81","relation:d966c172a888f5eba66f","relation:dc8fac0a340c32a28717","relation:e2f048e16fb3b033652a","relation:fd69a7fc56e110ce3c46"],"semantic_review":false,"source":"documents/changelog/sections/024-source.tex","status_markers_as_written":[],"summary_excerpt":"External-review integration (v83) and release hygiene. Manifest –check mode and the release rule; holomorphy pins [formula in source] (the unique even unimodular rank-8 lattice theory). Sheet diamond and centered form (v94/v95). All four flavor operators are points of one two-parameter surface [formula in source] ; centered cross [formula in source] , [formula in source] with the cofactor seam normal [formula in sour","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-11","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8822,"byte_start":8294,"id":"section:6b03fdb0bab2125a7ce4","kind":"subsection","labels":[],"line_end":118,"line_start":109,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:27d0bce645e0553f35fb","relation:33a8d2840d898be9a084","relation:36e646d0c9aba4817727","relation:4d86bfc75a99530f0bff","relation:9608d31ead0581caebe3","relation:9668bdc6dfbbf3fa2440","relation:a03bdc77bb21445f688f","relation:b3623cc7c0c5d5e2375c","relation:cddbd6da9d41d3f47a1d","relation:d9f0b6349936d710bffc","relation:ede106bfc40b78326864","relation:f86d32f1bb6deb278097","relation:ffd8ebf19a9cc08b95e5"],"semantic_review":false,"source":"documents/changelog/sections/024-source.tex","status_markers_as_written":[],"summary_excerpt":"B/C/D round closed. Koide attractor toy model (v93), glue uniqueness (v92), the Wolfram extension as the independent second verification path, Lean hardening; papers and website synced with the round. Content rounds v96–v100. 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Machine-enforced prediction registry ( predictions_frozen.json): exactly one [formula in source] number of record before JUNO; conditional entries carry their hypotheses by name. Research-contracts document added to the set.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-06-09","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9744,"byte_start":9156,"id":"section:b7a05826756c1fc3ef1e","kind":"subsection","labels":[],"line_end":136,"line_start":127,"occurrence":1,"owner_documents":["document:changelog","document:introduction"],"relation_ids":["relation:2c0f2c294ebb3c05f56a","relation:4256925bf66ca920c70e","relation:64528dbad8abe0ff9e3a","relation:760e2193d4bbda73ccef","relation:be25fc8ed2410f2a9942","relation:ea7ff3c9e6fa5f221e85"],"semantic_review":false,"source":"documents/changelog/sections/024-source.tex","status_markers_as_written":[],"summary_excerpt":"Compiler-closure consolidation. 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TFPT papers and website baseline: electromagnetic closure and flavor transport (UFE bridge, birefringence seed, dyonic intercept), PDF-download tracking, accessibility and metadata passes.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2026-04-27","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2500,"byte_start":0,"id":"section:01e6b4359c05da0e8680","kind":"frontmatter","labels":[],"line_end":60,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/lean4-carrier-rigidity/note_carrier_rigidity_lean4"],"relation_ids":["relation:3402c46fa34e9c39f447","relation:40bbbcc94cbed1035bea","relation:4fa6ef950e7564c2f07c","relation:52c56ea87769344b28cf","relation:5f975760c289249e200a","relation:7f1eb82342de237dd4d0"],"semantic_review":false,"source":"documents/experiments--lean4-carrier-rigidity--note_carrier_rigidity_lean4/preamble.tex","status_markers_as_written":["[L]"],"summary_excerpt":"tfptgray TFPT Lean Note: Carrier Rigidity Audit Harness tfptgray","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"tfptblue Formal Verification of TFPT Carrier Rigidity in Lean 4\\\\[0.4em] An Audited Dependency Graph from the Boundary Involution\\\\ to the Standard-Model [formula in source] \\ Hypercharge Carrier","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":12111,"byte_start":0,"id":"section:25a09b35c9322690a2b6","kind":"frontmatter","labels":[],"line_end":267,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/lean4-carrier-rigidity/note_carrier_rigidity_lean4"],"relation_ids":["relation:159d65f80057abbade05","relation:2e4eec900e02f0dd9eb4","relation:318b0fd4e98acef1484a","relation:41cbaec5eb55f18d215f","relation:50b3a04bd07d489d0c73","relation:779ab7039c9880a32d99","relation:7dcbbc900e9155444c7d","relation:8b07b276f6dd4c8a9a2a","relation:8d8238b6860172f0a229","relation:8ed1c6cb34d27a0d1cdd","relation:91192e17c2124b631d79","relation:bfcdc58da3178e36c7a9","relation:cecab021e2c3070de2ad","relation:cf8ac06c791f26537fbb","relation:f871224430fd64ccbfc1"],"semantic_review":false,"source":"documents/experiments--lean4-carrier-rigidity--note_carrier_rigidity_lean4/sections/001-section-what-this-note-is-about.tex","status_markers_as_written":[],"summary_excerpt":"This note documents a Lean 4 formalisation of the algebraic carrier rigidity theorem of TFPT Paper 2 ( Carrier Rigidity, Hypercharge, and the Standard-Model Packet from Boundary Polarization), up to and including the determinant-normalised [formula in source] hypercharge carrier [formula in source] . 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TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Layer 6c — Yukawa Stage C (primitive indecomposable coupling)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":8025,"byte_start":3303,"id":"section:80f5430a98e66833b910","kind":"subsection","labels":[],"line_end":201,"line_start":89,"occurrence":1,"owner_documents":["document:experiments/lean4-carrier-rigidity/note_carrier_rigidity_lean4"],"relation_ids":["relation:224d11b55a848ef5ff7c","relation:ad449f9d369f563df3b2"],"semantic_review":false,"source":"documents/experiments--lean4-carrier-rigidity--note_carrier_rigidity_lean4/sections/003-subsection-layer-6b-yukawa-stage-b-algebraic-content.tex","status_markers_as_written":[],"summary_excerpt":"For every alternating trilinear form [formula in source] , the associated contraction map [formula in source] is constructible as a LinearMap. The Lean construction uses exteriorPower.alternatingMapLinearEquiv (to convert between [formula in source] and the space of [formula in source] -valued alternating maps on [formula in source] ) and AlternatingMap.curryLeft (to split off the first argument).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Layer 6d — Yukawa Stage D (primary trilinear form)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":8382,"byte_start":8025,"id":"section:054c02ea3d6a19cf35e1","kind":"subsection","labels":[],"line_end":210,"line_start":202,"occurrence":1,"owner_documents":["document:experiments/lean4-carrier-rigidity/note_carrier_rigidity_lean4"],"relation_ids":["relation:9279efdda3cf37c652d2"],"semantic_review":false,"source":"documents/experiments--lean4-carrier-rigidity--note_carrier_rigidity_lean4/sections/003-subsection-layer-6b-yukawa-stage-b-algebraic-content.tex","status_markers_as_written":[],"summary_excerpt":"A TFPT.Carrier.Polarization on a ring [formula in source] is canonically a Mathlib CompleteOrthogonalIdempotents on the pair [formula in source] . A converse map ofCompleteOrthogonalIdempotents is also provided.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Layer 7 — Mathlib bridge","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":9416,"byte_start":8382,"id":"section:ee6b6e1460d0b7b1bd43","kind":"subsection","labels":[],"line_end":238,"line_start":211,"occurrence":1,"owner_documents":["document:experiments/lean4-carrier-rigidity/note_carrier_rigidity_lean4"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--lean4-carrier-rigidity--note_carrier_rigidity_lean4/sections/003-subsection-layer-6b-yukawa-stage-b-algebraic-content.tex","status_markers_as_written":[],"summary_excerpt":"The carrier-rigidity payload of the project is the following set of bundled theorems on CarrierPremises K M:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Layer 8 — Bundled main theorems","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":9853,"byte_start":9416,"id":"section:95d9cf94bda42fc0f31e","kind":"subsection","labels":[],"line_end":248,"line_start":239,"occurrence":1,"owner_documents":["document:experiments/lean4-carrier-rigidity/note_carrier_rigidity_lean4"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--lean4-carrier-rigidity--note_carrier_rigidity_lean4/sections/003-subsection-layer-6b-yukawa-stage-b-algebraic-content.tex","status_markers_as_written":[],"summary_excerpt":"On the concrete [formula in source] rational diagonal model, [formula in source] satisfies [formula in source] and [formula in source] , proved by direct per-entry rational arithmetic.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Concrete realisation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10046,"byte_start":9853,"id":"section:f391f960dd599e630069","kind":"section","labels":["sec:significance"],"line_end":255,"line_start":249,"occurrence":1,"owner_documents":["document:experiments/lean4-carrier-rigidity/note_carrier_rigidity_lean4"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--lean4-carrier-rigidity--note_carrier_rigidity_lean4/sections/003-subsection-layer-6b-yukawa-stage-b-algebraic-content.tex","status_markers_as_written":[],"summary_excerpt":"The two load-bearing chains, with all hypotheses explicitly visible, are:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Significance","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10849,"byte_start":10046,"id":"section:35a557d0d4bb41900f4f","kind":"paragraph","labels":[],"line_end":281,"line_start":256,"occurrence":1,"owner_documents":["document:experiments/lean4-carrier-rigidity/note_carrier_rigidity_lean4"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--lean4-carrier-rigidity--note_carrier_rigidity_lean4/sections/003-subsection-layer-6b-yukawa-stage-b-algebraic-content.tex","status_markers_as_written":[],"summary_excerpt":"[formula in source] together with the rank discharges [formula in source] and the determinant-normalised coefficient choice [formula in source] give, via TraceProjection, [formula in source] The Yukawa input is now an alternating trilinear form with two explicit Prop predicates. The contraction iso and the rank-3 conclusion are both derived theorems.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Chain A — trace identity.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":11362,"byte_start":10849,"id":"section:950d3549a66e5fd478a0","kind":"paragraph","labels":[],"line_end":300,"line_start":282,"occurrence":1,"owner_documents":["document:experiments/lean4-carrier-rigidity/note_carrier_rigidity_lean4"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--lean4-carrier-rigidity--note_carrier_rigidity_lean4/sections/003-subsection-layer-6b-yukawa-stage-b-algebraic-content.tex","status_markers_as_written":[],"summary_excerpt":"The trace-zero condition [formula in source] follows from the universal- [formula in source] determinant character. Combined with the primitivity and orientation conditions [formula in source] the general [formula in source] rigidity theorem gives [formula in source] For [formula in source] this specialises to [formula in source] . The integer answer is a corollary of a parametric theorem; it is not hard-coded.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Chain B — integer rigidity.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":11876,"byte_start":11362,"id":"section:992cf28e93a790907da4","kind":"paragraph","labels":[],"line_end":310,"line_start":301,"occurrence":1,"owner_documents":["document:experiments/lean4-carrier-rigidity/note_carrier_rigidity_lean4"],"relation_ids":["relation:d81b028cb8a643fca3bd"],"semantic_review":false,"source":"documents/experiments--lean4-carrier-rigidity--note_carrier_rigidity_lean4/sections/003-subsection-layer-6b-yukawa-stage-b-algebraic-content.tex","status_markers_as_written":[],"summary_excerpt":"The carrier polynomial [formula in source] is a consequence of the polarization layer alone (it does not need either rank discharge). The trace identity [formula in source] requires the rank discharges. The integer pair [formula in source] requires the primitive oriented determinant-preserving condition together with [formula in source] . The bundled theorem hypercharge_carrier_packet is the unique statement that req","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Why both chains matter together.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":12377,"byte_start":11876,"id":"section:623844c7d7161b1e3813","kind":"paragraph","labels":[],"line_end":319,"line_start":311,"occurrence":1,"owner_documents":["document:experiments/lean4-carrier-rigidity/note_carrier_rigidity_lean4"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--lean4-carrier-rigidity--note_carrier_rigidity_lean4/sections/003-subsection-layer-6b-yukawa-stage-b-algebraic-content.tex","status_markers_as_written":[],"summary_excerpt":"The [formula in source] multiplet [formula in source] is the carrier. The full Standard-Model hypercharge spectrum — all chiral-multiplet hypercharges including duals, exterior powers, and tensor products — is not formalised in this experiment. The title and main theorem both say \" [formula in source] hypercharge carrier\", not \"SM hypercharge spectrum\".","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"What is not claimed.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":4548,"byte_start":0,"id":"section:18f9d14a7232cd74c3b7","kind":"section","labels":["sec:interface-table"],"line_end":109,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/lean4-carrier-rigidity/note_carrier_rigidity_lean4"],"relation_ids":["relation:064882ba07ad6a02bd8f","relation:12a110a3dd8f14c3ba7f","relation:19bab407cf4c68518f52","relation:26c613bf81c5936857a4","relation:276ee1b067d5464bce94","relation:2b5dd215b57201ec5c3d","relation:976fbaa4f5109bf25abc","relation:aa790ba67873abbbd5b4","relation:b8de1830c9f7fa58bfc8","relation:c84c854386d6f15c7487","relation:d1ee6c46a81e8a8d4a58"],"semantic_review":false,"source":"documents/experiments--lean4-carrier-rigidity--note_carrier_rigidity_lean4/sections/004-section-interface-table-tfpt-paper-2-texorpdfstring-left.tex","status_markers_as_written":[],"summary_excerpt":"The following table maps each load-bearing claim of TFPT Paper 2 to its current Lean status and the still-missing upstream proof. It is the primary defence against scope-creep: the present note formalises columns 1 and 2; column 3 is explicitly out of scope.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Interface Table: TFPT Paper 2 [formula in source] <-> Lean Status","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":4659,"byte_start":4548,"id":"section:afeac5dd63b853c239be","kind":"section","labels":["sec:limits"],"line_end":113,"line_start":110,"occurrence":1,"owner_documents":["document:experiments/lean4-carrier-rigidity/note_carrier_rigidity_lean4"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--lean4-carrier-rigidity--note_carrier_rigidity_lean4/sections/004-section-interface-table-tfpt-paper-2-texorpdfstring-left.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Limitations","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":5615,"byte_start":4659,"id":"section:5b5deee14edc9e9ff37f","kind":"paragraph","labels":[],"line_end":134,"line_start":114,"occurrence":1,"owner_documents":["document:experiments/lean4-carrier-rigidity/note_carrier_rigidity_lean4"],"relation_ids":["relation:57c28209e50ace6d9807","relation:9b24c7f69fba366f24da","relation:a89601a23c48c943993a","relation:b42af3c83f7af2a3c985","relation:d312fe09920ebd09b834","relation:d9358508e2952371bf77"],"semantic_review":false,"source":"documents/experiments--lean4-carrier-rigidity--note_carrier_rigidity_lean4/sections/004-section-interface-table-tfpt-paper-2-texorpdfstring-left.tex","status_markers_as_written":[],"summary_excerpt":"The v5 critique of Stage C was that it bundled the contraction iso as data, so it was equivalent (in finite dimensions) to [formula in source] and did not \"explain\" the rank. v6 resolved this by introducing Stage D; v7 renamed its operational predicates to keep semantic-load words out of the Lean interface:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Yukawa: Stage D resolves the v5 critique.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6232,"byte_start":5615,"id":"section:c0b758d352b686c50e93","kind":"paragraph","labels":[],"line_end":146,"line_start":135,"occurrence":1,"owner_documents":["document:experiments/lean4-carrier-rigidity/note_carrier_rigidity_lean4"],"relation_ids":["relation:29a0cf5a5834c1a61855","relation:37c7d1fd8c849cc4283d","relation:869b10800fb266941707","relation:f63c647ea8ce0a217b4b"],"semantic_review":false,"source":"documents/experiments--lean4-carrier-rigidity--note_carrier_rigidity_lean4/sections/004-section-interface-table-tfpt-paper-2-texorpdfstring-left.tex","status_markers_as_written":[],"summary_excerpt":"Without the non-triviality hypothesis the rank-3 slogan would be false: for [formula in source] the spaces [formula in source] and [formula in source] are both zero, the contraction [formula in source] is trivially bijective, both operational predicates hold vacuously, but [formula in source] . The transparency theorem finrank_E_eq_zero_or_three (v9) records the unconditional disjunction [formula in source] ; the ran","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Why Nontrivial\\, [formula in source] is necessary.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":7080,"byte_start":6232,"id":"section:7da7283875b2911aa2f3","kind":"paragraph","labels":[],"line_end":166,"line_start":147,"occurrence":1,"owner_documents":["document:experiments/lean4-carrier-rigidity/note_carrier_rigidity_lean4"],"relation_ids":["relation:1b3ae93dfbb19aa616c4","relation:347c3e8587f23acda31d","relation:42f67c6b86d99ab39ad1","relation:7b7a60896fcc13767c90","relation:83ea407b2cbf73741ef0","relation:8639a9f045a18a73dd79","relation:96e3e7ad1ec44270630e","relation:c6f86b200a943d3ceb60","relation:d2f7a5230c008aa3e5f6"],"semantic_review":false,"source":"documents/experiments--lean4-carrier-rigidity--note_carrier_rigidity_lean4/sections/004-section-interface-table-tfpt-paper-2-texorpdfstring-left.tex","status_markers_as_written":[],"summary_excerpt":"For all four Yukawa stages the note now proves the full characterisation [formula in source] . For Stage D, under Nontrivial\\, [formula in source] : [formula in source] The forward direction is finrank_E_eq_three_of_condition; the backward direction is YukawaStageDExistence.exists_yukawaTrilinearForm_of_finrank_eq_three, proved via Module.Basis.det transported through exteriorPower.alternatingMapLinearEquiv and direc","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Stage D characterisation, both directions formalised (v10).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":8182,"byte_start":7080,"id":"section:458a3ef36e2c278139fa","kind":"paragraph","labels":[],"line_end":190,"line_start":167,"occurrence":1,"owner_documents":["document:experiments/lean4-carrier-rigidity/note_carrier_rigidity_lean4"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--lean4-carrier-rigidity--note_carrier_rigidity_lean4/sections/004-section-interface-table-tfpt-paper-2-texorpdfstring-left.tex","status_markers_as_written":[],"summary_excerpt":"The Lean chain takes the Stage D quadruple [formula in source] as input. The remaining open question is whether TFPT itself produces such a quadruple from the boundary kernel. Concretely:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"What remains is upstream TFPT theory work.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10583,"byte_start":8182,"id":"section:35345827b51908140e58","kind":"paragraph","labels":[],"line_end":238,"line_start":191,"occurrence":1,"owner_documents":["document:experiments/lean4-carrier-rigidity/note_carrier_rigidity_lean4"],"relation_ids":["relation:03f3b62f014d84921bc8","relation:0b93793069c9d1e89ff5","relation:633362dfa83f1d787d90","relation:6b12daa4394a6c5b84d5","relation:899fa32be05a69f4e17b","relation:8c0c510434789cb1d31b","relation:a140b5855e55cc11916a","relation:bd598a7479bc785db503","relation:d739bd471f02143ffb75"],"semantic_review":false,"source":"documents/experiments--lean4-carrier-rigidity--note_carrier_rigidity_lean4/sections/004-section-interface-table-tfpt-paper-2-texorpdfstring-left.tex","status_markers_as_written":[],"summary_excerpt":"Calder\\'on: two structural layers formalised, analytic input of the polarisation open.\\ CalderonProjector proves [formula in source] , and BoundaryPolarization (v10) shows that any direct-sum decomposition [formula in source] of a [formula in source] -module produces such an idempotent via Mathlib's IsCompl.projection. What remains is the analytic Paper 1 theorem producing the boundary spectral decomposition itself —","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Remaining limitations of the Lean chain itself.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":11168,"byte_start":10583,"id":"section:02393735276ef9585ebf","kind":"paragraph","labels":[],"line_end":251,"line_start":239,"occurrence":1,"owner_documents":["document:experiments/lean4-carrier-rigidity/note_carrier_rigidity_lean4"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--lean4-carrier-rigidity--note_carrier_rigidity_lean4/sections/004-section-interface-table-tfpt-paper-2-texorpdfstring-left.tex","status_markers_as_written":[],"summary_excerpt":"Full [formula in source] -quotient theorem for [formula in source] . Derived Standard-Model representations (dual, exterior powers, tensor products); the diagonal formalised here is the carrier hypercharge, not the full SM hypercharge spectrum. 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Abstract carrier polynomial: Polarization.sixY_carrier_polynomial. Boundary involution [formula in source] projectors: InvolutionProjectors.CarrierInvolution.toPolarization. Mathlib bridge: MathlibBridge.Polarization.toCompleteOrthogonalIdempotents. General integer rigidity: LatticeRigidityGeneral.primitive_trace_free_pair_general. Structural trace identity: TraceProjection.trace_linear_c","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Result","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":18053,"byte_start":17248,"id":"section:05eb30f183fbe41ac436","kind":"section","labels":[],"line_end":418,"line_start":388,"occurrence":1,"owner_documents":["document:experiments/lean4-carrier-rigidity/note_carrier_rigidity_lean4"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--lean4-carrier-rigidity--note_carrier_rigidity_lean4/sections/006-subsection-v6-yukawa-stage-d-and-calder-n-interface.tex","status_markers_as_written":[],"summary_excerpt":"# 1. Install elan (Lean toolchain manager) curl -sSf https://raw.githubusercontent.com/leanprover/elan/master/elan-init.sh \\ | sh -s – -y –default-toolchain none export PATH=\" [formula in source] PATH\"","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproducing the Build and Audit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":5148,"byte_start":0,"id":"section:d8d76f3a909d7e32148b","kind":"frontmatter","labels":[],"line_end":133,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/preamble.tex","status_markers_as_written":["[L]"],"summary_excerpt":"unicodehyperref hyphensurl dvipsnames,svgnames,x11namesxcolor ngerman, 10pt, a4paper, ]article Scale=MatchLowercase Ligatures=TeX,Scale=1","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":64,"byte_start":0,"id":"section:aee56601ea432371ddad","kind":"frontmatter","labels":[],"line_end":6,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/001-section-tfpt-universalraum-gemeinsame-schatten-und-ein.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":417,"byte_start":64,"id":"section:de8b0d058e8d3a741c50","kind":"section","labels":["tfpt-universalraum-gemeinsame-schatten-und-ein-urspruxfcnglicher-kausaler-prozess"],"line_end":14,"line_start":7,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/001-section-tfpt-universalraum-gemeinsame-schatten-und-ein.tex","status_markers_as_written":[],"summary_excerpt":"Vollständige Fortschreibung v1.6.8, 15. September 2026. Forschungsbericht und unabhängige Prüfung der nachgereichten Forschungssynthese 1.0. Keine vollständige TOE.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TFPT / Universalraum: gemeinsame Schatten und ein ursprünglicher kausaler Prozess","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2906,"byte_start":417,"id":"section:62333968feb6f8b25580","kind":"subsection","labels":["ergebnis-und-leseschluxfcssel"],"line_end":59,"line_start":15,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/001-section-tfpt-universalraum-gemeinsame-schatten-und-ein.tex","status_markers_as_written":[],"summary_excerpt":"Die drei parallel bearbeiteten Aufgaben liefern diesmal konkrete mathematische Anschlüsse: einen kleinen ursprünglichen Singulettmechanismus, die vollständige bedingte Schattenkarte des hellen Raums und einen kausalen Eingriff unter dem unveränderten Hamiltonoperator. Die nachgereichte Forschungssynthese verbindet diese Aufgaben sinnvoll durch gemeinsame Operationsgeschichten. Ihre mitgelieferten Rechnungen sind repr","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Ergebnis und Leseschlüssel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4873,"byte_start":2906,"id":"section:8fc907113cbfc5c7a92b","kind":"subsection","labels":["pruxfcfung-des-nachgereichten-forschungspapers"],"line_end":103,"line_start":60,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/001-section-tfpt-universalraum-gemeinsame-schatten-und-ein.tex","status_markers_as_written":[],"summary_excerpt":"Geprüft wurden das 33-seitige PDF, sein vollständiger Markdowntext, Prüfprotokoll, Quellenmanifest und eigene Ergebnisdatei sowie das zusätzlich vorhandene Reproduktionsarchiv. Die vollständige Synthese wurde gelesen; nicht jede der 74 historischen Quellen wurde neu bewiesen. Die relevanten PDF-Seiten 16 bis 20 und 22 wurden zusätzlich bildlich geprüft.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Prüfung des nachgereichten Forschungspapers","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6231,"byte_start":4873,"id":"section:c9c85c5c37f019438516","kind":"subsubsection","labels":["tatsuxe4chliche-korrektur-die-erste-zeile-genuxfcgt-wenn-sie-vollstuxe4ndig-ist"],"line_end":134,"line_start":104,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/001-section-tfpt-universalraum-gemeinsame-schatten-und-ein.tex","status_markers_as_written":[],"summary_excerpt":"Für eine unter Produkt und Adjungieren abgeschlossene Wortalgebra gilt definitionsgemäß","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2.1 Tatsächliche Korrektur: die erste Zeile genügt, wenn sie vollständig ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7547,"byte_start":6231,"id":"section:a28d5bf4b965ffd38a72","kind":"subsubsection","labels":["welche-gleichheit-ist-tatsuxe4chlich-beobachtbar"],"line_end":162,"line_start":135,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/001-section-tfpt-universalraum-gemeinsame-schatten-und-ein.tex","status_markers_as_written":[],"summary_excerpt":"Ein markierter komplexer Wortkern ist stärker als eine Liste gewöhnlicher Quantenkanäle. Beispielsweise liefern [formula in source] und [formula in source] für jeden Zustand denselben Kanal:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2.2 Welche Gleichheit ist tatsächlich beobachtbar?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8670,"byte_start":7547,"id":"section:967b9474cfa969355efc","kind":"subsubsection","labels":["referenzsystem-richtige-bilanz-keine-kostenlose-operation"],"line_end":183,"line_start":163,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/001-section-tfpt-universalraum-gemeinsame-schatten-und-ein.tex","status_markers_as_written":[],"summary_excerpt":"Die Synthese ergänzt den früher zusätzlich gemischten Vierzustandskanal um eine zweistufige Referenz. Das acht-dimensionale Gesamtmodell erhält die betrachtete innere Cartanladung. Auf einem invarianten vierdimensionalen Unterraum ist sein Hamiltonoperator exakt der alte Transferblock plus ein skalares Energieglied. Die frühere Transferschranke wird deshalb korrekt übertragen, nicht neu aus der nativen Quelle erzeugt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2.3 Referenzsystem: richtige Bilanz, keine kostenlose Operation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10219,"byte_start":8670,"id":"section:929d1f5b9cb7d0da0534","kind":"subsubsection","labels":["projektorgeometrie-tragfuxe4hig-aber-noch-nicht-nativ"],"line_end":218,"line_start":184,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/001-section-tfpt-universalraum-gemeinsame-schatten-und-ein.tex","status_markers_as_written":[],"summary_excerpt":"Für eine Isometriefamilie J mit [formula in source] gilt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2.4 Projektorgeometrie: tragfähig, aber noch nicht nativ","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10907,"byte_start":10219,"id":"section:b999ac31aa91662dbd8c","kind":"subsubsection","labels":["weitere-uxfcbernommene-richtungen"],"line_end":231,"line_start":219,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/001-section-tfpt-universalraum-gemeinsame-schatten-und-ein.tex","status_markers_as_written":[],"summary_excerpt":"Die Blockresolventenformel und der endliche Duhamel-Adapterfehlervertrag sind korrekt und brauchbar. Die einfache Restschranke [formula in source] wird nahe der reellen Achse schwach; sie bestimmt keinen scharfen physikalischen Pol. Gemischte Wort- und Matrixmomente sind eine passende Fortsetzung der verzweigten Hamiltonkette. Das neue Paper hat diese größere Kontraktionsrechnung selbst noch nicht ausgeführt. Es lief","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2.5 Weitere übernommene Richtungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13602,"byte_start":10907,"id":"section:57772ac08ac91a741561","kind":"subsection","labels":["der-gemeinsame-urspruxfcngliche-ausgangspunkt"],"line_end":295,"line_start":232,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/001-section-tfpt-universalraum-gemeinsame-schatten-und-ein.tex","status_markers_as_written":[],"summary_excerpt":"Alle drei eigenen Stränge verwenden denselben eingefrorenen Tensor W mit 60 Zeilen, 2016 Paarspalten und 480 signierten Einträgen. Es gilt exakt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Der gemeinsame ursprüngliche Ausgangspunkt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16612,"byte_start":13602,"id":"section:fd3a5f9639910524cdbd","kind":"subsection","labels":["einfachster-mechanismus-zwei-zustuxe4nde-und-eine-genaue-operationsgrenze"],"line_end":376,"line_start":296,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/001-section-tfpt-universalraum-gemeinsame-schatten-und-ein.tex","status_markers_as_written":[],"summary_excerpt":"Mit der aus W hergeleiteten invarianten Paarung [formula in source] definiere","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Einfachster Mechanismus: zwei Zustände und eine genaue Operationsgrenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2111,"byte_start":0,"id":"section:d30e1cd43987a7996ad3","kind":"subsection","labels":["gemeinsame-schattenkarte-welche-bilder-reichen"],"line_end":52,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/002-subsection-5-gemeinsame-schattenkarte-welche-bilder.tex","status_markers_as_written":[],"summary_excerpt":"Der native Kodierer [formula in source] bildet den inneren 60-Raum isometrisch in den Fermionpaarraum ab. Für jeden gewährten Operator O wird dessen Schatten auf demselben Zustand berechnet:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Gemeinsame Schattenkarte: welche Bilder reichen?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4743,"byte_start":2111,"id":"section:13a3222d1a97eb35468b","kind":"subsection","labels":["eigenes-bindeglied-aus-schatten-zu-mehreren-zeiten-die-fehlende-phase-zuruxfcckgewinnen"],"line_end":119,"line_start":53,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/002-subsection-5-gemeinsame-schattenkarte-welche-bilder.tex","status_markers_as_written":[],"summary_excerpt":"Schreibe die gemeinsame Zustandsmatrix in Paar-/Bosonblöcken. Die vier inneren hermiteschen Matrizen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Eigenes Bindeglied: aus Schatten zu mehreren Zeiten die fehlende Phase zurückgewinnen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5559,"byte_start":4743,"id":"section:cfb4d1e7813394b4eaf0","kind":"subsubsection","labels":["warum-nur-ein-schatten-auch-nach-beliebig-langer-zeit-nicht-reicht"],"line_end":137,"line_start":120,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/002-subsection-5-gemeinsame-schattenkarte-welche-bilder.tex","status_markers_as_written":[],"summary_excerpt":"Für alle t gilt exakt [formula in source] . Der Operatororbit einer einzigen Paarsonde hat auf dem Zweizustandsfaktor Rang drei statt vier. Mit sämtlichen inneren Sonden bleibt der unsichtbare Raum","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum nur ein Schatten auch nach beliebig langer Zeit nicht reicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8307,"byte_start":5559,"id":"section:afba40297c2741826ac5","kind":"subsection","labels":["echter-kausaler-eingriff-ohne-zusuxe4tzlichen-hoppingterm"],"line_end":202,"line_start":138,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/002-subsection-5-gemeinsame-schattenkarte-welche-bilder.tex","status_markers_as_written":[],"summary_excerpt":"Jede aktive W-Spalte gehört genau einer Zeile; jede Zeile enthält acht disjunkte Fermionpaare. Der ganze N=2-Raum zerfällt deshalb in 60 invariante neundimensionale Sterne und 1536 ungekoppelte Paare. Einschließlich der sieben dunklen Richtungen je Stern ergibt sich wieder dunkle Dimension 1956.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. Echter kausaler Eingriff ohne zusätzlichen Hoppingterm","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11240,"byte_start":8307,"id":"section:d2df40940374fd1870ee","kind":"subsubsection","labels":["noch-kleiner-derselbe-dreizustandsraum-truxe4gt-schatten-und-eingriff"],"line_end":270,"line_start":203,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/002-subsection-5-gemeinsame-schattenkarte-welche-bilder.tex","status_markers_as_written":[],"summary_excerpt":"Für den gerade beschriebenen Versuch genügt sogar der gemeinsame Raum","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7.1 Noch kleiner: derselbe Dreizustandsraum trägt Schatten und Eingriff","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12135,"byte_start":11240,"id":"section:b365ea01b4bcb2c6fb10","kind":"subsection","labels":["was-holografie-hier-sinnvoll-bedeutet"],"line_end":287,"line_start":271,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/002-subsection-5-gemeinsame-schattenkarte-welche-bilder.tex","status_markers_as_written":[],"summary_excerpt":"Bildlich sind die verschiedenen Beschreibungen Ansichten derselben Maschine. Eine Ansicht zeigt Besetzungen, eine andere innere Paarstruktur, eine dritte das spätere Verhalten nach einem Eingriff. Ihre gemeinsame Kalibrierung kann die verborgenen Phasen bestimmen. Abschnitt 6 realisiert genau diese Idee im endlichen hellen Raum.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8. Was Holografie hier sinnvoll bedeutet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14715,"byte_start":12135,"id":"section:e4ae9efc928c62ceaf4a","kind":"subsection","labels":["nuxe4chste-entscheidende-nachweise"],"line_end":333,"line_start":288,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/002-subsection-5-gemeinsame-schattenkarte-welche-bilder.tex","status_markers_as_written":[],"summary_excerpt":"Übergeordnete Frage: Welche ursprüngliche Kompositionsregel erzeugt gemeinsam unterscheidbare Vorkommen, ihre Bewegung, ihren Zustand und ihre Instrumente? Die letzte nachgereichte fundamentale Reduktion trifft diese Frage. Ein genaueres lokales Spektrum kann sie nicht ersetzen. Die folgenden kleinen Prüfungen dienen als überprüfbare Annahmekriterien für eine solche Regel; sie sind keine Ersatzdefinition von Raum und","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. Nächste entscheidende Nachweise","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17214,"byte_start":14715,"id":"section:121e2885e363b2a9b3eb","kind":"subsection","labels":["t1-bis-t8-nach-dieser-runde"],"line_end":388,"line_start":334,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/002-subsection-5-gemeinsame-schattenkarte-welche-bilder.tex","status_markers_as_written":[],"summary_excerpt":"Die Bezeichnungen folgen der Arbeitszuordnung der geprüften Synthese; die jeweiligen vollständigen Tore bleiben offen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10. T1 bis T8 nach dieser Runde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":1012,"byte_start":0,"id":"section:49f368bb92a717229580","kind":"subsection","labels":["reproduktionsumfang"],"line_end":20,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/003-subsection-11-reproduktionsumfang-label-reproduktionsumf.tex","status_markers_as_written":[],"summary_excerpt":"Der gemeinsame Replay führt alle eigenen mathematischen Prüfer normal und optimiert mit Warnungen als Fehler aus. Die Teilberichte unterscheiden exakte Identitäten von numerischen Kontrollen. Die 57 Prüfbedingungen des gelieferten Papers und dessen 20 übernommene Kettenprüfungen werden separat ausgewiesen, nicht als neue eigene Entdeckungen addiert. Sie decken nicht automatisch jeden Satz des Papers ab; die Korrektur","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"11. Reproduktionsumfang","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1545,"byte_start":1012,"id":"section:d9f84c42ae1ceaa24a9b","kind":"section","labels":["nachgereichte-texte-neue-norm-korrigierte-zustandszuordnung-und-feldadapter"],"line_end":30,"line_start":21,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/003-subsection-11-reproduktionsumfang-label-reproduktionsumf.tex","status_markers_as_written":[],"summary_excerpt":"Die drei während der laufenden Prüfung nachgereichten Texte wurden vollständig gelesen und unverändert eingefroren. Sie sind keine Anweisungen, Ergebnisse ungeprüft zu übernehmen. Zwei Texte vereinfachen ältere Arbeitsstände stark; die dritte längere Forschungsnotiz enthält ausführlichere Beweise einer bereits bekannten grundsätzlichen Diagnose.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nachgereichte Texte: neue Norm, korrigierte Zustandszuordnung und Feldadapter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":3946,"byte_start":1545,"id":"section:67f587e4426f179afcee","kind":"subsection","labels":["a.-ein-tatsuxe4chlich-neuer-rechenwert-truxe4gt-eine-stuxe4rkere-schranke"],"line_end":87,"line_start":31,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":["relation:05840ecd0a55de01d740","relation:60d00f1247f4ceb6330b","relation:6ed7de40c15fa0d349f2","relation:6f811d2bfd4e6afb165b","relation:af3ddad85db07a54f74d"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/003-subsection-11-reproduktionsumfang-label-reproduktionsumf.tex","status_markers_as_written":[],"summary_excerpt":"Die Norm der fünften reinen Bosonstufe ist gegenüber dem hiesigen v1.6.7-Snapshot neu:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"A. Ein tatsächlich neuer Rechenwert trägt eine stärkere Schranke","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6265,"byte_start":3946,"id":"section:221a1ad5a4cec6ca9d6e","kind":"subsection","labels":["b.-die-einfache-darstellung-vermischt-zwei-nuxe4herungszustuxe4nde"],"line_end":128,"line_start":88,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":["relation:2a0ac0f7e1e17bdb5413","relation:c8e87c1690008b1f0afd"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/003-subsection-11-reproduktionsumfang-label-reproduktionsumf.tex","status_markers_as_written":[],"summary_excerpt":"Die Werte um -1.138476Δ, mittlere Bosonzahl 1.0177445, Überlappung mit F von 0.3498904 und Bosonzahl-Shannonwert 1.8712436 Bit gehören zum größeren siebendimensionalen Ritz-Zustand. Die im selben Text genannten Gewichte 0.973684 und 0.026316 gehören dagegen ausdrücklich zu der älteren fünfdimensionalen Basis v0 bis v3 plus w2. Deren Energie liegt um -1.0942319Δ und ihre mittlere Bosonzahl um 0.8421159.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B. Die einfache Darstellung vermischt zwei Näherungszustände","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8449,"byte_start":6265,"id":"section:5bd8c33339b55df5cb39","kind":"subsection","labels":["c.-ein-neuer-entscheidender-test-am-feldprojektor"],"line_end":178,"line_start":129,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/003-subsection-11-reproduktionsumfang-label-reproduktionsumf.tex","status_markers_as_written":[],"summary_excerpt":"Der Spin-1/2-Projektor im zweiten Text trägt unter einer bestimmten Händigkeit. 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Ihr stärkster Satz trägt: Bei invariantem H, invariantem Ω und irreduzibler innerer Entnahmefamilie gilt für die gesamte lokale Antwort","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"E. 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Was die tatsächlichen Quellen konstruieren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6112,"byte_start":4034,"id":"section:b766321aff43d5c9ecd8","kind":"subsection","labels":["geschlossener-erhaltungssatz-fuxfcr-das-dokumentierte-alphabet"],"line_end":138,"line_start":78,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/004-subsection-1-was-die-tats-chlichen-quellen.tex","status_markers_as_written":[],"summary_excerpt":"hat jedes der 480 signierten Wechselwirkungsmonome Ladung +2−1−1=0. Nb, alle Modenbesetzungen und alle passiven Bilineare f†Af beziehungsweise b†Cb sind ebenfalls neutral. Die dokumentierten inneren Liegeneratoren werden genau auf diese Weise zweitquantisiert. Die Clock schickt f† nach GF f† und b† nach GB b†, mischt also keine Erzeuger mit Vernichtern.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Geschlossener Erhaltungssatz für das dokumentierte Alphabet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7096,"byte_start":6112,"id":"section:fb26754998e4c34dde02","kind":"subsubsection","labels":["instrumente-und-die-genaue-ancilla-grenze"],"line_end":157,"line_start":139,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/004-subsection-1-was-die-tats-chlichen-quellen.tex","status_markers_as_written":[],"summary_excerpt":"Ein Instrument mit Krausoperatoren Kx aus A0 kann aus einem scharfen N-Sektor keinen anderen erzeugen. Eine spurtreue Summe solcher Zweige erhält die gesamte Sektorverteilung. Selektive Konditionierung kann die Gewichte einer bereits vorhandenen Mischung verändern, aber keine neue Sektorstütze erzeugen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Instrumente und die genaue Ancilla-Grenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9292,"byte_start":7096,"id":"section:276011355834b8427140","kind":"subsection","labels":["die-kleinste-zusuxe4tzliche-operation-ist-schon-algebraisch-ausreichend"],"line_end":205,"line_start":158,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/004-subsection-1-was-die-tats-chlichen-quellen.tex","status_markers_as_written":[],"summary_excerpt":"Dabei ist der zweite Bosonindex BAR(A). Es gibt dreißig solche ungeordneten Paare. Die vollständige Invarianz von η wird an allen 45+15 ursprünglichen Liegeneratoren geprüft. Die 60 verschiedenen Bosongewichte und der zusammenhängende Lie-Wirkungsgraph beweisen zusätzlich, dass diese Paarung bis auf einen Skalar eindeutig ist.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Die kleinste zusätzliche Operation ist schon algebraisch ausreichend","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":11791,"byte_start":9292,"id":"section:5f71a6a383662a3bcf5d","kind":"subsection","labels":["ein-neuer-kleiner-urspruxfcnglicher-singulettmechanismus"],"line_end":265,"line_start":206,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/004-subsection-1-was-die-tats-chlichen-quellen.tex","status_markers_as_written":[],"summary_excerpt":"Beide Zustände sind volle G-Singuletts und haben N=4. β enthält zwei Bosonen; ρ enthält einen Boson und zwei Fermionen. Ihre Orthogonalität folgt schon aus den unterschiedlichen Besetzungszahlen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Ein neuer kleiner ursprünglicher Singulettmechanismus","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13957,"byte_start":11791,"id":"section:05406e9edfc7a1b539b8","kind":"subsection","labels":["exakter-gemeinsamer-dreizustandsprozess-mit-voller-innerer-symmetrie"],"line_end":327,"line_start":266,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/004-subsection-1-was-die-tats-chlichen-quellen.tex","status_markers_as_written":[],"summary_excerpt":"Man gewähre eine Referenz R mit zwei G-trivialen Zuständen 0⟩R und 4⟩R, deren N_R-Ladungen null beziehungsweise vier sind. Setze","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. 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Sie ersetzt den dortigen Transferzeugen nicht und beweist dessen native Herkunft nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Anschluss an das nachgereichte Forschungspaper","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":2772,"byte_start":0,"id":"section:730fbc4f55abaa00acc6","kind":"subsection","labels":["ressourcenbilanz-und-der-jetzt-konkrete-nuxe4chste-nachweis"],"line_end":58,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/005-subsection-6-ressourcenbilanz-und-der-jetzt-konkrete-n-c.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333@ Ressource & Herkunft im geprüften Vertrag & Was noch zu liefern wäre \\\\ W, η, innere Darstellung, endliche Clock & Tatsächliche Quellkonstruktion und erneuter exakter Replay & Physische Identifikation des Trägers \\\\ Hnat mit Δ,g & Bestehender ausdrücklich festgelegter Modellvertrag & Physische Auswahl und Kalibrierung \\\\ Zweizustandsblock β↔ρ & Neue volls","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. 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Der Replay liest nur die eingefrorenen Eingaben und braucht weder das ursprüngliche Repository noch Netzwerkzugriff. freeze.py ist nur das Herkunftswerkzeug für die erste Archivierung und gehört nicht zum wissenschaftlichen Replay.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. 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Eine konkrete endliche Famili","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ergebnis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8007,"byte_start":5739,"id":"section:ed5c4bd1cc110dc79bd2","kind":"subsection","labels":["ein-gemeinsamer-truxe4ger-mehrere-schatten"],"line_end":176,"line_start":122,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/005-subsection-6-ressourcenbilanz-und-der-jetzt-konkrete-n-c.tex","status_markers_as_written":[],"summary_excerpt":"Mit V=W†/√8 gilt V†V=I auf C\\^60. Für eine logische Dichtematrix ρ lautet der Schatten eines Fermionoperators O","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. 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Hinzu kommt unsere kleine CAR-Auswertung, die die geladenen ersten Momente auf den richtigen größeren Ritz-Zustand hebt. Das verbessert nachprüfbar die Rechnung im bestehenden nativen Modell.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Was daran spannend ist und was als nächstes trägt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9126,"byte_start":7728,"id":"section:a1472e09f611fa71fe50","kind":"subsection","labels":["reproduktionsbelege"],"line_end":198,"line_start":171,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":["relation:08829841dfddb300450e","relation:08d83b1b992b4a887cb0","relation:270b2866046e82e8325f","relation:aad3cc477b729121216e","relation:c2244ce5a2ca78d87e1b","relation:d38dd515bb19d021a740"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/008-subsection-3-der-text-vermischt-drei-verschiedene.tex","status_markers_as_written":[],"summary_excerpt":"late_a/verify.py prüft elf eingefrorene Eingaben, führt die ν1-ν5- Spurnetzwerke frisch aus und baut beide Ritzpolynome unabhängig neu auf. Es gibt 46 eigene Prüfbedingungen: 36 exakte beziehungsweise faktische Prüfungen und 10 numerische Konsistenzprüfungen, separat dazu 1239 ausgeführte Quellguards der Normkonstruktion. Die Guardzahl zählt keine unabhängigen mathematischen Theoreme.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproduktionsbelege","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":9265,"byte_start":9126,"id":"section:7b23b85d247031c90996","kind":"section","labels":["nachtragspruxfcfung-b-feldprojektor-und-lorentz-huxe4ndigkeit"],"line_end":201,"line_start":199,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/008-subsection-3-der-text-vermischt-drei-verschiedene.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Nachtragsprüfung B: Feldprojektor und Lorentz-Händigkeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9898,"byte_start":9265,"id":"section:005317c4e11df3cb27cc","kind":"section","labels":["nachgereichter-text-b-korrekturen-und-ein-neuer-pruxfcfbarer-feldadapter"],"line_end":212,"line_start":202,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":["relation:9db69a157e794983338c"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/008-subsection-3-der-text-vermischt-drei-verschiedene.tex","status_markers_as_written":[],"summary_excerpt":"Der Text mit 45 Zeilen wurde vollständig gelesen. Seine unveränderte Kopie steht in late_sources/attachment_B.txt, SHA-256 9aaf5e18cbc6a84d610b88429872df9b69e6078365bfdc8133c8f17e2c1c3801. Die für die neue Prüfung maßgebliche field_dictionary.py ist gesondert eingefroren, SHA-256 a581bacd17c08dd9a766ae439bfe1e8e35e6d30b9509cb9d98053b897d8ecc13. Die bereits abgeschlossenen Schatten-Dateien wurden nicht verändert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nachgereichter Text B: Korrekturen und ein neuer prüfbarer Feldadapter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14292,"byte_start":9898,"id":"section:567e0df11a4f065c263b","kind":"subsection","labels":["uxfcbernahmeentscheidung"],"line_end":293,"line_start":213,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/008-subsection-3-der-text-vermischt-drei-verschiedene.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 2 ) * 0.5000 > p( - 2 ) * 0.5000@ Aussage im Text & Belastbare Fassung / konkrete Folge \\\\ 1,44 Milliarden unsichtbare Freiheiten im kleinsten nichttrivialen Sektor & 1444233216 ist die komplexe Kommutantdimension des gewährten Kontrollsatzes X,Nb im N=3-Sektor. Im N=2-Sektor lautet die entsprechende Zahl 3829536. Weder Zahl zählt direkt physische Freiheitsgrade. \\\\ Mit voller Symmetrie sieben, mit Modenzähl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Übernahmeentscheidung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15110,"byte_start":14292,"id":"section:968f8303e93d217d1597","kind":"subsection","labels":["neuer-exakter-kontrollgegenzeuge"],"line_end":310,"line_start":294,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/008-subsection-3-der-text-vermischt-drei-verschiedene.tex","status_markers_as_written":[],"summary_excerpt":"Die gewöhnlichen drei Spin-1-Matrizen J_x,J_y,J_z auf C³ erfüllen [J_x,J_y]=iJ_z und zyklisch. Bereits J_x und J_z haben ausschließlich skalare gemeinsame Kommutanten. Der dynamische Lie-Raum ist trotzdem nur su(2) mit Dimension drei, nicht su(3) mit Dimension acht. Das wird im neuen Prüfer durch exakte Ränge und alle drei Kommutatoren kontrolliert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Neuer exakter Kontrollgegenzeuge","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16734,"byte_start":15110,"id":"section:8fc3e9d40860c6413a57","kind":"subsection","labels":["was-am-spin-12-projektor-stimmt"],"line_end":357,"line_start":311,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/008-subsection-3-der-text-vermischt-drei-verschiedene.tex","status_markers_as_written":[],"summary_excerpt":"Die Feldquelle verwendet die sechs unnormierten Koordinaten","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Was am Spin-1/2-Projektor stimmt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2539,"byte_start":0,"id":"section:59531f0bd7a8c1cbd5ce","kind":"subsection","labels":["die-neue-pruxe4zise-huxe4ndigkeitsschranke"],"line_end":63,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/009-subsection-3-die-neue-pr-zise.tex","status_markers_as_written":[],"summary_excerpt":"Die eingefrorene Tabelle in field_dictionary.py, Zeile 327, bezeichnet den zweiten Faktor als f dagger (1/2,0). Dafür muss die Feldabbildung explizit festgelegt werden. Für ein tatsächliches adjungiertes linkes Weylfeld gilt dagegen ψ† in (0,1/2). Hermitesche Konjugation vertauscht diese Darstellungen; siehe https://arxiv.org/pdf/0812.1594\\#page=9Dreiner, Haber und Martin, Abschnitt 2.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Die neue präzise Händigkeitsschranke","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4194,"byte_start":2539,"id":"section:caac54d3544216cd4525","kind":"subsection","labels":["konkreter-nuxe4chster-annahmetest"],"line_end":100,"line_start":64,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/009-subsection-3-die-neue-pr-zise.tex","status_markers_as_written":[],"summary_excerpt":"Der Anschlussauftrag ist jetzt endlich und entscheidbar formuliert:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Konkreter nächster Annahmetest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5103,"byte_start":4194,"id":"section:14c7352aa21ce1d385e6","kind":"subsection","labels":["reproduktion"],"line_end":123,"line_start":101,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":["relation:98b4fb1e2cd3bf240d35","relation:be147958ec09154bb6be"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/009-subsection-3-die-neue-pr-zise.tex","status_markers_as_written":[],"summary_excerpt":"Benötigt werden nur Python und SymPy. Der separate Lauf verifiziert zwei Quellenpins sowie 36 exakte Bedingungen pro Modus, keine numerischen Bedingungen. Normaler Lauf und -OO ergeben byte-identische JSON-Ausgaben; Warnungen gelten als Fehler und alle Guards bleiben unter Optimierung aktiv. Die vollständigen Matrizen stehen in late_field.normal.json.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproduktion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":5248,"byte_start":5103,"id":"section:368d4191482bfe3c413c","kind":"section","labels":["nachtragspruxfcfung-c-fundamentale-reduktion-und-globale-quelle"],"line_end":126,"line_start":124,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/009-subsection-3-die-neue-pr-zise.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Nachtragsprüfung C: fundamentale Reduktion und globale Quelle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5401,"byte_start":5248,"id":"section:c72e6bc56a056fdf065f","kind":"section","labels":["nachtrag-c-uxfcberwiegend-bereits-abgedeckte-fundamentale-reduktion"],"line_end":129,"line_start":127,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/009-subsection-3-die-neue-pr-zise.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Nachtrag C: überwiegend bereits abgedeckte fundamentale Reduktion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6425,"byte_start":5401,"id":"section:fac3e071baead3b636c1","kind":"subsection","labels":["uxfcbernahmeurteil"],"line_end":151,"line_start":130,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":["relation:325b63b52b1e0fa76c4c","relation:f91aaf79f1f3b7e6c285"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/009-subsection-3-die-neue-pr-zise.tex","status_markers_as_written":[],"summary_excerpt":"Der neue Text ist eine ausführlichere Fassung der bereits eingefrorenen fundamentalen Reduktion, ergänzt um die weitgehend gleiche frühere Gesprächszusammenfassung. Er bringt keinen neuen H-Term, keine neue Operationsquelle und keinen neuen Transferbeweis. Seine wesentlichen mathematischen Einschränkungen sind richtig und bleiben in der gemeinsamen Darstellung erhalten. 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Gilt für die volle beschränkte Spektralfunktion, nicht nur einen dominanten Pol. 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Keine fremde Quelldatei wurde verändert. Die Herkunftsdateien gehören zu parallel fortgeschriebenen Arbeitsständen; Dateipins sind deshalb wichtiger als Versionsnamen allein.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2.1 Quellenstand und Reproduktionsgrenzen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7443,"byte_start":5224,"id":"section:508a0b2a02495fedc9e9","kind":"subsubsection","labels":["uxfcbernahmeentscheidung-1"],"line_end":156,"line_start":109,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/010-subsection-1-das-gesamtbild-grammatik-prozess-zustand.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 2 ) * 0.5000 > p( - 2 ) * 0.5000@ Aussage aus den Eingaben & Entscheidung für v1.6.7 \\\\ Korrigierter Anfangskommutant 3829536 / 1444233216 & Bestätigt; keine neue Größe gegenüber v1.6.6 \\\\ Nur SU(4) oder nur Spin(10) als zusätzliche Kontrollen & Übernommen; echte Zwischenstufen statt binärer Verfügbarkeit \\\\ Volle Gruppe plus alle Modenbesetzungen erzeugt volle Sektoralgebra & Unabhängig bestätigt, ausdrückl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2.2 Übernahmeentscheidung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7590,"byte_start":7443,"id":"section:1d612adfa548697a92fe","kind":"subsection","labels":["vollstuxe4ndig-geluxf6st-der-erste-verzweigte-singulettbereich"],"line_end":159,"line_start":157,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/010-subsection-1-das-gesamtbild-grammatik-prozess-zustand.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"3. 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Das ergibt [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.2 Nicht nur gezählt: die vier Zustände und ihre Kopplungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13299,"byte_start":12349,"id":"section:0221a8169e3904f117ae","kind":"subsubsection","labels":["der-vollstuxe4ndig-bestimmte-sechszustands-ausschnitt"],"line_end":310,"line_start":282,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/010-subsection-1-das-gesamtbild-grammatik-prozess-zustand.tex","status_markers_as_written":[],"summary_excerpt":"Die Kompression auf alle Singuletts mit k kleiner oder gleich zwei ist exakt äquivalent zu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.3 Der vollständig bestimmte Sechszustands-Ausschnitt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13418,"byte_start":13299,"id":"section:5294be5341a1a11e9e13","kind":"subsection","labels":["die-richtige-einfache-kette-wiederholung-von-h"],"line_end":313,"line_start":311,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/010-subsection-1-das-gesamtbild-grammatik-prozess-zustand.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"4. Die richtige einfache Kette: Wiederholung von H","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14460,"byte_start":13418,"id":"section:9897cdc249c3b571a0e8","kind":"subsubsection","labels":["der-fehler-war-die-gleichsetzung-zweier-verschiedener-stufen"],"line_end":337,"line_start":314,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/010-subsection-1-das-gesamtbild-grammatik-prozess-zustand.tex","status_markers_as_written":[],"summary_excerpt":"Die Vektoren [formula in source] sind nach Bosonzahl geordnet. Schon bekannt ist","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.1 Der Fehler war die Gleichsetzung zweier verschiedener Stufen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16018,"byte_start":14460,"id":"section:86296a592dc5d204bb87","kind":"subsubsection","labels":["die-ersten-fuxfcnf-glieder-sind-jetzt-exakt-bestimmt"],"line_end":386,"line_start":338,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":["relation:1fa8fcea2880fe8bacb1","relation:a79ef786f796dae3e373"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/010-subsection-1-das-gesamtbild-grammatik-prozess-zustand.tex","status_markers_as_written":[],"summary_excerpt":"Für die normierte Lanczos-Basis [formula in source] schreiben wir","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.2 Die ersten fünf Glieder sind jetzt exakt bestimmt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1607,"byte_start":0,"id":"section:2446e42b1616f184fb5c","kind":"subsubsection","labels":["zehn-vollstuxe4ndige-energiemomente-der-gefuxfcllten-referenz"],"line_end":46,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/011-subsubsection-4-3-zehn-vollst-ndige-energiemomente-der-g.tex","status_markers_as_written":[],"summary_excerpt":"Die Fünfer-Kompression bestimmt [formula in source] für n von 0 bis 9 exakt. Ein Weg, der den nächsten nicht enthaltenen Lanczos-Vektor erreicht und nach F zurückkehrt, benötigt mindestens zehn Schritte. Aus der Tridiagonalität folgt deshalb die angegebene Momentengenauigkeit, ohne die übrige Kette zu erfinden.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.3 Zehn vollständige Energiemomente der gefüllten Referenz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2622,"byte_start":1607,"id":"section:af78984579a78a083df4","kind":"subsubsection","labels":["kleine-rigorose-verschuxe4rfung-der-energiegrenze"],"line_end":75,"line_start":47,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/011-subsubsection-4-3-zehn-vollst-ndige-energiemomente-der-g.tex","status_markers_as_written":[],"summary_excerpt":"Am Prüfpunkt g geteilt durch Delta gleich 1/20 hat die niedrigste Eigenenergie der Fünfer-Kompression die durch rationale Sturm-Zählung zertifizierte Lage","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.4 Kleine, rigorose Verschärfung der Energiegrenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4283,"byte_start":2622,"id":"section:4d6a7360e14985993664","kind":"subsection","labels":["vollstuxe4ndig-geluxf6st-die-innere-bilineare-zerlegung"],"line_end":114,"line_start":76,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/011-subsubsection-4-3-zehn-vollst-ndige-energiemomente-der-g.tex","status_markers_as_written":[],"summary_excerpt":"Die sechs Dimensionen sind 1, 45, 210, 15, 675 und 3150. Der offene Rest ist also nicht mehr unbestimmt:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Vollständig gelöst: die innere bilineare Zerlegung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4417,"byte_start":4283,"id":"section:be28fc631b0f53b48a8c","kind":"subsection","labels":["welche-operationen-wirklich-verfuxfcgbar-sein-muxfcssten"],"line_end":117,"line_start":115,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/011-subsubsection-4-3-zehn-vollst-ndige-energiemomente-der-g.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"6. Welche Operationen wirklich verfügbar sein müssten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6255,"byte_start":4417,"id":"section:c89679d2ebae680064e7","kind":"subsubsection","labels":["die-algebraische-frage-ist-pruxe4ziser-beantwortet"],"line_end":160,"line_start":118,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/011-subsubsection-4-3-zehn-vollst-ndige-energiemomente-der-g.tex","status_markers_as_written":[],"summary_excerpt":"Im N=3-Sektor bleiben für verschiedene angenommene Operationsalphabete folgende komplexe Kommutantdimensionen:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6.1 Die algebraische Frage ist präziser beantwortet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7206,"byte_start":6255,"id":"section:30bda1816c3dc0b64295","kind":"subsubsection","labels":["warum-blouxdfes-lesen-noch-keine-fehlende-bewegung-erzeugt"],"line_end":178,"line_start":161,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/011-subsubsection-4-3-zehn-vollst-ndige-energiemomente-der-g.tex","status_markers_as_written":[],"summary_excerpt":"Ohne die zusätzlich gewährten Gruppenkontrollen erhalten X, Nb, der Clock und alle Modenbesetzungen weiterhin mindestens eine nichtskalare Farb-Cartanladung. Jede Komposition dieser Operatoren behält diese Erhaltung. Die alleinige Erlaubnis, mehr Moden zu unterscheiden, hebt das Hindernis also nicht auf.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6.2 Warum bloßes Lesen noch keine fehlende Bewegung erzeugt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8845,"byte_start":7206,"id":"section:1aa30160a731766248cf","kind":"subsection","labels":["feldwuxf6rterbuch-gesicherte-teile-und-korrigierte-reichweite"],"line_end":209,"line_start":179,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/011-subsubsection-4-3-zehn-vollst-ndige-energiemomente-der-g.tex","status_markers_as_written":[],"summary_excerpt":"Für die unveränderte antisymmetrische Paarmatrix und gleichhändige Weylfelder verschwindet die ableitungsfreie skalare Kontraktion. Die drei symmetrischen Spinortensoren tragen einen nichtverschwindenden Kanal des Typs (1,0), mit konjugiertem Typ (0,1). Das ist am gesamten ursprünglichen Tensor neu geprüft.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. Feldwörterbuch: gesicherte Teile und korrigierte Reichweite","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8955,"byte_start":8845,"id":"section:4b99482911cacb29642d","kind":"subsection","labels":["die-fundamentale-frage-was-fehlt-wirklich"],"line_end":212,"line_start":210,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/011-subsubsection-4-3-zehn-vollst-ndige-energiemomente-der-g.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"8. Die fundamentale Frage: was fehlt wirklich?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10348,"byte_start":8955,"id":"section:b791ebe659805af6a046","kind":"subsubsection","labels":["ein-uxfcberpruxfcfbarer-unterbestimmtheitssatz"],"line_end":241,"line_start":213,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/011-subsubsection-4-3-zehn-vollst-ndige-energiemomente-der-g.tex","status_markers_as_written":[],"summary_excerpt":"Betrachte bei festem W dieselbe Familie [formula in source] . Alle diese Hamiltonoperatoren besitzen die gleiche innere Quellsymmetrie, dieselbe Ladungserhaltung und denselben kommutierenden endlichen Clock. Dennoch unterscheiden sie sich dynamisch. Schon für dieselbe gefüllte Referenz F ist die dimensionslose Momentenkombination","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.1 Ein überprüfbarer Unterbestimmtheitssatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11685,"byte_start":10348,"id":"section:b476aa871cb782c70e7e","kind":"subsubsection","labels":["der-kleinste-tragfuxe4hige-forschungsansatz"],"line_end":264,"line_start":242,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/011-subsubsection-4-3-zehn-vollst-ndige-energiemomente-der-g.tex","status_markers_as_written":[],"summary_excerpt":"Für eine einzelne Antwortrechnung sollte der relevante Raum nicht von vornherein der gesamte Fockraum sein. Der zyklische Raum der tatsächlichen Operationen auf dem angegebenen Startzustand ist der kleinere Arbeitsraum. Die H-Lanczos-Kette ist eine exakte Darstellung eines solchen Raums. Mehrere Präparationen, Messungen oder Compileroperationen können jedoch einen größeren gemeinsamen Prozessraum verlangen. Ihre Komp","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.2 Der kleinste tragfähige Forschungsansatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14136,"byte_start":11685,"id":"section:40ba66d2b86d563aefe3","kind":"subsection","labels":["aktueller-stand-t1-bis-t8"],"line_end":319,"line_start":265,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/011-subsubsection-4-3-zehn-vollst-ndige-energiemomente-der-g.tex","status_markers_as_written":[],"summary_excerpt":"Die folgende Tabelle ordnet die Beiträge dieser Runde den bisherigen offenen Beweispflichten zu; sie benennt keine neue Definition der ursprünglichen Tore.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. Aktueller Stand T1 bis T8","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":15667,"byte_start":14136,"id":"section:a20ed184808f1db88d53","kind":"subsection","labels":["die-drei-nuxe4chsten-entscheidenden-untersuchungen"],"line_end":352,"line_start":320,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/011-subsubsection-4-3-zehn-vollst-ndige-energiemomente-der-g.tex","status_markers_as_written":[],"summary_excerpt":"Den minimalen Ursprungsvertrag auswählen. Teil B klassifiziert die kleinen symmetrieverträglichen Terme und trennt echte Erweiterungen von einem bloßen Wechsel der Bosonvariablen. Der Compiler muss diese Auswahl und die relativen Parameter begründen. Symmetrie allein tut das noch nicht. Die gemeinsame Schattenkarte am vorhandenen Tensor prüfen. Derselbe Zustand und dieselben Operationen müssen die verschiedenen Ausle","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10. 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Die ausgelieferte ZIP wird nach dem Entpacken erneut geprüft.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"11. Reproduktion und Veröffentlichung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":394,"byte_start":0,"id":"section:b287aa485f0679779f86","kind":"subsubsection","labels":["schluss-in-einem-satz"],"line_end":9,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/012-subsubsection-schluss-in-einem-satz-label-schluss-in-ein.tex","status_markers_as_written":[],"summary_excerpt":"Die einfache Regel ist vorhanden; ihr erster verzweigter Zustandsbereich und die richtige kleine Rechenkette sind jetzt genauer gelöst. Was noch fehlt, ist die aus dem Ursprung folgende Auswahl und Ausführung dieses Prozesses als dieselbe physikalische Welt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Schluss in einem Satz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":545,"byte_start":394,"id":"section:a7476b13be7db9e3191d","kind":"section","labels":["neue-vogelperspektive-derselbe-prozess-in-verschiedenen-ansichten"],"line_end":12,"line_start":10,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/012-subsubsection-schluss-in-einem-satz-label-schluss-in-ein.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Neue Vogelperspektive: derselbe Prozess in verschiedenen Ansichten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3147,"byte_start":545,"id":"section:2af0eb79a1478169bd48","kind":"subsection","labels":["b1.-was-sich-durch-die-drei-weiteren-texte-uxe4ndert"],"line_end":67,"line_start":13,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":["relation:204c609f6c1243f37866","relation:5a118edf33baf0281a52","relation:e98fd27bb8f4723e12c6"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/012-subsubsection-schluss-in-einem-satz-label-schluss-in-ein.tex","status_markers_as_written":[],"summary_excerpt":"Die nachgereichten Texte werden als Vorschläge geprüft, nicht als bewiesene Ergebnisse oder neue Arbeitsanweisungen übernommen. Die stärkste gemeinsame Idee trägt: Innere Identität, Zusammensetzung, Ort, Zeit und Auslese dürfen nicht stillschweigend dasselbe Label erhalten. Eine immer genauere Rechnung innerhalb einer Bank ersetzt diese Verbindungen nicht. Die voranstehenden lokalen Ergebnisse bleiben gültig; die fun","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B1. Was sich durch die drei weiteren Texte ändert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5543,"byte_start":3147,"id":"section:241cc65d5f3d1f2d1c6c","kind":"subsection","labels":["b2.-noethers-frage-welche-unterschiede-kann-die-dynamik-uxfcberhaupt-veruxe4ndern"],"line_end":120,"line_start":68,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/012-subsubsection-schluss-in-einem-satz-label-schluss-in-ein.tex","status_markers_as_written":[],"summary_excerpt":"Bei ungebrochener innerer Gruppe G zerfällt ein Zustandsraum als","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B2. Noethers Frage: Welche Unterschiede kann die Dynamik überhaupt verändern?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7935,"byte_start":5543,"id":"section:cac38694d999ad339b62","kind":"subsection","labels":["b3.-korrelation-ist-noch-kein-eingriff-ein-exakt-geluxf6stes-gegenbeispiel"],"line_end":173,"line_start":121,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/012-subsubsection-schluss-in-einem-satz-label-schluss-in-ein.tex","status_markers_as_written":[],"summary_excerpt":"Die Kreuzkorrelation startet bei null und verändert sich mit der Zeit. Es gibt dennoch keinerlei Signal von A nach B: Alle A-lokalen Operationen kommutieren mit jedem zeitentwickelten B-lokalen Observablen. Für jedes spurtreue lokale Quanteninstrument bleibt daher die unbedingte B-Statistik unverändert. Eine Konditionierung auf ein Messergebnis in A wäre etwas anderes.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B3. Korrelation ist noch kein Eingriff: ein exakt gelöstes Gegenbeispiel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9112,"byte_start":7935,"id":"section:04131e3b1b1d3f4ea86f","kind":"subsection","labels":["b4.-die-einfachste-fehlende-auswahl-warum-genau-dieser-hamiltonoperator"],"line_end":197,"line_start":174,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/012-subsubsection-schluss-in-einem-satz-label-schluss-in-ein.tex","status_markers_as_written":[],"summary_excerpt":"Die Z4-Idee besitzt einen präzisen Kern. Ein ganzzahliger, auf jedem Grad konstanter Ladungslift mit neutralem Grad null müsste bei den entsprechenden nichtverschwindenden Klammern erfüllen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B4. Die einfachste fehlende Auswahl: Warum genau dieser Hamiltonoperator?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12953,"byte_start":9112,"id":"section:6307984fc61752991128","kind":"subsubsection","labels":["b4.1-zwei-zusuxe4tzliche-terme-am-unveruxe4nderten-tensor"],"line_end":281,"line_start":198,"numbered_or_version_tokens_as_written":["B4.1"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/012-subsubsection-schluss-in-einem-satz-label-schluss-in-ein.tex","status_markers_as_written":[],"summary_excerpt":"Der Bosonträger (10,6) besitzt eine symmetrische reelle invariante Paarung eta. In der nativen Gewichtsbasis koppelt sie entgegengesetzte Spin- Vektorgewichte und komplementäre Farbpaare. Es gilt eta Quadrat gleich eins. Damit sind bereits","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B4.1 Zwei zusätzliche Terme am unveränderten Tensor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15144,"byte_start":12953,"id":"section:b8942f44eecb86a5a53f","kind":"subsubsection","labels":["b4.2-eine-weitere-vereinfachung-neue-dynamik-oder-andere-teilchenvariablen"],"line_end":330,"line_start":282,"numbered_or_version_tokens_as_written":["B4.2"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/012-subsubsection-schluss-in-einem-satz-label-schluss-in-ein.tex","status_markers_as_written":[],"summary_excerpt":"Manche scheinbaren Erweiterungen beschreiben nur andere Bosonvariablen. Auf der reellen, phasengleichen Teilfamilie setze man","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B4.2 Eine weitere Vereinfachung: neue Dynamik oder andere Teilchenvariablen?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15284,"byte_start":15144,"id":"section:321b71c361d29872c383","kind":"subsection","labels":["b5.-holografie-und-schatten-die-konkrete-native-verbindung"],"line_end":333,"line_start":331,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/012-subsubsection-schluss-in-einem-satz-label-schluss-in-ein.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"B5. Holografie und Schatten: die konkrete native Verbindung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16790,"byte_start":15284,"id":"section:f4ca3aa11a1cdc782ec3","kind":"subsubsection","labels":["b5.1-ein-kodierer-ist-bereits-vorhanden"],"line_end":368,"line_start":334,"numbered_or_version_tokens_as_written":["B5.1"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/012-subsubsection-schluss-in-einem-satz-label-schluss-in-ein.tex","status_markers_as_written":[],"summary_excerpt":"Der vorhandene, frisch geprüfte Tensor erfüllt WW dagger gleich 8 I60. Daher ist","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B5.1 Ein Kodierer ist bereits vorhanden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1657,"byte_start":0,"id":"section:fe80f1737b1c51a7e02c","kind":"subsubsection","labels":["b5.2-warum-das-noch-kein-holografischer-fehlerkorrekturcode-ist"],"line_end":34,"line_start":1,"numbered_or_version_tokens_as_written":["B5.2"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/013-subsubsection-b5-2-warum-das-noch-kein-holografischer.tex","status_markers_as_written":[],"summary_excerpt":"Für jeden der 64 Fermionmoden wurde die logische Kompression seiner Besetzungsmessung berechnet:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B5.2 Warum das noch kein holografischer Fehlerkorrekturcode ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4279,"byte_start":1657,"id":"section:b51d4041807ceaecc1fc","kind":"subsubsection","labels":["b5.3-was-mehrere-schatten-gemeinsam-eindeutig-machen-kuxf6nnen"],"line_end":89,"line_start":35,"numbered_or_version_tokens_as_written":["B5.3"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/013-subsubsection-b5-2-warum-das-noch-kein-holografischer.tex","status_markers_as_written":[],"summary_excerpt":"Seien Ri festgelegte Mess- oder Reduktionsabbildungen eines gemeinsamen Zustands rho. Für eine endliche, nicht eingeschränkte Zustandsklasse sind alle Zustände aus den Schatten Ri(rho) genau dann unterscheidbar, wenn auf den hermiteschen spurlosen Differenzen gilt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B5.3 Was mehrere Schatten gemeinsam eindeutig machen können","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6470,"byte_start":4279,"id":"section:b8b6bd3008572063dd46","kind":"subsubsection","labels":["b5.4-die-drei-wuxe4nde-muxfcssen-unterschiedlich-gepruxfcft-werden"],"line_end":136,"line_start":90,"numbered_or_version_tokens_as_written":["B5.4"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/013-subsubsection-b5-2-warum-das-noch-kein-holografischer.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333@ Gemeinte Wand & Was sie gegenwärtig bedeutet & Welcher Anschluss fehlt \\\\ Universalraum & Grenze zwischen gemeinsamem Operatorobjekt und seinen reduzierten Ansichten & Ein gemeinsamer verfügbarer Operationssatz, Zustand und Rekonstruktionsvertrag \\\\ TFPT & Grenze zwischen interner Compilerstruktur und physikalischer Realisierung & Herleitung der Ausführun","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B5.4 Die drei Wände müssen unterschiedlich geprüft werden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9798,"byte_start":6470,"id":"section:2ca1ddb995d492e4a46c","kind":"subsection","labels":["b6.-die-einfachste-neue-arbeitsrichtung-und-ihre-abnahmekriterien"],"line_end":198,"line_start":137,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/013-subsubsection-b5-2-warum-das-noch-kein-holografischer.tex","status_markers_as_written":[],"summary_excerpt":"Der plausible übersehene Punkt ist kein weiterer großer Tensor: Wir brauchen die gemeinsame Regel, die festlegt, welche Operationen, Teilchenvariablen und Ansichten tatsächlich dieselbe Ausführung beschreiben. Noethers Symmetrieprüfung sagt, was erhalten bleibt. Die Schattenprüfung sagt, was überhaupt unterscheidbar ist. Der Eingriffstest sagt, was etwas anderes beeinflussen kann. Zusammen sind diese drei kleinen Fra","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B6. Die einfachste neue Arbeitsrichtung und ihre Abnahmekriterien","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14322,"byte_start":9798,"id":"section:6dabfc25b4f8a3240215","kind":"subsection","labels":["b7.-abgleich-des-zuletzt-eingesandten-berichts-v1.6.3"],"line_end":283,"line_start":199,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/013-subsubsection-b5-2-warum-das-noch-kein-holografischer.tex","status_markers_as_written":[],"summary_excerpt":"Der sechste Text dieser Runde, „Operationssatz, nativer Grundzustand und Feldwörterbuch``, enthält überwiegend bereits berücksichtigte Befunde: die Kommutantenleiter, das Lochbild, die Normen der ersten Stufen, den nichtverschwindenden Seitenzweig und den verschwindenden Weyl-Skalarkanal. Seine zweite vorgeschlagene Folgeaufgabe wurde inzwischen wesentlich weitergeführt: Alle vier Zwei-Boson-Singuletts sind konstruie","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B7. Abgleich des zuletzt eingesandten Berichts v1.6.3","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14767,"byte_start":14322,"id":"section:ec9e31bbdf525854ea3d","kind":"section","labels":["historischer-anhang-vollstuxe4ndige-fassung-v1.6.6"],"line_end":292,"line_start":284,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/013-subsubsection-b5-2-warum-das-noch-kein-holografischer.tex","status_markers_as_written":[],"summary_excerpt":"Die folgende vollständige Fassung wird unverändert bewahrt. Maßgeblich für den aktuellen Status sind die vorangestellten Kapitel v1.6.7. 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Die Frage aus dem neuen Text ist damit auf algebraischer Ebene beantwortet.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. 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Das ist ein Forschungsauftrag, kein Widerspruch zur bisherigen Schranke.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7.1 Eine sinnvolle Hypothese, kein bereits identifiziertes universelles Objekt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4487,"byte_start":3835,"id":"section:db68bc621808c9892222","kind":"subsubsection","labels":["der-vorgeschlagene-kill-test-muss-korrigiert-werden"],"line_end":96,"line_start":85,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/015-subsection-6-das-feldw-rterbuch-eine-basis-nderung-allei.tex","status_markers_as_written":[],"summary_excerpt":"Für unabhängige orthogonale Banken kann Π_AΠ_B deren gemeinsame Parität sein. 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Ein nichtverschwindender Kommutator mit einer lok","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7.2 Der vorgeschlagene Kill-Test muss korrigiert werden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6493,"byte_start":4487,"id":"section:d542d8812cc4a7cf74ac","kind":"subsubsection","labels":["der-einfachste-false-positive-ein-signal-ohne-bewegung"],"line_end":142,"line_start":97,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/015-subsection-6-das-feldw-rterbuch-eine-basis-nderung-allei.tex","status_markers_as_written":[],"summary_excerpt":"Seien a=c1, b=(c1+c2)/√2 auf zwei globalen CAR-Moden und H=ωN. Dann haben die beiden Einteilchen-Chartzustände bereits Überlappung 1/√2. In ihrer nichtorthogonalen Basis ist K=ωS mit einem nichtverschwindenden Offdiagonalelement. Trotzdem bleibt die betreffende Wahrscheinlichkeit zu jeder Zeit genau 1/2. Es wurde nichts transportiert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7.3 Der einfachste False-Positive: Ein Signal ohne Bewegung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8388,"byte_start":6493,"id":"section:b8b779ad01af6e46aaa6","kind":"subsubsection","labels":["was-nicht-automatisch-folgt"],"line_end":186,"line_start":143,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/015-subsection-6-das-feldw-rterbuch-eine-basis-nderung-allei.tex","status_markers_as_written":[],"summary_excerpt":"Zeit: Für einen Grundzustand ist e \\-itH\\Ω=e \\-itE0\\Ω; sein physischer Zustand bleibt gleich. Das ist kein eigener Zeitpfeil. Nichtstationäre Präparation, Korrelationen und Records müssen ausgewiesen werden. Eichfeld: Für bloße Basiswechsel Uxy=Vx†Vy teleskopiert jede geschlossene Holonomie zu I. Echte Krümmung braucht zusätzliche Verbindungs-/Transportdaten oder einen nachgewiesenen Mechanismus. Spin: Zwei Orientier","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7.4 Was nicht automatisch folgt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10880,"byte_start":8388,"id":"section:ea0714b4c66468db184f","kind":"subsection","labels":["t1-t8-gemeinsamer-fortschritt-ohne-statusinflation"],"line_end":237,"line_start":187,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/015-subsection-6-das-feldw-rterbuch-eine-basis-nderung-allei.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333@ Front & In dieser Revision weitergekommen & Noch erforderlicher Nachweis \\\\ T1 - Ursprung und Auswahl & Explizite Identität zwischen Quell-Clock und innerer Spinwirkung; Operationsverträge genauer & Primitive Auswahl von P1/P2, Träger, erlaubten Instrumenten und Zustand \\\\ T2 - Half-Charge/E8-Feld & Bestehender geladener Pol bleibt abgesichert, innere Dar","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8. T1-T8: gemeinsamer Fortschritt ohne Statusinflation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":12757,"byte_start":10880,"id":"section:ac91837a081a9cfa5c7c","kind":"subsection","labels":["die-nuxe4chsten-drei-arbeiten---klein-gemeinsam-und-entscheidbar"],"line_end":271,"line_start":238,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/015-subsection-6-das-feldw-rterbuch-eine-basis-nderung-allei.tex","status_markers_as_written":[],"summary_excerpt":"A. Den gemeinsamen Quellenvertrag wirklich hinschreiben. Zwei lokale Einbettungen, ihr CAR-Gram, globale Parität und Ladung, ursprüngliche Operationen und ein einziges H angeben. Abbruch für eine Kandidatenfassung, wenn sie nur zwei Koordinatenansichten desselben unveränderten Signals umbenennt. Die gemeinsamen Generatoren müssen einen nachweislich neuen Antwortprozess ermöglichen, nicht nur eine andere Beschriftung.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. Die nächsten drei Arbeiten - klein, gemeinsam und entscheidbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13858,"byte_start":12757,"id":"section:6a66c45dec9591f482eb","kind":"subsection","labels":["belege-und-reproduzierbarkeit"],"line_end":293,"line_start":272,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/015-subsection-6-das-feldw-rterbuch-eine-basis-nderung-allei.tex","status_markers_as_written":[],"summary_excerpt":"Die drei Eingangstexte bleiben unverändert im Prüfpaket. Ein Teil-Audit reproduziert die 1127 gelieferten Guards; eigene Programme behandeln Clock/Casimir, Quellenreichweite, direkte Krylov-Kontraktion, basisunabhängige Feldbedingungen, den tatsächlichen Vierzustandskanal und die Überlappungsgegenkontrollen. Exakte und numerische Teile sind in den jeweiligen Ergebnisdateien getrennt markiert. Die abschließenden Zählu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10. Belege und Reproduzierbarkeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":13989,"byte_start":13858,"id":"section:a5f6c8cf65a5bdc858ef","kind":"section","labels":["anhang-a-quellenpruxfcfung-symmetrie-und-verfuxfcgbarkeit"],"line_end":296,"line_start":294,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/015-subsection-6-das-feldw-rterbuch-eine-basis-nderung-allei.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Anhang A: Quellenprüfung Symmetrie und Verfügbarkeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14360,"byte_start":13989,"id":"section:ed249ca472af3c4b9ed2","kind":"section","labels":["quellenpruxfcfung-quellsymmetrie-verfuxfcgbarkeit-und-lorentztypen"],"line_end":304,"line_start":297,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/015-subsection-6-das-feldw-rterbuch-eine-basis-nderung-allei.tex","status_markers_as_written":[],"summary_excerpt":"Stand: 15. September 2026. Eigenständiger Teil-Audit der ersten neuen Anlage und dreier Programme. Keine Änderung der gelieferten Programme, Ergebnisdateien oder Dokumente. Keine Aussage, dass T1-T8 geschlossen seien.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Quellenprüfung: Quellsymmetrie, Verfügbarkeit und Lorentztypen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":16735,"byte_start":14360,"id":"section:0cdc64dd074df2c50572","kind":"subsection","labels":["reproduktion-1"],"line_end":366,"line_start":305,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":["relation:df9cb3be7e703be7cca7"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/015-subsection-6-das-feldw-rterbuch-eine-basis-nderung-allei.tex","status_markers_as_written":[],"summary_excerpt":"Alle drei Programme wurden vollständig gelesen und anschließend in isolierten Kopien ausgeführt. Die relevanten Tensoren wurden an ihre von den unveränderten Programmen erwarteten relativen Orte kopiert. Normaler und optimierter Lauf reproduzieren jeweils die gelieferten Ergebnisdateien byteidentisch, ohne Standardfehlerausgabe:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Reproduktion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":1972,"byte_start":0,"id":"section:4057c857762bd578f50a","kind":"subsection","labels":["bestuxe4tigte-mathematik"],"line_end":51,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/016-subsection-2-best-tigte-mathematik-label-bestuxe4tigte-m.tex","status_markers_as_written":[],"summary_excerpt":"Der N=3-Raum zerfällt als Darstellung von Spin(10) × SU(4) in sieben Isotypien. Drei haben Multiplizität zwei, die anderen vier Multiplizität eins. Die zwei Fockteile Λ³(C⁶⁴) und C⁶⁰⊗C⁶⁴ sind jeweils multiplizitätsfrei; der gesamte N=3-Raum ist es ausdrücklich nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Bestätigte Mathematik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":3838,"byte_start":1972,"id":"section:351dd34005cc76b6fa0a","kind":"subsection","labels":["invarianz-und-kovarianz-auseinanderhalten"],"line_end":88,"line_start":52,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/016-subsection-2-best-tigte-mathematik-label-bestuxe4tigte-m.tex","status_markers_as_written":[],"summary_excerpt":"Dann gilt A0 ⊂ C, dim A0=14 und dim C=Σ m_i²=16. Jedes Wort aus X und Nb kommutiert mit ρ(G). Nichtzentrale Lie-Erzeuger können deshalb aus diesem Alphabet nicht entstehen. Dieser Ausschluss ist korrekt und bleibt richtig, wenn nur ein fixes H statt zweier unabhängiger Kontrollen gewährt ist.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Invarianz und Kovarianz auseinanderhalten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5424,"byte_start":3838,"id":"section:f50690c3a37cb97a41a0","kind":"subsection","labels":["verfuxfcgbarkeit-ist-keine-universelle-janein-frage"],"line_end":129,"line_start":89,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/016-subsection-2-best-tigte-mathematik-label-bestuxe4tigte-m.tex","status_markers_as_written":[],"summary_excerpt":"Ein vorgegebener Hamiltonoperator allein gewährt nicht bereits das unabhängige Schalten von X und Nb. Am erklärten Punkt g/Δ=1/20 besitzt ein fixes H im N=3-Raum acht verschiedene Energien, also nur eine acht-dimensionale kommutative Spektralalgebra. Die großzügigere Annahme unabhängiger Kontrollen X,Nb ergibt 14.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Verfügbarkeit ist keine universelle Ja/Nein-Frage","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6422,"byte_start":5424,"id":"section:d4a842653c33d0323e73","kind":"subsection","labels":["der-clock-satz-ist-im-gelieferten-checker-nicht-gepruxfcft"],"line_end":148,"line_start":130,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/016-subsection-2-best-tigte-mathematik-label-bestuxe4tigte-m.tex","status_markers_as_written":[],"summary_excerpt":"operation_symmetry.py:478 schreibt den Normalisator- und Nichts-hinzufügen-Satz als need(True, ...). Insgesamt enthält diese Datei neun solche als Prüfbedingungen gezählten theoretischen Folgerungen. Einige sind durch die vorausgehende Mathematik gut begründet; der bloße grüne Guard zertifiziert sie jedoch nicht unabhängig.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Der Clock-Satz ist im gelieferten Checker nicht geprüft","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":8101,"byte_start":6422,"id":"section:29368439a9f5743a201c","kind":"subsection","labels":["feldtyp-was-tatsuxe4chlich-erzwungen-ist"],"line_end":180,"line_start":149,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/016-subsection-2-best-tigte-mathematik-label-bestuxe4tigte-m.tex","status_markers_as_written":[],"summary_excerpt":"Für ein lokales, ableitungsfreies Bilinear zweier gleichhändiger Weylfelder, das alle 64 inneren Quellenmarken unverändert als unabhängige innere Komponenten und genau den gegebenen antisymmetrischen Tensor W verwendet, gilt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Feldtyp: was tatsächlich erzwungen ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9235,"byte_start":8101,"id":"section:142eff8b54f11afb64e1","kind":"subsubsection","labels":["konkreter-gegencheck-jenseits-der-ableitungsfreien-klasse"],"line_end":203,"line_start":181,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/016-subsection-2-best-tigte-mathematik-label-bestuxe4tigte-m.tex","status_markers_as_written":[],"summary_excerpt":"Der allgemeine Satz »ein Vektor verlangt ψ†ψ und scheitert deshalb an der Ladung« ist falsch, sobald Ableitungen zugelassen werden. Beispielsweise ist","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Konkreter Gegencheck jenseits der ableitungsfreien Klasse","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9765,"byte_start":9235,"id":"section:a92a6a8e3381896c7398","kind":"subsection","labels":["konsequenz"],"line_end":215,"line_start":204,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/016-subsection-2-best-tigte-mathematik-label-bestuxe4tigte-m.tex","status_markers_as_written":[],"summary_excerpt":"Die neuen Quellen verkleinern und präzisieren den endlichen N=3-Operationsraum. 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Geprüft wird die Anlage 7380c383-f364-4ef8-8066-24aa4d180d85 gegen den Vertrag universalraum-native-operations-ground-response-20260915. Fremde Quellen und Ausgaben wurden nicht verändert. Die hier angegebenen Matrix- und Graphbefunde beziehen sich auf denselben gepinnten Tensor W mit SHA-256 3f00a0892157a691e4ef26920c3702772c7bf76a250fad98ff04a079bb64b763.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Unabhängige Prüfung: Krylov-Verzweigung und Feldwörterbuch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11822,"byte_start":10450,"id":"section:89cbd2da26194873790e","kind":"subsection","labels":["der-neue-nichtschluss-ist-exakt-bestuxe4tigt"],"line_end":269,"line_start":230,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/016-subsection-2-best-tigte-mathematik-label-bestuxe4tigte-m.tex","status_markers_as_written":[],"summary_excerpt":"Für v_n=(T†) n F habe ich u=T T† v_2=T v_3 unmittelbar aus den 480 nativen Paaren neu kontrahiert. Das materialisiert nicht die 15.252.960 Komponenten von v₃. Es arbeitet mit 108.240 Komponenten von v₂ und 293.280 nichtverschwindenden Komponenten des Ergebnisses u. Es wurden 45.771.360 zulässige Erzeugungsübergänge und 139.289.760 anschließende Entnahmebeiträge exakt mit ganzzahliger Fermion-Parität und Boson-Multipl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Der neue Nichtschluss ist exakt bestätigt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12956,"byte_start":11822,"id":"section:3d715ba92c3ce45637dc","kind":"subsection","labels":["das-mitgelieferte-ground-json-ist-veraltet-und-teilweise-falsch"],"line_end":295,"line_start":270,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/016-subsection-2-best-tigte-mathematik-label-bestuxe4tigte-m.tex","status_markers_as_written":[],"summary_excerpt":"Die aktuelle Pythonquelle hat SHA-256 8ae0f2f103ba0cb0a5cb832681a33130b6756fe627395368b6be635587a2eb02. 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Durch Eliminieren der einzigen neuen w₂-Koordinate bekommt die v₃-Diagonale die exakt bestimmte energieabhängige Korrektur","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Die sechste Dezimalstelle ist richtig - aber nur für die eine zusätzliche Richtung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15973,"byte_start":14707,"id":"section:4ec48b926851b247cda7","kind":"subsubsection","labels":["eigene-einfache-folgeherleitung-das-vollstuxe4ndige-ritz-residuum"],"line_end":368,"line_start":341,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/016-subsection-2-best-tigte-mathematik-label-bestuxe4tigte-m.tex","status_markers_as_written":[],"summary_excerpt":"Sei ψ₃ der normierte Ritz-Eigenvektor in span(v₀,…,v₃), und c₃ seine Komponente entlang v₃/√ν₃. Außerhalb dieses Raums führt Hψ₃ genau in zwei orthogonale Richtungen: v₄ und w₂. Deshalb gilt exakt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eigene einfache Folgeherleitung: Das vollständige Ritz-Residuum","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1536,"byte_start":0,"id":"section:87916f5e0b331e568bc5","kind":"subsection","labels":["der-bereits-bewiesene-native-grundsatz-bleibt-guxfcltig"],"line_end":27,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/017-subsection-4-der-bereits-bewiesene-native-grundsatz-blei.tex","status_markers_as_written":[],"summary_excerpt":"Der ältere, gepinnte Beweis lautet: Für Δ 0 und 0 g /Δ≤1/20 besitzt der unveränderte μ=0-Hamiltonoperator einen eindeutigen globalen Grundzustand in N=64; er ist ein Spin(10)×SU(4)-Singulett. Bei 1/20 bestehen außerdem positive Lücke und die bekannten Energie-, Besetzungs- und Polschranken.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. 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Die Matrix der Hamilton-Matrixelemente in diesen beiden Chartvektoren ist","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Noch wichtiger: Ein Überlappungsmatrixelement ist kein Transport","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10667,"byte_start":8974,"id":"section:e610b93b798c9c3b9ae2","kind":"subsection","labels":["chartwechsel-verbindungen-und-kruxfcmmung-sind-verschiedene-daten"],"line_end":248,"line_start":214,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/019-subsubsection-6-4-kleinste-noch-zu-suchende.tex","status_markers_as_written":[],"summary_excerpt":"Wenn mehrere Charts lediglich vollständige orthonormale Rahmen R_x desselben festen Vektorraums sind, lauten die Basiswechsel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Chartwechsel, Verbindungen und Krümmung sind verschiedene Daten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11811,"byte_start":10667,"id":"section:abd6c216a0d1e705d69e","kind":"subsection","labels":["zeit-ein-grundzustand-bewegt-sich-unter-seinem-h-nicht-beobachtbar"],"line_end":270,"line_start":249,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/019-subsubsection-6-4-kleinste-noch-zu-suchende.tex","status_markers_as_written":[],"summary_excerpt":"Die im Anhang skizzierte Entwicklung Ω -> exp(−itH)Ω erzeugt bei einem Energieeigenzustand lediglich exp(−itE₀)Ω. Der Dichteoperator bleibt exakt gleich. Der Checker bestätigt das an einem kleinen Fockzustand.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Zeit: Ein Grundzustand bewegt sich unter seinem H nicht beobachtbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":13364,"byte_start":11811,"id":"section:a6645ebe076862c5a20c","kind":"subsection","labels":["der-binuxe4re-index-muss-als-freiheitsgrad-bewiesen-werden"],"line_end":305,"line_start":271,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/019-subsubsection-6-4-kleinste-noch-zu-suchende.tex","status_markers_as_written":[],"summary_excerpt":"Die skalare Hilfsdublett-Reparatur braucht zwei unabhängige, gleichgeladene Komponenten, auf denen eine nichtentartete antisymmetrische Form wirkt. Eine Orientierung der Überlappungsgeometrie könnte so etwas liefern, tut es aber nicht allein durch das Vorhandensein zweier Bezeichnungen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Der binäre Index muss als Freiheitsgrad bewiesen werden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14968,"byte_start":13364,"id":"section:c3674be65ff2990fd8fc","kind":"subsection","labels":["operationsgeometrie-benuxf6tigt-mehr-als-erreichbarkeit"],"line_end":337,"line_start":306,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/019-subsubsection-6-4-kleinste-noch-zu-suchende.tex","status_markers_as_written":[],"summary_excerpt":"Minimale Kosten erfüllen unter geeigneter Komposition eine Dreiecksungleichung. Ohne reversible Operationen mit symmetrischen Kosten ist die resultierende Funktion jedoch nur eine gerichtete Distanz; der Checker liefert den gerichteten Dreierzyklus mit d(A,B)=1, d(B,A)=2. Unerreichbarkeit ergibt unendliche Distanzen. Kostenfreie Chartwechsel können verschiedene Beschreibungen auf Distanz null setzen; dann muss zunäch","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. Operationsgeometrie benötigt mehr als Erreichbarkeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":15774,"byte_start":14968,"id":"section:5be6e3e0a8f2bde702f1","kind":"subsection","labels":["gravitation-bleibt-eine-dynamische-verpflichtung"],"line_end":353,"line_start":338,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/019-subsubsection-6-4-kleinste-noch-zu-suchende.tex","status_markers_as_written":[],"summary_excerpt":"Die linearen Fluktuationen einer aus der Quelle bestimmten globalen Geometrie zu prüfen, ist ein sinnvoller Forschungsauftrag. Eine transversale spurfreie Tensorzerlegung allein garantiert aber weder einen masselosen physikalischen Spin-2-Pol noch positive Norm, genau zwei Helizitäten oder universelle Kopplung. Selbst ein gesunder linearer Spin-2-Sektor ersetzt nicht den Nachweis seiner nichtlinearen Eich-/Zwangsstru","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8. Gravitation bleibt eine dynamische Verpflichtung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16821,"byte_start":15774,"id":"section:6d4f11ce103cc2026d0b","kind":"subsection","labels":["p-versus-np-eine-konkrete-korrektur"],"line_end":373,"line_start":354,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/019-subsubsection-6-4-kleinste-noch-zu-suchende.tex","status_markers_as_written":[],"summary_excerpt":"Der Anhang sagt, P≠NP würde einen intrinsisch exponentiellen Suchaufwand bedeuten. Das ist falsch. P≠NP würde ausschließen, dass jedes NP-Entscheidungsproblem deterministisch in Polynomialzeit gelöst werden kann. Es folgt daraus keine exponentielle untere Schranke: Eine hypothetische Laufzeit wie 2 (√n) ist superpolynomiell und zugleich subexponentiell. Stärkere Exponentialzeitaussagen benötigen zusätzliche Sätze bez","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. P versus NP: eine konkrete Korrektur","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1969,"byte_start":0,"id":"section:09a3fac710237b339246","kind":"subsection","labels":["ein-korrigierter-wirklich-entscheidbarer-anschluss-test"],"line_end":44,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/020-subsection-10-ein-korrigierter-wirklich-entscheidbarer.tex","status_markers_as_written":[],"summary_excerpt":"Ein sinnvoller nächster Versuch besteht nicht nur aus einem unbeschrifteten P U_AB P. Er sollte zusammen liefern:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10. Ein korrigierter, wirklich entscheidbarer Anschluss-Test","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2074,"byte_start":1969,"id":"section:670e7412787728f186ef","kind":"section","labels":["anhang-e-arithmetischer-schleifenvorschlag"],"line_end":47,"line_start":45,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/020-subsection-10-ein-korrigierter-wirklich-entscheidbarer.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Anhang E: arithmetischer Schleifenvorschlag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2636,"byte_start":2074,"id":"section:d36cc029c6bedc022f41","kind":"section","labels":["zusatzpruxfcfung-schleifen-primzahlen-und-der-universalraum-vorschlag"],"line_end":62,"line_start":48,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/020-subsection-10-ein-korrigierter-wirklich-entscheidbarer.tex","status_markers_as_written":[],"summary_excerpt":"September 2026, v1.6.6. Quellenprüfung des nachgereichten Textes 59dc0059-8914-48ca-953d-85933f66e00b, kein neuer RH-Beweis und kein neuer arithmetischer Quellenoperator. Seine Aussagen über gemeinsame lokale Beschreibungen werden getrennt im Überlappungsaudit behandelt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zusatzprüfung: Schleifen, Primzahlen und der Universalraum-Vorschlag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":3056,"byte_start":2636,"id":"section:1c12262e7bfa1adc13ac","kind":"subsection","labels":["urteil-1"],"line_end":71,"line_start":63,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/020-subsection-10-ein-korrigierter-wirklich-entscheidbarer.tex","status_markers_as_written":[],"summary_excerpt":"Ein globaler Wegraum ist eine sinnvolle Suchklasse; ein Eulerprodukt über primitive Wege ist noch nicht das Eulerprodukt der Riemannschen Zetafunktion. Die im Text vorgeschlagene Xi-Determinante bleibt ein hinreichendes Ziel unter expliziten Operatorannahmen. Das Umbenennen ihres noch fehlenden Operators in „Generator der primitiven Schleifen`` konstruiert ihn nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Urteil","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":4396,"byte_start":3056,"id":"section:1c7886264b00443951b2","kind":"subsection","labels":["was-die-endliche-bank-tatsuxe4chlich-ausschlieuxdft"],"line_end":100,"line_start":72,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/020-subsection-10-ein-korrigierter-wirklich-entscheidbarer.tex","status_markers_as_written":[],"summary_excerpt":"Der beibehaltene Beweis aus v1.6.5 gilt für den ursprünglichen Hamiltonoperator mit 64 Fermion- und 60 Bosonmoden, Δ 0. Der Hilbertraum ist wegen der Bosonen nicht endlichdimensional. Endlich ist die Zahl der Moden. Mit C=960g²/Δ folgt aus quadratischem Ergänzen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Was die endliche Bank tatsächlich ausschließt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6630,"byte_start":4396,"id":"section:5f63dd1876ef44b98547","kind":"subsection","labels":["der-kleinste-gegencheck-zur-primzahl-automatik"],"line_end":146,"line_start":101,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/020-subsection-10-ein-korrigierter-wirklich-entscheidbarer.tex","status_markers_as_written":[],"summary_excerpt":"Nehmen wir einen gerichteten Knoten mit zwei erlaubten Schleifen a und b. Neben a und b ist auch ab ein primitiver periodischer Weg: Es ist keine Potenz eines kürzeren Wortes. Ebenso entstehen weitere gemischte primitive Wörter. Setzen wir nachträglich L(a)=log 2, L(b)=log 3, so hat ab die Länge log 6. Die 6 ist keine Primzahl. „Primitiver Weg`` bedeutet nicht „arithmetische Primzahl``.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Der kleinste Gegencheck zur Primzahl-Automatik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":7728,"byte_start":6630,"id":"section:ff5ad2304ffc99eed6d1","kind":"subsection","labels":["die-richtige-rh-zielbedingung"],"line_end":175,"line_start":147,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/020-subsection-10-ein-korrigierter-wirklich-entscheidbarer.tex","status_markers_as_written":[],"summary_excerpt":"Sei A strikt positiv und selbstadjungiert, mit kompakter Inverser und A \\-2\\ von Spurklasse. Dann ist der Fredholm-Ausdruck","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Die richtige RH-Zielbedingung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9479,"byte_start":7728,"id":"section:d8290f7f2a87f0e5da5e","kind":"subsection","labels":["vorarbeiten-und-aktuelle-grenze-der-quellenpruxfcfung"],"line_end":208,"line_start":176,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":["relation:4a3be14560baad708113","relation:b10e27ca848383d66868","relation:ba545cf0218f7551b283"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/020-subsection-10-ein-korrigierter-wirklich-entscheidbarer.tex","status_markers_as_written":[],"summary_excerpt":"Der installierte Leitfaden rh-graph-research und die projektspezifische Korpussuche wurden angewandt. Die aktuelle Konsistenzprüfung und der anschließende Wiederaufbauversuch brachen mit","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Vorarbeiten und aktuelle Grenze der Quellenprüfung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10542,"byte_start":9479,"id":"section:6d9a0e919f4a27117bb8","kind":"subsection","labels":["tragfuxe4higer-anschluss-ohne-acht-versprechen-an-ein-unbekanntes-objekt"],"line_end":229,"line_start":209,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/020-subsection-10-ein-korrigierter-wirklich-entscheidbarer.tex","status_markers_as_written":[],"summary_excerpt":"Der nächste arithmetische Test wäre erst nach Definition einer tatsächlichen Quell-Wegstruktur sinnvoll: primitive Bahnen, ihre Längen, Amplituden und die Spur gemeinsam bestimmen, ohne Primlisten oder Nullstellen einzusetzen. Ein positiver Kontrolltest muss insbesondere gemischte Zyklen erklären und den archimedischen Anteil auf demselben Träger liefern. Gelingt nur ein generisches Graph-Eulerprodukt, ist das ein Gr","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. 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Mit der Dreiecksungleichung, [formula in source] und der gesondert geprüften Positivität vor dem Quadrieren folgt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.5 Dieselbe ursprüngliche Fermionantwort ohne anfänglichen Filter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1635,"byte_start":0,"id":"section:f3ff7e7662efcd7ae6c8","kind":"subsection","labels":["warum-die-herkunftsluxfccke-nicht-durch-luxe4ngeres-rechnen-verschwindet"],"line_end":30,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/022-subsection-5-warum-die-herkunftsl-cke-nicht-durch-l-nger.tex","status_markers_as_written":[],"summary_excerpt":"Sei [formula in source] die lokale Fermionparität. Die bisher angegebenen bankinternen Paarumwandlungen, Zahloperationen, zahlenerhaltenden Symmetrielifts sowie reine Bosonverbindungen kommutieren mit jeder [formula in source] . Jede endliche Komposition, lineare Kombination, Adjungierung und jeder durch solche Operatoren realisierte einzelne Messzweig tut das ebenfalls. Starke beschränkte Grenzwerte bleiben im Kommu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Warum die Herkunftslücke nicht durch längeres Rechnen verschwindet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1755,"byte_start":1635,"id":"section:4ed1ac11a23f60e69796","kind":"subsection","labels":["was-von-der-arithmetischen-untersuchung-truxe4gt"],"line_end":33,"line_start":31,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/022-subsection-5-warum-die-herkunftsl-cke-nicht-durch-l-nger.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"6. Was von der arithmetischen Untersuchung trägt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3373,"byte_start":1755,"id":"section:fc7923d296ae26c35372","kind":"subsubsection","labels":["eine-einzelne-endliche-bank-ist-nicht-der-volle-logarithmusgenerator"],"line_end":70,"line_start":34,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/022-subsection-5-warum-die-herkunftsl-cke-nicht-durch-l-nger.tex","status_markers_as_written":[],"summary_excerpt":"Quadratisches Ergänzen liefert mit der nativen Casimirnorm [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6.1 Eine einzelne endliche Bank ist nicht der volle Logarithmusgenerator","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4940,"byte_start":3373,"id":"section:e3b031accbaec6f14145","kind":"subsubsection","labels":["primzahlen-kuxf6nnen-eine-gewuxe4hlte-dynamik-organisieren-erzwingen-sie-aber-nicht"],"line_end":101,"line_start":71,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/022-subsection-5-warum-die-herkunftsl-cke-nicht-durch-l-nger.tex","status_markers_as_written":[],"summary_excerpt":"Auf [formula in source] kann man [formula in source] definieren. Die additive Primfaktorbesetzung erklärt dann die Eulerstruktur. Der Definitionsbereich lautet [formula in source] . Dass quantenstatistische Systeme mit Zeta-Zustandssumme existieren, ist bereits ein Ergebnis von https://alainconnes.org/wp-content/uploads/bostconnesscan.pdfBost und Connes. Das ist ein relevanter Anschluss, nicht die fehlende native Her","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6.2 Primzahlen können eine gewählte Dynamik organisieren, erzwingen sie aber nicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":5923,"byte_start":4940,"id":"section:ea84c978b177bbb378c1","kind":"subsubsection","labels":["der-rh-zielsatz-bleibt-unbewiesen"],"line_end":125,"line_start":102,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/022-subsection-5-warum-die-herkunftsl-cke-nicht-durch-l-nger.tex","status_markers_as_written":[],"summary_excerpt":"für einen strikt positiven selbstadjungierten Operator [formula in source] mit kompakter Inverser und [formula in source] von Spurklasse wäre tatsächlich hinreichend: Die gesamte rechte Funktion hat ihre Nullstellen nur bei reellen [formula in source] , einschließlich Multiplizitäten. Aber dieser Operator und die gesamte Funktionsidentität sind nicht konstruiert. Ein Operator mit lediglich den Imaginärteilen der Null","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6.3 Der RH-Zielsatz bleibt unbewiesen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8067,"byte_start":5923,"id":"section:7caa31259cdd7b4b2998","kind":"subsection","labels":["die-lokale-polnuxe4herung-wird-pruxe4ziser-das-relativistische-feld-bleibt-offen"],"line_end":169,"line_start":126,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":["relation:498d0b6fdfa727fe1f0e"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/022-subsection-5-warum-die-herkunftsl-cke-nicht-durch-l-nger.tex","status_markers_as_written":[],"summary_excerpt":"Die externe Resolventenabschätzung ist korrekt: Im Kreis mit Radius [formula in source] um den tatsächlichen, unbekannten negativen Pol [formula in source] gilt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. Die lokale Polnäherung wird präziser, das relativistische Feld bleibt offen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10790,"byte_start":8067,"id":"section:dcca08f91b7edee05576","kind":"subsection","labels":["wuxe4hrend-der-arbeit-entdeckte-uxe4nderung-kommutant-7-richtig-einordnen"],"line_end":228,"line_start":170,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/022-subsection-5-warum-die-herkunftsl-cke-nicht-durch-l-nger.tex","status_markers_as_written":[],"summary_excerpt":"Die strikte Originalquellenprüfung stoppte korrekt, als eine andere Arbeit den früheren nativen Bericht ergänzte. Der alte Stand mit Hash 1062e13fe0fb79cce015657a7b4d40a61e9639922ff95fa60c689c0068c38ffc blieb eingefroren. Der gesonderte geänderte Entwurf hat Hash ab745e74b1232b1ddf35dd0e0d0da4ace0176c797d769e5db8bedd0010bcba6a. Die in dieser Revision verwendeten Energie- und Polzertifikate änderten sich bei dieser Pr","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8. Während der Arbeit entdeckte Änderung: „Kommutant 7`` richtig einordnen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13168,"byte_start":10790,"id":"section:f991bff1349931c38313","kind":"subsection","labels":["t1-t8-was-dieses-ergebnis-beitruxe4gt-und-nicht-beitruxe4gt"],"line_end":279,"line_start":229,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/022-subsection-5-warum-die-herkunftsl-cke-nicht-durch-l-nger.tex","status_markers_as_written":[],"summary_excerpt":"Die Begriffe folgen der aktuellen offenen Problemliste und ihrer Forschungszuordnung. Keine Akzeptanzmarkierung wurde heraufgesetzt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. T1-T8: was dieses Ergebnis beiträgt und nicht beiträgt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15592,"byte_start":13168,"id":"section:cd23bef8ed23468afe54","kind":"subsection","labels":["nuxe4chste-entscheidende-arbeiten-mit-klaren-abbruchkriterien"],"line_end":322,"line_start":280,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/022-subsection-5-warum-die-herkunftsl-cke-nicht-durch-l-nger.tex","status_markers_as_written":[],"summary_excerpt":"A. Die Quelle des geraden Gesamtlinks finden. Nicht noch eine riesige Kontrollmatrix bauen, sondern für jeden tatsächlich ursprünglichen Generator [formula in source] prüfen, ob [formula in source] bei erhaltener Gesamtparität möglich ist. Eine positive Antwort muss Generator, Teilbereichsdefinition, Hilbertraum, Gaussreferenz und Matrixelement liefern. Bleiben alle Generatoren lokal gerade, ist die Suche nach dem Li","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10. Nächste entscheidende Arbeiten mit klaren Abbruchkriterien","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16962,"byte_start":15592,"id":"section:2ee22f63ade64ca4a39b","kind":"subsection","labels":["reproduktion-und-ehrliche-liefergrenze"],"line_end":349,"line_start":323,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":["relation:91da7fa40d0f998e6523","relation:a55fcda9ccf0c86628c0"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/022-subsection-5-warum-die-herkunftsl-cke-nicht-durch-l-nger.tex","status_markers_as_written":[],"summary_excerpt":"replay.py –frozen-only führt die fünf Prüfer normal und mit -OO aus, vergleicht beide JSON-Ergebnisse und die zwei externen Originalberichte, prüft alle eingefrorenen Quellen und protokolliert Änderungen der Originalorte gesondert. Ein Fehler führt zu FAIL. Der zuvor aufgetretene Live-Quellenfehler bleibt in source_drift_failure_receipt.json sichtbar.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"11. Reproduktion und ehrliche Liefergrenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17648,"byte_start":16962,"id":"section:24fdb11a5e076ed03e90","kind":"section","labels":["nachpruxfcfung-der-beiden-zuletzt-eingegangenen-untersuchungen"],"line_end":363,"line_start":350,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/022-subsection-5-warum-die-herkunftsl-cke-nicht-durch-l-nger.tex","status_markers_as_written":[],"summary_excerpt":"Quellen: die Anlagen 8e110ae1-19e2-4d47-bfc8-ebe4fe9ab81b und b928b72a-6669-4c67-a75d-124095791c6f, unverändert eingefroren. Zusätzlich wurden die vier genannten Programme t1_fixed.py, stabilizer.py, t5_twobank.py, t5_varresp.py vollständig gelesen und archiviert. Eine eigene Nachrechnung prüft die kritischen Folgerungen; sie ist kein vollständiger Replay aller sechs Sonden des fremden Arbeitsordners.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nachprüfung der beiden zuletzt eingegangenen Untersuchungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2938,"byte_start":0,"id":"section:d4f5f2814089be46405c","kind":"subsection","labels":["uxfcbersicht-uxfcbernehmen-korrigieren-oder-offenlassen"],"line_end":60,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/023-subsection-1-bersicht-bernehmen-korrigieren-oder.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 2 ) * 0.5000 > p( - 2 ) * 0.5000@ Neue Aussage & Ergebnis der Prüfung \\\\ Innerer Viererzyklus erhält alle 60 W-Kanäle & Bestätigt, jetzt einschließlich der richtigen Fermion-Vorzeichen und explizitem Bosonlift \\\\ Grundzustandseindeutigkeit/Singulett/Gaplücke weiterhin unbekannt & Überholter Stand: unter dem festgelegten nativen Vertrag bereits bewiesen; voller Vektor weiter unbekannt \\\\ Leerer Grundzustand f","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Übersicht: übernehmen, korrigieren oder offenlassen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4537,"byte_start":2938,"id":"section:b9163ae6d15607350f87","kind":"subsection","labels":["positiver-neuer-anschluss-der-korrekt-angehobene-viererzyklus"],"line_end":93,"line_start":61,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/023-subsection-1-bersicht-bernehmen-korrigieren-oder.tex","status_markers_as_written":[],"summary_excerpt":"Die Abbildung der Fermionmarken lautet [formula in source] . Auf Paaren ist zwingend das Exteriorvorzeichen zu beachten: Falls [formula in source] , erhält das sortierte Paar ein Minuszeichen. Der gelieferte stabilizer.py lässt dieses Zeichen weg. Das wäre im Allgemeinen falsch; für den untersuchten Viererzyklus überlebt das positive Resultat jedoch auch den korrekten Test.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Positiver neuer Anschluss: der korrekt angehobene Viererzyklus","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6292,"byte_start":4537,"id":"section:956b82a6da4c66a928bf","kind":"subsection","labels":["warum-der-einteilchen-abschluss-den-fock-operationssatz-nicht-schlieuxdft"],"line_end":126,"line_start":94,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/023-subsection-1-bersicht-bernehmen-korrigieren-oder.tex","status_markers_as_written":[],"summary_excerpt":"Die Irreduzibilität der Einteilchendarstellung kann ihre assoziative Matrixalgebra zu [formula in source] machen. Daraus folgt nicht, dass jede Matrix als ein zulässiges physisches Wort verfügbar ist, und auch nicht, dass ihre zweite Quantisierung bereits erzeugt wird.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Warum der Einteilchen-Abschluss den Fock-Operationssatz nicht schließt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7940,"byte_start":6292,"id":"section:01fd58449b8b33f3662c","kind":"subsection","labels":["zustandswahl-keine-ruxfcckkehr-vor-den-abgesicherten-grundsatz"],"line_end":159,"line_start":127,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/023-subsection-1-bersicht-bernehmen-korrigieren-oder.tex","status_markers_as_written":[],"summary_excerpt":"Der vorhandene native Satz beweist Eindeutigkeit, N=64, Singulett und positive Lücke bei μ=0 im angegebenen Kopplungsbereich. Eine komplette Clebsch-Gordan-Serie oder Voll-Diagonalisierung ist dafür nicht nötig; Vergleichsungleichungen und Minmax waren gerade der einfache Ausweg. Die physische Auswahl von H beziehungsweise μ=0 bleibt eine andere Frage.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Zustandswahl: keine Rückkehr vor den abgesicherten Grundsatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":8096,"byte_start":7940,"id":"section:19147e75f9939c3a3782","kind":"subsection","labels":["feldtheorie-falsche-verbote-entfernen-echte-bedingungen-behalten"],"line_end":162,"line_start":160,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/023-subsection-1-bersicht-bernehmen-korrigieren-oder.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"5. 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Insbesondere hat der Energie-Impuls-Tensor [formula in source] , mit passender Spurbehandlung, Dimension [formula in source] . 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Konsequenz für die nächste Forschungsrevision","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15075,"byte_start":14556,"id":"section:2a26f6d442de76283ca7","kind":"section","labels":["historischer-beweisanhang-vollstuxe4ndiger-nativer-herleitungsstand-v1.6.4"],"line_end":311,"line_start":301,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/023-subsection-1-bersicht-bernehmen-korrigieren-oder.tex","status_markers_as_written":[],"summary_excerpt":"Dieser Anhang bewahrt die frühere Herleitung vollständig. 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Sie ergänzt die bisherigen Hauptdokumente; sie ist keine verkürzte Neufassung des vollständigen Hauptbuchs. Die vorhandenen Haupt- und Update-PDFs wurden in dieser Runde nicht verändert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TFPT / Universalraum: nativer Pol, Bewegungsgleichung und minimale Feldtypen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18048,"byte_start":15670,"id":"section:077bed1f14df694c7232","kind":"subsection","labels":["ergebnis-in-einem-satz"],"line_end":378,"line_start":324,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/023-subsection-1-bersicht-bernehmen-korrigieren-oder.tex","status_markers_as_written":[],"summary_excerpt":"Auf dem abgesicherten Grundzustand des festgelegten nativen Fockmodells existiert eine isolierte ursprüngliche Fermion-Entnahmelinie; nach Kombination beider Rechnungen trägt sie mehr als 88,007628 \\% des gesamten normierten Spektralgewichts pro Mode. Die zusätzliche Antwort ist jedoch nicht exakt auf eine einzige weitere Linie reduzierbar. Ihr erster Rückwirkungsschritt wird direkt von derselben ursprünglichen Wechs","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Ergebnis in einem Satz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1159,"byte_start":0,"id":"section:386cbc067ca6999310f9","kind":"subsection","labels":["ein-unveruxe4nderter-modellvertrag"],"line_end":28,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/024-subsection-2-ein-unver-nderter.tex","status_markers_as_written":[],"summary_excerpt":"Es werden keine Hopping-, Massen-, Ladungs- oder Projektionsglieder zu H hinzugefügt:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. 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Der Prüfer wurde normal und optimiert wiederholt: 317 Prüfbedingungen, identische JSON-Bytes auch zum gelieferten Bericht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.2 Das neu eingegangene Polergebnis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6465,"byte_start":4674,"id":"section:be3be5121dccb289c5cb","kind":"subsection","labels":["der-einfache-native-anschluss-bewegungsgleichung-statt-umdeutung"],"line_end":156,"line_start":110,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/024-subsection-2-ein-unver-nderter.tex","status_markers_as_written":[],"summary_excerpt":"Erweitere jede W-Zeile zur antisymmetrischen Matrix [formula in source] mit [formula in source] für i j. 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Dieselbe Antwort auf demselben Grundzustand","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8978,"byte_start":7659,"id":"section:706a80627495a7e97b53","kind":"subsubsection","labels":["herleitung-des-dritten-moments"],"line_end":222,"line_start":194,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/024-subsection-2-ein-unver-nderter.tex","status_markers_as_written":[],"summary_excerpt":"Setze [formula in source] . Stationarität macht diesen Operator symmetrisch in der positiven, nach Nullvektoren quotientierten Metrik [formula in source] . 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Invarianz und Besetzung ergeben","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Der Polsatz und seine zusätzliche Verschärfung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":13501,"byte_start":12687,"id":"section:cd54c29108d0c855c875","kind":"subsection","labels":["einfache-organisation-aber-keine-falsche-zwei-linien-luxf6sung"],"line_end":348,"line_start":331,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/024-subsection-2-ein-unver-nderter.tex","status_markers_as_written":[],"summary_excerpt":"Die ersten zwei orthonormalen Operatoren sind f und [formula in source] . Die erste Resolventenreduktion hat deshalb die exakte Form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. Einfache Organisation, aber keine falsche Zwei-Linien-Lösung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15056,"byte_start":13501,"id":"section:2a35e40e30a677274a04","kind":"subsubsection","labels":["warum-man-die-ruxfcckwirkung-nicht-exakt-weglassen-darf"],"line_end":388,"line_start":349,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/024-subsection-2-ein-unver-nderter.tex","status_markers_as_written":[],"summary_excerpt":"Angenommen, es gäbe nur je eine Entnahme- und Additionslinie mit Energien [formula in source] . Symmetrie macht diese für alle r gleich. Dann liefern die Bewegungsgleichungen auf demselben Grundzustand","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7.1 Warum man die Rückwirkung nicht exakt weglassen darf","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2162,"byte_start":0,"id":"section:0643f20f9a729b3054a0","kind":"subsection","labels":["was-der-operationssatz-jetzt-tatsuxe4chlich-hergibt"],"line_end":57,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/025-subsection-8-was-der-operationssatz-jetzt-tats-chlich.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333@ Vertrag & Mathematisch abgesichert & Nicht dadurch verfügbar \\\\ Markierter endlicher Matrixcompiler & Matrizen, Ordnungen, konkrete endliche Syntheseidentitäten & Vollständiges Fockinstrument, Präparation, physischer Zeitgenerator \\\\ H allein & Modellzeitentwicklung & Unabhängiges Schalten von X und [formula in source] \\\\ X und [formula in source] , wenn ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8. Was der Operationssatz jetzt tatsächlich hergibt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2914,"byte_start":2162,"id":"section:f334ddf0d171d0767f17","kind":"subsubsection","labels":["konkrete-pruxe4parationsgrenze"],"line_end":73,"line_start":58,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/025-subsection-8-was-der-operationssatz-jetzt-tats-chlich.tex","status_markers_as_written":[],"summary_excerpt":"Alle genannten Fockkontrollen erhalten N. Ein Wort aus ihnen und jeder einzeln zahlenerhaltende ausgewählte Messzweig bleiben im Ausgangssektor. Sie können aus dem leeren N=0-Zustand nicht den N=64-Grundzustand erzeugen. Diese Aussage betrifft zahlenerhaltende Krauszweige; eine bloß U(1)-kovariante offene Dynamik kann sehr wohl geladene Krausoperatoren haben.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.1 Konkrete Präparationsgrenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3644,"byte_start":2914,"id":"section:045305c6f2772a363613","kind":"subsubsection","labels":["der-kleinste-konkrete-ladungstest"],"line_end":88,"line_start":74,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/025-subsection-8-was-der-operationssatz-jetzt-tats-chlich.tex","status_markers_as_written":[],"summary_excerpt":"Ein Kandidat ist eine explizite Referenzmode c mit [formula in source] . Sie erhält die gemeinsame Ladung, verändert aber die Ladung der ursprünglichen Bank. Der endliche Austausch- und Detuningtest ist exakt; dieses T wurde nicht als neuer nativer Hamiltonterm eingeführt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.2 Der kleinste konkrete Ladungstest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4100,"byte_start":3644,"id":"section:033fcf3ac86ffe513190","kind":"subsection","labels":["relativistisches-wuxf6rterbuch-ausschluss-und-zwei-pruxe4zise-alternativen"],"line_end":97,"line_start":89,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/025-subsection-8-was-der-operationssatz-jetzt-tats-chlich.tex","status_markers_as_written":[],"summary_excerpt":"Die Indexfrage darf nicht nachträglich durch einen Namen beantwortet werden. Die Konventionen für Zweikomponentenspinoren wurden mit https://arxiv.org/abs/0812.1594Dreiner, Haber und Martin abgeglichen; die folgenden speziellen W-Tests sind eigene exakte Tensorrechnungen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. Relativistisches Wörterbuch: Ausschluss und zwei präzise Alternativen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4588,"byte_start":4100,"id":"section:5648cb7a660c49b82d60","kind":"subsubsection","labels":["was-nicht-funktioniert"],"line_end":106,"line_start":98,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/025-subsection-8-was-der-operationssatz-jetzt-tats-chlich.tex","status_markers_as_written":[],"summary_excerpt":"Für 64 gleichhändige Weylfelder mit innerem Index I und einen skalaren Vermittler ist [formula in source] symmetrisch. Die Grassmann-Antisymmetrisierung verschwindet daher identisch, für alle 60 W-Zeilen. Außerdem lässt die volle irreduzible innere Darstellung [formula in source] auf denselben 64 Komponenten nach Schur keine zusätzliche kommutierende nichttriviale Lorentzspinorwirkung zu.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9.1 Was nicht funktioniert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5003,"byte_start":4588,"id":"section:1c93df5f627f64e7f1e2","kind":"subsubsection","labels":["bereits-bekannter-nichtverschwindender-typ"],"line_end":115,"line_start":107,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/025-subsection-8-was-der-operationssatz-jetzt-tats-chlich.tex","status_markers_as_written":[],"summary_excerpt":"Ein symmetrischer Lorentzspinortensor koppelt an das antisymmetrische M. Der Vermittler hat dann einen passenden dualen (1,0)-Typ samt adjungiertem Typ. Diese Variante besteht den algebraischen Nichtnulltest, aber noch keinen vollständigen Kinetik-, Positivitäts-, Constraints- oder Herkunftstest.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9.2 Bereits bekannter nichtverschwindender Typ","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6756,"byte_start":5003,"id":"section:e31760b868d7adc39363","kind":"subsubsection","labels":["neue-minimale-skalare-alternative---ausdruxfccklich-zusuxe4tzlich"],"line_end":149,"line_start":116,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/025-subsection-8-was-der-operationssatz-jetzt-tats-chlich.tex","status_markers_as_written":[],"summary_excerpt":"Will man zugleich W, gleiche Weylhand, lokale Bilinearität und einen skalaren Vermittler behalten, kann man einen unabhängigen Hilfsindex a=1,2 mit alternierender Form einführen:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9.3 Neue minimale skalare Alternative - ausdrücklich zusätzlich","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10037,"byte_start":6756,"id":"section:b92edcd7e2ad2ab5befd","kind":"subsection","labels":["nuxe4chste-schritte-mit-eindeutiger-erfolgskontrolle"],"line_end":220,"line_start":150,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/025-subsection-8-was-der-operationssatz-jetzt-tats-chlich.tex","status_markers_as_written":[],"summary_excerpt":"Native Quelle des Austauschoperators bestimmen. Ein tatsächliches Operationswort mit Anfangszustand, Detektor, Adjungiertem, Ladungsbilanz und Record angeben. Ein weiteres neutrales Wort oder bloßer Algebraabschluss schließt diese Aufgabe nicht. Den Rest der nativen Antwort kontrollieren. Das nächste Ziel ist [formula in source] beziehungsweise sein erster Norm- und Momentkoeffizient, gemeinsam in N=63,64,65. Die vor","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10. Nächste Schritte mit eindeutiger Erfolgskontrolle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11045,"byte_start":10037,"id":"section:8cd53be0ec3e4d70d664","kind":"subsection","labels":["erratum-und-versionsdisziplin"],"line_end":240,"line_start":221,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/025-subsection-8-was-der-operationssatz-jetzt-tats-chlich.tex","status_markers_as_written":[],"summary_excerpt":"Im eigenen v1.6.2-Text fehlte in Abschnitt 5.2 zwischen Entnahme- und Additionsresolvente ein Pluszeichen. Richtig ist auf der dortigen N=4-Referenz [formula in source] . Die früheren Prüfrechnungen verwendeten die additive CAR-Gewichtsregel; der Darstellungsfehler wird hier ausdrücklich korrigiert. Die archivierte v1.6.2 wird nicht stillschweigend umgeschrieben.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"11. Erratum und Versionsdisziplin","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14747,"byte_start":0,"id":"section:b57f220d5154552d3a00","kind":"section","labels":["nutzerquelle-a-vollstuxe4ndige-runde-v1.6.3"],"line_end":246,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":["relation:42b959fa6362b3558946"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/026-section-nutzerquelle-a-vollst-ndige-runde.tex","status_markers_as_written":[],"summary_excerpt":"Unveränderte Quelle. Nicht alle Aussagen darin werden übernommen. Entscheidend sind die Quellenprüfung und Korrekturen in v1.6.7.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nutzerquelle A: vollständige Runde v1.6.3","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15252,"byte_start":14747,"id":"section:e636090ab1318e4b1fa5","kind":"section","labels":["nutzerquelle-b-korrektur-und-zwischenbericht"],"line_end":258,"line_start":247,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/026-section-nutzerquelle-a-vollst-ndige-runde.tex","status_markers_as_written":[],"summary_excerpt":"Unveränderte Quelle. Nicht alle Aussagen darin werden übernommen. Entscheidend sind die Quellenprüfung und Korrekturen in v1.6.7.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nutzerquelle B: Korrektur und Zwischenbericht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15495,"byte_start":15252,"id":"section:ac6c56f7399828678406","kind":"section","labels":["zwischenbericht-tfptuniversalraum---fundamentale-luxf6sung-stand-15.09.2026-1145"],"line_end":262,"line_start":259,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/026-section-nutzerquelle-a-vollst-ndige-runde.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Zwischenbericht: TFPT/Universalraum - fundamentale Lösung, Stand 15.09.2026, 11:45","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17265,"byte_start":15495,"id":"section:f287f9658931cccdb510","kind":"subsection","labels":["gesamtlage-zwei-spuren"],"line_end":307,"line_start":263,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/026-section-nutzerquelle-a-vollst-ndige-runde.tex","status_markers_as_written":[],"summary_excerpt":"Es existieren jetzt zwei Contract-Ordner, die sich unabhängig auf denselben Kernpunkt zubewegt haben:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"0. Gesamtlage: zwei Spuren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18386,"byte_start":17265,"id":"section:cd3999e95765380ce21d","kind":"subsection","labels":["fundament-meiner-session-native_source.py-neu-npz-frei"],"line_end":328,"line_start":308,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/026-section-nutzerquelle-a-vollst-ndige-runde.tex","status_markers_as_written":[],"summary_excerpt":"Problem: der gepinnte Tensor ( spinor_tensors.npz, SHA-256 3f00a089…) liegt unter /Documents - für die Agenten-Shell macOS-gesperrt (TCC). Die bisherigen Verträge sind von dieser Shell nicht reproduzierbar.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Fundament meiner Session: native_source.py (neu, npz-frei)1. Fundament meiner Session: (neu, npz-frei)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18679,"byte_start":18386,"id":"section:8437e6f03d1b1440c84b","kind":"subsection","labels":["wp-a-der-verfuxfcgbare-operationssatz-fertig-307-exakte-guards"],"line_end":334,"line_start":329,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/026-section-nutzerquelle-a-vollst-ndige-runde.tex","status_markers_as_written":[],"summary_excerpt":"Frage (v1.6.2 §10.3/§14): Wie groß ist die unsichtbare Freiheit (Kommutant) unter dem tatsächlich verfügbaren Operationssatz?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. WP-A: Der verfügbare Operationssatz (fertig, 307 exakte Guards)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":19736,"byte_start":18679,"id":"section:c01237afb611d27afb7e","kind":"subsubsection","labels":["die-kommutanten-leiter-n3-sektor-45-504-dim"],"line_end":363,"line_start":335,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":["relation:f430fdbe02cd237b4367"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/026-section-nutzerquelle-a-vollst-ndige-runde.tex","status_markers_as_written":[],"summary_excerpt":"@lrr@ Operationssatz & erzeugte Algebra & Kommutante \\\\ S0: \\X, N_b\\ & 14 & 1 444 233 216 \\\\ S1: + Spin(10)×SU(4)-Rahmen & 743 583 744 & 7 \\\\ S2: + Clock-Lift & unverändert & 7 \\\\ S3: + Modenbesetzungen \\n_r, m_A\\ & M₄₅₅₀₄ (2 070 614 016) & 1 \\\\ S4: + geladene f-Instrumente & M₄₇₅₈₀ (N=2∪N=3) & 1 \\\\","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Kommutanten-Leiter (N=3-Sektor, 45 504-dim)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1403,"byte_start":0,"id":"section:8f570d65c4d134ce3119","kind":"subsubsection","labels":["die-isotypie-zerlegung-von-n3-beide-spuren-unabhuxe4ngig-identisch"],"line_end":30,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/027-subsubsection-die-isotypie-zerlegung-von-n-3-beide-spure.tex","status_markers_as_written":[],"summary_excerpt":"@lrrrll@ Block & Dim & Mult & S-Eigenwert & (C_S, C_U) & Rolle \\\\ (144, 20) & 2880 & 2 & 7 & (85, 39) & hell, X-gekoppelt \\\\ (144, 4̄) & 576 & 2 & 10 & (85, 15) & hell, X-gekoppelt \\\\ (16′, 20) & 320 & 2 & 12 & (45, 39) & hell, X-gekoppelt \\\\ (16′, 4̄) & 64 & 1 & 0 (ker S) & (45, 15) & χ-Kompositblock \\\\ (672, 4̄) & 2688 & 1 & - & (165, 15) & dunkel \\\\ (1200, 20) & 24 000 & 1 & - & (141, 39) & dunkel \\\\ (560, 20′) & ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Isotypie-Zerlegung von N=3 (beide Spuren unabhängig, identisch)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2603,"byte_start":1403,"id":"section:79e6c1b533d8873f2f4a","kind":"subsubsection","labels":["das-verfuxfcgbarkeits-theorem-parallelsession-symmetry_availability.py"],"line_end":52,"line_start":31,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/027-subsubsection-die-isotypie-zerlegung-von-n-3-beide-spure.tex","status_markers_as_written":[],"summary_excerpt":"Die gewährte Dynamik (Wörter aus X, N_b) liegt in der Verflechteralgebra (Dim Σmᵢ² = 16); die 60 Lie-Erzeuger liegen nicht darin - keine Komposition gewährter Dynamik erzeugt sie. Die Symmetrie ist ein eigenständiges Primitiv: gewährt oder nicht gewährt. Der gesamte verbleibende symmetrieverträgliche Spielraum ist exakt 2 Dimensionen breit = die Fähigkeit, die drei dunklen Blöcke getrennt anzusprechen (= beide Casimi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das Verfügbarkeits-Theorem (Parallelsession, symmetry_availability.py)Das Verfügbarkeits-Theorem (Parallelsession, )","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4895,"byte_start":2603,"id":"section:35f0d2cac921715c85a2","kind":"subsection","labels":["wp-c-relativistisches-feldwuxf6rterbuch-fertig-2161-exakte-guards--oo-stabil"],"line_end":104,"line_start":53,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/027-subsubsection-die-isotypie-zerlegung-von-n-3-beide-spure.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.3000 > p( - 4 ) * 0.4000 > p( - 4 ) * 0.3000@ Kanal & Norm² pro Zeile & Status \\\\ Skalar, gleichhändig ε_\\αβ\\ψψ & 0 (alle 60 Zeilen, exakt) & verboten \\\\ Skalar, gepunktet (0,0) & 0 & verboten \\\\ (1,0) symmetrisch \\I, σˣ, σᶻ\\ & je 64, Summe 192 & erlaubt - der Vertex ist rein (1,0)+h.c. \\\\ (0,1) konjugiert & je 64 & erlaubt \\\\","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. WP-C: Relativistisches Feldwörterbuch (fertig, 2161 exakte Guards, -OO-stabil)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6923,"byte_start":4895,"id":"section:2593f00f0f808a33e03f","kind":"subsection","labels":["wp-b-nativer-grundzustand-parallelsession-v1.6.4-meine-laufende-sonde"],"line_end":153,"line_start":105,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/027-subsubsection-die-isotypie-zerlegung-von-n-3-beide-spure.tex","status_markers_as_written":[],"summary_excerpt":"@rrr@ k & Bosonkonfigurationen vollständig enumeriert & ‖Q₊ᵏF‖² \\\\ 0 & analytisch & 1 \\\\ 1 & 60 Kanäle / 480 Paare & 480 \\\\ 2 & 1 830 & 439 680 \\\\ 3 & 37 820 & 575 078 400 \\\\ 4 & 595 665 & 952 296 652 800 \\\\","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. WP-B: Nativer Grundzustand (Parallelsession v1.6.4 + meine laufende Sonde)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8566,"byte_start":6923,"id":"section:b017f13b9505f7130c50","kind":"subsection","labels":["wp-d-geladene-antwort-auf-dem-grundzustand-parallelsession-v1.6.4"],"line_end":193,"line_start":154,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/027-subsubsection-die-isotypie-zerlegung-von-n-3-beide-spure.tex","status_markers_as_written":[],"summary_excerpt":"Genau die geforderte „dieselbe geladene Antwort auf dem abgesicherten Zustand'':","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. WP-D: Geladene Antwort auf dem Grundzustand (Parallelsession v1.6.4)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10142,"byte_start":8566,"id":"section:5841f284e45a57163d4e","kind":"subsection","labels":["kreuzvalidierung-der-beiden-spuren"],"line_end":232,"line_start":194,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/027-subsubsection-die-isotypie-zerlegung-von-n-3-beide-spure.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 6 ) * 0.2500 > p( - 6 ) * 0.2500 > p( - 6 ) * 0.2500 > p( - 6 ) * 0.2500@ Befund & Meine Session & Parallelsession & Status \\\\ N=3-Zerlegung (7 Blöcke, Mults 2,2,2,1,1,1,1) & ✓ & ✓ & identisch \\\\ Casimirwerte (je Block) & (45,15), (85,15), & C = (C_S+C_U)/4 = 15, 25, 45, 21, 31, 45, 45 & identisch (zwei Normierungen) \\\\ Kommutant S1 (volle Symmetrie) & 7 & 7 & identisch \\\\ Kommutant S0 (X, N_b) & 1 452 961 7","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Kreuzvalidierung der beiden Spuren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":11895,"byte_start":10142,"id":"section:00514c48aadd83abd394","kind":"subsection","labels":["offen-nuxe4chste-schritte-in-der-reihenfolge-der-direktive"],"line_end":274,"line_start":233,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/027-subsubsection-die-isotypie-zerlegung-von-n-3-beide-spure.tex","status_markers_as_written":[],"summary_excerpt":"Sonde abschließen (läuft): mult₂-Zertifikat, β-Kette, Sektorfloors → unabhängige Reproduktion der v1.6.4-Kernzahlen. Volle 33-Niveau-Kette: falls mult_k=1 weiter trägt, ist die Singulett-Kette durch die Normsequenz ‖Q₊ᵏF‖² (k≤32) bestimmt - dafür ist die Symmetriespur-Resummation nötig (die „vier Symmetriespuren'' des Workers), nicht rohe Enumeration. Σ₂ kontrollieren (erster Norm-/Momentkoeffizient, N=63/64/65 gemei","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. Offen / nächste Schritte (in der Reihenfolge der Direktive)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16991,"byte_start":0,"id":"section:7399d2b0808093b71fa5","kind":"section","labels":["nutzerquelle-c-multiplizitaeten-und-z4"],"line_end":332,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/028-section-nutzerquelle-c-multiplizitaeten-und.tex","status_markers_as_written":[],"summary_excerpt":"Unveraenderte Nutzerquelle, als Vorschlag und nicht als Beweis uebernommen. Die Pruefung und eigene Fortsetzung stehen in Teil B.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nutzerquelle C: Multiplizitaeten und Z4","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10484,"byte_start":0,"id":"section:f8feb7dc8c3bc9483966","kind":"section","labels":["nutzerquelle-d-fundamentale-reduktion"],"line_end":180,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/029-section-nutzerquelle-d-fundamentale.tex","status_markers_as_written":[],"summary_excerpt":"Unveraenderte Nutzerquelle, als Vorschlag und nicht als Beweis uebernommen. Die Pruefung und eigene Fortsetzung stehen in Teil B.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nutzerquelle D: fundamentale Reduktion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":22803,"byte_start":0,"id":"section:e7a8e550e2e7c2010910","kind":"section","labels":["nutzerquelle-e-gemeinsamer-ausfuehrbarer-prozess"],"line_end":363,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/030-section-nutzerquelle-e-gemeinsamer-ausfuehrbarer.tex","status_markers_as_written":[],"summary_excerpt":"Unveraenderte Nutzerquelle, als Vorschlag und nicht als Beweis uebernommen. Die Pruefung und eigene Fortsetzung stehen in Teil B.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nutzerquelle E: gemeinsamer ausfuehrbarer Prozess","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":23094,"byte_start":22803,"id":"section:8925055aa81b02fbdfc3","kind":"section","labels":["nutzerquelle-f-operationssatz-grundzustand-und-feldwoerterbuch-v1.6.3"],"line_end":370,"line_start":364,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/030-section-nutzerquelle-e-gemeinsamer-ausfuehrbarer.tex","status_markers_as_written":[],"summary_excerpt":"Unveraenderte Nutzerquelle, als Vorschlag und nicht als Beweis uebernommen. Die Pruefung und eigene Fortsetzung stehen in Teil B.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nutzerquelle F: Operationssatz, Grundzustand und Feldwoerterbuch v1.6.3","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":860,"byte_start":0,"id":"section:116a5ef14f4ada43e9e5","kind":"section","labels":["tfpt-universalraum-operationssatz-nativer-grundzustand-und-feldwuxf6rterbuch"],"line_end":15,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/031-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Diese Runde bearbeitet die vier Prioritäten aus v1.6.2 §14 in der dort festgelegten Reihenfolge: den tatsächlich verfügbaren Operationssatz exakt abgrenzen, den berichteten nativen Grundzustand mit seinem ursprünglichen Hamilton- und Sektorvertrag reproduzieren und darauf die geladene Antwort berechnen, das relativistische Feldwörterbuch am tatsächlichen Tensor festhalten. Eine räumliche Skalierungsrechnung ist ausdr","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TFPT / Universalraum: Operationssatz, nativer Grundzustand und Feldwörterbuch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2267,"byte_start":860,"id":"section:7fd773dfe62f1ade8aac","kind":"subsection","labels":["ergebnis-in-einem-absatz"],"line_end":37,"line_start":16,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/031-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Der N=64-Sektor des nativen Modells ist exakt als Loch-Paarerzeugung auf dem gefüllten Zustand realisiert; seine Krylov-Kette ist bis zu 15 252 960 Einträgen exakt berechnet, ihre Normen ν₁ ν₄ sind auf zwei völlig unabhängigen Wegen (Besetzungsbild und Onishi/Wick-Spurnetzwerke) identisch. Die Kette schließt bei zwei Bosonen exakt nicht (Defekt 2,9·10⁻⁵), das Modell ist also nicht allein durch seine Normen lösbar, nu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Ergebnis in einem Absatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3222,"byte_start":2267,"id":"section:0a0955454adeb5051086","kind":"subsection","labels":["unveruxe4nderte-quelle-und-konventionen"],"line_end":56,"line_start":38,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/031-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Der Tensor wird repo-lokal gelesen (SHA-256 3f00a0892157a691e4ef26920c3702772c7bf76a250fad98ff04a079bb64b763), der Clock-Konstruktor ist gepinnt ( 9bf99de7…). common.py prüft: 60 Kanäle × 8 disjunkte Paare, jede Mode in 15 Kanälen; Gewichtserhaltung auf allen 480 Paaren; die Casimir-Identität 8WᵀW + 𝒞_S + 𝒞_C − 120 I = 0 auf allen 2016 Zweiteilchenzuständen (𝒞 = −ΣL², d. h. viermal der Standard-Casimir); induzierte B","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Unveränderte Quelle und Konventionen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3665,"byte_start":3222,"id":"section:ba9f0e5266a89da23879","kind":"subsection","labels":["operationssatz-und-kommutant"],"line_end":66,"line_start":57,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/031-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Gemessen wird die Dimension des Kommutanten der von einer Operationsstufe erzeugten Algebra auf dem Sektor: kleiner Kommutant bedeutet weniger unsichtbare Freiheit. Das Spektralzertifikat für N=3 ist reproduziert (S = C₃C₃ᵀ wird von ∏(S−r), r ∈ \\0,7,10,12\\, exakt annulliert; Multiplizitäten 64, 2880, 576, 320 aus rationalen Projektorspuren).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Operationssatz und Kommutant","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5472,"byte_start":3665,"id":"section:da3ab7c3d6ce787c3765","kind":"subsubsection","labels":["exakte-irreduzibel-zerlegung-huxf6chstgewichtsvektoren"],"line_end":108,"line_start":67,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/031-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 8 ) * 0.1875 > p( - 8 ) * 0.1875 > p( - 8 ) * 0.2500 > p( - 8 ) * 0.1875 > p( - 8 ) * 0.1875@ Sektor & Block & Dim & Zerlegung unter so(10)⊕ su(4) & (𝒞_S, 𝒞_C) \\\\ N=2 & helle Paare ↔ Bosonen & 60 & (10, 6) & (36, 20) \\\\ N=2 & dunkle Paare & 1956 & (120, 10) ⊕ (126, 6) & (84,36), (100,20) \\\\ N=3 & dunkle Tripel = ker C₃ & 37888 & (560, 20″) ⊕ (1200, 20) ⊕ (672, 4̄) & (117,63), (141,39), (165,15) \\\\ N=3 & ker ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.1 Exakte Irreduzibel-Zerlegung (Höchstgewichtsvektoren)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7553,"byte_start":5472,"id":"section:c5721e1100fdcf3ab99f","kind":"subsubsection","labels":["kommutanten-leiter"],"line_end":154,"line_start":109,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/031-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.2727 > p( - 4 ) * 0.3636 > p( - 4 ) * 0.3636@ Verfügbare Operationen & N=2 & N=3 \\\\ A: \\X, N_b\\ (die zwei bisher geprüften Kontrollen) & 3 829 536 & 1 444 233 216 \\\\ B: A + Clock (Ordnung 6) & 641 760 & 240 742 144 \\\\ Cc: A + 15 su(4)-Generatoren & 30 376 & 2 247 168 \\\\ Cs: A + 45 so(10)-Generatoren & 172 & 1 648 \\\\ C: A + alle 60 Generatoren & 3 & 7 \\\\ D: B + C & 3 & 7 \\\\ B(H_N) & 1 & 1 \\\\","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.2 Kommutanten-Leiter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7634,"byte_start":7553,"id":"section:45b1f97827e97e44db5c","kind":"subsection","labels":["der-native-n64-grundzustand"],"line_end":157,"line_start":155,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/031-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"4. Der native N=64-Grundzustand","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8251,"byte_start":7634,"id":"section:4b78fa1e7e16e1fe8352","kind":"subsubsection","labels":["lochbild"],"line_end":172,"line_start":158,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/031-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Mit h_i = f_i† ist F⟩ = f₀† f₆₃† 0⟩ das Lochvakuum und als Operatoridentität P_A = −Q_A† mit Q_A† = Σ_\\i j\\W_\\A,ij\\h_i†h_j†. Unter (−1)\\^\\N_b\\ ist H äquivalent zu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.1 Lochbild","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9514,"byte_start":8251,"id":"section:c1cb2c314c9e58ac928f","kind":"subsubsection","labels":["exakte-krylov-kette"],"line_end":203,"line_start":173,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/031-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"@rrrl@ n & Einträge in v_n & ν_n = ‖v_n‖² & ν_n/ν_\\n−1\\ \\\\ 0 & 1 & 1 & - \\\\ 1 & 480 & 480 & 480 \\\\ 2 & 108 240 & 439 680 & 916 = 4·229 \\\\ 3 & 15 252 960 & 575 078 400 & 299520/229 \\\\ 4 & (nur Spurnetzwerk) & 952 296 652 800 & ≈ 1656,0 \\\\ 5 & (nur Spurnetzwerk) & siehe norms_by_traces.json & \\\\","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.2 Exakte Krylov-Kette","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10124,"byte_start":9514,"id":"section:40ec3774bb3662e2f3e0","kind":"subsubsection","labels":["schlieuxdfung"],"line_end":217,"line_start":204,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/031-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Der Zwei-Boson-Singulettraum ist also mehr als eindimensional; die Kette ist exakt nicht geschlossen, und das Modell ist nicht allein durch die ν_n lösbar. Numerisch ist die Korrektur vernachlässigbar: w₂ koppelt nur an v₃ mit g·√(‖w₂‖²/ν₃) = 0,195 g.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.3 Schließung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11156,"byte_start":10124,"id":"section:d687cd83046aff4a8c81","kind":"subsubsection","labels":["ritz-obergrenzen"],"line_end":243,"line_start":218,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/031-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"In der orthonormierten Basis \\v₀ v_K, w₂\\ ist H (Δ = 1) tridiagonal plus w₂-Zweig: Diagonale n bzw. 2; Nebendiagonalen g·4√30, g·2√229, g·48√29770/229, ; w₂-Kopplung g·3√598377/11908.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.4 Ritz-Obergrenzen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11738,"byte_start":11156,"id":"section:a5f20016b683c3b163e4","kind":"subsubsection","labels":["observablen-auf-dem-ritz-zustand-gux3b4-120-k3"],"line_end":254,"line_start":244,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/031-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"⟨N_b⟩ = 0,8421 (Hellmann-Feynman ∂E/∂Δ = 0,8421); ⟨F Ω⟩ ² = 0,397; Bosonzahlverteilung 0,397 / 0,397 / 0,172 / 0,034; Shannon-Untergrenze der Boson-Loch-Verschränkung 1,66 bit (rigoros, weil die reduzierte Bosondichte in N_b blockdiagonal ist). Die Worker-Angaben „Überlapp 1/4`` und „Verschränkung 0,811 bit`` sind damit konsistent, aber auf einem nichtkonvergierten Zustand.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.5 Observablen auf dem Ritz-Zustand (g/Δ = 1/20, K=3)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":12337,"byte_start":11738,"id":"section:e72e8d58b5b8fa431ca8","kind":"subsubsection","labels":["geladene-ein-teilchen-antwort"],"line_end":270,"line_start":255,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/031-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Für jede Mode r (Guard r ∈ \\0, 5, 63\\; Transitivität der Quellsymmetrie):","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.6 Geladene Ein-Teilchen-Antwort","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13554,"byte_start":12337,"id":"section:ae0e5c7b2416182d1fcd","kind":"subsubsection","labels":["sektorauswahl-und-die-worker-behauptung"],"line_end":300,"line_start":271,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/031-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Untergrenzen aus der Casimir-Identität und quadratischer Ergänzung, H ≥ (1−θ)ΔN_b − (15g²/2θΔ)N_f, ausgewertet als max_θ min_\\N_b\\ je Sektor:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.7 Sektorauswahl und die Worker-Behauptung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13664,"byte_start":13554,"id":"section:fe423b8fbd9c53bd02df","kind":"subsection","labels":["feldwuxf6rterbuch-am-tatsuxe4chlichen-tensor"],"line_end":303,"line_start":301,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/031-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"5. Feldwörterbuch am tatsächlichen Tensor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15253,"byte_start":13664,"id":"section:7e19e21c6da792414609","kind":"subsubsection","labels":["symmetrieregel"],"line_end":343,"line_start":304,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/031-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Für Grassmann-Felder ψ_\\I,a\\ ist Σ_\\IJ\\Σ_\\ab\\ W_\\IJ\\K_\\ab\\ψ_\\I,a\\ψ_\\J,b\\ = ½Σ(T − Tᵀ) mit T_\\(Ia),(Jb)\\ = W_\\IJ\\K_\\ab\\. Weil W antisymmetrisch ist, verschwindet die Kopplung genau dann, wenn K antisymmetrisch ist; nur der symmetrische Teil des Spinorkerns koppelt. Auf allen 60 Zeilen explizit geprüft:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5.1 Symmetrieregel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":17183,"byte_start":15253,"id":"section:72f53f23c670b98d404e","kind":"subsubsection","labels":["chiralituxe4tsgradierungen"],"line_end":389,"line_start":344,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/031-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Der Trägergraph (64 Moden, 480 Kanten, Grad 15, dreiecksfrei) ist nicht bipartit; ein ungerader Zyklus ist [16, 45, 0, 30, 37]. Es gibt daher keine globale Chiralitätsaufteilung, unter der alle 60 Bosonen Vektoren wären. Für jede der 44 G-kovarianten Gradierungen ist jeder Kanal rein (nie gemischt), aber der Bosonmultiplett zerfällt:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5.2 Chiralitätsgradierungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1154,"byte_start":0,"id":"section:e41512d8a5f6e6e290e0","kind":"subsection","labels":["spurnetzwerk-normen"],"line_end":21,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/032-subsection-6-spurnetzwerk-normen-label-spurnetzwerk-norm.tex","status_markers_as_written":[],"summary_excerpt":"über bosonische Kohärenzzustände, die Onishi-Determinante det(1 − M̄M)\\^\\1/2\\ und Wick-Paarung der z-Variablen. Jedes Netzwerk ist eine Kontraktion von n Kopien des Tensors Φ_\\ij,kl\\ = Σ_A(M_A) \\ij\\(M_A)\\kl\\ (Einträge in \\−1,0,1\\). Netzwerke werden als 4-Bein-Multigraphen unter Knotenumbenennung und Slot-Tausch kanonisiert (n=4: 120 → 27 Klassen). Exaktheit: float64-Kontraktion mit Absolutwert-Begleitkontraktion ( Σa","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Spurnetzwerk-Normen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2735,"byte_start":1154,"id":"section:db3cd3f398aea37bc140","kind":"subsection","labels":["t1-t8"],"line_end":62,"line_start":22,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/032-subsection-6-spurnetzwerk-normen-label-spurnetzwerk-norm.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333@ Tor & Beitrag dieser Runde & Weiter offen \\\\ T1 & Exakte Kommutanten-Leiter A→B→Cc→Cs→C; Clock als äußeres Symmetrieelement & Welche Symmetrieoperationen der Compiler tatsächlich bereitstellt \\\\ T2 & Lochbild bewiesen; Z_h + Z_add = 1; ε_h, ε_add & Konvergierter Zustand, Renormierung, Grenzraum \\\\ T3 & - (ausgeklammert) & Räumlicher Träger \\\\ T4 & Kern-Sy","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. T1-T8","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3854,"byte_start":2735,"id":"section:b2985e5f28d80172d59a","kind":"subsection","labels":["die-jetzt-entscheidenden-pruxfcfungen"],"line_end":89,"line_start":63,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/032-subsection-6-spurnetzwerk-normen-label-spurnetzwerk-norm.tex","status_markers_as_written":[],"summary_excerpt":"Untergrenzen verschärfen. Die Casimir-Schranke trennt N=64 bei 1/20 nicht von N=62 und N=66. Eine Jacobi-Vergleichsschranke mit rigorosen Normschranken für TT† je Bosonzahl oder eine Temple-Schranke auf der Ritz-Kette würde den Beweisbereich anheben. Den Zwei-Boson-Singulettraum ausschreiben. w₂ ist der erste Zeuge; die volle Lanczos-Kette von H (nicht nur von T†) ab Tiefe 4 braucht w₂ und seine Nachfolger. Operation","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8. Die jetzt entscheidenden Prüfungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":5318,"byte_start":3854,"id":"section:e00312dd04a50beaef17","kind":"subsection","labels":["verifikation-und-nicht-uxfcbernommene-behauptungen"],"line_end":116,"line_start":90,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-common-process-20260915--tmp--pdfs--TFPT_Universalraum_Gemeinsamer_Prozess_Konsolidierung_2026-09-15_v1.6.8/sections/032-subsection-6-spurnetzwerk-normen-label-spurnetzwerk-norm.tex","status_markers_as_written":[],"summary_excerpt":"replay.py führt fünf Prüfer normal und unter -OO aus und verlangt byteidentische Ausgaben; Status, Hashes und Guardsummen stehen in replay_manifest.json. Guardzahlen zählen Prüfbedingungen, keine unabhängigen Theoreme. Exakt heißt ganzzahlig/rational; numerisch heißt float64 mit Toleranz-Guard (Ritz-Eigenwerte ab 3×3, Observablen, Erste-Moment-Auswertungen).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. Verifikation und nicht übernommene Behauptungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":1074,"byte_start":0,"id":"section:2c91d319f950b6b851fb","kind":"frontmatter","labels":[],"line_end":25,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/fable-runde3/paper/tfpt_anschluss_zellen_seam_2026-09-14"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-fable-kernfragen-20260910--fable-runde3--paper--tfpt_anschluss_zellen_seam_2026-09-14/preamble.tex","status_markers_as_written":[],"summary_excerpt":"satzSatz lemma[satz]Lemma TFPT-Anschluss: Zustandsgate, Trägerzellen und der [formula in source] -Faktor des Seams\\\\ Ergebnisse der Fable-Runden 3 (11.–14.\\ September 2026) als Fortsetzung des Manuskripts Vom geometrischen Compiler zum Prozess mit Aufzeichnung (Version 1.1) Claude Fable 5.1 im Cursor-Fenster tfpt-theoryv4\\\\ für Stefan Hamann\\\\ Prüfer und Zahlen: experiments/theory-contracts/\\\\ universalraum-fable-ker","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TFPT-Anschluss: Zustandsgate, Trägerzellen und der [formula in source] -Faktor des Seams\\\\ Ergebnisse der Fable-Runden 3 (11.–14.\\ September 2026) als Fortsetzung des Manuskripts Vom geometrischen Compiler zum Prozess mit Aufzeichnung (Version 1.1)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":29,"byte_start":0,"id":"section:356cc134d2b0054e3ef5","kind":"frontmatter","labels":[],"line_end":3,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/fable-runde3/paper/tfpt_anschluss_zellen_seam_2026-09-14"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-fable-kernfragen-20260910--fable-runde3--paper--tfpt_anschluss_zellen_seam_2026-09-14/sections/001-section-evidenzkonvention-und-abgrenzung.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":800,"byte_start":29,"id":"section:5f952ab932298d5fceb2","kind":"section","labels":[],"line_end":6,"line_start":4,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/fable-runde3/paper/tfpt_anschluss_zellen_seam_2026-09-14"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-fable-kernfragen-20260910--fable-runde3--paper--tfpt_anschluss_zellen_seam_2026-09-14/sections/001-section-evidenzkonvention-und-abgrenzung.tex","status_markers_as_written":[],"summary_excerpt":"Wie im Manuskript: gesetzt bezeichnet eine Ausgangsannahme, exakt eine Identität oder einen Beweis unter genannten Voraussetzungen, bedingt eine Folgerung mit zusätzlicher physikalischer Zuordnung, offen eine ungeschlossene Herkunfts- oder Existenzfrage. Alle Zahlen stammen aus den in Anhang A genannten Prüfern; jeder läuft normal und unter python -OO bytegleich. Kein Marker im Ledger wurde bewegt. Alle physikalische","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Evidenzkonvention und Abgrenzung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":4838,"byte_start":800,"id":"section:5b6b5fa61e78c1af1dcc","kind":"section","labels":[],"line_end":19,"line_start":7,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/fable-runde3/paper/tfpt_anschluss_zellen_seam_2026-09-14"],"relation_ids":["relation:343a9be0eb89a68c26df","relation:92f39ab8f5285c470ad1"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-fable-kernfragen-20260910--fable-runde3--paper--tfpt_anschluss_zellen_seam_2026-09-14/sections/001-section-evidenzkonvention-und-abgrenzung.tex","status_markers_as_written":[],"summary_excerpt":"Das Manuskript vom 14.\\ September endet mit drei Fragen: Folgt die Wechselwirkung aus dem Compiler? Wie entsteht Veränderung und eine auslesbare Uhr? Was passiert bei vielen gekoppelten Zellen? Alle drei werden hier gerechnet, nicht vorgeschlagen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zusammenfassung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5708,"byte_start":4838,"id":"section:5926380330792d2bbe2b","kind":"section","labels":[],"line_end":26,"line_start":20,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/fable-runde3/paper/tfpt_anschluss_zellen_seam_2026-09-14"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-fable-kernfragen-20260910--fable-runde3--paper--tfpt_anschluss_zellen_seam_2026-09-14/sections/001-section-evidenzkonvention-und-abgrenzung.tex","status_markers_as_written":[],"summary_excerpt":"Das Manuskript (Version 1.1) konstruiert auf den 60 Quellstrahlen des Compilers eine endliche Kette mit klassischem und quantenmechanischem Schatten, eine Vor-Messung mit Registern und ein ausdrücklich zusätzlich gesetztes Vierträger-Austauschmodell [formula in source] mit eindeutigem antisymmetrischem Grundzustand [formula in source] , Gap [formula in source] , dem Spektrum [formula in source] , [formula in source] ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ausgangslage","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5748,"byte_start":5708,"id":"section:4d49ddd0990f5786695b","kind":"section","labels":[],"line_end":27,"line_start":27,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/fable-runde3/paper/tfpt_anschluss_zellen_seam_2026-09-14"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-fable-kernfragen-20260910--fable-runde3--paper--tfpt_anschluss_zellen_seam_2026-09-14/sections/001-section-evidenzkonvention-und-abgrenzung.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Der Compiler wählt die Zelle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7653,"byte_start":5748,"id":"section:e6e4893a70280b706b85","kind":"subsection","labels":[],"line_end":43,"line_start":28,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/fable-runde3/paper/tfpt_anschluss_zellen_seam_2026-09-14"],"relation_ids":["relation:ff6e84b2b98d2c43558d"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-fable-kernfragen-20260910--fable-runde3--paper--tfpt_anschluss_zellen_seam_2026-09-14/sections/001-section-evidenzkonvention-und-abgrenzung.tex","status_markers_as_written":[],"summary_excerpt":"Mit der [formula in source] -Realisierung der 240 Wurzeln, [formula in source] auf den Koordinaten [formula in source] und [formula in source] auf [formula in source] , liest man die [formula in source] -Gewichte der 248 ab: [formula in source] also [formula in source] . Von den beiden Zweiträgersektoren [formula in source] kommt nur [formula in source] vor. Der Paarterm [formula in source] des Tetramers ist der Proj","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zweiträgersektoren in [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8333,"byte_start":7653,"id":"section:8a47a2f0d4bfbf803d88","kind":"subsection","labels":[],"line_end":46,"line_start":44,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/fable-runde3/paper/tfpt_anschluss_zellen_seam_2026-09-14"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-fable-kernfragen-20260910--fable-runde3--paper--tfpt_anschluss_zellen_seam_2026-09-14/sections/001-section-evidenzkonvention-und-abgrenzung.tex","status_markers_as_written":[],"summary_excerpt":"Für alle geordneten Paare [formula in source] mit [formula in source] liegt [formula in source] in [formula in source] ; es gibt 960 solche Paare und kein Ziel in [formula in source] oder [formula in source] . Repräsentationstheoretisch: [formula in source] . Eine über den Spinorsektor vermittelte Träger–Träger-Kopplung erzeugt daher nur antisymmetrische Paare. Die Ableitung eines effektiven [formula in source] aus d","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Klammer antisymmetrisiert Trägerindizes","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8360,"byte_start":8333,"id":"section:26435e5bead5b769d643","kind":"section","labels":[],"line_end":47,"line_start":47,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/fable-runde3/paper/tfpt_anschluss_zellen_seam_2026-09-14"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-fable-kernfragen-20260910--fable-runde3--paper--tfpt_anschluss_zellen_seam_2026-09-14/sections/001-section-evidenzkonvention-und-abgrenzung.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die relative Uhr","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9066,"byte_start":8360,"id":"section:0a13ef85d898cd076bfb","kind":"subsection","labels":[],"line_end":55,"line_start":48,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/fable-runde3/paper/tfpt_anschluss_zellen_seam_2026-09-14"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-fable-kernfragen-20260910--fable-runde3--paper--tfpt_anschluss_zellen_seam_2026-09-14/sections/001-section-evidenzkonvention-und-abgrenzung.tex","status_markers_as_written":[],"summary_excerpt":"Auf [formula in source] gilt [formula in source] für jede [formula in source] -Matrix [formula in source] ; jede kollektive Operation ändert nur eine globale Phase. Für einen Tick auf genau einem Träger gilt exakt [formula in source] wobei [formula in source] die Paarmarginale nach dem Tick ist. Beweis der Paarformel: [formula in source] . Beide Identitäten sind auf dem expliziten Singulett numerisch bestätigt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kollektiv unsichtbar, relativ sichtbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10909,"byte_start":9066,"id":"section:eb5830602d5801bd979a","kind":"subsection","labels":[],"line_end":74,"line_start":56,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/fable-runde3/paper/tfpt_anschluss_zellen_seam_2026-09-14"],"relation_ids":["relation:2631a3ec8455ece604aa","relation:e6e44d2ab6a08f95c127"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-fable-kernfragen-20260910--fable-runde3--paper--tfpt_anschluss_zellen_seam_2026-09-14/sections/001-section-evidenzkonvention-und-abgrenzung.tex","status_markers_as_written":[],"summary_excerpt":"Die Uhr des Compilers ist [formula in source] , der Familien-3-Zykel auf [formula in source] mit festem Anker [formula in source] ( v774), mit Lift [formula in source] , [formula in source] , [formula in source] . In [formula in source] fixiert [formula in source] genau drei der 15 Klassen [formula in source] ; nach der Punkt/Geraden-Dualität von [formula in source] ( v783: Klassen [formula in source] Kontexte) sind ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Lift ist chart-unabhängig fixiert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10943,"byte_start":10909,"id":"section:6590c50e3470c9a861d7","kind":"section","labels":[],"line_end":75,"line_start":75,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/fable-runde3/paper/tfpt_anschluss_zellen_seam_2026-09-14"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-fable-kernfragen-20260910--fable-runde3--paper--tfpt_anschluss_zellen_seam_2026-09-14/sections/001-section-evidenzkonvention-und-abgrenzung.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Von der Zelle zur Kette","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11556,"byte_start":10943,"id":"section:9fcbe6fd9447cc219992","kind":"subsection","labels":[],"line_end":78,"line_start":76,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/fable-runde3/paper/tfpt_anschluss_zellen_seam_2026-09-14"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-fable-kernfragen-20260910--fable-runde3--paper--tfpt_anschluss_zellen_seam_2026-09-14/sections/001-section-evidenzkonvention-und-abgrenzung.tex","status_markers_as_written":[],"summary_excerpt":"[formula in source] liegt in der Algebra der symmetrischen Gruppe [formula in source] auf [formula in source] . Nach Schur–Weyl zerfällt der Raum in [formula in source] ; [formula in source] wirkt als [formula in source] . [formula in source] wird in Youngs Orthogonalform aus den benachbarten Transpositionen aufgebaut (dünnbesetzt, zwei Einträge pro Zeile), die SU(4)-Vielfachheit folgt aus der Hook-Content-Formel. Fü","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Methode","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12345,"byte_start":11556,"id":"section:98212216b94bf8a6c792","kind":"subsection","labels":[],"line_end":92,"line_start":79,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/fable-runde3/paper/tfpt_anschluss_zellen_seam_2026-09-14"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-fable-kernfragen-20260910--fable-runde3--paper--tfpt_anschluss_zellen_seam_2026-09-14/sections/001-section-evidenzkonvention-und-abgrenzung.tex","status_markers_as_written":[],"summary_excerpt":"@rccccc@ [formula in source] & [formula in source] & Vielfachheit & Gap & Manuskript-Schranke [formula in source] & Grund-Irrep\\\\ 0 & 0 & 1 & 2,000 & 2,000 & [formula in source] \\\\ 0,5 & 0,2974 & 1 & 1,922 & 1,6875 & [formula in source] \\\\ 1 & 0,5635 & 1 & 1,818 & 1,375 & [formula in source] \\\\ 2 & 1,0000 & 1 & 1,586 & 0,750 & [formula in source] \\\\ 3,2 & 1,3729 & 1 & 1,340 & 0 & [formula in source] \\\\ 6 & 1,8377 & 1","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei vollständige Zellen mit einer Brücke","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13281,"byte_start":12345,"id":"section:d47832ca5a693daf34f7","kind":"subsection","labels":[],"line_end":104,"line_start":93,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/fable-runde3/paper/tfpt_anschluss_zellen_seam_2026-09-14"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-fable-kernfragen-20260910--fable-runde3--paper--tfpt_anschluss_zellen_seam_2026-09-14/sections/001-section-evidenzkonvention-und-abgrenzung.tex","status_markers_as_written":[],"summary_excerpt":"Offene Ketten aus [formula in source] Viererketten-Segmenten (nächste-Nachbar-Bindungen, Zwischenkopplung [formula in source] ), erste Anregung stets in der Adjungierten-Familie [formula in source] : @lccc@ Gap & [formula in source] ( [formula in source] ) & [formula in source] ( [formula in source] ) & [formula in source] ( [formula in source] )\\\\ [formula in source] & 0,2664 & 0,2552 & 0,2497\\\\ [formula in source] ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ketten von Zellen: gapped für [formula in source] , kritisch bei [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14630,"byte_start":13281,"id":"section:d6f4b2322476e4c7a6db","kind":"subsection","labels":[],"line_end":113,"line_start":105,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/fable-runde3/paper/tfpt_anschluss_zellen_seam_2026-09-14"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-fable-kernfragen-20260910--fable-runde3--paper--tfpt_anschluss_zellen_seam_2026-09-14/sections/001-section-evidenzkonvention-und-abgrenzung.tex","status_markers_as_written":[],"summary_excerpt":"Uniforme periodische Ringe [formula in source] ergeben [formula in source] mit der Sutherland-Geschwindigkeit [formula in source] (für [formula in source] ) und dem konformen Gewicht [formula in source] der [formula in source] in SU(4) [formula in source] . Die Grundenergie pro Träger extrapoliert zu [formula in source] gegen [formula in source] mit Sutherlands [formula in source] ; der [formula in source] -Koeffizie","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der uniforme Ring ist [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16273,"byte_start":14630,"id":"section:f943ac460349d7240fef","kind":"section","labels":[],"line_end":128,"line_start":114,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/fable-runde3/paper/tfpt_anschluss_zellen_seam_2026-09-14"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-fable-kernfragen-20260910--fable-runde3--paper--tfpt_anschluss_zellen_seam_2026-09-14/sections/001-section-evidenzkonvention-und-abgrenzung.tex","status_markers_as_written":[],"summary_excerpt":"Auf dem vollen neutralen Gauß-Sektor des Rotor/CAR-Rings (70 Materiemasken [formula in source] Schleifenfluss, 1190 Zustände) wurde geprüft, ob der Grundzustand den Generator in der lokalen Klasse [formula in source] über den Kovarianzkern [formula in source] bestimmt (modulo [formula in source] und der Sektoridentität [formula in source] ).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das Zustandsgate am Ringparent","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18041,"byte_start":16273,"id":"section:ba9522cc4af6db9d84e8","kind":"section","labels":[],"line_end":143,"line_start":129,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/fable-runde3/paper/tfpt_anschluss_zellen_seam_2026-09-14"],"relation_ids":["relation:5054ef1e4535e008ed91","relation:bc98e1a7b8ee3fbc60f4","relation:f7c408e591f57902df61"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-fable-kernfragen-20260910--fable-runde3--paper--tfpt_anschluss_zellen_seam_2026-09-14/sections/001-section-evidenzkonvention-und-abgrenzung.tex","status_markers_as_written":["[X]"],"summary_excerpt":"QFT4D.RGTEST.01 trägt [X] für den reinen SM-Lauf. Mit dem Inhalt aus PS.ALGEBRA.01 – Eichgruppe [formula in source] , Skalare nur aus [formula in source] , kein 126 – ist die Zweistufe [formula in source] bei 1-Loop ein lineares System und reproduziert v249 ziffergenau. Bei 2-Loop (gauge-only, Machacek–Vaughn; validiert an [formula in source] , [formula in source] , [formula in source] ): @lcccccc@ Inhalt oberhalb [f","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kopplungsvereinigung mit dem quelleigenen Pati–Salam-Inhalt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18072,"byte_start":18041,"id":"section:c31154d9ce63fcaa1448","kind":"section","labels":[],"line_end":144,"line_start":144,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/fable-runde3/paper/tfpt_anschluss_zellen_seam_2026-09-14"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-fable-kernfragen-20260910--fable-runde3--paper--tfpt_anschluss_zellen_seam_2026-09-14/sections/001-section-evidenzkonvention-und-abgrenzung.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Zwei Präzisierungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18665,"byte_start":18072,"id":"section:bdb9d2ad81791492cab1","kind":"paragraph","labels":[],"line_end":145,"line_start":145,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/fable-runde3/paper/tfpt_anschluss_zellen_seam_2026-09-14"],"relation_ids":["relation:37abd80dd1082b05d14a","relation:8b5d75ee23a40674a4f2","relation:e51cc22e8b791ec01d35"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-fable-kernfragen-20260910--fable-runde3--paper--tfpt_anschluss_zellen_seam_2026-09-14/sections/001-section-evidenzkonvention-und-abgrenzung.tex","status_markers_as_written":[],"summary_excerpt":"Auf den 248 Strömen der Stufe 1 des [formula in source] -Vakuummoduls hat die innere Glue- [formula in source] (Phasen [formula in source] auf [formula in source] ) die Spur [formula in source] , die geometrische Vierteldrehung [formula in source] die Spur [formula in source] ; die Quadrate sind [formula in source] bzw.\\ [formula in source] . Die transitive Identifikation Glue = konforme Monodromie ( QGEO.SYM.01) = e","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei [formula in source] .","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":19446,"byte_start":18665,"id":"section:5da3c2dfd59709ee909c","kind":"paragraph","labels":[],"line_end":147,"line_start":146,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/fable-runde3/paper/tfpt_anschluss_zellen_seam_2026-09-14"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-fable-kernfragen-20260910--fable-runde3--paper--tfpt_anschluss_zellen_seam_2026-09-14/sections/001-section-evidenzkonvention-und-abgrenzung.tex","status_markers_as_written":[],"summary_excerpt":"Mit [formula in source] (Kawahigashi–Longo–Müger), die das Repo für den Glue-Index 4 benutzt, gilt für jedes injektive [formula in source] : [formula in source] = Hecke-Überlagerungsindex von [formula in source] auf [formula in source] (Zählfunktion [formula in source] , Pol bei [formula in source] ). Pimsner–Popa macht [formula in source] zur bedingten Entropie; das Vakuum ist unter den Dualgruppen-Automorphismen fe","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Hecke-Index = Jones-Index.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":20420,"byte_start":19446,"id":"section:eb1aa8a2e4d55b3cc2c4","kind":"section","labels":[],"line_end":156,"line_start":148,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/fable-runde3/paper/tfpt_anschluss_zellen_seam_2026-09-14"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-fable-kernfragen-20260910--fable-runde3--paper--tfpt_anschluss_zellen_seam_2026-09-14/sections/001-section-evidenzkonvention-und-abgrenzung.tex","status_markers_as_written":[],"summary_excerpt":"Der Hüllensatz fixiert Zellstruktur und Vorzeichen, nicht [formula in source] , nicht den Graphen, nicht die Cross-Register-Kopplung der Vor-Messung. Die Superaustausch-Ableitung von [formula in source] aus den [formula in source] -Strukturkonstanten ist formuliert, nicht ausgeführt. Die Uhr ist ein Protokoll auf einem gesetzten Modell; eine Zeit in Sekunden folgt nicht. Die Phasenreferenz für die Periode 12 ist eine","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Grenzen und offene Punkte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":21338,"byte_start":20420,"id":"section:e153c335b069ee599fe9","kind":"section","labels":[],"line_end":165,"line_start":157,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/fable-runde3/paper/tfpt_anschluss_zellen_seam_2026-09-14"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-fable-kernfragen-20260910--fable-runde3--paper--tfpt_anschluss_zellen_seam_2026-09-14/sections/001-section-evidenzkonvention-und-abgrenzung.tex","status_markers_as_written":[],"summary_excerpt":"Superaustausch aus der Klammer: effektive Träger–Träger-Kopplung zweiter Ordnung über [formula in source] ; Erfolg: [formula in source] und Graph aus Strukturkonstanten; Kill: jede Freiheit, die [formula in source] erlaubt. [formula in source] an [formula in source] koppeln: SU(4)-Kette plus zehn Majorana-Moden mit Kondo-artiger [formula in source] -Kopplung; Ziel: [formula in source] und die [formula in source] -Ver","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nächste Schritte in Rangfolge","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":22528,"byte_start":21338,"id":"section:5cd560246f81af39b2ac","kind":"section","labels":[],"line_end":180,"line_start":166,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/fable-runde3/paper/tfpt_anschluss_zellen_seam_2026-09-14"],"relation_ids":["relation:097a541d087dd74f5f0e","relation:200d8c97ce7fc33d0ec6","relation:274d69ede5246a671997","relation:2e0528f3c427ba333ee1","relation:3efc6f9db108c0cc7162","relation:48390e2f21a722848a7c","relation:49ff17c8817052e02404","relation:7d0cf29c2e25ab8efd58","relation:b26d10fafe83d2dc7aa9","relation:b3bd9e52121483eeb885","relation:bd6c937c288d125cb253","relation:c61abcd3c62dbdd7335f","relation:d596c8fb724591468308","relation:dcb178e1e53706d6e20d"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-fable-kernfragen-20260910--fable-runde3--paper--tfpt_anschluss_zellen_seam_2026-09-14/sections/001-section-evidenzkonvention-und-abgrenzung.tex","status_markers_as_written":[],"summary_excerpt":"Alle Prüfer liegen in experiments/theory-contracts/ universalraum-fable-kernfragen-20260910/ fable-runde3/; Hashes in QUELLEN.json. @p6.2cmp7.2cml@ Prüfer & Inhalt & Laufzeit\\\\ check_followups_q1q2q3.py & Hüllensatz, Klammer, Lift-Spuren, offene Ketten [formula in source] & 22 s\\\\ check_cells_and_clock.py & [formula in source] -Inhalt, Uhrtabelle, zwei Zellen, Ringe [formula in source] & 4,5 min\\\\ check_state_selects","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproduktion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":22546,"byte_start":22528,"id":"section:508113d1cb6c6ef93388","kind":"section","labels":[],"line_end":181,"line_start":181,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/fable-runde3/paper/tfpt_anschluss_zellen_seam_2026-09-14"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-fable-kernfragen-20260910--fable-runde3--paper--tfpt_anschluss_zellen_seam_2026-09-14/sections/001-section-evidenzkonvention-und-abgrenzung.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Formeln","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":22947,"byte_start":22546,"id":"section:618506c20406404aedc4","kind":"paragraph","labels":[],"line_end":182,"line_start":182,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/fable-runde3/paper/tfpt_anschluss_zellen_seam_2026-09-14"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-fable-kernfragen-20260910--fable-runde3--paper--tfpt_anschluss_zellen_seam_2026-09-14/sections/001-section-evidenzkonvention-und-abgrenzung.tex","status_markers_as_written":[],"summary_excerpt":"Für ein Standard-Young-Tableau [formula in source] der Form [formula in source] und benachbarte Einträge [formula in source] mit axialem Abstand [formula in source] gilt [formula in source] , [formula in source] = Tableau mit vertauschten [formula in source] . Beliebige Transpositionen sind Konjugierte benachbarter. 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Der Universalraum soll diese Grammatik als einen ausführbaren Prozess realisieren. Der entscheidende Unterschied ist der zwischen einem erlaubten Zusammenhang und einer tatsächlich erzeugten physikalischen Entwicklung.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. 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Keine fremde Quelldatei wurde verändert. Die Herkunftsdateien gehören zu parallel fortgeschriebenen Arbeitsständen; Dateipins sind deshalb wichtiger als Versionsnamen allein.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2.1 Quellenstand und Reproduktionsgrenzen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10361,"byte_start":8144,"id":"section:3d098c396e2b41ecae95","kind":"subsubsection","labels":["uxfcbernahmeentscheidung"],"line_end":215,"line_start":168,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/001-section-tfpt-universalraum-die-richtige-einfache.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 2 ) * 0.5000 > p( - 2 ) * 0.5000@ Aussage aus den Eingaben & Entscheidung für v1.6.7 \\\\ Korrigierter Anfangskommutant 3829536 / 1444233216 & Bestätigt; keine neue Größe gegenüber v1.6.6 \\\\ Nur SU(4) oder nur Spin(10) als zusätzliche Kontrollen & Übernommen; echte Zwischenstufen statt binärer Verfügbarkeit \\\\ Volle Gruppe plus alle Modenbesetzungen erzeugt volle Sektoralgebra & Unabhängig bestätigt, ausdrückl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2.2 Übernahmeentscheidung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10508,"byte_start":10361,"id":"section:9081a9f406c0cb70f91f","kind":"subsection","labels":["vollstuxe4ndig-geluxf6st-der-erste-verzweigte-singulettbereich"],"line_end":218,"line_start":216,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/001-section-tfpt-universalraum-die-richtige-einfache.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"3. 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Bei k Bosonen gibt es 2k Löcher. Der Singulettbereich auf dieser Stufe liegt in","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.1 Warum vier und nicht eins?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15267,"byte_start":13143,"id":"section:e2cb44847159afcbe6bb","kind":"subsubsection","labels":["nicht-nur-gezuxe4hlt-die-vier-zustuxe4nde-und-ihre-kopplungen"],"line_end":340,"line_start":286,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":["relation:2455d4c6138933cf6e6d","relation:251db3664b66bebcdda3","relation:9f5c0115c79ace32137f"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/001-section-tfpt-universalraum-die-richtige-einfache.tex","status_markers_as_written":[],"summary_excerpt":"In der durch eine Bosonparität äquivalenten Lochdarstellung sei [formula in source] . Alle 108240 von null verschiedenen Koeffizienten von [formula in source] wurden neu berechnet, einschließlich der Boson-Fakultätsnormen. Das ergibt [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.2 Nicht nur gezählt: die vier Zustände und ihre Kopplungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16217,"byte_start":15267,"id":"section:6c92ba064e3f267fb228","kind":"subsubsection","labels":["der-vollstuxe4ndig-bestimmte-sechszustands-ausschnitt"],"line_end":369,"line_start":341,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/001-section-tfpt-universalraum-die-richtige-einfache.tex","status_markers_as_written":[],"summary_excerpt":"Die Kompression auf alle Singuletts mit k kleiner oder gleich zwei ist exakt äquivalent zu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.3 Der vollständig bestimmte Sechszustands-Ausschnitt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":119,"byte_start":0,"id":"section:f03b61e373e667910bc8","kind":"subsection","labels":["die-richtige-einfache-kette-wiederholung-von-h"],"line_end":3,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/002-subsection-4-die-richtige-einfache-kette-wiederholung-vo.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"4. Die richtige einfache Kette: Wiederholung von H","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1161,"byte_start":119,"id":"section:df3bbb59b4db4dd5bdad","kind":"subsubsection","labels":["der-fehler-war-die-gleichsetzung-zweier-verschiedener-stufen"],"line_end":27,"line_start":4,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/002-subsection-4-die-richtige-einfache-kette-wiederholung-vo.tex","status_markers_as_written":[],"summary_excerpt":"Die Vektoren [formula in source] sind nach Bosonzahl geordnet. 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Ein Weg, der den nächsten nicht enthaltenen Lanczos-Vektor erreicht und nach F zurückkehrt, benötigt mindestens zehn Schritte. Aus der Tridiagonalität folgt deshalb die angegebene Momentengenauigkeit, ohne die übrige Kette zu erfinden.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.3 Zehn vollständige Energiemomente der gefüllten Referenz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5341,"byte_start":4326,"id":"section:82c239ef7a656535357c","kind":"subsubsection","labels":["kleine-rigorose-verschuxe4rfung-der-energiegrenze"],"line_end":151,"line_start":123,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/002-subsection-4-die-richtige-einfache-kette-wiederholung-vo.tex","status_markers_as_written":[],"summary_excerpt":"Am Prüfpunkt g geteilt durch Delta gleich 1/20 hat die niedrigste Eigenenergie der Fünfer-Kompression die durch rationale Sturm-Zählung zertifizierte Lage","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.4 Kleine, rigorose Verschärfung der Energiegrenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7002,"byte_start":5341,"id":"section:ad6f2d9224228edcd21b","kind":"subsection","labels":["vollstuxe4ndig-geluxf6st-die-innere-bilineare-zerlegung"],"line_end":190,"line_start":152,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/002-subsection-4-die-richtige-einfache-kette-wiederholung-vo.tex","status_markers_as_written":[],"summary_excerpt":"Die sechs Dimensionen sind 1, 45, 210, 15, 675 und 3150. Der offene Rest ist also nicht mehr unbestimmt:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Vollständig gelöst: die innere bilineare Zerlegung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7136,"byte_start":7002,"id":"section:ae68cd72148d4908d6b9","kind":"subsection","labels":["welche-operationen-wirklich-verfuxfcgbar-sein-muxfcssten"],"line_end":193,"line_start":191,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/002-subsection-4-die-richtige-einfache-kette-wiederholung-vo.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"6. Welche Operationen wirklich verfügbar sein müssten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8974,"byte_start":7136,"id":"section:97b96fcb8a41f3079dd6","kind":"subsubsection","labels":["die-algebraische-frage-ist-pruxe4ziser-beantwortet"],"line_end":236,"line_start":194,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/002-subsection-4-die-richtige-einfache-kette-wiederholung-vo.tex","status_markers_as_written":[],"summary_excerpt":"Im N=3-Sektor bleiben für verschiedene angenommene Operationsalphabete folgende komplexe Kommutantdimensionen:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6.1 Die algebraische Frage ist präziser beantwortet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9925,"byte_start":8974,"id":"section:da20778dd4ad016cdf5f","kind":"subsubsection","labels":["warum-blouxdfes-lesen-noch-keine-fehlende-bewegung-erzeugt"],"line_end":254,"line_start":237,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/002-subsection-4-die-richtige-einfache-kette-wiederholung-vo.tex","status_markers_as_written":[],"summary_excerpt":"Ohne die zusätzlich gewährten Gruppenkontrollen erhalten X, Nb, der Clock und alle Modenbesetzungen weiterhin mindestens eine nichtskalare Farb-Cartanladung. Jede Komposition dieser Operatoren behält diese Erhaltung. Die alleinige Erlaubnis, mehr Moden zu unterscheiden, hebt das Hindernis also nicht auf.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6.2 Warum bloßes Lesen noch keine fehlende Bewegung erzeugt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11564,"byte_start":9925,"id":"section:ed10beafbda3e99a04f7","kind":"subsection","labels":["feldwuxf6rterbuch-gesicherte-teile-und-korrigierte-reichweite"],"line_end":285,"line_start":255,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/002-subsection-4-die-richtige-einfache-kette-wiederholung-vo.tex","status_markers_as_written":[],"summary_excerpt":"Für die unveränderte antisymmetrische Paarmatrix und gleichhändige Weylfelder verschwindet die ableitungsfreie skalare Kontraktion. 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Die fundamentale Frage: was fehlt wirklich?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13067,"byte_start":11674,"id":"section:ca85b38f56bcb0ad399a","kind":"subsubsection","labels":["ein-uxfcberpruxfcfbarer-unterbestimmtheitssatz"],"line_end":317,"line_start":289,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/002-subsection-4-die-richtige-einfache-kette-wiederholung-vo.tex","status_markers_as_written":[],"summary_excerpt":"Betrachte bei festem W dieselbe Familie [formula in source] . Alle diese Hamiltonoperatoren besitzen die gleiche innere Quellsymmetrie, dieselbe Ladungserhaltung und denselben kommutierenden endlichen Clock. Dennoch unterscheiden sie sich dynamisch. Schon für dieselbe gefüllte Referenz F ist die dimensionslose Momentenkombination","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.1 Ein überprüfbarer Unterbestimmtheitssatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14404,"byte_start":13067,"id":"section:ce881e140cfebded6a33","kind":"subsubsection","labels":["der-kleinste-tragfuxe4hige-forschungsansatz"],"line_end":340,"line_start":318,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/002-subsection-4-die-richtige-einfache-kette-wiederholung-vo.tex","status_markers_as_written":[],"summary_excerpt":"Für eine einzelne Antwortrechnung sollte der relevante Raum nicht von vornherein der gesamte Fockraum sein. 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Ihre Komp","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.2 Der kleinste tragfähige Forschungsansatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16855,"byte_start":14404,"id":"section:fe56ad5839cc30693707","kind":"subsection","labels":["aktueller-stand-t1-bis-t8"],"line_end":395,"line_start":341,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/002-subsection-4-die-richtige-einfache-kette-wiederholung-vo.tex","status_markers_as_written":[],"summary_excerpt":"Die folgende Tabelle ordnet die Beiträge dieser Runde den bisherigen offenen Beweispflichten zu; sie benennt keine neue Definition der ursprünglichen Tore.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. Aktueller Stand T1 bis T8","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":1531,"byte_start":0,"id":"section:42ab33c3e318578f6c48","kind":"subsection","labels":["die-drei-nuxe4chsten-entscheidenden-untersuchungen"],"line_end":33,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/003-subsection-10-die-drei-n-chsten-entscheidenden.tex","status_markers_as_written":[],"summary_excerpt":"Den minimalen Ursprungsvertrag auswählen. Teil B klassifiziert die kleinen symmetrieverträglichen Terme und trennt echte Erweiterungen von einem bloßen Wechsel der Bosonvariablen. Der Compiler muss diese Auswahl und die relativen Parameter begründen. Symmetrie allein tut das noch nicht. Die gemeinsame Schattenkarte am vorhandenen Tensor prüfen. Derselbe Zustand und dieselben Operationen müssen die verschiedenen Ausle","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10. 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Die ausgelieferte ZIP wird nach dem Entpacken erneut geprüft.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"11. Reproduktion und Veröffentlichung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3103,"byte_start":2709,"id":"section:24062bfa1aa8db3b6e0a","kind":"subsubsection","labels":["schluss-in-einem-satz"],"line_end":66,"line_start":58,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/003-subsection-10-die-drei-n-chsten-entscheidenden.tex","status_markers_as_written":[],"summary_excerpt":"Die einfache Regel ist vorhanden; ihr erster verzweigter Zustandsbereich und die richtige kleine Rechenkette sind jetzt genauer gelöst. Was noch fehlt, ist die aus dem Ursprung folgende Auswahl und Ausführung dieses Prozesses als dieselbe physikalische Welt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Schluss in einem Satz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3254,"byte_start":3103,"id":"section:686ead9d83dc4fed71fe","kind":"section","labels":["neue-vogelperspektive-derselbe-prozess-in-verschiedenen-ansichten"],"line_end":69,"line_start":67,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/003-subsection-10-die-drei-n-chsten-entscheidenden.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Neue Vogelperspektive: derselbe Prozess in verschiedenen Ansichten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5856,"byte_start":3254,"id":"section:445bc93b9a567224b8da","kind":"subsection","labels":["b1.-was-sich-durch-die-drei-weiteren-texte-uxe4ndert"],"line_end":124,"line_start":70,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":["relation:5d5b5de1320c4c868760","relation:607c367d03f5ca2d60a0","relation:d249ee1b19bcf87999e7"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/003-subsection-10-die-drei-n-chsten-entscheidenden.tex","status_markers_as_written":[],"summary_excerpt":"Die nachgereichten Texte werden als Vorschläge geprüft, nicht als bewiesene Ergebnisse oder neue Arbeitsanweisungen übernommen. Die stärkste gemeinsame Idee trägt: Innere Identität, Zusammensetzung, Ort, Zeit und Auslese dürfen nicht stillschweigend dasselbe Label erhalten. Eine immer genauere Rechnung innerhalb einer Bank ersetzt diese Verbindungen nicht. Die voranstehenden lokalen Ergebnisse bleiben gültig; die fun","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B1. Was sich durch die drei weiteren Texte ändert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8252,"byte_start":5856,"id":"section:bb57f2d79e3d7a50a419","kind":"subsection","labels":["b2.-noethers-frage-welche-unterschiede-kann-die-dynamik-uxfcberhaupt-veruxe4ndern"],"line_end":177,"line_start":125,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/003-subsection-10-die-drei-n-chsten-entscheidenden.tex","status_markers_as_written":[],"summary_excerpt":"Bei ungebrochener innerer Gruppe G zerfällt ein Zustandsraum als","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B2. Noethers Frage: Welche Unterschiede kann die Dynamik überhaupt verändern?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10644,"byte_start":8252,"id":"section:cea93c1ca326f1224317","kind":"subsection","labels":["b3.-korrelation-ist-noch-kein-eingriff-ein-exakt-geluxf6stes-gegenbeispiel"],"line_end":230,"line_start":178,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/003-subsection-10-die-drei-n-chsten-entscheidenden.tex","status_markers_as_written":[],"summary_excerpt":"Die Kreuzkorrelation startet bei null und verändert sich mit der Zeit. Es gibt dennoch keinerlei Signal von A nach B: Alle A-lokalen Operationen kommutieren mit jedem zeitentwickelten B-lokalen Observablen. Für jedes spurtreue lokale Quanteninstrument bleibt daher die unbedingte B-Statistik unverändert. Eine Konditionierung auf ein Messergebnis in A wäre etwas anderes.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B3. Korrelation ist noch kein Eingriff: ein exakt gelöstes Gegenbeispiel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11821,"byte_start":10644,"id":"section:a92237e565747471c9c5","kind":"subsection","labels":["b4.-die-einfachste-fehlende-auswahl-warum-genau-dieser-hamiltonoperator"],"line_end":254,"line_start":231,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/003-subsection-10-die-drei-n-chsten-entscheidenden.tex","status_markers_as_written":[],"summary_excerpt":"Die Z4-Idee besitzt einen präzisen Kern. Ein ganzzahliger, auf jedem Grad konstanter Ladungslift mit neutralem Grad null müsste bei den entsprechenden nichtverschwindenden Klammern erfüllen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B4. Die einfachste fehlende Auswahl: Warum genau dieser Hamiltonoperator?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15662,"byte_start":11821,"id":"section:672bee44f4eee0f2f51e","kind":"subsubsection","labels":["b4.1-zwei-zusuxe4tzliche-terme-am-unveruxe4nderten-tensor"],"line_end":338,"line_start":255,"numbered_or_version_tokens_as_written":["B4.1"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/003-subsection-10-die-drei-n-chsten-entscheidenden.tex","status_markers_as_written":[],"summary_excerpt":"Der Bosonträger (10,6) besitzt eine symmetrische reelle invariante Paarung eta. In der nativen Gewichtsbasis koppelt sie entgegengesetzte Spin- Vektorgewichte und komplementäre Farbpaare. Es gilt eta Quadrat gleich eins. Damit sind bereits","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B4.1 Zwei zusätzliche Terme am unveränderten Tensor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17853,"byte_start":15662,"id":"section:a16af0d89acc08f425a9","kind":"subsubsection","labels":["b4.2-eine-weitere-vereinfachung-neue-dynamik-oder-andere-teilchenvariablen"],"line_end":387,"line_start":339,"numbered_or_version_tokens_as_written":["B4.2"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/003-subsection-10-die-drei-n-chsten-entscheidenden.tex","status_markers_as_written":[],"summary_excerpt":"Manche scheinbaren Erweiterungen beschreiben nur andere Bosonvariablen. Auf der reellen, phasengleichen Teilfamilie setze man","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B4.2 Eine weitere Vereinfachung: neue Dynamik oder andere Teilchenvariablen?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":140,"byte_start":0,"id":"section:2fcfc96bc22dbc74f05d","kind":"subsection","labels":["b5.-holografie-und-schatten-die-konkrete-native-verbindung"],"line_end":3,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/004-subsection-b5-holografie-und-schatten-die-konkrete-nativ.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"B5. Holografie und Schatten: die konkrete native Verbindung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1646,"byte_start":140,"id":"section:3e09be34309db8bf91d2","kind":"subsubsection","labels":["b5.1-ein-kodierer-ist-bereits-vorhanden"],"line_end":38,"line_start":4,"numbered_or_version_tokens_as_written":["B5.1"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/004-subsection-b5-holografie-und-schatten-die-konkrete-nativ.tex","status_markers_as_written":[],"summary_excerpt":"Der vorhandene, frisch geprüfte Tensor erfüllt WW dagger gleich 8 I60. Daher ist","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B5.1 Ein Kodierer ist bereits vorhanden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3303,"byte_start":1646,"id":"section:22ba02a1978cc24aac56","kind":"subsubsection","labels":["b5.2-warum-das-noch-kein-holografischer-fehlerkorrekturcode-ist"],"line_end":72,"line_start":39,"numbered_or_version_tokens_as_written":["B5.2"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/004-subsection-b5-holografie-und-schatten-die-konkrete-nativ.tex","status_markers_as_written":[],"summary_excerpt":"Für jeden der 64 Fermionmoden wurde die logische Kompression seiner Besetzungsmessung berechnet:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B5.2 Warum das noch kein holografischer Fehlerkorrekturcode ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5925,"byte_start":3303,"id":"section:2241b5bfd4aae3ecbc49","kind":"subsubsection","labels":["b5.3-was-mehrere-schatten-gemeinsam-eindeutig-machen-kuxf6nnen"],"line_end":127,"line_start":73,"numbered_or_version_tokens_as_written":["B5.3"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/004-subsection-b5-holografie-und-schatten-die-konkrete-nativ.tex","status_markers_as_written":[],"summary_excerpt":"Seien Ri festgelegte Mess- oder Reduktionsabbildungen eines gemeinsamen Zustands rho. Für eine endliche, nicht eingeschränkte Zustandsklasse sind alle Zustände aus den Schatten Ri(rho) genau dann unterscheidbar, wenn auf den hermiteschen spurlosen Differenzen gilt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B5.3 Was mehrere Schatten gemeinsam eindeutig machen können","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8116,"byte_start":5925,"id":"section:b0820169f203319d8117","kind":"subsubsection","labels":["b5.4-die-drei-wuxe4nde-muxfcssen-unterschiedlich-gepruxfcft-werden"],"line_end":174,"line_start":128,"numbered_or_version_tokens_as_written":["B5.4"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/004-subsection-b5-holografie-und-schatten-die-konkrete-nativ.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333@ Gemeinte Wand & Was sie gegenwärtig bedeutet & Welcher Anschluss fehlt \\\\ Universalraum & Grenze zwischen gemeinsamem Operatorobjekt und seinen reduzierten Ansichten & Ein gemeinsamer verfügbarer Operationssatz, Zustand und Rekonstruktionsvertrag \\\\ TFPT & Grenze zwischen interner Compilerstruktur und physikalischer Realisierung & Herleitung der Ausführun","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B5.4 Die drei Wände müssen unterschiedlich geprüft werden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11444,"byte_start":8116,"id":"section:bac834d63effa8b50392","kind":"subsection","labels":["b6.-die-einfachste-neue-arbeitsrichtung-und-ihre-abnahmekriterien"],"line_end":236,"line_start":175,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/004-subsection-b5-holografie-und-schatten-die-konkrete-nativ.tex","status_markers_as_written":[],"summary_excerpt":"Der plausible übersehene Punkt ist kein weiterer großer Tensor: Wir brauchen die gemeinsame Regel, die festlegt, welche Operationen, Teilchenvariablen und Ansichten tatsächlich dieselbe Ausführung beschreiben. Noethers Symmetrieprüfung sagt, was erhalten bleibt. Die Schattenprüfung sagt, was überhaupt unterscheidbar ist. Der Eingriffstest sagt, was etwas anderes beeinflussen kann. Zusammen sind diese drei kleinen Fra","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B6. Die einfachste neue Arbeitsrichtung und ihre Abnahmekriterien","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15968,"byte_start":11444,"id":"section:4d22b60b777cb9a7c604","kind":"subsection","labels":["b7.-abgleich-des-zuletzt-eingesandten-berichts-v1.6.3"],"line_end":321,"line_start":237,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/004-subsection-b5-holografie-und-schatten-die-konkrete-nativ.tex","status_markers_as_written":[],"summary_excerpt":"Der sechste Text dieser Runde, „Operationssatz, nativer Grundzustand und Feldwörterbuch``, enthält überwiegend bereits berücksichtigte Befunde: die Kommutantenleiter, das Lochbild, die Normen der ersten Stufen, den nichtverschwindenden Seitenzweig und den verschwindenden Weyl-Skalarkanal. Seine zweite vorgeschlagene Folgeaufgabe wurde inzwischen wesentlich weitergeführt: Alle vier Zwei-Boson-Singuletts sind konstruie","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B7. Abgleich des zuletzt eingesandten Berichts v1.6.3","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16413,"byte_start":15968,"id":"section:de75af879906bbb81aef","kind":"section","labels":["historischer-anhang-vollstuxe4ndige-fassung-v1.6.6"],"line_end":330,"line_start":322,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/004-subsection-b5-holografie-und-schatten-die-konkrete-nativ.tex","status_markers_as_written":[],"summary_excerpt":"Die folgende vollständige Fassung wird unverändert bewahrt. Maßgeblich für den aktuellen Status sind die vorangestellten Kapitel v1.6.7. 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Die Frage aus dem neuen Text ist damit auf algebraischer Ebene beantwortet.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. 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Das ist ein Forschungsauftrag, kein Widerspruch zur bisherigen Schranke.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7.1 Eine sinnvolle Hypothese, kein bereits identifiziertes universelles Objekt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7895,"byte_start":7243,"id":"section:2eed1f99e63e3750a943","kind":"subsubsection","labels":["der-vorgeschlagene-kill-test-muss-korrigiert-werden"],"line_end":176,"line_start":165,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/006-subsection-5-neuer-kleiner-transportzeuge-mit-tats-chlic.tex","status_markers_as_written":[],"summary_excerpt":"Für unabhängige orthogonale Banken kann Π_AΠ_B deren gemeinsame Parität sein. 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Ein nichtverschwindender Kommutator mit einer lok","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7.2 Der vorgeschlagene Kill-Test muss korrigiert werden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9901,"byte_start":7895,"id":"section:d65d24be8d2a5a187004","kind":"subsubsection","labels":["der-einfachste-false-positive-ein-signal-ohne-bewegung"],"line_end":222,"line_start":177,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/006-subsection-5-neuer-kleiner-transportzeuge-mit-tats-chlic.tex","status_markers_as_written":[],"summary_excerpt":"Seien a=c1, b=(c1+c2)/√2 auf zwei globalen CAR-Moden und H=ωN. Dann haben die beiden Einteilchen-Chartzustände bereits Überlappung 1/√2. In ihrer nichtorthogonalen Basis ist K=ωS mit einem nichtverschwindenden Offdiagonalelement. Trotzdem bleibt die betreffende Wahrscheinlichkeit zu jeder Zeit genau 1/2. Es wurde nichts transportiert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7.3 Der einfachste False-Positive: Ein Signal ohne Bewegung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11796,"byte_start":9901,"id":"section:4c568723e7fcc766c4fd","kind":"subsubsection","labels":["was-nicht-automatisch-folgt"],"line_end":266,"line_start":223,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/006-subsection-5-neuer-kleiner-transportzeuge-mit-tats-chlic.tex","status_markers_as_written":[],"summary_excerpt":"Zeit: Für einen Grundzustand ist e \\-itH\\Ω=e \\-itE0\\Ω; sein physischer Zustand bleibt gleich. Das ist kein eigener Zeitpfeil. Nichtstationäre Präparation, Korrelationen und Records müssen ausgewiesen werden. Eichfeld: Für bloße Basiswechsel Uxy=Vx†Vy teleskopiert jede geschlossene Holonomie zu I. Echte Krümmung braucht zusätzliche Verbindungs-/Transportdaten oder einen nachgewiesenen Mechanismus. Spin: Zwei Orientier","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7.4 Was nicht automatisch folgt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14288,"byte_start":11796,"id":"section:9bd14da4f52922be1ca1","kind":"subsection","labels":["t1-t8-gemeinsamer-fortschritt-ohne-statusinflation"],"line_end":317,"line_start":267,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/006-subsection-5-neuer-kleiner-transportzeuge-mit-tats-chlic.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333@ Front & In dieser Revision weitergekommen & Noch erforderlicher Nachweis \\\\ T1 - Ursprung und Auswahl & Explizite Identität zwischen Quell-Clock und innerer Spinwirkung; Operationsverträge genauer & Primitive Auswahl von P1/P2, Träger, erlaubten Instrumenten und Zustand \\\\ T2 - Half-Charge/E8-Feld & Bestehender geladener Pol bleibt abgesichert, innere Dar","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8. T1-T8: gemeinsamer Fortschritt ohne Statusinflation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":16165,"byte_start":14288,"id":"section:82f943ae344b0b28e23a","kind":"subsection","labels":["die-nuxe4chsten-drei-arbeiten---klein-gemeinsam-und-entscheidbar"],"line_end":351,"line_start":318,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/006-subsection-5-neuer-kleiner-transportzeuge-mit-tats-chlic.tex","status_markers_as_written":[],"summary_excerpt":"A. Den gemeinsamen Quellenvertrag wirklich hinschreiben. Zwei lokale Einbettungen, ihr CAR-Gram, globale Parität und Ladung, ursprüngliche Operationen und ein einziges H angeben. Abbruch für eine Kandidatenfassung, wenn sie nur zwei Koordinatenansichten desselben unveränderten Signals umbenennt. Die gemeinsamen Generatoren müssen einen nachweislich neuen Antwortprozess ermöglichen, nicht nur eine andere Beschriftung.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. Die nächsten drei Arbeiten - klein, gemeinsam und entscheidbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17266,"byte_start":16165,"id":"section:71c070fdfefb31f444ca","kind":"subsection","labels":["belege-und-reproduzierbarkeit"],"line_end":373,"line_start":352,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/006-subsection-5-neuer-kleiner-transportzeuge-mit-tats-chlic.tex","status_markers_as_written":[],"summary_excerpt":"Die drei Eingangstexte bleiben unverändert im Prüfpaket. Ein Teil-Audit reproduziert die 1127 gelieferten Guards; eigene Programme behandeln Clock/Casimir, Quellenreichweite, direkte Krylov-Kontraktion, basisunabhängige Feldbedingungen, den tatsächlichen Vierzustandskanal und die Überlappungsgegenkontrollen. Exakte und numerische Teile sind in den jeweiligen Ergebnisdateien getrennt markiert. Die abschließenden Zählu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10. Belege und Reproduzierbarkeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":131,"byte_start":0,"id":"section:bcdb82e35b18b77efffc","kind":"section","labels":["anhang-a-quellenpruxfcfung-symmetrie-und-verfuxfcgbarkeit"],"line_end":3,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/007-section-anhang-a-quellenpr-fung-symmetrie-und.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Anhang A: Quellenprüfung Symmetrie und Verfügbarkeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":502,"byte_start":131,"id":"section:894639b2cfe62cfe99b4","kind":"section","labels":["quellenpruxfcfung-quellsymmetrie-verfuxfcgbarkeit-und-lorentztypen"],"line_end":11,"line_start":4,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/007-section-anhang-a-quellenpr-fung-symmetrie-und.tex","status_markers_as_written":[],"summary_excerpt":"Stand: 15. September 2026. Eigenständiger Teil-Audit der ersten neuen Anlage und dreier Programme. Keine Änderung der gelieferten Programme, Ergebnisdateien oder Dokumente. Keine Aussage, dass T1-T8 geschlossen seien.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Quellenprüfung: Quellsymmetrie, Verfügbarkeit und Lorentztypen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":2875,"byte_start":502,"id":"section:0d757e0e39d27b470e10","kind":"subsection","labels":["reproduktion"],"line_end":73,"line_start":12,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":["relation:3a09d6d456f717d489ee"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/007-section-anhang-a-quellenpr-fung-symmetrie-und.tex","status_markers_as_written":[],"summary_excerpt":"Alle drei Programme wurden vollständig gelesen und anschließend in isolierten Kopien ausgeführt. Die relevanten Tensoren wurden an ihre von den unveränderten Programmen erwarteten relativen Orte kopiert. Normaler und optimierter Lauf reproduzieren jeweils die gelieferten Ergebnisdateien byteidentisch, ohne Standardfehlerausgabe:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Reproduktion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":4847,"byte_start":2875,"id":"section:85142be72ce3d6468a74","kind":"subsection","labels":["bestuxe4tigte-mathematik"],"line_end":124,"line_start":74,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/007-section-anhang-a-quellenpr-fung-symmetrie-und.tex","status_markers_as_written":[],"summary_excerpt":"Der N=3-Raum zerfällt als Darstellung von Spin(10) × SU(4) in sieben Isotypien. Drei haben Multiplizität zwei, die anderen vier Multiplizität eins. Die zwei Fockteile Λ³(C⁶⁴) und C⁶⁰⊗C⁶⁴ sind jeweils multiplizitätsfrei; der gesamte N=3-Raum ist es ausdrücklich nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Bestätigte Mathematik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":6713,"byte_start":4847,"id":"section:fddbb93f6de02d05deb8","kind":"subsection","labels":["invarianz-und-kovarianz-auseinanderhalten"],"line_end":161,"line_start":125,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/007-section-anhang-a-quellenpr-fung-symmetrie-und.tex","status_markers_as_written":[],"summary_excerpt":"Dann gilt A0 ⊂ C, dim A0=14 und dim C=Σ m_i²=16. 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Invarianz und Kovarianz auseinanderhalten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8299,"byte_start":6713,"id":"section:50ab2cc7c5be13c7ecb8","kind":"subsection","labels":["verfuxfcgbarkeit-ist-keine-universelle-janein-frage"],"line_end":202,"line_start":162,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/007-section-anhang-a-quellenpr-fung-symmetrie-und.tex","status_markers_as_written":[],"summary_excerpt":"Ein vorgegebener Hamiltonoperator allein gewährt nicht bereits das unabhängige Schalten von X und Nb. Am erklärten Punkt g/Δ=1/20 besitzt ein fixes H im N=3-Raum acht verschiedene Energien, also nur eine acht-dimensionale kommutative Spektralalgebra. Die großzügigere Annahme unabhängiger Kontrollen X,Nb ergibt 14.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Verfügbarkeit ist keine universelle Ja/Nein-Frage","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9297,"byte_start":8299,"id":"section:a648cf4752a0982ddf0c","kind":"subsection","labels":["der-clock-satz-ist-im-gelieferten-checker-nicht-gepruxfcft"],"line_end":221,"line_start":203,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/007-section-anhang-a-quellenpr-fung-symmetrie-und.tex","status_markers_as_written":[],"summary_excerpt":"operation_symmetry.py:478 schreibt den Normalisator- und Nichts-hinzufügen-Satz als need(True, ...). Insgesamt enthält diese Datei neun solche als Prüfbedingungen gezählten theoretischen Folgerungen. Einige sind durch die vorausgehende Mathematik gut begründet; der bloße grüne Guard zertifiziert sie jedoch nicht unabhängig.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Der Clock-Satz ist im gelieferten Checker nicht geprüft","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":10976,"byte_start":9297,"id":"section:5e6560b3a22bfb6e8dbd","kind":"subsection","labels":["feldtyp-was-tatsuxe4chlich-erzwungen-ist"],"line_end":253,"line_start":222,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/007-section-anhang-a-quellenpr-fung-symmetrie-und.tex","status_markers_as_written":[],"summary_excerpt":"Für ein lokales, ableitungsfreies Bilinear zweier gleichhändiger Weylfelder, das alle 64 inneren Quellenmarken unverändert als unabhängige innere Komponenten und genau den gegebenen antisymmetrischen Tensor W verwendet, gilt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Feldtyp: was tatsächlich erzwungen ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12110,"byte_start":10976,"id":"section:4bb44b7b9170f62dd64b","kind":"subsubsection","labels":["konkreter-gegencheck-jenseits-der-ableitungsfreien-klasse"],"line_end":276,"line_start":254,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/007-section-anhang-a-quellenpr-fung-symmetrie-und.tex","status_markers_as_written":[],"summary_excerpt":"Der allgemeine Satz »ein Vektor verlangt ψ†ψ und scheitert deshalb an der Ladung« ist falsch, sobald Ableitungen zugelassen werden. Beispielsweise ist","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Konkreter Gegencheck jenseits der ableitungsfreien Klasse","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12640,"byte_start":12110,"id":"section:81081fe79e97b3c58a91","kind":"subsection","labels":["konsequenz"],"line_end":288,"line_start":277,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/007-section-anhang-a-quellenpr-fung-symmetrie-und.tex","status_markers_as_written":[],"summary_excerpt":"Die neuen Quellen verkleinern und präzisieren den endlichen N=3-Operationsraum. 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Die hier angegebenen Matrix- und Graphbefunde beziehen sich auf denselben gepinnten Tensor W mit SHA-256 3f00a0892157a691e4ef26920c3702772c7bf76a250fad98ff04a079bb64b763.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Unabhängige Prüfung: Krylov-Verzweigung und Feldwörterbuch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14697,"byte_start":13325,"id":"section:1f221bad829a9a79a9fb","kind":"subsection","labels":["der-neue-nichtschluss-ist-exakt-bestuxe4tigt"],"line_end":342,"line_start":303,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/007-section-anhang-a-quellenpr-fung-symmetrie-und.tex","status_markers_as_written":[],"summary_excerpt":"Für v_n=(T†) n F habe ich u=T T† v_2=T v_3 unmittelbar aus den 480 nativen Paaren neu kontrahiert. 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Der neue Nichtschluss ist exakt bestätigt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15831,"byte_start":14697,"id":"section:b2383295bdec0cf9049d","kind":"subsection","labels":["das-mitgelieferte-ground-json-ist-veraltet-und-teilweise-falsch"],"line_end":368,"line_start":343,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/007-section-anhang-a-quellenpr-fung-symmetrie-und.tex","status_markers_as_written":[],"summary_excerpt":"Die aktuelle Pythonquelle hat SHA-256 8ae0f2f103ba0cb0a5cb832681a33130b6756fe627395368b6be635587a2eb02. 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Die sechste Dezimalstelle ist richtig - aber nur für die eine zusätzliche Richtung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3017,"byte_start":1751,"id":"section:2b3d92e6e57ef70696e1","kind":"subsubsection","labels":["eigene-einfache-folgeherleitung-das-vollstuxe4ndige-ritz-residuum"],"line_end":73,"line_start":46,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/008-subsection-3-die-sechste-dezimalstelle-ist-richtig-aber-.tex","status_markers_as_written":[],"summary_excerpt":"Sei ψ₃ der normierte Ritz-Eigenvektor in span(v₀,…,v₃), und c₃ seine Komponente entlang v₃/√ν₃. 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Deshalb gilt exakt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eigene einfache Folgeherleitung: Das vollständige Ritz-Residuum","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4553,"byte_start":3017,"id":"section:47e25be8c27c2eda6cf2","kind":"subsection","labels":["der-bereits-bewiesene-native-grundsatz-bleibt-guxfcltig"],"line_end":100,"line_start":74,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/008-subsection-3-die-sechste-dezimalstelle-ist-richtig-aber-.tex","status_markers_as_written":[],"summary_excerpt":"Der ältere, gepinnte Beweis lautet: Für Δ 0 und 0 g /Δ≤1/20 besitzt der unveränderte μ=0-Hamiltonoperator einen eindeutigen globalen Grundzustand in N=64; er ist ein Spin(10)×SU(4)-Singulett. Bei 1/20 bestehen außerdem positive Lücke und die bekannten Energie-, Besetzungs- und Polschranken.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. 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Was die neue Perspektive sinnvoll beiträgt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9206,"byte_start":7322,"id":"section:da3c5395f0e644fd7fd8","kind":"subsection","labels":["exakter-zwei-moden-gegenbeleg-zum-vorgeschlagenen-parituxe4tstest"],"line_end":228,"line_start":175,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/010-subsubsection-6-3-clock-mittelung-ist-m-glich-aber-der-f.tex","status_markers_as_written":[],"summary_excerpt":"Jeder Chart ist für sich ein gültiger Einmoden-CAR-Raum, aber","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Exakter Zwei-Moden-Gegenbeleg zum vorgeschlagenen Paritätstest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11352,"byte_start":9206,"id":"section:41fedcb10849d4c55e77","kind":"subsection","labels":["noch-wichtiger-ein-uxfcberlappungsmatrixelement-ist-kein-transport"],"line_end":279,"line_start":229,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/010-subsubsection-6-3-clock-mittelung-ist-m-glich-aber-der-f.tex","status_markers_as_written":[],"summary_excerpt":"Wähle den vollkommen trivialen Hamiltonoperator H₀=ωN, mit N=c₁†c₁+c₂†c₂. Die Matrix der Hamilton-Matrixelemente in diesen beiden Chartvektoren ist","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Noch wichtiger: Ein Überlappungsmatrixelement ist kein Transport","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13045,"byte_start":11352,"id":"section:d36068fc31a17e2c0558","kind":"subsection","labels":["chartwechsel-verbindungen-und-kruxfcmmung-sind-verschiedene-daten"],"line_end":314,"line_start":280,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/010-subsubsection-6-3-clock-mittelung-ist-m-glich-aber-der-f.tex","status_markers_as_written":[],"summary_excerpt":"Wenn mehrere Charts lediglich vollständige orthonormale Rahmen R_x desselben festen Vektorraums sind, lauten die Basiswechsel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Chartwechsel, Verbindungen und Krümmung sind verschiedene Daten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14189,"byte_start":13045,"id":"section:1dddffa923faeaa96440","kind":"subsection","labels":["zeit-ein-grundzustand-bewegt-sich-unter-seinem-h-nicht-beobachtbar"],"line_end":336,"line_start":315,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/010-subsubsection-6-3-clock-mittelung-ist-m-glich-aber-der-f.tex","status_markers_as_written":[],"summary_excerpt":"Die im Anhang skizzierte Entwicklung Ω -> exp(−itH)Ω erzeugt bei einem Energieeigenzustand lediglich exp(−itE₀)Ω. Der Dichteoperator bleibt exakt gleich. Der Checker bestätigt das an einem kleinen Fockzustand.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Zeit: Ein Grundzustand bewegt sich unter seinem H nicht beobachtbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":15742,"byte_start":14189,"id":"section:21c2bf0544a0c097c05b","kind":"subsection","labels":["der-binuxe4re-index-muss-als-freiheitsgrad-bewiesen-werden"],"line_end":371,"line_start":337,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/010-subsubsection-6-3-clock-mittelung-ist-m-glich-aber-der-f.tex","status_markers_as_written":[],"summary_excerpt":"Die skalare Hilfsdublett-Reparatur braucht zwei unabhängige, gleichgeladene Komponenten, auf denen eine nichtentartete antisymmetrische Form wirkt. Eine Orientierung der Überlappungsgeometrie könnte so etwas liefern, tut es aber nicht allein durch das Vorhandensein zweier Bezeichnungen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Der binäre Index muss als Freiheitsgrad bewiesen werden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1604,"byte_start":0,"id":"section:9150e79375c4dc1e5efa","kind":"subsection","labels":["operationsgeometrie-benuxf6tigt-mehr-als-erreichbarkeit"],"line_end":32,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/011-subsection-7-operationsgeometrie-ben-tigt-mehr-als.tex","status_markers_as_written":[],"summary_excerpt":"Minimale Kosten erfüllen unter geeigneter Komposition eine Dreiecksungleichung. Ohne reversible Operationen mit symmetrischen Kosten ist die resultierende Funktion jedoch nur eine gerichtete Distanz; der Checker liefert den gerichteten Dreierzyklus mit d(A,B)=1, d(B,A)=2. Unerreichbarkeit ergibt unendliche Distanzen. Kostenfreie Chartwechsel können verschiedene Beschreibungen auf Distanz null setzen; dann muss zunäch","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. Operationsgeometrie benötigt mehr als Erreichbarkeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":2410,"byte_start":1604,"id":"section:4be44d7258e8058d58c0","kind":"subsection","labels":["gravitation-bleibt-eine-dynamische-verpflichtung"],"line_end":48,"line_start":33,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/011-subsection-7-operationsgeometrie-ben-tigt-mehr-als.tex","status_markers_as_written":[],"summary_excerpt":"Die linearen Fluktuationen einer aus der Quelle bestimmten globalen Geometrie zu prüfen, ist ein sinnvoller Forschungsauftrag. Eine transversale spurfreie Tensorzerlegung allein garantiert aber weder einen masselosen physikalischen Spin-2-Pol noch positive Norm, genau zwei Helizitäten oder universelle Kopplung. Selbst ein gesunder linearer Spin-2-Sektor ersetzt nicht den Nachweis seiner nichtlinearen Eich-/Zwangsstru","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8. Gravitation bleibt eine dynamische Verpflichtung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3457,"byte_start":2410,"id":"section:efc61bbbe61163eb3b63","kind":"subsection","labels":["p-versus-np-eine-konkrete-korrektur"],"line_end":68,"line_start":49,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/011-subsection-7-operationsgeometrie-ben-tigt-mehr-als.tex","status_markers_as_written":[],"summary_excerpt":"Der Anhang sagt, P≠NP würde einen intrinsisch exponentiellen Suchaufwand bedeuten. Das ist falsch. P≠NP würde ausschließen, dass jedes NP-Entscheidungsproblem deterministisch in Polynomialzeit gelöst werden kann. Es folgt daraus keine exponentielle untere Schranke: Eine hypothetische Laufzeit wie 2 (√n) ist superpolynomiell und zugleich subexponentiell. Stärkere Exponentialzeitaussagen benötigen zusätzliche Sätze bez","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. P versus NP: eine konkrete Korrektur","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5426,"byte_start":3457,"id":"section:62e5f2af7d10d053189c","kind":"subsection","labels":["ein-korrigierter-wirklich-entscheidbarer-anschluss-test"],"line_end":112,"line_start":69,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/011-subsection-7-operationsgeometrie-ben-tigt-mehr-als.tex","status_markers_as_written":[],"summary_excerpt":"Ein sinnvoller nächster Versuch besteht nicht nur aus einem unbeschrifteten P U_AB P. Er sollte zusammen liefern:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10. Ein korrigierter, wirklich entscheidbarer Anschluss-Test","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5531,"byte_start":5426,"id":"section:dc05aca490c520afb278","kind":"section","labels":["anhang-e-arithmetischer-schleifenvorschlag"],"line_end":115,"line_start":113,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/011-subsection-7-operationsgeometrie-ben-tigt-mehr-als.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Anhang E: arithmetischer Schleifenvorschlag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6093,"byte_start":5531,"id":"section:7dfef19386e6d6283d12","kind":"section","labels":["zusatzpruxfcfung-schleifen-primzahlen-und-der-universalraum-vorschlag"],"line_end":130,"line_start":116,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/011-subsection-7-operationsgeometrie-ben-tigt-mehr-als.tex","status_markers_as_written":[],"summary_excerpt":"September 2026, v1.6.6. Quellenprüfung des nachgereichten Textes 59dc0059-8914-48ca-953d-85933f66e00b, kein neuer RH-Beweis und kein neuer arithmetischer Quellenoperator. Seine Aussagen über gemeinsame lokale Beschreibungen werden getrennt im Überlappungsaudit behandelt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zusatzprüfung: Schleifen, Primzahlen und der Universalraum-Vorschlag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":6511,"byte_start":6093,"id":"section:b5e8372221d2709cbea6","kind":"subsection","labels":["urteil"],"line_end":139,"line_start":131,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/011-subsection-7-operationsgeometrie-ben-tigt-mehr-als.tex","status_markers_as_written":[],"summary_excerpt":"Ein globaler Wegraum ist eine sinnvolle Suchklasse; ein Eulerprodukt über primitive Wege ist noch nicht das Eulerprodukt der Riemannschen Zetafunktion. Die im Text vorgeschlagene Xi-Determinante bleibt ein hinreichendes Ziel unter expliziten Operatorannahmen. Das Umbenennen ihres noch fehlenden Operators in „Generator der primitiven Schleifen`` konstruiert ihn nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Urteil","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":7851,"byte_start":6511,"id":"section:94d32a5ca2d7e1840685","kind":"subsection","labels":["was-die-endliche-bank-tatsuxe4chlich-ausschlieuxdft"],"line_end":168,"line_start":140,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/011-subsection-7-operationsgeometrie-ben-tigt-mehr-als.tex","status_markers_as_written":[],"summary_excerpt":"Der beibehaltene Beweis aus v1.6.5 gilt für den ursprünglichen Hamiltonoperator mit 64 Fermion- und 60 Bosonmoden, Δ 0. Der Hilbertraum ist wegen der Bosonen nicht endlichdimensional. Endlich ist die Zahl der Moden. Mit C=960g²/Δ folgt aus quadratischem Ergänzen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Was die endliche Bank tatsächlich ausschließt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10085,"byte_start":7851,"id":"section:a1fb63c69d3aa985705b","kind":"subsection","labels":["der-kleinste-gegencheck-zur-primzahl-automatik"],"line_end":214,"line_start":169,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/011-subsection-7-operationsgeometrie-ben-tigt-mehr-als.tex","status_markers_as_written":[],"summary_excerpt":"Nehmen wir einen gerichteten Knoten mit zwei erlaubten Schleifen a und b. Neben a und b ist auch ab ein primitiver periodischer Weg: Es ist keine Potenz eines kürzeren Wortes. Ebenso entstehen weitere gemischte primitive Wörter. Setzen wir nachträglich L(a)=log 2, L(b)=log 3, so hat ab die Länge log 6. Die 6 ist keine Primzahl. „Primitiver Weg`` bedeutet nicht „arithmetische Primzahl``.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Der kleinste Gegencheck zur Primzahl-Automatik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":11183,"byte_start":10085,"id":"section:8cd31d8a135a9f71d577","kind":"subsection","labels":["die-richtige-rh-zielbedingung"],"line_end":243,"line_start":215,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/011-subsection-7-operationsgeometrie-ben-tigt-mehr-als.tex","status_markers_as_written":[],"summary_excerpt":"Sei A strikt positiv und selbstadjungiert, mit kompakter Inverser und A \\-2\\ von Spurklasse. Dann ist der Fredholm-Ausdruck","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. 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Die aktuelle Konsistenzprüfung und der anschließende Wiederaufbauversuch brachen mit","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. 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Mit der Dreiecksungleichung, [formula in source] und der gesondert geprüften Positivität vor dem Quadrieren folgt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.5 Dieselbe ursprüngliche Fermionantwort ohne anfänglichen Filter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3115,"byte_start":1480,"id":"section:c9e74845acb006a04a9a","kind":"subsection","labels":["warum-die-herkunftsluxfccke-nicht-durch-luxe4ngeres-rechnen-verschwindet"],"line_end":65,"line_start":36,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/013-subsubsection-4-5-dieselbe-urspr-ngliche-fermionantwort-.tex","status_markers_as_written":[],"summary_excerpt":"Sei [formula in source] die lokale Fermionparität. Die bisher angegebenen bankinternen Paarumwandlungen, Zahloperationen, zahlenerhaltenden Symmetrielifts sowie reine Bosonverbindungen kommutieren mit jeder [formula in source] . Jede endliche Komposition, lineare Kombination, Adjungierung und jeder durch solche Operatoren realisierte einzelne Messzweig tut das ebenfalls. Starke beschränkte Grenzwerte bleiben im Kommu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Warum die Herkunftslücke nicht durch längeres Rechnen verschwindet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3235,"byte_start":3115,"id":"section:dd40ef739793d9437293","kind":"subsection","labels":["was-von-der-arithmetischen-untersuchung-truxe4gt"],"line_end":68,"line_start":66,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/013-subsubsection-4-5-dieselbe-urspr-ngliche-fermionantwort-.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"6. Was von der arithmetischen Untersuchung trägt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4853,"byte_start":3235,"id":"section:1c322e4f9d7016c99efc","kind":"subsubsection","labels":["eine-einzelne-endliche-bank-ist-nicht-der-volle-logarithmusgenerator"],"line_end":105,"line_start":69,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/013-subsubsection-4-5-dieselbe-urspr-ngliche-fermionantwort-.tex","status_markers_as_written":[],"summary_excerpt":"Quadratisches Ergänzen liefert mit der nativen Casimirnorm [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6.1 Eine einzelne endliche Bank ist nicht der volle Logarithmusgenerator","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6420,"byte_start":4853,"id":"section:96445a07838ee8ca073c","kind":"subsubsection","labels":["primzahlen-kuxf6nnen-eine-gewuxe4hlte-dynamik-organisieren-erzwingen-sie-aber-nicht"],"line_end":136,"line_start":106,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/013-subsubsection-4-5-dieselbe-urspr-ngliche-fermionantwort-.tex","status_markers_as_written":[],"summary_excerpt":"Auf [formula in source] kann man [formula in source] definieren. Die additive Primfaktorbesetzung erklärt dann die Eulerstruktur. Der Definitionsbereich lautet [formula in source] . Dass quantenstatistische Systeme mit Zeta-Zustandssumme existieren, ist bereits ein Ergebnis von https://alainconnes.org/wp-content/uploads/bostconnesscan.pdfBost und Connes. Das ist ein relevanter Anschluss, nicht die fehlende native Her","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6.2 Primzahlen können eine gewählte Dynamik organisieren, erzwingen sie aber nicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":7403,"byte_start":6420,"id":"section:856ac53b2edc89047b41","kind":"subsubsection","labels":["der-rh-zielsatz-bleibt-unbewiesen"],"line_end":160,"line_start":137,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/013-subsubsection-4-5-dieselbe-urspr-ngliche-fermionantwort-.tex","status_markers_as_written":[],"summary_excerpt":"für einen strikt positiven selbstadjungierten Operator [formula in source] mit kompakter Inverser und [formula in source] von Spurklasse wäre tatsächlich hinreichend: Die gesamte rechte Funktion hat ihre Nullstellen nur bei reellen [formula in source] , einschließlich Multiplizitäten. Aber dieser Operator und die gesamte Funktionsidentität sind nicht konstruiert. Ein Operator mit lediglich den Imaginärteilen der Null","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6.3 Der RH-Zielsatz bleibt unbewiesen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9547,"byte_start":7403,"id":"section:f2a2540bf039e794a727","kind":"subsection","labels":["die-lokale-polnuxe4herung-wird-pruxe4ziser-das-relativistische-feld-bleibt-offen"],"line_end":204,"line_start":161,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":["relation:54d08e401a94ea8d76ec"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/013-subsubsection-4-5-dieselbe-urspr-ngliche-fermionantwort-.tex","status_markers_as_written":[],"summary_excerpt":"Die externe Resolventenabschätzung ist korrekt: Im Kreis mit Radius [formula in source] um den tatsächlichen, unbekannten negativen Pol [formula in source] gilt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. Die lokale Polnäherung wird präziser, das relativistische Feld bleibt offen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12270,"byte_start":9547,"id":"section:91c4733af4b09a9f4ebf","kind":"subsection","labels":["wuxe4hrend-der-arbeit-entdeckte-uxe4nderung-kommutant-7-richtig-einordnen"],"line_end":263,"line_start":205,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/013-subsubsection-4-5-dieselbe-urspr-ngliche-fermionantwort-.tex","status_markers_as_written":[],"summary_excerpt":"Die strikte Originalquellenprüfung stoppte korrekt, als eine andere Arbeit den früheren nativen Bericht ergänzte. Der alte Stand mit Hash 1062e13fe0fb79cce015657a7b4d40a61e9639922ff95fa60c689c0068c38ffc blieb eingefroren. Der gesonderte geänderte Entwurf hat Hash ab745e74b1232b1ddf35dd0e0d0da4ace0176c797d769e5db8bedd0010bcba6a. Die in dieser Revision verwendeten Energie- und Polzertifikate änderten sich bei dieser Pr","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8. Während der Arbeit entdeckte Änderung: „Kommutant 7`` richtig einordnen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14648,"byte_start":12270,"id":"section:16f68578e90c6a20f967","kind":"subsection","labels":["t1-t8-was-dieses-ergebnis-beitruxe4gt-und-nicht-beitruxe4gt"],"line_end":314,"line_start":264,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/013-subsubsection-4-5-dieselbe-urspr-ngliche-fermionantwort-.tex","status_markers_as_written":[],"summary_excerpt":"Die Begriffe folgen der aktuellen offenen Problemliste und ihrer Forschungszuordnung. Keine Akzeptanzmarkierung wurde heraufgesetzt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. T1-T8: was dieses Ergebnis beiträgt und nicht beiträgt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17072,"byte_start":14648,"id":"section:9cbe99dc0228188f4a66","kind":"subsection","labels":["nuxe4chste-entscheidende-arbeiten-mit-klaren-abbruchkriterien"],"line_end":357,"line_start":315,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/013-subsubsection-4-5-dieselbe-urspr-ngliche-fermionantwort-.tex","status_markers_as_written":[],"summary_excerpt":"A. Die Quelle des geraden Gesamtlinks finden. Nicht noch eine riesige Kontrollmatrix bauen, sondern für jeden tatsächlich ursprünglichen Generator [formula in source] prüfen, ob [formula in source] bei erhaltener Gesamtparität möglich ist. Eine positive Antwort muss Generator, Teilbereichsdefinition, Hilbertraum, Gaussreferenz und Matrixelement liefern. Bleiben alle Generatoren lokal gerade, ist die Suche nach dem Li","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10. Nächste entscheidende Arbeiten mit klaren Abbruchkriterien","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1370,"byte_start":0,"id":"section:64f62dbd4fd0f6e0c693","kind":"subsection","labels":["reproduktion-und-ehrliche-liefergrenze"],"line_end":27,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":["relation:8f80301f6a3a0e678deb","relation:e9025b99e29f1b8a69ae"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/014-subsection-11-reproduktion-und-ehrliche.tex","status_markers_as_written":[],"summary_excerpt":"replay.py –frozen-only führt die fünf Prüfer normal und mit -OO aus, vergleicht beide JSON-Ergebnisse und die zwei externen Originalberichte, prüft alle eingefrorenen Quellen und protokolliert Änderungen der Originalorte gesondert. Ein Fehler führt zu FAIL. Der zuvor aufgetretene Live-Quellenfehler bleibt in source_drift_failure_receipt.json sichtbar.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"11. Reproduktion und ehrliche Liefergrenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2056,"byte_start":1370,"id":"section:074d4990ac31521f5585","kind":"section","labels":["nachpruxfcfung-der-beiden-zuletzt-eingegangenen-untersuchungen"],"line_end":41,"line_start":28,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/014-subsection-11-reproduktion-und-ehrliche.tex","status_markers_as_written":[],"summary_excerpt":"Quellen: die Anlagen 8e110ae1-19e2-4d47-bfc8-ebe4fe9ab81b und b928b72a-6669-4c67-a75d-124095791c6f, unverändert eingefroren. Zusätzlich wurden die vier genannten Programme t1_fixed.py, stabilizer.py, t5_twobank.py, t5_varresp.py vollständig gelesen und archiviert. Eine eigene Nachrechnung prüft die kritischen Folgerungen; sie ist kein vollständiger Replay aller sechs Sonden des fremden Arbeitsordners.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nachprüfung der beiden zuletzt eingegangenen Untersuchungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4994,"byte_start":2056,"id":"section:3d61301ff3737f40b15d","kind":"subsection","labels":["uxfcbersicht-uxfcbernehmen-korrigieren-oder-offenlassen"],"line_end":101,"line_start":42,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/014-subsection-11-reproduktion-und-ehrliche.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 2 ) * 0.5000 > p( - 2 ) * 0.5000@ Neue Aussage & Ergebnis der Prüfung \\\\ Innerer Viererzyklus erhält alle 60 W-Kanäle & Bestätigt, jetzt einschließlich der richtigen Fermion-Vorzeichen und explizitem Bosonlift \\\\ Grundzustandseindeutigkeit/Singulett/Gaplücke weiterhin unbekannt & Überholter Stand: unter dem festgelegten nativen Vertrag bereits bewiesen; voller Vektor weiter unbekannt \\\\ Leerer Grundzustand f","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Übersicht: übernehmen, korrigieren oder offenlassen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6593,"byte_start":4994,"id":"section:254e468686efe63f8666","kind":"subsection","labels":["positiver-neuer-anschluss-der-korrekt-angehobene-viererzyklus"],"line_end":134,"line_start":102,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/014-subsection-11-reproduktion-und-ehrliche.tex","status_markers_as_written":[],"summary_excerpt":"Die Abbildung der Fermionmarken lautet [formula in source] . Auf Paaren ist zwingend das Exteriorvorzeichen zu beachten: Falls [formula in source] , erhält das sortierte Paar ein Minuszeichen. Der gelieferte stabilizer.py lässt dieses Zeichen weg. Das wäre im Allgemeinen falsch; für den untersuchten Viererzyklus überlebt das positive Resultat jedoch auch den korrekten Test.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Positiver neuer Anschluss: der korrekt angehobene Viererzyklus","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8348,"byte_start":6593,"id":"section:3904c826f732c2af7138","kind":"subsection","labels":["warum-der-einteilchen-abschluss-den-fock-operationssatz-nicht-schlieuxdft"],"line_end":167,"line_start":135,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/014-subsection-11-reproduktion-und-ehrliche.tex","status_markers_as_written":[],"summary_excerpt":"Die Irreduzibilität der Einteilchendarstellung kann ihre assoziative Matrixalgebra zu [formula in source] machen. Daraus folgt nicht, dass jede Matrix als ein zulässiges physisches Wort verfügbar ist, und auch nicht, dass ihre zweite Quantisierung bereits erzeugt wird.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. 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Insbesondere hat der Energie-Impuls-Tensor [formula in source] , mit passender Spurbehandlung, Dimension [formula in source] . Ein Energie-Impuls-Tensor kann bereits in einer festen Hintergrundraumzeit definiert werden; dynamische Diffeomorphismen müssen nicht vorausgesetzt werden, um dieses Gegenbeis","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5.2 Der behauptete Spin-2-Ausschluss ist falsch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13837,"byte_start":12897,"id":"section:d1eecc704232b73b096b","kind":"subsubsection","labels":["kinetik-ist-nicht-generell-verboten"],"line_end":284,"line_start":263,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/014-subsection-11-reproduktion-und-ehrliche.tex","status_markers_as_written":[],"summary_excerpt":"Der bilineare Ein-Ableitungs-Term mit einem (1,0)-Feld und seinem Adjungierten besitzt keinen Lorentzskalar. Mit zwei Ableitungen existiert aber etwa","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5.3 (1,0)-Kinetik ist nicht generell verboten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14993,"byte_start":13837,"id":"section:ee8a6678c12f45685a1f","kind":"subsection","labels":["die-vierzustandsrechnung-richtig-lesen"],"line_end":305,"line_start":285,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/014-subsection-11-reproduktion-und-ehrliche.tex","status_markers_as_written":[],"summary_excerpt":"Das Modell mit [formula in source] , Bosonverbindung η und Diagonalen (0,Δ,Δ,0) erlaubt kohärenten Paartransport. Die exakte Identität [formula in source] stimmt. Unsere unabhängige Fließkomma-Abtastung reproduziert auf [formula in source] mit Schrittweite .05 den größten gefundenen Wert .998920021869 bei 2484.05. Der erste Gitter-Lokalhöchstwert liegt bereits bei 6.05. Weder „erster Maximalzeitpunkt`` noch ein globa","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Die Vierzustandsrechnung richtig lesen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16612,"byte_start":14993,"id":"section:dabd4f5ef9c631420d40","kind":"subsection","labels":["konsequenz-fuxfcr-die-nuxe4chste-forschungsrevision"],"line_end":341,"line_start":306,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/014-subsection-11-reproduktion-und-ehrliche.tex","status_markers_as_written":[],"summary_excerpt":"Die sinnvollen positiven Anschlüsse sind jetzt schärfer:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. Konsequenz für die nächste Forschungsrevision","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17131,"byte_start":16612,"id":"section:af18f417563cb829f222","kind":"section","labels":["historischer-beweisanhang-vollstuxe4ndiger-nativer-herleitungsstand-v1.6.4"],"line_end":352,"line_start":342,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/014-subsection-11-reproduktion-und-ehrliche.tex","status_markers_as_written":[],"summary_excerpt":"Dieser Anhang bewahrt die frühere Herleitung vollständig. Seine damaligen Statussätze werden durch die aktuelle Konsolidierung und den Nachtrag oben ergänzt; er ist kein ungeprüft übernommener neuer Gesamtstatus. Die externe laufende Symmetrieergänzung wurde separat geprüft und ist nicht unbemerkt in diesen eingefrorenen Anhang eingegangen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Historischer Beweisanhang: vollständiger nativer Herleitungsstand v1.6.4","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17726,"byte_start":17131,"id":"section:8353c443ba62a431f4c2","kind":"section","labels":["tfpt-universalraum-nativer-pol-bewegungsgleichung-und-minimale-feldtypen"],"line_end":364,"line_start":353,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/014-subsection-11-reproduktion-und-ehrliche.tex","status_markers_as_written":[],"summary_excerpt":"Diese Revision verbindet den während der Arbeit neu eingegangenen Polsatz v1.6.3 mit einer unabhängig begonnenen Untersuchung der nativen Bewegungsgleichung. Sie ergänzt die bisherigen Hauptdokumente; sie ist keine verkürzte Neufassung des vollständigen Hauptbuchs. Die vorhandenen Haupt- und Update-PDFs wurden in dieser Runde nicht verändert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TFPT / Universalraum: nativer Pol, Bewegungsgleichung und minimale Feldtypen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2378,"byte_start":0,"id":"section:b730707a91cc1f2b7caf","kind":"subsection","labels":["ergebnis-in-einem-satz"],"line_end":55,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/015-subsection-1-ergebnis-in-einem-satz-label-ergebnis-in-ei.tex","status_markers_as_written":[],"summary_excerpt":"Auf dem abgesicherten Grundzustand des festgelegten nativen Fockmodells existiert eine isolierte ursprüngliche Fermion-Entnahmelinie; nach Kombination beider Rechnungen trägt sie mehr als 88,007628 \\% des gesamten normierten Spektralgewichts pro Mode. Die zusätzliche Antwort ist jedoch nicht exakt auf eine einzige weitere Linie reduzierbar. Ihr erster Rückwirkungsschritt wird direkt von derselben ursprünglichen Wechs","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Ergebnis in einem Satz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3537,"byte_start":2378,"id":"section:47172b152daf56f1fe56","kind":"subsection","labels":["ein-unveruxe4nderter-modellvertrag"],"line_end":83,"line_start":56,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/015-subsection-1-ergebnis-in-einem-satz-label-ergebnis-in-ei.tex","status_markers_as_written":[],"summary_excerpt":"Es werden keine Hopping-, Massen-, Ladungs- oder Projektionsglieder zu H hinzugefügt:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Ein unveränderter Modellvertrag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3643,"byte_start":3537,"id":"section:1cbbbd4c3c1a3b9c11de","kind":"subsection","labels":["was-tatsuxe4chlich-erneut-gepruxfcft-wurde"],"line_end":86,"line_start":84,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/015-subsection-1-ergebnis-in-einem-satz-label-ergebnis-in-ei.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"3. Was tatsächlich erneut geprüft wurde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6107,"byte_start":3643,"id":"section:a73613a159bcdd4dc679","kind":"subsubsection","labels":["grundzustand-frische-berechnung-statt-blouxdfer-statusuxfcbernahme"],"line_end":143,"line_start":87,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/015-subsection-1-ergebnis-in-einem-satz-label-ergebnis-in-ei.tex","status_markers_as_written":[],"summary_excerpt":"Die ursprünglichen Programme wurden mit fixierten Dateihashes in eine eigene Arbeitskopie übernommen. Die Paar-Konfigurationen wurden frisch mit neu kompiliertem Quellcode berechnet:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.1 Grundzustand: frische Berechnung statt bloßer Statusübernahme","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":7052,"byte_start":6107,"id":"section:acf4431acc80c8b2654d","kind":"subsubsection","labels":["das-neu-eingegangene-polergebnis"],"line_end":164,"line_start":144,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":["relation:614c4aa0c5ff8cac086f"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/015-subsection-1-ergebnis-in-einem-satz-label-ergebnis-in-ei.tex","status_markers_as_written":[],"summary_excerpt":"Der vollständige technische Bericht v1.6.3 und sein 248-zeiliger Prüfer wurden gelesen; Quellen, Bericht, Ergebnismatrix und Prüfpaket wurden unverändert archiviert. Der Prüfer wurde normal und optimiert wiederholt: 317 Prüfbedingungen, identische JSON-Bytes auch zum gelieferten Bericht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.2 Das neu eingegangene Polergebnis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8843,"byte_start":7052,"id":"section:6b1c1790fb32a71b13ef","kind":"subsection","labels":["der-einfache-native-anschluss-bewegungsgleichung-statt-umdeutung"],"line_end":211,"line_start":165,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/015-subsection-1-ergebnis-in-einem-satz-label-ergebnis-in-ei.tex","status_markers_as_written":[],"summary_excerpt":"Erweitere jede W-Zeile zur antisymmetrischen Matrix [formula in source] mit [formula in source] für i j. 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Der einfache native Anschluss: Bewegungsgleichung statt Umdeutung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10037,"byte_start":8843,"id":"section:1a69a383ac54acf54364","kind":"subsection","labels":["dieselbe-antwort-auf-demselben-grundzustand"],"line_end":248,"line_start":212,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/015-subsection-1-ergebnis-in-einem-satz-label-ergebnis-in-ei.tex","status_markers_as_written":[],"summary_excerpt":"Die innere Symmetrie macht G diagonal und alle Diagonalelemente gleich. Schreibe mit positiven Entnahme- und Additionsmaßen auf [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Dieselbe Antwort auf demselben Grundzustand","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11356,"byte_start":10037,"id":"section:d249a82d3fb9d46b7ae8","kind":"subsubsection","labels":["herleitung-des-dritten-moments"],"line_end":277,"line_start":249,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/015-subsection-1-ergebnis-in-einem-satz-label-ergebnis-in-ei.tex","status_markers_as_written":[],"summary_excerpt":"Setze [formula in source] . Stationarität macht diesen Operator symmetrisch in der positiven, nach Nullvektoren quotientierten Metrik [formula in source] . Direkte Normalordnung ergibt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5.1 Herleitung des dritten Moments","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13313,"byte_start":11356,"id":"section:caa4b807b78e0e81b4bc","kind":"subsubsection","labels":["neue-engere-dichte--und-gewichtsgrenzen"],"line_end":335,"line_start":278,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/015-subsection-1-ergebnis-in-einem-satz-label-ergebnis-in-ei.tex","status_markers_as_written":[],"summary_excerpt":"Positivität der beiden Antwort-Grammatrizen beziehungsweise zweimal Cauchy-Schwarz liefern","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5.2 Neue engere Dichte- und Gewichtsgrenzen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15065,"byte_start":13313,"id":"section:afa12163ab34b8af960b","kind":"subsection","labels":["der-polsatz-und-seine-zusuxe4tzliche-verschuxe4rfung"],"line_end":385,"line_start":336,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/015-subsection-1-ergebnis-in-einem-satz-label-ergebnis-in-ei.tex","status_markers_as_written":[],"summary_excerpt":"Der eingegangene Beweis verwendet [formula in source] . Invarianz und Besetzung ergeben","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Der Polsatz und seine zusätzliche Verschärfung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":814,"byte_start":0,"id":"section:17072b2bc70f09c099ef","kind":"subsection","labels":["einfache-organisation-aber-keine-falsche-zwei-linien-luxf6sung"],"line_end":18,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/016-subsection-7-einfache-organisation-aber-keine-falsche.tex","status_markers_as_written":[],"summary_excerpt":"Die ersten zwei orthonormalen Operatoren sind f und [formula in source] . Die erste Resolventenreduktion hat deshalb die exakte Form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. Einfache Organisation, aber keine falsche Zwei-Linien-Lösung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2369,"byte_start":814,"id":"section:97f6c40a07ffcc6a2be8","kind":"subsubsection","labels":["warum-man-die-ruxfcckwirkung-nicht-exakt-weglassen-darf"],"line_end":58,"line_start":19,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/016-subsection-7-einfache-organisation-aber-keine-falsche.tex","status_markers_as_written":[],"summary_excerpt":"Angenommen, es gäbe nur je eine Entnahme- und Additionslinie mit Energien [formula in source] . Symmetrie macht diese für alle r gleich. Dann liefern die Bewegungsgleichungen auf demselben Grundzustand","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7.1 Warum man die Rückwirkung nicht exakt weglassen darf","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4531,"byte_start":2369,"id":"section:241a7c31dcc45c566a81","kind":"subsection","labels":["was-der-operationssatz-jetzt-tatsuxe4chlich-hergibt"],"line_end":115,"line_start":59,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/016-subsection-7-einfache-organisation-aber-keine-falsche.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333@ Vertrag & Mathematisch abgesichert & Nicht dadurch verfügbar \\\\ Markierter endlicher Matrixcompiler & Matrizen, Ordnungen, konkrete endliche Syntheseidentitäten & Vollständiges Fockinstrument, Präparation, physischer Zeitgenerator \\\\ H allein & Modellzeitentwicklung & Unabhängiges Schalten von X und [formula in source] \\\\ X und [formula in source] , wenn ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8. Was der Operationssatz jetzt tatsächlich hergibt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5283,"byte_start":4531,"id":"section:a053c7de09481b95f1f5","kind":"subsubsection","labels":["konkrete-pruxe4parationsgrenze"],"line_end":131,"line_start":116,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/016-subsection-7-einfache-organisation-aber-keine-falsche.tex","status_markers_as_written":[],"summary_excerpt":"Alle genannten Fockkontrollen erhalten N. Ein Wort aus ihnen und jeder einzeln zahlenerhaltende ausgewählte Messzweig bleiben im Ausgangssektor. Sie können aus dem leeren N=0-Zustand nicht den N=64-Grundzustand erzeugen. Diese Aussage betrifft zahlenerhaltende Krauszweige; eine bloß U(1)-kovariante offene Dynamik kann sehr wohl geladene Krausoperatoren haben.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.1 Konkrete Präparationsgrenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6013,"byte_start":5283,"id":"section:47c55b9e5e11c5d817ec","kind":"subsubsection","labels":["der-kleinste-konkrete-ladungstest"],"line_end":146,"line_start":132,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/016-subsection-7-einfache-organisation-aber-keine-falsche.tex","status_markers_as_written":[],"summary_excerpt":"Ein Kandidat ist eine explizite Referenzmode c mit [formula in source] . Sie erhält die gemeinsame Ladung, verändert aber die Ladung der ursprünglichen Bank. Der endliche Austausch- und Detuningtest ist exakt; dieses T wurde nicht als neuer nativer Hamiltonterm eingeführt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.2 Der kleinste konkrete Ladungstest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6469,"byte_start":6013,"id":"section:c917fa797476e6c6afed","kind":"subsection","labels":["relativistisches-wuxf6rterbuch-ausschluss-und-zwei-pruxe4zise-alternativen"],"line_end":155,"line_start":147,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/016-subsection-7-einfache-organisation-aber-keine-falsche.tex","status_markers_as_written":[],"summary_excerpt":"Die Indexfrage darf nicht nachträglich durch einen Namen beantwortet werden. Die Konventionen für Zweikomponentenspinoren wurden mit https://arxiv.org/abs/0812.1594Dreiner, Haber und Martin abgeglichen; die folgenden speziellen W-Tests sind eigene exakte Tensorrechnungen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. Relativistisches Wörterbuch: Ausschluss und zwei präzise Alternativen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6957,"byte_start":6469,"id":"section:169621d97b7255fccf37","kind":"subsubsection","labels":["was-nicht-funktioniert"],"line_end":164,"line_start":156,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/016-subsection-7-einfache-organisation-aber-keine-falsche.tex","status_markers_as_written":[],"summary_excerpt":"Für 64 gleichhändige Weylfelder mit innerem Index I und einen skalaren Vermittler ist [formula in source] symmetrisch. Die Grassmann-Antisymmetrisierung verschwindet daher identisch, für alle 60 W-Zeilen. Außerdem lässt die volle irreduzible innere Darstellung [formula in source] auf denselben 64 Komponenten nach Schur keine zusätzliche kommutierende nichttriviale Lorentzspinorwirkung zu.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9.1 Was nicht funktioniert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7372,"byte_start":6957,"id":"section:8aecb49fc9ca113cc68b","kind":"subsubsection","labels":["bereits-bekannter-nichtverschwindender-typ"],"line_end":173,"line_start":165,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/016-subsection-7-einfache-organisation-aber-keine-falsche.tex","status_markers_as_written":[],"summary_excerpt":"Ein symmetrischer Lorentzspinortensor koppelt an das antisymmetrische M. Der Vermittler hat dann einen passenden dualen (1,0)-Typ samt adjungiertem Typ. Diese Variante besteht den algebraischen Nichtnulltest, aber noch keinen vollständigen Kinetik-, Positivitäts-, Constraints- oder Herkunftstest.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9.2 Bereits bekannter nichtverschwindender Typ","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9125,"byte_start":7372,"id":"section:90ceb80f7bbde317523b","kind":"subsubsection","labels":["neue-minimale-skalare-alternative---ausdruxfccklich-zusuxe4tzlich"],"line_end":207,"line_start":174,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/016-subsection-7-einfache-organisation-aber-keine-falsche.tex","status_markers_as_written":[],"summary_excerpt":"Will man zugleich W, gleiche Weylhand, lokale Bilinearität und einen skalaren Vermittler behalten, kann man einen unabhängigen Hilfsindex a=1,2 mit alternierender Form einführen:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9.3 Neue minimale skalare Alternative - ausdrücklich zusätzlich","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12406,"byte_start":9125,"id":"section:9110b136e3d3df0cbec8","kind":"subsection","labels":["nuxe4chste-schritte-mit-eindeutiger-erfolgskontrolle"],"line_end":278,"line_start":208,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/016-subsection-7-einfache-organisation-aber-keine-falsche.tex","status_markers_as_written":[],"summary_excerpt":"Native Quelle des Austauschoperators bestimmen. Ein tatsächliches Operationswort mit Anfangszustand, Detektor, Adjungiertem, Ladungsbilanz und Record angeben. Ein weiteres neutrales Wort oder bloßer Algebraabschluss schließt diese Aufgabe nicht. Den Rest der nativen Antwort kontrollieren. Das nächste Ziel ist [formula in source] beziehungsweise sein erster Norm- und Momentkoeffizient, gemeinsam in N=63,64,65. Die vor","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10. Nächste Schritte mit eindeutiger Erfolgskontrolle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13414,"byte_start":12406,"id":"section:680ca42e62d0dbe3cc1d","kind":"subsection","labels":["erratum-und-versionsdisziplin"],"line_end":298,"line_start":279,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/016-subsection-7-einfache-organisation-aber-keine-falsche.tex","status_markers_as_written":[],"summary_excerpt":"Im eigenen v1.6.2-Text fehlte in Abschnitt 5.2 zwischen Entnahme- und Additionsresolvente ein Pluszeichen. Richtig ist auf der dortigen N=4-Referenz [formula in source] . Die früheren Prüfrechnungen verwendeten die additive CAR-Gewichtsregel; der Darstellungsfehler wird hier ausdrücklich korrigiert. Die archivierte v1.6.2 wird nicht stillschweigend umgeschrieben.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"11. Erratum und Versionsdisziplin","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14747,"byte_start":0,"id":"section:1e75ebc4ced1784f3e81","kind":"section","labels":["nutzerquelle-a-vollstuxe4ndige-runde-v1.6.3"],"line_end":246,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":["relation:1239e66c1271c0d01d1d"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/017-section-nutzerquelle-a-vollst-ndige-runde.tex","status_markers_as_written":[],"summary_excerpt":"Unveränderte Quelle. Nicht alle Aussagen darin werden übernommen. Entscheidend sind die Quellenprüfung und Korrekturen in v1.6.7.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nutzerquelle A: vollständige Runde v1.6.3","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15252,"byte_start":14747,"id":"section:f6a8ca405992a24f46d7","kind":"section","labels":["nutzerquelle-b-korrektur-und-zwischenbericht"],"line_end":258,"line_start":247,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/017-section-nutzerquelle-a-vollst-ndige-runde.tex","status_markers_as_written":[],"summary_excerpt":"Unveränderte Quelle. Nicht alle Aussagen darin werden übernommen. Entscheidend sind die Quellenprüfung und Korrekturen in v1.6.7.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nutzerquelle B: Korrektur und Zwischenbericht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15450,"byte_start":15252,"id":"section:4a9b837d3b4fb0a08af8","kind":"section","labels":["zwischenbericht-tfptuniversalraum---fundamentale-luxf6sung-stand-15.09.2026-1145"],"line_end":262,"line_start":259,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/017-section-nutzerquelle-a-vollst-ndige-runde.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Zwischenbericht: TFPT/Universalraum - fundamentale Lösung, Stand 15.09.2026, 11:45","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17220,"byte_start":15450,"id":"section:2c0485b0b478f27065aa","kind":"subsection","labels":["gesamtlage-zwei-spuren"],"line_end":307,"line_start":263,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/017-section-nutzerquelle-a-vollst-ndige-runde.tex","status_markers_as_written":[],"summary_excerpt":"Es existieren jetzt zwei Contract-Ordner, die sich unabhängig auf denselben Kernpunkt zubewegt haben:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"0. Gesamtlage: zwei Spuren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18341,"byte_start":17220,"id":"section:8d56f131462551b05dea","kind":"subsection","labels":["fundament-meiner-session-native_source.py-neu-npz-frei"],"line_end":328,"line_start":308,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/017-section-nutzerquelle-a-vollst-ndige-runde.tex","status_markers_as_written":[],"summary_excerpt":"Problem: der gepinnte Tensor ( spinor_tensors.npz, SHA-256 3f00a089…) liegt unter /Documents - für die Agenten-Shell macOS-gesperrt (TCC). Die bisherigen Verträge sind von dieser Shell nicht reproduzierbar.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Fundament meiner Session: native_source.py (neu, npz-frei)1. Fundament meiner Session: (neu, npz-frei)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18634,"byte_start":18341,"id":"section:a425ac96db4cd72379ba","kind":"subsection","labels":["wp-a-der-verfuxfcgbare-operationssatz-fertig-307-exakte-guards"],"line_end":334,"line_start":329,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/017-section-nutzerquelle-a-vollst-ndige-runde.tex","status_markers_as_written":[],"summary_excerpt":"Frage (v1.6.2 §10.3/§14): Wie groß ist die unsichtbare Freiheit (Kommutant) unter dem tatsächlich verfügbaren Operationssatz?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. WP-A: Der verfügbare Operationssatz (fertig, 307 exakte Guards)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":19691,"byte_start":18634,"id":"section:8649c6a9a78ca1e3a245","kind":"subsubsection","labels":["die-kommutanten-leiter-n3-sektor-45-504-dim"],"line_end":363,"line_start":335,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":["relation:72940f2c69a281e2c22c"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/017-section-nutzerquelle-a-vollst-ndige-runde.tex","status_markers_as_written":[],"summary_excerpt":"@lrr@ Operationssatz & erzeugte Algebra & Kommutante \\\\ S0: \\X, N_b\\ & 14 & 1 444 233 216 \\\\ S1: + Spin(10)×SU(4)-Rahmen & 743 583 744 & 7 \\\\ S2: + Clock-Lift & unverändert & 7 \\\\ S3: + Modenbesetzungen \\n_r, m_A\\ & M₄₅₅₀₄ (2 070 614 016) & 1 \\\\ S4: + geladene f-Instrumente & M₄₇₅₈₀ (N=2∪N=3) & 1 \\\\","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Kommutanten-Leiter (N=3-Sektor, 45 504-dim)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1403,"byte_start":0,"id":"section:b5e2e60700246f44d1d7","kind":"subsubsection","labels":["die-isotypie-zerlegung-von-n3-beide-spuren-unabhuxe4ngig-identisch"],"line_end":30,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/018-subsubsection-die-isotypie-zerlegung-von-n-3-beide-spure.tex","status_markers_as_written":[],"summary_excerpt":"@lrrrll@ Block & Dim & Mult & S-Eigenwert & (C_S, C_U) & Rolle \\\\ (144, 20) & 2880 & 2 & 7 & (85, 39) & hell, X-gekoppelt \\\\ (144, 4̄) & 576 & 2 & 10 & (85, 15) & hell, X-gekoppelt \\\\ (16′, 20) & 320 & 2 & 12 & (45, 39) & hell, X-gekoppelt \\\\ (16′, 4̄) & 64 & 1 & 0 (ker S) & (45, 15) & χ-Kompositblock \\\\ (672, 4̄) & 2688 & 1 & - & (165, 15) & dunkel \\\\ (1200, 20) & 24 000 & 1 & - & (141, 39) & dunkel \\\\ (560, 20′) & ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Isotypie-Zerlegung von N=3 (beide Spuren unabhängig, identisch)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2603,"byte_start":1403,"id":"section:a04f6efe04777d89b399","kind":"subsubsection","labels":["das-verfuxfcgbarkeits-theorem-parallelsession-symmetry_availability.py"],"line_end":52,"line_start":31,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/018-subsubsection-die-isotypie-zerlegung-von-n-3-beide-spure.tex","status_markers_as_written":[],"summary_excerpt":"Die gewährte Dynamik (Wörter aus X, N_b) liegt in der Verflechteralgebra (Dim Σmᵢ² = 16); die 60 Lie-Erzeuger liegen nicht darin - keine Komposition gewährter Dynamik erzeugt sie. Die Symmetrie ist ein eigenständiges Primitiv: gewährt oder nicht gewährt. Der gesamte verbleibende symmetrieverträgliche Spielraum ist exakt 2 Dimensionen breit = die Fähigkeit, die drei dunklen Blöcke getrennt anzusprechen (= beide Casimi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das Verfügbarkeits-Theorem (Parallelsession, symmetry_availability.py)Das Verfügbarkeits-Theorem (Parallelsession, )","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4895,"byte_start":2603,"id":"section:fa058c94fbeda7b27859","kind":"subsection","labels":["wp-c-relativistisches-feldwuxf6rterbuch-fertig-2161-exakte-guards--oo-stabil"],"line_end":104,"line_start":53,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/018-subsubsection-die-isotypie-zerlegung-von-n-3-beide-spure.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.3000 > p( - 4 ) * 0.4000 > p( - 4 ) * 0.3000@ Kanal & Norm² pro Zeile & Status \\\\ Skalar, gleichhändig ε_\\αβ\\ψψ & 0 (alle 60 Zeilen, exakt) & verboten \\\\ Skalar, gepunktet (0,0) & 0 & verboten \\\\ (1,0) symmetrisch \\I, σˣ, σᶻ\\ & je 64, Summe 192 & erlaubt - der Vertex ist rein (1,0)+h.c. \\\\ (0,1) konjugiert & je 64 & erlaubt \\\\","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. WP-C: Relativistisches Feldwörterbuch (fertig, 2161 exakte Guards, -OO-stabil)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6923,"byte_start":4895,"id":"section:9fe4ba4921c2eb618010","kind":"subsection","labels":["wp-b-nativer-grundzustand-parallelsession-v1.6.4-meine-laufende-sonde"],"line_end":153,"line_start":105,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/018-subsubsection-die-isotypie-zerlegung-von-n-3-beide-spure.tex","status_markers_as_written":[],"summary_excerpt":"@rrr@ k & Bosonkonfigurationen vollständig enumeriert & ‖Q₊ᵏF‖² \\\\ 0 & analytisch & 1 \\\\ 1 & 60 Kanäle / 480 Paare & 480 \\\\ 2 & 1 830 & 439 680 \\\\ 3 & 37 820 & 575 078 400 \\\\ 4 & 595 665 & 952 296 652 800 \\\\","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. WP-B: Nativer Grundzustand (Parallelsession v1.6.4 + meine laufende Sonde)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8566,"byte_start":6923,"id":"section:34ba6c3178cc4eee4c35","kind":"subsection","labels":["wp-d-geladene-antwort-auf-dem-grundzustand-parallelsession-v1.6.4"],"line_end":193,"line_start":154,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/018-subsubsection-die-isotypie-zerlegung-von-n-3-beide-spure.tex","status_markers_as_written":[],"summary_excerpt":"Genau die geforderte „dieselbe geladene Antwort auf dem abgesicherten Zustand'':","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. WP-D: Geladene Antwort auf dem Grundzustand (Parallelsession v1.6.4)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10142,"byte_start":8566,"id":"section:4337292367397f5af33d","kind":"subsection","labels":["kreuzvalidierung-der-beiden-spuren"],"line_end":232,"line_start":194,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/018-subsubsection-die-isotypie-zerlegung-von-n-3-beide-spure.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 6 ) * 0.2500 > p( - 6 ) * 0.2500 > p( - 6 ) * 0.2500 > p( - 6 ) * 0.2500@ Befund & Meine Session & Parallelsession & Status \\\\ N=3-Zerlegung (7 Blöcke, Mults 2,2,2,1,1,1,1) & ✓ & ✓ & identisch \\\\ Casimirwerte (je Block) & (45,15), (85,15), & C = (C_S+C_U)/4 = 15, 25, 45, 21, 31, 45, 45 & identisch (zwei Normierungen) \\\\ Kommutant S1 (volle Symmetrie) & 7 & 7 & identisch \\\\ Kommutant S0 (X, N_b) & 1 452 961 7","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Kreuzvalidierung der beiden Spuren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":11895,"byte_start":10142,"id":"section:c27732c57179ba9e03e3","kind":"subsection","labels":["offen-nuxe4chste-schritte-in-der-reihenfolge-der-direktive"],"line_end":274,"line_start":233,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/018-subsubsection-die-isotypie-zerlegung-von-n-3-beide-spure.tex","status_markers_as_written":[],"summary_excerpt":"Sonde abschließen (läuft): mult₂-Zertifikat, β-Kette, Sektorfloors → unabhängige Reproduktion der v1.6.4-Kernzahlen. Volle 33-Niveau-Kette: falls mult_k=1 weiter trägt, ist die Singulett-Kette durch die Normsequenz ‖Q₊ᵏF‖² (k≤32) bestimmt - dafür ist die Symmetriespur-Resummation nötig (die „vier Symmetriespuren'' des Workers), nicht rohe Enumeration. Σ₂ kontrollieren (erster Norm-/Momentkoeffizient, N=63/64/65 gemei","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. 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Die Pruefung und eigene Fortsetzung stehen in Teil B.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nutzerquelle C: Multiplizitaeten und Z4","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10484,"byte_start":0,"id":"section:01d244e6aa6dba0fc743","kind":"section","labels":["nutzerquelle-d-fundamentale-reduktion"],"line_end":180,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/020-section-nutzerquelle-d-fundamentale.tex","status_markers_as_written":[],"summary_excerpt":"Unveraenderte Nutzerquelle, als Vorschlag und nicht als Beweis uebernommen. Die Pruefung und eigene Fortsetzung stehen in Teil B.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nutzerquelle D: fundamentale Reduktion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":22803,"byte_start":0,"id":"section:03dc40de26fb9251a289","kind":"section","labels":["nutzerquelle-e-gemeinsamer-ausfuehrbarer-prozess"],"line_end":363,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/021-section-nutzerquelle-e-gemeinsamer-ausfuehrbarer.tex","status_markers_as_written":[],"summary_excerpt":"Unveraenderte Nutzerquelle, als Vorschlag und nicht als Beweis uebernommen. Die Pruefung und eigene Fortsetzung stehen in Teil B.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nutzerquelle E: gemeinsamer ausfuehrbarer Prozess","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":23094,"byte_start":22803,"id":"section:cc07e91654931ba01589","kind":"section","labels":["nutzerquelle-f-operationssatz-grundzustand-und-feldwoerterbuch-v1.6.3"],"line_end":370,"line_start":364,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/021-section-nutzerquelle-e-gemeinsamer-ausfuehrbarer.tex","status_markers_as_written":[],"summary_excerpt":"Unveraenderte Nutzerquelle, als Vorschlag und nicht als Beweis uebernommen. Die Pruefung und eigene Fortsetzung stehen in Teil B.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nutzerquelle F: Operationssatz, Grundzustand und Feldwoerterbuch v1.6.3","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":860,"byte_start":0,"id":"section:380fa2223c68b6b9ccf1","kind":"section","labels":["tfpt-universalraum-operationssatz-nativer-grundzustand-und-feldwuxf6rterbuch"],"line_end":15,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/022-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Diese Runde bearbeitet die vier Prioritäten aus v1.6.2 §14 in der dort festgelegten Reihenfolge: den tatsächlich verfügbaren Operationssatz exakt abgrenzen, den berichteten nativen Grundzustand mit seinem ursprünglichen Hamilton- und Sektorvertrag reproduzieren und darauf die geladene Antwort berechnen, das relativistische Feldwörterbuch am tatsächlichen Tensor festhalten. Eine räumliche Skalierungsrechnung ist ausdr","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TFPT / Universalraum: Operationssatz, nativer Grundzustand und Feldwörterbuch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2267,"byte_start":860,"id":"section:0873d6220245dac1471a","kind":"subsection","labels":["ergebnis-in-einem-absatz"],"line_end":37,"line_start":16,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/022-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Der N=64-Sektor des nativen Modells ist exakt als Loch-Paarerzeugung auf dem gefüllten Zustand realisiert; seine Krylov-Kette ist bis zu 15 252 960 Einträgen exakt berechnet, ihre Normen ν₁ ν₄ sind auf zwei völlig unabhängigen Wegen (Besetzungsbild und Onishi/Wick-Spurnetzwerke) identisch. Die Kette schließt bei zwei Bosonen exakt nicht (Defekt 2,9·10⁻⁵), das Modell ist also nicht allein durch seine Normen lösbar, nu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Ergebnis in einem Absatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3222,"byte_start":2267,"id":"section:72501efd09c2c6cdf803","kind":"subsection","labels":["unveruxe4nderte-quelle-und-konventionen"],"line_end":56,"line_start":38,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/022-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Der Tensor wird repo-lokal gelesen (SHA-256 3f00a0892157a691e4ef26920c3702772c7bf76a250fad98ff04a079bb64b763), der Clock-Konstruktor ist gepinnt ( 9bf99de7…). common.py prüft: 60 Kanäle × 8 disjunkte Paare, jede Mode in 15 Kanälen; Gewichtserhaltung auf allen 480 Paaren; die Casimir-Identität 8WᵀW + 𝒞_S + 𝒞_C − 120 I = 0 auf allen 2016 Zweiteilchenzuständen (𝒞 = −ΣL², d. h. viermal der Standard-Casimir); induzierte B","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Unveränderte Quelle und Konventionen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3665,"byte_start":3222,"id":"section:3dde5c94d455a076403d","kind":"subsection","labels":["operationssatz-und-kommutant"],"line_end":66,"line_start":57,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/022-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Gemessen wird die Dimension des Kommutanten der von einer Operationsstufe erzeugten Algebra auf dem Sektor: kleiner Kommutant bedeutet weniger unsichtbare Freiheit. Das Spektralzertifikat für N=3 ist reproduziert (S = C₃C₃ᵀ wird von ∏(S−r), r ∈ \\0,7,10,12\\, exakt annulliert; Multiplizitäten 64, 2880, 576, 320 aus rationalen Projektorspuren).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Operationssatz und Kommutant","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5472,"byte_start":3665,"id":"section:6a3db80772733882ff3c","kind":"subsubsection","labels":["exakte-irreduzibel-zerlegung-huxf6chstgewichtsvektoren"],"line_end":108,"line_start":67,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/022-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 8 ) * 0.1875 > p( - 8 ) * 0.1875 > p( - 8 ) * 0.2500 > p( - 8 ) * 0.1875 > p( - 8 ) * 0.1875@ Sektor & Block & Dim & Zerlegung unter so(10)⊕ su(4) & (𝒞_S, 𝒞_C) \\\\ N=2 & helle Paare ↔ Bosonen & 60 & (10, 6) & (36, 20) \\\\ N=2 & dunkle Paare & 1956 & (120, 10) ⊕ (126, 6) & (84,36), (100,20) \\\\ N=3 & dunkle Tripel = ker C₃ & 37888 & (560, 20″) ⊕ (1200, 20) ⊕ (672, 4̄) & (117,63), (141,39), (165,15) \\\\ N=3 & ker ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.1 Exakte Irreduzibel-Zerlegung (Höchstgewichtsvektoren)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7553,"byte_start":5472,"id":"section:1bcdbc12178b53b4f799","kind":"subsubsection","labels":["kommutanten-leiter"],"line_end":154,"line_start":109,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/022-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.2727 > p( - 4 ) * 0.3636 > p( - 4 ) * 0.3636@ Verfügbare Operationen & N=2 & N=3 \\\\ A: \\X, N_b\\ (die zwei bisher geprüften Kontrollen) & 3 829 536 & 1 444 233 216 \\\\ B: A + Clock (Ordnung 6) & 641 760 & 240 742 144 \\\\ Cc: A + 15 su(4)-Generatoren & 30 376 & 2 247 168 \\\\ Cs: A + 45 so(10)-Generatoren & 172 & 1 648 \\\\ C: A + alle 60 Generatoren & 3 & 7 \\\\ D: B + C & 3 & 7 \\\\ B(H_N) & 1 & 1 \\\\","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.2 Kommutanten-Leiter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7634,"byte_start":7553,"id":"section:fb2b73b5db6091cf311a","kind":"subsection","labels":["der-native-n64-grundzustand"],"line_end":157,"line_start":155,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/022-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"4. Der native N=64-Grundzustand","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8251,"byte_start":7634,"id":"section:00ead132d378b03b3e0f","kind":"subsubsection","labels":["lochbild"],"line_end":172,"line_start":158,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/022-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Mit h_i = f_i† ist F⟩ = f₀† f₆₃† 0⟩ das Lochvakuum und als Operatoridentität P_A = −Q_A† mit Q_A† = Σ_\\i j\\W_\\A,ij\\h_i†h_j†. Unter (−1)\\^\\N_b\\ ist H äquivalent zu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.1 Lochbild","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9514,"byte_start":8251,"id":"section:f5c45739f916efb7032c","kind":"subsubsection","labels":["exakte-krylov-kette"],"line_end":203,"line_start":173,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/022-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"@rrrl@ n & Einträge in v_n & ν_n = ‖v_n‖² & ν_n/ν_\\n−1\\ \\\\ 0 & 1 & 1 & - \\\\ 1 & 480 & 480 & 480 \\\\ 2 & 108 240 & 439 680 & 916 = 4·229 \\\\ 3 & 15 252 960 & 575 078 400 & 299520/229 \\\\ 4 & (nur Spurnetzwerk) & 952 296 652 800 & ≈ 1656,0 \\\\ 5 & (nur Spurnetzwerk) & siehe norms_by_traces.json & \\\\","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.2 Exakte Krylov-Kette","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10124,"byte_start":9514,"id":"section:7226f7ab3a966723970e","kind":"subsubsection","labels":["schlieuxdfung"],"line_end":217,"line_start":204,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/022-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Der Zwei-Boson-Singulettraum ist also mehr als eindimensional; die Kette ist exakt nicht geschlossen, und das Modell ist nicht allein durch die ν_n lösbar. Numerisch ist die Korrektur vernachlässigbar: w₂ koppelt nur an v₃ mit g·√(‖w₂‖²/ν₃) = 0,195 g.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.3 Schließung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11156,"byte_start":10124,"id":"section:846aad100c11e8a9f9a3","kind":"subsubsection","labels":["ritz-obergrenzen"],"line_end":243,"line_start":218,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/022-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"In der orthonormierten Basis \\v₀ v_K, w₂\\ ist H (Δ = 1) tridiagonal plus w₂-Zweig: Diagonale n bzw. 2; Nebendiagonalen g·4√30, g·2√229, g·48√29770/229, ; w₂-Kopplung g·3√598377/11908.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.4 Ritz-Obergrenzen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11738,"byte_start":11156,"id":"section:8c304b9e50a8d199df5d","kind":"subsubsection","labels":["observablen-auf-dem-ritz-zustand-gux3b4-120-k3"],"line_end":254,"line_start":244,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/022-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"⟨N_b⟩ = 0,8421 (Hellmann-Feynman ∂E/∂Δ = 0,8421); ⟨F Ω⟩ ² = 0,397; Bosonzahlverteilung 0,397 / 0,397 / 0,172 / 0,034; Shannon-Untergrenze der Boson-Loch-Verschränkung 1,66 bit (rigoros, weil die reduzierte Bosondichte in N_b blockdiagonal ist). Die Worker-Angaben „Überlapp 1/4`` und „Verschränkung 0,811 bit`` sind damit konsistent, aber auf einem nichtkonvergierten Zustand.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.5 Observablen auf dem Ritz-Zustand (g/Δ = 1/20, K=3)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":12337,"byte_start":11738,"id":"section:89449f6293994bb8b7f8","kind":"subsubsection","labels":["geladene-ein-teilchen-antwort"],"line_end":270,"line_start":255,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/022-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Für jede Mode r (Guard r ∈ \\0, 5, 63\\; Transitivität der Quellsymmetrie):","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.6 Geladene Ein-Teilchen-Antwort","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13554,"byte_start":12337,"id":"section:fc516775162c044c9222","kind":"subsubsection","labels":["sektorauswahl-und-die-worker-behauptung"],"line_end":300,"line_start":271,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/022-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Untergrenzen aus der Casimir-Identität und quadratischer Ergänzung, H ≥ (1−θ)ΔN_b − (15g²/2θΔ)N_f, ausgewertet als max_θ min_\\N_b\\ je Sektor:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.7 Sektorauswahl und die Worker-Behauptung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13664,"byte_start":13554,"id":"section:4e2750d369f6032c45da","kind":"subsection","labels":["feldwuxf6rterbuch-am-tatsuxe4chlichen-tensor"],"line_end":303,"line_start":301,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/022-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"5. Feldwörterbuch am tatsächlichen Tensor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15253,"byte_start":13664,"id":"section:810019e1b1a14e21406f","kind":"subsubsection","labels":["symmetrieregel"],"line_end":343,"line_start":304,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/022-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Für Grassmann-Felder ψ_\\I,a\\ ist Σ_\\IJ\\Σ_\\ab\\ W_\\IJ\\K_\\ab\\ψ_\\I,a\\ψ_\\J,b\\ = ½Σ(T − Tᵀ) mit T_\\(Ia),(Jb)\\ = W_\\IJ\\K_\\ab\\. Weil W antisymmetrisch ist, verschwindet die Kopplung genau dann, wenn K antisymmetrisch ist; nur der symmetrische Teil des Spinorkerns koppelt. Auf allen 60 Zeilen explizit geprüft:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5.1 Symmetrieregel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":17183,"byte_start":15253,"id":"section:569b31b9512fea8a7407","kind":"subsubsection","labels":["chiralituxe4tsgradierungen"],"line_end":389,"line_start":344,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/022-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Der Trägergraph (64 Moden, 480 Kanten, Grad 15, dreiecksfrei) ist nicht bipartit; ein ungerader Zyklus ist [16, 45, 0, 30, 37]. Es gibt daher keine globale Chiralitätsaufteilung, unter der alle 60 Bosonen Vektoren wären. Für jede der 44 G-kovarianten Gradierungen ist jeder Kanal rein (nie gemischt), aber der Bosonmultiplett zerfällt:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5.2 Chiralitätsgradierungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1154,"byte_start":0,"id":"section:0377c64894447d336229","kind":"subsection","labels":["spurnetzwerk-normen"],"line_end":21,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/023-subsection-6-spurnetzwerk-normen-label-spurnetzwerk-norm.tex","status_markers_as_written":[],"summary_excerpt":"über bosonische Kohärenzzustände, die Onishi-Determinante det(1 − M̄M)\\^\\1/2\\ und Wick-Paarung der z-Variablen. Jedes Netzwerk ist eine Kontraktion von n Kopien des Tensors Φ_\\ij,kl\\ = Σ_A(M_A) \\ij\\(M_A)\\kl\\ (Einträge in \\−1,0,1\\). Netzwerke werden als 4-Bein-Multigraphen unter Knotenumbenennung und Slot-Tausch kanonisiert (n=4: 120 → 27 Klassen). Exaktheit: float64-Kontraktion mit Absolutwert-Begleitkontraktion ( Σa","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Spurnetzwerk-Normen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2735,"byte_start":1154,"id":"section:0c390300aac19f496bef","kind":"subsection","labels":["t1-t8"],"line_end":62,"line_start":22,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/023-subsection-6-spurnetzwerk-normen-label-spurnetzwerk-norm.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333@ Tor & Beitrag dieser Runde & Weiter offen \\\\ T1 & Exakte Kommutanten-Leiter A→B→Cc→Cs→C; Clock als äußeres Symmetrieelement & Welche Symmetrieoperationen der Compiler tatsächlich bereitstellt \\\\ T2 & Lochbild bewiesen; Z_h + Z_add = 1; ε_h, ε_add & Konvergierter Zustand, Renormierung, Grenzraum \\\\ T3 & - (ausgeklammert) & Räumlicher Träger \\\\ T4 & Kern-Sy","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. T1-T8","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3854,"byte_start":2735,"id":"section:05bd93a177dfeb8a3137","kind":"subsection","labels":["die-jetzt-entscheidenden-pruxfcfungen"],"line_end":89,"line_start":63,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/023-subsection-6-spurnetzwerk-normen-label-spurnetzwerk-norm.tex","status_markers_as_written":[],"summary_excerpt":"Untergrenzen verschärfen. Die Casimir-Schranke trennt N=64 bei 1/20 nicht von N=62 und N=66. Eine Jacobi-Vergleichsschranke mit rigorosen Normschranken für TT† je Bosonzahl oder eine Temple-Schranke auf der Ritz-Kette würde den Beweisbereich anheben. Den Zwei-Boson-Singulettraum ausschreiben. w₂ ist der erste Zeuge; die volle Lanczos-Kette von H (nicht nur von T†) ab Tiefe 4 braucht w₂ und seine Nachfolger. Operation","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8. Die jetzt entscheidenden Prüfungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":5318,"byte_start":3854,"id":"section:24fabfcc98fe25546496","kind":"subsection","labels":["verifikation-und-nicht-uxfcbernommene-behauptungen"],"line_end":116,"line_start":90,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-singlet-observable-20260915--tmp--pdfs--TFPT_Universalraum_Richtige_Kette_Konsolidierung_2026-09-15_v1.6.7/sections/023-subsection-6-spurnetzwerk-normen-label-spurnetzwerk-norm.tex","status_markers_as_written":[],"summary_excerpt":"replay.py führt fünf Prüfer normal und unter -OO aus und verlangt byteidentische Ausgaben; Status, Hashes und Guardsummen stehen in replay_manifest.json. Guardzahlen zählen Prüfbedingungen, keine unabhängigen Theoreme. Exakt heißt ganzzahlig/rational; numerisch heißt float64 mit Toleranz-Guard (Ritz-Eigenwerte ab 3×3, Observablen, Erste-Moment-Auswertungen).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. Verifikation und nicht übernommene Behauptungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":5149,"byte_start":0,"id":"section:6098bae64342e098615c","kind":"frontmatter","labels":[],"line_end":134,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/preamble.tex","status_markers_as_written":["[L]"],"summary_excerpt":"unicodehyperref hyphensurl dvipsnames,svgnames,x11namesxcolor ngerman, 10pt, a4paper, ]article Scale=MatchLowercase Ligatures=TeX,Scale=1","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":64,"byte_start":0,"id":"section:dd78193b70d6b75c03fc","kind":"frontmatter","labels":[],"line_end":6,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/001-section-tfpt-universalraum-zusammensetzung-aus-der-gemei.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":294,"byte_start":64,"id":"section:0aa70cb7f4b32d7be811","kind":"section","labels":["tfpt-universalraum-zusammensetzung-aus-der-gemeinsamen-antwort"],"line_end":12,"line_start":7,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/001-section-tfpt-universalraum-zusammensetzung-aus-der-gemei.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"TFPT / Universalraum: Zusammensetzung aus der gemeinsamen Antwort","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3243,"byte_start":294,"id":"section:dded658071cb9c9ef2ff","kind":"subsection","labels":["ergebnis-die-fehlende-verbindung-wird-berechenbar-aber-noch-nicht-urspruxfcnglich-ausgewuxe4hlt"],"line_end":69,"line_start":13,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/001-section-tfpt-universalraum-zusammensetzung-aus-der-gemei.tex","status_markers_as_written":[],"summary_excerpt":"Die drei beauftragten Arbeitslinien wurden parallel ausgeführt: ursprüngliche Komposition, ein kompletter kleiner Ablauf und ein früher relativistischer Feldtest. Hinzu kommt eine unabhängige globale CAR-Rechnung im Hauptstrang. Sie ergeben keinen Abschluss der TOE, aber vier konkrete Fortschritte:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Ergebnis: Die fehlende Verbindung wird berechenbar, aber noch nicht ursprünglich ausgewählt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5903,"byte_start":3243,"id":"section:0166c6c882b1a35c632b","kind":"subsection","labels":["einfaches-gesamtbild"],"line_end":125,"line_start":70,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/001-section-tfpt-universalraum-zusammensetzung-aus-der-gemei.tex","status_markers_as_written":[],"summary_excerpt":"Man kann sich den ursprünglichen Tensor wie eine Kupplung vorstellen: Zwei Fermionen können gemeinsam in ein Boson übergehen und zurück. Diese Kupplung ist intern wesentlich besser bestimmt, als es die offenen Grundsatzfragen vermuten lassen. Die offene Frage lautet aber noch: Welche Kupplungen greifen auf dieselben Ressourcen zu, und welche sind unabhängig?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Einfaches Gesamtbild","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9011,"byte_start":5903,"id":"section:34a3191290937a7c4578","kind":"subsection","labels":["quellenweg-urspruxfcnglicher-clock-ist-keine-kopiermaschine"],"line_end":195,"line_start":126,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/001-section-tfpt-universalraum-zusammensetzung-aus-der-gemei.tex","status_markers_as_written":[],"summary_excerpt":"Die alten Quellen wurden bis zu ihren tatsächlichen Trägern zurückverfolgt. Die sieben frühen Wörter wirken auf demselben C3; ihre 49 Produkte schließen dort eine siebendimensionale Algebra. Die 60 ursprünglichen Gaußwurzelstrahlen wirken auf demselben C4. Der spätere W-Konstruktor liefert einen gemeinsamen 64-Fermionträger und 60 Bosonkanäle. Keiner dieser Schritte darf allein durch neue Indexnamen zu Raumorten oder","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Quellenweg: ursprünglicher Clock ist keine Kopiermaschine","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11851,"byte_start":9011,"id":"section:7777e421ff2ae6beb87e","kind":"subsection","labels":["stuxe4rkerer-vergleich-selbst-gleiche-gesamte-zweiladungsspektren-reichen-nicht"],"line_end":254,"line_start":196,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/001-section-tfpt-universalraum-zusammensetzung-aus-der-gemei.tex","status_markers_as_written":[],"summary_excerpt":"Eine unabhängige Familie verwendet nur eine gemeinsame Bosonbank und einen zusätzlichen symmetrischen normierten Tensor C auf L Fermionkopien. Ihre globalen Paarmatrizen sind [formula in source] . In dieser Familie bleiben das globale Paargramm [formula in source] und das gesamte N=2-Hamiltonspektrum unverändert. Die lokalen Einzelkopienamplituden bleiben dagegen nicht unverändert; diese Annahme ist ausdrücklich vers","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Stärkerer Vergleich: selbst gleiche gesamte Zweiladungsspektren reichen nicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":14798,"byte_start":11851,"id":"section:75687a0b6611171356a6","kind":"subsection","labels":["vereinfachter-vollstuxe4ndiger-prozess-mit-einer-echten-aufzeichnung"],"line_end":322,"line_start":255,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/001-section-tfpt-universalraum-zusammensetzung-aus-der-gemei.tex","status_markers_as_written":[],"summary_excerpt":"Der native Dreizustandsraum [formula in source] aus v1.6.8 bleibt unverändert. Neu ist die mittlere Operation:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Vereinfachter vollständiger Prozess mit einer echten Aufzeichnung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17436,"byte_start":14798,"id":"section:4c7dd3095ac459fd8d28","kind":"subsection","labels":["relativistischer-anschluss-ein-positiver-adapter-und-ein-negativer-kinetiktest"],"line_end":377,"line_start":323,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/001-section-tfpt-universalraum-zusammensetzung-aus-der-gemei.tex","status_markers_as_written":[],"summary_excerpt":"Für ein gemischthändiges Komposit [formula in source] ist ohne zusätzliche Lorentzstruktur keine lineare Auslese in einen linken Weylspinor möglich. 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Relativistischer Anschluss: ein positiver Adapter und ein negativer Kinetiktest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1933,"byte_start":0,"id":"section:7f30f4dca8448353b86e","kind":"subsection","labels":["was-die-vier-rechnungen-gemeinsam-haben-und-was-nicht"],"line_end":44,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/002-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 6 ) * 0.2500 > p( - 6 ) * 0.2500 > p( - 6 ) * 0.2500 > p( - 6 ) * 0.2500@ Rechnung & Tatsächlicher Träger & Neue Voraussetzung & Nicht übertragen \\\\ Zwei Charts & 128 Fermionmoden, zwei Bosonbanken, N=2 & Überlappung c und globale Vertexsumme & Keine native Auswahl von c \\\\ Ein normierter C-Tensor & 64L Fermionmoden, eine Bosonbank, N=2 und 3 & Normiertes symmetrisches C & Keine unveränderte lokale Einzelkop","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. Was die vier Rechnungen gemeinsam haben und was nicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4435,"byte_start":1933,"id":"section:e259313e6fa7f0efdfc6","kind":"subsection","labels":["t1-t8-konkrete-bewegung-der-grenze"],"line_end":99,"line_start":45,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/002-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"Die Benennungen folgen der Arbeitszuordnung der vollständigen v1.6.8. Kein vollständiges T-Gate wird geschlossen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8. T1-T8: konkrete Bewegung der Grenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4527,"byte_start":4435,"id":"section:030299d1051b0ed4cb96","kind":"subsection","labels":["der-effektivste-nuxe4chste-versuch"],"line_end":102,"line_start":100,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/002-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"9. Der effektivste nächste Versuch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5450,"byte_start":4527,"id":"section:f9bec9d4b8977886c4f3","kind":"subsubsection","labels":["a.-quellstrahlen-zu-gemeinsamem-truxe4ger---erster-fehlender-pfeil"],"line_end":119,"line_start":103,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/002-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"Aus den tatsächlichen Originalobjekten sollen zwei Einbettungen E_L,E_R sowie Bosonbank- und Vertexzuordnung folgen. Nicht nur eine bekannte Überlappungszahl einsetzen, sondern Typen, Gruppenwirkung, CAR und Operationen mitliefern. Das unmittelbar entscheidbare Ziel ist [formula in source] , bei skalarem Ansatz cI.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"A. Quellstrahlen zu gemeinsamem Träger - erster fehlender Pfeil","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6206,"byte_start":5450,"id":"section:1d42ba22c24bae896e22","kind":"subsubsection","labels":["b.-autonomer-eingriff-statt-gewuxe4hltem-puls"],"line_end":135,"line_start":120,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/002-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"Den benötigten Nb-Eingriff und den Zeigerkoppler als Teile eines gemeinsamen zeitunabhängigen Controller-System-Modells konstruieren. Es muss die schon gerechnete Wirkung reproduzieren, Gesamtladung und Gesamtenergie mitführen und den Zustand des Controllers vor und nach dem Versuch angeben. Eine beliebig angesetzte Taktsequenz wäre noch keine ursprüngliche Uhr.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B. Autonomer Eingriff statt gewähltem Puls","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7156,"byte_start":6206,"id":"section:3e58c3481f2374007870","kind":"subsubsection","labels":["c.-einen-nichtnullen-vertexkonsistenten-feldkanal-auf-derselben-quelle"],"line_end":154,"line_start":136,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/002-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"Nicht den freien masselosen Nullansatz weiter ausbauen. Zuerst die tatsächlichen Feldkomponenten zum Vertex und zur geladenen nativen Antwort festlegen; dann das konkrete Matrixelement der Quelle unter der vorgeschlagenen wechselwirkenden oder massiven Kinetik berechnen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"C. Einen nichtnullen, vertexkonsistenten Feldkanal auf derselben Quelle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8532,"byte_start":7156,"id":"section:0c1e55c1118719ee8513","kind":"subsection","labels":["pruxfcf--und-veruxf6ffentlichungsstand"],"line_end":180,"line_start":155,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/002-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"Vier neue Stränge wurden aus eingefrorenen Eingaben normal und optimiert ausgeführt, mit Warnungen als Fehler und identischen Ergebnisbytes: 514 eigene exakt arbeitende Bedingungen und vier numerische Kontrollen je Variante. Die exakte Kategorie enthält auch Quellenpins und Strukturguards, nicht nur mathematische Sätze. Separat wurden 17 native Konstruktionsguards und 1073 alte P0/P1-Quellguards wiederholt. Die gesam","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10. Prüf- und Veröffentlichungsstand","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9260,"byte_start":8532,"id":"section:2951fa7033df9008b60b","kind":"subsubsection","labels":["automatisch-aus-dem-abgeschlossenen-replay"],"line_end":205,"line_start":181,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/002-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"@lrr@ Eigener Strang & Exakte Bedingungen & Numerische Bedingungen \\\\ composition & 67 & 0 \\\\ field & 85 & 0 \\\\ protocol & 92 & 4 \\\\ source & 270 & 0 \\\\","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Automatisch aus dem abgeschlossenen Replay","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9417,"byte_start":9260,"id":"section:374cd20b88a9ce296e23","kind":"section","labels":["vollstuxe4ndiger-beweis-huxf6here-antwort-und-positive-kopplungsmatrix"],"line_end":208,"line_start":206,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/002-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Vollständiger Beweis: höhere Antwort und positive Kopplungsmatrix","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":9719,"byte_start":9417,"id":"section:e39b18cf83ae6c0de5d0","kind":"section","labels":["eine-huxf6here-antwort-liest-die-zusammensetzung-aus"],"line_end":219,"line_start":209,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/002-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Eine höhere Antwort liest die Zusammensetzung aus","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10606,"byte_start":9719,"id":"section:166e281bb36316653ee2","kind":"subsection","labels":["frage-und-ergebnis"],"line_end":236,"line_start":220,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/002-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"Kann die innere W-Struktur schon bestimmen, wie mehrere Vorkommen gemeinsam wirken? Für eine ausdrücklich erklärte, besonders einfache Familie lässt sich die Frage exakt beantworten: Nein, nicht aus W und auch nicht aus dem gesamten Zweiladungsspektrum allein. Die Dreiladungsantwort bestimmt jedoch genau die zusätzlich gewählte positive Kopplungsmatrix. Das ist ein konstruktiver Anschluss für die vom Benutzer vorgesc","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Frage und Ergebnis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":12167,"byte_start":10606,"id":"section:8f4d1d53853f6ca56ef2","kind":"subsection","labels":["gemeinsame-urspruxfcngliche-daten"],"line_end":278,"line_start":237,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/002-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"Wir verwenden den unveränderten realen Tensor W mit 60 Kanälen und 2016 Fermionpaarspalten. Aus jeder Zeile wird eine antisymmetrische 64-mal-64-Matrix A_A: oberhalb der Diagonale steht W, unterhalb sein negatives Transponiertes. Direkt aus allen 480 Vertices folgt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Gemeinsame ursprüngliche Daten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13559,"byte_start":12167,"id":"section:4a155b98d22508396150","kind":"subsection","labels":["ein-zusuxe4tzlicher-symmetrischer-kompositionstensor"],"line_end":308,"line_start":279,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/002-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"Fermionen erhalten einen zusätzlichen L-dimensionalen Multiplizitätsfaktor; die 60 Bosonen bleiben eine einzige gemeinsame Bank. Wähle eine komplex-symmetrische Matrix C mit [formula in source] . Die antisymmetrischen globalen Paarmatrizen lauten","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Ein zusätzlicher symmetrischer Kompositionstensor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15206,"byte_start":13559,"id":"section:e0abf53daa3d1aa5f478","kind":"subsection","labels":["gleiche-vollstuxe4ndige-zweiladungsspektren-unterschiedliche-globale-dynamik"],"line_end":346,"line_start":309,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/002-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"wobei J_L die Matrix aus lauter Einsen bezeichnet. Beide sind symmetrisch, normiert, invariant unter Permutation der Kopien und stimmen für L=1 mit dem nativen Modell überein. Sie liefern jedoch verschiedene spätere Physik. Permutationssymmetrie ist dabei keine geometrische Lokalität.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Gleiche vollständige Zweiladungsspektren, unterschiedliche globale Dynamik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":2746,"byte_start":0,"id":"section:0ac7a366399ea6ae0da6","kind":"subsection","labels":["allgemeine-car-identituxe4t-auf-n3"],"line_end":72,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/003-subsection-5-allgemeine-car-identit-t-auf.tex","status_markers_as_written":[],"summary_excerpt":"Bezeichne die globale Dreifermion-zu-Boson-Fermion-Abbildung mit [formula in source] . Die Boson-Fermion-Zeilen werden als [formula in source] angeordnet. Aus der Paar-CAR-Kontraktion folgt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Allgemeine CAR-Identität auf N=3","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3968,"byte_start":2746,"id":"section:b231fbba6279ce15d1ab","kind":"subsection","labels":["positive-ruxfcckrechnung-der-schatten-bestimmt-q"],"line_end":98,"line_start":73,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/003-subsection-5-allgemeine-car-identit-t-auf.tex","status_markers_as_written":[],"summary_excerpt":"Die obige Identität lässt sich tatsächlich invertieren. Mit [formula in source] gilt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Positive Rückrechnung: der Schatten bestimmt Q","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5121,"byte_start":3968,"id":"section:bfc2eb0442d4578e9c03","kind":"subsubsection","labels":["anschluss-an-dieselbe-bosonzahl-auslese"],"line_end":123,"line_start":99,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/003-subsection-5-allgemeine-car-identit-t-auf.tex","status_markers_as_written":[],"summary_excerpt":"Auf N=3 hat H_C die Blockform [formula in source] . Für einen normierten Eingang v auf der Boson-Fermion-Seite gilt exakt im Taylor-Anfang","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Anschluss an dieselbe Bosonzahl-Auslese","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6741,"byte_start":5121,"id":"section:1de0e03cad35137ea4ca","kind":"subsection","labels":["warum-ein-einzelnes-c-muxf6glicherweise-zu-einfach-fuxfcr-gerichteten-ladungstransport-ist"],"line_end":152,"line_start":124,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/003-subsection-5-allgemeine-car-identit-t-auf.tex","status_markers_as_written":[],"summary_excerpt":"Jede komplex-symmetrische endliche Matrix besitzt eine Takagi-Zerlegung [formula in source] mit unitärem U und nichtnegativem diagonalem D. Eine Standardreferenz ist https://arxiv.org/abs/2009.03990Haber, A tale of three diagonalizations, Abschnitt 7. Der Prüfer kontrolliert zusätzlich ein nichtreelles rationales Beispiel. Der allgemeine Existenzsatz wird aus der linearen Algebra übernommen, nicht aus diesem Beispiel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. Warum ein einzelnes C möglicherweise zu einfach für gerichteten Ladungstransport ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7597,"byte_start":6741,"id":"section:b6f67208bc142d379c6e","kind":"subsection","labels":["pruxe4zise-nuxe4chste-entscheidung"],"line_end":168,"line_start":153,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/003-subsection-5-allgemeine-car-identit-t-auf.tex","status_markers_as_written":[],"summary_excerpt":"Der einfachste nächste Auftrag ist kein neuer großer Tensorraum. Er ist eine typisierte Quellvorschrift für zwei Einbettungen E_L,E_R und ihre Überlappung [formula in source] , einschließlich der Bosonbankzuordnung. Die vorhandenen Quellstrahlen enthalten diskrete Überlappungszahlen, aber der direkte Import ihrer internen C4-Projektoren als neue triviale Kopien ist nicht äquivariant begründet.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8. Präzise nächste Entscheidung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8432,"byte_start":7597,"id":"section:788a1aba5110cb5503e6","kind":"subsection","labels":["reproduktion-und-grenze"],"line_end":185,"line_start":169,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/003-subsection-5-allgemeine-car-identit-t-auf.tex","status_markers_as_written":[],"summary_excerpt":"verify_composition.py führt 67 explizite exakt arbeitende Prüfbedingungen aus, einschließlich Quellenpins und Strukturguards. Es gibt keine numerischen Toleranzprüfungen. Die allgemeine Formel und ihre Inversion sind oben algebraisch hergeleitet; drei vollständige N=3-CAR-Aufbauten kontrollieren Normalisierung, Vorzeichen und komplexe Konvention unabhängig.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. Reproduktion und Grenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":8577,"byte_start":8432,"id":"section:866633a172e15cfadf39","kind":"section","labels":["teilbericht-a-urspruxfcngliche-quelle-und-uxfcberlappende-charts"],"line_end":188,"line_start":186,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/003-subsection-5-allgemeine-car-identit-t-auf.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Teilbericht A: ursprüngliche Quelle und überlappende Charts","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8930,"byte_start":8577,"id":"section:64b4d09869f02bb67a55","kind":"section","labels":["quellenkomposition-dieselben-lokalen-vertices-verschiedene-gemeinsame-fermionen"],"line_end":200,"line_start":189,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/003-subsection-5-allgemeine-car-identit-t-auf.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Quellenkomposition: dieselben lokalen Vertices, verschiedene gemeinsame Fermionen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10152,"byte_start":8930,"id":"section:1a4f1df5290db5a83c1a","kind":"subsection","labels":["stuxe4rkstes-neues-ergebnis"],"line_end":223,"line_start":201,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/003-subsection-5-allgemeine-car-identit-t-auf.tex","status_markers_as_written":[],"summary_excerpt":"Die geprüfte Quelle bestimmt bereits einen gemeinsamen lokalen CAR-Träger mit 64 Fermionmoden, nicht 480 unabhängige Wechselwirkungsbanken. Jeder dieser Fermionmoden kommt in genau 15 der 480 nichtverschwindenden Vertices vor. 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Der Zähler J_PC_P hat Rang zwei und sein Quadrat ist null. Er ist somit kein Projektor; der massive Ausdruck lässt sich nicht durch bloßes Einsetzen von P²=0 fortsetzen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was auf dem Lichtkegel scheitert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2535,"byte_start":1135,"id":"section:dd143c9728433efb2133","kind":"subsection","labels":["ein-expliziter-ruxfcckweg-mit-zusuxe4tzlicher-referenz"],"line_end":58,"line_start":22,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/006-subsubsection-was-auf-dem-lichtkegel.tex","status_markers_as_written":[],"summary_excerpt":"Für ein zukünftiges Null-P und ein zukünftiges zeitartiges Q ist σ 0, also ist der Rückweg endlich. 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Mit sämtlichen inneren Sonden bleibt der unsichtbare Raum","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum nur ein Schatten auch nach beliebig langer Zeit nicht reicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3564,"byte_start":816,"id":"section:ea037044821446e02345","kind":"subsection","labels":["echter-kausaler-eingriff-ohne-zusuxe4tzlichen-hoppingterm"],"line_end":83,"line_start":19,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/008-subsubsection-warum-nur-ein-schatten-auch-nach-beliebig-.tex","status_markers_as_written":[],"summary_excerpt":"Jede aktive W-Spalte gehört genau einer Zeile; jede Zeile enthält acht disjunkte Fermionpaare. 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Was Holografie hier sinnvoll bedeutet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9972,"byte_start":7392,"id":"section:04c75bbf95e8991debdc","kind":"subsection","labels":["nuxe4chste-entscheidende-nachweise"],"line_end":214,"line_start":169,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/008-subsubsection-warum-nur-ein-schatten-auch-nach-beliebig-.tex","status_markers_as_written":[],"summary_excerpt":"Übergeordnete Frage: Welche ursprüngliche Kompositionsregel erzeugt gemeinsam unterscheidbare Vorkommen, ihre Bewegung, ihren Zustand und ihre Instrumente? Die letzte nachgereichte fundamentale Reduktion trifft diese Frage. Ein genaueres lokales Spektrum kann sie nicht ersetzen. Die folgenden kleinen Prüfungen dienen als überprüfbare Annahmekriterien für eine solche Regel; sie sind keine Ersatzdefinition von Raum und","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. Nächste entscheidende Nachweise","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12471,"byte_start":9972,"id":"section:80ea341e2883438e9aab","kind":"subsection","labels":["t1-bis-t8-nach-dieser-runde"],"line_end":269,"line_start":215,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/008-subsubsection-warum-nur-ein-schatten-auch-nach-beliebig-.tex","status_markers_as_written":[],"summary_excerpt":"Die Bezeichnungen folgen der Arbeitszuordnung der geprüften Synthese; die jeweiligen vollständigen Tore bleiben offen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10. T1 bis T8 nach dieser Runde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":13483,"byte_start":12471,"id":"section:3aebf92bc523335a23d5","kind":"subsection","labels":["reproduktionsumfang"],"line_end":289,"line_start":270,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/008-subsubsection-warum-nur-ein-schatten-auch-nach-beliebig-.tex","status_markers_as_written":[],"summary_excerpt":"Der gemeinsame Replay führt alle eigenen mathematischen Prüfer normal und optimiert mit Warnungen als Fehler aus. Die Teilberichte unterscheiden exakte Identitäten von numerischen Kontrollen. Die 57 Prüfbedingungen des gelieferten Papers und dessen 20 übernommene Kettenprüfungen werden separat ausgewiesen, nicht als neue eigene Entdeckungen addiert. Sie decken nicht automatisch jeden Satz des Papers ab; die Korrektur","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"11. Reproduktionsumfang","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14016,"byte_start":13483,"id":"section:eeb3a1cf7d416dca7171","kind":"section","labels":["nachgereichte-texte-neue-norm-korrigierte-zustandszuordnung-und-feldadapter"],"line_end":299,"line_start":290,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/008-subsubsection-warum-nur-ein-schatten-auch-nach-beliebig-.tex","status_markers_as_written":[],"summary_excerpt":"Die drei während der laufenden Prüfung nachgereichten Texte wurden vollständig gelesen und unverändert eingefroren. Sie sind keine Anweisungen, Ergebnisse ungeprüft zu übernehmen. Zwei Texte vereinfachen ältere Arbeitsstände stark; die dritte längere Forschungsnotiz enthält ausführlichere Beweise einer bereits bekannten grundsätzlichen Diagnose.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nachgereichte Texte: neue Norm, korrigierte Zustandszuordnung und Feldadapter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":16417,"byte_start":14016,"id":"section:4c36dfde61d7f687cb6f","kind":"subsection","labels":["a.-ein-tatsuxe4chlich-neuer-rechenwert-truxe4gt-eine-stuxe4rkere-schranke"],"line_end":356,"line_start":300,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":["relation:20f2aa55216b9498e745","relation:50dc7895f539a6a6c633","relation:57586133cbcb10daba3b","relation:6513451a8a7e20a3c212","relation:ba53de3b54fb35c7835b"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/008-subsubsection-warum-nur-ein-schatten-auch-nach-beliebig-.tex","status_markers_as_written":[],"summary_excerpt":"Die Norm der fünften reinen Bosonstufe ist gegenüber dem hiesigen v1.6.7-Snapshot neu:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"A. Ein tatsächlich neuer Rechenwert trägt eine stärkere Schranke","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2319,"byte_start":0,"id":"section:13dfcc4824dcb1fca550","kind":"subsection","labels":["b.-die-einfache-darstellung-vermischt-zwei-nuxe4herungszustuxe4nde"],"line_end":41,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":["relation:6b4e0f7ffdfc57f6bea3","relation:b1038832c15a5d2c8fed"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/009-subsection-b-die-einfache-darstellung-vermischt-zwei.tex","status_markers_as_written":[],"summary_excerpt":"Die Werte um -1.138476Δ, mittlere Bosonzahl 1.0177445, Überlappung mit F von 0.3498904 und Bosonzahl-Shannonwert 1.8712436 Bit gehören zum größeren siebendimensionalen Ritz-Zustand. Die im selben Text genannten Gewichte 0.973684 und 0.026316 gehören dagegen ausdrücklich zu der älteren fünfdimensionalen Basis v0 bis v3 plus w2. Deren Energie liegt um -1.0942319Δ und ihre mittlere Bosonzahl um 0.8421159.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B. Die einfache Darstellung vermischt zwei Näherungszustände","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4503,"byte_start":2319,"id":"section:44be18e562bb6fc844ed","kind":"subsection","labels":["c.-ein-neuer-entscheidender-test-am-feldprojektor"],"line_end":91,"line_start":42,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/009-subsection-b-die-einfache-darstellung-vermischt-zwei.tex","status_markers_as_written":[],"summary_excerpt":"Der Spin-1/2-Projektor im zweiten Text trägt unter einer bestimmten Händigkeit. Für","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"C. Ein neuer entscheidender Test am Feldprojektor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5845,"byte_start":4503,"id":"section:23e4bf7f620689d0d6e4","kind":"subsection","labels":["d.-weitere-uxfcbernahmegrenzen"],"line_end":122,"line_start":92,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/009-subsection-b-die-einfache-darstellung-vermischt-zwei.tex","status_markers_as_written":[],"summary_excerpt":"Die Clock ist nach der späteren konkreten Konstruktion ein Element der inneren Spin(10)-Darstellung. Die ältere Formulierung „äußerer Handgriff`` wird nicht als neue Herkunftstatsache übernommen. Die große Kommutantdimension zählt nicht direkt physische Freiheitsgrade. Ein skalarer Kommutant bedeutet nicht automatisch beliebige dynamische Kontrolle. Als exakter Gegenzeuge haben Spin-1-Kontrollen einen skalaren Kommut","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"D. Weitere Übernahmegrenzen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9126,"byte_start":5845,"id":"section:2d7535bce1d81317b2ba","kind":"subsection","labels":["e.-die-dritte-notiz-richtige-richtung-uxfcberwiegend-bereits-beruxfccksichtigt"],"line_end":187,"line_start":123,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/009-subsection-b-die-einfache-darstellung-vermischt-zwei.tex","status_markers_as_written":[],"summary_excerpt":"Die längere fundamentale Reduktion ergänzt den bereits eingefrorenen früheren Kommentar um die ausführliche Herleitung. Ihr stärkster Satz trägt: Bei invariantem H, invariantem Ω und irreduzibler innerer Entnahmefamilie gilt für die gesamte lokale Antwort","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"E. Die dritte Notiz: richtige Richtung, überwiegend bereits berücksichtigt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10124,"byte_start":9126,"id":"section:6f960b0865221bd7a677","kind":"subsubsection","labels":["automatisch-aus-dem-abgeschlossenen-replay-1"],"line_end":219,"line_start":188,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/009-subsection-b-die-einfache-darstellung-vermischt-zwei.tex","status_markers_as_written":[],"summary_excerpt":"@lrr@ Eigener Strang & Exakte Bedingungen & Numerische Bedingungen \\\\ causal & 662 & 10 \\\\ common3 & 43 & 0 \\\\ late_field & 36 & 0 \\\\ late_moments & 2 & 2 \\\\ late_norm & 36 & 10 \\\\ mechanism & 261 & 0 \\\\ phase_bridge & 32 & 0 \\\\ resource_boundary & 24 & 0 \\\\ shadows & 5417 & 17 \\\\","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Automatisch aus dem abgeschlossenen Replay","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10267,"byte_start":10124,"id":"section:cb2e0d13e76f8fcef9c0","kind":"section","labels":["teilbericht-a-urspruxfcnglicher-mechanismus-und-referenzbilanz"],"line_end":222,"line_start":220,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/009-subsection-b-die-einfache-darstellung-vermischt-zwei.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Teilbericht A: ursprünglicher Mechanismus und Referenzbilanz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10446,"byte_start":10267,"id":"section:efe8f5dd8b6d006bb578","kind":"section","labels":["urspruxfcnglicher-mechanismus-erhaltung-und-die-kleinste-zusuxe4tzliche-ressource"],"line_end":226,"line_start":223,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/009-subsection-b-die-einfache-darstellung-vermischt-zwei.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Ursprünglicher Mechanismus, Erhaltung und die kleinste zusätzliche Ressource","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11997,"byte_start":10446,"id":"section:3df20848201665083544","kind":"subsection","labels":["ergebnis-1"],"line_end":259,"line_start":227,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/009-subsection-b-die-einfache-darstellung-vermischt-zwei.tex","status_markers_as_written":[],"summary_excerpt":"Exakt neu: Am unveränderten Tensor schließt ein zweidimensionaler G-Singulett-Unterraum mit physischer Ladung N=4 unter dem gesamten nativen H. Seine Matrix ist","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ergebnis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16031,"byte_start":11997,"id":"section:4dfac91e690eb39a3ac0","kind":"subsection","labels":["was-die-tatsuxe4chlichen-quellen-konstruieren"],"line_end":336,"line_start":260,"numbered_or_version_tokens_as_written":["S0.1","S0.4"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":["relation:01c334c4dcd8e2dfae3e","relation:4cabdd181a342c819aad","relation:e75a35358e573d572c6b"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/009-subsection-b-die-einfache-darstellung-vermischt-zwei.tex","status_markers_as_written":[],"summary_excerpt":"Alle zwölf verwendeten Eingaben sind unter inputs/ unverändert eingefroren; inputs_manifest.json enthält ihre ursprünglichen Pfade, Größen und SHA-256. Das maßgebliche Tensorarchiv besitzt weiter den SHA-256 3f00a0892157a691e4ef26920c3702772c7bf76a250fad98ff04a079bb64b763.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Was die tatsächlichen Quellen konstruieren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18109,"byte_start":16031,"id":"section:69e77f4b070658d968e2","kind":"subsection","labels":["geschlossener-erhaltungssatz-fuxfcr-das-dokumentierte-alphabet"],"line_end":397,"line_start":337,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/009-subsection-b-die-einfache-darstellung-vermischt-zwei.tex","status_markers_as_written":[],"summary_excerpt":"hat jedes der 480 signierten Wechselwirkungsmonome Ladung +2−1−1=0. Nb, alle Modenbesetzungen und alle passiven Bilineare f†Af beziehungsweise b†Cb sind ebenfalls neutral. Die dokumentierten inneren Liegeneratoren werden genau auf diese Weise zweitquantisiert. Die Clock schickt f† nach GF f† und b† nach GB b†, mischt also keine Erzeuger mit Vernichtern.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Geschlossener Erhaltungssatz für das dokumentierte Alphabet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":984,"byte_start":0,"id":"section:dbca6f7e5c6f2a411693","kind":"subsubsection","labels":["instrumente-und-die-genaue-ancilla-grenze"],"line_end":19,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/010-subsubsection-instrumente-und-die-genaue.tex","status_markers_as_written":[],"summary_excerpt":"Ein Instrument mit Krausoperatoren Kx aus A0 kann aus einem scharfen N-Sektor keinen anderen erzeugen. Eine spurtreue Summe solcher Zweige erhält die gesamte Sektorverteilung. Selektive Konditionierung kann die Gewichte einer bereits vorhandenen Mischung verändern, aber keine neue Sektorstütze erzeugen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Instrumente und die genaue Ancilla-Grenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3180,"byte_start":984,"id":"section:833648cb12b6eb75534f","kind":"subsection","labels":["die-kleinste-zusuxe4tzliche-operation-ist-schon-algebraisch-ausreichend"],"line_end":67,"line_start":20,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/010-subsubsection-instrumente-und-die-genaue.tex","status_markers_as_written":[],"summary_excerpt":"Dabei ist der zweite Bosonindex BAR(A). Es gibt dreißig solche ungeordneten Paare. Die vollständige Invarianz von η wird an allen 45+15 ursprünglichen Liegeneratoren geprüft. Die 60 verschiedenen Bosongewichte und der zusammenhängende Lie-Wirkungsgraph beweisen zusätzlich, dass diese Paarung bis auf einen Skalar eindeutig ist.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. 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Ein neuer kleiner ursprünglicher Singulettmechanismus","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7845,"byte_start":5679,"id":"section:9860e2429e187f5304de","kind":"subsection","labels":["exakter-gemeinsamer-dreizustandsprozess-mit-voller-innerer-symmetrie"],"line_end":189,"line_start":128,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/010-subsubsection-instrumente-und-die-genaue.tex","status_markers_as_written":[],"summary_excerpt":"Man gewähre eine Referenz R mit zwei G-trivialen Zuständen 0⟩R und 4⟩R, deren N_R-Ladungen null beziehungsweise vier sind. Setze","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. 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Sie ersetzt den dortigen Transferzeugen nicht und beweist dessen native Herkunft nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Anschluss an das nachgereichte Forschungspaper","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":12583,"byte_start":9811,"id":"section:6bb0c3d699ea68a4ed20","kind":"subsection","labels":["ressourcenbilanz-und-der-jetzt-konkrete-nuxe4chste-nachweis"],"line_end":289,"line_start":232,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/010-subsubsection-instrumente-und-die-genaue.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333@ Ressource & Herkunft im geprüften Vertrag & Was noch zu liefern wäre \\\\ W, η, innere Darstellung, endliche Clock & Tatsächliche Quellkonstruktion und erneuter exakter Replay & Physische Identifikation des Trägers \\\\ Hnat mit Δ,g & Bestehender ausdrücklich festgelegter Modellvertrag & Physische Auswahl und Kalibrierung \\\\ Zweizustandsblock β↔ρ & Neue volls","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Ressourcenbilanz und der jetzt konkrete nächste Nachweis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14226,"byte_start":12583,"id":"section:9d03100e28aedb943e61","kind":"subsection","labels":["reproduktion-und-beweisumfang"],"line_end":325,"line_start":290,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/010-subsubsection-instrumente-und-die-genaue.tex","status_markers_as_written":[],"summary_excerpt":"Benötigt werden Python, NumPy, SciPy und SymPy. Der Replay liest nur die eingefrorenen Eingaben und braucht weder das ursprüngliche Repository noch Netzwerkzugriff. freeze.py ist nur das Herkunftswerkzeug für die erste Archivierung und gehört nicht zum wissenschaftlichen Replay.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. Reproduktion und Beweisumfang","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":14345,"byte_start":14226,"id":"section:e72259dd43e8195415d6","kind":"section","labels":["teilbericht-b-vollstuxe4ndige-innere-schattenkarte"],"line_end":328,"line_start":326,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/010-subsubsection-instrumente-und-die-genaue.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Teilbericht B: vollständige innere Schattenkarte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14535,"byte_start":14345,"id":"section:f0c73c5a499d4d5e9f02","kind":"section","labels":["gemeinsame-schattenkarte-auf-dem-urspruxfcnglichen-w"],"line_end":333,"line_start":329,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/010-subsubsection-instrumente-und-die-genaue.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Gemeinsame Schattenkarte auf dem ursprünglichen W","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15550,"byte_start":14535,"id":"section:7e3a3c73111fd6c8e9c7","kind":"subsection","labels":["ergebnis-2"],"line_end":352,"line_start":334,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/010-subsubsection-instrumente-und-die-genaue.tex","status_markers_as_written":[],"summary_excerpt":"Der ursprüngliche Tensor liefert jetzt eine vollständig berechnete gemeinsame Schattenkarte für den inneren hellen N=2-Code. 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Eine konkrete endliche Famili","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ergebnis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2268,"byte_start":0,"id":"section:19ee6e20c2c1d79f4487","kind":"subsection","labels":["ein-gemeinsamer-truxe4ger-mehrere-schatten"],"line_end":55,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/011-subsection-1-ein-gemeinsamer-tr-ger-mehrere.tex","status_markers_as_written":[],"summary_excerpt":"Mit V=W†/√8 gilt V†V=I auf C\\^60. Für eine logische Dichtematrix ρ lautet der Schatten eines Fermionoperators O","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Ein gemeinsamer Träger, mehrere Schatten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4351,"byte_start":2268,"id":"section:a3a3802cb3302c9a3660","kind":"subsection","labels":["exakter-rangbeweis-am-tensor"],"line_end":103,"line_start":56,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/011-subsection-1-ein-gemeinsamer-tr-ger-mehrere.tex","status_markers_as_written":[],"summary_excerpt":"Die Datei enthält zehn symmetrische 16×16-Matrizen β_k. Mit den sechs antisymmetrischen 4×4-Farbmatrizen ε_c gilt eintragsweise","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Exakter Rangbeweis am Tensor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":5559,"byte_start":4351,"id":"section:ae2b3cdf009ddae4c556","kind":"subsubsection","labels":["was-genau-fehlt"],"line_end":133,"line_start":104,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/011-subsection-1-ein-gemeinsamer-tr-ger-mehrere.tex","status_markers_as_written":[],"summary_excerpt":"Die gesamte Hermitesche Algebra zerfällt in den beiden reellen Faktoren als","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was genau fehlt?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6884,"byte_start":5559,"id":"section:ad5210cd516b161bf899","kind":"subsection","labels":["zwei-orthogonale-zustuxe4nde-mit-identischen-eingeschruxe4nkten-schatten"],"line_end":169,"line_start":134,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/011-subsection-1-ein-gemeinsamer-tr-ger-mehrere.tex","status_markers_as_written":[],"summary_excerpt":"In der ursprünglichen logischen Gewichtsbasis, nullbasiert mit A=6k+c, setze","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Zwei orthogonale Zustände mit identischen eingeschränkten Schatten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9861,"byte_start":6884,"id":"section:ffcf50b97e6b31f9945f","kind":"subsection","labels":["endliche-minimale-familie-fuxfcr-vollstuxe4ndige-rekonstruktion"],"line_end":242,"line_start":170,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/011-subsection-1-ein-gemeinsamer-tr-ger-mehrere.tex","status_markers_as_written":[],"summary_excerpt":"Jede unterstützte Paarspalte des W hat genau einen Eintrag±1. Daher gilt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Endliche, minimale Familie für vollständige Rekonstruktion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10908,"byte_start":9861,"id":"section:3519d5bc3c1bf4f72709","kind":"subsubsection","labels":["unabhuxe4ngige-rekonstruktionspruxfcfung"],"line_end":262,"line_start":243,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/011-subsection-1-ein-gemeinsamer-tr-ger-mehrere.tex","status_markers_as_written":[],"summary_excerpt":"Die Familie wird ohne Zustandsdaten festgelegt. Anschließend werden die beiden obigen reinen Zustände sowie sechs deterministisch zufällige Zustände der Ränge 1, 2, 5, 17, 60, 60 in derselben ursprünglichen W-Codebasis verwendet. Aus ihren 3599 kalibrierten Schatten rekonstruiert der Prüfer die vollständigen Dichtematrizen. 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Der exakte lineare Inversenrechner liefert mit der Frobenius-Normschranke","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bedingte Fehlergrenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":967,"byte_start":0,"id":"section:b3cf658dea351b1b3072","kind":"subsection","labels":["beweisumfang"],"line_end":20,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":["relation:1a95449240063992ffdb","relation:62137a14a13f7a53b361","relation:f7b210222978e9c2625a"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/013-subsection-beweisumfang-label-beweisumfang.tex","status_markers_as_written":[],"summary_excerpt":"verify_common3.py prüft den eingefrorenen W, die Isometrie, alle Intertwining-Identitäten, den ausdrücklichen n5-Leckterm, die zwei kausalen Endwahrscheinlichkeiten, beide symbolischen Determinanten und die rationale Inversen-Normschranke. common3.json und common3_OO.json sind die normalen und optimierten Replays. Der frühere Bericht und Prüfer wurden nicht geändert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Beweisumfang","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":1128,"byte_start":967,"id":"section:348114a2d414af3f02e0","kind":"section","labels":["nachtragspruxfcfung-a-neue-fuxfcnfte-norm-und-richtige-antwortzustuxe4nde"],"line_end":23,"line_start":21,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/013-subsection-beweisumfang-label-beweisumfang.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Nachtragsprüfung A: neue fünfte Norm und richtige Antwortzustände","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":1269,"byte_start":1128,"id":"section:315ae129b3254892e07e","kind":"section","labels":["nachtrag-a-was-am-neuen-v1.6.3-erkluxe4rtext-wirklich-neu-ist"],"line_end":26,"line_start":24,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/013-subsection-beweisumfang-label-beweisumfang.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Nachtrag A: Was am neuen v1.6.3-Erklärtext wirklich neu ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":2296,"byte_start":1269,"id":"section:1a1728fd2ea0bb1d4b6b","kind":"subsection","labels":["urteil"],"line_end":45,"line_start":27,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/013-subsection-beweisumfang-label-beweisumfang.tex","status_markers_as_written":[],"summary_excerpt":"Ja, ein belastbarer neuer Rechenschritt ist enthalten: Die zuvor fehlende Norm ν5 liegt jetzt mit passendem Quellstand vor. 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Besonders problematisch ist die Vermischun","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Urteil","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":5082,"byte_start":2296,"id":"section:e2bfcce95c5b774160cd","kind":"subsection","labels":["ux3bd5-ist-jetzt-ein-ergebnis-nicht-mehr-nur-eine-programmeinstellung"],"line_end":99,"line_start":46,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/013-subsection-beweisumfang-label-beweisumfang.tex","status_markers_as_written":[],"summary_excerpt":"Der v1.6.7-Snapshot hatte zu Recht festgehalten, dass damals norms_by_traces.json und ein abgeschlossener zugehöriger Replay fehlten. Dieser konkrete Quellenstand hat sich geändert. Der neue Checkerhash be72c728e128ae0ef605980a5bae88ea31049e29e2fd17c43167fbd6ad1d0c89 passt jetzt zum Ergebnis; auch der Common-Hash stimmt. Die vorhandenen normalen und optimierten Normausgaben sind byteidentisch. Der gespeicherte JSON-I","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. ν5 ist jetzt ein Ergebnis, nicht mehr nur eine Programmeinstellung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":7955,"byte_start":5082,"id":"section:865c0a43e38007bd1d69","kind":"subsection","labels":["ist-eine-echte-bessere-variationsgrenze"],"line_end":170,"line_start":100,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":["relation:07aed1edb8bc949247be","relation:18eeaa7a7d10757f768b","relation:3a14080ff93b7f36f99c","relation:3eaf2b8012dfdfd6d1a9","relation:403c9fdbf78af01b06e3","relation:958f15d9ea117db2ea95","relation:9ba9de6d08ebd878bb00","relation:a0ec5854664bfe819735","relation:af9cfb0e14cfaec609bb","relation:b71f6a3caa2784135d58","relation:d7c57e8c060ef6ba81e2","relation:e8871055a57f76c1f239"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/013-subsection-beweisumfang-label-beweisumfang.tex","status_markers_as_written":[],"summary_excerpt":"Die Unterräume aus den normierten bosonweise geordneten Vektoren [formula in source] sind nicht invariant, aber sie sind gültige Variationsräume. Da unterschiedliche k orthogonal sind und H die Bosonzahl höchstens um eins ändert, besitzt die Kompression auf v0, ,v5 exakt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. −1,138 ist eine echte bessere Variationsgrenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10898,"byte_start":7955,"id":"section:8a924ef8eba766c36438","kind":"subsection","labels":["der-text-vermischt-drei-verschiedene-nuxe4herungszustuxe4nde"],"line_end":236,"line_start":171,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":["relation:0c6e4dc4b6c0bdef2eca","relation:2d60ccb46fda14e990d6","relation:52b0da72bb3545289ec5","relation:633e39e0bb6c677a0511","relation:9621139e031be8b3397b"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/013-subsection-beweisumfang-label-beweisumfang.tex","status_markers_as_written":[],"summary_excerpt":"Die neuen kleinen Matrizen wurden unabhängig diagonalisiert. Sie bestätigen die gespeicherten numerischen Ritz-Erwartungswerte, aber nicht deren Umdeutung zu exakten Eigenschaften von Ω.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Der Text vermischt drei verschiedene Näherungszustände","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":12559,"byte_start":10898,"id":"section:ec3804e1a8260dcf8442","kind":"subsubsection","labels":["die-mittleren-antwortenergien-lassen-sich-ohne-riesige-zustandsdateien-korrigieren"],"line_end":276,"line_start":237,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":["relation:994cc4ed6c1432688a96"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/013-subsection-beweisumfang-label-beweisumfang.tex","status_markers_as_written":[],"summary_excerpt":"Aus den CAR folgen für jeden normierten G-Singulettzustand mit N=64:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die mittleren Antwortenergien lassen sich ohne riesige Zustandsdateien korrigieren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":14767,"byte_start":12559,"id":"section:38c5fefe918ee0afdd3b","kind":"subsection","labels":["was-bereits-uxfcberholt-ist"],"line_end":323,"line_start":277,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/013-subsection-beweisumfang-label-beweisumfang.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 2 ) * 0.5000 > p( - 2 ) * 0.5000@ Aussage der Anlage & Prüfung \\\\ Clock sei ein äußerer Handgriff, weil er Gewichte verschiebt & Bereits in v1.6.6/7 durch das explizite Spin(10)-Wort widerlegt. Nichtskalare Wirkung innerhalb eines Irreps bedeutet keine äußere Symmetrie. Die aktuelle Mechanismusprüfung reproduziert zudem den ursprünglichen Clock und seinen passiven Focklift. \\\\ Mit allen gewährten inneren Kon","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. 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Hinzu kommt unsere kleine CAR-Auswertung, die die geladenen ersten Momente auf den richtigen größeren Ritz-Zustand hebt. Das verbessert nachprüfbar die Rechnung im bestehenden nativen Modell.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Was daran spannend ist und was als nächstes trägt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":17081,"byte_start":15683,"id":"section:d85f88be07929d79fd46","kind":"subsection","labels":["reproduktionsbelege"],"line_end":368,"line_start":341,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":["relation:0eac74b1e367ad4aa074","relation:1ae657061a1df506444e","relation:2a4895cb2ab828ce68e6","relation:48990d12a0f765de9b1f","relation:4d36a8d73c76120fd9d7","relation:72d125158e394cfcea2f"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/013-subsection-beweisumfang-label-beweisumfang.tex","status_markers_as_written":[],"summary_excerpt":"late_a/verify.py prüft elf eingefrorene Eingaben, führt die ν1-ν5- Spurnetzwerke frisch aus und baut beide Ritzpolynome unabhängig neu auf. Es gibt 46 eigene Prüfbedingungen: 36 exakte beziehungsweise faktische Prüfungen und 10 numerische Konsistenzprüfungen, separat dazu 1239 ausgeführte Quellguards der Normkonstruktion. Die Guardzahl zählt keine unabhängigen mathematischen Theoreme.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproduktionsbelege","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":17220,"byte_start":17081,"id":"section:24c5dbad4c6fe3d45612","kind":"section","labels":["nachtragspruxfcfung-b-feldprojektor-und-lorentz-huxe4ndigkeit"],"line_end":371,"line_start":369,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/013-subsection-beweisumfang-label-beweisumfang.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Nachtragsprüfung B: Feldprojektor und Lorentz-Händigkeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":633,"byte_start":0,"id":"section:0e43df34119bdd37430d","kind":"section","labels":["nachgereichter-text-b-korrekturen-und-ein-neuer-pruxfcfbarer-feldadapter"],"line_end":11,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":["relation:39f70f7a44f238cc02f6"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/014-section-nachgereichter-text-b-korrekturen-und-ein-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"Der Text mit 45 Zeilen wurde vollständig gelesen. Seine unveränderte Kopie steht in late_sources/attachment_B.txt, SHA-256 9aaf5e18cbc6a84d610b88429872df9b69e6078365bfdc8133c8f17e2c1c3801. Die für die neue Prüfung maßgebliche field_dictionary.py ist gesondert eingefroren, SHA-256 a581bacd17c08dd9a766ae439bfe1e8e35e6d30b9509cb9d98053b897d8ecc13. Die bereits abgeschlossenen Schatten-Dateien wurden nicht verändert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nachgereichter Text B: Korrekturen und ein neuer prüfbarer Feldadapter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5027,"byte_start":633,"id":"section:b2ad4443ec9715ec4881","kind":"subsection","labels":["uxfcbernahmeentscheidung"],"line_end":92,"line_start":12,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/014-section-nachgereichter-text-b-korrekturen-und-ein-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 2 ) * 0.5000 > p( - 2 ) * 0.5000@ Aussage im Text & Belastbare Fassung / konkrete Folge \\\\ 1,44 Milliarden unsichtbare Freiheiten im kleinsten nichttrivialen Sektor & 1444233216 ist die komplexe Kommutantdimension des gewährten Kontrollsatzes X,Nb im N=3-Sektor. Im N=2-Sektor lautet die entsprechende Zahl 3829536. Weder Zahl zählt direkt physische Freiheitsgrade. \\\\ Mit voller Symmetrie sieben, mit Modenzähl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Übernahmeentscheidung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5845,"byte_start":5027,"id":"section:3eed02b154827d2cbfc3","kind":"subsection","labels":["neuer-exakter-kontrollgegenzeuge"],"line_end":109,"line_start":93,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/014-section-nachgereichter-text-b-korrekturen-und-ein-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"Die gewöhnlichen drei Spin-1-Matrizen J_x,J_y,J_z auf C³ erfüllen [J_x,J_y]=iJ_z und zyklisch. Bereits J_x und J_z haben ausschließlich skalare gemeinsame Kommutanten. Der dynamische Lie-Raum ist trotzdem nur su(2) mit Dimension drei, nicht su(3) mit Dimension acht. Das wird im neuen Prüfer durch exakte Ränge und alle drei Kommutatoren kontrolliert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Neuer exakter Kontrollgegenzeuge","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7469,"byte_start":5845,"id":"section:a87f5847efc0340c07e3","kind":"subsection","labels":["was-am-spin-12-projektor-stimmt"],"line_end":156,"line_start":110,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/014-section-nachgereichter-text-b-korrekturen-und-ein-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"Die Feldquelle verwendet die sechs unnormierten Koordinaten","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Was am Spin-1/2-Projektor stimmt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10008,"byte_start":7469,"id":"section:cc4b77877f0ae3b4c963","kind":"subsection","labels":["die-neue-pruxe4zise-huxe4ndigkeitsschranke"],"line_end":219,"line_start":157,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/014-section-nachgereichter-text-b-korrekturen-und-ein-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"Die eingefrorene Tabelle in field_dictionary.py, Zeile 327, bezeichnet den zweiten Faktor als f dagger (1/2,0). Dafür muss die Feldabbildung explizit festgelegt werden. Für ein tatsächliches adjungiertes linkes Weylfeld gilt dagegen ψ† in (0,1/2). Hermitesche Konjugation vertauscht diese Darstellungen; siehe https://arxiv.org/pdf/0812.1594\\#page=9Dreiner, Haber und Martin, Abschnitt 2.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Die neue präzise Händigkeitsschranke","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11663,"byte_start":10008,"id":"section:544ace0c93ee061c1a45","kind":"subsection","labels":["konkreter-nuxe4chster-annahmetest"],"line_end":256,"line_start":220,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/014-section-nachgereichter-text-b-korrekturen-und-ein-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"Der Anschlussauftrag ist jetzt endlich und entscheidbar formuliert:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Konkreter nächster Annahmetest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12572,"byte_start":11663,"id":"section:1912b4c782961b3d7159","kind":"subsection","labels":["reproduktion"],"line_end":279,"line_start":257,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":["relation:c0b367b7970ecac06a6d","relation:e28654014be0fd54538e"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/014-section-nachgereichter-text-b-korrekturen-und-ein-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"Benötigt werden nur Python und SymPy. Der separate Lauf verifiziert zwei Quellenpins sowie 36 exakte Bedingungen pro Modus, keine numerischen Bedingungen. Normaler Lauf und -OO ergeben byte-identische JSON-Ausgaben; Warnungen gelten als Fehler und alle Guards bleiben unter Optimierung aktiv. Die vollständigen Matrizen stehen in late_field.normal.json.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproduktion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":12717,"byte_start":12572,"id":"section:8cc2b374dfe814142897","kind":"section","labels":["nachtragspruxfcfung-c-fundamentale-reduktion-und-globale-quelle"],"line_end":282,"line_start":280,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/014-section-nachgereichter-text-b-korrekturen-und-ein-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Nachtragsprüfung C: fundamentale Reduktion und globale Quelle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12870,"byte_start":12717,"id":"section:b13af8d4c2156629fcd2","kind":"section","labels":["nachtrag-c-uxfcberwiegend-bereits-abgedeckte-fundamentale-reduktion"],"line_end":285,"line_start":283,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/014-section-nachgereichter-text-b-korrekturen-und-ein-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Nachtrag C: überwiegend bereits abgedeckte fundamentale Reduktion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13894,"byte_start":12870,"id":"section:a7c3414e2e89d8cff6ee","kind":"subsection","labels":["uxfcbernahmeurteil"],"line_end":307,"line_start":286,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":["relation:5b3f033f1e6979a6788f","relation:c41f38c78774383ee7a5"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/014-section-nachgereichter-text-b-korrekturen-und-ein-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"Der neue Text ist eine ausführlichere Fassung der bereits eingefrorenen fundamentalen Reduktion, ergänzt um die weitgehend gleiche frühere Gesprächszusammenfassung. Er bringt keinen neuen H-Term, keine neue Operationsquelle und keinen neuen Transferbeweis. Seine wesentlichen mathematischen Einschränkungen sind richtig und bleiben in der gemeinsamen Darstellung erhalten. Eine neue Großrechnung ist dafür nicht notwendi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Übernahmeurteil","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":16714,"byte_start":13894,"id":"section:273366a1ac898172af63","kind":"subsection","labels":["was-bestuxe4tigt-und-bereits-abgedeckt-ist"],"line_end":362,"line_start":308,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/014-section-nachgereichter-text-b-korrekturen-und-ein-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 2 ) * 0.5000 > p( - 2 ) * 0.5000@ Aussage & Urteil und Grenze \\\\ Volle Schur-Antwort T†F(H−E0)T=γF I64 & Richtig bei gruppeninvariantem H und Grundzustand sowie irreduziblem ursprünglichem Entnahmemultiplett. Gilt für die volle beschränkte Spektralfunktion, nicht nur einen dominanten Pol. Schon in v1.6.7 BIG_PICTURE B2 und der eingefrorenen Kurzfassung enthalten. \\\\ Aus C_rs(t)=δ_rs c(t) folgt kein Ortsindex","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was bestätigt und bereits abgedeckt ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2035,"byte_start":0,"id":"section:0377e6e2bd5ba4b80818","kind":"subsection","labels":["ux3bcux3b450-gegen-die-uxe4lteren-gepinnten-zertifikate-bestuxe4tigt"],"line_end":46,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":["relation:143cd41e86a7a7fbf879","relation:655cb5516c14277ad80f","relation:b528a1faaca5cdbfb9f7","relation:c23ef1f5f6b1dc507600","relation:d88c5baae30c27777f6c"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/015-subsection-50-gegen-die-lteren-gepinnten-zertifikate.tex","status_markers_as_written":[],"summary_excerpt":"Das ältere universalraum-native-ground-response-20260915/ground_replay/weak_coupling_ground_normal.json enthält genau die genannte Grenze: g/Δ=1/20, μ/Δ=1/50 und neuer Grundsektor N=0. Sein SHA-256 ist e1cd19988edd33c6799ec6b80f0a52d56e1a532bfe1b56870623a4efaf06bd0c; dies stimmt mit ground_replay_manifest.json überein. Normaler und optimierter vorhandener Bericht sind weiterhin bytegleich. Der eingetragene Programmpi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"μ=Δ/50: gegen die älteren gepinnten Zertifikate bestätigt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3169,"byte_start":2035,"id":"section:c426a010a3695093e0ca","kind":"subsection","labels":["zwei-pruxe4zisierungen-bei-der-uxfcbernahme"],"line_end":73,"line_start":47,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/015-subsection-50-gegen-die-lteren-gepinnten-zertifikate.tex","status_markers_as_written":[],"summary_excerpt":"In §7 sollte „ein positiver Unterschied`` durch „eine nichtverschwindende Differenz`` ersetzt werden. Ein negativer signierter Unterschied ist ebenso ein kausaler Interventionsnachweis; genau dies zeigt der neue N=2-Phasenversuch. Die globale Sektorwahl und die Beobachtbarkeit innerhalb eines festen Gesamtsektors getrennt halten. Ein System-Referenz-Vergleich kann relative Ladungsenergien aufdecken; ein Zusatz μN_tot","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei Präzisierungen bei der Übernahme","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3577,"byte_start":3169,"id":"section:db2201637a8a61196517","kind":"section","labels":["historischer-teil-vollstuxe4ndige-hauptfassung-v1.6.7"],"line_end":81,"line_start":74,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/015-subsection-50-gegen-die-lteren-gepinnten-zertifikate.tex","status_markers_as_written":[],"summary_excerpt":"Die folgende Fassung bleibt wortgetreu erhalten. Den aktuellen Stand liefern die vorangestellten Kapitel v1.6.8. Frühere Aussagen, Fragen und Vorhaben werden dadurch nicht rückwirkend neu bewiesen. Die neue Synthese ist separat vollständig im eingefrorenen Prüfpaket enthalten.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Historischer Teil: vollständige Hauptfassung v1.6.7","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3692,"byte_start":3577,"id":"section:42f81bb4f59413f7752b","kind":"section","labels":["tfpt-universalraum-die-richtige-einfache-kette"],"line_end":84,"line_start":82,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/015-subsection-50-gegen-die-lteren-gepinnten-zertifikate.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"TFPT / Universalraum: die richtige einfache Kette","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3829,"byte_start":3692,"id":"section:29c803f533bc381243f0","kind":"subsection","labels":["vollstuxe4ndige-konsolidierung-v1.6.7---15.-september-2026"],"line_end":87,"line_start":85,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/015-subsection-50-gegen-die-lteren-gepinnten-zertifikate.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Vollständige Konsolidierung v1.6.7 - 15. September 2026","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6435,"byte_start":3829,"id":"section:956a0de4bed7881a86c1","kind":"subsubsection","labels":["ergebnis-und-leseschluxfcssel-1"],"line_end":134,"line_start":88,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/015-subsection-50-gegen-die-lteren-gepinnten-zertifikate.tex","status_markers_as_written":[],"summary_excerpt":"Die zuletzt ergänzte Vogelperspektive steht im Teil B dieser Fassung: Gesucht wird der kleinste gemeinsame beobachtbare Prozess hinter den verschiedenen Ansichten. Ein nativer Rang-60-Kodierer ist bereits vorhanden. Seine Informationsverluste, die minimalen symmetrieverträglichen Dynamiken und der Unterschied zwischen Korrelation und kausalem Eingriff wurden neu berechnet. Das verschiebt die fundamentale Priorität vo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ergebnis und Leseschlüssel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9350,"byte_start":6435,"id":"section:67ea04d03d2a5047dce8","kind":"subsection","labels":["das-gesamtbild-grammatik-prozess-zustand-antwort"],"line_end":199,"line_start":135,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/015-subsection-50-gegen-die-lteren-gepinnten-zertifikate.tex","status_markers_as_written":[],"summary_excerpt":"TFPTs Compiler beschreibt zunächst eine markierte algebraische Grammatik: welche Bausteine zusammenpassen, welche Symmetrien gelten und welche Zahlen innerhalb dieser Konstruktion folgen. Der Universalraum soll diese Grammatik als einen ausführbaren Prozess realisieren. Der entscheidende Unterschied ist der zwischen einem erlaubten Zusammenhang und einer tatsächlich erzeugten physikalischen Entwicklung.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Das Gesamtbild: Grammatik, Prozess, Zustand, Antwort","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9448,"byte_start":9350,"id":"section:0e4e4c20b0a2475bb7ad","kind":"subsection","labels":["was-die-beiden-neuen-texte-beitragen"],"line_end":202,"line_start":200,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/015-subsection-50-gegen-die-lteren-gepinnten-zertifikate.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"2. Was die beiden neuen Texte beitragen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11659,"byte_start":9448,"id":"section:deddae51f738a43765ff","kind":"subsubsection","labels":["quellenstand-und-reproduktionsgrenzen"],"line_end":242,"line_start":203,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/015-subsection-50-gegen-die-lteren-gepinnten-zertifikate.tex","status_markers_as_written":[],"summary_excerpt":"17 ausgewählte Eingaben wurden mit SHA-256 eingefroren: beide Nutzertexte, die zugehörigen Programme und Ergebnisdateien, der native Tensor sowie die vollständige frühere Fassung mit Prüfpaket. Keine fremde Quelldatei wurde verändert. Die Herkunftsdateien gehören zu parallel fortgeschriebenen Arbeitsständen; Dateipins sind deshalb wichtiger als Versionsnamen allein.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2.1 Quellenstand und Reproduktionsgrenzen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13878,"byte_start":11659,"id":"section:b8f8ea1d34b9f50cee46","kind":"subsubsection","labels":["uxfcbernahmeentscheidung-1"],"line_end":290,"line_start":243,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/015-subsection-50-gegen-die-lteren-gepinnten-zertifikate.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 2 ) * 0.5000 > p( - 2 ) * 0.5000@ Aussage aus den Eingaben & Entscheidung für v1.6.7 \\\\ Korrigierter Anfangskommutant 3829536 / 1444233216 & Bestätigt; keine neue Größe gegenüber v1.6.6 \\\\ Nur SU(4) oder nur Spin(10) als zusätzliche Kontrollen & Übernommen; echte Zwischenstufen statt binärer Verfügbarkeit \\\\ Volle Gruppe plus alle Modenbesetzungen erzeugt volle Sektoralgebra & Unabhängig bestätigt, ausdrückl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2.2 Übernahmeentscheidung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14025,"byte_start":13878,"id":"section:cd15e4a423ba47e73fe5","kind":"subsection","labels":["vollstuxe4ndig-geluxf6st-der-erste-verzweigte-singulettbereich"],"line_end":293,"line_start":291,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/015-subsection-50-gegen-die-lteren-gepinnten-zertifikate.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"3. 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Bei k Bosonen gibt es 2k Löcher. Der Singulettbereich auf dieser Stufe liegt in","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.1 Warum vier und nicht eins?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2124,"byte_start":0,"id":"section:2768a3b4bb6c4fa174b5","kind":"subsubsection","labels":["nicht-nur-gezuxe4hlt-die-vier-zustuxe4nde-und-ihre-kopplungen"],"line_end":55,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":["relation:74a2be01099a9e11ea86","relation:fad35dfd1783a65999ae","relation:faf8b60590df9a082fd9"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/016-subsubsection-3-2-nicht-nur-gez-hlt-die-vier-zust-nde-un.tex","status_markers_as_written":[],"summary_excerpt":"In der durch eine Bosonparität äquivalenten Lochdarstellung sei [formula in source] . 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Das ergibt [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.2 Nicht nur gezählt: die vier Zustände und ihre Kopplungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3074,"byte_start":2124,"id":"section:2b55091e1342eb1d98ff","kind":"subsubsection","labels":["der-vollstuxe4ndig-bestimmte-sechszustands-ausschnitt"],"line_end":84,"line_start":56,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/016-subsubsection-3-2-nicht-nur-gez-hlt-die-vier-zust-nde-un.tex","status_markers_as_written":[],"summary_excerpt":"Die Kompression auf alle Singuletts mit k kleiner oder gleich zwei ist exakt äquivalent zu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.3 Der vollständig bestimmte Sechszustands-Ausschnitt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3193,"byte_start":3074,"id":"section:35466c3b02fffb5a8452","kind":"subsection","labels":["die-richtige-einfache-kette-wiederholung-von-h"],"line_end":87,"line_start":85,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/016-subsubsection-3-2-nicht-nur-gez-hlt-die-vier-zust-nde-un.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"4. Die richtige einfache Kette: Wiederholung von H","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4235,"byte_start":3193,"id":"section:d6947daf5d209a326106","kind":"subsubsection","labels":["der-fehler-war-die-gleichsetzung-zweier-verschiedener-stufen"],"line_end":111,"line_start":88,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/016-subsubsection-3-2-nicht-nur-gez-hlt-die-vier-zust-nde-un.tex","status_markers_as_written":[],"summary_excerpt":"Die Vektoren [formula in source] sind nach Bosonzahl geordnet. Schon bekannt ist","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.1 Der Fehler war die Gleichsetzung zweier verschiedener Stufen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5793,"byte_start":4235,"id":"section:95d2e131943728b362df","kind":"subsubsection","labels":["die-ersten-fuxfcnf-glieder-sind-jetzt-exakt-bestimmt"],"line_end":160,"line_start":112,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":["relation:655d1bac4cb8d337626f","relation:6db26683fad673a4ac15"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/016-subsubsection-3-2-nicht-nur-gez-hlt-die-vier-zust-nde-un.tex","status_markers_as_written":[],"summary_excerpt":"Für die normierte Lanczos-Basis [formula in source] schreiben wir","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.2 Die ersten fünf Glieder sind jetzt exakt bestimmt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7400,"byte_start":5793,"id":"section:0cd824c4399f1fef4f2e","kind":"subsubsection","labels":["zehn-vollstuxe4ndige-energiemomente-der-gefuxfcllten-referenz"],"line_end":206,"line_start":161,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/016-subsubsection-3-2-nicht-nur-gez-hlt-die-vier-zust-nde-un.tex","status_markers_as_written":[],"summary_excerpt":"Die Fünfer-Kompression bestimmt [formula in source] für n von 0 bis 9 exakt. Ein Weg, der den nächsten nicht enthaltenen Lanczos-Vektor erreicht und nach F zurückkehrt, benötigt mindestens zehn Schritte. Aus der Tridiagonalität folgt deshalb die angegebene Momentengenauigkeit, ohne die übrige Kette zu erfinden.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.3 Zehn vollständige Energiemomente der gefüllten Referenz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8415,"byte_start":7400,"id":"section:9bf6eba25b6d1d0245b8","kind":"subsubsection","labels":["kleine-rigorose-verschuxe4rfung-der-energiegrenze"],"line_end":235,"line_start":207,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/016-subsubsection-3-2-nicht-nur-gez-hlt-die-vier-zust-nde-un.tex","status_markers_as_written":[],"summary_excerpt":"Am Prüfpunkt g geteilt durch Delta gleich 1/20 hat die niedrigste Eigenenergie der Fünfer-Kompression die durch rationale Sturm-Zählung zertifizierte Lage","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.4 Kleine, rigorose Verschärfung der Energiegrenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10076,"byte_start":8415,"id":"section:76b3fbf654e8a8f60e4f","kind":"subsection","labels":["vollstuxe4ndig-geluxf6st-die-innere-bilineare-zerlegung"],"line_end":274,"line_start":236,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/016-subsubsection-3-2-nicht-nur-gez-hlt-die-vier-zust-nde-un.tex","status_markers_as_written":[],"summary_excerpt":"Die sechs Dimensionen sind 1, 45, 210, 15, 675 und 3150. Der offene Rest ist also nicht mehr unbestimmt:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. 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Die alleinige Erlaubnis, mehr Moden zu unterscheiden, hebt das Hindernis also nicht auf.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6.2 Warum bloßes Lesen noch keine fehlende Bewegung erzeugt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14638,"byte_start":12999,"id":"section:e1bb581f56c807c212c2","kind":"subsection","labels":["feldwuxf6rterbuch-gesicherte-teile-und-korrigierte-reichweite"],"line_end":369,"line_start":339,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/016-subsubsection-3-2-nicht-nur-gez-hlt-die-vier-zust-nde-un.tex","status_markers_as_written":[],"summary_excerpt":"Für die unveränderte antisymmetrische Paarmatrix und gleichhändige Weylfelder verschwindet die ableitungsfreie skalare Kontraktion. Die drei symmetrischen Spinortensoren tragen einen nichtverschwindenden Kanal des Typs (1,0), mit konjugiertem Typ (0,1). Das ist am gesamten ursprünglichen Tensor neu geprüft.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. Feldwörterbuch: gesicherte Teile und korrigierte Reichweite","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":110,"byte_start":0,"id":"section:cf8a5611a9f07f443052","kind":"subsection","labels":["die-fundamentale-frage-was-fehlt-wirklich"],"line_end":3,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/017-subsection-8-die-fundamentale-frage-was-fehlt.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"8. Die fundamentale Frage: was fehlt wirklich?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1503,"byte_start":110,"id":"section:48f27c1f8b110beb5c62","kind":"subsubsection","labels":["ein-uxfcberpruxfcfbarer-unterbestimmtheitssatz"],"line_end":32,"line_start":4,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/017-subsection-8-die-fundamentale-frage-was-fehlt.tex","status_markers_as_written":[],"summary_excerpt":"Betrachte bei festem W dieselbe Familie [formula in source] . Alle diese Hamiltonoperatoren besitzen die gleiche innere Quellsymmetrie, dieselbe Ladungserhaltung und denselben kommutierenden endlichen Clock. Dennoch unterscheiden sie sich dynamisch. Schon für dieselbe gefüllte Referenz F ist die dimensionslose Momentenkombination","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.1 Ein überprüfbarer Unterbestimmtheitssatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2840,"byte_start":1503,"id":"section:223465661a14fe681563","kind":"subsubsection","labels":["der-kleinste-tragfuxe4hige-forschungsansatz"],"line_end":55,"line_start":33,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/017-subsection-8-die-fundamentale-frage-was-fehlt.tex","status_markers_as_written":[],"summary_excerpt":"Für eine einzelne Antwortrechnung sollte der relevante Raum nicht von vornherein der gesamte Fockraum sein. Der zyklische Raum der tatsächlichen Operationen auf dem angegebenen Startzustand ist der kleinere Arbeitsraum. Die H-Lanczos-Kette ist eine exakte Darstellung eines solchen Raums. Mehrere Präparationen, Messungen oder Compileroperationen können jedoch einen größeren gemeinsamen Prozessraum verlangen. Ihre Komp","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.2 Der kleinste tragfähige Forschungsansatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5291,"byte_start":2840,"id":"section:6ed2c3a6c24a0590bc37","kind":"subsection","labels":["aktueller-stand-t1-bis-t8"],"line_end":110,"line_start":56,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/017-subsection-8-die-fundamentale-frage-was-fehlt.tex","status_markers_as_written":[],"summary_excerpt":"Die folgende Tabelle ordnet die Beiträge dieser Runde den bisherigen offenen Beweispflichten zu; sie benennt keine neue Definition der ursprünglichen Tore.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. Aktueller Stand T1 bis T8","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6822,"byte_start":5291,"id":"section:0bf936c8e2a97e9cf4f9","kind":"subsection","labels":["die-drei-nuxe4chsten-entscheidenden-untersuchungen"],"line_end":143,"line_start":111,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/017-subsection-8-die-fundamentale-frage-was-fehlt.tex","status_markers_as_written":[],"summary_excerpt":"Den minimalen Ursprungsvertrag auswählen. Teil B klassifiziert die kleinen symmetrieverträglichen Terme und trennt echte Erweiterungen von einem bloßen Wechsel der Bosonvariablen. Der Compiler muss diese Auswahl und die relativen Parameter begründen. Symmetrie allein tut das noch nicht. Die gemeinsame Schattenkarte am vorhandenen Tensor prüfen. Derselbe Zustand und dieselben Operationen müssen die verschiedenen Ausle","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10. Die drei nächsten entscheidenden Untersuchungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8000,"byte_start":6822,"id":"section:bcf8a968d07f46b36fdc","kind":"subsection","labels":["reproduktion-und-veruxf6ffentlichung"],"line_end":167,"line_start":144,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/017-subsection-8-die-fundamentale-frage-was-fehlt.tex","status_markers_as_written":[],"summary_excerpt":"Das Prüfpaket enthält sechs neue Python-Prüfer, die eingefrorenen Quellen, die alte und neu wiederholte Kontraktion, Ergebnisdateien, Quellenmanifest und die vollständige v1.6.6 als historische Basis. replay.py prüft alle Pins, beide Python-Modi und die C++-Kontraktion. Die ausgelieferte ZIP wird nach dem Entpacken erneut geprüft.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"11. Reproduktion und Veröffentlichung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8394,"byte_start":8000,"id":"section:3045f4377445f67011eb","kind":"subsubsection","labels":["schluss-in-einem-satz"],"line_end":176,"line_start":168,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/017-subsection-8-die-fundamentale-frage-was-fehlt.tex","status_markers_as_written":[],"summary_excerpt":"Die einfache Regel ist vorhanden; ihr erster verzweigter Zustandsbereich und die richtige kleine Rechenkette sind jetzt genauer gelöst. Was noch fehlt, ist die aus dem Ursprung folgende Auswahl und Ausführung dieses Prozesses als dieselbe physikalische Welt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Schluss in einem Satz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8545,"byte_start":8394,"id":"section:f22fa118b08e5f7e185b","kind":"section","labels":["neue-vogelperspektive-derselbe-prozess-in-verschiedenen-ansichten"],"line_end":179,"line_start":177,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/017-subsection-8-die-fundamentale-frage-was-fehlt.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Neue Vogelperspektive: derselbe Prozess in verschiedenen Ansichten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11147,"byte_start":8545,"id":"section:130cc59fbd01d0b0a4f6","kind":"subsection","labels":["b1.-was-sich-durch-die-drei-weiteren-texte-uxe4ndert"],"line_end":234,"line_start":180,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":["relation:5be3c27f577167009ace","relation:a013d2513358a562b4b9","relation:e157b0acb036d4e0e150"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/017-subsection-8-die-fundamentale-frage-was-fehlt.tex","status_markers_as_written":[],"summary_excerpt":"Die nachgereichten Texte werden als Vorschläge geprüft, nicht als bewiesene Ergebnisse oder neue Arbeitsanweisungen übernommen. Die stärkste gemeinsame Idee trägt: Innere Identität, Zusammensetzung, Ort, Zeit und Auslese dürfen nicht stillschweigend dasselbe Label erhalten. Eine immer genauere Rechnung innerhalb einer Bank ersetzt diese Verbindungen nicht. Die voranstehenden lokalen Ergebnisse bleiben gültig; die fun","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B1. Was sich durch die drei weiteren Texte ändert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13543,"byte_start":11147,"id":"section:60481da614058c6b744a","kind":"subsection","labels":["b2.-noethers-frage-welche-unterschiede-kann-die-dynamik-uxfcberhaupt-veruxe4ndern"],"line_end":287,"line_start":235,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/017-subsection-8-die-fundamentale-frage-was-fehlt.tex","status_markers_as_written":[],"summary_excerpt":"Bei ungebrochener innerer Gruppe G zerfällt ein Zustandsraum als","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B2. Noethers Frage: Welche Unterschiede kann die Dynamik überhaupt verändern?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15935,"byte_start":13543,"id":"section:efae809ab8e6f2b08bb8","kind":"subsection","labels":["b3.-korrelation-ist-noch-kein-eingriff-ein-exakt-geluxf6stes-gegenbeispiel"],"line_end":340,"line_start":288,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/017-subsection-8-die-fundamentale-frage-was-fehlt.tex","status_markers_as_written":[],"summary_excerpt":"Die Kreuzkorrelation startet bei null und verändert sich mit der Zeit. Es gibt dennoch keinerlei Signal von A nach B: Alle A-lokalen Operationen kommutieren mit jedem zeitentwickelten B-lokalen Observablen. Für jedes spurtreue lokale Quanteninstrument bleibt daher die unbedingte B-Statistik unverändert. Eine Konditionierung auf ein Messergebnis in A wäre etwas anderes.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B3. Korrelation ist noch kein Eingriff: ein exakt gelöstes Gegenbeispiel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17112,"byte_start":15935,"id":"section:fbcf40233a0f193ea09c","kind":"subsection","labels":["b4.-die-einfachste-fehlende-auswahl-warum-genau-dieser-hamiltonoperator"],"line_end":364,"line_start":341,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/017-subsection-8-die-fundamentale-frage-was-fehlt.tex","status_markers_as_written":[],"summary_excerpt":"Die Z4-Idee besitzt einen präzisen Kern. Ein ganzzahliger, auf jedem Grad konstanter Ladungslift mit neutralem Grad null müsste bei den entsprechenden nichtverschwindenden Klammern erfüllen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B4. Die einfachste fehlende Auswahl: Warum genau dieser Hamiltonoperator?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3841,"byte_start":0,"id":"section:c1bfa03a2f4b50d42ea7","kind":"subsubsection","labels":["b4.1-zwei-zusuxe4tzliche-terme-am-unveruxe4nderten-tensor"],"line_end":84,"line_start":1,"numbered_or_version_tokens_as_written":["B4.1"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/018-subsubsection-b4-1-zwei-zus-tzliche-terme-am-unver-ndert.tex","status_markers_as_written":[],"summary_excerpt":"Der Bosonträger (10,6) besitzt eine symmetrische reelle invariante Paarung eta. In der nativen Gewichtsbasis koppelt sie entgegengesetzte Spin- Vektorgewichte und komplementäre Farbpaare. Es gilt eta Quadrat gleich eins. Damit sind bereits","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B4.1 Zwei zusätzliche Terme am unveränderten Tensor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6032,"byte_start":3841,"id":"section:fa23964ac61e246531cc","kind":"subsubsection","labels":["b4.2-eine-weitere-vereinfachung-neue-dynamik-oder-andere-teilchenvariablen"],"line_end":133,"line_start":85,"numbered_or_version_tokens_as_written":["B4.2"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/018-subsubsection-b4-1-zwei-zus-tzliche-terme-am-unver-ndert.tex","status_markers_as_written":[],"summary_excerpt":"Manche scheinbaren Erweiterungen beschreiben nur andere Bosonvariablen. Auf der reellen, phasengleichen Teilfamilie setze man","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B4.2 Eine weitere Vereinfachung: neue Dynamik oder andere Teilchenvariablen?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6172,"byte_start":6032,"id":"section:70760755737bcf577939","kind":"subsection","labels":["b5.-holografie-und-schatten-die-konkrete-native-verbindung"],"line_end":136,"line_start":134,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/018-subsubsection-b4-1-zwei-zus-tzliche-terme-am-unver-ndert.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"B5. Holografie und Schatten: die konkrete native Verbindung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7678,"byte_start":6172,"id":"section:7edff83e2e2d07611f5d","kind":"subsubsection","labels":["b5.1-ein-kodierer-ist-bereits-vorhanden"],"line_end":171,"line_start":137,"numbered_or_version_tokens_as_written":["B5.1"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/018-subsubsection-b4-1-zwei-zus-tzliche-terme-am-unver-ndert.tex","status_markers_as_written":[],"summary_excerpt":"Der vorhandene, frisch geprüfte Tensor erfüllt WW dagger gleich 8 I60. Daher ist","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B5.1 Ein Kodierer ist bereits vorhanden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9335,"byte_start":7678,"id":"section:f731c859f568f02bf3a1","kind":"subsubsection","labels":["b5.2-warum-das-noch-kein-holografischer-fehlerkorrekturcode-ist"],"line_end":205,"line_start":172,"numbered_or_version_tokens_as_written":["B5.2"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/018-subsubsection-b4-1-zwei-zus-tzliche-terme-am-unver-ndert.tex","status_markers_as_written":[],"summary_excerpt":"Für jeden der 64 Fermionmoden wurde die logische Kompression seiner Besetzungsmessung berechnet:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B5.2 Warum das noch kein holografischer Fehlerkorrekturcode ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11957,"byte_start":9335,"id":"section:dcdc3463a7db1cf6608d","kind":"subsubsection","labels":["b5.3-was-mehrere-schatten-gemeinsam-eindeutig-machen-kuxf6nnen"],"line_end":260,"line_start":206,"numbered_or_version_tokens_as_written":["B5.3"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/018-subsubsection-b4-1-zwei-zus-tzliche-terme-am-unver-ndert.tex","status_markers_as_written":[],"summary_excerpt":"Seien Ri festgelegte Mess- oder Reduktionsabbildungen eines gemeinsamen Zustands rho. 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Noethers Symmetrieprüfung sagt, was erhalten bleibt. Die Schattenprüfung sagt, was überhaupt unterscheidbar ist. Der Eingriffstest sagt, was etwas anderes beeinflussen kann. Zusammen sind diese drei kleinen Fra","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B6. Die einfachste neue Arbeitsrichtung und ihre Abnahmekriterien","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4524,"byte_start":0,"id":"section:6743926d763d0a4ceaf7","kind":"subsection","labels":["b7.-abgleich-des-zuletzt-eingesandten-berichts-v1.6.3"],"line_end":85,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/019-subsection-b7-abgleich-des-zuletzt-eingesandten-berichts.tex","status_markers_as_written":[],"summary_excerpt":"Der sechste Text dieser Runde, „Operationssatz, nativer Grundzustand und Feldwörterbuch``, enthält überwiegend bereits berücksichtigte Befunde: die Kommutantenleiter, das Lochbild, die Normen der ersten Stufen, den nichtverschwindenden Seitenzweig und den verschwindenden Weyl-Skalarkanal. 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Ältere Vorhaben, Modellannahmen und Zahlen erhalten dadurch keinen neuen Beweisstatus; die kleinen Energieverschärfungen und die neuen Singulett- und Bilinearergebnisse stehen oben.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Historischer Anhang: vollständige Fassung v1.6.6","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5137,"byte_start":4969,"id":"section:a3bdc0392d81f39cd0c6","kind":"section","labels":["tfpt-universalraum-clock-gemeinsame-quelle-und-tatsuxe4chlicher-transport"],"line_end":98,"line_start":95,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/019-subsection-b7-abgleich-des-zuletzt-eingesandten-berichts.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"TFPT / Universalraum: Clock, gemeinsame Quelle und tatsächlicher Transport","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6515,"byte_start":5137,"id":"section:bc612f56d3f582c049a4","kind":"subsection","labels":["konsolidierung-und-eigene-forschungsfortsetzung-v1.6.6---15.-september-2026"],"line_end":124,"line_start":99,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/019-subsection-b7-abgleich-des-zuletzt-eingesandten-berichts.tex","status_markers_as_written":[],"summary_excerpt":"Ergebnis: Der dokumentierte endliche Clock ist jetzt ausdrücklich als Element der vorhandenen inneren Spin(10)-Symmetrie konstruiert. 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Numerisch: berechneter Näherungswert, ohne zertifizierte Einschließung. Bedingt: exakter Satz erst nach ausdrücklich zusätzlicher Ressource. Offen: fehlende Herleitung oder physikalische Identifikation.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Leseschlüssel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9306,"byte_start":7182,"id":"section:9ab448fb9071d7a4a1b8","kind":"subsection","labels":["die-unveruxe4nderte-gemeinsame-grundlage"],"line_end":195,"line_start":146,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/019-subsection-b7-abgleich-des-zuletzt-eingesandten-berichts.tex","status_markers_as_written":[],"summary_excerpt":"Mit 64 Fermionmoden, 60 Bosonmoden und demselben gepinnten Tensor gilt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. 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Die Clock-Normalisatorbehauptung gehörte dazu; Abschnitt 3 ersetzt sie durch eine explizite Konstru","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2.1 Bestätigte Zerlegung, korrigierte Operationsaussagen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":15046,"byte_start":12690,"id":"section:a3c72ad2e4a0de7cab3d","kind":"subsubsection","labels":["der-grundzustandsbericht-enthuxe4lt-einen-versionskonflikt"],"line_end":333,"line_start":279,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/019-subsection-b7-abgleich-des-zuletzt-eingesandten-berichts.tex","status_markers_as_written":[],"summary_excerpt":"Der neue Text hat die Nichtschlussnorm bereits korrigiert, das danebenliegende native_ground_state.json stammt jedoch von einer älteren Codefassung. Sein als PASS markierter Wert ist um 229² zu groß; die dortige relative orthogonale Norm ist sogar größer als eins. Der daraus berechnete Ritzwert −1,18826198 wird nicht übernommen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2.2 Der Grundzustandsbericht enthält einen Versionskonflikt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15189,"byte_start":15046,"id":"section:127dbd716177be564464","kind":"subsection","labels":["neuer-exakter-anschluss-der-clock-liegt-bereits-in-spin10"],"line_end":336,"line_start":334,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/019-subsection-b7-abgleich-des-zuletzt-eingesandten-berichts.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"3. Neuer exakter Anschluss: Der Clock liegt bereits in Spin(10)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15899,"byte_start":15189,"id":"section:63a27b0ec600c3a1eb6c","kind":"subsubsection","labels":["ausgangspunkt-ist-der-tatsuxe4chliche-quell-clock"],"line_end":353,"line_start":337,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/019-subsection-b7-abgleich-des-zuletzt-eingesandten-berichts.tex","status_markers_as_written":[],"summary_excerpt":"Der gepinnte endliche Compilerpräfix liefert auf fünf Hilfsachsen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.1 Ausgangspunkt ist der tatsächliche Quell-Clock","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2036,"byte_start":0,"id":"section:4e6f48f952338e4482fd","kind":"subsubsection","labels":["ein-ausdruxfcckliches-spinwort"],"line_end":57,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/020-subsubsection-3-2-ein-ausdr-ckliches.tex","status_markers_as_written":[],"summary_excerpt":"R_ab ist das Produkt zweier reeller Einheitsvektoren der Cliffordalgebra, also ein Spin(10)-Element. Direkt gilt R_ab=i Γ((ab)). Da p=(01)(02)(34) mit rechts zuerst angewandter Permutation, folgt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.2 Ein ausdrückliches Spinwort","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5295,"byte_start":2036,"id":"section:b6d7ce2905be67bf79e5","kind":"subsection","labels":["clock-und-getrennte-casimire-lassen-sich-gemeinsam-auslesen"],"line_end":136,"line_start":58,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/020-subsubsection-3-2-ein-ausdr-ckliches.tex","status_markers_as_written":[],"summary_excerpt":"Weil G aus Spin(10) stammt und auf SU(4) trivial wirkt, kommutiert es mit beiden getrennten Casimiren, auch auf ihren Fockhebungen. Die Frage aus dem neuen Text ist damit auf algebraischer Ebene beantwortet.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Clock und getrennte Casimire lassen sich gemeinsam auslesen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":8703,"byte_start":5295,"id":"section:efa2a864b946065db832","kind":"subsection","labels":["neuer-kleiner-transportzeuge-mit-tatsuxe4chlichen-w-kanuxe4len"],"line_end":216,"line_start":137,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/020-subsubsection-3-2-ein-ausdr-ckliches.tex","status_markers_as_written":[],"summary_excerpt":"Ein gemeinsamer Fermion-/Boson-Dreierstern hätte die einfache Identität","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Neuer kleiner Transportzeuge mit tatsächlichen W-Kanälen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11378,"byte_start":8703,"id":"section:0d6eca02800f99389633","kind":"subsection","labels":["das-feldwuxf6rterbuch-eine-basisuxe4nderung-allein-reicht-nicht"],"line_end":275,"line_start":217,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/020-subsubsection-3-2-ein-ausdr-ckliches.tex","status_markers_as_written":[],"summary_excerpt":"Der bestätigte Grundfehler bleibt: M_A⊗ε_Lorentz ist symmetrisch und verschwindet als Grassmann-Bilinear. Das betrifft die lokale ableitungsfreie Zuordnung einer gleichhändigen Weylkopie je ursprünglichem Label bei unverändertem antisymmetrischem W. Der nichtverschwindende gleichhändige Kanal trägt (1,0); daraus folgt noch keine gesunde Kinetik.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Das Feldwörterbuch: eine Basisänderung allein reicht nicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11500,"byte_start":11378,"id":"section:d19fab6162eaa0fc4291","kind":"subsection","labels":["was-der-nachgereichte-universalraum-text-truxe4gt"],"line_end":278,"line_start":276,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/020-subsubsection-3-2-ein-ausdr-ckliches.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"7. 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Sie können Voraussetzungen der lokalen Paritätsschranke ändern. Das ist ein Forschungsauftrag, kein Widerspruch zur bisherigen Schranke.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7.1 Eine sinnvolle Hypothese, kein bereits identifiziertes universelles Objekt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13190,"byte_start":12538,"id":"section:c5d35e9c3b0a91249f5d","kind":"subsubsection","labels":["der-vorgeschlagene-kill-test-muss-korrigiert-werden"],"line_end":312,"line_start":301,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/020-subsubsection-3-2-ein-ausdr-ckliches.tex","status_markers_as_written":[],"summary_excerpt":"Für unabhängige orthogonale Banken kann Π_AΠ_B deren gemeinsame Parität sein. 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Ein nichtverschwindender Kommutator mit einer lok","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7.2 Der vorgeschlagene Kill-Test muss korrigiert werden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15196,"byte_start":13190,"id":"section:0f1c4212a56baa98b45e","kind":"subsubsection","labels":["der-einfachste-false-positive-ein-signal-ohne-bewegung"],"line_end":358,"line_start":313,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/020-subsubsection-3-2-ein-ausdr-ckliches.tex","status_markers_as_written":[],"summary_excerpt":"Seien a=c1, b=(c1+c2)/√2 auf zwei globalen CAR-Moden und H=ωN. Dann haben die beiden Einteilchen-Chartzustände bereits Überlappung 1/√2. In ihrer nichtorthogonalen Basis ist K=ωS mit einem nichtverschwindenden Offdiagonalelement. Trotzdem bleibt die betreffende Wahrscheinlichkeit zu jeder Zeit genau 1/2. Es wurde nichts transportiert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7.3 Der einfachste False-Positive: Ein Signal ohne Bewegung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1895,"byte_start":0,"id":"section:0447acf518e14d1d23f3","kind":"subsubsection","labels":["was-nicht-automatisch-folgt"],"line_end":44,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/021-subsubsection-7-4-was-nicht-automatisch.tex","status_markers_as_written":[],"summary_excerpt":"Zeit: Für einen Grundzustand ist e \\-itH\\Ω=e \\-itE0\\Ω; sein physischer Zustand bleibt gleich. Das ist kein eigener Zeitpfeil. Nichtstationäre Präparation, Korrelationen und Records müssen ausgewiesen werden. Eichfeld: Für bloße Basiswechsel Uxy=Vx†Vy teleskopiert jede geschlossene Holonomie zu I. Echte Krümmung braucht zusätzliche Verbindungs-/Transportdaten oder einen nachgewiesenen Mechanismus. Spin: Zwei Orientier","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7.4 Was nicht automatisch folgt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4387,"byte_start":1895,"id":"section:8f0745b9a7bf731d3833","kind":"subsection","labels":["t1-t8-gemeinsamer-fortschritt-ohne-statusinflation"],"line_end":95,"line_start":45,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/021-subsubsection-7-4-was-nicht-automatisch.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333@ Front & In dieser Revision weitergekommen & Noch erforderlicher Nachweis \\\\ T1 - Ursprung und Auswahl & Explizite Identität zwischen Quell-Clock und innerer Spinwirkung; Operationsverträge genauer & Primitive Auswahl von P1/P2, Träger, erlaubten Instrumenten und Zustand \\\\ T2 - Half-Charge/E8-Feld & Bestehender geladener Pol bleibt abgesichert, innere Dar","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8. T1-T8: gemeinsamer Fortschritt ohne Statusinflation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6264,"byte_start":4387,"id":"section:d3349639b7c0eb3ff39d","kind":"subsection","labels":["die-nuxe4chsten-drei-arbeiten---klein-gemeinsam-und-entscheidbar"],"line_end":129,"line_start":96,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/021-subsubsection-7-4-was-nicht-automatisch.tex","status_markers_as_written":[],"summary_excerpt":"A. Den gemeinsamen Quellenvertrag wirklich hinschreiben. Zwei lokale Einbettungen, ihr CAR-Gram, globale Parität und Ladung, ursprüngliche Operationen und ein einziges H angeben. Abbruch für eine Kandidatenfassung, wenn sie nur zwei Koordinatenansichten desselben unveränderten Signals umbenennt. Die gemeinsamen Generatoren müssen einen nachweislich neuen Antwortprozess ermöglichen, nicht nur eine andere Beschriftung.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. Die nächsten drei Arbeiten - klein, gemeinsam und entscheidbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7365,"byte_start":6264,"id":"section:fd81b831cecc5146c252","kind":"subsection","labels":["belege-und-reproduzierbarkeit"],"line_end":151,"line_start":130,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/021-subsubsection-7-4-was-nicht-automatisch.tex","status_markers_as_written":[],"summary_excerpt":"Die drei Eingangstexte bleiben unverändert im Prüfpaket. Ein Teil-Audit reproduziert die 1127 gelieferten Guards; eigene Programme behandeln Clock/Casimir, Quellenreichweite, direkte Krylov-Kontraktion, basisunabhängige Feldbedingungen, den tatsächlichen Vierzustandskanal und die Überlappungsgegenkontrollen. Exakte und numerische Teile sind in den jeweiligen Ergebnisdateien getrennt markiert. Die abschließenden Zählu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10. 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September 2026. Eigenständiger Teil-Audit der ersten neuen Anlage und dreier Programme. Keine Änderung der gelieferten Programme, Ergebnisdateien oder Dokumente. 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Was die neue Perspektive sinnvoll beiträgt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15952,"byte_start":14068,"id":"section:b4b2f51fdc6149bdda16","kind":"subsection","labels":["exakter-zwei-moden-gegenbeleg-zum-vorgeschlagenen-parituxe4tstest"],"line_end":390,"line_start":337,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/024-subsection-5-was-dies-f-r-die-fundamentale-suche.tex","status_markers_as_written":[],"summary_excerpt":"Jeder Chart ist für sich ein gültiger Einmoden-CAR-Raum, aber","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Exakter Zwei-Moden-Gegenbeleg zum vorgeschlagenen Paritätstest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2146,"byte_start":0,"id":"section:005d2520baf477082814","kind":"subsection","labels":["noch-wichtiger-ein-uxfcberlappungsmatrixelement-ist-kein-transport"],"line_end":51,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/025-subsection-3-noch-wichtiger-ein-berlappungsmatrixelement.tex","status_markers_as_written":[],"summary_excerpt":"Wähle den vollkommen trivialen Hamiltonoperator H₀=ωN, mit N=c₁†c₁+c₂†c₂. 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Noch wichtiger: Ein Überlappungsmatrixelement ist kein Transport","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3839,"byte_start":2146,"id":"section:5205b3a78f5e3dfab6be","kind":"subsection","labels":["chartwechsel-verbindungen-und-kruxfcmmung-sind-verschiedene-daten"],"line_end":86,"line_start":52,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/025-subsection-3-noch-wichtiger-ein-berlappungsmatrixelement.tex","status_markers_as_written":[],"summary_excerpt":"Wenn mehrere Charts lediglich vollständige orthonormale Rahmen R_x desselben festen Vektorraums sind, lauten die Basiswechsel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Chartwechsel, Verbindungen und Krümmung sind verschiedene Daten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4983,"byte_start":3839,"id":"section:f792d0cb4c350d5a8c45","kind":"subsection","labels":["zeit-ein-grundzustand-bewegt-sich-unter-seinem-h-nicht-beobachtbar"],"line_end":108,"line_start":87,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/025-subsection-3-noch-wichtiger-ein-berlappungsmatrixelement.tex","status_markers_as_written":[],"summary_excerpt":"Die im Anhang skizzierte Entwicklung Ω -> exp(−itH)Ω erzeugt bei einem Energieeigenzustand lediglich exp(−itE₀)Ω. 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Operationsgeometrie benötigt mehr als Erreichbarkeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":8946,"byte_start":8140,"id":"section:a4011a2247c565d87527","kind":"subsection","labels":["gravitation-bleibt-eine-dynamische-verpflichtung"],"line_end":191,"line_start":176,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/025-subsection-3-noch-wichtiger-ein-berlappungsmatrixelement.tex","status_markers_as_written":[],"summary_excerpt":"Die linearen Fluktuationen einer aus der Quelle bestimmten globalen Geometrie zu prüfen, ist ein sinnvoller Forschungsauftrag. 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Gravitation bleibt eine dynamische Verpflichtung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9993,"byte_start":8946,"id":"section:709b4ce3d183974d7f8b","kind":"subsection","labels":["p-versus-np-eine-konkrete-korrektur"],"line_end":211,"line_start":192,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/025-subsection-3-noch-wichtiger-ein-berlappungsmatrixelement.tex","status_markers_as_written":[],"summary_excerpt":"Der Anhang sagt, P≠NP würde einen intrinsisch exponentiellen Suchaufwand bedeuten. 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P versus NP: eine konkrete Korrektur","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11962,"byte_start":9993,"id":"section:a5def148beed3d5bc2d1","kind":"subsection","labels":["ein-korrigierter-wirklich-entscheidbarer-anschluss-test"],"line_end":255,"line_start":212,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/025-subsection-3-noch-wichtiger-ein-berlappungsmatrixelement.tex","status_markers_as_written":[],"summary_excerpt":"Ein sinnvoller nächster Versuch besteht nicht nur aus einem unbeschrifteten P U_AB P. Er sollte zusammen liefern:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10. 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Quellenprüfung des nachgereichten Textes 59dc0059-8914-48ca-953d-85933f66e00b, kein neuer RH-Beweis und kein neuer arithmetischer Quellenoperator. Seine Aussagen über gemeinsame lokale Beschreibungen werden getrennt im Überlappungsaudit behandelt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zusatzprüfung: Schleifen, Primzahlen und der Universalraum-Vorschlag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":13049,"byte_start":12629,"id":"section:74a52cc37e021dc1c345","kind":"subsection","labels":["urteil-1"],"line_end":282,"line_start":274,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/025-subsection-3-noch-wichtiger-ein-berlappungsmatrixelement.tex","status_markers_as_written":[],"summary_excerpt":"Ein globaler Wegraum ist eine sinnvolle Suchklasse; ein Eulerprodukt über primitive Wege ist noch nicht das Eulerprodukt der Riemannschen Zetafunktion. Die im Text vorgeschlagene Xi-Determinante bleibt ein hinreichendes Ziel unter expliziten Operatorannahmen. Das Umbenennen ihres noch fehlenden Operators in „Generator der primitiven Schleifen`` konstruiert ihn nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Urteil","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":14389,"byte_start":13049,"id":"section:68604973d1f583335217","kind":"subsection","labels":["was-die-endliche-bank-tatsuxe4chlich-ausschlieuxdft"],"line_end":311,"line_start":283,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/025-subsection-3-noch-wichtiger-ein-berlappungsmatrixelement.tex","status_markers_as_written":[],"summary_excerpt":"Der beibehaltene Beweis aus v1.6.5 gilt für den ursprünglichen Hamiltonoperator mit 64 Fermion- und 60 Bosonmoden, Δ 0. 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Was die endliche Bank tatsächlich ausschließt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":16623,"byte_start":14389,"id":"section:609ab4b9935a42bdd8ec","kind":"subsection","labels":["der-kleinste-gegencheck-zur-primzahl-automatik"],"line_end":357,"line_start":312,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/025-subsection-3-noch-wichtiger-ein-berlappungsmatrixelement.tex","status_markers_as_written":[],"summary_excerpt":"Nehmen wir einen gerichteten Knoten mit zwei erlaubten Schleifen a und b. Neben a und b ist auch ab ein primitiver periodischer Weg: Es ist keine Potenz eines kürzeren Wortes. Ebenso entstehen weitere gemischte primitive Wörter. Setzen wir nachträglich L(a)=log 2, L(b)=log 3, so hat ab die Länge log 6. Die 6 ist keine Primzahl. „Primitiver Weg`` bedeutet nicht „arithmetische Primzahl``.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Der kleinste Gegencheck zur Primzahl-Automatik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":1098,"byte_start":0,"id":"section:8063931177ac2511d6e2","kind":"subsection","labels":["die-richtige-rh-zielbedingung"],"line_end":29,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/026-subsection-3-die-richtige.tex","status_markers_as_written":[],"summary_excerpt":"Sei A strikt positiv und selbstadjungiert, mit kompakter Inverser und A \\-2\\ von Spurklasse. Dann ist der Fredholm-Ausdruck","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Die richtige RH-Zielbedingung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2849,"byte_start":1098,"id":"section:48ee5cd752fc813ac663","kind":"subsection","labels":["vorarbeiten-und-aktuelle-grenze-der-quellenpruxfcfung"],"line_end":62,"line_start":30,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":["relation:3cf30fc4db07f67eb5e1","relation:5e30fb3f70bdf2b0575f","relation:a0f4103ecf1cf64dd419"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/026-subsection-3-die-richtige.tex","status_markers_as_written":[],"summary_excerpt":"Der installierte Leitfaden rh-graph-research und die projektspezifische Korpussuche wurden angewandt. Die aktuelle Konsistenzprüfung und der anschließende Wiederaufbauversuch brachen mit","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Vorarbeiten und aktuelle Grenze der Quellenprüfung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3912,"byte_start":2849,"id":"section:984ad9de526cde029138","kind":"subsection","labels":["tragfuxe4higer-anschluss-ohne-acht-versprechen-an-ein-unbekanntes-objekt"],"line_end":83,"line_start":63,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/026-subsection-3-die-richtige.tex","status_markers_as_written":[],"summary_excerpt":"Der nächste arithmetische Test wäre erst nach Definition einer tatsächlichen Quell-Wegstruktur sinnvoll: primitive Bahnen, ihre Längen, Amplituden und die Spur gemeinsam bestimmen, ohne Primlisten oder Nullstellen einzusetzen. 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Tragfähiger Anschluss, ohne acht Versprechen an ein unbekanntes Objekt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4348,"byte_start":3912,"id":"section:c6834d91a743322cbb61","kind":"section","labels":["historischer-vollstuxe4ndiger-herleitungsstand-v1.6.5-einschlieuxdflich-v1.6.4"],"line_end":92,"line_start":84,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/026-subsection-3-die-richtige.tex","status_markers_as_written":[],"summary_excerpt":"Der folgende Text wird unverändert bewahrt. Neue Gesamtstatusaussagen und Reichweitenkorrekturen stehen in der vorangestellten Revision v1.6.6. Historische Arbeitsaufträge oder Verfügbarkeitsannahmen werden dadurch nicht erneut zu aktuellen Beweisen erklärt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Historischer vollständiger Herleitungsstand v1.6.5 einschließlich v1.6.4","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4551,"byte_start":4348,"id":"section:f16870934b4ad7077c9f","kind":"section","labels":["tfpt-universalraum-kontrollierter-zwei-banken-transfer"],"line_end":97,"line_start":93,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/026-subsection-3-die-richtige.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"TFPT / Universalraum: kontrollierter Zwei-Banken-Transfer","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7537,"byte_start":4551,"id":"section:48a1dded4af8293f18a4","kind":"subsection","labels":["ergebnis-und-geltungsbereich"],"line_end":162,"line_start":98,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/026-subsection-3-die-richtige.tex","status_markers_as_written":[],"summary_excerpt":"Eine konkrete bisher offene Rechnung lässt sich schließen: Im ausdrücklich um einen Rotor-Link erweiterten Modell zweier nativer Fermion-Boson-Banken ist der Transfer der isolierten Lochanregung mit einer Fehlergrenze gegenüber dem vollständigen physikalischen Zustandsraum kontrollierbar. Dafür ist keine Diagonalisierung dieses enorm großen Raums nötig. Die vorhandene Casimiridentität, Ladungserhaltung und eine Spekt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ergebnis und Geltungsbereich","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9444,"byte_start":7537,"id":"section:b99a78128c4df5f41a04","kind":"subsection","labels":["welche-quellen-zusammengefuxfchrt-werden"],"line_end":208,"line_start":163,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":["relation:123113ac3d3ee693a7d9","relation:ce7af0159e04a927e30e","relation:ea67853cd5f6442e936a"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/026-subsection-3-die-richtige.tex","status_markers_as_written":[],"summary_excerpt":"Die Benutzeranlage addbf22d-4764-4685-bdfe-f422bfc563d0/pasted-text.txt, eingefroren unter sources/user_attachment.txt. 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Ihre sechs Zustände sind der vollständige Gausssektor eines Vierfermion-Modells mit einem Link. Der zertifizierte Wert bei [formula in source] betrifft diesen Parent und diesen vorbereiteten Zustand. Er ist weder eine Zwei-64-Moden-Banken-Simulation noch ein Beweis für deren ursprüngliche Auswahl. Unser folgender Satz ist davon unabhängig und benutzt die ta","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.3 Das ältere 99,8718-\\%-Beispiel ist ein anderer Träger","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":14939,"byte_start":14798,"id":"section:373666ee2fe211a841c0","kind":"subsection","labels":["neuer-satz-vollstuxe4ndige-kontrolle-des-einloch-transfers"],"line_end":333,"line_start":331,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/026-subsection-3-die-richtige.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"4. Neuer Satz: vollständige Kontrolle des Einloch-Transfers","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16597,"byte_start":14939,"id":"section:49a40946f01488977560","kind":"subsubsection","labels":["den-richtigen-physikalischen-sektor-festlegen"],"line_end":375,"line_start":334,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/026-subsection-3-die-richtige.tex","status_markers_as_written":[],"summary_excerpt":"Für genau ein Loch ist eine Ladungsreferenz notwendig. Wir deklarieren Hintergründe [formula in source] und fordern","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.1 Den richtigen physikalischen Sektor festlegen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2540,"byte_start":0,"id":"section:313fd3b9adb8acc0b9f8","kind":"subsubsection","labels":["die-luxfccke-zum-gesamten-uxfcbrigen-raum"],"line_end":62,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/027-subsubsection-4-2-die-l-cke-zum-gesamten-brigen.tex","status_markers_as_written":[],"summary_excerpt":"Die native, nicht nur perturbative Casimiridentität lautet","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.2 Die Lücke zum gesamten übrigen Raum","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4151,"byte_start":2540,"id":"section:ac5b5edb8d277b84f7e1","kind":"subsubsection","labels":["gleichmuxe4uxdfige-auslaufkontrolle-und-endliche-transferzeit"],"line_end":102,"line_start":63,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/027-subsubsection-4-2-die-l-cke-zum-gesamten-brigen.tex","status_markers_as_written":[],"summary_excerpt":"Setze [formula in source] und fordere [formula in source] . Sei [formula in source] das obere Eigenwertende von [formula in source] . Minmax liefert ein Spektralband [formula in source] von [formula in source] derselben Dimension 128, dessen oberer Rand ≤ [formula in source] ist. Die Kompression [formula in source] liegt ≥ [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.3 Gleichmäßige Auslaufkontrolle und endliche Transferzeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6398,"byte_start":4151,"id":"section:bcbfd922fe0a30d7a382","kind":"subsubsection","labels":["ein-vollstuxe4ndig-numerisch-spezifizierter-rational-zertifizierter-punkt"],"line_end":164,"line_start":103,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/027-subsubsection-4-2-die-l-cke-zum-gesamten-brigen.tex","status_markers_as_written":[],"summary_excerpt":"Diese Zahlen sind ein konservativer Existenzpunkt, keine aus TFPT abgeleiteten Konstanten und keine Behauptung schneller oder optimaler Übertragung. Die physikalische Sekundenskala ist nicht bestimmt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.4 Ein vollständig numerisch spezifizierter, rational zertifizierter Punkt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7878,"byte_start":6398,"id":"section:c20adc9022c89ad461f9","kind":"subsubsection","labels":["dieselbe-urspruxfcngliche-fermionantwort-ohne-anfuxe4nglichen-filter"],"line_end":199,"line_start":165,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/027-subsubsection-4-2-die-l-cke-zum-gesamten-brigen.tex","status_markers_as_written":[],"summary_excerpt":"Die Auslaufnorm in umgekehrter Richtung erfüllt ebenfalls [formula in source] , indem man die obige Schranke adjungiert und die Zeit umkehrt. Der unerwünschte Anteil kann also nicht beliebig stark destruktiv in das niedrige Zielband einstreuen. Mit der Dreiecksungleichung, [formula in source] und der gesondert geprüften Positivität vor dem Quadrieren folgt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.5 Dieselbe ursprüngliche Fermionantwort ohne anfänglichen Filter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9513,"byte_start":7878,"id":"section:644d9e82dd7d9349fdd3","kind":"subsection","labels":["warum-die-herkunftsluxfccke-nicht-durch-luxe4ngeres-rechnen-verschwindet"],"line_end":229,"line_start":200,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/027-subsubsection-4-2-die-l-cke-zum-gesamten-brigen.tex","status_markers_as_written":[],"summary_excerpt":"Sei [formula in source] die lokale Fermionparität. Die bisher angegebenen bankinternen Paarumwandlungen, Zahloperationen, zahlenerhaltenden Symmetrielifts sowie reine Bosonverbindungen kommutieren mit jeder [formula in source] . Jede endliche Komposition, lineare Kombination, Adjungierung und jeder durch solche Operatoren realisierte einzelne Messzweig tut das ebenfalls. Starke beschränkte Grenzwerte bleiben im Kommu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Warum die Herkunftslücke nicht durch längeres Rechnen verschwindet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9633,"byte_start":9513,"id":"section:2d2724f6adbca96b6d37","kind":"subsection","labels":["was-von-der-arithmetischen-untersuchung-truxe4gt"],"line_end":232,"line_start":230,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/027-subsubsection-4-2-die-l-cke-zum-gesamten-brigen.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"6. Was von der arithmetischen Untersuchung trägt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11251,"byte_start":9633,"id":"section:48a74526cfa32e7090f2","kind":"subsubsection","labels":["eine-einzelne-endliche-bank-ist-nicht-der-volle-logarithmusgenerator"],"line_end":269,"line_start":233,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/027-subsubsection-4-2-die-l-cke-zum-gesamten-brigen.tex","status_markers_as_written":[],"summary_excerpt":"Quadratisches Ergänzen liefert mit der nativen Casimirnorm [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6.1 Eine einzelne endliche Bank ist nicht der volle Logarithmusgenerator","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12818,"byte_start":11251,"id":"section:cc4fcf2ba9ea3af45a10","kind":"subsubsection","labels":["primzahlen-kuxf6nnen-eine-gewuxe4hlte-dynamik-organisieren-erzwingen-sie-aber-nicht"],"line_end":300,"line_start":270,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/027-subsubsection-4-2-die-l-cke-zum-gesamten-brigen.tex","status_markers_as_written":[],"summary_excerpt":"Auf [formula in source] kann man [formula in source] definieren. Die additive Primfaktorbesetzung erklärt dann die Eulerstruktur. Der Definitionsbereich lautet [formula in source] . Dass quantenstatistische Systeme mit Zeta-Zustandssumme existieren, ist bereits ein Ergebnis von https://alainconnes.org/wp-content/uploads/bostconnesscan.pdfBost und Connes. Das ist ein relevanter Anschluss, nicht die fehlende native Her","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6.2 Primzahlen können eine gewählte Dynamik organisieren, erzwingen sie aber nicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":13801,"byte_start":12818,"id":"section:94cdaafe93ffec6d323e","kind":"subsubsection","labels":["der-rh-zielsatz-bleibt-unbewiesen"],"line_end":324,"line_start":301,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/027-subsubsection-4-2-die-l-cke-zum-gesamten-brigen.tex","status_markers_as_written":[],"summary_excerpt":"für einen strikt positiven selbstadjungierten Operator [formula in source] mit kompakter Inverser und [formula in source] von Spurklasse wäre tatsächlich hinreichend: Die gesamte rechte Funktion hat ihre Nullstellen nur bei reellen [formula in source] , einschließlich Multiplizitäten. Aber dieser Operator und die gesamte Funktionsidentität sind nicht konstruiert. Ein Operator mit lediglich den Imaginärteilen der Null","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6.3 Der RH-Zielsatz bleibt unbewiesen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15945,"byte_start":13801,"id":"section:dfeba346f975da88a986","kind":"subsection","labels":["die-lokale-polnuxe4herung-wird-pruxe4ziser-das-relativistische-feld-bleibt-offen"],"line_end":368,"line_start":325,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":["relation:084cf1103a1aa3f1afd0"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/027-subsubsection-4-2-die-l-cke-zum-gesamten-brigen.tex","status_markers_as_written":[],"summary_excerpt":"Die externe Resolventenabschätzung ist korrekt: Im Kreis mit Radius [formula in source] um den tatsächlichen, unbekannten negativen Pol [formula in source] gilt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. Die lokale Polnäherung wird präziser, das relativistische Feld bleibt offen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2723,"byte_start":0,"id":"section:6cf7a5fb816c82b1a606","kind":"subsection","labels":["wuxe4hrend-der-arbeit-entdeckte-uxe4nderung-kommutant-7-richtig-einordnen"],"line_end":59,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/028-subsection-8-w-hrend-der-arbeit-entdeckte-nderung-kommut.tex","status_markers_as_written":[],"summary_excerpt":"Die strikte Originalquellenprüfung stoppte korrekt, als eine andere Arbeit den früheren nativen Bericht ergänzte. Der alte Stand mit Hash 1062e13fe0fb79cce015657a7b4d40a61e9639922ff95fa60c689c0068c38ffc blieb eingefroren. Der gesonderte geänderte Entwurf hat Hash ab745e74b1232b1ddf35dd0e0d0da4ace0176c797d769e5db8bedd0010bcba6a. Die in dieser Revision verwendeten Energie- und Polzertifikate änderten sich bei dieser Pr","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8. Während der Arbeit entdeckte Änderung: „Kommutant 7`` richtig einordnen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5101,"byte_start":2723,"id":"section:1f3e63da88a10eb077e7","kind":"subsection","labels":["t1-t8-was-dieses-ergebnis-beitruxe4gt-und-nicht-beitruxe4gt"],"line_end":110,"line_start":60,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/028-subsection-8-w-hrend-der-arbeit-entdeckte-nderung-kommut.tex","status_markers_as_written":[],"summary_excerpt":"Die Begriffe folgen der aktuellen offenen Problemliste und ihrer Forschungszuordnung. Keine Akzeptanzmarkierung wurde heraufgesetzt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. T1-T8: was dieses Ergebnis beiträgt und nicht beiträgt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7525,"byte_start":5101,"id":"section:019c7f258239b27db4f3","kind":"subsection","labels":["nuxe4chste-entscheidende-arbeiten-mit-klaren-abbruchkriterien"],"line_end":153,"line_start":111,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/028-subsection-8-w-hrend-der-arbeit-entdeckte-nderung-kommut.tex","status_markers_as_written":[],"summary_excerpt":"A. Die Quelle des geraden Gesamtlinks finden. Nicht noch eine riesige Kontrollmatrix bauen, sondern für jeden tatsächlich ursprünglichen Generator [formula in source] prüfen, ob [formula in source] bei erhaltener Gesamtparität möglich ist. Eine positive Antwort muss Generator, Teilbereichsdefinition, Hilbertraum, Gaussreferenz und Matrixelement liefern. Bleiben alle Generatoren lokal gerade, ist die Suche nach dem Li","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10. Nächste entscheidende Arbeiten mit klaren Abbruchkriterien","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8895,"byte_start":7525,"id":"section:80665bde558497a5b4bd","kind":"subsection","labels":["reproduktion-und-ehrliche-liefergrenze"],"line_end":180,"line_start":154,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":["relation:002ae73fa0d64d73766a","relation:f70070abc39147d20900"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/028-subsection-8-w-hrend-der-arbeit-entdeckte-nderung-kommut.tex","status_markers_as_written":[],"summary_excerpt":"replay.py –frozen-only führt die fünf Prüfer normal und mit -OO aus, vergleicht beide JSON-Ergebnisse und die zwei externen Originalberichte, prüft alle eingefrorenen Quellen und protokolliert Änderungen der Originalorte gesondert. Ein Fehler führt zu FAIL. Der zuvor aufgetretene Live-Quellenfehler bleibt in source_drift_failure_receipt.json sichtbar.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"11. Reproduktion und ehrliche Liefergrenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9581,"byte_start":8895,"id":"section:5f71b47057c9702114c6","kind":"section","labels":["nachpruxfcfung-der-beiden-zuletzt-eingegangenen-untersuchungen"],"line_end":194,"line_start":181,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/028-subsection-8-w-hrend-der-arbeit-entdeckte-nderung-kommut.tex","status_markers_as_written":[],"summary_excerpt":"Quellen: die Anlagen 8e110ae1-19e2-4d47-bfc8-ebe4fe9ab81b und b928b72a-6669-4c67-a75d-124095791c6f, unverändert eingefroren. Zusätzlich wurden die vier genannten Programme t1_fixed.py, stabilizer.py, t5_twobank.py, t5_varresp.py vollständig gelesen und archiviert. Eine eigene Nachrechnung prüft die kritischen Folgerungen; sie ist kein vollständiger Replay aller sechs Sonden des fremden Arbeitsordners.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nachprüfung der beiden zuletzt eingegangenen Untersuchungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12519,"byte_start":9581,"id":"section:4a315b932f4d252121a0","kind":"subsection","labels":["uxfcbersicht-uxfcbernehmen-korrigieren-oder-offenlassen"],"line_end":254,"line_start":195,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/028-subsection-8-w-hrend-der-arbeit-entdeckte-nderung-kommut.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 2 ) * 0.5000 > p( - 2 ) * 0.5000@ Neue Aussage & Ergebnis der Prüfung \\\\ Innerer Viererzyklus erhält alle 60 W-Kanäle & Bestätigt, jetzt einschließlich der richtigen Fermion-Vorzeichen und explizitem Bosonlift \\\\ Grundzustandseindeutigkeit/Singulett/Gaplücke weiterhin unbekannt & Überholter Stand: unter dem festgelegten nativen Vertrag bereits bewiesen; voller Vektor weiter unbekannt \\\\ Leerer Grundzustand f","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Übersicht: übernehmen, korrigieren oder offenlassen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14118,"byte_start":12519,"id":"section:94eb71b738c9853e4c06","kind":"subsection","labels":["positiver-neuer-anschluss-der-korrekt-angehobene-viererzyklus"],"line_end":287,"line_start":255,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/028-subsection-8-w-hrend-der-arbeit-entdeckte-nderung-kommut.tex","status_markers_as_written":[],"summary_excerpt":"Die Abbildung der Fermionmarken lautet [formula in source] . Auf Paaren ist zwingend das Exteriorvorzeichen zu beachten: Falls [formula in source] , erhält das sortierte Paar ein Minuszeichen. Der gelieferte stabilizer.py lässt dieses Zeichen weg. Das wäre im Allgemeinen falsch; für den untersuchten Viererzyklus überlebt das positive Resultat jedoch auch den korrekten Test.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Positiver neuer Anschluss: der korrekt angehobene Viererzyklus","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15873,"byte_start":14118,"id":"section:fa3bb81ea8a4883d51d4","kind":"subsection","labels":["warum-der-einteilchen-abschluss-den-fock-operationssatz-nicht-schlieuxdft"],"line_end":320,"line_start":288,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/028-subsection-8-w-hrend-der-arbeit-entdeckte-nderung-kommut.tex","status_markers_as_written":[],"summary_excerpt":"Die Irreduzibilität der Einteilchendarstellung kann ihre assoziative Matrixalgebra zu [formula in source] machen. Daraus folgt nicht, dass jede Matrix als ein zulässiges physisches Wort verfügbar ist, und auch nicht, dass ihre zweite Quantisierung bereits erzeugt wird.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Warum der Einteilchen-Abschluss den Fock-Operationssatz nicht schließt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17521,"byte_start":15873,"id":"section:c5a5f275e3387c45650e","kind":"subsection","labels":["zustandswahl-keine-ruxfcckkehr-vor-den-abgesicherten-grundsatz"],"line_end":353,"line_start":321,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/028-subsection-8-w-hrend-der-arbeit-entdeckte-nderung-kommut.tex","status_markers_as_written":[],"summary_excerpt":"Der vorhandene native Satz beweist Eindeutigkeit, N=64, Singulett und positive Lücke bei μ=0 im angegebenen Kopplungsbereich. Eine komplette Clebsch-Gordan-Serie oder Voll-Diagonalisierung ist dafür nicht nötig; Vergleichsungleichungen und Minmax waren gerade der einfache Ausweg. Die physische Auswahl von H beziehungsweise μ=0 bleibt eine andere Frage.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Zustandswahl: keine Rückkehr vor den abgesicherten Grundsatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":17677,"byte_start":17521,"id":"section:acc1acfb8b9173cfbf8f","kind":"subsection","labels":["feldtheorie-falsche-verbote-entfernen-echte-bedingungen-behalten"],"line_end":356,"line_start":354,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/028-subsection-8-w-hrend-der-arbeit-entdeckte-nderung-kommut.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"5. Feldtheorie: falsche Verbote entfernen, echte Bedingungen behalten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1561,"byte_start":0,"id":"section:c6cb202af45569b1ffaf","kind":"subsubsection","labels":["anomalien"],"line_end":32,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/029-subsubsection-5-1-anomalien-label-anomalien.tex","status_markers_as_written":[],"summary_excerpt":"Für die zusätzlich angenommene 3+1D-Weylinterpretation lautet das lokale Anomaliepolynom bis auf Konventionsvorzeichen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5.1 Anomalien","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2745,"byte_start":1561,"id":"section:ecbc4696c85a91f15864","kind":"subsubsection","labels":["der-behauptete-spin-2-ausschluss-ist-falsch"],"line_end":59,"line_start":33,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/029-subsubsection-5-1-anomalien-label-anomalien.tex","status_markers_as_written":[],"summary_excerpt":"Eine Ableitung des Vektorbilinears [formula in source] kann daher einen symmetrischen spurfreien (1,1)-Tensor bilden. Insbesondere hat der Energie-Impuls-Tensor [formula in source] , mit passender Spurbehandlung, Dimension [formula in source] . Ein Energie-Impuls-Tensor kann bereits in einer festen Hintergrundraumzeit definiert werden; dynamische Diffeomorphismen müssen nicht vorausgesetzt werden, um dieses Gegenbeis","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5.2 Der behauptete Spin-2-Ausschluss ist falsch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3685,"byte_start":2745,"id":"section:f23dd81cd29ed654df52","kind":"subsubsection","labels":["kinetik-ist-nicht-generell-verboten"],"line_end":81,"line_start":60,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/029-subsubsection-5-1-anomalien-label-anomalien.tex","status_markers_as_written":[],"summary_excerpt":"Der bilineare Ein-Ableitungs-Term mit einem (1,0)-Feld und seinem Adjungierten besitzt keinen Lorentzskalar. Mit zwei Ableitungen existiert aber etwa","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5.3 (1,0)-Kinetik ist nicht generell verboten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4841,"byte_start":3685,"id":"section:12671b12c999a9761d9b","kind":"subsection","labels":["die-vierzustandsrechnung-richtig-lesen"],"line_end":102,"line_start":82,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/029-subsubsection-5-1-anomalien-label-anomalien.tex","status_markers_as_written":[],"summary_excerpt":"Das Modell mit [formula in source] , Bosonverbindung η und Diagonalen (0,Δ,Δ,0) erlaubt kohärenten Paartransport. Die exakte Identität [formula in source] stimmt. Unsere unabhängige Fließkomma-Abtastung reproduziert auf [formula in source] mit Schrittweite .05 den größten gefundenen Wert .998920021869 bei 2484.05. Der erste Gitter-Lokalhöchstwert liegt bereits bei 6.05. Weder „erster Maximalzeitpunkt`` noch ein globa","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Die Vierzustandsrechnung richtig lesen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6460,"byte_start":4841,"id":"section:2aa5339ece51d738e133","kind":"subsection","labels":["konsequenz-fuxfcr-die-nuxe4chste-forschungsrevision"],"line_end":138,"line_start":103,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/029-subsubsection-5-1-anomalien-label-anomalien.tex","status_markers_as_written":[],"summary_excerpt":"Die sinnvollen positiven Anschlüsse sind jetzt schärfer:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. Konsequenz für die nächste Forschungsrevision","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6979,"byte_start":6460,"id":"section:c9b69df333f6d33064c0","kind":"section","labels":["historischer-beweisanhang-vollstuxe4ndiger-nativer-herleitungsstand-v1.6.4"],"line_end":149,"line_start":139,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/029-subsubsection-5-1-anomalien-label-anomalien.tex","status_markers_as_written":[],"summary_excerpt":"Dieser Anhang bewahrt die frühere Herleitung vollständig. Seine damaligen Statussätze werden durch die aktuelle Konsolidierung und den Nachtrag oben ergänzt; er ist kein ungeprüft übernommener neuer Gesamtstatus. Die externe laufende Symmetrieergänzung wurde separat geprüft und ist nicht unbemerkt in diesen eingefrorenen Anhang eingegangen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Historischer Beweisanhang: vollständiger nativer Herleitungsstand v1.6.4","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7574,"byte_start":6979,"id":"section:bf79ebce7aaa9cb20e49","kind":"section","labels":["tfpt-universalraum-nativer-pol-bewegungsgleichung-und-minimale-feldtypen"],"line_end":161,"line_start":150,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/029-subsubsection-5-1-anomalien-label-anomalien.tex","status_markers_as_written":[],"summary_excerpt":"Diese Revision verbindet den während der Arbeit neu eingegangenen Polsatz v1.6.3 mit einer unabhängig begonnenen Untersuchung der nativen Bewegungsgleichung. Sie ergänzt die bisherigen Hauptdokumente; sie ist keine verkürzte Neufassung des vollständigen Hauptbuchs. Die vorhandenen Haupt- und Update-PDFs wurden in dieser Runde nicht verändert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TFPT / Universalraum: nativer Pol, Bewegungsgleichung und minimale Feldtypen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9952,"byte_start":7574,"id":"section:b37fa78850f4f787e3ee","kind":"subsection","labels":["ergebnis-in-einem-satz"],"line_end":216,"line_start":162,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/029-subsubsection-5-1-anomalien-label-anomalien.tex","status_markers_as_written":[],"summary_excerpt":"Auf dem abgesicherten Grundzustand des festgelegten nativen Fockmodells existiert eine isolierte ursprüngliche Fermion-Entnahmelinie; nach Kombination beider Rechnungen trägt sie mehr als 88,007628 \\% des gesamten normierten Spektralgewichts pro Mode. 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Ergebnis in einem Satz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11111,"byte_start":9952,"id":"section:40cbf710704487cb9b8a","kind":"subsection","labels":["ein-unveruxe4nderter-modellvertrag"],"line_end":244,"line_start":217,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/029-subsubsection-5-1-anomalien-label-anomalien.tex","status_markers_as_written":[],"summary_excerpt":"Es werden keine Hopping-, Massen-, Ladungs- oder Projektionsglieder zu H hinzugefügt:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Ein unveränderter Modellvertrag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11217,"byte_start":11111,"id":"section:b1f3d2de8d1ab60edd4e","kind":"subsection","labels":["was-tatsuxe4chlich-erneut-gepruxfcft-wurde"],"line_end":247,"line_start":245,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/029-subsubsection-5-1-anomalien-label-anomalien.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"3. 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Die Paar-Konfigurationen wurden frisch mit neu kompiliertem Quellcode berechnet:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.1 Grundzustand: frische Berechnung statt bloßer Statusübernahme","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":14626,"byte_start":13681,"id":"section:f36d8cc4812bac7bfda4","kind":"subsubsection","labels":["das-neu-eingegangene-polergebnis"],"line_end":325,"line_start":305,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":["relation:37ebf290fb8c1bb21290"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/029-subsubsection-5-1-anomalien-label-anomalien.tex","status_markers_as_written":[],"summary_excerpt":"Der vollständige technische Bericht v1.6.3 und sein 248-zeiliger Prüfer wurden gelesen; Quellen, Bericht, Ergebnismatrix und Prüfpaket wurden unverändert archiviert. Der Prüfer wurde normal und optimiert wiederholt: 317 Prüfbedingungen, identische JSON-Bytes auch zum gelieferten Bericht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.2 Das neu eingegangene Polergebnis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16417,"byte_start":14626,"id":"section:2b1a08182bc4da87b92a","kind":"subsection","labels":["der-einfache-native-anschluss-bewegungsgleichung-statt-umdeutung"],"line_end":372,"line_start":326,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/029-subsubsection-5-1-anomalien-label-anomalien.tex","status_markers_as_written":[],"summary_excerpt":"Erweitere jede W-Zeile zur antisymmetrischen Matrix [formula in source] mit [formula in source] für i j. 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Der einfache native Anschluss: Bewegungsgleichung statt Umdeutung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1194,"byte_start":0,"id":"section:67bc110cadc86e13a50c","kind":"subsection","labels":["dieselbe-antwort-auf-demselben-grundzustand"],"line_end":37,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/030-subsection-5-dieselbe-antwort-auf-demselben.tex","status_markers_as_written":[],"summary_excerpt":"Die innere Symmetrie macht G diagonal und alle Diagonalelemente gleich. 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Dieselbe Antwort auf demselben Grundzustand","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2513,"byte_start":1194,"id":"section:9b3259e819a19fa8013d","kind":"subsubsection","labels":["herleitung-des-dritten-moments"],"line_end":66,"line_start":38,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/030-subsection-5-dieselbe-antwort-auf-demselben.tex","status_markers_as_written":[],"summary_excerpt":"Setze [formula in source] . Stationarität macht diesen Operator symmetrisch in der positiven, nach Nullvektoren quotientierten Metrik [formula in source] . 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Invarianz und Besetzung ergeben","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Der Polsatz und seine zusätzliche Verschärfung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":7036,"byte_start":6222,"id":"section:3d842e82969086850bdb","kind":"subsection","labels":["einfache-organisation-aber-keine-falsche-zwei-linien-luxf6sung"],"line_end":192,"line_start":175,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/030-subsection-5-dieselbe-antwort-auf-demselben.tex","status_markers_as_written":[],"summary_excerpt":"Die ersten zwei orthonormalen Operatoren sind f und [formula in source] . Die erste Resolventenreduktion hat deshalb die exakte Form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. Einfache Organisation, aber keine falsche Zwei-Linien-Lösung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8591,"byte_start":7036,"id":"section:ef481b103378392a2cc9","kind":"subsubsection","labels":["warum-man-die-ruxfcckwirkung-nicht-exakt-weglassen-darf"],"line_end":232,"line_start":193,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/030-subsection-5-dieselbe-antwort-auf-demselben.tex","status_markers_as_written":[],"summary_excerpt":"Angenommen, es gäbe nur je eine Entnahme- und Additionslinie mit Energien [formula in source] . Symmetrie macht diese für alle r gleich. Dann liefern die Bewegungsgleichungen auf demselben Grundzustand","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7.1 Warum man die Rückwirkung nicht exakt weglassen darf","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10753,"byte_start":8591,"id":"section:ac171a227805b18f43c2","kind":"subsection","labels":["was-der-operationssatz-jetzt-tatsuxe4chlich-hergibt"],"line_end":289,"line_start":233,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/030-subsection-5-dieselbe-antwort-auf-demselben.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333@ Vertrag & Mathematisch abgesichert & Nicht dadurch verfügbar \\\\ Markierter endlicher Matrixcompiler & Matrizen, Ordnungen, konkrete endliche Syntheseidentitäten & Vollständiges Fockinstrument, Präparation, physischer Zeitgenerator \\\\ H allein & Modellzeitentwicklung & Unabhängiges Schalten von X und [formula in source] \\\\ X und [formula in source] , wenn ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8. 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Ein Wort aus ihnen und jeder einzeln zahlenerhaltende ausgewählte Messzweig bleiben im Ausgangssektor. Sie können aus dem leeren N=0-Zustand nicht den N=64-Grundzustand erzeugen. Diese Aussage betrifft zahlenerhaltende Krauszweige; eine bloß U(1)-kovariante offene Dynamik kann sehr wohl geladene Krausoperatoren haben.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.1 Konkrete Präparationsgrenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12235,"byte_start":11505,"id":"section:2539e11b11afb180433f","kind":"subsubsection","labels":["der-kleinste-konkrete-ladungstest"],"line_end":320,"line_start":306,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/030-subsection-5-dieselbe-antwort-auf-demselben.tex","status_markers_as_written":[],"summary_excerpt":"Ein Kandidat ist eine explizite Referenzmode c mit [formula in source] . Sie erhält die gemeinsame Ladung, verändert aber die Ladung der ursprünglichen Bank. Der endliche Austausch- und Detuningtest ist exakt; dieses T wurde nicht als neuer nativer Hamiltonterm eingeführt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.2 Der kleinste konkrete Ladungstest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12691,"byte_start":12235,"id":"section:fe1ee70da0bdb10ba9ca","kind":"subsection","labels":["relativistisches-wuxf6rterbuch-ausschluss-und-zwei-pruxe4zise-alternativen"],"line_end":329,"line_start":321,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/030-subsection-5-dieselbe-antwort-auf-demselben.tex","status_markers_as_written":[],"summary_excerpt":"Die Indexfrage darf nicht nachträglich durch einen Namen beantwortet werden. Die Konventionen für Zweikomponentenspinoren wurden mit https://arxiv.org/abs/0812.1594Dreiner, Haber und Martin abgeglichen; die folgenden speziellen W-Tests sind eigene exakte Tensorrechnungen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. Relativistisches Wörterbuch: Ausschluss und zwei präzise Alternativen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13179,"byte_start":12691,"id":"section:6aac67b074ff94690e57","kind":"subsubsection","labels":["was-nicht-funktioniert"],"line_end":338,"line_start":330,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/030-subsection-5-dieselbe-antwort-auf-demselben.tex","status_markers_as_written":[],"summary_excerpt":"Für 64 gleichhändige Weylfelder mit innerem Index I und einen skalaren Vermittler ist [formula in source] symmetrisch. Die Grassmann-Antisymmetrisierung verschwindet daher identisch, für alle 60 W-Zeilen. Außerdem lässt die volle irreduzible innere Darstellung [formula in source] auf denselben 64 Komponenten nach Schur keine zusätzliche kommutierende nichttriviale Lorentzspinorwirkung zu.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9.1 Was nicht funktioniert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13594,"byte_start":13179,"id":"section:059398a687e7009b1760","kind":"subsubsection","labels":["bereits-bekannter-nichtverschwindender-typ"],"line_end":347,"line_start":339,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/030-subsection-5-dieselbe-antwort-auf-demselben.tex","status_markers_as_written":[],"summary_excerpt":"Ein symmetrischer Lorentzspinortensor koppelt an das antisymmetrische M. Der Vermittler hat dann einen passenden dualen (1,0)-Typ samt adjungiertem Typ. Diese Variante besteht den algebraischen Nichtnulltest, aber noch keinen vollständigen Kinetik-, Positivitäts-, Constraints- oder Herkunftstest.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9.2 Bereits bekannter nichtverschwindender Typ","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15347,"byte_start":13594,"id":"section:dc10f004b4554f1b3a89","kind":"subsubsection","labels":["neue-minimale-skalare-alternative---ausdruxfccklich-zusuxe4tzlich"],"line_end":381,"line_start":348,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/030-subsection-5-dieselbe-antwort-auf-demselben.tex","status_markers_as_written":[],"summary_excerpt":"Will man zugleich W, gleiche Weylhand, lokale Bilinearität und einen skalaren Vermittler behalten, kann man einen unabhängigen Hilfsindex a=1,2 mit alternierender Form einführen:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9.3 Neue minimale skalare Alternative - ausdrücklich zusätzlich","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3281,"byte_start":0,"id":"section:f394209b4eef8f22ecdd","kind":"subsection","labels":["nuxe4chste-schritte-mit-eindeutiger-erfolgskontrolle"],"line_end":71,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/031-subsection-10-n-chste-schritte-mit-eindeutiger.tex","status_markers_as_written":[],"summary_excerpt":"Native Quelle des Austauschoperators bestimmen. Ein tatsächliches Operationswort mit Anfangszustand, Detektor, Adjungiertem, Ladungsbilanz und Record angeben. Ein weiteres neutrales Wort oder bloßer Algebraabschluss schließt diese Aufgabe nicht. Den Rest der nativen Antwort kontrollieren. Das nächste Ziel ist [formula in source] beziehungsweise sein erster Norm- und Momentkoeffizient, gemeinsam in N=63,64,65. Die vor","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10. Nächste Schritte mit eindeutiger Erfolgskontrolle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4289,"byte_start":3281,"id":"section:8f453f5b126181127352","kind":"subsection","labels":["erratum-und-versionsdisziplin"],"line_end":91,"line_start":72,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/031-subsection-10-n-chste-schritte-mit-eindeutiger.tex","status_markers_as_written":[],"summary_excerpt":"Im eigenen v1.6.2-Text fehlte in Abschnitt 5.2 zwischen Entnahme- und Additionsresolvente ein Pluszeichen. Richtig ist auf der dortigen N=4-Referenz [formula in source] . Die früheren Prüfrechnungen verwendeten die additive CAR-Gewichtsregel; der Darstellungsfehler wird hier ausdrücklich korrigiert. Die archivierte v1.6.2 wird nicht stillschweigend umgeschrieben.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"11. Erratum und Versionsdisziplin","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":19036,"byte_start":4289,"id":"section:253022760aa2b0ff8ac7","kind":"section","labels":["nutzerquelle-a-vollstuxe4ndige-runde-v1.6.3"],"line_end":337,"line_start":92,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":["relation:afdf014d7e28f2fb7193"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/031-subsection-10-n-chste-schritte-mit-eindeutiger.tex","status_markers_as_written":[],"summary_excerpt":"Unveränderte Quelle. Nicht alle Aussagen darin werden übernommen. Entscheidend sind die Quellenprüfung und Korrekturen in v1.6.7.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nutzerquelle A: vollständige Runde v1.6.3","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":19541,"byte_start":19036,"id":"section:1c6e70faa192a6741fc0","kind":"section","labels":["nutzerquelle-b-korrektur-und-zwischenbericht"],"line_end":349,"line_start":338,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/031-subsection-10-n-chste-schritte-mit-eindeutiger.tex","status_markers_as_written":[],"summary_excerpt":"Unveränderte Quelle. Nicht alle Aussagen darin werden übernommen. Entscheidend sind die Quellenprüfung und Korrekturen in v1.6.7.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nutzerquelle B: Korrektur und Zwischenbericht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":19784,"byte_start":19541,"id":"section:d00bd61e30197abf1418","kind":"section","labels":["zwischenbericht-tfptuniversalraum---fundamentale-luxf6sung-stand-15.09.2026-1145"],"line_end":353,"line_start":350,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/031-subsection-10-n-chste-schritte-mit-eindeutiger.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Zwischenbericht: TFPT/Universalraum - fundamentale Lösung, Stand 15.09.2026, 11:45","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1770,"byte_start":0,"id":"section:e9f621dcf54a9f7c4fe6","kind":"subsection","labels":["gesamtlage-zwei-spuren"],"line_end":45,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/032-subsection-0-gesamtlage-zwei-spuren-label-gesamtlage-zwe.tex","status_markers_as_written":[],"summary_excerpt":"Es existieren jetzt zwei Contract-Ordner, die sich unabhängig auf denselben Kernpunkt zubewegt haben:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"0. Gesamtlage: zwei Spuren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2891,"byte_start":1770,"id":"section:bd8218d5ac36071f426d","kind":"subsection","labels":["fundament-meiner-session-native_source.py-neu-npz-frei"],"line_end":66,"line_start":46,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/032-subsection-0-gesamtlage-zwei-spuren-label-gesamtlage-zwe.tex","status_markers_as_written":[],"summary_excerpt":"Problem: der gepinnte Tensor ( spinor_tensors.npz, SHA-256 3f00a089…) liegt unter /Documents - für die Agenten-Shell macOS-gesperrt (TCC). Die bisherigen Verträge sind von dieser Shell nicht reproduzierbar.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Fundament meiner Session: native_source.py (neu, npz-frei)1. Fundament meiner Session: (neu, npz-frei)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3184,"byte_start":2891,"id":"section:f3c3d7aed47aca10f7eb","kind":"subsection","labels":["wp-a-der-verfuxfcgbare-operationssatz-fertig-307-exakte-guards"],"line_end":72,"line_start":67,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/032-subsection-0-gesamtlage-zwei-spuren-label-gesamtlage-zwe.tex","status_markers_as_written":[],"summary_excerpt":"Frage (v1.6.2 §10.3/§14): Wie groß ist die unsichtbare Freiheit (Kommutant) unter dem tatsächlich verfügbaren Operationssatz?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. WP-A: Der verfügbare Operationssatz (fertig, 307 exakte Guards)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4241,"byte_start":3184,"id":"section:22aea8f8401e903b0354","kind":"subsubsection","labels":["die-kommutanten-leiter-n3-sektor-45-504-dim"],"line_end":101,"line_start":73,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":["relation:1945e9678c5d6087322f"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/032-subsection-0-gesamtlage-zwei-spuren-label-gesamtlage-zwe.tex","status_markers_as_written":[],"summary_excerpt":"@lrr@ Operationssatz & erzeugte Algebra & Kommutante \\\\ S0: \\X, N_b\\ & 14 & 1 444 233 216 \\\\ S1: + Spin(10)×SU(4)-Rahmen & 743 583 744 & 7 \\\\ S2: + Clock-Lift & unverändert & 7 \\\\ S3: + Modenbesetzungen \\n_r, m_A\\ & M₄₅₅₀₄ (2 070 614 016) & 1 \\\\ S4: + geladene f-Instrumente & M₄₇₅₈₀ (N=2∪N=3) & 1 \\\\","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Kommutanten-Leiter (N=3-Sektor, 45 504-dim)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5644,"byte_start":4241,"id":"section:c5a23310574e7caa23dd","kind":"subsubsection","labels":["die-isotypie-zerlegung-von-n3-beide-spuren-unabhuxe4ngig-identisch"],"line_end":131,"line_start":102,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/032-subsection-0-gesamtlage-zwei-spuren-label-gesamtlage-zwe.tex","status_markers_as_written":[],"summary_excerpt":"@lrrrll@ Block & Dim & Mult & S-Eigenwert & (C_S, C_U) & Rolle \\\\ (144, 20) & 2880 & 2 & 7 & (85, 39) & hell, X-gekoppelt \\\\ (144, 4̄) & 576 & 2 & 10 & (85, 15) & hell, X-gekoppelt \\\\ (16′, 20) & 320 & 2 & 12 & (45, 39) & hell, X-gekoppelt \\\\ (16′, 4̄) & 64 & 1 & 0 (ker S) & (45, 15) & χ-Kompositblock \\\\ (672, 4̄) & 2688 & 1 & - & (165, 15) & dunkel \\\\ (1200, 20) & 24 000 & 1 & - & (141, 39) & dunkel \\\\ (560, 20′) & ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Isotypie-Zerlegung von N=3 (beide Spuren unabhängig, identisch)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6844,"byte_start":5644,"id":"section:07e6cbc4eee55cbfbfe0","kind":"subsubsection","labels":["das-verfuxfcgbarkeits-theorem-parallelsession-symmetry_availability.py"],"line_end":153,"line_start":132,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/032-subsection-0-gesamtlage-zwei-spuren-label-gesamtlage-zwe.tex","status_markers_as_written":[],"summary_excerpt":"Die gewährte Dynamik (Wörter aus X, N_b) liegt in der Verflechteralgebra (Dim Σmᵢ² = 16); die 60 Lie-Erzeuger liegen nicht darin - keine Komposition gewährter Dynamik erzeugt sie. Die Symmetrie ist ein eigenständiges Primitiv: gewährt oder nicht gewährt. Der gesamte verbleibende symmetrieverträgliche Spielraum ist exakt 2 Dimensionen breit = die Fähigkeit, die drei dunklen Blöcke getrennt anzusprechen (= beide Casimi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das Verfügbarkeits-Theorem (Parallelsession, symmetry_availability.py)Das Verfügbarkeits-Theorem (Parallelsession, )","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9136,"byte_start":6844,"id":"section:40ca3a041da6aca37d9d","kind":"subsection","labels":["wp-c-relativistisches-feldwuxf6rterbuch-fertig-2161-exakte-guards--oo-stabil"],"line_end":205,"line_start":154,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/032-subsection-0-gesamtlage-zwei-spuren-label-gesamtlage-zwe.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.3000 > p( - 4 ) * 0.4000 > p( - 4 ) * 0.3000@ Kanal & Norm² pro Zeile & Status \\\\ Skalar, gleichhändig ε_\\αβ\\ψψ & 0 (alle 60 Zeilen, exakt) & verboten \\\\ Skalar, gepunktet (0,0) & 0 & verboten \\\\ (1,0) symmetrisch \\I, σˣ, σᶻ\\ & je 64, Summe 192 & erlaubt - der Vertex ist rein (1,0)+h.c. \\\\ (0,1) konjugiert & je 64 & erlaubt \\\\","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. WP-C: Relativistisches Feldwörterbuch (fertig, 2161 exakte Guards, -OO-stabil)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":11164,"byte_start":9136,"id":"section:16878d30a44896fbed7d","kind":"subsection","labels":["wp-b-nativer-grundzustand-parallelsession-v1.6.4-meine-laufende-sonde"],"line_end":254,"line_start":206,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/032-subsection-0-gesamtlage-zwei-spuren-label-gesamtlage-zwe.tex","status_markers_as_written":[],"summary_excerpt":"@rrr@ k & Bosonkonfigurationen vollständig enumeriert & ‖Q₊ᵏF‖² \\\\ 0 & analytisch & 1 \\\\ 1 & 60 Kanäle / 480 Paare & 480 \\\\ 2 & 1 830 & 439 680 \\\\ 3 & 37 820 & 575 078 400 \\\\ 4 & 595 665 & 952 296 652 800 \\\\","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. WP-B: Nativer Grundzustand (Parallelsession v1.6.4 + meine laufende Sonde)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12807,"byte_start":11164,"id":"section:d57b3596e6616c1b5860","kind":"subsection","labels":["wp-d-geladene-antwort-auf-dem-grundzustand-parallelsession-v1.6.4"],"line_end":294,"line_start":255,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/032-subsection-0-gesamtlage-zwei-spuren-label-gesamtlage-zwe.tex","status_markers_as_written":[],"summary_excerpt":"Genau die geforderte „dieselbe geladene Antwort auf dem abgesicherten Zustand'':","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. WP-D: Geladene Antwort auf dem Grundzustand (Parallelsession v1.6.4)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14383,"byte_start":12807,"id":"section:c11ccebd9d03dce1530e","kind":"subsection","labels":["kreuzvalidierung-der-beiden-spuren"],"line_end":333,"line_start":295,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/032-subsection-0-gesamtlage-zwei-spuren-label-gesamtlage-zwe.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 6 ) * 0.2500 > p( - 6 ) * 0.2500 > p( - 6 ) * 0.2500 > p( - 6 ) * 0.2500@ Befund & Meine Session & Parallelsession & Status \\\\ N=3-Zerlegung (7 Blöcke, Mults 2,2,2,1,1,1,1) & ✓ & ✓ & identisch \\\\ Casimirwerte (je Block) & (45,15), (85,15), & C = (C_S+C_U)/4 = 15, 25, 45, 21, 31, 45, 45 & identisch (zwei Normierungen) \\\\ Kommutant S1 (volle Symmetrie) & 7 & 7 & identisch \\\\ Kommutant S0 (X, N_b) & 1 452 961 7","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Kreuzvalidierung der beiden Spuren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":16136,"byte_start":14383,"id":"section:6f1184244bc8d6b74290","kind":"subsection","labels":["offen-nuxe4chste-schritte-in-der-reihenfolge-der-direktive"],"line_end":375,"line_start":334,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/032-subsection-0-gesamtlage-zwei-spuren-label-gesamtlage-zwe.tex","status_markers_as_written":[],"summary_excerpt":"Sonde abschließen (läuft): mult₂-Zertifikat, β-Kette, Sektorfloors → unabhängige Reproduktion der v1.6.4-Kernzahlen. Volle 33-Niveau-Kette: falls mult_k=1 weiter trägt, ist die Singulett-Kette durch die Normsequenz ‖Q₊ᵏF‖² (k≤32) bestimmt - dafür ist die Symmetriespur-Resummation nötig (die „vier Symmetriespuren'' des Workers), nicht rohe Enumeration. Σ₂ kontrollieren (erster Norm-/Momentkoeffizient, N=63/64/65 gemei","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. Offen / nächste Schritte (in der Reihenfolge der Direktive)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16991,"byte_start":0,"id":"section:967a2574b80f1093c610","kind":"section","labels":["nutzerquelle-c-multiplizitaeten-und-z4"],"line_end":332,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/033-section-nutzerquelle-c-multiplizitaeten-und.tex","status_markers_as_written":[],"summary_excerpt":"Unveraenderte Nutzerquelle, als Vorschlag und nicht als Beweis uebernommen. Die Pruefung und eigene Fortsetzung stehen in Teil B.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nutzerquelle C: Multiplizitaeten und Z4","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10484,"byte_start":0,"id":"section:3871de63a8f2ae8a0aa6","kind":"section","labels":["nutzerquelle-d-fundamentale-reduktion"],"line_end":180,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/034-section-nutzerquelle-d-fundamentale.tex","status_markers_as_written":[],"summary_excerpt":"Unveraenderte Nutzerquelle, als Vorschlag und nicht als Beweis uebernommen. Die Pruefung und eigene Fortsetzung stehen in Teil B.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nutzerquelle D: fundamentale Reduktion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":22803,"byte_start":0,"id":"section:437eab5c22c17dba1ec3","kind":"section","labels":["nutzerquelle-e-gemeinsamer-ausfuehrbarer-prozess"],"line_end":363,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/035-section-nutzerquelle-e-gemeinsamer-ausfuehrbarer.tex","status_markers_as_written":[],"summary_excerpt":"Unveraenderte Nutzerquelle, als Vorschlag und nicht als Beweis uebernommen. Die Pruefung und eigene Fortsetzung stehen in Teil B.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nutzerquelle E: gemeinsamer ausfuehrbarer Prozess","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":23094,"byte_start":22803,"id":"section:dc0f94519145c443519c","kind":"section","labels":["nutzerquelle-f-operationssatz-grundzustand-und-feldwoerterbuch-v1.6.3"],"line_end":370,"line_start":364,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/035-section-nutzerquelle-e-gemeinsamer-ausfuehrbarer.tex","status_markers_as_written":[],"summary_excerpt":"Unveraenderte Nutzerquelle, als Vorschlag und nicht als Beweis uebernommen. Die Pruefung und eigene Fortsetzung stehen in Teil B.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nutzerquelle F: Operationssatz, Grundzustand und Feldwoerterbuch v1.6.3","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":860,"byte_start":0,"id":"section:50856e0195ad2eecc731","kind":"section","labels":["tfpt-universalraum-operationssatz-nativer-grundzustand-und-feldwuxf6rterbuch"],"line_end":15,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/036-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Diese Runde bearbeitet die vier Prioritäten aus v1.6.2 §14 in der dort festgelegten Reihenfolge: den tatsächlich verfügbaren Operationssatz exakt abgrenzen, den berichteten nativen Grundzustand mit seinem ursprünglichen Hamilton- und Sektorvertrag reproduzieren und darauf die geladene Antwort berechnen, das relativistische Feldwörterbuch am tatsächlichen Tensor festhalten. Eine räumliche Skalierungsrechnung ist ausdr","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TFPT / Universalraum: Operationssatz, nativer Grundzustand und Feldwörterbuch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2267,"byte_start":860,"id":"section:83452ccf744c880bba18","kind":"subsection","labels":["ergebnis-in-einem-absatz"],"line_end":37,"line_start":16,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/036-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Der N=64-Sektor des nativen Modells ist exakt als Loch-Paarerzeugung auf dem gefüllten Zustand realisiert; seine Krylov-Kette ist bis zu 15 252 960 Einträgen exakt berechnet, ihre Normen ν₁ ν₄ sind auf zwei völlig unabhängigen Wegen (Besetzungsbild und Onishi/Wick-Spurnetzwerke) identisch. Die Kette schließt bei zwei Bosonen exakt nicht (Defekt 2,9·10⁻⁵), das Modell ist also nicht allein durch seine Normen lösbar, nu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Ergebnis in einem Absatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3222,"byte_start":2267,"id":"section:20621f13f2fbf4b2f7c3","kind":"subsection","labels":["unveruxe4nderte-quelle-und-konventionen"],"line_end":56,"line_start":38,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/036-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Der Tensor wird repo-lokal gelesen (SHA-256 3f00a0892157a691e4ef26920c3702772c7bf76a250fad98ff04a079bb64b763), der Clock-Konstruktor ist gepinnt ( 9bf99de7…). common.py prüft: 60 Kanäle × 8 disjunkte Paare, jede Mode in 15 Kanälen; Gewichtserhaltung auf allen 480 Paaren; die Casimir-Identität 8WᵀW + 𝒞_S + 𝒞_C − 120 I = 0 auf allen 2016 Zweiteilchenzuständen (𝒞 = −ΣL², d. h. viermal der Standard-Casimir); induzierte B","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Unveränderte Quelle und Konventionen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3665,"byte_start":3222,"id":"section:69822f34bd3c5ec6c249","kind":"subsection","labels":["operationssatz-und-kommutant"],"line_end":66,"line_start":57,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/036-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Gemessen wird die Dimension des Kommutanten der von einer Operationsstufe erzeugten Algebra auf dem Sektor: kleiner Kommutant bedeutet weniger unsichtbare Freiheit. Das Spektralzertifikat für N=3 ist reproduziert (S = C₃C₃ᵀ wird von ∏(S−r), r ∈ \\0,7,10,12\\, exakt annulliert; Multiplizitäten 64, 2880, 576, 320 aus rationalen Projektorspuren).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Operationssatz und Kommutant","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5472,"byte_start":3665,"id":"section:e2ad718fc647c1c93e2f","kind":"subsubsection","labels":["exakte-irreduzibel-zerlegung-huxf6chstgewichtsvektoren"],"line_end":108,"line_start":67,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/036-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 8 ) * 0.1875 > p( - 8 ) * 0.1875 > p( - 8 ) * 0.2500 > p( - 8 ) * 0.1875 > p( - 8 ) * 0.1875@ Sektor & Block & Dim & Zerlegung unter so(10)⊕ su(4) & (𝒞_S, 𝒞_C) \\\\ N=2 & helle Paare ↔ Bosonen & 60 & (10, 6) & (36, 20) \\\\ N=2 & dunkle Paare & 1956 & (120, 10) ⊕ (126, 6) & (84,36), (100,20) \\\\ N=3 & dunkle Tripel = ker C₃ & 37888 & (560, 20″) ⊕ (1200, 20) ⊕ (672, 4̄) & (117,63), (141,39), (165,15) \\\\ N=3 & ker ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.1 Exakte Irreduzibel-Zerlegung (Höchstgewichtsvektoren)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7553,"byte_start":5472,"id":"section:58dcab59504f3a5dd8fb","kind":"subsubsection","labels":["kommutanten-leiter"],"line_end":154,"line_start":109,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/036-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.2727 > p( - 4 ) * 0.3636 > p( - 4 ) * 0.3636@ Verfügbare Operationen & N=2 & N=3 \\\\ A: \\X, N_b\\ (die zwei bisher geprüften Kontrollen) & 3 829 536 & 1 444 233 216 \\\\ B: A + Clock (Ordnung 6) & 641 760 & 240 742 144 \\\\ Cc: A + 15 su(4)-Generatoren & 30 376 & 2 247 168 \\\\ Cs: A + 45 so(10)-Generatoren & 172 & 1 648 \\\\ C: A + alle 60 Generatoren & 3 & 7 \\\\ D: B + C & 3 & 7 \\\\ B(H_N) & 1 & 1 \\\\","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.2 Kommutanten-Leiter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7634,"byte_start":7553,"id":"section:2ca74ce385025f13c199","kind":"subsection","labels":["der-native-n64-grundzustand"],"line_end":157,"line_start":155,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/036-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"4. Der native N=64-Grundzustand","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8251,"byte_start":7634,"id":"section:4cef7bfcc304c0def08c","kind":"subsubsection","labels":["lochbild"],"line_end":172,"line_start":158,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/036-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Mit h_i = f_i† ist F⟩ = f₀† f₆₃† 0⟩ das Lochvakuum und als Operatoridentität P_A = −Q_A† mit Q_A† = Σ_\\i j\\W_\\A,ij\\h_i†h_j†. Unter (−1)\\^\\N_b\\ ist H äquivalent zu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.1 Lochbild","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9514,"byte_start":8251,"id":"section:942b2fd05b5a66105c03","kind":"subsubsection","labels":["exakte-krylov-kette"],"line_end":203,"line_start":173,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/036-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"@rrrl@ n & Einträge in v_n & ν_n = ‖v_n‖² & ν_n/ν_\\n−1\\ \\\\ 0 & 1 & 1 & - \\\\ 1 & 480 & 480 & 480 \\\\ 2 & 108 240 & 439 680 & 916 = 4·229 \\\\ 3 & 15 252 960 & 575 078 400 & 299520/229 \\\\ 4 & (nur Spurnetzwerk) & 952 296 652 800 & ≈ 1656,0 \\\\ 5 & (nur Spurnetzwerk) & siehe norms_by_traces.json & \\\\","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.2 Exakte Krylov-Kette","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10124,"byte_start":9514,"id":"section:c528b97128013ce97705","kind":"subsubsection","labels":["schlieuxdfung"],"line_end":217,"line_start":204,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/036-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Der Zwei-Boson-Singulettraum ist also mehr als eindimensional; die Kette ist exakt nicht geschlossen, und das Modell ist nicht allein durch die ν_n lösbar. Numerisch ist die Korrektur vernachlässigbar: w₂ koppelt nur an v₃ mit g·√(‖w₂‖²/ν₃) = 0,195 g.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.3 Schließung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11156,"byte_start":10124,"id":"section:31d4ebabdacb6158a805","kind":"subsubsection","labels":["ritz-obergrenzen"],"line_end":243,"line_start":218,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/036-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"In der orthonormierten Basis \\v₀ v_K, w₂\\ ist H (Δ = 1) tridiagonal plus w₂-Zweig: Diagonale n bzw. 2; Nebendiagonalen g·4√30, g·2√229, g·48√29770/229, ; w₂-Kopplung g·3√598377/11908.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.4 Ritz-Obergrenzen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11738,"byte_start":11156,"id":"section:8ac014f6fd8527de0b6d","kind":"subsubsection","labels":["observablen-auf-dem-ritz-zustand-gux3b4-120-k3"],"line_end":254,"line_start":244,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/036-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"⟨N_b⟩ = 0,8421 (Hellmann-Feynman ∂E/∂Δ = 0,8421); ⟨F Ω⟩ ² = 0,397; Bosonzahlverteilung 0,397 / 0,397 / 0,172 / 0,034; Shannon-Untergrenze der Boson-Loch-Verschränkung 1,66 bit (rigoros, weil die reduzierte Bosondichte in N_b blockdiagonal ist). Die Worker-Angaben „Überlapp 1/4`` und „Verschränkung 0,811 bit`` sind damit konsistent, aber auf einem nichtkonvergierten Zustand.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.5 Observablen auf dem Ritz-Zustand (g/Δ = 1/20, K=3)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":12337,"byte_start":11738,"id":"section:4ae3300d6a597b606370","kind":"subsubsection","labels":["geladene-ein-teilchen-antwort"],"line_end":270,"line_start":255,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/036-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Für jede Mode r (Guard r ∈ \\0, 5, 63\\; Transitivität der Quellsymmetrie):","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.6 Geladene Ein-Teilchen-Antwort","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13554,"byte_start":12337,"id":"section:69654a2f47953a9907ae","kind":"subsubsection","labels":["sektorauswahl-und-die-worker-behauptung"],"line_end":300,"line_start":271,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/036-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Untergrenzen aus der Casimir-Identität und quadratischer Ergänzung, H ≥ (1−θ)ΔN_b − (15g²/2θΔ)N_f, ausgewertet als max_θ min_\\N_b\\ je Sektor:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.7 Sektorauswahl und die Worker-Behauptung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13664,"byte_start":13554,"id":"section:db9d3bd2c19d58358275","kind":"subsection","labels":["feldwuxf6rterbuch-am-tatsuxe4chlichen-tensor"],"line_end":303,"line_start":301,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/036-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"5. Feldwörterbuch am tatsächlichen Tensor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15253,"byte_start":13664,"id":"section:182f8a6eb8c72c6c9f9e","kind":"subsubsection","labels":["symmetrieregel"],"line_end":343,"line_start":304,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/036-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Für Grassmann-Felder ψ_\\I,a\\ ist Σ_\\IJ\\Σ_\\ab\\ W_\\IJ\\K_\\ab\\ψ_\\I,a\\ψ_\\J,b\\ = ½Σ(T − Tᵀ) mit T_\\(Ia),(Jb)\\ = W_\\IJ\\K_\\ab\\. Weil W antisymmetrisch ist, verschwindet die Kopplung genau dann, wenn K antisymmetrisch ist; nur der symmetrische Teil des Spinorkerns koppelt. Auf allen 60 Zeilen explizit geprüft:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5.1 Symmetrieregel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":17183,"byte_start":15253,"id":"section:b3660ea71083433cc933","kind":"subsubsection","labels":["chiralituxe4tsgradierungen"],"line_end":389,"line_start":344,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/036-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Der Trägergraph (64 Moden, 480 Kanten, Grad 15, dreiecksfrei) ist nicht bipartit; ein ungerader Zyklus ist [16, 45, 0, 30, 37]. Es gibt daher keine globale Chiralitätsaufteilung, unter der alle 60 Bosonen Vektoren wären. Für jede der 44 G-kovarianten Gradierungen ist jeder Kanal rein (nie gemischt), aber der Bosonmultiplett zerfällt:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5.2 Chiralitätsgradierungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1154,"byte_start":0,"id":"section:a702ddc800dcb902a636","kind":"subsection","labels":["spurnetzwerk-normen"],"line_end":21,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/037-subsection-6-spurnetzwerk-normen-label-spurnetzwerk-norm.tex","status_markers_as_written":[],"summary_excerpt":"über bosonische Kohärenzzustände, die Onishi-Determinante det(1 − M̄M)\\^\\1/2\\ und Wick-Paarung der z-Variablen. Jedes Netzwerk ist eine Kontraktion von n Kopien des Tensors Φ_\\ij,kl\\ = Σ_A(M_A) \\ij\\(M_A)\\kl\\ (Einträge in \\−1,0,1\\). Netzwerke werden als 4-Bein-Multigraphen unter Knotenumbenennung und Slot-Tausch kanonisiert (n=4: 120 → 27 Klassen). Exaktheit: float64-Kontraktion mit Absolutwert-Begleitkontraktion ( Σa","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Spurnetzwerk-Normen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2735,"byte_start":1154,"id":"section:d91ea2aab4be56260dcf","kind":"subsection","labels":["t1-t8"],"line_end":62,"line_start":22,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/037-subsection-6-spurnetzwerk-normen-label-spurnetzwerk-norm.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333@ Tor & Beitrag dieser Runde & Weiter offen \\\\ T1 & Exakte Kommutanten-Leiter A→B→Cc→Cs→C; Clock als äußeres Symmetrieelement & Welche Symmetrieoperationen der Compiler tatsächlich bereitstellt \\\\ T2 & Lochbild bewiesen; Z_h + Z_add = 1; ε_h, ε_add & Konvergierter Zustand, Renormierung, Grenzraum \\\\ T3 & - (ausgeklammert) & Räumlicher Träger \\\\ T4 & Kern-Sy","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. T1-T8","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3854,"byte_start":2735,"id":"section:0b1d4ed09aadcc68c2ae","kind":"subsection","labels":["die-jetzt-entscheidenden-pruxfcfungen"],"line_end":89,"line_start":63,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/037-subsection-6-spurnetzwerk-normen-label-spurnetzwerk-norm.tex","status_markers_as_written":[],"summary_excerpt":"Untergrenzen verschärfen. Die Casimir-Schranke trennt N=64 bei 1/20 nicht von N=62 und N=66. Eine Jacobi-Vergleichsschranke mit rigorosen Normschranken für TT† je Bosonzahl oder eine Temple-Schranke auf der Ritz-Kette würde den Beweisbereich anheben. Den Zwei-Boson-Singulettraum ausschreiben. w₂ ist der erste Zeuge; die volle Lanczos-Kette von H (nicht nur von T†) ab Tiefe 4 braucht w₂ und seine Nachfolger. Operation","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8. Die jetzt entscheidenden Prüfungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":5318,"byte_start":3854,"id":"section:e47ac6958bb9f4a17992","kind":"subsection","labels":["verifikation-und-nicht-uxfcbernommene-behauptungen"],"line_end":116,"line_start":90,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-source-composition-20260915--tmp--pdfs--TFPT_Universalraum_Quellkomposition_Konsolidierung_2026-09-15_v1.6.9/sections/037-subsection-6-spurnetzwerk-normen-label-spurnetzwerk-norm.tex","status_markers_as_written":[],"summary_excerpt":"replay.py führt fünf Prüfer normal und unter -OO aus und verlangt byteidentische Ausgaben; Status, Hashes und Guardsummen stehen in replay_manifest.json. Guardzahlen zählen Prüfbedingungen, keine unabhängigen Theoreme. Exakt heißt ganzzahlig/rational; numerisch heißt float64 mit Toleranz-Guard (Ritz-Eigenwerte ab 3×3, Observablen, Erste-Moment-Auswertungen).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. 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Nicht sämtliche mehr als 30.000 Zeilen der aktuellen Theorie samt allen einge","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Was die erneute Grundlagenlektüre verändert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":5683,"byte_start":4437,"id":"section:61882718578432157047","kind":"subsection","labels":["pruxfcfung-der-zugeschickten-arbeit"],"line_end":113,"line_start":90,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/001-section-tfpt-universalraum-den-verlorenen-spin-lift-wied.tex","status_markers_as_written":[],"summary_excerpt":"Die Arbeit TFPT / Universalraum: eine gemeinsame Quelle auf dem Prüfstand, Fortsetzung 1.2, enthält 15 Seiten. 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Ein festgelegter minimaler Kandidat","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7821,"byte_start":6975,"id":"section:067b008a06718da2be66","kind":"subsubsection","labels":["der-gemeinsame-clock-ist-eine-wirkliche-symmetrie-dieses-kandidaten"],"line_end":157,"line_start":141,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/001-section-tfpt-universalraum-den-verlorenen-spin-lift-wied.tex","status_markers_as_written":[],"summary_excerpt":"[formula in source] . 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Ihre vierte Potenz ist bei [formula in source] die gesamte Fermionparität, ihre achte Potenz die Identität.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.1 Der gemeinsame Clock ist eine wirkliche Symmetrie dieses Kandidaten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9293,"byte_start":7821,"id":"section:d4e68070cbc789e46d10","kind":"subsubsection","labels":["paarinformation-verliert-ein-vorzeichen"],"line_end":188,"line_start":158,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/001-section-tfpt-universalraum-den-verlorenen-spin-lift-wied.tex","status_markers_as_written":[],"summary_excerpt":"Schreibe [formula in source] . 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Für [formula in source] gilt [formula in source] , also bei [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6.1 Die drei einfachen Schranken","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17597,"byte_start":16721,"id":"section:7fa737a719c55df67309","kind":"subsubsection","labels":["warum-dabei-keine-unendlichen-zustuxe4nde-unterschlagen-werden"],"line_end":369,"line_start":354,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/001-section-tfpt-universalraum-den-verlorenen-spin-lift-wied.tex","status_markers_as_written":[],"summary_excerpt":"Es gibt endlich viele Fermion- und Bosonmoden, aber beliebige Bosonbesetzungen. Die Kopplung ist relativ zu [formula in source] infinitesimal beschränkt: Auf dem Übergang von k zu k+1 Bosonen hat [formula in source] die Normschranke [formula in source] . Daraus folgen Selbstadjungiertheit auf der Zahloperator-Domäne und kompakte Resolvente. Die oberen Ladungssektoren sind durch die explizite Schranke gleichzeitig aus","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6.2 Warum dabei keine unendlichen Zustände unterschlagen werden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":320,"byte_start":0,"id":"section:4eebb369ba73ffddf8e0","kind":"subsection","labels":["derselbe-grundzustand-besitzt-eine-kontrollierte-geladene-antwort"],"line_end":8,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/002-subsection-7-derselbe-grundzustand-besitzt-eine-kontroll.tex","status_markers_as_written":[],"summary_excerpt":"Für die präzisen Energie- und Gewichtsschranken verwenden wir den engeren Bereich","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. 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Dann [formula in source] . Für [formula in source] schreibe","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7.1 Der gesamte Rest wird als konvergente Resolvente kontrolliert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4296,"byte_start":2490,"id":"section:bce5b863a30d41cf949c","kind":"subsubsection","labels":["zwei-isolierte-entnahmelinien"],"line_end":92,"line_start":56,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/002-subsection-7-derselbe-grundzustand-besitzt-eine-kontroll.tex","status_markers_as_written":[],"summary_excerpt":"Im bosonfreien N=255-Sektor gibt es genau ein Loch. Normalordnen beziehungsweise die lokale Casimir-Identität liefern dort exakt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7.2 Zwei isolierte Entnahmelinien","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6002,"byte_start":4296,"id":"section:f9cc0b37d80e23ff37ff","kind":"subsubsection","labels":["ein-urspruxfcngliches-clockaufgeluxf6stes-fermion-sieht-die-linie"],"line_end":127,"line_start":93,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/002-subsection-7-derselbe-grundzustand-besitzt-eine-kontroll.tex","status_markers_as_written":[],"summary_excerpt":"Für den Grundzustand und die vier niedrigen Einlochblöcke ergibt die Resolventenschranke dieselbe untere Überlappung mit dem jeweiligen bosonfreien Referenzzustand:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7.3 Ein ursprüngliches, clockaufgelöstes Fermion sieht die Linie","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":6160,"byte_start":6002,"id":"section:3df3f074da0cb86ab9aa","kind":"subsection","labels":["was-wir-bei-der-einfachheit-muxf6glicherweise-falsch-verlangt-haben"],"line_end":131,"line_start":128,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/002-subsection-7-derselbe-grundzustand-besitzt-eine-kontroll.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"8. Was wir bei der Einfachheit möglicherweise falsch verlangt haben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7794,"byte_start":6160,"id":"section:c34f80be21ab88f38276","kind":"subsubsection","labels":["quadratische-erzeugung-ist-nicht-vollstuxe4ndige-dynamische-steuerbarkeit"],"line_end":161,"line_start":132,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":["relation:01b865d5abd986066e0a","relation:ef90fb1314a7821cc2df"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/002-subsection-7-derselbe-grundzustand-besitzt-eine-kontroll.tex","status_markers_as_written":[],"summary_excerpt":"Der alte Prüfer v111_quadratic_transport.py zeigt korrekt, dass quadratische Cliffordwörter auf dem 16-dimensionalen geraden Fockraum eine volle assoziative Matrixalgebra aufspannen. Daraus folgt nicht, dass zeitabhängige quadratische Hamiltonoperatoren jede unitäre Operation erzeugen. Ihre dynamische Lie-Algebra hat Dimension 45, nicht 255.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.1 Quadratische Erzeugung ist nicht vollständige dynamische Steuerbarkeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9299,"byte_start":7794,"id":"section:1fcd3ec291c3b502e674","kind":"subsubsection","labels":["ein-eindeutiges-mikroskopisches-netz-ist-nicht-zwingend-nuxf6tig"],"line_end":192,"line_start":162,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/002-subsection-7-derselbe-grundzustand-besitzt-eine-kontroll.tex","status_markers_as_written":[],"summary_excerpt":"Die Petersen-/Prisma-Gegenmodelle beweisen eine endliche Unterbestimmtheit, aber keine Verschiedenheit aller denkbaren großskaligen Grenztheorien. Unterschiedliche Mikroregeln können derselben Universalitätsklasse angehören. Das ist ein wesentlicher Grund, nicht immer feinere Graph-Eindeutigkeit zu verlangen, bevor eine physische Grenzrechnung begonnen wird. Siehe den ursprünglichen RG-Rahmen von https://theory.tifr.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.2 Ein eindeutiges mikroskopisches Netz ist nicht zwingend nötig","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":11727,"byte_start":9299,"id":"section:877ac061657cfd573a19","kind":"subsection","labels":["was-die-alte-e8-kaskade-wirklich-beisteuert"],"line_end":241,"line_start":193,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":["relation:656ac946c4d1c188dfd0","relation:70d0210794ffdea23ca9","relation:cdfc42bc15beaa5ace82"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/002-subsection-7-derselbe-grundzustand-besitzt-eine-kontroll.tex","status_markers_as_written":[],"summary_excerpt":"Die gewünschte Archivdatei ist ein LaTeX-Umschlag einer ausdrücklich als bestmögliche PDF-Textextraktion bezeichneten 81-seitigen Fassung. Einige Formeln und Figuren sind in dieser Darstellung beschädigt oder fehlen. Aus solchen Schäden werden hier keine mathematischen Gegenbeweise konstruiert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. Was die alte E8-Kaskade wirklich beisteuert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":12888,"byte_start":11727,"id":"section:8473c1181bddf2dbf3df","kind":"subsection","labels":["einstein-noether-und-dirac-als-arbeitsprinzipien"],"line_end":265,"line_start":242,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/002-subsection-7-derselbe-grundzustand-besitzt-eine-kontroll.tex","status_markers_as_written":[],"summary_excerpt":"Noether: Die erhaltene Ladung [formula in source] ist hier kein dekoratives Etikett. Sie reduziert den globalen Grundzustandsvergleich auf untere, mittlere und obere Ladungssektoren und macht den kurzen Beweis möglich.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10. 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T1-T8 bleiben einzeln sichtbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16670,"byte_start":14985,"id":"section:7a51d8a16859f2d73a3c","kind":"subsection","labels":["die-nuxe4chsten-entscheidenden-pruxfcfungen"],"line_end":348,"line_start":313,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/002-subsection-7-derselbe-grundzustand-besitzt-eine-kontroll.tex","status_markers_as_written":[],"summary_excerpt":"Ursprüngliche Quelle statt weiterer freier Graphen: Eine konkrete Abbildung von TFPTs Seam-/Cliffordoperationen auf das gewählte q-Feld angeben, die CAR, Clock, W-Vertex und Zustand gemeinsam erhält. Abschnitt 15 präzisiert den Angriffspunkt: die gemeinsame Vertex-/Kantenreflexion. Übereinstimmung der Clockordnung oder einer abstrakten dihedralen Relation allein reicht nicht. Scheitert die Zustandsverträglichkeit, is","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"12. Die nächsten entscheidenden Prüfungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17702,"byte_start":16670,"id":"section:1d121fa86acdab3e383f","kind":"subsection","labels":["reproduktion-und-lesereihenfolge"],"line_end":368,"line_start":349,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":["relation:84909481badd8ecbb89d"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/002-subsection-7-derselbe-grundzustand-besitzt-eine-kontroll.tex","status_markers_as_written":[],"summary_excerpt":"verify_spin_lift.py prüft native Tensorpins, die vollständige benötigte Casimir-Grundlage, die N3-Reduktion, Vorzeichenklassen, unabhängige CAR-Kontrollen, exakte Momente, rationale Restkonstanten sowie die Operations- und Archivpräzisierungen. replay.py wiederholt diese Rechnung normal und optimiert und führt den historischen v480-Zeugen separat aus. Der vollständige analytische Grundzustands-/Antwortbeweis steht in","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"13. Reproduktion und Lesereihenfolge","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":579,"byte_start":0,"id":"section:39459acb94439c248899","kind":"subsection","labels":["nachpruxfcfung-der-beiden-zuletzt-zugeschickten-perspektiven"],"line_end":11,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/003-subsection-14-nachpr-fung-der-beiden-zuletzt-zugeschickt.tex","status_markers_as_written":[],"summary_excerpt":"Die beiden Texte mit den Anfängen „Ja. Nach dem erneuten Querschnitt `` und „Ich sehe keine bereits versteckte Formel `` wurden vollständig gelesen. Ihre Vorschläge sind Prüfhypothesen, keine übernommenen Arbeitsanweisungen oder bereits bewiesene Resultate. Beide Originale liegen mit Hashes unverändert im Prüfpaket. Die folgende Prüfung ergänzt die Spin-Lift-Rechnung, ersetzt sie nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"14. Nachprüfung der beiden zuletzt zugeschickten Perspektiven","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2933,"byte_start":579,"id":"section:0c37e901d0dd9b30468e","kind":"subsubsection","labels":["tragender-gemeinsamer-kern-aber-keine-automatische-quellenauswahl"],"line_end":55,"line_start":12,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/003-subsection-14-nachpr-fung-der-beiden-zuletzt-zugeschickt.tex","status_markers_as_written":[],"summary_excerpt":"ist eine gute gemeinsame Beschreibung der erreichbaren Vorgänge. Ist eine unital vorgegebene C*-Algebra mit ihrer Multiplikation und einem Zustand gegeben, bestimmt die GNS-Konstruktion die zyklische Darstellung bis auf eine zustands- und algebraerhaltende unitäre Äquivalenz. Bei vollständig zeit- und instrumentmarkierten Kernen werden die so markierten Prozesse mit rekonstruiert. Das ist die präzise Bedeutung von „g","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"14.1 Tragender gemeinsamer Kern, aber keine automatische Quellenauswahl","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6402,"byte_start":2933,"id":"section:1a03b23c5e989101be90","kind":"subsubsection","labels":["die-modulare-zeitidee-ist-relevant-aber-noch-nicht-unser-fehlender-hamiltonoperator"],"line_end":125,"line_start":56,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/003-subsection-14-nachpr-fung-der-beiden-zuletzt-zugeschickt.tex","status_markers_as_written":[],"summary_excerpt":"Die vorgeschlagene Verbindung zu Connes und Rovelli ist sachlich richtig: Ihre https://arxiv.org/abs/gr-qc/9406019Thermal-Time-Arbeit postuliert eine physische Interpretation des vom Zustand bestimmten modularen Flusses. Das ist eine physische Hypothese auf Grundlage eines mathematischen Satzes, kein allgemeiner Beweis, dass jeder modulare Fluss eine physische Uhr ist.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"14.2 Die modulare Zeitidee ist relevant, aber noch nicht unser fehlender Hamiltonoperator","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":7894,"byte_start":6402,"id":"section:2f681d09d80bba0167f6","kind":"subsubsection","labels":["neue-schranke-fuxfcr-den-vorgeschlagenen-kausalituxe4tstest"],"line_end":154,"line_start":126,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/003-subsection-14-nachpr-fung-der-beiden-zuletzt-zugeschickt.tex","status_markers_as_written":[],"summary_excerpt":"Die Konstruktion von Raumzeit aus relativen modularen Flüssen ist eine ernsthafte Richtung. Sie verlangt zusätzliche Relationen der Algebren, nicht bloß einige ähnliche Eigenwerte. Ein relevanter mathematischer Rahmen sind halbseitige modulare Inklusionen; einen präzisierten Struktursatz geben https://arxiv.org/abs/math/0412061Araki und Zsido.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"14.3 Neue Schranke für den vorgeschlagenen Kausalitätstest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10459,"byte_start":7894,"id":"section:ad521dc859fbdc1ec46b","kind":"subsubsection","labels":["phasen-gesamtsymmetrie-und-unsichtbarkeit-kleiner-tests"],"line_end":202,"line_start":155,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/003-subsection-14-nachpr-fung-der-beiden-zuletzt-zugeschickt.tex","status_markers_as_written":[],"summary_excerpt":"Der zweite Text trägt in drei Punkten unmittelbar:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"14.4 Phasen, Gesamtsymmetrie und Unsichtbarkeit kleiner Tests","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11528,"byte_start":10459,"id":"section:e7543c0d1bef96b44825","kind":"subsubsection","labels":["konsequenz-fuxfcr-die-weitere-arbeit"],"line_end":222,"line_start":203,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/003-subsection-14-nachpr-fung-der-beiden-zuletzt-zugeschickt.tex","status_markers_as_written":[],"summary_excerpt":"Die Priorität wird präziser, nicht breiter: Quelle samt fermionischem Lift und realem Operationssatz bestimmen; auf ihr Zustand und Antworten gemeinsam berechnen; dann lokale Algebren und ihre Skalierung prüfen. Ein unabhängig gewonnener treuer Teilzustand und eine nichttriviale modulare Vergleichsrelation wären ein echter zusätzlicher Anschluss. Ein aus H definierter Gibbszustand oder ein bereits zeitmarkierter voll","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"14.5 Konsequenz für die weitere Arbeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11917,"byte_start":11528,"id":"section:38076c0cb1756b3e7594","kind":"subsection","labels":["fortgesetzte-auswahlpruxfcfung-fehlt-eine-spiegelungsrelation"],"line_end":230,"line_start":223,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/003-subsection-14-nachpr-fung-der-beiden-zuletzt-zugeschickt.tex","status_markers_as_written":[],"summary_excerpt":"Der Nutzer bat während der Konsolidierung um weitere Arbeit. Deshalb wurde nicht nur die neue Quelle beschrieben, sondern unmittelbar die wichtigste noch verdeckte Wahl angegriffen: Warum gerade die gleichstarke Nachbarmischung?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"15. Fortgesetzte Auswahlprüfung: fehlt eine Spiegelungsrelation?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13635,"byte_start":11917,"id":"section:d3ea5bd40603c295acbc","kind":"subsubsection","labels":["ein-gegenmodell-gegen-eine-zu-starke-deutung-des-grundzustandssatzes"],"line_end":263,"line_start":231,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/003-subsection-14-nachpr-fung-der-beiden-zuletzt-zugeschickt.tex","status_markers_as_written":[],"summary_excerpt":"Ersetze die festgelegte Quelle zunächst durch die einfache reelle Familie","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"15.1 Ein Gegenmodell gegen eine zu starke Deutung des Grundzustandssatzes","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16241,"byte_start":13635,"id":"section:96c77b7ea577900be786","kind":"subsubsection","labels":["eine-kleine-spiegelungsregel-wuxfcrde-die-gewichtung-bestimmen"],"line_end":313,"line_start":264,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/003-subsection-14-nachpr-fung-der-beiden-zuletzt-zugeschickt.tex","status_markers_as_written":[],"summary_excerpt":"Für beide Lifts wähle den reellen signierten Reflexionsoperator J durch","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"15.2 Eine kleine Spiegelungsregel würde die Gewichtung bestimmen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18510,"byte_start":16241,"id":"section:8f77a4d0f75af29d8c13","kind":"subsubsection","labels":["tatsuxe4chlicher-anschluss-an-uxe4ltere-tfpt-struktur"],"line_end":353,"line_start":314,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":["relation:43209f6f597dfbd777e7","relation:487be1e18d9cbdcf2927","relation:58dd4dd03a279200b0a2","relation:878c299ba56e56b47234","relation:a27f8c58901370de4f07","relation:b2f9c7beced880004dae"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/003-subsection-14-nachpr-fung-der-beiden-zuletzt-zugeschickt.tex","status_markers_as_written":[],"summary_excerpt":"In origin_theory.tex ist die Relation [formula in source] bereits Teil der geometrischen Normalform. v177_seam_marking_kernel.py verwendet explizit [formula in source] und [formula in source] auf den vier Marken. v180_clock_is_mobius.py trennt die Clock-Geometrie weiterhin von der ursprünglichen Realisierungsvoraussetzung. 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Darin enthalten sind wiederholte Quellen-, Vorzeichen- und CAR-Prüfungen; die Zahl zählt keine unabhängigen Theoreme. Der allgemeine Grundzustands- und Antwortbeweis ist in Abschnitten 5-7 ausgeschrieben. Die Zusatzprüfung der beiden späten Perspektivtexte umfasst 61 weitere Bedingungen, ebenfalls normal/optimiert byteidentisch. Ihre all","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Abgeschlossener eigener Replay","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":562,"byte_start":0,"id":"section:78361d4ce34a5362eac3","kind":"section","labels":["historischer-bestand-vollstuxe4ndige-hauptfassung-v1.6.9"],"line_end":11,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/004-section-historischer-bestand-vollst-ndige-hauptfassung.tex","status_markers_as_written":[],"summary_excerpt":"Die vorherige Hauptfassung folgt vollständig und unverändert. 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Die neue N=256-Konstruktion darf nicht rückwirkend in diese alten Sätze eingesetzt werden.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Historischer Bestand: vollständige Hauptfassung v1.6.9","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":792,"byte_start":562,"id":"section:f87b3bfe1382abc86cc3","kind":"section","labels":["tfpt-universalraum-zusammensetzung-aus-der-gemeinsamen-antwort"],"line_end":17,"line_start":12,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/004-section-historischer-bestand-vollst-ndige-hauptfassung.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"TFPT / Universalraum: Zusammensetzung aus der gemeinsamen Antwort","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3741,"byte_start":792,"id":"section:88d218fc42e29b9cc352","kind":"subsection","labels":["ergebnis-die-fehlende-verbindung-wird-berechenbar-aber-noch-nicht-urspruxfcnglich-ausgewuxe4hlt"],"line_end":74,"line_start":18,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/004-section-historischer-bestand-vollst-ndige-hauptfassung.tex","status_markers_as_written":[],"summary_excerpt":"Die drei beauftragten Arbeitslinien wurden parallel ausgeführt: ursprüngliche Komposition, ein kompletter kleiner Ablauf und ein früher relativistischer Feldtest. Hinzu kommt eine unabhängige globale CAR-Rechnung im Hauptstrang. Sie ergeben keinen Abschluss der TOE, aber vier konkrete Fortschritte:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Ergebnis: Die fehlende Verbindung wird berechenbar, aber noch nicht ursprünglich ausgewählt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":6401,"byte_start":3741,"id":"section:f37af42956109f5032e6","kind":"subsection","labels":["einfaches-gesamtbild"],"line_end":130,"line_start":75,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/004-section-historischer-bestand-vollst-ndige-hauptfassung.tex","status_markers_as_written":[],"summary_excerpt":"Man kann sich den ursprünglichen Tensor wie eine Kupplung vorstellen: Zwei Fermionen können gemeinsam in ein Boson übergehen und zurück. 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Einfaches Gesamtbild","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":9509,"byte_start":6401,"id":"section:024d57f8a44059142cc6","kind":"subsection","labels":["quellenweg-urspruxfcnglicher-clock-ist-keine-kopiermaschine"],"line_end":200,"line_start":131,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/004-section-historischer-bestand-vollst-ndige-hauptfassung.tex","status_markers_as_written":[],"summary_excerpt":"Die alten Quellen wurden bis zu ihren tatsächlichen Trägern zurückverfolgt. 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Vereinfachter vollständiger Prozess mit einer echten Aufzeichnung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":17934,"byte_start":15296,"id":"section:04b70e9419497cecdfc6","kind":"subsection","labels":["relativistischer-anschluss-ein-positiver-adapter-und-ein-negativer-kinetiktest"],"line_end":382,"line_start":328,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/004-section-historischer-bestand-vollst-ndige-hauptfassung.tex","status_markers_as_written":[],"summary_excerpt":"Für ein gemischthändiges Komposit [formula in source] ist ohne zusätzliche Lorentzstruktur keine lineare Auslese in einen linken Weylspinor möglich. Mit genau einem Impulsfaktor P gibt es dagegen einen bis auf Normierung eindeutigen solchen Operator C_P. Für jedes P≠0 hat er Rang zwei und einen vierdimensionalen Kern.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Relativistischer Anschluss: ein positiver Adapter und ein negativer Kinetiktest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":1933,"byte_start":0,"id":"section:470f4e35d7c2055b0316","kind":"subsection","labels":["was-die-vier-rechnungen-gemeinsam-haben-und-was-nicht"],"line_end":44,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/005-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 6 ) * 0.2500 > p( - 6 ) * 0.2500 > p( - 6 ) * 0.2500 > p( - 6 ) * 0.2500@ Rechnung & Tatsächlicher Träger & Neue Voraussetzung & Nicht übertragen \\\\ Zwei Charts & 128 Fermionmoden, zwei Bosonbanken, N=2 & Überlappung c und globale Vertexsumme & Keine native Auswahl von c \\\\ Ein normierter C-Tensor & 64L Fermionmoden, eine Bosonbank, N=2 und 3 & Normiertes symmetrisches C & Keine unveränderte lokale Einzelkop","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. Was die vier Rechnungen gemeinsam haben und was nicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4435,"byte_start":1933,"id":"section:b9fa3a98e0a680e063e3","kind":"subsection","labels":["t1-t8-konkrete-bewegung-der-grenze"],"line_end":99,"line_start":45,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/005-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"Die Benennungen folgen der Arbeitszuordnung der vollständigen v1.6.8. Kein vollständiges T-Gate wird geschlossen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8. T1-T8: konkrete Bewegung der Grenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4527,"byte_start":4435,"id":"section:fcce4e2a0a051f874f83","kind":"subsection","labels":["der-effektivste-nuxe4chste-versuch"],"line_end":102,"line_start":100,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/005-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"9. Der effektivste nächste Versuch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5450,"byte_start":4527,"id":"section:f9e8aa10368279e73f4d","kind":"subsubsection","labels":["a.-quellstrahlen-zu-gemeinsamem-truxe4ger---erster-fehlender-pfeil"],"line_end":119,"line_start":103,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/005-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"Aus den tatsächlichen Originalobjekten sollen zwei Einbettungen E_L,E_R sowie Bosonbank- und Vertexzuordnung folgen. Nicht nur eine bekannte Überlappungszahl einsetzen, sondern Typen, Gruppenwirkung, CAR und Operationen mitliefern. Das unmittelbar entscheidbare Ziel ist [formula in source] , bei skalarem Ansatz cI.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"A. Quellstrahlen zu gemeinsamem Träger - erster fehlender Pfeil","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6206,"byte_start":5450,"id":"section:bc5fda00825607ba0cf8","kind":"subsubsection","labels":["b.-autonomer-eingriff-statt-gewuxe4hltem-puls"],"line_end":135,"line_start":120,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/005-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"Den benötigten Nb-Eingriff und den Zeigerkoppler als Teile eines gemeinsamen zeitunabhängigen Controller-System-Modells konstruieren. Es muss die schon gerechnete Wirkung reproduzieren, Gesamtladung und Gesamtenergie mitführen und den Zustand des Controllers vor und nach dem Versuch angeben. Eine beliebig angesetzte Taktsequenz wäre noch keine ursprüngliche Uhr.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B. Autonomer Eingriff statt gewähltem Puls","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7156,"byte_start":6206,"id":"section:1baf0c473321ab633b9e","kind":"subsubsection","labels":["c.-einen-nichtnullen-vertexkonsistenten-feldkanal-auf-derselben-quelle"],"line_end":154,"line_start":136,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/005-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"Nicht den freien masselosen Nullansatz weiter ausbauen. Zuerst die tatsächlichen Feldkomponenten zum Vertex und zur geladenen nativen Antwort festlegen; dann das konkrete Matrixelement der Quelle unter der vorgeschlagenen wechselwirkenden oder massiven Kinetik berechnen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"C. Einen nichtnullen, vertexkonsistenten Feldkanal auf derselben Quelle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8532,"byte_start":7156,"id":"section:796208657edfb7ad292f","kind":"subsection","labels":["pruxfcf--und-veruxf6ffentlichungsstand"],"line_end":180,"line_start":155,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/005-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"Vier neue Stränge wurden aus eingefrorenen Eingaben normal und optimiert ausgeführt, mit Warnungen als Fehler und identischen Ergebnisbytes: 514 eigene exakt arbeitende Bedingungen und vier numerische Kontrollen je Variante. Die exakte Kategorie enthält auch Quellenpins und Strukturguards, nicht nur mathematische Sätze. Separat wurden 17 native Konstruktionsguards und 1073 alte P0/P1-Quellguards wiederholt. Die gesam","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10. Prüf- und Veröffentlichungsstand","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9260,"byte_start":8532,"id":"section:3dd2b707e7b5e794b8ea","kind":"subsubsection","labels":["automatisch-aus-dem-abgeschlossenen-replay"],"line_end":205,"line_start":181,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/005-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"@lrr@ Eigener Strang & Exakte Bedingungen & Numerische Bedingungen \\\\ composition & 67 & 0 \\\\ field & 85 & 0 \\\\ protocol & 92 & 4 \\\\ source & 270 & 0 \\\\","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Automatisch aus dem abgeschlossenen Replay","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9417,"byte_start":9260,"id":"section:a843b3ad750f655cedf6","kind":"section","labels":["vollstuxe4ndiger-beweis-huxf6here-antwort-und-positive-kopplungsmatrix"],"line_end":208,"line_start":206,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/005-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Vollständiger Beweis: höhere Antwort und positive Kopplungsmatrix","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":9719,"byte_start":9417,"id":"section:d7091677661704dd91de","kind":"section","labels":["eine-huxf6here-antwort-liest-die-zusammensetzung-aus"],"line_end":219,"line_start":209,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/005-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Eine höhere Antwort liest die Zusammensetzung aus","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10606,"byte_start":9719,"id":"section:abfb4f2dd42053deda5e","kind":"subsection","labels":["frage-und-ergebnis"],"line_end":236,"line_start":220,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/005-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"Kann die innere W-Struktur schon bestimmen, wie mehrere Vorkommen gemeinsam wirken? Für eine ausdrücklich erklärte, besonders einfache Familie lässt sich die Frage exakt beantworten: Nein, nicht aus W und auch nicht aus dem gesamten Zweiladungsspektrum allein. Die Dreiladungsantwort bestimmt jedoch genau die zusätzlich gewählte positive Kopplungsmatrix. Das ist ein konstruktiver Anschluss für die vom Benutzer vorgesc","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Frage und Ergebnis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":12167,"byte_start":10606,"id":"section:97d1a4a48548d301d454","kind":"subsection","labels":["gemeinsame-urspruxfcngliche-daten"],"line_end":278,"line_start":237,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/005-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"Wir verwenden den unveränderten realen Tensor W mit 60 Kanälen und 2016 Fermionpaarspalten. Aus jeder Zeile wird eine antisymmetrische 64-mal-64-Matrix A_A: oberhalb der Diagonale steht W, unterhalb sein negatives Transponiertes. Direkt aus allen 480 Vertices folgt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Gemeinsame ursprüngliche Daten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13559,"byte_start":12167,"id":"section:2fdbddf312e36928bf9a","kind":"subsection","labels":["ein-zusuxe4tzlicher-symmetrischer-kompositionstensor"],"line_end":308,"line_start":279,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/005-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"Fermionen erhalten einen zusätzlichen L-dimensionalen Multiplizitätsfaktor; die 60 Bosonen bleiben eine einzige gemeinsame Bank. Wähle eine komplex-symmetrische Matrix C mit [formula in source] . Die antisymmetrischen globalen Paarmatrizen lauten","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Ein zusätzlicher symmetrischer Kompositionstensor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15206,"byte_start":13559,"id":"section:6e6f40763fa9b9a72e59","kind":"subsection","labels":["gleiche-vollstuxe4ndige-zweiladungsspektren-unterschiedliche-globale-dynamik"],"line_end":346,"line_start":309,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/005-subsection-7-was-die-vier-rechnungen-gemeinsam-haben-und.tex","status_markers_as_written":[],"summary_excerpt":"wobei J_L die Matrix aus lauter Einsen bezeichnet. Beide sind symmetrisch, normiert, invariant unter Permutation der Kopien und stimmen für L=1 mit dem nativen Modell überein. Sie liefern jedoch verschiedene spätere Physik. Permutationssymmetrie ist dabei keine geometrische Lokalität.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Gleiche vollständige Zweiladungsspektren, unterschiedliche globale Dynamik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":2746,"byte_start":0,"id":"section:e6d5a840ff3885073e8a","kind":"subsection","labels":["allgemeine-car-identituxe4t-auf-n3"],"line_end":72,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/006-subsection-5-allgemeine-car-identit-t-auf.tex","status_markers_as_written":[],"summary_excerpt":"Bezeichne die globale Dreifermion-zu-Boson-Fermion-Abbildung mit [formula in source] . Die Boson-Fermion-Zeilen werden als [formula in source] angeordnet. Aus der Paar-CAR-Kontraktion folgt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Allgemeine CAR-Identität auf N=3","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3968,"byte_start":2746,"id":"section:ab35c937beeced7a47d2","kind":"subsection","labels":["positive-ruxfcckrechnung-der-schatten-bestimmt-q"],"line_end":98,"line_start":73,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/006-subsection-5-allgemeine-car-identit-t-auf.tex","status_markers_as_written":[],"summary_excerpt":"Die obige Identität lässt sich tatsächlich invertieren. Mit [formula in source] gilt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Positive Rückrechnung: der Schatten bestimmt Q","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5121,"byte_start":3968,"id":"section:2bb986d3f55d450bbff7","kind":"subsubsection","labels":["anschluss-an-dieselbe-bosonzahl-auslese"],"line_end":123,"line_start":99,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/006-subsection-5-allgemeine-car-identit-t-auf.tex","status_markers_as_written":[],"summary_excerpt":"Auf N=3 hat H_C die Blockform [formula in source] . Für einen normierten Eingang v auf der Boson-Fermion-Seite gilt exakt im Taylor-Anfang","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Anschluss an dieselbe Bosonzahl-Auslese","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6741,"byte_start":5121,"id":"section:d8a479a6451aca09d841","kind":"subsection","labels":["warum-ein-einzelnes-c-muxf6glicherweise-zu-einfach-fuxfcr-gerichteten-ladungstransport-ist"],"line_end":152,"line_start":124,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/006-subsection-5-allgemeine-car-identit-t-auf.tex","status_markers_as_written":[],"summary_excerpt":"Jede komplex-symmetrische endliche Matrix besitzt eine Takagi-Zerlegung [formula in source] mit unitärem U und nichtnegativem diagonalem D. Eine Standardreferenz ist https://arxiv.org/abs/2009.03990Haber, A tale of three diagonalizations, Abschnitt 7. Der Prüfer kontrolliert zusätzlich ein nichtreelles rationales Beispiel. Der allgemeine Existenzsatz wird aus der linearen Algebra übernommen, nicht aus diesem Beispiel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. Warum ein einzelnes C möglicherweise zu einfach für gerichteten Ladungstransport ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7597,"byte_start":6741,"id":"section:0eb57afbcf6a33f20527","kind":"subsection","labels":["pruxe4zise-nuxe4chste-entscheidung"],"line_end":168,"line_start":153,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/006-subsection-5-allgemeine-car-identit-t-auf.tex","status_markers_as_written":[],"summary_excerpt":"Der einfachste nächste Auftrag ist kein neuer großer Tensorraum. Er ist eine typisierte Quellvorschrift für zwei Einbettungen E_L,E_R und ihre Überlappung [formula in source] , einschließlich der Bosonbankzuordnung. Die vorhandenen Quellstrahlen enthalten diskrete Überlappungszahlen, aber der direkte Import ihrer internen C4-Projektoren als neue triviale Kopien ist nicht äquivariant begründet.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8. Präzise nächste Entscheidung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8432,"byte_start":7597,"id":"section:75a5b17d46805571db9d","kind":"subsection","labels":["reproduktion-und-grenze"],"line_end":185,"line_start":169,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/006-subsection-5-allgemeine-car-identit-t-auf.tex","status_markers_as_written":[],"summary_excerpt":"verify_composition.py führt 67 explizite exakt arbeitende Prüfbedingungen aus, einschließlich Quellenpins und Strukturguards. Es gibt keine numerischen Toleranzprüfungen. Die allgemeine Formel und ihre Inversion sind oben algebraisch hergeleitet; drei vollständige N=3-CAR-Aufbauten kontrollieren Normalisierung, Vorzeichen und komplexe Konvention unabhängig.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. Reproduktion und Grenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":8577,"byte_start":8432,"id":"section:1bbfb2d55f96d4ca5c79","kind":"section","labels":["teilbericht-a-urspruxfcngliche-quelle-und-uxfcberlappende-charts"],"line_end":188,"line_start":186,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/006-subsection-5-allgemeine-car-identit-t-auf.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Teilbericht A: ursprüngliche Quelle und überlappende Charts","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8930,"byte_start":8577,"id":"section:30e48c5cf5171e139e4f","kind":"section","labels":["quellenkomposition-dieselben-lokalen-vertices-verschiedene-gemeinsame-fermionen"],"line_end":200,"line_start":189,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/006-subsection-5-allgemeine-car-identit-t-auf.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Quellenkomposition: dieselben lokalen Vertices, verschiedene gemeinsame Fermionen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10152,"byte_start":8930,"id":"section:2ae9ca843a857014b40f","kind":"subsection","labels":["stuxe4rkstes-neues-ergebnis"],"line_end":223,"line_start":201,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/006-subsection-5-allgemeine-car-identit-t-auf.tex","status_markers_as_written":[],"summary_excerpt":"Die geprüfte Quelle bestimmt bereits einen gemeinsamen lokalen CAR-Träger mit 64 Fermionmoden, nicht 480 unabhängige Wechselwirkungsbanken. Jeder dieser Fermionmoden kommt in genau 15 der 480 nichtverschwindenden Vertices vor. Aber die Quelle bestimmt in den untersuchten Konstruktionen noch keine Überlappung zweier vollständiger Kopplungs-Charts dieses Trägers.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Stärkstes neues Ergebnis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14249,"byte_start":10152,"id":"section:0360327baf7e82aba7c3","kind":"subsection","labels":["was-die-gelesenen-quellen-tatsuxe4chlich-zusammensetzen"],"line_end":299,"line_start":224,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":["relation:3ddb48cb231b3df17b03","relation:5139e02d5fc7c3216168","relation:76920186f5558e49df97","relation:8fe5a414acef5771a320","relation:96c86d546313c19a648c","relation:a2c1720ac7eafad15e75","relation:b12a2d5286c36eb00e1e","relation:c303702d97fe4d3fd4c5","relation:e96a131d42be6665718d","relation:f25e00ee93f542f2f9da","relation:fafd3f9be91b7b5fe7ee"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/006-subsection-5-allgemeine-car-identit-t-auf.tex","status_markers_as_written":[],"summary_excerpt":"Alle genannten Dateien sind in inputs/inputs eingefroren; Originalpfade, Bytezahlen und SHA-256 stehen im inputs_manifest.jsonManifest. Der Prüfer importiert keine beweglichen Repository-Dateien.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Was die gelesenen Quellen tatsächlich zusammensetzen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15038,"byte_start":14249,"id":"section:1cdd9ef055477889cf66","kind":"subsubsection","labels":["clock-ist-keine-automatische-vervielfuxe4ltigung"],"line_end":317,"line_start":300,"numbered_or_version_tokens_as_written":["S0.1","S0.4"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":["relation:5228d16533777f5b0f3a"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/006-subsection-5-allgemeine-car-identit-t-auf.tex","status_markers_as_written":[],"summary_excerpt":"Der ursprüngliche Clock wird aus experiments/tfpt-discovery/seam_state_derivation_probe.py, S0.1-S0.4, neu ausgeführt. Sein dokumentierter passiver Lift erfüllt mit L=Λ²GF:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Clock ist keine automatische Vervielfältigung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17546,"byte_start":15038,"id":"section:541b5ec93557f35953ec","kind":"subsection","labels":["kleinstes-skalares-uxfcberlappungs-gegenmodell"],"line_end":372,"line_start":318,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/006-subsection-5-allgemeine-car-identit-t-auf.tex","status_markers_as_written":[],"summary_excerpt":"Seien a_i,d_i, i=0, ,63, zwei kanonische Familien auf einer gemeinsamen CAR-Fockbasis. Setze für 0 c 1 und s=√(1−c²):","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Kleinstes skalares Überlappungs-Gegenmodell","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3613,"byte_start":0,"id":"section:5d5b208e173bfdbc42eb","kind":"subsection","labels":["exakt-geschlossener-ablauf-und-messbarer-unterschied"],"line_end":82,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/007-subsection-3-exakt-geschlossener-ablauf-und-messbarer.tex","status_markers_as_written":[],"summary_excerpt":"Auf N=2 hat die gemeinsame Paarabbildung C_c exakt den Gramoperator","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Exakt geschlossener Ablauf und messbarer Unterschied","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5134,"byte_start":3613,"id":"section:52742dc47a60567d5bb2","kind":"subsection","labels":["echter-gemeinsamer-ressourcenanteil-keine-versteckte-einzelkopienzerlegung"],"line_end":111,"line_start":83,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/007-subsection-3-exakt-geschlossener-ablauf-und-messbarer.tex","status_markers_as_written":[],"summary_excerpt":"Die beiden reellen symmetrischen Flavor-Kopplungstensoren lauten CL=uuᵀ und CR=vvᵀ, u=(1,0), v=(c,s). Sie erfüllen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Echter gemeinsamer Ressourcenanteil, keine versteckte Einzelkopienzerlegung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7580,"byte_start":5134,"id":"section:4f039276edd20d650029","kind":"subsection","labels":["liefern-fruxfche-quellprojektoren-bereits-c"],"line_end":162,"line_start":112,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/007-subsection-3-exakt-geschlossener-ablauf-und-messbarer.tex","status_markers_as_written":[],"summary_excerpt":"Der neu ausgeführte Original-P0/P1-Weg bestätigt exakt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Liefern frühe Quellprojektoren bereits c?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8252,"byte_start":7580,"id":"section:2aa9887306ea3a2783b7","kind":"subsection","labels":["nuxe4chster-erster-fehlender-quellschritt"],"line_end":177,"line_start":163,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/007-subsection-3-exakt-geschlossener-ablauf-und-messbarer.tex","status_markers_as_written":[],"summary_excerpt":"Gesucht ist eine explizite, typisierte globale Zuordnung","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Nächster erster fehlender Quellschritt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9782,"byte_start":8252,"id":"section:3734a1f46b6c06b9d17f","kind":"subsection","labels":["reproduktion-und-pruxfcfgrenze"],"line_end":207,"line_start":178,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/007-subsection-3-exakt-geschlossener-ablauf-und-messbarer.tex","status_markers_as_written":[],"summary_excerpt":"python3 verify.py –output results_normal.json und python3 -OO verify.py –output results_optimized.json; REPLAY.json versiegelt Exitcodes, Prüferhash und identische Resultatbytes. replay.py führt beide Varianten lokal aus. 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W bleibt 3f00a0892157a691e4ef26920c3702772c7bf76a250fad98ff04a079bb64b763.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. 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Exakter unbedingter Eingriff","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16513,"byte_start":15113,"id":"section:8b1f199c3f33aa6fa069","kind":"subsubsection","labels":["strikter-endlicher-nachweis"],"line_end":371,"line_start":332,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/007-subsection-3-exakt-geschlossener-ablauf-und-messbarer.tex","status_markers_as_written":[],"summary_excerpt":"Für Δ 0 und 0 g²≤5Δ²/128 gilt 2/3≤d 1. 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Die Isometrie","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Ein echtes, die Paarkohärenz erhaltendes Aufzeichnungsinstrument","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6689,"byte_start":5267,"id":"section:ff13ecd8ff820fa447a8","kind":"subsection","labels":["warum-reine-innere-symmetrieimpulse-diese-rolle-nicht-uxfcbernehmen"],"line_end":149,"line_start":120,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/008-subsection-3-schaltbarkeit-und-arbeit-werden.tex","status_markers_as_written":[],"summary_excerpt":"Sei V ein tatsächlicher innerer Gruppenimpuls. 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Ihr Rang ist bei jedem von null verschiedenen p exakt zwei, auch auf dem Lichtkegel.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ergebnis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11970,"byte_start":10804,"id":"section:e5ba72ca699b50e04217","kind":"subsection","labels":["pruxe4zise-zusuxe4tzliche-eingabe"],"line_end":258,"line_start":228,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/008-subsection-3-schaltbarkeit-und-arbeit-werden.tex","status_markers_as_written":[],"summary_excerpt":"Seien V und V̄ die beiden fundamentalen Weylräume. Der neue Vertrag setzt explizit","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Präzise zusätzliche Eingabe","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13669,"byte_start":11970,"id":"section:748f03fe9b21aac90aaa","kind":"subsection","labels":["explizite-auslese-und-minimalituxe4t"],"line_end":305,"line_start":259,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/008-subsection-3-schaltbarkeit-und-arbeit-werden.tex","status_markers_as_written":[],"summary_excerpt":"Mit ε als alternierender Form lautet die Auslese","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. 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Deshalb ist der Rang für jede von null verschiedene komplexe Matrix P exakt zwei, unabhängig von det P. Alle folgenden Aussagen sind symbolische Identitäten, keine numerischen Rangschätzungen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. 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Der Zähler J_PC_P hat Rang zwei und sein Quadrat ist null. Er ist somit kein Projektor; der massive Ausdruck lässt sich nicht durch bloßes Einsetzen von P²=0 fortsetzen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was auf dem Lichtkegel scheitert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2535,"byte_start":1135,"id":"section:ad696a391f375d923573","kind":"subsection","labels":["ein-expliziter-ruxfcckweg-mit-zusuxe4tzlicher-referenz"],"line_end":58,"line_start":22,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/009-subsubsection-was-auf-dem-lichtkegel.tex","status_markers_as_written":[],"summary_excerpt":"Für ein zukünftiges Null-P und ein zukünftiges zeitartiges Q ist σ 0, also ist der Rückweg endlich. 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Er prüft vier eingefrorene Quellenpins und 85 exakte Bedingungen je Modus. Es gibt keine numerischen Prüfbedingungen. 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Die frühere vollständige Reproduktion ist als unverändertes Archiv eingefroren.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Historischer Teil: vollständige Hauptfassung v1.6.8","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":12751,"byte_start":12398,"id":"section:c162f0d15765adebe78b","kind":"section","labels":["tfpt-universalraum-gemeinsame-schatten-und-ein-urspruxfcnglicher-kausaler-prozess"],"line_end":283,"line_start":276,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/009-subsubsection-was-auf-dem-lichtkegel.tex","status_markers_as_written":[],"summary_excerpt":"Vollständige Fortschreibung v1.6.8, 15. 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Keine vollständige TOE.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TFPT / Universalraum: gemeinsame Schatten und ein ursprünglicher kausaler Prozess","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15240,"byte_start":12751,"id":"section:243c7d319cc66be45a33","kind":"subsection","labels":["ergebnis-und-leseschluxfcssel"],"line_end":328,"line_start":284,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/009-subsubsection-was-auf-dem-lichtkegel.tex","status_markers_as_written":[],"summary_excerpt":"Die drei parallel bearbeiteten Aufgaben liefern diesmal konkrete mathematische Anschlüsse: einen kleinen ursprünglichen Singulettmechanismus, die vollständige bedingte Schattenkarte des hellen Raums und einen kausalen Eingriff unter dem unveränderten Hamiltonoperator. 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Es lief","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2.5 Weitere übernommene Richtungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8729,"byte_start":6034,"id":"section:4b8db5552e2c9a258b75","kind":"subsection","labels":["der-gemeinsame-urspruxfcngliche-ausgangspunkt"],"line_end":192,"line_start":129,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/010-subsubsection-2-1-tats-chliche-korrektur-die-erste-zeile.tex","status_markers_as_written":[],"summary_excerpt":"Alle drei eigenen Stränge verwenden denselben eingefrorenen Tensor W mit 60 Zeilen, 2016 Paarspalten und 480 signierten Einträgen. Es gilt exakt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Der gemeinsame ursprüngliche Ausgangspunkt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11739,"byte_start":8729,"id":"section:2912ba23edb5d4bb635b","kind":"subsection","labels":["einfachster-mechanismus-zwei-zustuxe4nde-und-eine-genaue-operationsgrenze"],"line_end":273,"line_start":193,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/010-subsubsection-2-1-tats-chliche-korrektur-die-erste-zeile.tex","status_markers_as_written":[],"summary_excerpt":"Mit der aus W hergeleiteten invarianten Paarung [formula in source] definiere","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Einfachster Mechanismus: zwei Zustände und eine genaue Operationsgrenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13850,"byte_start":11739,"id":"section:f5f1930b34f9bb8272d0","kind":"subsection","labels":["gemeinsame-schattenkarte-welche-bilder-reichen"],"line_end":325,"line_start":274,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/010-subsubsection-2-1-tats-chliche-korrektur-die-erste-zeile.tex","status_markers_as_written":[],"summary_excerpt":"Der native Kodierer [formula in source] bildet den inneren 60-Raum isometrisch in den Fermionpaarraum ab. Für jeden gewährten Operator O wird dessen Schatten auf demselben Zustand berechnet:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Gemeinsame Schattenkarte: welche Bilder reichen?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16482,"byte_start":13850,"id":"section:874c8687549451199fea","kind":"subsection","labels":["eigenes-bindeglied-aus-schatten-zu-mehreren-zeiten-die-fehlende-phase-zuruxfcckgewinnen"],"line_end":392,"line_start":326,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/010-subsubsection-2-1-tats-chliche-korrektur-die-erste-zeile.tex","status_markers_as_written":[],"summary_excerpt":"Schreibe die gemeinsame Zustandsmatrix in Paar-/Bosonblöcken. Die vier inneren hermiteschen Matrizen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Eigenes Bindeglied: aus Schatten zu mehreren Zeiten die fehlende Phase zurückgewinnen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":816,"byte_start":0,"id":"section:d06985aeba32c5dd4149","kind":"subsubsection","labels":["warum-nur-ein-schatten-auch-nach-beliebig-langer-zeit-nicht-reicht"],"line_end":18,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/011-subsubsection-warum-nur-ein-schatten-auch-nach-beliebig-.tex","status_markers_as_written":[],"summary_excerpt":"Für alle t gilt exakt [formula in source] . Der Operatororbit einer einzigen Paarsonde hat auf dem Zweizustandsfaktor Rang drei statt vier. Mit sämtlichen inneren Sonden bleibt der unsichtbare Raum","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum nur ein Schatten auch nach beliebig langer Zeit nicht reicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3564,"byte_start":816,"id":"section:5f71a25380204025716e","kind":"subsection","labels":["echter-kausaler-eingriff-ohne-zusuxe4tzlichen-hoppingterm"],"line_end":83,"line_start":19,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/011-subsubsection-warum-nur-ein-schatten-auch-nach-beliebig-.tex","status_markers_as_written":[],"summary_excerpt":"Jede aktive W-Spalte gehört genau einer Zeile; jede Zeile enthält acht disjunkte Fermionpaare. Der ganze N=2-Raum zerfällt deshalb in 60 invariante neundimensionale Sterne und 1536 ungekoppelte Paare. Einschließlich der sieben dunklen Richtungen je Stern ergibt sich wieder dunkle Dimension 1956.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. Echter kausaler Eingriff ohne zusätzlichen Hoppingterm","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6497,"byte_start":3564,"id":"section:91ca3c743fa0c7a1f37c","kind":"subsubsection","labels":["noch-kleiner-derselbe-dreizustandsraum-truxe4gt-schatten-und-eingriff"],"line_end":151,"line_start":84,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/011-subsubsection-warum-nur-ein-schatten-auch-nach-beliebig-.tex","status_markers_as_written":[],"summary_excerpt":"Für den gerade beschriebenen Versuch genügt sogar der gemeinsame Raum","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7.1 Noch kleiner: derselbe Dreizustandsraum trägt Schatten und Eingriff","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7392,"byte_start":6497,"id":"section:8b5e740dbf81ecee9db2","kind":"subsection","labels":["was-holografie-hier-sinnvoll-bedeutet"],"line_end":168,"line_start":152,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/011-subsubsection-warum-nur-ein-schatten-auch-nach-beliebig-.tex","status_markers_as_written":[],"summary_excerpt":"Bildlich sind die verschiedenen Beschreibungen Ansichten derselben Maschine. Eine Ansicht zeigt Besetzungen, eine andere innere Paarstruktur, eine dritte das spätere Verhalten nach einem Eingriff. Ihre gemeinsame Kalibrierung kann die verborgenen Phasen bestimmen. Abschnitt 6 realisiert genau diese Idee im endlichen hellen Raum.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8. Was Holografie hier sinnvoll bedeutet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9972,"byte_start":7392,"id":"section:078d6c637c24584897e3","kind":"subsection","labels":["nuxe4chste-entscheidende-nachweise"],"line_end":214,"line_start":169,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/011-subsubsection-warum-nur-ein-schatten-auch-nach-beliebig-.tex","status_markers_as_written":[],"summary_excerpt":"Übergeordnete Frage: Welche ursprüngliche Kompositionsregel erzeugt gemeinsam unterscheidbare Vorkommen, ihre Bewegung, ihren Zustand und ihre Instrumente? Die letzte nachgereichte fundamentale Reduktion trifft diese Frage. Ein genaueres lokales Spektrum kann sie nicht ersetzen. Die folgenden kleinen Prüfungen dienen als überprüfbare Annahmekriterien für eine solche Regel; sie sind keine Ersatzdefinition von Raum und","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. Nächste entscheidende Nachweise","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12471,"byte_start":9972,"id":"section:d57750297e42968b9812","kind":"subsection","labels":["t1-bis-t8-nach-dieser-runde"],"line_end":269,"line_start":215,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/011-subsubsection-warum-nur-ein-schatten-auch-nach-beliebig-.tex","status_markers_as_written":[],"summary_excerpt":"Die Bezeichnungen folgen der Arbeitszuordnung der geprüften Synthese; die jeweiligen vollständigen Tore bleiben offen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10. T1 bis T8 nach dieser Runde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":13483,"byte_start":12471,"id":"section:6853147bda45a2d9adc7","kind":"subsection","labels":["reproduktionsumfang"],"line_end":289,"line_start":270,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/011-subsubsection-warum-nur-ein-schatten-auch-nach-beliebig-.tex","status_markers_as_written":[],"summary_excerpt":"Der gemeinsame Replay führt alle eigenen mathematischen Prüfer normal und optimiert mit Warnungen als Fehler aus. Die Teilberichte unterscheiden exakte Identitäten von numerischen Kontrollen. Die 57 Prüfbedingungen des gelieferten Papers und dessen 20 übernommene Kettenprüfungen werden separat ausgewiesen, nicht als neue eigene Entdeckungen addiert. Sie decken nicht automatisch jeden Satz des Papers ab; die Korrektur","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"11. Reproduktionsumfang","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14016,"byte_start":13483,"id":"section:7ad9bcc07d5bf9f5c569","kind":"section","labels":["nachgereichte-texte-neue-norm-korrigierte-zustandszuordnung-und-feldadapter"],"line_end":299,"line_start":290,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/011-subsubsection-warum-nur-ein-schatten-auch-nach-beliebig-.tex","status_markers_as_written":[],"summary_excerpt":"Die drei während der laufenden Prüfung nachgereichten Texte wurden vollständig gelesen und unverändert eingefroren. Sie sind keine Anweisungen, Ergebnisse ungeprüft zu übernehmen. Zwei Texte vereinfachen ältere Arbeitsstände stark; die dritte längere Forschungsnotiz enthält ausführlichere Beweise einer bereits bekannten grundsätzlichen Diagnose.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nachgereichte Texte: neue Norm, korrigierte Zustandszuordnung und Feldadapter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":16417,"byte_start":14016,"id":"section:0c8dd47f89d27bd0b24a","kind":"subsection","labels":["a.-ein-tatsuxe4chlich-neuer-rechenwert-truxe4gt-eine-stuxe4rkere-schranke"],"line_end":356,"line_start":300,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":["relation:06bdc80659ca29c2a474","relation:0a5d7dca108c909930b3","relation:19668dfb40c0cbfc93c0","relation:2f02fdaaf986b84ad6f3","relation:b4b93d9599431479b575"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/011-subsubsection-warum-nur-ein-schatten-auch-nach-beliebig-.tex","status_markers_as_written":[],"summary_excerpt":"Die Norm der fünften reinen Bosonstufe ist gegenüber dem hiesigen v1.6.7-Snapshot neu:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"A. Ein tatsächlich neuer Rechenwert trägt eine stärkere Schranke","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2319,"byte_start":0,"id":"section:1543945e9a9a2efc90e3","kind":"subsection","labels":["b.-die-einfache-darstellung-vermischt-zwei-nuxe4herungszustuxe4nde"],"line_end":41,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":["relation:d4d82fb2d20f4de06b9f","relation:e72c8c18248da8a0bc67"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/012-subsection-b-die-einfache-darstellung-vermischt-zwei.tex","status_markers_as_written":[],"summary_excerpt":"Die Werte um -1.138476Δ, mittlere Bosonzahl 1.0177445, Überlappung mit F von 0.3498904 und Bosonzahl-Shannonwert 1.8712436 Bit gehören zum größeren siebendimensionalen Ritz-Zustand. Die im selben Text genannten Gewichte 0.973684 und 0.026316 gehören dagegen ausdrücklich zu der älteren fünfdimensionalen Basis v0 bis v3 plus w2. Deren Energie liegt um -1.0942319Δ und ihre mittlere Bosonzahl um 0.8421159.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B. Die einfache Darstellung vermischt zwei Näherungszustände","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4503,"byte_start":2319,"id":"section:89218bc13bb8b32c5598","kind":"subsection","labels":["c.-ein-neuer-entscheidender-test-am-feldprojektor"],"line_end":91,"line_start":42,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/012-subsection-b-die-einfache-darstellung-vermischt-zwei.tex","status_markers_as_written":[],"summary_excerpt":"Der Spin-1/2-Projektor im zweiten Text trägt unter einer bestimmten Händigkeit. Für","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"C. Ein neuer entscheidender Test am Feldprojektor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5845,"byte_start":4503,"id":"section:246cfdedbed58dff3e43","kind":"subsection","labels":["d.-weitere-uxfcbernahmegrenzen"],"line_end":122,"line_start":92,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/012-subsection-b-die-einfache-darstellung-vermischt-zwei.tex","status_markers_as_written":[],"summary_excerpt":"Die Clock ist nach der späteren konkreten Konstruktion ein Element der inneren Spin(10)-Darstellung. Die ältere Formulierung „äußerer Handgriff`` wird nicht als neue Herkunftstatsache übernommen. Die große Kommutantdimension zählt nicht direkt physische Freiheitsgrade. Ein skalarer Kommutant bedeutet nicht automatisch beliebige dynamische Kontrolle. Als exakter Gegenzeuge haben Spin-1-Kontrollen einen skalaren Kommut","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"D. Weitere Übernahmegrenzen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9126,"byte_start":5845,"id":"section:d5a9d180dd7ebbcadff6","kind":"subsection","labels":["e.-die-dritte-notiz-richtige-richtung-uxfcberwiegend-bereits-beruxfccksichtigt"],"line_end":187,"line_start":123,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/012-subsection-b-die-einfache-darstellung-vermischt-zwei.tex","status_markers_as_written":[],"summary_excerpt":"Die längere fundamentale Reduktion ergänzt den bereits eingefrorenen früheren Kommentar um die ausführliche Herleitung. Ihr stärkster Satz trägt: Bei invariantem H, invariantem Ω und irreduzibler innerer Entnahmefamilie gilt für die gesamte lokale Antwort","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"E. Die dritte Notiz: richtige Richtung, überwiegend bereits berücksichtigt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10124,"byte_start":9126,"id":"section:fb34bbce845a1194a007","kind":"subsubsection","labels":["automatisch-aus-dem-abgeschlossenen-replay-1"],"line_end":219,"line_start":188,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/012-subsection-b-die-einfache-darstellung-vermischt-zwei.tex","status_markers_as_written":[],"summary_excerpt":"@lrr@ Eigener Strang & Exakte Bedingungen & Numerische Bedingungen \\\\ causal & 662 & 10 \\\\ common3 & 43 & 0 \\\\ late_field & 36 & 0 \\\\ late_moments & 2 & 2 \\\\ late_norm & 36 & 10 \\\\ mechanism & 261 & 0 \\\\ phase_bridge & 32 & 0 \\\\ resource_boundary & 24 & 0 \\\\ shadows & 5417 & 17 \\\\","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Automatisch aus dem abgeschlossenen Replay","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10267,"byte_start":10124,"id":"section:68bcd46c8e1113254b83","kind":"section","labels":["teilbericht-a-urspruxfcnglicher-mechanismus-und-referenzbilanz"],"line_end":222,"line_start":220,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/012-subsection-b-die-einfache-darstellung-vermischt-zwei.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Teilbericht A: ursprünglicher Mechanismus und Referenzbilanz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10446,"byte_start":10267,"id":"section:8d467d07fa151fa984fc","kind":"section","labels":["urspruxfcnglicher-mechanismus-erhaltung-und-die-kleinste-zusuxe4tzliche-ressource"],"line_end":226,"line_start":223,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/012-subsection-b-die-einfache-darstellung-vermischt-zwei.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Ursprünglicher Mechanismus, Erhaltung und die kleinste zusätzliche Ressource","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11997,"byte_start":10446,"id":"section:8bc8a0db62da0b0f8474","kind":"subsection","labels":["ergebnis-1"],"line_end":259,"line_start":227,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/012-subsection-b-die-einfache-darstellung-vermischt-zwei.tex","status_markers_as_written":[],"summary_excerpt":"Exakt neu: Am unveränderten Tensor schließt ein zweidimensionaler G-Singulett-Unterraum mit physischer Ladung N=4 unter dem gesamten nativen H. Seine Matrix ist","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ergebnis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16031,"byte_start":11997,"id":"section:f6d634dd592d2af948ee","kind":"subsection","labels":["was-die-tatsuxe4chlichen-quellen-konstruieren"],"line_end":336,"line_start":260,"numbered_or_version_tokens_as_written":["S0.1","S0.4"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":["relation:4f80eca1e517b8cba66b","relation:e734fbc7361d32bc3ec0","relation:f51b0ea080f04b2ff95e"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/012-subsection-b-die-einfache-darstellung-vermischt-zwei.tex","status_markers_as_written":[],"summary_excerpt":"Alle zwölf verwendeten Eingaben sind unter inputs/ unverändert eingefroren; inputs_manifest.json enthält ihre ursprünglichen Pfade, Größen und SHA-256. Das maßgebliche Tensorarchiv besitzt weiter den SHA-256 3f00a0892157a691e4ef26920c3702772c7bf76a250fad98ff04a079bb64b763.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Was die tatsächlichen Quellen konstruieren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18109,"byte_start":16031,"id":"section:1d736fe9280e1976c887","kind":"subsection","labels":["geschlossener-erhaltungssatz-fuxfcr-das-dokumentierte-alphabet"],"line_end":397,"line_start":337,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/012-subsection-b-die-einfache-darstellung-vermischt-zwei.tex","status_markers_as_written":[],"summary_excerpt":"hat jedes der 480 signierten Wechselwirkungsmonome Ladung +2−1−1=0. Nb, alle Modenbesetzungen und alle passiven Bilineare f†Af beziehungsweise b†Cb sind ebenfalls neutral. Die dokumentierten inneren Liegeneratoren werden genau auf diese Weise zweitquantisiert. Die Clock schickt f† nach GF f† und b† nach GB b†, mischt also keine Erzeuger mit Vernichtern.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Geschlossener Erhaltungssatz für das dokumentierte Alphabet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":984,"byte_start":0,"id":"section:0d8b7fd7098304489674","kind":"subsubsection","labels":["instrumente-und-die-genaue-ancilla-grenze"],"line_end":19,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/013-subsubsection-instrumente-und-die-genaue.tex","status_markers_as_written":[],"summary_excerpt":"Ein Instrument mit Krausoperatoren Kx aus A0 kann aus einem scharfen N-Sektor keinen anderen erzeugen. Eine spurtreue Summe solcher Zweige erhält die gesamte Sektorverteilung. Selektive Konditionierung kann die Gewichte einer bereits vorhandenen Mischung verändern, aber keine neue Sektorstütze erzeugen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Instrumente und die genaue Ancilla-Grenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3180,"byte_start":984,"id":"section:6286b00f90233e51fe93","kind":"subsection","labels":["die-kleinste-zusuxe4tzliche-operation-ist-schon-algebraisch-ausreichend"],"line_end":67,"line_start":20,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/013-subsubsection-instrumente-und-die-genaue.tex","status_markers_as_written":[],"summary_excerpt":"Dabei ist der zweite Bosonindex BAR(A). Es gibt dreißig solche ungeordneten Paare. Die vollständige Invarianz von η wird an allen 45+15 ursprünglichen Liegeneratoren geprüft. Die 60 verschiedenen Bosongewichte und der zusammenhängende Lie-Wirkungsgraph beweisen zusätzlich, dass diese Paarung bis auf einen Skalar eindeutig ist.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Die kleinste zusätzliche Operation ist schon algebraisch ausreichend","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":5679,"byte_start":3180,"id":"section:2871bb16f25d4c61ae01","kind":"subsection","labels":["ein-neuer-kleiner-urspruxfcnglicher-singulettmechanismus"],"line_end":127,"line_start":68,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/013-subsubsection-instrumente-und-die-genaue.tex","status_markers_as_written":[],"summary_excerpt":"Beide Zustände sind volle G-Singuletts und haben N=4. β enthält zwei Bosonen; ρ enthält einen Boson und zwei Fermionen. Ihre Orthogonalität folgt schon aus den unterschiedlichen Besetzungszahlen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Ein neuer kleiner ursprünglicher Singulettmechanismus","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7845,"byte_start":5679,"id":"section:4879b9aa463c77bdd369","kind":"subsection","labels":["exakter-gemeinsamer-dreizustandsprozess-mit-voller-innerer-symmetrie"],"line_end":189,"line_start":128,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/013-subsubsection-instrumente-und-die-genaue.tex","status_markers_as_written":[],"summary_excerpt":"Man gewähre eine Referenz R mit zwei G-trivialen Zuständen 0⟩R und 4⟩R, deren N_R-Ladungen null beziehungsweise vier sind. Setze","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Exakter gemeinsamer Dreizustandsprozess mit voller innerer Symmetrie","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9066,"byte_start":7845,"id":"section:a36d7bddd133a3261b58","kind":"subsubsection","labels":["die-referenz-verschwindet-nicht-aus-der-rechnung"],"line_end":218,"line_start":190,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/013-subsubsection-instrumente-und-die-genaue.tex","status_markers_as_written":[],"summary_excerpt":"Ein allgemeiner gemeinsamer Zustand in K hat die Form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Referenz verschwindet nicht aus der Rechnung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9811,"byte_start":9066,"id":"section:e0ea4cb658f768d8b822","kind":"subsubsection","labels":["anschluss-an-das-nachgereichte-forschungspaper"],"line_end":231,"line_start":219,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/013-subsubsection-instrumente-und-die-genaue.tex","status_markers_as_written":[],"summary_excerpt":"Abschnitt 9 des nachgereichten Papers benutzt dasselbe Prinzip einer mitgerechneten Ladungsreferenz. Sein dortiger N=9-Vierzustandstransfer erhält mit der neuen Referenz eine einzelne innere Cartanladung. Unsere Konstruktion betrifft stattdessen N und erhält die vollständige innere Gruppe, erzeugt aber keine räumliche Übertragung. Sie ersetzt den dortigen Transferzeugen nicht und beweist dessen native Herkunft nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Anschluss an das nachgereichte Forschungspaper","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":12583,"byte_start":9811,"id":"section:15fb5c0744a62d382fd9","kind":"subsection","labels":["ressourcenbilanz-und-der-jetzt-konkrete-nuxe4chste-nachweis"],"line_end":289,"line_start":232,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/013-subsubsection-instrumente-und-die-genaue.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333@ Ressource & Herkunft im geprüften Vertrag & Was noch zu liefern wäre \\\\ W, η, innere Darstellung, endliche Clock & Tatsächliche Quellkonstruktion und erneuter exakter Replay & Physische Identifikation des Trägers \\\\ Hnat mit Δ,g & Bestehender ausdrücklich festgelegter Modellvertrag & Physische Auswahl und Kalibrierung \\\\ Zweizustandsblock β↔ρ & Neue volls","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Ressourcenbilanz und der jetzt konkrete nächste Nachweis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14226,"byte_start":12583,"id":"section:47648ea2c2cbecf26795","kind":"subsection","labels":["reproduktion-und-beweisumfang"],"line_end":325,"line_start":290,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/013-subsubsection-instrumente-und-die-genaue.tex","status_markers_as_written":[],"summary_excerpt":"Benötigt werden Python, NumPy, SciPy und SymPy. 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Sie bestätigen die gespeicherten numerischen Ritz-Erwartungswerte, aber nicht deren Umdeutung zu exakten Eigenschaften von Ω.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Der Text vermischt drei verschiedene Näherungszustände","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":12559,"byte_start":10898,"id":"section:91351fb6a30f88ebb0c8","kind":"subsubsection","labels":["die-mittleren-antwortenergien-lassen-sich-ohne-riesige-zustandsdateien-korrigieren"],"line_end":276,"line_start":237,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":["relation:bbd8b956e1acc3575ce4"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/016-subsection-beweisumfang-label-beweisumfang.tex","status_markers_as_written":[],"summary_excerpt":"Aus den CAR folgen für jeden normierten G-Singulettzustand mit N=64:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die mittleren Antwortenergien lassen sich ohne riesige Zustandsdateien korrigieren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":14767,"byte_start":12559,"id":"section:90ec09e62f7374419228","kind":"subsection","labels":["was-bereits-uxfcberholt-ist"],"line_end":323,"line_start":277,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/016-subsection-beweisumfang-label-beweisumfang.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 2 ) * 0.5000 > p( - 2 ) * 0.5000@ Aussage der Anlage & Prüfung \\\\ Clock sei ein äußerer Handgriff, weil er Gewichte verschiebt & Bereits in v1.6.6/7 durch das explizite Spin(10)-Wort widerlegt. Nichtskalare Wirkung innerhalb eines Irreps bedeutet keine äußere Symmetrie. Die aktuelle Mechanismusprüfung reproduziert zudem den ursprünglichen Clock und seinen passiven Focklift. \\\\ Mit allen gewährten inneren Kon","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Was bereits überholt ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":15683,"byte_start":14767,"id":"section:a4a034f9bf291416ebb0","kind":"subsection","labels":["was-daran-spannend-ist-und-was-als-nuxe4chstes-truxe4gt"],"line_end":340,"line_start":324,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/016-subsection-beweisumfang-label-beweisumfang.tex","status_markers_as_written":[],"summary_excerpt":"Der gute neue Schritt ist die tatsächlich abgeschlossene fünfte Spurnetzwerk-Norm mit der daraus folgenden stärkeren strengen Energie- und Entnahmeschranke. Hinzu kommt unsere kleine CAR-Auswertung, die die geladenen ersten Momente auf den richtigen größeren Ritz-Zustand hebt. Das verbessert nachprüfbar die Rechnung im bestehenden nativen Modell.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Was daran spannend ist und was als nächstes trägt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":17081,"byte_start":15683,"id":"section:a278949d0f68d35bb6a5","kind":"subsection","labels":["reproduktionsbelege"],"line_end":368,"line_start":341,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":["relation:00ad58c486f5d099c99f","relation:12e99c70ffab37e20105","relation:14cdc46ac997016c1a23","relation:28c71a17dd31cd8aec4b","relation:56a6425dc3669b7bc953","relation:77892ee62cd01ddd5ec2"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/016-subsection-beweisumfang-label-beweisumfang.tex","status_markers_as_written":[],"summary_excerpt":"late_a/verify.py prüft elf eingefrorene Eingaben, führt die ν1-ν5- Spurnetzwerke frisch aus und baut beide Ritzpolynome unabhängig neu auf. Es gibt 46 eigene Prüfbedingungen: 36 exakte beziehungsweise faktische Prüfungen und 10 numerische Konsistenzprüfungen, separat dazu 1239 ausgeführte Quellguards der Normkonstruktion. Die Guardzahl zählt keine unabhängigen mathematischen Theoreme.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproduktionsbelege","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":17220,"byte_start":17081,"id":"section:0ce6fc96b738e14f2bf6","kind":"section","labels":["nachtragspruxfcfung-b-feldprojektor-und-lorentz-huxe4ndigkeit"],"line_end":371,"line_start":369,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/016-subsection-beweisumfang-label-beweisumfang.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Nachtragsprüfung B: Feldprojektor und Lorentz-Händigkeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":633,"byte_start":0,"id":"section:d373729a83875aae09ca","kind":"section","labels":["nachgereichter-text-b-korrekturen-und-ein-neuer-pruxfcfbarer-feldadapter"],"line_end":11,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":["relation:b50a3186b482c0a912b7"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/017-section-nachgereichter-text-b-korrekturen-und-ein-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"Der Text mit 45 Zeilen wurde vollständig gelesen. Seine unveränderte Kopie steht in late_sources/attachment_B.txt, SHA-256 9aaf5e18cbc6a84d610b88429872df9b69e6078365bfdc8133c8f17e2c1c3801. Die für die neue Prüfung maßgebliche field_dictionary.py ist gesondert eingefroren, SHA-256 a581bacd17c08dd9a766ae439bfe1e8e35e6d30b9509cb9d98053b897d8ecc13. Die bereits abgeschlossenen Schatten-Dateien wurden nicht verändert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nachgereichter Text B: Korrekturen und ein neuer prüfbarer Feldadapter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5027,"byte_start":633,"id":"section:dc7f670608079853f25a","kind":"subsection","labels":["uxfcbernahmeentscheidung"],"line_end":92,"line_start":12,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/017-section-nachgereichter-text-b-korrekturen-und-ein-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 2 ) * 0.5000 > p( - 2 ) * 0.5000@ Aussage im Text & Belastbare Fassung / konkrete Folge \\\\ 1,44 Milliarden unsichtbare Freiheiten im kleinsten nichttrivialen Sektor & 1444233216 ist die komplexe Kommutantdimension des gewährten Kontrollsatzes X,Nb im N=3-Sektor. Im N=2-Sektor lautet die entsprechende Zahl 3829536. Weder Zahl zählt direkt physische Freiheitsgrade. \\\\ Mit voller Symmetrie sieben, mit Modenzähl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Übernahmeentscheidung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5845,"byte_start":5027,"id":"section:c09f8f4ccc5f58fd8b99","kind":"subsection","labels":["neuer-exakter-kontrollgegenzeuge"],"line_end":109,"line_start":93,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/017-section-nachgereichter-text-b-korrekturen-und-ein-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"Die gewöhnlichen drei Spin-1-Matrizen J_x,J_y,J_z auf C³ erfüllen [J_x,J_y]=iJ_z und zyklisch. Bereits J_x und J_z haben ausschließlich skalare gemeinsame Kommutanten. Der dynamische Lie-Raum ist trotzdem nur su(2) mit Dimension drei, nicht su(3) mit Dimension acht. Das wird im neuen Prüfer durch exakte Ränge und alle drei Kommutatoren kontrolliert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Neuer exakter Kontrollgegenzeuge","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7469,"byte_start":5845,"id":"section:d99bdbaf221e8a732da1","kind":"subsection","labels":["was-am-spin-12-projektor-stimmt"],"line_end":156,"line_start":110,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/017-section-nachgereichter-text-b-korrekturen-und-ein-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"Die Feldquelle verwendet die sechs unnormierten Koordinaten","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Was am Spin-1/2-Projektor stimmt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10008,"byte_start":7469,"id":"section:5a66fcc5ae711cc77875","kind":"subsection","labels":["die-neue-pruxe4zise-huxe4ndigkeitsschranke"],"line_end":219,"line_start":157,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/017-section-nachgereichter-text-b-korrekturen-und-ein-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"Die eingefrorene Tabelle in field_dictionary.py, Zeile 327, bezeichnet den zweiten Faktor als f dagger (1/2,0). Dafür muss die Feldabbildung explizit festgelegt werden. Für ein tatsächliches adjungiertes linkes Weylfeld gilt dagegen ψ† in (0,1/2). Hermitesche Konjugation vertauscht diese Darstellungen; siehe https://arxiv.org/pdf/0812.1594\\#page=9Dreiner, Haber und Martin, Abschnitt 2.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Die neue präzise Händigkeitsschranke","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11663,"byte_start":10008,"id":"section:c737a1a2f0b72f64b05d","kind":"subsection","labels":["konkreter-nuxe4chster-annahmetest"],"line_end":256,"line_start":220,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/017-section-nachgereichter-text-b-korrekturen-und-ein-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"Der Anschlussauftrag ist jetzt endlich und entscheidbar formuliert:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Konkreter nächster Annahmetest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12572,"byte_start":11663,"id":"section:c6260e25e90627165dc9","kind":"subsection","labels":["reproduktion"],"line_end":279,"line_start":257,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":["relation:276d6d9968c18e7b740d","relation:81d2c6e2c7f9b74f8dd7"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/017-section-nachgereichter-text-b-korrekturen-und-ein-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"Benötigt werden nur Python und SymPy. Der separate Lauf verifiziert zwei Quellenpins sowie 36 exakte Bedingungen pro Modus, keine numerischen Bedingungen. Normaler Lauf und -OO ergeben byte-identische JSON-Ausgaben; Warnungen gelten als Fehler und alle Guards bleiben unter Optimierung aktiv. Die vollständigen Matrizen stehen in late_field.normal.json.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproduktion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":12717,"byte_start":12572,"id":"section:d3c0a088a5586a2a0ec9","kind":"section","labels":["nachtragspruxfcfung-c-fundamentale-reduktion-und-globale-quelle"],"line_end":282,"line_start":280,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/017-section-nachgereichter-text-b-korrekturen-und-ein-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Nachtragsprüfung C: fundamentale Reduktion und globale Quelle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12870,"byte_start":12717,"id":"section:34a1fbf3ae6036ac6c58","kind":"section","labels":["nachtrag-c-uxfcberwiegend-bereits-abgedeckte-fundamentale-reduktion"],"line_end":285,"line_start":283,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/017-section-nachgereichter-text-b-korrekturen-und-ein-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Nachtrag C: überwiegend bereits abgedeckte fundamentale Reduktion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13894,"byte_start":12870,"id":"section:f4e2353eddc385df8327","kind":"subsection","labels":["uxfcbernahmeurteil"],"line_end":307,"line_start":286,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":["relation:24099fb62f4a152ea6e8","relation:69320fd27b81e323ca81"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/017-section-nachgereichter-text-b-korrekturen-und-ein-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"Der neue Text ist eine ausführlichere Fassung der bereits eingefrorenen fundamentalen Reduktion, ergänzt um die weitgehend gleiche frühere Gesprächszusammenfassung. 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Gilt für die volle beschränkte Spektralfunktion, nicht nur einen dominanten Pol. 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Der eingetragene Programmpi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"μ=Δ/50: gegen die älteren gepinnten Zertifikate bestätigt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3169,"byte_start":2035,"id":"section:b93eca81fe8243a88f5a","kind":"subsection","labels":["zwei-pruxe4zisierungen-bei-der-uxfcbernahme"],"line_end":73,"line_start":47,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/018-subsection-50-gegen-die-lteren-gepinnten-zertifikate.tex","status_markers_as_written":[],"summary_excerpt":"In §7 sollte „ein positiver Unterschied`` durch „eine nichtverschwindende Differenz`` ersetzt werden. 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Keine fremde Quelldatei wurde verändert. Die Herkunftsdateien gehören zu parallel fortgeschriebenen Arbeitsständen; Dateipins sind deshalb wichtiger als Versionsnamen allein.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2.1 Quellenstand und Reproduktionsgrenzen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13882,"byte_start":11659,"id":"section:4dba61194e3f14b294c9","kind":"subsubsection","labels":["uxfcbernahmeentscheidung-1"],"line_end":290,"line_start":243,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/018-subsection-50-gegen-die-lteren-gepinnten-zertifikate.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 2 ) * 0.5000 > p( - 2 ) * 0.5000@ Aussage aus den Eingaben & Entscheidung für v1.6.7 \\\\ Korrigierter Anfangskommutant 3829536 / 1444233216 & Bestätigt; keine neue Größe gegenüber v1.6.6 \\\\ Nur SU(4) oder nur Spin(10) als zusätzliche Kontrollen & Übernommen; echte Zwischenstufen statt binärer Verfügbarkeit \\\\ Volle Gruppe plus alle Modenbesetzungen erzeugt volle Sektoralgebra & Unabhängig bestätigt, ausdrückl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2.2 Übernahmeentscheidung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14029,"byte_start":13882,"id":"section:d356742f420aa6f8eabd","kind":"subsection","labels":["vollstuxe4ndig-geluxf6st-der-erste-verzweigte-singulettbereich"],"line_end":293,"line_start":291,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/018-subsection-50-gegen-die-lteren-gepinnten-zertifikate.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"3. 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Das ergibt [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.2 Nicht nur gezählt: die vier Zustände und ihre Kopplungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3074,"byte_start":2124,"id":"section:d09ccd6e9c184a435bdb","kind":"subsubsection","labels":["der-vollstuxe4ndig-bestimmte-sechszustands-ausschnitt"],"line_end":84,"line_start":56,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/019-subsubsection-3-2-nicht-nur-gez-hlt-die-vier-zust-nde-un.tex","status_markers_as_written":[],"summary_excerpt":"Die Kompression auf alle Singuletts mit k kleiner oder gleich zwei ist exakt äquivalent zu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.3 Der vollständig bestimmte Sechszustands-Ausschnitt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3193,"byte_start":3074,"id":"section:5fd0f7c7ae1e792ce761","kind":"subsection","labels":["die-richtige-einfache-kette-wiederholung-von-h"],"line_end":87,"line_start":85,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/019-subsubsection-3-2-nicht-nur-gez-hlt-die-vier-zust-nde-un.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"4. Die richtige einfache Kette: Wiederholung von H","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4235,"byte_start":3193,"id":"section:2184b5d5980e35658802","kind":"subsubsection","labels":["der-fehler-war-die-gleichsetzung-zweier-verschiedener-stufen"],"line_end":111,"line_start":88,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/019-subsubsection-3-2-nicht-nur-gez-hlt-die-vier-zust-nde-un.tex","status_markers_as_written":[],"summary_excerpt":"Die Vektoren [formula in source] sind nach Bosonzahl geordnet. 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Ein Weg, der den nächsten nicht enthaltenen Lanczos-Vektor erreicht und nach F zurückkehrt, benötigt mindestens zehn Schritte. Aus der Tridiagonalität folgt deshalb die angegebene Momentengenauigkeit, ohne die übrige Kette zu erfinden.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.3 Zehn vollständige Energiemomente der gefüllten Referenz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8415,"byte_start":7400,"id":"section:6b5e01a1f0b7b2d5045a","kind":"subsubsection","labels":["kleine-rigorose-verschuxe4rfung-der-energiegrenze"],"line_end":235,"line_start":207,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/019-subsubsection-3-2-nicht-nur-gez-hlt-die-vier-zust-nde-un.tex","status_markers_as_written":[],"summary_excerpt":"Am Prüfpunkt g geteilt durch Delta gleich 1/20 hat die niedrigste Eigenenergie der Fünfer-Kompression die durch rationale Sturm-Zählung zertifizierte Lage","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.4 Kleine, rigorose Verschärfung der Energiegrenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10076,"byte_start":8415,"id":"section:13149eabfc476fcff371","kind":"subsection","labels":["vollstuxe4ndig-geluxf6st-die-innere-bilineare-zerlegung"],"line_end":274,"line_start":236,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/019-subsubsection-3-2-nicht-nur-gez-hlt-die-vier-zust-nde-un.tex","status_markers_as_written":[],"summary_excerpt":"Die sechs Dimensionen sind 1, 45, 210, 15, 675 und 3150. Der offene Rest ist also nicht mehr unbestimmt:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Vollständig gelöst: die innere bilineare Zerlegung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10210,"byte_start":10076,"id":"section:3a9e1bdcabd9b1b8e669","kind":"subsection","labels":["welche-operationen-wirklich-verfuxfcgbar-sein-muxfcssten"],"line_end":277,"line_start":275,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/019-subsubsection-3-2-nicht-nur-gez-hlt-die-vier-zust-nde-un.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"6. 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Jede Komposition dieser Operatoren behält diese Erhaltung. Die alleinige Erlaubnis, mehr Moden zu unterscheiden, hebt das Hindernis also nicht auf.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6.2 Warum bloßes Lesen noch keine fehlende Bewegung erzeugt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14638,"byte_start":12999,"id":"section:c1061254d29efc0b0f1f","kind":"subsection","labels":["feldwuxf6rterbuch-gesicherte-teile-und-korrigierte-reichweite"],"line_end":369,"line_start":339,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/019-subsubsection-3-2-nicht-nur-gez-hlt-die-vier-zust-nde-un.tex","status_markers_as_written":[],"summary_excerpt":"Für die unveränderte antisymmetrische Paarmatrix und gleichhändige Weylfelder verschwindet die ableitungsfreie skalare Kontraktion. 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Die fundamentale Frage: was fehlt wirklich?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1503,"byte_start":110,"id":"section:7f06ec0c70ab2a24d278","kind":"subsubsection","labels":["ein-uxfcberpruxfcfbarer-unterbestimmtheitssatz"],"line_end":32,"line_start":4,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/020-subsection-8-die-fundamentale-frage-was-fehlt.tex","status_markers_as_written":[],"summary_excerpt":"Betrachte bei festem W dieselbe Familie [formula in source] . Alle diese Hamiltonoperatoren besitzen die gleiche innere Quellsymmetrie, dieselbe Ladungserhaltung und denselben kommutierenden endlichen Clock. Dennoch unterscheiden sie sich dynamisch. Schon für dieselbe gefüllte Referenz F ist die dimensionslose Momentenkombination","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.1 Ein überprüfbarer Unterbestimmtheitssatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2840,"byte_start":1503,"id":"section:316f6149d5feb631a72f","kind":"subsubsection","labels":["der-kleinste-tragfuxe4hige-forschungsansatz"],"line_end":55,"line_start":33,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/020-subsection-8-die-fundamentale-frage-was-fehlt.tex","status_markers_as_written":[],"summary_excerpt":"Für eine einzelne Antwortrechnung sollte der relevante Raum nicht von vornherein der gesamte Fockraum sein. Der zyklische Raum der tatsächlichen Operationen auf dem angegebenen Startzustand ist der kleinere Arbeitsraum. Die H-Lanczos-Kette ist eine exakte Darstellung eines solchen Raums. Mehrere Präparationen, Messungen oder Compileroperationen können jedoch einen größeren gemeinsamen Prozessraum verlangen. Ihre Komp","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.2 Der kleinste tragfähige Forschungsansatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5291,"byte_start":2840,"id":"section:be988edcf21afe0f230a","kind":"subsection","labels":["aktueller-stand-t1-bis-t8"],"line_end":110,"line_start":56,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/020-subsection-8-die-fundamentale-frage-was-fehlt.tex","status_markers_as_written":[],"summary_excerpt":"Die folgende Tabelle ordnet die Beiträge dieser Runde den bisherigen offenen Beweispflichten zu; sie benennt keine neue Definition der ursprünglichen Tore.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. Aktueller Stand T1 bis T8","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6822,"byte_start":5291,"id":"section:a4b872b85951d6ba1a87","kind":"subsection","labels":["die-drei-nuxe4chsten-entscheidenden-untersuchungen"],"line_end":143,"line_start":111,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/020-subsection-8-die-fundamentale-frage-was-fehlt.tex","status_markers_as_written":[],"summary_excerpt":"Den minimalen Ursprungsvertrag auswählen. Teil B klassifiziert die kleinen symmetrieverträglichen Terme und trennt echte Erweiterungen von einem bloßen Wechsel der Bosonvariablen. Der Compiler muss diese Auswahl und die relativen Parameter begründen. Symmetrie allein tut das noch nicht. Die gemeinsame Schattenkarte am vorhandenen Tensor prüfen. Derselbe Zustand und dieselben Operationen müssen die verschiedenen Ausle","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10. 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Die ausgelieferte ZIP wird nach dem Entpacken erneut geprüft.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"11. Reproduktion und Veröffentlichung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8394,"byte_start":8000,"id":"section:ebdef79ffad8067cb4e9","kind":"subsubsection","labels":["schluss-in-einem-satz"],"line_end":176,"line_start":168,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/020-subsection-8-die-fundamentale-frage-was-fehlt.tex","status_markers_as_written":[],"summary_excerpt":"Die einfache Regel ist vorhanden; ihr erster verzweigter Zustandsbereich und die richtige kleine Rechenkette sind jetzt genauer gelöst. Was noch fehlt, ist die aus dem Ursprung folgende Auswahl und Ausführung dieses Prozesses als dieselbe physikalische Welt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Schluss in einem Satz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8545,"byte_start":8394,"id":"section:7c0dc9b5f3800a9b8b0e","kind":"section","labels":["neue-vogelperspektive-derselbe-prozess-in-verschiedenen-ansichten"],"line_end":179,"line_start":177,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/020-subsection-8-die-fundamentale-frage-was-fehlt.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Neue Vogelperspektive: derselbe Prozess in verschiedenen Ansichten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11147,"byte_start":8545,"id":"section:f617402b6fa30f7c4613","kind":"subsection","labels":["b1.-was-sich-durch-die-drei-weiteren-texte-uxe4ndert"],"line_end":234,"line_start":180,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":["relation:57a5812577f054bb06a5","relation:7feb334b9f45f49a5c7c","relation:f6ee514ebedfbb724ee3"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/020-subsection-8-die-fundamentale-frage-was-fehlt.tex","status_markers_as_written":[],"summary_excerpt":"Die nachgereichten Texte werden als Vorschläge geprüft, nicht als bewiesene Ergebnisse oder neue Arbeitsanweisungen übernommen. Die stärkste gemeinsame Idee trägt: Innere Identität, Zusammensetzung, Ort, Zeit und Auslese dürfen nicht stillschweigend dasselbe Label erhalten. Eine immer genauere Rechnung innerhalb einer Bank ersetzt diese Verbindungen nicht. Die voranstehenden lokalen Ergebnisse bleiben gültig; die fun","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B1. Was sich durch die drei weiteren Texte ändert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13543,"byte_start":11147,"id":"section:030e0693c77684ad1988","kind":"subsection","labels":["b2.-noethers-frage-welche-unterschiede-kann-die-dynamik-uxfcberhaupt-veruxe4ndern"],"line_end":287,"line_start":235,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/020-subsection-8-die-fundamentale-frage-was-fehlt.tex","status_markers_as_written":[],"summary_excerpt":"Bei ungebrochener innerer Gruppe G zerfällt ein Zustandsraum als","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B2. Noethers Frage: Welche Unterschiede kann die Dynamik überhaupt verändern?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15935,"byte_start":13543,"id":"section:bc975c23a1ebffb4e56e","kind":"subsection","labels":["b3.-korrelation-ist-noch-kein-eingriff-ein-exakt-geluxf6stes-gegenbeispiel"],"line_end":340,"line_start":288,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/020-subsection-8-die-fundamentale-frage-was-fehlt.tex","status_markers_as_written":[],"summary_excerpt":"Die Kreuzkorrelation startet bei null und verändert sich mit der Zeit. Es gibt dennoch keinerlei Signal von A nach B: Alle A-lokalen Operationen kommutieren mit jedem zeitentwickelten B-lokalen Observablen. Für jedes spurtreue lokale Quanteninstrument bleibt daher die unbedingte B-Statistik unverändert. Eine Konditionierung auf ein Messergebnis in A wäre etwas anderes.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B3. Korrelation ist noch kein Eingriff: ein exakt gelöstes Gegenbeispiel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17112,"byte_start":15935,"id":"section:e92954078672cae8e465","kind":"subsection","labels":["b4.-die-einfachste-fehlende-auswahl-warum-genau-dieser-hamiltonoperator"],"line_end":364,"line_start":341,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/020-subsection-8-die-fundamentale-frage-was-fehlt.tex","status_markers_as_written":[],"summary_excerpt":"Die Z4-Idee besitzt einen präzisen Kern. Ein ganzzahliger, auf jedem Grad konstanter Ladungslift mit neutralem Grad null müsste bei den entsprechenden nichtverschwindenden Klammern erfüllen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B4. Die einfachste fehlende Auswahl: Warum genau dieser Hamiltonoperator?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3841,"byte_start":0,"id":"section:065f7f9e235fca7fedf7","kind":"subsubsection","labels":["b4.1-zwei-zusuxe4tzliche-terme-am-unveruxe4nderten-tensor"],"line_end":84,"line_start":1,"numbered_or_version_tokens_as_written":["B4.1"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/021-subsubsection-b4-1-zwei-zus-tzliche-terme-am-unver-ndert.tex","status_markers_as_written":[],"summary_excerpt":"Der Bosonträger (10,6) besitzt eine symmetrische reelle invariante Paarung eta. In der nativen Gewichtsbasis koppelt sie entgegengesetzte Spin- Vektorgewichte und komplementäre Farbpaare. Es gilt eta Quadrat gleich eins. Damit sind bereits","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B4.1 Zwei zusätzliche Terme am unveränderten Tensor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6032,"byte_start":3841,"id":"section:cdad006b6f1b4120a8f6","kind":"subsubsection","labels":["b4.2-eine-weitere-vereinfachung-neue-dynamik-oder-andere-teilchenvariablen"],"line_end":133,"line_start":85,"numbered_or_version_tokens_as_written":["B4.2"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/021-subsubsection-b4-1-zwei-zus-tzliche-terme-am-unver-ndert.tex","status_markers_as_written":[],"summary_excerpt":"Manche scheinbaren Erweiterungen beschreiben nur andere Bosonvariablen. Auf der reellen, phasengleichen Teilfamilie setze man","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B4.2 Eine weitere Vereinfachung: neue Dynamik oder andere Teilchenvariablen?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6172,"byte_start":6032,"id":"section:998fc3c594dafe88d9c3","kind":"subsection","labels":["b5.-holografie-und-schatten-die-konkrete-native-verbindung"],"line_end":136,"line_start":134,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/021-subsubsection-b4-1-zwei-zus-tzliche-terme-am-unver-ndert.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"B5. Holografie und Schatten: die konkrete native Verbindung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7678,"byte_start":6172,"id":"section:5cac2ec7d752a7986bbb","kind":"subsubsection","labels":["b5.1-ein-kodierer-ist-bereits-vorhanden"],"line_end":171,"line_start":137,"numbered_or_version_tokens_as_written":["B5.1"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/021-subsubsection-b4-1-zwei-zus-tzliche-terme-am-unver-ndert.tex","status_markers_as_written":[],"summary_excerpt":"Der vorhandene, frisch geprüfte Tensor erfüllt WW dagger gleich 8 I60. Daher ist","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B5.1 Ein Kodierer ist bereits vorhanden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9335,"byte_start":7678,"id":"section:7042d1a31ab37cc31ed3","kind":"subsubsection","labels":["b5.2-warum-das-noch-kein-holografischer-fehlerkorrekturcode-ist"],"line_end":205,"line_start":172,"numbered_or_version_tokens_as_written":["B5.2"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/021-subsubsection-b4-1-zwei-zus-tzliche-terme-am-unver-ndert.tex","status_markers_as_written":[],"summary_excerpt":"Für jeden der 64 Fermionmoden wurde die logische Kompression seiner Besetzungsmessung berechnet:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B5.2 Warum das noch kein holografischer Fehlerkorrekturcode ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11957,"byte_start":9335,"id":"section:ddcea03d428c4a34887a","kind":"subsubsection","labels":["b5.3-was-mehrere-schatten-gemeinsam-eindeutig-machen-kuxf6nnen"],"line_end":260,"line_start":206,"numbered_or_version_tokens_as_written":["B5.3"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/021-subsubsection-b4-1-zwei-zus-tzliche-terme-am-unver-ndert.tex","status_markers_as_written":[],"summary_excerpt":"Seien Ri festgelegte Mess- oder Reduktionsabbildungen eines gemeinsamen Zustands rho. Für eine endliche, nicht eingeschränkte Zustandsklasse sind alle Zustände aus den Schatten Ri(rho) genau dann unterscheidbar, wenn auf den hermiteschen spurlosen Differenzen gilt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B5.3 Was mehrere Schatten gemeinsam eindeutig machen können","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14148,"byte_start":11957,"id":"section:5ea80db298148b04d640","kind":"subsubsection","labels":["b5.4-die-drei-wuxe4nde-muxfcssen-unterschiedlich-gepruxfcft-werden"],"line_end":307,"line_start":261,"numbered_or_version_tokens_as_written":["B5.4"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/021-subsubsection-b4-1-zwei-zus-tzliche-terme-am-unver-ndert.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333@ Gemeinte Wand & Was sie gegenwärtig bedeutet & Welcher Anschluss fehlt \\\\ Universalraum & Grenze zwischen gemeinsamem Operatorobjekt und seinen reduzierten Ansichten & Ein gemeinsamer verfügbarer Operationssatz, Zustand und Rekonstruktionsvertrag \\\\ TFPT & Grenze zwischen interner Compilerstruktur und physikalischer Realisierung & Herleitung der Ausführun","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B5.4 Die drei Wände müssen unterschiedlich geprüft werden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17476,"byte_start":14148,"id":"section:5e2722c4b773dffe738f","kind":"subsection","labels":["b6.-die-einfachste-neue-arbeitsrichtung-und-ihre-abnahmekriterien"],"line_end":369,"line_start":308,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/021-subsubsection-b4-1-zwei-zus-tzliche-terme-am-unver-ndert.tex","status_markers_as_written":[],"summary_excerpt":"Der plausible übersehene Punkt ist kein weiterer großer Tensor: Wir brauchen die gemeinsame Regel, die festlegt, welche Operationen, Teilchenvariablen und Ansichten tatsächlich dieselbe Ausführung beschreiben. Noethers Symmetrieprüfung sagt, was erhalten bleibt. Die Schattenprüfung sagt, was überhaupt unterscheidbar ist. Der Eingriffstest sagt, was etwas anderes beeinflussen kann. Zusammen sind diese drei kleinen Fra","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B6. Die einfachste neue Arbeitsrichtung und ihre Abnahmekriterien","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4524,"byte_start":0,"id":"section:d58bf41bd62909fdbbde","kind":"subsection","labels":["b7.-abgleich-des-zuletzt-eingesandten-berichts-v1.6.3"],"line_end":85,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/022-subsection-b7-abgleich-des-zuletzt-eingesandten-berichts.tex","status_markers_as_written":[],"summary_excerpt":"Der sechste Text dieser Runde, „Operationssatz, nativer Grundzustand und Feldwörterbuch``, enthält überwiegend bereits berücksichtigte Befunde: die Kommutantenleiter, das Lochbild, die Normen der ersten Stufen, den nichtverschwindenden Seitenzweig und den verschwindenden Weyl-Skalarkanal. Seine zweite vorgeschlagene Folgeaufgabe wurde inzwischen wesentlich weitergeführt: Alle vier Zwei-Boson-Singuletts sind konstruie","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"B7. 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Maßgeblich für den aktuellen Status sind die vorangestellten Kapitel v1.6.7. 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Das ist ein Forschungsauftrag, kein Widerspruch zur bisherigen Schranke.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7.1 Eine sinnvolle Hypothese, kein bereits identifiziertes universelles Objekt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13202,"byte_start":12550,"id":"section:813bdd207e56b625fb6d","kind":"subsubsection","labels":["der-vorgeschlagene-kill-test-muss-korrigiert-werden"],"line_end":312,"line_start":301,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/023-subsubsection-3-2-ein-ausdr-ckliches.tex","status_markers_as_written":[],"summary_excerpt":"Für unabhängige orthogonale Banken kann Π_AΠ_B deren gemeinsame Parität sein. 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Ein nichtverschwindender Kommutator mit einer lok","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7.2 Der vorgeschlagene Kill-Test muss korrigiert werden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15208,"byte_start":13202,"id":"section:bd5a4872fda196bcc130","kind":"subsubsection","labels":["der-einfachste-false-positive-ein-signal-ohne-bewegung"],"line_end":358,"line_start":313,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/023-subsubsection-3-2-ein-ausdr-ckliches.tex","status_markers_as_written":[],"summary_excerpt":"Seien a=c1, b=(c1+c2)/√2 auf zwei globalen CAR-Moden und H=ωN. Dann haben die beiden Einteilchen-Chartzustände bereits Überlappung 1/√2. In ihrer nichtorthogonalen Basis ist K=ωS mit einem nichtverschwindenden Offdiagonalelement. Trotzdem bleibt die betreffende Wahrscheinlichkeit zu jeder Zeit genau 1/2. Es wurde nichts transportiert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7.3 Der einfachste False-Positive: Ein Signal ohne Bewegung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1895,"byte_start":0,"id":"section:23130b07cbb342e42089","kind":"subsubsection","labels":["was-nicht-automatisch-folgt"],"line_end":44,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/024-subsubsection-7-4-was-nicht-automatisch.tex","status_markers_as_written":[],"summary_excerpt":"Zeit: Für einen Grundzustand ist e \\-itH\\Ω=e \\-itE0\\Ω; sein physischer Zustand bleibt gleich. Das ist kein eigener Zeitpfeil. Nichtstationäre Präparation, Korrelationen und Records müssen ausgewiesen werden. Eichfeld: Für bloße Basiswechsel Uxy=Vx†Vy teleskopiert jede geschlossene Holonomie zu I. Echte Krümmung braucht zusätzliche Verbindungs-/Transportdaten oder einen nachgewiesenen Mechanismus. Spin: Zwei Orientier","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7.4 Was nicht automatisch folgt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4387,"byte_start":1895,"id":"section:647b51d5509c9a9c81db","kind":"subsection","labels":["t1-t8-gemeinsamer-fortschritt-ohne-statusinflation"],"line_end":95,"line_start":45,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/024-subsubsection-7-4-was-nicht-automatisch.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333@ Front & In dieser Revision weitergekommen & Noch erforderlicher Nachweis \\\\ T1 - Ursprung und Auswahl & Explizite Identität zwischen Quell-Clock und innerer Spinwirkung; Operationsverträge genauer & Primitive Auswahl von P1/P2, Träger, erlaubten Instrumenten und Zustand \\\\ T2 - Half-Charge/E8-Feld & Bestehender geladener Pol bleibt abgesichert, innere Dar","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8. T1-T8: gemeinsamer Fortschritt ohne Statusinflation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6264,"byte_start":4387,"id":"section:b50f635ff03edfdf0669","kind":"subsection","labels":["die-nuxe4chsten-drei-arbeiten---klein-gemeinsam-und-entscheidbar"],"line_end":129,"line_start":96,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/024-subsubsection-7-4-was-nicht-automatisch.tex","status_markers_as_written":[],"summary_excerpt":"A. Den gemeinsamen Quellenvertrag wirklich hinschreiben. Zwei lokale Einbettungen, ihr CAR-Gram, globale Parität und Ladung, ursprüngliche Operationen und ein einziges H angeben. Abbruch für eine Kandidatenfassung, wenn sie nur zwei Koordinatenansichten desselben unveränderten Signals umbenennt. Die gemeinsamen Generatoren müssen einen nachweislich neuen Antwortprozess ermöglichen, nicht nur eine andere Beschriftung.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. Die nächsten drei Arbeiten - klein, gemeinsam und entscheidbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7365,"byte_start":6264,"id":"section:54f4776c1da819c64ef6","kind":"subsection","labels":["belege-und-reproduzierbarkeit"],"line_end":151,"line_start":130,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/024-subsubsection-7-4-was-nicht-automatisch.tex","status_markers_as_written":[],"summary_excerpt":"Die drei Eingangstexte bleiben unverändert im Prüfpaket. Ein Teil-Audit reproduziert die 1127 gelieferten Guards; eigene Programme behandeln Clock/Casimir, Quellenreichweite, direkte Krylov-Kontraktion, basisunabhängige Feldbedingungen, den tatsächlichen Vierzustandskanal und die Überlappungsgegenkontrollen. Exakte und numerische Teile sind in den jeweiligen Ergebnisdateien getrennt markiert. Die abschließenden Zählu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10. Belege und Reproduzierbarkeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":7496,"byte_start":7365,"id":"section:9f67ee52909b9e8025d3","kind":"section","labels":["anhang-a-quellenpruxfcfung-symmetrie-und-verfuxfcgbarkeit"],"line_end":154,"line_start":152,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/024-subsubsection-7-4-was-nicht-automatisch.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Anhang A: Quellenprüfung Symmetrie und Verfügbarkeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7867,"byte_start":7496,"id":"section:a44fbc0812f8307d9880","kind":"section","labels":["quellenpruxfcfung-quellsymmetrie-verfuxfcgbarkeit-und-lorentztypen"],"line_end":162,"line_start":155,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/024-subsubsection-7-4-was-nicht-automatisch.tex","status_markers_as_written":[],"summary_excerpt":"Stand: 15. September 2026. Eigenständiger Teil-Audit der ersten neuen Anlage und dreier Programme. Keine Änderung der gelieferten Programme, Ergebnisdateien oder Dokumente. Keine Aussage, dass T1-T8 geschlossen seien.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Quellenprüfung: Quellsymmetrie, Verfügbarkeit und Lorentztypen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10242,"byte_start":7867,"id":"section:0a28a38683110fc6d278","kind":"subsection","labels":["reproduktion-1"],"line_end":224,"line_start":163,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":["relation:8b888ae2d4239664608a"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/024-subsubsection-7-4-was-nicht-automatisch.tex","status_markers_as_written":[],"summary_excerpt":"Alle drei Programme wurden vollständig gelesen und anschließend in isolierten Kopien ausgeführt. Die relevanten Tensoren wurden an ihre von den unveränderten Programmen erwarteten relativen Orte kopiert. Normaler und optimierter Lauf reproduzieren jeweils die gelieferten Ergebnisdateien byteidentisch, ohne Standardfehlerausgabe:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Reproduktion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":12214,"byte_start":10242,"id":"section:8a19c202369cc314cb41","kind":"subsection","labels":["bestuxe4tigte-mathematik"],"line_end":275,"line_start":225,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/024-subsubsection-7-4-was-nicht-automatisch.tex","status_markers_as_written":[],"summary_excerpt":"Der N=3-Raum zerfällt als Darstellung von Spin(10) × SU(4) in sieben Isotypien. Drei haben Multiplizität zwei, die anderen vier Multiplizität eins. Die zwei Fockteile Λ³(C⁶⁴) und C⁶⁰⊗C⁶⁴ sind jeweils multiplizitätsfrei; der gesamte N=3-Raum ist es ausdrücklich nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Bestätigte Mathematik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":14080,"byte_start":12214,"id":"section:7bb22cd4a70d4314ce87","kind":"subsection","labels":["invarianz-und-kovarianz-auseinanderhalten"],"line_end":312,"line_start":276,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/024-subsubsection-7-4-was-nicht-automatisch.tex","status_markers_as_written":[],"summary_excerpt":"Dann gilt A0 ⊂ C, dim A0=14 und dim C=Σ m_i²=16. Jedes Wort aus X und Nb kommutiert mit ρ(G). Nichtzentrale Lie-Erzeuger können deshalb aus diesem Alphabet nicht entstehen. Dieser Ausschluss ist korrekt und bleibt richtig, wenn nur ein fixes H statt zweier unabhängiger Kontrollen gewährt ist.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Invarianz und Kovarianz auseinanderhalten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15666,"byte_start":14080,"id":"section:759cf6ea27265d6ebcee","kind":"subsection","labels":["verfuxfcgbarkeit-ist-keine-universelle-janein-frage"],"line_end":353,"line_start":313,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/024-subsubsection-7-4-was-nicht-automatisch.tex","status_markers_as_written":[],"summary_excerpt":"Ein vorgegebener Hamiltonoperator allein gewährt nicht bereits das unabhängige Schalten von X und Nb. Am erklärten Punkt g/Δ=1/20 besitzt ein fixes H im N=3-Raum acht verschiedene Energien, also nur eine acht-dimensionale kommutative Spektralalgebra. Die großzügigere Annahme unabhängiger Kontrollen X,Nb ergibt 14.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Verfügbarkeit ist keine universelle Ja/Nein-Frage","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16664,"byte_start":15666,"id":"section:011cec9b73c9589be7a9","kind":"subsection","labels":["der-clock-satz-ist-im-gelieferten-checker-nicht-gepruxfcft"],"line_end":372,"line_start":354,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/024-subsubsection-7-4-was-nicht-automatisch.tex","status_markers_as_written":[],"summary_excerpt":"operation_symmetry.py:478 schreibt den Normalisator- und Nichts-hinzufügen-Satz als need(True, ...). Insgesamt enthält diese Datei neun solche als Prüfbedingungen gezählten theoretischen Folgerungen. Einige sind durch die vorausgehende Mathematik gut begründet; der bloße grüne Guard zertifiziert sie jedoch nicht unabhängig.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Der Clock-Satz ist im gelieferten Checker nicht geprüft","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":1679,"byte_start":0,"id":"section:aadf543c685fe83f9b63","kind":"subsection","labels":["feldtyp-was-tatsuxe4chlich-erzwungen-ist"],"line_end":32,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/025-subsection-6-feldtyp-was-tats-chlich-erzwungen.tex","status_markers_as_written":[],"summary_excerpt":"Für ein lokales, ableitungsfreies Bilinear zweier gleichhändiger Weylfelder, das alle 64 inneren Quellenmarken unverändert als unabhängige innere Komponenten und genau den gegebenen antisymmetrischen Tensor W verwendet, gilt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Feldtyp: was tatsächlich erzwungen ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2813,"byte_start":1679,"id":"section:cc1572e1bc51f23e766d","kind":"subsubsection","labels":["konkreter-gegencheck-jenseits-der-ableitungsfreien-klasse"],"line_end":55,"line_start":33,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/025-subsection-6-feldtyp-was-tats-chlich-erzwungen.tex","status_markers_as_written":[],"summary_excerpt":"Der allgemeine Satz »ein Vektor verlangt ψ†ψ und scheitert deshalb an der Ladung« ist falsch, sobald Ableitungen zugelassen werden. Beispielsweise ist","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Konkreter Gegencheck jenseits der ableitungsfreien Klasse","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3343,"byte_start":2813,"id":"section:6af98943100615ff2f10","kind":"subsection","labels":["konsequenz"],"line_end":67,"line_start":56,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/025-subsection-6-feldtyp-was-tats-chlich-erzwungen.tex","status_markers_as_written":[],"summary_excerpt":"Die neuen Quellen verkleinern und präzisieren den endlichen N=3-Operationsraum. 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Die hier angegebenen Matrix- und Graphbefunde beziehen sich auf denselben gepinnten Tensor W mit SHA-256 3f00a0892157a691e4ef26920c3702772c7bf76a250fad98ff04a079bb64b763.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Unabhängige Prüfung: Krylov-Verzweigung und Feldwörterbuch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5400,"byte_start":4028,"id":"section:ba4b2f7292a59b400c07","kind":"subsection","labels":["der-neue-nichtschluss-ist-exakt-bestuxe4tigt"],"line_end":121,"line_start":82,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/025-subsection-6-feldtyp-was-tats-chlich-erzwungen.tex","status_markers_as_written":[],"summary_excerpt":"Für v_n=(T†) n F habe ich u=T T† v_2=T v_3 unmittelbar aus den 480 nativen Paaren neu kontrahiert. 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Der neue Nichtschluss ist exakt bestätigt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6534,"byte_start":5400,"id":"section:b2c5ada82dde693b1731","kind":"subsection","labels":["das-mitgelieferte-ground-json-ist-veraltet-und-teilweise-falsch"],"line_end":147,"line_start":122,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/025-subsection-6-feldtyp-was-tats-chlich-erzwungen.tex","status_markers_as_written":[],"summary_excerpt":"Die aktuelle Pythonquelle hat SHA-256 8ae0f2f103ba0cb0a5cb832681a33130b6756fe627395368b6be635587a2eb02. 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Die sechste Dezimalstelle ist richtig - aber nur für die eine zusätzliche Richtung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9551,"byte_start":8285,"id":"section:305a3b6d9b02e7000695","kind":"subsubsection","labels":["eigene-einfache-folgeherleitung-das-vollstuxe4ndige-ritz-residuum"],"line_end":220,"line_start":193,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/025-subsection-6-feldtyp-was-tats-chlich-erzwungen.tex","status_markers_as_written":[],"summary_excerpt":"Sei ψ₃ der normierte Ritz-Eigenvektor in span(v₀,…,v₃), und c₃ seine Komponente entlang v₃/√ν₃. 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Noch wichtiger: Ein Überlappungsmatrixelement ist kein Transport","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3839,"byte_start":2146,"id":"section:adbb191046232f07599e","kind":"subsection","labels":["chartwechsel-verbindungen-und-kruxfcmmung-sind-verschiedene-daten"],"line_end":86,"line_start":52,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/028-subsection-3-noch-wichtiger-ein-berlappungsmatrixelement.tex","status_markers_as_written":[],"summary_excerpt":"Wenn mehrere Charts lediglich vollständige orthonormale Rahmen R_x desselben festen Vektorraums sind, lauten die Basiswechsel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Chartwechsel, Verbindungen und Krümmung sind verschiedene Daten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4983,"byte_start":3839,"id":"section:eaab327b0b19ebbbffee","kind":"subsection","labels":["zeit-ein-grundzustand-bewegt-sich-unter-seinem-h-nicht-beobachtbar"],"line_end":108,"line_start":87,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/028-subsection-3-noch-wichtiger-ein-berlappungsmatrixelement.tex","status_markers_as_written":[],"summary_excerpt":"Die im Anhang skizzierte Entwicklung Ω -> exp(−itH)Ω erzeugt bei einem Energieeigenzustand lediglich exp(−itE₀)Ω. Der Dichteoperator bleibt exakt gleich. Der Checker bestätigt das an einem kleinen Fockzustand.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Zeit: Ein Grundzustand bewegt sich unter seinem H nicht beobachtbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":6536,"byte_start":4983,"id":"section:f1e67e3031dd346080ca","kind":"subsection","labels":["der-binuxe4re-index-muss-als-freiheitsgrad-bewiesen-werden"],"line_end":143,"line_start":109,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/028-subsection-3-noch-wichtiger-ein-berlappungsmatrixelement.tex","status_markers_as_written":[],"summary_excerpt":"Die skalare Hilfsdublett-Reparatur braucht zwei unabhängige, gleichgeladene Komponenten, auf denen eine nichtentartete antisymmetrische Form wirkt. Eine Orientierung der Überlappungsgeometrie könnte so etwas liefern, tut es aber nicht allein durch das Vorhandensein zweier Bezeichnungen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Der binäre Index muss als Freiheitsgrad bewiesen werden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8140,"byte_start":6536,"id":"section:2e6b08b985dca3de433f","kind":"subsection","labels":["operationsgeometrie-benuxf6tigt-mehr-als-erreichbarkeit"],"line_end":175,"line_start":144,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/028-subsection-3-noch-wichtiger-ein-berlappungsmatrixelement.tex","status_markers_as_written":[],"summary_excerpt":"Minimale Kosten erfüllen unter geeigneter Komposition eine Dreiecksungleichung. Ohne reversible Operationen mit symmetrischen Kosten ist die resultierende Funktion jedoch nur eine gerichtete Distanz; der Checker liefert den gerichteten Dreierzyklus mit d(A,B)=1, d(B,A)=2. Unerreichbarkeit ergibt unendliche Distanzen. Kostenfreie Chartwechsel können verschiedene Beschreibungen auf Distanz null setzen; dann muss zunäch","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. Operationsgeometrie benötigt mehr als Erreichbarkeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":8946,"byte_start":8140,"id":"section:d9b8a75b8f26739f7602","kind":"subsection","labels":["gravitation-bleibt-eine-dynamische-verpflichtung"],"line_end":191,"line_start":176,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/028-subsection-3-noch-wichtiger-ein-berlappungsmatrixelement.tex","status_markers_as_written":[],"summary_excerpt":"Die linearen Fluktuationen einer aus der Quelle bestimmten globalen Geometrie zu prüfen, ist ein sinnvoller Forschungsauftrag. Eine transversale spurfreie Tensorzerlegung allein garantiert aber weder einen masselosen physikalischen Spin-2-Pol noch positive Norm, genau zwei Helizitäten oder universelle Kopplung. Selbst ein gesunder linearer Spin-2-Sektor ersetzt nicht den Nachweis seiner nichtlinearen Eich-/Zwangsstru","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8. Gravitation bleibt eine dynamische Verpflichtung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9993,"byte_start":8946,"id":"section:1f07896da1fbd267816d","kind":"subsection","labels":["p-versus-np-eine-konkrete-korrektur"],"line_end":211,"line_start":192,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/028-subsection-3-noch-wichtiger-ein-berlappungsmatrixelement.tex","status_markers_as_written":[],"summary_excerpt":"Der Anhang sagt, P≠NP würde einen intrinsisch exponentiellen Suchaufwand bedeuten. Das ist falsch. P≠NP würde ausschließen, dass jedes NP-Entscheidungsproblem deterministisch in Polynomialzeit gelöst werden kann. Es folgt daraus keine exponentielle untere Schranke: Eine hypothetische Laufzeit wie 2 (√n) ist superpolynomiell und zugleich subexponentiell. Stärkere Exponentialzeitaussagen benötigen zusätzliche Sätze bez","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. P versus NP: eine konkrete Korrektur","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11962,"byte_start":9993,"id":"section:31cf89d9280a346934bd","kind":"subsection","labels":["ein-korrigierter-wirklich-entscheidbarer-anschluss-test"],"line_end":255,"line_start":212,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/028-subsection-3-noch-wichtiger-ein-berlappungsmatrixelement.tex","status_markers_as_written":[],"summary_excerpt":"Ein sinnvoller nächster Versuch besteht nicht nur aus einem unbeschrifteten P U_AB P. Er sollte zusammen liefern:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10. Ein korrigierter, wirklich entscheidbarer Anschluss-Test","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12067,"byte_start":11962,"id":"section:3eaa87e8274bb21ee42d","kind":"section","labels":["anhang-e-arithmetischer-schleifenvorschlag"],"line_end":258,"line_start":256,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/028-subsection-3-noch-wichtiger-ein-berlappungsmatrixelement.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Anhang E: arithmetischer Schleifenvorschlag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12629,"byte_start":12067,"id":"section:b1559e93664b821ba487","kind":"section","labels":["zusatzpruxfcfung-schleifen-primzahlen-und-der-universalraum-vorschlag"],"line_end":273,"line_start":259,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/028-subsection-3-noch-wichtiger-ein-berlappungsmatrixelement.tex","status_markers_as_written":[],"summary_excerpt":"September 2026, v1.6.6. Quellenprüfung des nachgereichten Textes 59dc0059-8914-48ca-953d-85933f66e00b, kein neuer RH-Beweis und kein neuer arithmetischer Quellenoperator. Seine Aussagen über gemeinsame lokale Beschreibungen werden getrennt im Überlappungsaudit behandelt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zusatzprüfung: Schleifen, Primzahlen und der Universalraum-Vorschlag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":13049,"byte_start":12629,"id":"section:1d8055ea9adeee9bac38","kind":"subsection","labels":["urteil-1"],"line_end":282,"line_start":274,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/028-subsection-3-noch-wichtiger-ein-berlappungsmatrixelement.tex","status_markers_as_written":[],"summary_excerpt":"Ein globaler Wegraum ist eine sinnvolle Suchklasse; ein Eulerprodukt über primitive Wege ist noch nicht das Eulerprodukt der Riemannschen Zetafunktion. Die im Text vorgeschlagene Xi-Determinante bleibt ein hinreichendes Ziel unter expliziten Operatorannahmen. Das Umbenennen ihres noch fehlenden Operators in „Generator der primitiven Schleifen`` konstruiert ihn nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Urteil","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":14389,"byte_start":13049,"id":"section:c0454137144db03e0764","kind":"subsection","labels":["was-die-endliche-bank-tatsuxe4chlich-ausschlieuxdft"],"line_end":311,"line_start":283,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/028-subsection-3-noch-wichtiger-ein-berlappungsmatrixelement.tex","status_markers_as_written":[],"summary_excerpt":"Der beibehaltene Beweis aus v1.6.5 gilt für den ursprünglichen Hamiltonoperator mit 64 Fermion- und 60 Bosonmoden, Δ 0. Der Hilbertraum ist wegen der Bosonen nicht endlichdimensional. Endlich ist die Zahl der Moden. Mit C=960g²/Δ folgt aus quadratischem Ergänzen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Was die endliche Bank tatsächlich ausschließt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":16623,"byte_start":14389,"id":"section:51d4254542c1cd4ece15","kind":"subsection","labels":["der-kleinste-gegencheck-zur-primzahl-automatik"],"line_end":357,"line_start":312,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/028-subsection-3-noch-wichtiger-ein-berlappungsmatrixelement.tex","status_markers_as_written":[],"summary_excerpt":"Nehmen wir einen gerichteten Knoten mit zwei erlaubten Schleifen a und b. Neben a und b ist auch ab ein primitiver periodischer Weg: Es ist keine Potenz eines kürzeren Wortes. Ebenso entstehen weitere gemischte primitive Wörter. Setzen wir nachträglich L(a)=log 2, L(b)=log 3, so hat ab die Länge log 6. Die 6 ist keine Primzahl. „Primitiver Weg`` bedeutet nicht „arithmetische Primzahl``.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Der kleinste Gegencheck zur Primzahl-Automatik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":1098,"byte_start":0,"id":"section:1dc0480e2edb142d81e8","kind":"subsection","labels":["die-richtige-rh-zielbedingung"],"line_end":29,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/029-subsection-3-die-richtige.tex","status_markers_as_written":[],"summary_excerpt":"Sei A strikt positiv und selbstadjungiert, mit kompakter Inverser und A \\-2\\ von Spurklasse. Dann ist der Fredholm-Ausdruck","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Die richtige RH-Zielbedingung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2849,"byte_start":1098,"id":"section:90855a6c1ffc4756eaac","kind":"subsection","labels":["vorarbeiten-und-aktuelle-grenze-der-quellenpruxfcfung"],"line_end":62,"line_start":30,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":["relation:065366b92533473889fe","relation:1483baafbb4370dd1ab4","relation:1c9de6f054903303050b"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/029-subsection-3-die-richtige.tex","status_markers_as_written":[],"summary_excerpt":"Der installierte Leitfaden rh-graph-research und die projektspezifische Korpussuche wurden angewandt. Die aktuelle Konsistenzprüfung und der anschließende Wiederaufbauversuch brachen mit","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Vorarbeiten und aktuelle Grenze der Quellenprüfung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3912,"byte_start":2849,"id":"section:d2f4c797fcb15019cf53","kind":"subsection","labels":["tragfuxe4higer-anschluss-ohne-acht-versprechen-an-ein-unbekanntes-objekt"],"line_end":83,"line_start":63,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/029-subsection-3-die-richtige.tex","status_markers_as_written":[],"summary_excerpt":"Der nächste arithmetische Test wäre erst nach Definition einer tatsächlichen Quell-Wegstruktur sinnvoll: primitive Bahnen, ihre Längen, Amplituden und die Spur gemeinsam bestimmen, ohne Primlisten oder Nullstellen einzusetzen. Ein positiver Kontrolltest muss insbesondere gemischte Zyklen erklären und den archimedischen Anteil auf demselben Träger liefern. Gelingt nur ein generisches Graph-Eulerprodukt, ist das ein Gr","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Tragfähiger Anschluss, ohne acht Versprechen an ein unbekanntes Objekt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4348,"byte_start":3912,"id":"section:d2a156e75004b899c2d6","kind":"section","labels":["historischer-vollstuxe4ndiger-herleitungsstand-v1.6.5-einschlieuxdflich-v1.6.4"],"line_end":92,"line_start":84,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/029-subsection-3-die-richtige.tex","status_markers_as_written":[],"summary_excerpt":"Der folgende Text wird unverändert bewahrt. Neue Gesamtstatusaussagen und Reichweitenkorrekturen stehen in der vorangestellten Revision v1.6.6. 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Was von der arithmetischen Untersuchung trägt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11251,"byte_start":9633,"id":"section:00ec70326d2cac2d9bec","kind":"subsubsection","labels":["eine-einzelne-endliche-bank-ist-nicht-der-volle-logarithmusgenerator"],"line_end":269,"line_start":233,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/030-subsubsection-4-2-die-l-cke-zum-gesamten-brigen.tex","status_markers_as_written":[],"summary_excerpt":"Quadratisches Ergänzen liefert mit der nativen Casimirnorm [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6.1 Eine einzelne endliche Bank ist nicht der volle Logarithmusgenerator","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12818,"byte_start":11251,"id":"section:a6cb9954a55bedb598a0","kind":"subsubsection","labels":["primzahlen-kuxf6nnen-eine-gewuxe4hlte-dynamik-organisieren-erzwingen-sie-aber-nicht"],"line_end":300,"line_start":270,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/030-subsubsection-4-2-die-l-cke-zum-gesamten-brigen.tex","status_markers_as_written":[],"summary_excerpt":"Auf [formula in source] kann man [formula in source] definieren. Die additive Primfaktorbesetzung erklärt dann die Eulerstruktur. Der Definitionsbereich lautet [formula in source] . Dass quantenstatistische Systeme mit Zeta-Zustandssumme existieren, ist bereits ein Ergebnis von https://alainconnes.org/wp-content/uploads/bostconnesscan.pdfBost und Connes. Das ist ein relevanter Anschluss, nicht die fehlende native Her","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6.2 Primzahlen können eine gewählte Dynamik organisieren, erzwingen sie aber nicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":13801,"byte_start":12818,"id":"section:3f24b8d7a83f19bd4160","kind":"subsubsection","labels":["der-rh-zielsatz-bleibt-unbewiesen"],"line_end":324,"line_start":301,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/030-subsubsection-4-2-die-l-cke-zum-gesamten-brigen.tex","status_markers_as_written":[],"summary_excerpt":"für einen strikt positiven selbstadjungierten Operator [formula in source] mit kompakter Inverser und [formula in source] von Spurklasse wäre tatsächlich hinreichend: Die gesamte rechte Funktion hat ihre Nullstellen nur bei reellen [formula in source] , einschließlich Multiplizitäten. Aber dieser Operator und die gesamte Funktionsidentität sind nicht konstruiert. Ein Operator mit lediglich den Imaginärteilen der Null","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6.3 Der RH-Zielsatz bleibt unbewiesen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15945,"byte_start":13801,"id":"section:7d207c4540c22f974615","kind":"subsection","labels":["die-lokale-polnuxe4herung-wird-pruxe4ziser-das-relativistische-feld-bleibt-offen"],"line_end":368,"line_start":325,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":["relation:471a827420e4a0c799a0"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/030-subsubsection-4-2-die-l-cke-zum-gesamten-brigen.tex","status_markers_as_written":[],"summary_excerpt":"Die externe Resolventenabschätzung ist korrekt: Im Kreis mit Radius [formula in source] um den tatsächlichen, unbekannten negativen Pol [formula in source] gilt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. Die lokale Polnäherung wird präziser, das relativistische Feld bleibt offen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2723,"byte_start":0,"id":"section:16bb0f861fcddb5ee63f","kind":"subsection","labels":["wuxe4hrend-der-arbeit-entdeckte-uxe4nderung-kommutant-7-richtig-einordnen"],"line_end":59,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/031-subsection-8-w-hrend-der-arbeit-entdeckte-nderung-kommut.tex","status_markers_as_written":[],"summary_excerpt":"Die strikte Originalquellenprüfung stoppte korrekt, als eine andere Arbeit den früheren nativen Bericht ergänzte. Der alte Stand mit Hash 1062e13fe0fb79cce015657a7b4d40a61e9639922ff95fa60c689c0068c38ffc blieb eingefroren. Der gesonderte geänderte Entwurf hat Hash ab745e74b1232b1ddf35dd0e0d0da4ace0176c797d769e5db8bedd0010bcba6a. Die in dieser Revision verwendeten Energie- und Polzertifikate änderten sich bei dieser Pr","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8. Während der Arbeit entdeckte Änderung: „Kommutant 7`` richtig einordnen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5101,"byte_start":2723,"id":"section:b7fd08302e8df03220c3","kind":"subsection","labels":["t1-t8-was-dieses-ergebnis-beitruxe4gt-und-nicht-beitruxe4gt"],"line_end":110,"line_start":60,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/031-subsection-8-w-hrend-der-arbeit-entdeckte-nderung-kommut.tex","status_markers_as_written":[],"summary_excerpt":"Die Begriffe folgen der aktuellen offenen Problemliste und ihrer Forschungszuordnung. Keine Akzeptanzmarkierung wurde heraufgesetzt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. T1-T8: was dieses Ergebnis beiträgt und nicht beiträgt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7525,"byte_start":5101,"id":"section:b204f1b50c9806b2e7e2","kind":"subsection","labels":["nuxe4chste-entscheidende-arbeiten-mit-klaren-abbruchkriterien"],"line_end":153,"line_start":111,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/031-subsection-8-w-hrend-der-arbeit-entdeckte-nderung-kommut.tex","status_markers_as_written":[],"summary_excerpt":"A. Die Quelle des geraden Gesamtlinks finden. Nicht noch eine riesige Kontrollmatrix bauen, sondern für jeden tatsächlich ursprünglichen Generator [formula in source] prüfen, ob [formula in source] bei erhaltener Gesamtparität möglich ist. Eine positive Antwort muss Generator, Teilbereichsdefinition, Hilbertraum, Gaussreferenz und Matrixelement liefern. Bleiben alle Generatoren lokal gerade, ist die Suche nach dem Li","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10. Nächste entscheidende Arbeiten mit klaren Abbruchkriterien","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8895,"byte_start":7525,"id":"section:ca4bc828cb954a8965dd","kind":"subsection","labels":["reproduktion-und-ehrliche-liefergrenze"],"line_end":180,"line_start":154,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":["relation:bad8733fa1da3ac8ef11","relation:d7d1d0bf2f3fa619bf07"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/031-subsection-8-w-hrend-der-arbeit-entdeckte-nderung-kommut.tex","status_markers_as_written":[],"summary_excerpt":"replay.py –frozen-only führt die fünf Prüfer normal und mit -OO aus, vergleicht beide JSON-Ergebnisse und die zwei externen Originalberichte, prüft alle eingefrorenen Quellen und protokolliert Änderungen der Originalorte gesondert. Ein Fehler führt zu FAIL. Der zuvor aufgetretene Live-Quellenfehler bleibt in source_drift_failure_receipt.json sichtbar.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"11. Reproduktion und ehrliche Liefergrenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9581,"byte_start":8895,"id":"section:151ef98b19887bc228be","kind":"section","labels":["nachpruxfcfung-der-beiden-zuletzt-eingegangenen-untersuchungen"],"line_end":194,"line_start":181,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/031-subsection-8-w-hrend-der-arbeit-entdeckte-nderung-kommut.tex","status_markers_as_written":[],"summary_excerpt":"Quellen: die Anlagen 8e110ae1-19e2-4d47-bfc8-ebe4fe9ab81b und b928b72a-6669-4c67-a75d-124095791c6f, unverändert eingefroren. Zusätzlich wurden die vier genannten Programme t1_fixed.py, stabilizer.py, t5_twobank.py, t5_varresp.py vollständig gelesen und archiviert. Eine eigene Nachrechnung prüft die kritischen Folgerungen; sie ist kein vollständiger Replay aller sechs Sonden des fremden Arbeitsordners.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nachprüfung der beiden zuletzt eingegangenen Untersuchungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12519,"byte_start":9581,"id":"section:f0428b474d0c975e4d37","kind":"subsection","labels":["uxfcbersicht-uxfcbernehmen-korrigieren-oder-offenlassen"],"line_end":254,"line_start":195,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/031-subsection-8-w-hrend-der-arbeit-entdeckte-nderung-kommut.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 2 ) * 0.5000 > p( - 2 ) * 0.5000@ Neue Aussage & Ergebnis der Prüfung \\\\ Innerer Viererzyklus erhält alle 60 W-Kanäle & Bestätigt, jetzt einschließlich der richtigen Fermion-Vorzeichen und explizitem Bosonlift \\\\ Grundzustandseindeutigkeit/Singulett/Gaplücke weiterhin unbekannt & Überholter Stand: unter dem festgelegten nativen Vertrag bereits bewiesen; voller Vektor weiter unbekannt \\\\ Leerer Grundzustand f","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Übersicht: übernehmen, korrigieren oder offenlassen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14118,"byte_start":12519,"id":"section:676bf813f3db067b4036","kind":"subsection","labels":["positiver-neuer-anschluss-der-korrekt-angehobene-viererzyklus"],"line_end":287,"line_start":255,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/031-subsection-8-w-hrend-der-arbeit-entdeckte-nderung-kommut.tex","status_markers_as_written":[],"summary_excerpt":"Die Abbildung der Fermionmarken lautet [formula in source] . Auf Paaren ist zwingend das Exteriorvorzeichen zu beachten: Falls [formula in source] , erhält das sortierte Paar ein Minuszeichen. Der gelieferte stabilizer.py lässt dieses Zeichen weg. Das wäre im Allgemeinen falsch; für den untersuchten Viererzyklus überlebt das positive Resultat jedoch auch den korrekten Test.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Positiver neuer Anschluss: der korrekt angehobene Viererzyklus","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15873,"byte_start":14118,"id":"section:36825088858a0e0e9fef","kind":"subsection","labels":["warum-der-einteilchen-abschluss-den-fock-operationssatz-nicht-schlieuxdft"],"line_end":320,"line_start":288,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/031-subsection-8-w-hrend-der-arbeit-entdeckte-nderung-kommut.tex","status_markers_as_written":[],"summary_excerpt":"Die Irreduzibilität der Einteilchendarstellung kann ihre assoziative Matrixalgebra zu [formula in source] machen. Daraus folgt nicht, dass jede Matrix als ein zulässiges physisches Wort verfügbar ist, und auch nicht, dass ihre zweite Quantisierung bereits erzeugt wird.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Warum der Einteilchen-Abschluss den Fock-Operationssatz nicht schließt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17521,"byte_start":15873,"id":"section:26c294848c4ee57b51a8","kind":"subsection","labels":["zustandswahl-keine-ruxfcckkehr-vor-den-abgesicherten-grundsatz"],"line_end":353,"line_start":321,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/031-subsection-8-w-hrend-der-arbeit-entdeckte-nderung-kommut.tex","status_markers_as_written":[],"summary_excerpt":"Der vorhandene native Satz beweist Eindeutigkeit, N=64, Singulett und positive Lücke bei μ=0 im angegebenen Kopplungsbereich. Eine komplette Clebsch-Gordan-Serie oder Voll-Diagonalisierung ist dafür nicht nötig; Vergleichsungleichungen und Minmax waren gerade der einfache Ausweg. Die physische Auswahl von H beziehungsweise μ=0 bleibt eine andere Frage.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Zustandswahl: keine Rückkehr vor den abgesicherten Grundsatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":17677,"byte_start":17521,"id":"section:76a1fb574236665e36d8","kind":"subsection","labels":["feldtheorie-falsche-verbote-entfernen-echte-bedingungen-behalten"],"line_end":356,"line_start":354,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/031-subsection-8-w-hrend-der-arbeit-entdeckte-nderung-kommut.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"5. 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Insbesondere hat der Energie-Impuls-Tensor [formula in source] , mit passender Spurbehandlung, Dimension [formula in source] . Ein Energie-Impuls-Tensor kann bereits in einer festen Hintergrundraumzeit definiert werden; dynamische Diffeomorphismen müssen nicht vorausgesetzt werden, um dieses Gegenbeis","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5.2 Der behauptete Spin-2-Ausschluss ist falsch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3685,"byte_start":2745,"id":"section:5d4847ed5ef4243e56d1","kind":"subsubsection","labels":["kinetik-ist-nicht-generell-verboten"],"line_end":81,"line_start":60,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/032-subsubsection-5-1-anomalien-label-anomalien.tex","status_markers_as_written":[],"summary_excerpt":"Der bilineare Ein-Ableitungs-Term mit einem (1,0)-Feld und seinem Adjungierten besitzt keinen Lorentzskalar. Mit zwei Ableitungen existiert aber etwa","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5.3 (1,0)-Kinetik ist nicht generell verboten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4841,"byte_start":3685,"id":"section:8589b030ff9051434c33","kind":"subsection","labels":["die-vierzustandsrechnung-richtig-lesen"],"line_end":102,"line_start":82,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/032-subsubsection-5-1-anomalien-label-anomalien.tex","status_markers_as_written":[],"summary_excerpt":"Das Modell mit [formula in source] , Bosonverbindung η und Diagonalen (0,Δ,Δ,0) erlaubt kohärenten Paartransport. Die exakte Identität [formula in source] stimmt. Unsere unabhängige Fließkomma-Abtastung reproduziert auf [formula in source] mit Schrittweite .05 den größten gefundenen Wert .998920021869 bei 2484.05. Der erste Gitter-Lokalhöchstwert liegt bereits bei 6.05. Weder „erster Maximalzeitpunkt`` noch ein globa","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Die Vierzustandsrechnung richtig lesen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6460,"byte_start":4841,"id":"section:d5f62ca4363e68968fe2","kind":"subsection","labels":["konsequenz-fuxfcr-die-nuxe4chste-forschungsrevision"],"line_end":138,"line_start":103,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/032-subsubsection-5-1-anomalien-label-anomalien.tex","status_markers_as_written":[],"summary_excerpt":"Die sinnvollen positiven Anschlüsse sind jetzt schärfer:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. Konsequenz für die nächste Forschungsrevision","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6979,"byte_start":6460,"id":"section:eb47e1c679e877d523c3","kind":"section","labels":["historischer-beweisanhang-vollstuxe4ndiger-nativer-herleitungsstand-v1.6.4"],"line_end":149,"line_start":139,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/032-subsubsection-5-1-anomalien-label-anomalien.tex","status_markers_as_written":[],"summary_excerpt":"Dieser Anhang bewahrt die frühere Herleitung vollständig. Seine damaligen Statussätze werden durch die aktuelle Konsolidierung und den Nachtrag oben ergänzt; er ist kein ungeprüft übernommener neuer Gesamtstatus. Die externe laufende Symmetrieergänzung wurde separat geprüft und ist nicht unbemerkt in diesen eingefrorenen Anhang eingegangen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Historischer Beweisanhang: vollständiger nativer Herleitungsstand v1.6.4","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":7574,"byte_start":6979,"id":"section:cef598d66a50e5309bc9","kind":"section","labels":["tfpt-universalraum-nativer-pol-bewegungsgleichung-und-minimale-feldtypen"],"line_end":161,"line_start":150,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/032-subsubsection-5-1-anomalien-label-anomalien.tex","status_markers_as_written":[],"summary_excerpt":"Diese Revision verbindet den während der Arbeit neu eingegangenen Polsatz v1.6.3 mit einer unabhängig begonnenen Untersuchung der nativen Bewegungsgleichung. Sie ergänzt die bisherigen Hauptdokumente; sie ist keine verkürzte Neufassung des vollständigen Hauptbuchs. Die vorhandenen Haupt- und Update-PDFs wurden in dieser Runde nicht verändert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TFPT / Universalraum: nativer Pol, Bewegungsgleichung und minimale Feldtypen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9952,"byte_start":7574,"id":"section:4f8da9a695fee547878c","kind":"subsection","labels":["ergebnis-in-einem-satz"],"line_end":216,"line_start":162,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/032-subsubsection-5-1-anomalien-label-anomalien.tex","status_markers_as_written":[],"summary_excerpt":"Auf dem abgesicherten Grundzustand des festgelegten nativen Fockmodells existiert eine isolierte ursprüngliche Fermion-Entnahmelinie; nach Kombination beider Rechnungen trägt sie mehr als 88,007628 \\% des gesamten normierten Spektralgewichts pro Mode. Die zusätzliche Antwort ist jedoch nicht exakt auf eine einzige weitere Linie reduzierbar. Ihr erster Rückwirkungsschritt wird direkt von derselben ursprünglichen Wechs","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Ergebnis in einem Satz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11111,"byte_start":9952,"id":"section:7617de644a08d01ba60d","kind":"subsection","labels":["ein-unveruxe4nderter-modellvertrag"],"line_end":244,"line_start":217,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/032-subsubsection-5-1-anomalien-label-anomalien.tex","status_markers_as_written":[],"summary_excerpt":"Es werden keine Hopping-, Massen-, Ladungs- oder Projektionsglieder zu H hinzugefügt:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Ein unveränderter Modellvertrag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11217,"byte_start":11111,"id":"section:6ed6cd592b54c956baba","kind":"subsection","labels":["was-tatsuxe4chlich-erneut-gepruxfcft-wurde"],"line_end":247,"line_start":245,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/032-subsubsection-5-1-anomalien-label-anomalien.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"3. Was tatsächlich erneut geprüft wurde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13681,"byte_start":11217,"id":"section:828142df79ecf7e27b7f","kind":"subsubsection","labels":["grundzustand-frische-berechnung-statt-blouxdfer-statusuxfcbernahme"],"line_end":304,"line_start":248,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/032-subsubsection-5-1-anomalien-label-anomalien.tex","status_markers_as_written":[],"summary_excerpt":"Die ursprünglichen Programme wurden mit fixierten Dateihashes in eine eigene Arbeitskopie übernommen. Die Paar-Konfigurationen wurden frisch mit neu kompiliertem Quellcode berechnet:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.1 Grundzustand: frische Berechnung statt bloßer Statusübernahme","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":14626,"byte_start":13681,"id":"section:df38823a08c2da378b7f","kind":"subsubsection","labels":["das-neu-eingegangene-polergebnis"],"line_end":325,"line_start":305,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":["relation:2094395014a01b4b8b8d"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/032-subsubsection-5-1-anomalien-label-anomalien.tex","status_markers_as_written":[],"summary_excerpt":"Der vollständige technische Bericht v1.6.3 und sein 248-zeiliger Prüfer wurden gelesen; Quellen, Bericht, Ergebnismatrix und Prüfpaket wurden unverändert archiviert. Der Prüfer wurde normal und optimiert wiederholt: 317 Prüfbedingungen, identische JSON-Bytes auch zum gelieferten Bericht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.2 Das neu eingegangene Polergebnis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16417,"byte_start":14626,"id":"section:47f8d646a33809dcd78d","kind":"subsection","labels":["der-einfache-native-anschluss-bewegungsgleichung-statt-umdeutung"],"line_end":372,"line_start":326,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/032-subsubsection-5-1-anomalien-label-anomalien.tex","status_markers_as_written":[],"summary_excerpt":"Erweitere jede W-Zeile zur antisymmetrischen Matrix [formula in source] mit [formula in source] für i j. Definiere","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Der einfache native Anschluss: Bewegungsgleichung statt Umdeutung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1194,"byte_start":0,"id":"section:27b546f8ad2839f03dee","kind":"subsection","labels":["dieselbe-antwort-auf-demselben-grundzustand"],"line_end":37,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/033-subsection-5-dieselbe-antwort-auf-demselben.tex","status_markers_as_written":[],"summary_excerpt":"Die innere Symmetrie macht G diagonal und alle Diagonalelemente gleich. Schreibe mit positiven Entnahme- und Additionsmaßen auf [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Dieselbe Antwort auf demselben Grundzustand","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2513,"byte_start":1194,"id":"section:d4af4642532a1898164e","kind":"subsubsection","labels":["herleitung-des-dritten-moments"],"line_end":66,"line_start":38,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/033-subsection-5-dieselbe-antwort-auf-demselben.tex","status_markers_as_written":[],"summary_excerpt":"Setze [formula in source] . Stationarität macht diesen Operator symmetrisch in der positiven, nach Nullvektoren quotientierten Metrik [formula in source] . Direkte Normalordnung ergibt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5.1 Herleitung des dritten Moments","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4470,"byte_start":2513,"id":"section:5611361d2519b252ba86","kind":"subsubsection","labels":["neue-engere-dichte--und-gewichtsgrenzen"],"line_end":124,"line_start":67,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/033-subsection-5-dieselbe-antwort-auf-demselben.tex","status_markers_as_written":[],"summary_excerpt":"Positivität der beiden Antwort-Grammatrizen beziehungsweise zweimal Cauchy-Schwarz liefern","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5.2 Neue engere Dichte- und Gewichtsgrenzen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6222,"byte_start":4470,"id":"section:0253e412f3dd3922d230","kind":"subsection","labels":["der-polsatz-und-seine-zusuxe4tzliche-verschuxe4rfung"],"line_end":174,"line_start":125,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/033-subsection-5-dieselbe-antwort-auf-demselben.tex","status_markers_as_written":[],"summary_excerpt":"Der eingegangene Beweis verwendet [formula in source] . Invarianz und Besetzung ergeben","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Der Polsatz und seine zusätzliche Verschärfung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":7036,"byte_start":6222,"id":"section:a5a563b414a713008b67","kind":"subsection","labels":["einfache-organisation-aber-keine-falsche-zwei-linien-luxf6sung"],"line_end":192,"line_start":175,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/033-subsection-5-dieselbe-antwort-auf-demselben.tex","status_markers_as_written":[],"summary_excerpt":"Die ersten zwei orthonormalen Operatoren sind f und [formula in source] . Die erste Resolventenreduktion hat deshalb die exakte Form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. Einfache Organisation, aber keine falsche Zwei-Linien-Lösung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8591,"byte_start":7036,"id":"section:d95f1d7c57cd126a8f4e","kind":"subsubsection","labels":["warum-man-die-ruxfcckwirkung-nicht-exakt-weglassen-darf"],"line_end":232,"line_start":193,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/033-subsection-5-dieselbe-antwort-auf-demselben.tex","status_markers_as_written":[],"summary_excerpt":"Angenommen, es gäbe nur je eine Entnahme- und Additionslinie mit Energien [formula in source] . Symmetrie macht diese für alle r gleich. Dann liefern die Bewegungsgleichungen auf demselben Grundzustand","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7.1 Warum man die Rückwirkung nicht exakt weglassen darf","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10753,"byte_start":8591,"id":"section:54cbcf599c630cf6bf53","kind":"subsection","labels":["was-der-operationssatz-jetzt-tatsuxe4chlich-hergibt"],"line_end":289,"line_start":233,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/033-subsection-5-dieselbe-antwort-auf-demselben.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333@ Vertrag & Mathematisch abgesichert & Nicht dadurch verfügbar \\\\ Markierter endlicher Matrixcompiler & Matrizen, Ordnungen, konkrete endliche Syntheseidentitäten & Vollständiges Fockinstrument, Präparation, physischer Zeitgenerator \\\\ H allein & Modellzeitentwicklung & Unabhängiges Schalten von X und [formula in source] \\\\ X und [formula in source] , wenn ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8. Was der Operationssatz jetzt tatsächlich hergibt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11505,"byte_start":10753,"id":"section:a842aa80d4afcd93581c","kind":"subsubsection","labels":["konkrete-pruxe4parationsgrenze"],"line_end":305,"line_start":290,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/033-subsection-5-dieselbe-antwort-auf-demselben.tex","status_markers_as_written":[],"summary_excerpt":"Alle genannten Fockkontrollen erhalten N. Ein Wort aus ihnen und jeder einzeln zahlenerhaltende ausgewählte Messzweig bleiben im Ausgangssektor. Sie können aus dem leeren N=0-Zustand nicht den N=64-Grundzustand erzeugen. Diese Aussage betrifft zahlenerhaltende Krauszweige; eine bloß U(1)-kovariante offene Dynamik kann sehr wohl geladene Krausoperatoren haben.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.1 Konkrete Präparationsgrenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12235,"byte_start":11505,"id":"section:1531ad804763168f277d","kind":"subsubsection","labels":["der-kleinste-konkrete-ladungstest"],"line_end":320,"line_start":306,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/033-subsection-5-dieselbe-antwort-auf-demselben.tex","status_markers_as_written":[],"summary_excerpt":"Ein Kandidat ist eine explizite Referenzmode c mit [formula in source] . Sie erhält die gemeinsame Ladung, verändert aber die Ladung der ursprünglichen Bank. Der endliche Austausch- und Detuningtest ist exakt; dieses T wurde nicht als neuer nativer Hamiltonterm eingeführt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.2 Der kleinste konkrete Ladungstest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12691,"byte_start":12235,"id":"section:29c9a0c7c003c3fa0a70","kind":"subsection","labels":["relativistisches-wuxf6rterbuch-ausschluss-und-zwei-pruxe4zise-alternativen"],"line_end":329,"line_start":321,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/033-subsection-5-dieselbe-antwort-auf-demselben.tex","status_markers_as_written":[],"summary_excerpt":"Die Indexfrage darf nicht nachträglich durch einen Namen beantwortet werden. Die Konventionen für Zweikomponentenspinoren wurden mit https://arxiv.org/abs/0812.1594Dreiner, Haber und Martin abgeglichen; die folgenden speziellen W-Tests sind eigene exakte Tensorrechnungen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. Relativistisches Wörterbuch: Ausschluss und zwei präzise Alternativen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13179,"byte_start":12691,"id":"section:8f931ab70c6db9cebc91","kind":"subsubsection","labels":["was-nicht-funktioniert"],"line_end":338,"line_start":330,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/033-subsection-5-dieselbe-antwort-auf-demselben.tex","status_markers_as_written":[],"summary_excerpt":"Für 64 gleichhändige Weylfelder mit innerem Index I und einen skalaren Vermittler ist [formula in source] symmetrisch. Die Grassmann-Antisymmetrisierung verschwindet daher identisch, für alle 60 W-Zeilen. Außerdem lässt die volle irreduzible innere Darstellung [formula in source] auf denselben 64 Komponenten nach Schur keine zusätzliche kommutierende nichttriviale Lorentzspinorwirkung zu.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9.1 Was nicht funktioniert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13594,"byte_start":13179,"id":"section:e2289fde0561e9823dbc","kind":"subsubsection","labels":["bereits-bekannter-nichtverschwindender-typ"],"line_end":347,"line_start":339,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/033-subsection-5-dieselbe-antwort-auf-demselben.tex","status_markers_as_written":[],"summary_excerpt":"Ein symmetrischer Lorentzspinortensor koppelt an das antisymmetrische M. Der Vermittler hat dann einen passenden dualen (1,0)-Typ samt adjungiertem Typ. Diese Variante besteht den algebraischen Nichtnulltest, aber noch keinen vollständigen Kinetik-, Positivitäts-, Constraints- oder Herkunftstest.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9.2 Bereits bekannter nichtverschwindender Typ","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15347,"byte_start":13594,"id":"section:32b8a9b90dbab0d5e1b6","kind":"subsubsection","labels":["neue-minimale-skalare-alternative---ausdruxfccklich-zusuxe4tzlich"],"line_end":381,"line_start":348,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/033-subsection-5-dieselbe-antwort-auf-demselben.tex","status_markers_as_written":[],"summary_excerpt":"Will man zugleich W, gleiche Weylhand, lokale Bilinearität und einen skalaren Vermittler behalten, kann man einen unabhängigen Hilfsindex a=1,2 mit alternierender Form einführen:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9.3 Neue minimale skalare Alternative - ausdrücklich zusätzlich","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3281,"byte_start":0,"id":"section:2f98921fe0b360549e99","kind":"subsection","labels":["nuxe4chste-schritte-mit-eindeutiger-erfolgskontrolle"],"line_end":71,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/034-subsection-10-n-chste-schritte-mit-eindeutiger.tex","status_markers_as_written":[],"summary_excerpt":"Native Quelle des Austauschoperators bestimmen. Ein tatsächliches Operationswort mit Anfangszustand, Detektor, Adjungiertem, Ladungsbilanz und Record angeben. Ein weiteres neutrales Wort oder bloßer Algebraabschluss schließt diese Aufgabe nicht. Den Rest der nativen Antwort kontrollieren. Das nächste Ziel ist [formula in source] beziehungsweise sein erster Norm- und Momentkoeffizient, gemeinsam in N=63,64,65. Die vor","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10. Nächste Schritte mit eindeutiger Erfolgskontrolle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4289,"byte_start":3281,"id":"section:85bee565367f7445fdac","kind":"subsection","labels":["erratum-und-versionsdisziplin"],"line_end":91,"line_start":72,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/034-subsection-10-n-chste-schritte-mit-eindeutiger.tex","status_markers_as_written":[],"summary_excerpt":"Im eigenen v1.6.2-Text fehlte in Abschnitt 5.2 zwischen Entnahme- und Additionsresolvente ein Pluszeichen. Richtig ist auf der dortigen N=4-Referenz [formula in source] . Die früheren Prüfrechnungen verwendeten die additive CAR-Gewichtsregel; der Darstellungsfehler wird hier ausdrücklich korrigiert. Die archivierte v1.6.2 wird nicht stillschweigend umgeschrieben.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"11. Erratum und Versionsdisziplin","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":19036,"byte_start":4289,"id":"section:8c5adbfd357f2448d664","kind":"section","labels":["nutzerquelle-a-vollstuxe4ndige-runde-v1.6.3"],"line_end":337,"line_start":92,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":["relation:6a7111be38b338335aec"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/034-subsection-10-n-chste-schritte-mit-eindeutiger.tex","status_markers_as_written":[],"summary_excerpt":"Unveränderte Quelle. Nicht alle Aussagen darin werden übernommen. Entscheidend sind die Quellenprüfung und Korrekturen in v1.6.7.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nutzerquelle A: vollständige Runde v1.6.3","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":19541,"byte_start":19036,"id":"section:889fde9228ba0b59b8ae","kind":"section","labels":["nutzerquelle-b-korrektur-und-zwischenbericht"],"line_end":349,"line_start":338,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/034-subsection-10-n-chste-schritte-mit-eindeutiger.tex","status_markers_as_written":[],"summary_excerpt":"Unveränderte Quelle. Nicht alle Aussagen darin werden übernommen. Entscheidend sind die Quellenprüfung und Korrekturen in v1.6.7.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nutzerquelle B: Korrektur und Zwischenbericht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":19784,"byte_start":19541,"id":"section:d530ee97280841088cad","kind":"section","labels":["zwischenbericht-tfptuniversalraum---fundamentale-luxf6sung-stand-15.09.2026-1145"],"line_end":353,"line_start":350,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/034-subsection-10-n-chste-schritte-mit-eindeutiger.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Zwischenbericht: TFPT/Universalraum - fundamentale Lösung, Stand 15.09.2026, 11:45","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1770,"byte_start":0,"id":"section:cdcf43a68074fc101f8f","kind":"subsection","labels":["gesamtlage-zwei-spuren"],"line_end":45,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/035-subsection-0-gesamtlage-zwei-spuren-label-gesamtlage-zwe.tex","status_markers_as_written":[],"summary_excerpt":"Es existieren jetzt zwei Contract-Ordner, die sich unabhängig auf denselben Kernpunkt zubewegt haben:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"0. Gesamtlage: zwei Spuren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2891,"byte_start":1770,"id":"section:5e83f84e2276b8fe1771","kind":"subsection","labels":["fundament-meiner-session-native_source.py-neu-npz-frei"],"line_end":66,"line_start":46,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/035-subsection-0-gesamtlage-zwei-spuren-label-gesamtlage-zwe.tex","status_markers_as_written":[],"summary_excerpt":"Problem: der gepinnte Tensor ( spinor_tensors.npz, SHA-256 3f00a089…) liegt unter /Documents - für die Agenten-Shell macOS-gesperrt (TCC). Die bisherigen Verträge sind von dieser Shell nicht reproduzierbar.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Fundament meiner Session: native_source.py (neu, npz-frei)1. Fundament meiner Session: (neu, npz-frei)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3184,"byte_start":2891,"id":"section:b1d02f53d21bddbd5065","kind":"subsection","labels":["wp-a-der-verfuxfcgbare-operationssatz-fertig-307-exakte-guards"],"line_end":72,"line_start":67,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/035-subsection-0-gesamtlage-zwei-spuren-label-gesamtlage-zwe.tex","status_markers_as_written":[],"summary_excerpt":"Frage (v1.6.2 §10.3/§14): Wie groß ist die unsichtbare Freiheit (Kommutant) unter dem tatsächlich verfügbaren Operationssatz?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. WP-A: Der verfügbare Operationssatz (fertig, 307 exakte Guards)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4241,"byte_start":3184,"id":"section:c25cbb8ae75baeb802fd","kind":"subsubsection","labels":["die-kommutanten-leiter-n3-sektor-45-504-dim"],"line_end":101,"line_start":73,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":["relation:c4737b2808cc92ace197"],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/035-subsection-0-gesamtlage-zwei-spuren-label-gesamtlage-zwe.tex","status_markers_as_written":[],"summary_excerpt":"@lrr@ Operationssatz & erzeugte Algebra & Kommutante \\\\ S0: \\X, N_b\\ & 14 & 1 444 233 216 \\\\ S1: + Spin(10)×SU(4)-Rahmen & 743 583 744 & 7 \\\\ S2: + Clock-Lift & unverändert & 7 \\\\ S3: + Modenbesetzungen \\n_r, m_A\\ & M₄₅₅₀₄ (2 070 614 016) & 1 \\\\ S4: + geladene f-Instrumente & M₄₇₅₈₀ (N=2∪N=3) & 1 \\\\","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Kommutanten-Leiter (N=3-Sektor, 45 504-dim)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5644,"byte_start":4241,"id":"section:abe08ea071bba6f43c37","kind":"subsubsection","labels":["die-isotypie-zerlegung-von-n3-beide-spuren-unabhuxe4ngig-identisch"],"line_end":131,"line_start":102,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/035-subsection-0-gesamtlage-zwei-spuren-label-gesamtlage-zwe.tex","status_markers_as_written":[],"summary_excerpt":"@lrrrll@ Block & Dim & Mult & S-Eigenwert & (C_S, C_U) & Rolle \\\\ (144, 20) & 2880 & 2 & 7 & (85, 39) & hell, X-gekoppelt \\\\ (144, 4̄) & 576 & 2 & 10 & (85, 15) & hell, X-gekoppelt \\\\ (16′, 20) & 320 & 2 & 12 & (45, 39) & hell, X-gekoppelt \\\\ (16′, 4̄) & 64 & 1 & 0 (ker S) & (45, 15) & χ-Kompositblock \\\\ (672, 4̄) & 2688 & 1 & - & (165, 15) & dunkel \\\\ (1200, 20) & 24 000 & 1 & - & (141, 39) & dunkel \\\\ (560, 20′) & ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Isotypie-Zerlegung von N=3 (beide Spuren unabhängig, identisch)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6844,"byte_start":5644,"id":"section:9251f4ff96eb011613de","kind":"subsubsection","labels":["das-verfuxfcgbarkeits-theorem-parallelsession-symmetry_availability.py"],"line_end":153,"line_start":132,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/035-subsection-0-gesamtlage-zwei-spuren-label-gesamtlage-zwe.tex","status_markers_as_written":[],"summary_excerpt":"Die gewährte Dynamik (Wörter aus X, N_b) liegt in der Verflechteralgebra (Dim Σmᵢ² = 16); die 60 Lie-Erzeuger liegen nicht darin - keine Komposition gewährter Dynamik erzeugt sie. Die Symmetrie ist ein eigenständiges Primitiv: gewährt oder nicht gewährt. Der gesamte verbleibende symmetrieverträgliche Spielraum ist exakt 2 Dimensionen breit = die Fähigkeit, die drei dunklen Blöcke getrennt anzusprechen (= beide Casimi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das Verfügbarkeits-Theorem (Parallelsession, symmetry_availability.py)Das Verfügbarkeits-Theorem (Parallelsession, )","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9136,"byte_start":6844,"id":"section:a6253490eb8dec616cdb","kind":"subsection","labels":["wp-c-relativistisches-feldwuxf6rterbuch-fertig-2161-exakte-guards--oo-stabil"],"line_end":205,"line_start":154,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/035-subsection-0-gesamtlage-zwei-spuren-label-gesamtlage-zwe.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.3000 > p( - 4 ) * 0.4000 > p( - 4 ) * 0.3000@ Kanal & Norm² pro Zeile & Status \\\\ Skalar, gleichhändig ε_\\αβ\\ψψ & 0 (alle 60 Zeilen, exakt) & verboten \\\\ Skalar, gepunktet (0,0) & 0 & verboten \\\\ (1,0) symmetrisch \\I, σˣ, σᶻ\\ & je 64, Summe 192 & erlaubt - der Vertex ist rein (1,0)+h.c. \\\\ (0,1) konjugiert & je 64 & erlaubt \\\\","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. WP-C: Relativistisches Feldwörterbuch (fertig, 2161 exakte Guards, -OO-stabil)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":11164,"byte_start":9136,"id":"section:9b75d995112cd1daae3d","kind":"subsection","labels":["wp-b-nativer-grundzustand-parallelsession-v1.6.4-meine-laufende-sonde"],"line_end":254,"line_start":206,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/035-subsection-0-gesamtlage-zwei-spuren-label-gesamtlage-zwe.tex","status_markers_as_written":[],"summary_excerpt":"@rrr@ k & Bosonkonfigurationen vollständig enumeriert & ‖Q₊ᵏF‖² \\\\ 0 & analytisch & 1 \\\\ 1 & 60 Kanäle / 480 Paare & 480 \\\\ 2 & 1 830 & 439 680 \\\\ 3 & 37 820 & 575 078 400 \\\\ 4 & 595 665 & 952 296 652 800 \\\\","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. WP-B: Nativer Grundzustand (Parallelsession v1.6.4 + meine laufende Sonde)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12807,"byte_start":11164,"id":"section:60a552c2697d56d6eeb6","kind":"subsection","labels":["wp-d-geladene-antwort-auf-dem-grundzustand-parallelsession-v1.6.4"],"line_end":294,"line_start":255,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/035-subsection-0-gesamtlage-zwei-spuren-label-gesamtlage-zwe.tex","status_markers_as_written":[],"summary_excerpt":"Genau die geforderte „dieselbe geladene Antwort auf dem abgesicherten Zustand'':","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. WP-D: Geladene Antwort auf dem Grundzustand (Parallelsession v1.6.4)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14383,"byte_start":12807,"id":"section:c42403b1b43926117d5c","kind":"subsection","labels":["kreuzvalidierung-der-beiden-spuren"],"line_end":333,"line_start":295,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/035-subsection-0-gesamtlage-zwei-spuren-label-gesamtlage-zwe.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 6 ) * 0.2500 > p( - 6 ) * 0.2500 > p( - 6 ) * 0.2500 > p( - 6 ) * 0.2500@ Befund & Meine Session & Parallelsession & Status \\\\ N=3-Zerlegung (7 Blöcke, Mults 2,2,2,1,1,1,1) & ✓ & ✓ & identisch \\\\ Casimirwerte (je Block) & (45,15), (85,15), & C = (C_S+C_U)/4 = 15, 25, 45, 21, 31, 45, 45 & identisch (zwei Normierungen) \\\\ Kommutant S1 (volle Symmetrie) & 7 & 7 & identisch \\\\ Kommutant S0 (X, N_b) & 1 452 961 7","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Kreuzvalidierung der beiden Spuren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":16136,"byte_start":14383,"id":"section:4eb997c766ec267764a3","kind":"subsection","labels":["offen-nuxe4chste-schritte-in-der-reihenfolge-der-direktive"],"line_end":375,"line_start":334,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/035-subsection-0-gesamtlage-zwei-spuren-label-gesamtlage-zwe.tex","status_markers_as_written":[],"summary_excerpt":"Sonde abschließen (läuft): mult₂-Zertifikat, β-Kette, Sektorfloors → unabhängige Reproduktion der v1.6.4-Kernzahlen. Volle 33-Niveau-Kette: falls mult_k=1 weiter trägt, ist die Singulett-Kette durch die Normsequenz ‖Q₊ᵏF‖² (k≤32) bestimmt - dafür ist die Symmetriespur-Resummation nötig (die „vier Symmetriespuren'' des Workers), nicht rohe Enumeration. Σ₂ kontrollieren (erster Norm-/Momentkoeffizient, N=63/64/65 gemei","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. Offen / nächste Schritte (in der Reihenfolge der Direktive)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16991,"byte_start":0,"id":"section:48bd2970813462018380","kind":"section","labels":["nutzerquelle-c-multiplizitaeten-und-z4"],"line_end":332,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/036-section-nutzerquelle-c-multiplizitaeten-und.tex","status_markers_as_written":[],"summary_excerpt":"Unveraenderte Nutzerquelle, als Vorschlag und nicht als Beweis uebernommen. Die Pruefung und eigene Fortsetzung stehen in Teil B.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nutzerquelle C: Multiplizitaeten und Z4","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10484,"byte_start":0,"id":"section:f0aaf8ab3570dcfe4c7c","kind":"section","labels":["nutzerquelle-d-fundamentale-reduktion"],"line_end":180,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/037-section-nutzerquelle-d-fundamentale.tex","status_markers_as_written":[],"summary_excerpt":"Unveraenderte Nutzerquelle, als Vorschlag und nicht als Beweis uebernommen. Die Pruefung und eigene Fortsetzung stehen in Teil B.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nutzerquelle D: fundamentale Reduktion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":22803,"byte_start":0,"id":"section:7999e08118d31c1e3143","kind":"section","labels":["nutzerquelle-e-gemeinsamer-ausfuehrbarer-prozess"],"line_end":363,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/038-section-nutzerquelle-e-gemeinsamer-ausfuehrbarer.tex","status_markers_as_written":[],"summary_excerpt":"Unveraenderte Nutzerquelle, als Vorschlag und nicht als Beweis uebernommen. Die Pruefung und eigene Fortsetzung stehen in Teil B.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nutzerquelle E: gemeinsamer ausfuehrbarer Prozess","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":23094,"byte_start":22803,"id":"section:af37ebe2d614b7bed3ab","kind":"section","labels":["nutzerquelle-f-operationssatz-grundzustand-und-feldwoerterbuch-v1.6.3"],"line_end":370,"line_start":364,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/038-section-nutzerquelle-e-gemeinsamer-ausfuehrbarer.tex","status_markers_as_written":[],"summary_excerpt":"Unveraenderte Nutzerquelle, als Vorschlag und nicht als Beweis uebernommen. Die Pruefung und eigene Fortsetzung stehen in Teil B.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nutzerquelle F: Operationssatz, Grundzustand und Feldwoerterbuch v1.6.3","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":860,"byte_start":0,"id":"section:37ba7647438ba0b50ef9","kind":"section","labels":["tfpt-universalraum-operationssatz-nativer-grundzustand-und-feldwuxf6rterbuch"],"line_end":15,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/039-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Diese Runde bearbeitet die vier Prioritäten aus v1.6.2 §14 in der dort festgelegten Reihenfolge: den tatsächlich verfügbaren Operationssatz exakt abgrenzen, den berichteten nativen Grundzustand mit seinem ursprünglichen Hamilton- und Sektorvertrag reproduzieren und darauf die geladene Antwort berechnen, das relativistische Feldwörterbuch am tatsächlichen Tensor festhalten. Eine räumliche Skalierungsrechnung ist ausdr","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TFPT / Universalraum: Operationssatz, nativer Grundzustand und Feldwörterbuch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2267,"byte_start":860,"id":"section:065459044dcf33bfe5d3","kind":"subsection","labels":["ergebnis-in-einem-absatz"],"line_end":37,"line_start":16,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/039-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Der N=64-Sektor des nativen Modells ist exakt als Loch-Paarerzeugung auf dem gefüllten Zustand realisiert; seine Krylov-Kette ist bis zu 15 252 960 Einträgen exakt berechnet, ihre Normen ν₁ ν₄ sind auf zwei völlig unabhängigen Wegen (Besetzungsbild und Onishi/Wick-Spurnetzwerke) identisch. Die Kette schließt bei zwei Bosonen exakt nicht (Defekt 2,9·10⁻⁵), das Modell ist also nicht allein durch seine Normen lösbar, nu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Ergebnis in einem Absatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3222,"byte_start":2267,"id":"section:1956d3258c2f67db19d8","kind":"subsection","labels":["unveruxe4nderte-quelle-und-konventionen"],"line_end":56,"line_start":38,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/039-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Der Tensor wird repo-lokal gelesen (SHA-256 3f00a0892157a691e4ef26920c3702772c7bf76a250fad98ff04a079bb64b763), der Clock-Konstruktor ist gepinnt ( 9bf99de7…). common.py prüft: 60 Kanäle × 8 disjunkte Paare, jede Mode in 15 Kanälen; Gewichtserhaltung auf allen 480 Paaren; die Casimir-Identität 8WᵀW + 𝒞_S + 𝒞_C − 120 I = 0 auf allen 2016 Zweiteilchenzuständen (𝒞 = −ΣL², d. h. viermal der Standard-Casimir); induzierte B","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Unveränderte Quelle und Konventionen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3665,"byte_start":3222,"id":"section:6dacbc46a67419be1baf","kind":"subsection","labels":["operationssatz-und-kommutant"],"line_end":66,"line_start":57,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/039-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Gemessen wird die Dimension des Kommutanten der von einer Operationsstufe erzeugten Algebra auf dem Sektor: kleiner Kommutant bedeutet weniger unsichtbare Freiheit. Das Spektralzertifikat für N=3 ist reproduziert (S = C₃C₃ᵀ wird von ∏(S−r), r ∈ \\0,7,10,12\\, exakt annulliert; Multiplizitäten 64, 2880, 576, 320 aus rationalen Projektorspuren).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Operationssatz und Kommutant","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5472,"byte_start":3665,"id":"section:519e3ef56e84c89a6ce1","kind":"subsubsection","labels":["exakte-irreduzibel-zerlegung-huxf6chstgewichtsvektoren"],"line_end":108,"line_start":67,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/039-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 8 ) * 0.1875 > p( - 8 ) * 0.1875 > p( - 8 ) * 0.2500 > p( - 8 ) * 0.1875 > p( - 8 ) * 0.1875@ Sektor & Block & Dim & Zerlegung unter so(10)⊕ su(4) & (𝒞_S, 𝒞_C) \\\\ N=2 & helle Paare ↔ Bosonen & 60 & (10, 6) & (36, 20) \\\\ N=2 & dunkle Paare & 1956 & (120, 10) ⊕ (126, 6) & (84,36), (100,20) \\\\ N=3 & dunkle Tripel = ker C₃ & 37888 & (560, 20″) ⊕ (1200, 20) ⊕ (672, 4̄) & (117,63), (141,39), (165,15) \\\\ N=3 & ker ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.1 Exakte Irreduzibel-Zerlegung (Höchstgewichtsvektoren)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7553,"byte_start":5472,"id":"section:d19c2bae43086ae13b0f","kind":"subsubsection","labels":["kommutanten-leiter"],"line_end":154,"line_start":109,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/039-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.2727 > p( - 4 ) * 0.3636 > p( - 4 ) * 0.3636@ Verfügbare Operationen & N=2 & N=3 \\\\ A: \\X, N_b\\ (die zwei bisher geprüften Kontrollen) & 3 829 536 & 1 444 233 216 \\\\ B: A + Clock (Ordnung 6) & 641 760 & 240 742 144 \\\\ Cc: A + 15 su(4)-Generatoren & 30 376 & 2 247 168 \\\\ Cs: A + 45 so(10)-Generatoren & 172 & 1 648 \\\\ C: A + alle 60 Generatoren & 3 & 7 \\\\ D: B + C & 3 & 7 \\\\ B(H_N) & 1 & 1 \\\\","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.2 Kommutanten-Leiter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7634,"byte_start":7553,"id":"section:076eeb2b8b4608fb5859","kind":"subsection","labels":["der-native-n64-grundzustand"],"line_end":157,"line_start":155,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/039-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"4. Der native N=64-Grundzustand","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8251,"byte_start":7634,"id":"section:e6dee9a078502df9ae42","kind":"subsubsection","labels":["lochbild"],"line_end":172,"line_start":158,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/039-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Mit h_i = f_i† ist F⟩ = f₀† f₆₃† 0⟩ das Lochvakuum und als Operatoridentität P_A = −Q_A† mit Q_A† = Σ_\\i j\\W_\\A,ij\\h_i†h_j†. Unter (−1)\\^\\N_b\\ ist H äquivalent zu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.1 Lochbild","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9514,"byte_start":8251,"id":"section:56ba3817bf1039481025","kind":"subsubsection","labels":["exakte-krylov-kette"],"line_end":203,"line_start":173,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/039-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"@rrrl@ n & Einträge in v_n & ν_n = ‖v_n‖² & ν_n/ν_\\n−1\\ \\\\ 0 & 1 & 1 & - \\\\ 1 & 480 & 480 & 480 \\\\ 2 & 108 240 & 439 680 & 916 = 4·229 \\\\ 3 & 15 252 960 & 575 078 400 & 299520/229 \\\\ 4 & (nur Spurnetzwerk) & 952 296 652 800 & ≈ 1656,0 \\\\ 5 & (nur Spurnetzwerk) & siehe norms_by_traces.json & \\\\","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.2 Exakte Krylov-Kette","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10124,"byte_start":9514,"id":"section:157010ea89818b8ccb1e","kind":"subsubsection","labels":["schlieuxdfung"],"line_end":217,"line_start":204,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/039-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Der Zwei-Boson-Singulettraum ist also mehr als eindimensional; die Kette ist exakt nicht geschlossen, und das Modell ist nicht allein durch die ν_n lösbar. Numerisch ist die Korrektur vernachlässigbar: w₂ koppelt nur an v₃ mit g·√(‖w₂‖²/ν₃) = 0,195 g.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.3 Schließung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11156,"byte_start":10124,"id":"section:3d0521cf47a516b6c6b4","kind":"subsubsection","labels":["ritz-obergrenzen"],"line_end":243,"line_start":218,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/039-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"In der orthonormierten Basis \\v₀ v_K, w₂\\ ist H (Δ = 1) tridiagonal plus w₂-Zweig: Diagonale n bzw. 2; Nebendiagonalen g·4√30, g·2√229, g·48√29770/229, ; w₂-Kopplung g·3√598377/11908.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.4 Ritz-Obergrenzen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11738,"byte_start":11156,"id":"section:f16c51f190739266991b","kind":"subsubsection","labels":["observablen-auf-dem-ritz-zustand-gux3b4-120-k3"],"line_end":254,"line_start":244,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/039-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"⟨N_b⟩ = 0,8421 (Hellmann-Feynman ∂E/∂Δ = 0,8421); ⟨F Ω⟩ ² = 0,397; Bosonzahlverteilung 0,397 / 0,397 / 0,172 / 0,034; Shannon-Untergrenze der Boson-Loch-Verschränkung 1,66 bit (rigoros, weil die reduzierte Bosondichte in N_b blockdiagonal ist). Die Worker-Angaben „Überlapp 1/4`` und „Verschränkung 0,811 bit`` sind damit konsistent, aber auf einem nichtkonvergierten Zustand.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.5 Observablen auf dem Ritz-Zustand (g/Δ = 1/20, K=3)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":12337,"byte_start":11738,"id":"section:9e812d9c912768995302","kind":"subsubsection","labels":["geladene-ein-teilchen-antwort"],"line_end":270,"line_start":255,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/039-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Für jede Mode r (Guard r ∈ \\0, 5, 63\\; Transitivität der Quellsymmetrie):","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.6 Geladene Ein-Teilchen-Antwort","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13554,"byte_start":12337,"id":"section:4015df5c075adfee331f","kind":"subsubsection","labels":["sektorauswahl-und-die-worker-behauptung"],"line_end":300,"line_start":271,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/039-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Untergrenzen aus der Casimir-Identität und quadratischer Ergänzung, H ≥ (1−θ)ΔN_b − (15g²/2θΔ)N_f, ausgewertet als max_θ min_\\N_b\\ je Sektor:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4.7 Sektorauswahl und die Worker-Behauptung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13664,"byte_start":13554,"id":"section:cdd42ed4ee51067bd067","kind":"subsection","labels":["feldwuxf6rterbuch-am-tatsuxe4chlichen-tensor"],"line_end":303,"line_start":301,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/039-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"5. Feldwörterbuch am tatsächlichen Tensor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15253,"byte_start":13664,"id":"section:cdadd3a02421a908cf8c","kind":"subsubsection","labels":["symmetrieregel"],"line_end":343,"line_start":304,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/039-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Für Grassmann-Felder ψ_\\I,a\\ ist Σ_\\IJ\\Σ_\\ab\\ W_\\IJ\\K_\\ab\\ψ_\\I,a\\ψ_\\J,b\\ = ½Σ(T − Tᵀ) mit T_\\(Ia),(Jb)\\ = W_\\IJ\\K_\\ab\\. Weil W antisymmetrisch ist, verschwindet die Kopplung genau dann, wenn K antisymmetrisch ist; nur der symmetrische Teil des Spinorkerns koppelt. Auf allen 60 Zeilen explizit geprüft:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5.1 Symmetrieregel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":17183,"byte_start":15253,"id":"section:25401bcf0e2036915053","kind":"subsubsection","labels":["chiralituxe4tsgradierungen"],"line_end":389,"line_start":344,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/039-section-tfpt-universalraum-operationssatz-nativer-grundz.tex","status_markers_as_written":[],"summary_excerpt":"Der Trägergraph (64 Moden, 480 Kanten, Grad 15, dreiecksfrei) ist nicht bipartit; ein ungerader Zyklus ist [16, 45, 0, 30, 37]. Es gibt daher keine globale Chiralitätsaufteilung, unter der alle 60 Bosonen Vektoren wären. Für jede der 44 G-kovarianten Gradierungen ist jeder Kanal rein (nie gemischt), aber der Bosonmultiplett zerfällt:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5.2 Chiralitätsgradierungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1154,"byte_start":0,"id":"section:ac65eec364da89e386be","kind":"subsection","labels":["spurnetzwerk-normen"],"line_end":21,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/040-subsection-6-spurnetzwerk-normen-label-spurnetzwerk-norm.tex","status_markers_as_written":[],"summary_excerpt":"über bosonische Kohärenzzustände, die Onishi-Determinante det(1 − M̄M)\\^\\1/2\\ und Wick-Paarung der z-Variablen. Jedes Netzwerk ist eine Kontraktion von n Kopien des Tensors Φ_\\ij,kl\\ = Σ_A(M_A) \\ij\\(M_A)\\kl\\ (Einträge in \\−1,0,1\\). Netzwerke werden als 4-Bein-Multigraphen unter Knotenumbenennung und Slot-Tausch kanonisiert (n=4: 120 → 27 Klassen). Exaktheit: float64-Kontraktion mit Absolutwert-Begleitkontraktion ( Σa","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Spurnetzwerk-Normen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2735,"byte_start":1154,"id":"section:225104527631ae50d5cb","kind":"subsection","labels":["t1-t8"],"line_end":62,"line_start":22,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/040-subsection-6-spurnetzwerk-normen-label-spurnetzwerk-norm.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333@ Tor & Beitrag dieser Runde & Weiter offen \\\\ T1 & Exakte Kommutanten-Leiter A→B→Cc→Cs→C; Clock als äußeres Symmetrieelement & Welche Symmetrieoperationen der Compiler tatsächlich bereitstellt \\\\ T2 & Lochbild bewiesen; Z_h + Z_add = 1; ε_h, ε_add & Konvergierter Zustand, Renormierung, Grenzraum \\\\ T3 & - (ausgeklammert) & Räumlicher Träger \\\\ T4 & Kern-Sy","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. T1-T8","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3854,"byte_start":2735,"id":"section:1135c3742886b607138b","kind":"subsection","labels":["die-jetzt-entscheidenden-pruxfcfungen"],"line_end":89,"line_start":63,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/040-subsection-6-spurnetzwerk-normen-label-spurnetzwerk-norm.tex","status_markers_as_written":[],"summary_excerpt":"Untergrenzen verschärfen. Die Casimir-Schranke trennt N=64 bei 1/20 nicht von N=62 und N=66. Eine Jacobi-Vergleichsschranke mit rigorosen Normschranken für TT† je Bosonzahl oder eine Temple-Schranke auf der Ritz-Kette würde den Beweisbereich anheben. Den Zwei-Boson-Singulettraum ausschreiben. w₂ ist der erste Zeuge; die volle Lanczos-Kette von H (nicht nur von T†) ab Tiefe 4 braucht w₂ und seine Nachfolger. Operation","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8. Die jetzt entscheidenden Prüfungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":5318,"byte_start":3854,"id":"section:c414daee7bf9df0ed44f","kind":"subsection","labels":["verifikation-und-nicht-uxfcbernommene-behauptungen"],"line_end":116,"line_start":90,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"documents/experiments--theory-contracts--universalraum-spin-lift-basics-20260915--tmp--pdfs--TFPT_Universalraum_Spinlift_Hauptdokument_2026-09-15_v1.6.10/sections/040-subsection-6-spurnetzwerk-normen-label-spurnetzwerk-norm.tex","status_markers_as_written":[],"summary_excerpt":"replay.py führt fünf Prüfer normal und unter -OO aus und verlangt byteidentische Ausgaben; Status, Hashes und Guardsummen stehen in replay_manifest.json. Guardzahlen zählen Prüfbedingungen, keine unabhängigen Theoreme. Exakt heißt ganzzahlig/rational; numerisch heißt float64 mit Toleranz-Guard (Ritz-Eigenwerte ab 3×3, Observablen, Erste-Moment-Auswertungen).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9. Verifikation und nicht übernommene Behauptungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":1926,"byte_start":0,"id":"section:551c7eb8333ae26ff5ba","kind":"frontmatter","labels":[],"line_end":53,"line_start":1,"occurrence":1,"owner_documents":["document:introduction","document:verification_catalog"],"relation_ids":[],"semantic_review":false,"source":"documents/introduction/preamble.tex","status_markers_as_written":[],"summary_excerpt":"positioning,arrows.meta,fit,backgrounds,calc,shapes.geometric,shapes.misc","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"-1.2cm Topological Fixed-Point Theory (TFPT)\\\\[1.5mm] A discrete compiler for the constants of physics\\\\[2.5mm] Two inputs — the boundary constant [formula in source] and a five-slot carrier — build [formula in source] \\\\ and read off the Standard Model: status assessment and reading guide","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":5854,"byte_start":0,"id":"section:ac978079d55f2c41f62b","kind":"frontmatter","labels":[],"line_end":86,"line_start":1,"occurrence":1,"owner_documents":["document:introduction"],"relation_ids":["relation:085d1df6c93eb9e038e6","relation:09a82cb6866c2f01a1b3","relation:4f604a4acd42a11408b3","relation:56948d758b91fc928dce","relation:59fdd57ecd15920b2338","relation:611d1deace905478adb4","relation:8baac771be671cb7fa67","relation:b805b8882316541a88cf","relation:c6e08754742f4bb3ad60","relation:dcb66569ec232f03e9b4"],"semantic_review":false,"source":"documents/introduction/sections/001-section-what-this-is-about-the-jump-in-construction-prin.tex","status_markers_as_written":["\\mC","\\mE","\\mO","\\mX"],"summary_excerpt":"Topological Fixed-Point Theory (TFPT) constructs, from exactly two inputs — a boundary constant [formula in source] (P1) and a five-slot carrier [formula in source] (P2) — a discrete compiler for the Standard-Model skeleton: the gauge group, three families, hypercharges and the flavor matrix, with [formula in source] ( [formula in source] ) as the consistency checksum. 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Three landmarks fix the coordinates. 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Deterministic, resource-bounded ge","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Three shared instincts","topic_suggestions":[]},{"byte_end":4960,"byte_start":2604,"id":"section:a3c39161cb6715a6d469","kind":"subsection","labels":[],"line_end":69,"line_start":38,"occurrence":1,"owner_documents":["document:introduction"],"relation_ids":["relation:38cb361308a4ae075a94"],"semantic_review":false,"source":"documents/introduction/sections/004-section-tfpt-in-the-light-of-algorithmic-physics-zuse-sc.tex","status_markers_as_written":[],"summary_excerpt":"One forced program, not an ensemble. Schmidhuber's shortest program computes all universes and privileges none; TFPT bets the opposite — an over-determined bootstrap fixed point that forces a single dimensionless skeleton ( [formula in source] fixed three independent ways). TFPT is a candidate for the short program of our constants, not a measure over programs. The description language is algebraic. TFPT's compressio","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Three deliberate divergences","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"}]},{"byte_end":6283,"byte_start":4960,"id":"section:f83ead6f871a1031922f","kind":"section","labels":[],"line_end":87,"line_start":70,"occurrence":1,"owner_documents":["document:introduction"],"relation_ids":[],"semantic_review":false,"source":"documents/introduction/sections/004-section-tfpt-in-the-light-of-algorithmic-physics-zuse-sc.tex","status_markers_as_written":[],"summary_excerpt":"Plausibility balance. Pro: (a) two inputs instead of many; (b) [formula in source] to [formula in source] (CODATA-2022, [formula in source] ) as a fixed point, not a fit; (c) [formula in source] constructed, not postulated; (d) one compiler generates several sectors [formula in source] fewer degrees of freedom, more predictive power. Contra/open: what remains are only standard steps (cluster expansion in the thermody","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Does this make the theory more probable?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"}]},{"byte_end":11562,"byte_start":6283,"id":"section:a0cca10d374154aa32f7","kind":"section","labels":[],"line_end":158,"line_start":88,"occurrence":1,"owner_documents":["document:introduction"],"relation_ids":["relation:0e0c84e830b971e3b06a","relation:0e90e3a22819b554a3a8","relation:229ff484c451be90c807","relation:371d2187d1a68e9e0e21","relation:464c617b86a599037203","relation:91480e1132415321c921","relation:a7b1274aa891eb9f1fb1","relation:c2b0479526206c67e921","relation:c2fb2ca8d6bbb33d1f83","relation:d0ec81187b50466414a5","relation:d71727083732a43a8e17","relation:e079e7119823b04a8079","relation:f2a217ab3ae28a6ae984","relation:f5377ea91e3472c2c4e2","relation:fc4aefb3f2f682bc6126"],"semantic_review":false,"source":"documents/introduction/sections/004-section-tfpt-in-the-light-of-algorithmic-physics-zuse-sc.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"Because one generator now sits behind the numbers, the theory makes a set of concrete, falsifiable statements that running or near-term experiments are actively testing. Each row gives the TFPT value, the new derivation behind it, the experiment, and an honest status.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Predictions for running and upcoming experiments","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":12413,"byte_start":11562,"id":"section:8fc4dd2cee34206067e0","kind":"section","labels":[],"line_end":170,"line_start":159,"occurrence":1,"owner_documents":["document:introduction"],"relation_ids":[],"semantic_review":false,"source":"documents/introduction/sections/004-section-tfpt-in-the-light-of-algorithmic-physics-zuse-sc.tex","status_markers_as_written":[],"summary_excerpt":"tocsectionConclusion TFPT's sectors form an impressive collection of closures sharing common numbers. The compiler closure explains why they are the same numbers: a small discrete generator [formula in source] builds, from two inputs [formula in source] via [formula in source] , the [formula in source] container and outputs the Standard Model, the constants and the scale grammar from there. The theory thereby becomes","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conclusion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":15362,"byte_start":12413,"id":"section:e77e5218c82783443690","kind":"section","labels":["fig:script-timeline"],"line_end":214,"line_start":171,"occurrence":1,"owner_documents":["document:introduction"],"relation_ids":["relation:0e741ed67655839a121a","relation:104faa58a312a5b65a8d","relation:1509cbadafcd7f1786bc","relation:2f0d812b45d70ace7c67","relation:581a1ed162551cacd039","relation:5be26566276b06193703","relation:633cae2e14c8d0555d8c","relation:7ccc11747aef2e9ecf6e","relation:83a047ce310aea706d7f","relation:93e7069af682703061bb","relation:946f550e69245d770b5c","relation:9ff5905ad8d2ad12acee","relation:a69cf455b84a41beeb8c","relation:abd758f15d4eee422fa9","relation:bee8a888c71b63b92bd5","relation:cd304b5dbfc208872dd3","relation:d8a4ba4b7bd47ac646db","relation:dadf533b1762fbab7ef6","relation:e447680752913986bb12","relation:ea616c7ee934712d0a0d"],"semantic_review":false,"source":"documents/introduction/sections/004-section-tfpt-in-the-light-of-algorithmic-physics-zuse-sc.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"Every claim in this document marked \\ (exact identity), \\ (Lie/lattice theorem) or \\ (numerical fixed point) is re-derived from the two axioms [formula in source] alone by a small, self-contained Python suite in the repository folder verification/. The inline references [verification/ [formula in source] ] throughout the documents point to the exact script; the table below is the master map (its source is the shared ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Appendix: computational verification (reproducibility)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":1765,"byte_start":0,"id":"section:a3f71cd206278c1f0330","kind":"frontmatter","labels":[],"line_end":46,"line_start":1,"occurrence":1,"owner_documents":["document:note_e8_gaussian_code"],"relation_ids":["relation:11d6f14959d63a9108da","relation:11f7a11e2b4dfae790ed","relation:19c7ab2fb560f5f4ea36","relation:2d77cd4531fb88b82de0","relation:3d29ca474c0835642f0c","relation:502f5d6381dfe587ea1f","relation:bfa728ed6e959482d8e4","relation:d9ec2410ecf78ab32442"],"semantic_review":false,"source":"documents/note_e8_gaussian_code/preamble.tex","status_markers_as_written":[],"summary_excerpt":"theoremTheorem lemma[theorem]Lemma corollary[theorem]Corollary remark remark[theorem]Remark","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Gaussian code bridge: [formula in source] over [formula in source] , the extended Hamming code, and a four-bit information layer","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"}]},{"byte_end":2475,"byte_start":0,"id":"section:f4e943b21e562624ca63","kind":"frontmatter","labels":[],"line_end":46,"line_start":1,"occurrence":1,"owner_documents":["document:note_e8_gaussian_code"],"relation_ids":[],"semantic_review":false,"source":"documents/note_e8_gaussian_code/sections/001-section-the-three-objects-label-sec-setup.tex","status_markers_as_written":[],"summary_excerpt":"Build the [formula in source] lattice by Construction A over the extended Hamming code [formula in source] , placed equivariantly with respect to four fixed coordinate pairs, and let [formula in source] be the complex structure that rotates each pair ( [formula in source] , [formula in source] ). Then [formula in source] becomes a unimodular Hermitian [formula in source] -lattice of rank [formula in source] , and red","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"}]},{"byte_end":2521,"byte_start":2475,"id":"section:24a19aa2c4d8f6248f58","kind":"section","labels":["sec:setup"],"line_end":48,"line_start":47,"occurrence":1,"owner_documents":["document:note_e8_gaussian_code"],"relation_ids":[],"semantic_review":false,"source":"documents/note_e8_gaussian_code/sections/001-section-the-three-objects-label-sec-setup.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"The three objects","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"}]},{"byte_end":3841,"byte_start":2521,"id":"section:9cfcbfb68fe8471a4d4f","kind":"subsection","labels":[],"line_end":73,"line_start":49,"numbered_or_version_tokens_as_written":["I0.1"],"occurrence":1,"owner_documents":["document:note_e8_gaussian_code"],"relation_ids":[],"semantic_review":false,"source":"documents/note_e8_gaussian_code/sections/001-section-the-three-objects-label-sec-setup.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the extended Hamming code [formula in source] — the unique doubly-even self-dual binary code of length [formula in source] , permutation equivalent to the first-order Reed–Muller code [formula in source] MS77. Its automorphism group has order [formula in source] , so [formula in source] admits exactly [formula in source] distinct placements (coordinate images) inside [formula in source] . F","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The code and its equivariant placement","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"}]},{"byte_end":4663,"byte_start":3841,"id":"section:cb914e5798258017a1a2","kind":"subsection","labels":["eq:douleven"],"line_end":89,"line_start":74,"occurrence":1,"owner_documents":["document:note_e8_gaussian_code"],"relation_ids":[],"semantic_review":false,"source":"documents/note_e8_gaussian_code/sections/001-section-the-three-objects-label-sec-setup.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the Construction-A lattice of [formula in source] CS99, with the standard inner product [formula in source] of [formula in source] . Then [formula in source] , and since [formula in source] is doubly even, writing [formula in source] with [formula in source] a codeword lift gives so every nonzero [formula in source] has [formula in source] : the minimum of [formula in source] is [formula in","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The lattice","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"}]},{"byte_end":6940,"byte_start":4663,"id":"section:e200cccfccb890e62271","kind":"subsection","labels":["lem:herm"],"line_end":135,"line_start":90,"numbered_or_version_tokens_as_written":["I0.2","I0.3"],"occurrence":1,"owner_documents":["document:note_e8_gaussian_code"],"relation_ids":["relation:0277cbfffb07f390474d","relation:9760ab8b13538fb07878","relation:a7b451084b20b5d2e37c","relation:abece7ec231f83127a95","relation:e1e4a99b98e3c78fe956"],"semantic_review":false,"source":"documents/note_e8_gaussian_code/sections/001-section-the-three-objects-label-sec-setup.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] rotate each [formula in source] pair, [formula in source] , and let [formula in source] be the pair [formula in source] -cycle [formula in source] , [formula in source] , fixing [formula in source] . Then (machine checks I0.2–I0.3; Lean theorems J_sq, J_skew, sigma_cubed_ambient, J_sigma_commute, lattice_J, lattice_sigma) [formula in source] where the last two use precisely the [formula in sou","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The complex structure and the clock","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":11232,"byte_start":6940,"id":"section:080a8e1bc2a51ba0adbf","kind":"section","labels":["rem:placement","sec:census","thm:census"],"line_end":226,"line_start":136,"numbered_or_version_tokens_as_written":["I2.2","I2.3","I2.5","I4.1","I4.2","I5.1"],"occurrence":1,"owner_documents":["document:note_e8_gaussian_code"],"relation_ids":["relation:12b7f43bf8a3ee7c149f","relation:45d4511c8f666eea1ec4","relation:530c2ffdde060bf3fc82","relation:61e6ff4aa3c303441e48","relation:7f5624330fc5d847194f","relation:80e7848016c773bd4e0d","relation:8f4e87025c0d5a173357","relation:cfd391a48dc42c71bac2","relation:d6a128882937f25d2caf","relation:fe36ef02abdfb9c2d8ba"],"semantic_review":false,"source":"documents/note_e8_gaussian_code/sections/001-section-the-three-objects-label-sec-setup.tex","status_markers_as_written":[],"summary_excerpt":"All checks of this section are from gaussian_code_bridge_probe.py ( [formula in source] checks, [formula in source] failures, verdict gaussian-code-bridge-exact; exact integer and Fraction arithmetic throughout, sympy only for the Smith normal form), with the finite certificates re-proved by the Lean kernel in GaussianCodeBridge.lean.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The four-bit quotient and the [formula in source] 15 x 16 census","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":16044,"byte_start":11232,"id":"section:5d71fdfd1d43434581f5","kind":"section","labels":["rem:notmod2","sec:info","thm:info"],"line_end":326,"line_start":227,"numbered_or_version_tokens_as_written":["I3.1","I3.2","I3.3"],"occurrence":1,"owner_documents":["document:note_e8_gaussian_code"],"relation_ids":["relation:00291f1876c2add44e58","relation:02f0f81f09a5b47c1154","relation:3618003c7bb75f63d6ed","relation:3f777288842b76cfb20c","relation:62984184cd5901d0002b","relation:94815eef5b266d7563d8","relation:b4ce76f3c87a70d60fb1","relation:b64cc1b59805d368d186","relation:b87b5df9e6e5bf83582a","relation:c36e6c7e07f25d101c3f","relation:d97f2d932abd8a37a994","relation:f20b3a17b4956f4e9e82"],"semantic_review":false,"source":"documents/note_e8_gaussian_code/sections/001-section-the-three-objects-label-sec-setup.tex","status_markers_as_written":[],"summary_excerpt":"Since [formula in source] is [formula in source] -linear and preserves [formula in source] , it preserves [formula in source] and descends to an [formula in source] -linear map [formula in source] on [formula in source] . (Well-definedness is itself a kernel certificate: the transport matrix of [formula in source] into Smith coordinates has even top-right block, Lean theorem sigma_label_block.)","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The information layer","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":3729,"byte_start":0,"id":"section:4924c7863d81853eba3d","kind":"section","labels":["rem:c7-audit","sec:coxeter-chars"],"line_end":93,"line_start":1,"occurrence":1,"owner_documents":["document:note_e8_gaussian_code"],"relation_ids":["relation:476b957f73298d672cc7"],"semantic_review":false,"source":"documents/note_e8_gaussian_code/sections/002-section-explicit-character-basis-of-the-eight-coxeter-ch.tex","status_markers_as_written":["[E]"],"summary_excerpt":"The exponents of [formula in source] are the totatives [formula in source] of the Coxeter number [formula in source] . As a multiplicative group this set has element orders [formula in source] in that listing — explicitly the pairs (unit, order) [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Explicit character basis of the eight Coxeter channels and the [formula in source] C2 x C4 audit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":4349,"byte_start":3729,"id":"section:26d581cb73120967ff17","kind":"section","labels":["sec:quartic"],"line_end":106,"line_start":94,"occurrence":1,"owner_documents":["document:note_e8_gaussian_code"],"relation_ids":["relation:7b4bde504d710aa21a82","relation:aaf34481934272183e65"],"semantic_review":false,"source":"documents/note_e8_gaussian_code/sections/002-section-explicit-character-basis-of-the-eight-coxeter-ch.tex","status_markers_as_written":[],"summary_excerpt":"All checks of this section are from quartic_half_probe.py ( [formula in source] checks, [formula in source] failures, verdict quartic-half-alive; exact Gaussian-integer and Gaussian-rational arithmetic, no floats anywhere), run in the standard doubled-coordinate model of [formula in source] (roots [formula in source] and [formula in source] with an even number of minus signs; norm [formula in source] ), which by Rema","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The quartic companion: [formula in source] G31 as the holomorphic [formula in source] mu4 shadow","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"}]},{"byte_end":5794,"byte_start":4349,"id":"section:27d62a1a418feeaac9ff","kind":"subsection","labels":[],"line_end":133,"line_start":107,"numbered_or_version_tokens_as_written":["II3.1"],"occurrence":1,"owner_documents":["document:note_e8_gaussian_code"],"relation_ids":[],"semantic_review":false,"source":"documents/note_e8_gaussian_code/sections/002-section-explicit-character-basis-of-the-eight-coxeter-ch.tex","status_markers_as_written":[],"summary_excerpt":"The exponents of [formula in source] are [formula in source] , the totatives of the Coxeter number [formula in source] Bou68. The character [formula in source] (residue mod [formula in source] ) splits them: the exponents [formula in source] are [formula in source] , and shifted by [formula in source] , [formula in source] the degree quadruple of the rank- [formula in source] complex reflection group [formula in sour","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The degree bookkeeping","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"}]},{"byte_end":10000,"byte_start":5794,"id":"section:636458c5f2b1b281e60a","kind":"subsection","labels":["thm:quartic"],"line_end":210,"line_start":134,"numbered_or_version_tokens_as_written":["II2.1","II2.2","II2.3","II2.5","II2.6","II3.2","II3.3","II3.5"],"occurrence":1,"owner_documents":["document:note_e8_gaussian_code"],"relation_ids":["relation:21c1bcd2d6a332378ee6","relation:239f02851c78ed9971cb","relation:2ea4b9645b1027ac996b","relation:3ded6cb96fe42c05b63e","relation:4c227fb21c00958dcede","relation:77d17ba7cd66ba629190","relation:849b3ee1015820fd8a8b","relation:9eac566f484cc84b6f4c","relation:aeb5a78b3762d4089530","relation:b55f3ebfead8f4b62175","relation:d79681e466ced1585afb","relation:d98ca480690f92e7c63d","relation:fee5fab671fadcc9c068"],"semantic_review":false,"source":"documents/note_e8_gaussian_code/sections/002-section-explicit-character-basis-of-the-eight-coxeter-ch.tex","status_markers_as_written":[],"summary_excerpt":"For [formula in source] let [formula in source] , summed over the [formula in source] roots, and let [formula in source] denote the restriction to [formula in source] , computed in the holomorphic weights [formula in source] , [formula in source] . Write [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The restriction theorem","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"}]},{"byte_end":12238,"byte_start":10000,"id":"section:66e6a3a06805473c0c05","kind":"subsection","labels":[],"line_end":252,"line_start":211,"numbered_or_version_tokens_as_written":["I4.1","I4.2","I4.3","I4.4"],"occurrence":1,"owner_documents":["document:note_e8_gaussian_code"],"relation_ids":[],"semantic_review":false,"source":"documents/note_e8_gaussian_code/sections/002-section-explicit-character-basis-of-the-eight-coxeter-ch.tex","status_markers_as_written":[],"summary_excerpt":"A structure claim needs controls that destroy it. Four are run (probe II4, all firing as demanded): Honest negative first. The natural candidate control — flipping the orientation of one pair, [formula in source] — does not fire: [formula in source] with the even sign flip [formula in source] , so [formula in source] preserves all [formula in source] roots. No signed-permutation complex structure can break root compa","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Must-fail controls","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"}]},{"byte_end":12294,"byte_start":12238,"id":"section:d86613b080270239c815","kind":"section","labels":["sec:verification"],"line_end":254,"line_start":253,"occurrence":1,"owner_documents":["document:note_e8_gaussian_code"],"relation_ids":[],"semantic_review":false,"source":"documents/note_e8_gaussian_code/sections/002-section-explicit-character-basis-of-the-eight-coxeter-ch.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Machine verification","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":14068,"byte_start":12294,"id":"section:0ee9c6150b29e6e55585","kind":"subsection","labels":[],"line_end":294,"line_start":255,"numbered_or_version_tokens_as_written":["I1.5","I5.1","II3.3"],"occurrence":1,"owner_documents":["document:note_e8_gaussian_code"],"relation_ids":["relation:1aebc4832fb6a9d4100f","relation:45c6454e17552adab088","relation:4861dfa9ee3e60dbe550","relation:7cb6d13f16100cb62ca9","relation:c05617987ce1c5a17880"],"semantic_review":false,"source":"documents/note_e8_gaussian_code/sections/002-section-explicit-character-basis-of-the-eight-coxeter-ch.tex","status_markers_as_written":[],"summary_excerpt":"@lccl@ probe & checks & verdict & arithmetic\\\\ gaussian_code_bridge_probe.py & [formula in source] & gaussian-code-bridge-exact & exact [formula in source] / Fraction; SNF via sympy\\\\ quartic_half_probe.py & [formula in source] & quartic-half-alive & exact [formula in source] / [formula in source] ; no floats\\\\ Both probes cross-validate their own machinery: the class map is computed twice (Hermite-normal-form labels","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The two probes","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"}]},{"byte_end":16042,"byte_start":14068,"id":"section:b38d0ecf7978648868bf","kind":"subsection","labels":[],"line_end":328,"line_start":295,"occurrence":1,"owner_documents":["document:note_e8_gaussian_code"],"relation_ids":["relation:50c2734aaf4cfadcfe14","relation:ee09680fb5f8ff9f1d97"],"semantic_review":false,"source":"documents/note_e8_gaussian_code/sections/002-section-explicit-character-basis-of-the-eight-coxeter-ch.tex","status_markers_as_written":[],"summary_excerpt":"The algebraic cores are formalized in two Lean 4 modules over Mathlib Moura21,mathlib, committed to the repository's Lean project ( lake build green, no sorry, no native_decide): GaussianCodeBridge.lean ( [formula in source] theorems) and QuarticHalf.lean ( [formula in source] theorems), [formula in source] kernel-checked theorems in total. 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the \\ premise stays unmoved. Dated addendum (2026-08-12, rounds 69–71): the successor contract is closed, and the answ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20954,"byte_start":18454,"id":"section:c68324ae80af75afdb89","kind":"section","labels":["fig:duality"],"line_end":301,"line_start":244,"occurrence":1,"owner_documents":["document:tfpt_1_architecture_e8"],"relation_ids":["relation:3db353d5b8050280c68e","relation:6cc43ff82035dfc3383d","relation:91df2859fbb37a00f032","relation:a9f0fb3a9853cde69d3b","relation:dfa2275df87d1751d2e4"],"semantic_review":false,"source":"documents/tfpt_1_architecture_e8/sections/004-source.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"The strongest new statement is that three of the theory's separate structures are the same truncated row of Pascal's triangle on the five-slot carrier.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Headline: the Pascal compiler on five carrier slots","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"}]},{"byte_end":24417,"byte_start":20954,"id":"section:33a1154dc0cb4b2f67f8","kind":"subsection","labels":[],"line_end":350,"line_start":302,"occurrence":1,"owner_documents":["document:tfpt_1_architecture_e8"],"relation_ids":["relation:21c3c023098b340e958f","relation:2af5fab145bed5200f06","relation:2dcc847498bb95690e17","relation:5f641933b0231b843a92","relation:9f9ce5e2f57f5a7ae9a4","relation:a47c7ace891fc50daabc","relation:b25c6f64405372b73dce","relation:b9a73100c6ea088c4605","relation:d8e0105ed16fae7f0aa0","relation:dbaee85f61ac50508fcb"],"semantic_review":false,"source":"documents/tfpt_1_architecture_e8/sections/004-source.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"A family is exactly the complete Pascal truncation to degree two: the unique positive-integer solution of [formula in source] . Proof of uniqueness. Direct evaluation gives [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] ; so [formula in source] is the only root in [formula in source] . For [formula in source] the forward difference is ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[formula in source] as the Pascal closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":25258,"byte_start":24417,"id":"section:e2ac56d63dc5b474ddb4","kind":"subsection","labels":[],"line_end":366,"line_start":351,"occurrence":1,"owner_documents":["document:tfpt_1_architecture_e8"],"relation_ids":["relation:e5f8f945e45819bfa2b2"],"semantic_review":false,"source":"documents/tfpt_1_architecture_e8/sections/004-source.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"With [formula in source] , the quadratic hypercharge trace on one family is [formula in source] , and it generates the whole integer chain: The flavor budget, the [formula in source] budget, the [formula in source] count and the second seam defect all hang on the second hypercharge moment [formula in source] . \\ Round-22 sharpening: the moment itself is one symbolic identity, [formula in source] — the Coxeter number ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"One master moment generates [formula in source] , [formula in source] , [formula in source] , [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":613,"byte_start":0,"id":"section:87aef64679791ec15f2e","kind":"subsection","labels":[],"line_end":12,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_1_architecture_e8/sections/005-source.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"with [formula in source] and [formula in source] . . 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The one-generation spinor packet is the even exterior algebra, equivalently the even-weight binary code The two carrier roots [formula in source] , [formula in source] generate all hypercharges ( [formula in source] , [formula in source] , [formula in","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Theorem 1 — the even carrier code","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"}]},{"byte_end":6000,"byte_start":2203,"id":"section:52f95907d935acc58bce","kind":"section","labels":[],"line_end":93,"line_start":35,"occurrence":1,"owner_documents":["document:tfpt_1_architecture_e8"],"relation_ids":["relation:1bb4aa4614fc34399ff3","relation:ba2b90f06351200b7f09"],"semantic_review":false,"source":"documents/tfpt_1_architecture_e8/sections/010-source.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"tocsectionTheorem 2 On [formula in source] the flip [formula in source] is even, so [formula in source] . The three relations [formula in source] form a symmetric association scheme (the even Hamming scheme on five bits) with The eigenvalues (computed directly) are [formula in source] and [formula in source] , with [formula in source] . The two graphs are named objects: The Standard-Model family is the valency side [","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Theorem 2 — Exterior–Action Duality","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"}]},{"byte_end":6713,"byte_start":6000,"id":"section:4b3c5060d4ff767121af","kind":"section","labels":[],"line_end":106,"line_start":94,"occurrence":1,"owner_documents":["document:tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_1_architecture_e8/sections/010-source.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"tocsectionTheorem 3 Requiring the even family to equal the action truncation through pair degree, [formula in source] , i.e. the unique positive-integer solution. At [formula in source] the two sides equal [formula in source] , so carrier exhaustion [formula in source] and the Coxeter period [formula in source] coincide only at five slots: [formula in source] and [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Theorem 3 — the Coxeter closure equation selects [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":7716,"byte_start":6713,"id":"section:1db99873008626f68f5f","kind":"section","labels":[],"line_end":125,"line_start":107,"occurrence":1,"owner_documents":["document:tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_1_architecture_e8/sections/010-source.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"tocsectionTheorem 4 From the three atoms [formula in source] , with [formula in source] and [formula in source] : The [formula in source] exponents are the primitive residues modulo [formula in source] , and [formula in source] . The local SM algebra and the root atlas are the two arithmetic projections of [formula in source] :","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Theorem 4 — the [formula in source] cyclotomic Coxeter compiler","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"}]},{"byte_end":9583,"byte_start":7716,"id":"section:9429252f6109289f9248","kind":"section","labels":[],"line_end":151,"line_start":126,"occurrence":1,"owner_documents":["document:tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_1_architecture_e8/sections/010-source.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"tocsectionTheorem 5 The directed even-flips of [formula in source] are the complete graph [formula in source] : ( [formula in source] .) So the positive [formula in source] roots are the unordered transitions of one family; the second hypercharge moment, the positive-root count and the sum of the [formula in source] exponents coincide at [formula in source] . The CP pairing [formula in source] of the exponents gives ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Theorem 5 — the root transition atlas and the positive-edge moment","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"}]},{"byte_end":14366,"byte_start":9583,"id":"section:13d2bafb9d80869cd4a2","kind":"section","labels":[],"line_end":227,"line_start":152,"occurrence":1,"owner_documents":["document:tfpt_1_architecture_e8"],"relation_ids":["relation:25122e07d334709a2266","relation:289c81f95c590920d0d5","relation:3fb8be5f7d4f57be9c13","relation:62542a43de715e5ec7c1"],"semantic_review":false,"source":"documents/tfpt_1_architecture_e8/sections/010-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"tocsectionTheorem 6 All discrete budgets and the seam seed are functions of [formula in source] : Two-graph product table. With the carrier-pair graph [formula in source] ( [formula in source] ) and the family-corner graph [formula in source] on [formula in source] ( [formula in source] , [formula in source] ), every large budget is a product of the two graphs: i.e.\\ ( [formula in source] , [formula in source] , [for","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Theorem 6 — downstream readouts from [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":16686,"byte_start":0,"id":"section:6b49d8830dc9fa3948be","kind":"section","labels":[],"line_end":248,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_1_architecture_e8"],"relation_ids":["relation:06265f8ab51f5ec3e072","relation:0797fc7a62ad710f1b14","relation:0c77fb3a5e969c5cb8d7","relation:0ff5ef841d1bc900db1f","relation:16e145a4eccf2fb302bb","relation:1983b9c04b160b4b3cc4","relation:1b838b683671f125f227","relation:1ea45314d5ded6ff30bf","relation:1ebf40586850d648fde6","relation:1edbd2fd04a37c37e0fa","relation:20711b8724497b44403e","relation:2788ebc3b59470d4fbbe","relation:2d8bbb923c2da333700d","relation:3496c86a7df3c716cbdb","relation:3f9d6a1d540c7192d533","relation:46b383549b48d33c4698","relation:4784d3b7a4a99f4eae16","relation:4c50002f0a6b9c6ec29d","relation:4e0e9a30290081e2e176","relation:576a809ef3e672395b9d","relation:64bfaebbe99b18bcea10","relation:76af6e331d7a56bcdb88","relation:7d785ceb555240d31a9c","relation:7f34863cae88d9dc4c73","relation:7ff7cc35436e99772dbd","relation:91ed792e64a04496c4ec","relation:98ce99c167c0bfa3f88d","relation:a95b6cb7086f55c70b02","relation:afa691cc4af0bda9d9e0","relation:b49ba8416383c356ef07","relation:b663b66c984168cbe191","relation:d17face8609d7cb35f00","relation:d2b4a5d384f1a9655c1f","relation:d8644a9eed5ce2e3f0a3","relation:e028418b2ebaa835f62f","relation:ee453135e53a540e238a","relation:eef8f4b51529c87dab0a","relation:f2417b616dffc1003ec6","relation:fc190a0aca2340888fd3","relation:fed7281064df567ad8e8"],"semantic_review":false,"source":"documents/tfpt_1_architecture_e8/sections/011-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"tocsectionTheorem 7 Since [formula in source] , one has the standard chain [formula in source] , with the exact branching (verified dimensions and root/weight counts): The adjoint [formula in source] of [formula in source] is [formula in source] and its spinor [formula in source] is [formula in source] . The TFPT dictionary makes each summand a known object: @llY@ piece & value & TFPT reading \\\\ [formula in source] &","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Theorem 7 — the [formula in source] lift of the [formula in source] atlas","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":20770,"byte_start":16686,"id":"section:5d8f619883df80c56b36","kind":"section","labels":[],"line_end":305,"line_start":249,"occurrence":1,"owner_documents":["document:tfpt_1_architecture_e8"],"relation_ids":["relation:2c4963b2fb5598c2858d","relation:2d34ca54f49e0aea7127","relation:a45802863419991fc6f8","relation:b1dafa85aabb2a0e429a","relation:ba953e67d6c017c7572b","relation:e5a5f49ac62595bd0078"],"semantic_review":false,"source":"documents/tfpt_1_architecture_e8/sections/011-source.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"tocsectionTheorem 8 — anchor microcode The parabolic flavor bundle [formula in source] on [formula in source] has splitting type [formula in source] , whose power sums [formula in source] generate the whole compiler budget:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Theorem 8 — the [formula in source] anchor microcode and the [formula in source] -ladder","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"}]},{"byte_end":24530,"byte_start":20770,"id":"section:2e4cf2c588758ec271e5","kind":"section","labels":[],"line_end":355,"line_start":306,"occurrence":1,"owner_documents":["document:tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_1_architecture_e8/sections/011-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"tocsectionMaster statement Five carrier slots give [formula in source] ,\\ four family corners give [formula in source] ,\\ and [formula in source] gives the [formula in source] atlas. Equivalently: [formula in source] , [formula in source] , [formula in source] ; [formula in source] , [formula in source] , the [formula in source] Coxeter structure and the action ladder read the same five-slot pair-decuple. The Standar","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Master statement and status","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":2740,"byte_start":0,"id":"section:765932d91e413167324a","kind":"section","labels":[],"line_end":47,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_1_architecture_e8/sections/012-source.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"The lift is reproducible by a short script (all entries below verified exactly).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Appendix: machine-checkable [formula in source] construction","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6368,"byte_start":2740,"id":"section:425aba2c23ff1800a427","kind":"part","labels":["fig:ablation","sec:ablation"],"line_end":119,"line_start":48,"occurrence":1,"owner_documents":["document:tfpt_1_architecture_e8"],"relation_ids":["relation:5ed6461bbfe36131a05d"],"semantic_review":false,"source":"documents/tfpt_1_architecture_e8/sections/012-source.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"The single sharpest reviewer test is: was the closure [formula in source] engineered so that [formula in source] comes out? 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It follows from three purely structural facts plus reflection positivity on the admissible branch:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"(3) Strong CP — decoupled from the mass-gap problem /","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":14380,"byte_start":6915,"id":"section:a29d0e884b184665e5ef","kind":"subsection","labels":[],"line_end":179,"line_start":92,"occurrence":1,"owner_documents":["document:tfpt_2_standard_model"],"relation_ids":["relation:03febb5e4b741e8a4677","relation:11bf69c973e3f43c8fc0","relation:1f20912a4e1d5e1bf73c","relation:2482cad9d835fae2ce43","relation:29d5a54a9f699feccf4e","relation:2ff40c32a80dfe9298ee","relation:3b16180e42f851c5cb1a","relation:482b627bd4f76895264c","relation:5500816d1d91d7f5b738","relation:84c8b8845753f5983a5d","relation:868e43e86abd3357d840","relation:8f7225e5a7a62a096b81","relation:98842114e63d68494dac","relation:a42a19ee42602433cb8d","relation:a770bf1f7a7b209e5e41","relation:b50b9a00359628d01209","relation:bcd1c293c50ffb342a28","relation:c36cf95a1f6060567a5b","relation:c624f3a2819b5ab0d960","relation:daa03b25a1afdc094c7c","relation:deedff1974c3f8fff1d1","relation:e643adad9a09318748e3","relation:fac31eadb5234972e6bf","relation:ff322991623a313a710d"],"semantic_review":false,"source":"documents/tfpt_2_standard_model/sections/007-subsection-2-gravity-the-classical-covariant-field-equat.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"This is the constructive QFT closure of the admissible physical sector — not the unprojected ambient theory: the unprojected ambient metric measure is not constructed here and remains the [formula in source] frontier item ( ambient QG). 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The Lean 4 proof ( lean4-carrier-rigidity, toolchain v4.29.1 [formula in source] Mathlib) builds cleanly: @lY@ Verified (Lean, 0 sorry) & Content \\\\ Polarization.sixY_carrier_polynomial & [formula in source] as a corollary of orthogonal idempotents \\\\ Rigidity.unique_carrier_pair & [formula in source] unique (integer rigidity) \\\\ Hypercharge.trace_Y, _carrier_polynomial &","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"(5) Axioms P1/P2 — P2 machine-verified, P1 as an interface /","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":21153,"byte_start":18807,"id":"section:b43296dde4735e40a025","kind":"section","labels":[],"line_end":278,"line_start":244,"occurrence":1,"owner_documents":["document:tfpt_2_standard_model"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_2_standard_model/sections/007-subsection-2-gravity-the-classical-covariant-field-equat.tex","status_markers_as_written":[],"summary_excerpt":"The same numbers, now as closed expressions instead of distributed theorems:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"How the original-paper predictions simplify","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"}]},{"byte_end":23471,"byte_start":21153,"id":"section:be245dd6a6eb1776e773","kind":"section","labels":[],"line_end":304,"line_start":279,"occurrence":1,"owner_documents":["document:tfpt_2_standard_model"],"relation_ids":["relation:0453e4aade6a0d01d470","relation:1184469773986f401310","relation:11ad84e6677a89c19385","relation:20da047258f0b04a3b63","relation:3c1db06366d3d16ad5f8","relation:3f13114f6dbe4dbb8a2e","relation:8a91a37af3229ba538f7","relation:d8b5262af8327018957d","relation:e2198a3e614794a1849f","relation:e49aaa11e4a77588a39a"],"semantic_review":false,"source":"documents/tfpt_2_standard_model/sections/007-subsection-2-gravity-the-classical-covariant-field-equat.tex","status_markers_as_written":["\\mC"],"summary_excerpt":"tocsectionConclusion The simplification is substantial: the discrete Standard-Model structure (charges, families, flavor operators) is derived under the axioms; [formula in source] D existence, chiral measure, mirror gap, couplings and neutrino dynamics are open. The [formula in source] -ladder formula [formula in source] with one seed [formula in source] and one fixed residue matrix whose spectral invariants ( [form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conclusion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":26949,"byte_start":23471,"id":"section:4842f867b01b3a29625f","kind":"part","labels":[],"line_end":349,"line_start":305,"occurrence":1,"owner_documents":["document:tfpt_2_standard_model"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_2_standard_model/sections/007-subsection-2-gravity-the-classical-covariant-field-equat.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"This note closes the last structural gap of the [formula in source] compiler by deriving the charged-fermion transport word-lengths [formula in source] , [formula in source] , [formula in source] — equivalently the residue triple [formula in source] and its [formula in source] orbit — from first principles, rather than from the legacy resolvent construction. The correct framework is parabolic Higgs/bundle theory on t","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The flavor block: parabolic weights and the transport theorem","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"}]},{"byte_end":3085,"byte_start":0,"id":"section:94523e5f47098f45239e","kind":"section","labels":[],"line_end":49,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_2_standard_model"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_2_standard_model/sections/008-section-the-setup-parabolic-data-on-the-family-curve.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"The family curve is the rigid four-punctured sphere [formula in source] , [formula in source] (the flavor construction above). The flavor bundle is a rank- [formula in source] parabolic bundle [formula in source] on [formula in source] . At each puncture the local monodromy is the order- [formula in source] cusp class with eigenvalues [formula in source] , [formula in source] ; by the Mehta–Seshadri dictionary the co","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The setup: parabolic data on the family curve","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":5212,"byte_start":3085,"id":"section:c491ce4d24c1e7428721","kind":"section","labels":[],"line_end":86,"line_start":50,"occurrence":1,"owner_documents":["document:tfpt_2_standard_model"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_2_standard_model/sections/008-section-the-setup-parabolic-data-on-the-family-curve.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"For a unitary (flat) family local system, [formula in source] is parabolic-polystable of parabolic degree zero (Mehta–Seshadri). With full flags and weights [formula in source] at each of the four punctures, The balanced (stable) underlying splitting is therefore [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Exact scaffolding (proved)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":7232,"byte_start":5212,"id":"section:075d23efb7b920a44ee1","kind":"section","labels":[],"line_end":114,"line_start":87,"occurrence":1,"owner_documents":["document:tfpt_2_standard_model"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_2_standard_model/sections/008-section-the-setup-parabolic-data-on-the-family-curve.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"Constructing the rigid [formula in source] -symmetric local system explicitly (four monodromies [formula in source] , [formula in source] , [formula in source] ), the closure [formula in source] is solvable to machine precision, and the unique rotation [formula in source] has eigenvalues [formula in source] : the [formula in source] Coxeter element. \\ This independently reproduces the corner-rotation [formula in sour","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Riemann–Hilbert side (what the monodromy fixes)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":11567,"byte_start":7232,"id":"section:95ef9c8e927ef9e25379","kind":"section","labels":[],"line_end":172,"line_start":115,"occurrence":1,"owner_documents":["document:tfpt_2_standard_model"],"relation_ids":["relation:4864e1fe47eaf76f1832","relation:89aa021035433704a417","relation:9f7f548b1346b2aac8cc","relation:ba53c8877c81499a8c6a"],"semantic_review":false,"source":"documents/tfpt_2_standard_model/sections/008-section-the-setup-parabolic-data-on-the-family-curve.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"Status (no drift). The splitting type is now closed: the unique partition [formula in source] fixes the anchor and [formula in source] fixes the residue branch (verified, below and v4_flavor_matrix.py), and the solar texture is built ( v9_neutrino_texture.py). The roadmap below is kept as the derivation record of how [formula in source] is obtained; it is no longer an open project. The only residual is the parabolic ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The parabolic-weight computation (resolved this round)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":18665,"byte_start":11567,"id":"section:74bb3766bdd1275dbd78","kind":"section","labels":[],"line_end":272,"line_start":173,"occurrence":1,"owner_documents":["document:tfpt_2_standard_model"],"relation_ids":["relation:077cfe7ba537ca87991f","relation:23a77a6ec8afb556e06d","relation:29a80ea3d702f6fdbe04","relation:2f42e8e48419b449f17c","relation:34993406531dbfea6f14","relation:37284b2c19fb785bbf89","relation:3a828b7e3ae08c436cc5","relation:51f008231edc04475af5","relation:54b863cc00ea9eea7879","relation:581ac74b11e11611f85c","relation:5a699f8851b63cd6c91e","relation:7122a856ec92ae0831e5","relation:7a8d9ee960b2bb051887","relation:7b5e22e03109d584239f","relation:820de5a9076aafb6b99a","relation:8bcb9847f701f171ac02","relation:8f21f44c47c9ec583293","relation:9d1b969f71e29156dbb7","relation:a2acc36ab8773a69b489","relation:a44004cd77f9a0e82eef","relation:adcb3f6050285cb847c8","relation:b2fa973cac38bb8111b2","relation:b45ade2b111234825fed","relation:b6a98d71548baa125fee","relation:b6ba501ba43e614a6dd0","relation:b736fd8a0c2812998adc","relation:c766e43733ddbafff0d7","relation:d47bc179118df065818d","relation:d74411b198bbbe9c142f","relation:d807f8674a3cd3805cb8","relation:e874b71dc941e8b98631","relation:f2c0d4d9d20abb0fc38a"],"semantic_review":false,"source":"documents/tfpt_2_standard_model/sections/008-section-the-setup-parabolic-data-on-the-family-curve.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"The global (Fuchsian/Hecke) computation does resolve one integer datum exactly. Work in the rotation eigenbasis [formula in source] and take the [formula in source] -symmetric Fuchsian residues [formula in source] with [formula in source] (the cusp exponents). Then the symmetrisation collapses exactly, because [formula in source] for [formula in source] (off-diagonal terms are summed fourth roots of unity). The expon","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Global computation: the anchor multiset is derived","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":20843,"byte_start":18665,"id":"section:9a0a5462c820fa2e8e9e","kind":"subsection","labels":[],"line_end":316,"line_start":273,"occurrence":1,"owner_documents":["document:tfpt_2_standard_model"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_2_standard_model/sections/008-section-the-setup-parabolic-data-on-the-family-curve.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"Every residue decomposes uniquely into a cusp index [formula in source] (the [formula in source] family phase, [formula in source] ) and a sheet parity [formula in source] (the [formula in source] deck involution), via the bijection [formula in source] : [formula in source] The full transport table in these parabolic coordinates is l|ccc|ccc & 3c|cusp index [formula in source] (g1,g2,g3) & 3csheet [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Part (ii): the [formula in source] structure of the residues, and the frontier","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":24910,"byte_start":20843,"id":"section:2084a73fd736c7360a0e","kind":"subsection","labels":["thm:flavor"],"line_end":378,"line_start":317,"occurrence":1,"owner_documents":["document:tfpt_2_standard_model"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_2_standard_model/sections/008-section-the-setup-parabolic-data-on-the-family-curve.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"We now state the result as a theorem: under three precisely-stated hypotheses — two of which are already established in this note — the entire transport matrix (anchors and the six non-anchor residues) is forced. The combinatorial core is proved by complete enumeration.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The flavor transport theorem","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":678,"byte_start":0,"id":"section:84fd98f7073bab7bd89c","kind":"section","labels":[],"line_end":13,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_2_standard_model"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_2_standard_model/sections/009-section-the-parabolic-anchor-compiler.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"The anchor vector [formula in source] — the absolute value of the splitting type [formula in source] — is the smallest parabolic object that encodes the three operative structures at once: The [formula in source] norm is the glue/anti-degree, the [formula in source] norm [formula in source] is the [formula in source] positive-root hexagon, and the product is the sheet parity.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Parabolic Anchor Compiler","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"}]},{"byte_end":1465,"byte_start":678,"id":"section:70b3e78782162a011e95","kind":"subsection","labels":[],"line_end":27,"line_start":14,"occurrence":1,"owner_documents":["document:tfpt_2_standard_model"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_2_standard_model/sections/009-section-the-parabolic-anchor-compiler.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"With [formula in source] fixed by parabolic degree zero, the entire integer landscape collapses: So [formula in source] and the spinor block [formula in source] are all functions of [formula in source] with the single new ingredient [formula in source] derived from parabolic degree zero (not posited).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Budget master table: everything is [formula in source] times a Coxeter datum","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":2827,"byte_start":1465,"id":"section:c24e9e51ac519b7d5719","kind":"subsection","labels":[],"line_end":50,"line_start":28,"occurrence":1,"owner_documents":["document:tfpt_2_standard_model"],"relation_ids":["relation:9bbf98ff849414d47eb0"],"semantic_review":false,"source":"documents/tfpt_2_standard_model/sections/009-section-the-parabolic-anchor-compiler.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"The flavor budget splits into anchor [formula in source] two equal Coxeter copies: The residue row sums and full row sums read named objects, and the generation (column) sums are [formula in source] . \\ Finally the scalaron exponent is the parabolic anti-degree plus the family rank, linking the stable family bundle [formula in source] directly to the inflation scale. The [formula in source] residue sum is the project","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Flavor budget split, row sums, scalaron deficit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"}]},{"byte_end":5769,"byte_start":2827,"id":"section:8547baff7ff2745f0533","kind":"subsection","labels":[],"line_end":99,"line_start":51,"occurrence":1,"owner_documents":["document:tfpt_2_standard_model"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_2_standard_model/sections/009-section-the-parabolic-anchor-compiler.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"/ / in 0/-2/blue!60!black, 1/-1/green!50!black, 2/-1/green!45!black (0,- 0.62) rectangle (2.6,- 0.62+0.5); at (1.3,- 0.62+0.25) [formula in source] ; at (1.3,0.95) splitting type\\\\[-1pt] [formula in source] ; at (1.3,-2.05) degrees [formula in source] anchor [formula in source] \\\\[-1pt] [formula in source] ;","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The anchor power compiler","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":12573,"byte_start":5769,"id":"section:649c3b4e330a4dfc876d","kind":"subsection","labels":[],"line_end":197,"line_start":100,"occurrence":1,"owner_documents":["document:tfpt_2_standard_model"],"relation_ids":["relation:0a5c418a8fb9036c31af","relation:3b92f7d81a6c039098a9","relation:3cc7189fc4d18cd1cb8f","relation:48d833f68cd93a0002d2","relation:7dc68e7ae7df883e1378","relation:84f949ba3d5d3a017a5c","relation:8b9e848f68c104598781","relation:abee1aa04478916b58a7","relation:b196c31b730e837bb558","relation:b7c373e09872f44d4dcb","relation:f189740e6ffff8fc8f5c"],"semantic_review":false,"source":"documents/tfpt_2_standard_model/sections/009-section-the-parabolic-anchor-compiler.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Hypotheses (H1),(H3) plus the unique sum- [formula in source] set fix the up and lepton sectors and reduce (H2) to a single binary choice in the down sector: [formula in source] versus its distinct-distance sibling [formula in source] (both contain the anchor [formula in source] , both have row sum [formula in source] , so sum rules do not separate them). The residue matrix [formula in source] (rows [formula in sourc","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Residue-matrix spectral selector — sharpening (H2)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":21167,"byte_start":12573,"id":"section:a660765e3a391c14ceef","kind":"section","labels":["lem:dd","prop:equiv","thm:h2","thm:ms"],"line_end":316,"line_start":198,"occurrence":1,"owner_documents":["document:tfpt_2_standard_model"],"relation_ids":["relation:483c6145b27238375720","relation:68421f99628b28e5cdff","relation:7ed10562498e7160dcde","relation:802fa82e1a5599f681fd","relation:acf0e30623996dc994cc","relation:ae9237e3119ad89f7df9","relation:b1a7248d3471c70d58d0","relation:b2be1aecba8ff008ee86","relation:c876daa2fb00a269fe3c","relation:f85ab73798037651b56b"],"semantic_review":false,"source":"documents/tfpt_2_standard_model/sections/009-section-the-parabolic-anchor-compiler.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"We promote the two genericity/equivalence steps to proved statements.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Closing the flavor block: two theorems","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":24594,"byte_start":21167,"id":"section:3c7d01d4ca9ca9023689","kind":"section","labels":[],"line_end":361,"line_start":317,"occurrence":1,"owner_documents":["document:tfpt_2_standard_model"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_2_standard_model/sections/009-section-the-parabolic-anchor-compiler.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"tocsectionStatus @p0.56 p0.08 Y@ Statement & Status & Note \\\\ weights [formula in source] from cusps [formula in source] data & & Mehta–Seshadri \\\\ [formula in source] & & exact \\\\ balanced bundle [formula in source] & & stable splitting \\\\ [formula in source] , [formula in source] degree, [formula in source] & & winding/residue split \\\\ [formula in source] , [formula in source] & & budget bookkeeping \\\\ rigid [formu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Status","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":25548,"byte_start":24594,"id":"section:c090e3872219b2913e9e","kind":"part","labels":[],"line_end":373,"line_start":362,"occurrence":1,"owner_documents":["document:tfpt_2_standard_model"],"relation_ids":["relation:af3a85472e89f6f0d281","relation:d56d0b095a11858cbca5"],"semantic_review":false,"source":"documents/tfpt_2_standard_model/sections/009-section-the-parabolic-anchor-compiler.tex","status_markers_as_written":["\\mC"],"summary_excerpt":"Scope and honesty. 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It does not force the items that stay typed transfer targets, never compiler powe","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Closing computations and proofs","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10397,"byte_start":0,"id":"section:cbcb5b486b59ced607c8","kind":"section","labels":["lem:gap","prop:qftmeasure"],"line_end":160,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_2_standard_model"],"relation_ids":["relation:398840fe82a947b26be3","relation:3c7491cce8e054b9543f","relation:995d43b647f0047f11f4","relation:c1fb7543dda854168e8d","relation:cbb61198dad47fc07871","relation:fc1461c0aeaac441d094"],"semantic_review":false,"source":"documents/tfpt_2_standard_model/sections/010-section-the-explicit-mass-gap-closes-dynamics-and-cluste.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"unique limit state and exponential clustering] The admissible [formula in source] transport transfer operator has the closed spectrum [formula in source] (the cusp cubic). 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[formula in source] (Prop. quark [formula in source] -rationals & / & hierarchy + source rat","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Status: what is now written out, and what is honestly left","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":27253,"byte_start":26084,"id":"section:59464fe2623d8f56dc12","kind":"section","labels":[],"line_end":376,"line_start":359,"occurrence":1,"owner_documents":["document:tfpt_2_standard_model"],"relation_ids":["relation:0ce4620efc73b6e4ecb1","relation:436b9435c25445f9e264","relation:527b46d39eaa92c2443e","relation:5be01b9f30c3ebea657d","relation:87ebff9a6b6ab8a6f3cd","relation:883003e9ef07adf69ecd","relation:b390359f9573d088eb8f","relation:b91e56ac32818af3f541","relation:c2f26dcdfd0e114f4d55","relation:cd8856135689cd37ff0d"],"semantic_review":false,"source":"documents/tfpt_2_standard_model/sections/011-subsection-seam-response-grammar-gravity-is-the-inverse-.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"The Standard-Model identities used here (marked , , ) are re-derived from [formula in source] and machine-checked by the suite in the repository folder verification/; the inline tags [verification/ [formula in source] ] point to the exact script. 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TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":4153,"byte_start":3451,"id":"section:04030e2b23cc7b5934a7","kind":"part","labels":[],"line_end":63,"line_start":54,"occurrence":1,"owner_documents":["document:tfpt_3_e8_audit_bootstrap"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_3_e8_audit_bootstrap/sections/001-part-the-e-8-secondary-branching-atlas.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"Purpose and discipline. This note does not introduce new physics. It builds an audit raster: the claim that every load-bearing TFPT number should appear in at least one [formula in source] branching projection. A number that appears in none is suspect; a number appearing in several independent projections becomes structurally strong. All arithmetic identities below are exact ; the physical readings are audit-level \\ ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The [formula in source] secondary-branching atlas","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":5832,"byte_start":4153,"id":"section:aef7632ebaf0e99d5614","kind":"section","labels":[],"line_end":86,"line_start":64,"occurrence":1,"owner_documents":["document:tfpt_3_e8_audit_bootstrap"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_3_e8_audit_bootstrap/sections/001-part-the-e-8-secondary-branching-atlas.tex","status_markers_as_written":[],"summary_excerpt":"The strongest current form of the theory is a five-layer compiler:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The compiler core (where this note sits)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10777,"byte_start":5832,"id":"section:133a1fc4804aced401e1","kind":"section","labels":[],"line_end":183,"line_start":87,"occurrence":1,"owner_documents":["document:tfpt_3_e8_audit_bootstrap"],"relation_ids":["relation:47a9099d126d961f1cef","relation:ba684a6db31f0cda5e42","relation:edb651ac167499d17f4d"],"semantic_review":false,"source":"documents/tfpt_3_e8_audit_bootstrap/sections/001-part-the-e-8-secondary-branching-atlas.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"The parabolic anchor [formula in source] (splitting type of [formula in source] ) is a miniature compiler. Its power sums [formula in source] generate the discrete budget:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The [formula in source] anchor microcode","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":12052,"byte_start":10777,"id":"section:84502bfa269b078ed37b","kind":"section","labels":[],"line_end":211,"line_start":184,"occurrence":1,"owner_documents":["document:tfpt_3_e8_audit_bootstrap"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_3_e8_audit_bootstrap/sections/001-part-the-e-8-secondary-branching-atlas.tex","status_markers_as_written":[],"summary_excerpt":"With the residue matrix [formula in source] and the full word-length matrix [formula in source] ( [formula in source] the rank-one winding), [formula in source] the spectral invariants are pure compiler numbers (all verified): @lYlY@ Invariant of [formula in source] & value & Invariant of [formula in source] & value \\\\ [formula in source] & [formula in source] & [formula in source] & [formula in source] \\\\ [formula i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The residue and length matrices as spectral objects","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":17482,"byte_start":12052,"id":"section:b041e1091a1644d75609","kind":"paragraph","labels":[],"line_end":295,"line_start":212,"occurrence":1,"owner_documents":["document:tfpt_3_e8_audit_bootstrap"],"relation_ids":["relation:0e08e929e6987e066ad3","relation:2fdf34a20451788ac803","relation:70c3040b4c308dce6416","relation:79312f72fbb748ca1486","relation:c3137de17159441f53dd","relation:f3afecdab88c4419b82f"],"semantic_review":false,"source":"documents/tfpt_3_e8_audit_bootstrap/sections/001-part-the-e-8-secondary-branching-atlas.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"With [formula in source] and [formula in source] (all verified): @c|cc@ 2.5emc|cc@ [formula in source] & [formula in source] & [formula in source] & [formula in source] & [formula in source] & [formula in source] \\\\ [formula in source] & [formula in source] & [formula in source] & [formula in source] & [formula in source] & [formula in source] \\\\ [formula in source] & [formula in source] & [formula in source] & [form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bilinear anchor forms.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":9400,"byte_start":0,"id":"section:8a517836f882378cde88","kind":"section","labels":["fig:slice_compression"],"line_end":149,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_3_e8_audit_bootstrap"],"relation_ids":["relation:36c52bfc073fc72a1611","relation:3b39a4d872cdbbad4735","relation:3b76b8726c51980fda89","relation:4fa42987981171c505cd","relation:77d2da6eda71c7ec0246","relation:94c501c3dea0fdd4f7fc","relation:b4bf674950930faf7ea0","relation:e5537b81816ca5fb53bd"],"semantic_review":false,"source":"documents/tfpt_3_e8_audit_bootstrap/sections/002-section-the-secondary-branching-atlas.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Each maximal subalgebra of [formula in source] mirrors a TFPT module. 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The regular clocks of [formula in source] against the compiler clock ( [formula in source] checks, [formula in source] \\,s, exact arithmetic). 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The calibration/scale-torsor audit of the [formula in source] interface ( [formula in source] checks, [formula in source] \\,s; verdict torsor closure pass). 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The honest question is: has the new compiler re-derived each of these,","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Sector inventory: have all the old-cascade sectors been computed?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":11084,"byte_start":8917,"id":"section:200db589cdbff42f04e6","kind":"section","labels":[],"line_end":145,"line_start":113,"occurrence":1,"owner_documents":["document:tfpt_3_e8_audit_bootstrap"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_3_e8_audit_bootstrap/sections/010-section-three-views-of-one-spine.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"The flavor selector [formula in source] is the terminal orbit of the [formula in source] cascade; the compiler is the cascade's IR endpoint. 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September Der Nutzer hat zu Recht beanstandet, dass die Untersuchung immer wieder dieselbe offene Wirkungsfrage reformuliert. Der zuletzt konstruierte E8-Quellkandidat wird deshalb als vorab gewähltes Zentrum der weiteren Suche zurückgenommen. Seine mathematischen Ergebnisse bleiben erhalten; ihre Existenz bestimmt nicht die Forschungspriorität.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Korrektur der Suchrichtung am 29. September","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"}]},{"byte_end":6435,"byte_start":5548,"id":"section:4c55da3afe73015d085e","kind":"section","labels":["sec:fixedpointproposalcheck"],"line_end":41,"line_start":36,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/001-section-korrektur-der-suchrichtung-am-29-september.tex","status_markers_as_written":[],"summary_excerpt":"tocsectionKurswechsel am 30. September: Der einfache Kern und seine vollständige Antwort","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kurswechsel am 30. September: Der einfache Kern und seine vollständige Antwort","topic_suggestions":[]},{"byte_end":8943,"byte_start":6435,"id":"section:10d2cdd4992d3f106230","kind":"subsection","labels":[],"line_end":68,"line_start":42,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/001-section-korrektur-der-suchrichtung-am-29-september.tex","status_markers_as_written":[],"summary_excerpt":"Für die ungeraden [formula in source] -Wurzelgitter besitzt die Diskriminantengruppe die Form [formula in source] . In der Konvention für konforme Spins, also Normquadrat geteilt durch zwei, gilt [formula in source] Die Form auf [formula in source] lautet [formula in source] . 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Die relative Matrix ist [formula in source] . lrrl Theorie & Ordnung [formula in source] & Ordnung [formula in source] & Grundgewichte\\\\ [formula in source] & 24 & 8 & [formula in source] \\\\ [formula in source] & 8 & 8 & [formula in source] \\\\ [","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die vorgeschlagene Ordnung 24 und die Ratenprüfung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":15936,"byte_start":12512,"id":"section:7fe2b9bd33d71d6cdb49","kind":"subsection","labels":[],"line_end":107,"line_start":93,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:49c3ac2776b81fc9a0cd","relation:97a6c8457f58308bcd95","relation:c3ffa700daa55082b6cb"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/001-section-korrektur-der-suchrichtung-am-29-september.tex","status_markers_as_written":[],"summary_excerpt":"Die Trennung ``alles Erfolgreiche ist invariant, alles Dynamische scheitert'' ist am Original zu grob. 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Das ist eine andere Aufgabe als die Existenz irgendeiner Dynamik.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was der funktionierende Rest über den Ursprung aussagt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":22252,"byte_start":15936,"id":"section:42df25f5e30b2291586f","kind":"subsection","labels":[],"line_end":139,"line_start":108,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:69cbbbf4c27d956dda94","relation:e44fdf5bd15ba9b52b75"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/001-section-korrektur-der-suchrichtung-am-29-september.tex","status_markers_as_written":[],"summary_excerpt":"Mehrere Programme können dieselbe Liste von Ergebnissen ausgeben. Ob sie dieselbe Regel ausführen, erkennt man daran, was nach Eingriffen passiert: dieselben Schritte anders anordnen, eine Phase vergleichen oder einen früheren Speicher nochmals benutzen. Der Ursprung wird durch diese Fortsetzungen bestimmt, nicht durch seine Dateiform oder die Namen seiner Matrizen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der andere Lösungsweg: Die Antworttreue zum Ausgangspunkt machen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"}]},{"byte_end":23159,"byte_start":22252,"id":"section:471351a7e3af79a7f252","kind":"section","labels":["sec:sourcedirectionaudit"],"line_end":145,"line_start":140,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:8e4929e9d1a27b206ab8","relation:927914b7b4f1b76f45c9"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/001-section-korrektur-der-suchrichtung-am-29-september.tex","status_markers_as_written":[],"summary_excerpt":"tocsectionErneute Gesamtprüfung: Die Auslese ist nicht die ganze Maschine","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Erneute Gesamtprüfung: Die Auslese ist nicht die ganze Maschine","topic_suggestions":[]},{"byte_end":24758,"byte_start":23159,"id":"section:61b9c4975de1b0044095","kind":"subsection","labels":[],"line_end":152,"line_start":146,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:47aa35cd2ecd8cc5a073"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/001-section-korrektur-der-suchrichtung-am-29-september.tex","status_markers_as_written":[],"summary_excerpt":"Die aktuelle Bestandsprüfung erfasst die Register und Einordnungen von 1028 Verifikationsskripten, 279 Theorie-Contracts, 59 Experimentverzeichnissen und 179 Lean-Dateiknoten einschließlich RH. Das ist keine Behauptung, jedes Skript neu ausgeführt oder jede Zeile vollständig semantisch geprüft zu haben. Die gezielte Originalprüfung verfolgt die tragenden Wege: P1/P2 und Compiler, Clock und Vergröberung, Quellen-/Dete","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was über den gesamten Bestand geprüft wurde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":27641,"byte_start":24758,"id":"section:563c0e0fe095f9430f2a","kind":"subsection","labels":[],"line_end":200,"line_start":153,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:033fcf06396bb1f2eddc","relation:41b3ba99edbea3a199b3","relation:63a4c32e50c4a8643af5","relation:d809df115be5ce007708"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/001-section-korrektur-der-suchrichtung-am-29-september.tex","status_markers_as_written":[],"summary_excerpt":"In verification/v993_minimal_defect_selector.py:169-212 ist die Clock [formula in source] und ihre neutrale Auslese [formula in source] Die Originalprüfung bestätigt Idempotenz, Positivität, Spurerhaltung und die Regel [formula in source] Das ist die Struktur einer bedingten Erwartung. Die Faktoren außerhalb von [formula in source] müssen dabei bereits neutral sein. Eine allgemeine Produktregel [formula in source] fo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der kleinste entscheidende Test an der vorhandenen Clock-Vergröberung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":30422,"byte_start":27641,"id":"section:3cca7fe7a1d199a93e2c","kind":"subsection","labels":[],"line_end":229,"line_start":201,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/001-section-korrektur-der-suchrichtung-am-29-september.tex","status_markers_as_written":[],"summary_excerpt":"Für das vorhandene Clock-Automorphismusdatum gibt es die vier Gradprojektionen [formula in source] Die ganze Zerlegung behält alle Operationen. Nur [formula in source] ist dabei eine positive bedingte Erwartung; die übrigen [formula in source] sind Spektralprojektionen, keine positiven Auslesungen. Keine einzelne Projektion wird deshalb multiplikativ. Die korrekte Produktregel lautet [formula in source] Im Zeugen ist","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Welche einfache vollständige Struktur tatsächlich erhalten werden muss","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":33434,"byte_start":30422,"id":"section:49081b131681f01ae9d6","kind":"subsection","labels":[],"line_end":250,"line_start":230,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:0cb6498612ee6118eb97","relation:4c89d11b71e3111c8920","relation:57c21791633dec187aca","relation:6d388332dae9a83dfa8a","relation:a080f45a1f40c3a4162a","relation:dddedf5bb2fd88b1abed","relation:e645e24e825e791f1f65"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/001-section-korrektur-der-suchrichtung-am-29-september.tex","status_markers_as_written":[],"summary_excerpt":"L29mmY Original & Belastbare Reichweite und verbleibender Anschluss\\\\ v991, v1014 & Bulk-/Randindex, Orientierung und endliche Determinantenlinie werden gemeinsam abgeglichen. Eine konstante Referenzphase und der kontinuierliche Anschluss mit Verbindung sind gesondert zu behandeln.\\\\ v1015 & Im ausgewählten QWZ-Kragen liefern die ursprüngliche demokratische Antwort und ihre Mutanten einen echten Auswahltest. Der fris","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was die tragenden Verifikationen wirklich schließen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":35479,"byte_start":33434,"id":"section:50a98a13a98faf94eaad","kind":"subsection","labels":[],"line_end":262,"line_start":251,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:349c82c757bc15345fc2","relation:5fc6631805c00214deb9","relation:6095ccb95daaf4a053a1","relation:7a2eed85b1609e919257","relation:d3382158654cd7b3fbf0","relation:ebd98930c277a5117927"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/001-section-korrektur-der-suchrichtung-am-29-september.tex","status_markers_as_written":[],"summary_excerpt":"Die vorhandene seed-consistency-Auswertung ist besonders relevant, weil sie mehrere Sektoren an einen gemeinsamen Seed bindet. Die Originalanalysen v4–v6 wurden in dieser Prüfung direkt mit ihren eingefrorenen Messdaten erneut ausgeführt: Der gemeinsame Fit liefert [formula in source] bei drei Freiheitsgraden; der eingefrorene TFPT-Seed liefert [formula in source] bei vier Freiheitsgraden. Keiner der 14 untersuchten ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was die Experimente als Rückbedingungen hinzufügen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":38046,"byte_start":35479,"id":"section:3c068534676f49153f21","kind":"subsection","labels":[],"line_end":281,"line_start":263,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:3b7338b3ebfd7f3154cb","relation:53896b43062a706ac4e8"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/001-section-korrektur-der-suchrichtung-am-29-september.tex","status_markers_as_written":[],"summary_excerpt":"Das vorhandene Programm enthält eine passende Vorwärtskette; sie muss nicht durch eine neue freie Matrix ersetzt werden: [formula in source] Die Symbole stehen für ursprünglichen Randkern, Zustand, Zeit, Reflexion und markierte Deckwirkung sowie ihre gemeinsame Operatorfamilie und Determinantenverbindung. Die Variationen nach Eichfeld [formula in source] , Metrik [formula in source] und Familientransport [formula in ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der zusammenhängende Weg zur gesuchten Lösung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":41259,"byte_start":38046,"id":"section:adf159777928dff103cb","kind":"section","labels":[],"line_end":302,"line_start":282,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/001-section-korrektur-der-suchrichtung-am-29-september.tex","status_markers_as_written":[],"summary_excerpt":"tocsectionWie dieses Dokument zu lesen ist Der Auftrag lautet, die vollständige Verbindung zu finden. Deshalb ist der Maßstab dieses Textes eine gemeinsame Herleitung mit denselben Feldern, demselben Zustand und derselben Dynamik. Eine Sammlung passender Zahlen, ein funktionierendes Hilfsmodell oder eine große Zahl grüner Prüfungen reicht dafür nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie dieses Dokument zu lesen ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":42338,"byte_start":41259,"id":"section:9031f8ca3225516f3a16","kind":"section","labels":["sec:globaloriginselection"],"line_end":307,"line_start":303,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/001-section-korrektur-der-suchrichtung-am-29-september.tex","status_markers_as_written":[],"summary_excerpt":"Der neue verbundene Befund lautet: Die ursprüngliche Zwei-Seiten-Geometrie lässt sich ohne vorab eingesetztes E8 global untersuchen. Widerspruchsfreiheit allein lässt unendlich viele größere Abschlüsse zu. Bereits ein einziger lokaler, spinorgeladener Strom vom konformen Gewicht eins würde ausschließlich die Viermarkenstruktur auswählen; die zuvor verlangte vollständige Stromerzeugung ist dafür nicht nötig. In der vo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zurück zum Ursprung: Ein allgemeiner Auswahltest für das ganze Gerüst","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"}]},{"byte_end":44146,"byte_start":42338,"id":"section:632a5b3efdd312054761","kind":"subsection","labels":[],"line_end":328,"line_start":308,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/001-section-korrektur-der-suchrichtung-am-29-september.tex","status_markers_as_written":[],"summary_excerpt":"Die ursprüngliche Naht wird auf zwei Arten gelesen. Die eine Seite liest Wege um ihre Marken; die andere liest Funktionen mit erlaubten Polen an denselben Marken. Bei vier Marken ergeben sich drei unabhängige Wegzyklen und fünf Funktionsplätze. Das ist der ursprüngliche Zusammenhang von Familien und Träger, nicht die Einführung zweier unabhängiger Räume.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das einfache Bild und die genaue Frage","topic_suggestions":[]},{"byte_end":46819,"byte_start":44146,"id":"section:595aebc66e674f120e34","kind":"subsection","labels":["eq:globalgluetower"],"line_end":374,"line_start":329,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:c9304ee215ee0d1cf92b"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/001-section-korrektur-der-suchrichtung-am-29-september.tex","status_markers_as_written":[],"summary_excerpt":"Satz 1. Ein solcher Abschluss existiert genau für","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die gesamte Abschlussklasse ist unendlich – ein globaler Satz","topic_suggestions":[]},{"byte_end":3484,"byte_start":0,"id":"section:503e5042572fe8d7e2ae","kind":"subsection","labels":["eq:currentcompleteness","eq:globalcurrentselection"],"line_end":47,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/002-subsection-der-entscheidende-selektor-vollst-ndigkeit-de.tex","status_markers_as_written":[],"summary_excerpt":"Eine allgemeinere und operativ verständliche Forderung als vorab vorgeschriebener diagonaler Glue lautet: Der vollständige Abschluss soll also von seinen Wurzeln erzeugt werden. Für die hier verwendete Gitter-VOA ist dies gleichbedeutend mit [formula in source] alle Felder entstehen durch Produkte, Ableitungen und Linearkombinationen der Ströme vom konformen Gewicht eins. Das Gewicht ist eine Eigenschaft der zweidime","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der entscheidende Selektor: Vollständigkeit der elementaren Ströme","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7102,"byte_start":3484,"id":"section:1890ff3254bb8da69e68","kind":"subsection","labels":[],"line_end":61,"line_start":48,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:1fd8292bff5e0ae35b77","relation:21d58d4c73441eba5c4f","relation:51bc8ecb48b1649cb90e","relation:7d5f059baf48e4016b73","relation:9d461b88086c1f13869c","relation:9ebb69180c4b219e68a1","relation:a409d78e8b67c605d9be","relation:a7333d1ee0673b1bc63c","relation:bfcf6780ac37a6128bfc","relation:e4d2020c4c51a83546d2","relation:e6ec63e56e90ccf77e68"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/002-subsection-der-entscheidende-selektor-vollst-ndigkeit-de.tex","status_markers_as_written":[],"summary_excerpt":"Im Original gibt es eine konkrete Vorstufe dieser Forderung: v502_celestial_wp5e_prefactor_level.py unterscheidet ganzzahligen Spin von der stärkeren Forderung, dass die Erweiterung auf Strömen mit [formula in source] schließt. Dort wird jedoch bereits die [formula in source] /E8-Architektur verwendet. SEAM.SIMPLECURRENT.GENERATOR.01 verlangt zudem einen tatsächlichen lokalen Erweiterungsgenerator; ein reiner Gitterz","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum das an den Originalansatz anschließt – und was hinzugefügt wird","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":8880,"byte_start":7102,"id":"section:6bcafa1df74eaddbdcb7","kind":"subsection","labels":["eq:onespinorselector","eq:primitivecurrentweight","sec:onespinorcurrent"],"line_end":84,"line_start":62,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/002-subsection-der-entscheidende-selektor-vollst-ndigkeit-de.tex","status_markers_as_written":[],"summary_excerpt":"Satz 3. Sei [formula in source] ein positiver gerader unimodularer Abschluss der angegebenen Familie [formula in source] . Enthält die zugehörige Gitterfeldalgebra wenigstens ein nichtverschwindendes Feld vom Gewicht eins in einem [formula in source] -Spinorsektor, dann gilt Weder ein bijektiver Glue noch die Erzeugung der gesamten Feldalgebra durch Ströme wird vorausgesetzt. Auch die konkrete [formula in source] -Di","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die stärkere Auswahl braucht nur einen gemeinsamen Strom","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":11637,"byte_start":8880,"id":"section:5b772b5d3b4a980239a4","kind":"subsection","labels":["eq:seamcontouridentity","sec:seamwardsource"],"line_end":107,"line_start":85,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/002-subsection-der-entscheidende-selektor-vollst-ndigkeit-de.tex","status_markers_as_written":[],"summary_excerpt":"Die Originalquelle liefert [formula in source] und Spektralfluss eins. Das ist ein topologischer Transportwert. Der normierte Seam-Modus und der im Original eingeführte Projektor [formula in source] sind noch kein lokaler chiraler Strom. Auch der Calderón-Projektor bestimmt zunächst Cauchy-Daten und Polarisation.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was Skalenfreiheit tatsächlich erzwingen würde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":19734,"byte_start":11637,"id":"section:7a0eed0a3d8bc9707c35","kind":"subsection","labels":["eq:a3d3twistisometry","eq:doubletwistope","eq:twistdoublecharge","sec:doubletwistbridge"],"line_end":173,"line_start":108,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:23b3e17b524d9cc98a4a","relation:738ee98cca5aa2409358"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/002-subsection-der-entscheidende-selektor-vollst-ndigkeit-de.tex","status_markers_as_written":[],"summary_excerpt":"Die bedingte Achtkanal-Fermionisierung enthält einen viel direkteren Kandidaten für diesen Strom. Sechzehn reelle CAR-Fermionen ergeben acht unabhängige komplexe Kanäle. In der gewählten [formula in source] -Zielmarkierung werden sie als [formula in source] , also fünf plus drei orthogonale Bosonisierungskoordinaten, organisiert. Die Kopienzahl allein leitet diese Blockwirkung nicht her. Die vier üblichen [formula in","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der konstruktive Anschluss: Zwei Vierteltwists ergeben das E8-Feld","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":26331,"byte_start":19734,"id":"section:8ccfe1dd89183bdd87e8","kind":"subsection","labels":["eq:eightcopyspinorpairrate","eq:microscopicweightonepair","eq:onecopyrawpairrate","sec:microscopicpairbridge"],"line_end":258,"line_start":174,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/002-subsection-der-entscheidende-selektor-vollst-ndigkeit-de.tex","status_markers_as_written":[],"summary_excerpt":"Die erneute Quellenprüfung korrigiert eine zu schwache Darstellung des vorhandenen Bestands. Der Vertrag microscopic-neutral-limit beweist für den unveränderten QWZ-Kragen mit Breite acht, Masse eins, Holonomiesektor [formula in source] , tatsächlichem gefülltem negativem Spektrum und Filterbreite [formula in source] bereits [formula in source] Dies ist der analytische Vergleich der vollständigen bewegten Geschichte,","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Mikrounterbau ist weiter geschlossen als zuvor ausgewiesen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":30032,"byte_start":26331,"id":"section:ac9e6e99bdf9248aded0","kind":"subsection","labels":[],"line_end":300,"line_start":259,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:df95c68d3fc255e1ca13"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/002-subsection-der-entscheidende-selektor-vollst-ndigkeit-de.tex","status_markers_as_written":[],"summary_excerpt":"Unter dem neuen Selektor wird das diskrete Gerüst auf einmal festgelegt: [formula in source] Das zusätzliche originale Auslesewörterbuch liest die drei Zyklusrichtungen als Familien und den Halbspinor als eine chirale Materiegeneration; damit folgen [formula in source] und die [formula in source] Weylkomponenten. Der globale Gitterbeweis allein macht aus einer Zyklusrichtung kein physisches Teilchen und beweist diese","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie die vorhandenen physikalischen Herleitungen zusammen zurückwirken","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":33416,"byte_start":30032,"id":"section:60cb81058c5a8e7865c4","kind":"subsection","labels":[],"line_end":326,"line_start":301,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/002-subsection-der-entscheidende-selektor-vollst-ndigkeit-de.tex","status_markers_as_written":[],"summary_excerpt":"Der Universalraum fordert eine vollständige, zusammensetzbare Darstellung der erlaubten Antworten. Für zwei Geschichten [formula in source] ist die sichere Gleichsetzung [formula in source] Die Testkontexte müssen auch spätere Operationen und zusammengesetzte Umgebungen erfassen. Besitzt die Prozesstheorie eine Parallelkomposition, müssen alle ihre zulässigen parallelen Registerkontexte ebenfalls enthalten sein. Bei ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was dies für den Universalraum und die vollständige Lösung bedeutet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":38141,"byte_start":33416,"id":"section:c5f60ba06a0d050803bb","kind":"section","labels":["sec:bigpicture"],"line_end":358,"line_start":327,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/002-subsection-der-entscheidende-selektor-vollst-ndigkeit-de.tex","status_markers_as_written":[],"summary_excerpt":"Das verbindende Bild ist ein Instrument mit einer einzigen inneren Mechanik. Topologie legt fest, welche Schleifen und Markierungen unterscheidbar sind. Algebra legt fest, wie Operationen zusammenwirken. Der Zustand bestimmt ihre gemeinsamen Antworten. Rekursion beschreibt, wie dieselben Antworten auf einer anderen Auflösung repräsentiert werden. Physik verlangt zusätzlich, dass dieses Instrument tatsächlich unsere r","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das Gesamtbild: Eine Quelle und mehrere Ansichten derselben Wirklichkeit","topic_suggestions":[]},{"byte_end":40303,"byte_start":38141,"id":"section:c414a975128ab2f44f7b","kind":"subsection","labels":[],"line_end":369,"line_start":359,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/002-subsection-der-entscheidende-selektor-vollst-ndigkeit-de.tex","status_markers_as_written":[],"summary_excerpt":"Die Marken legen ein gemeinsames Gerüst fest. Der P1/P2-Bootstrap, die [formula in source] -Ladungszerlegung, der Familienrang und die [formula in source] -Verklebung beschränken dieselbe Architektur. Ihre Auswahlklassen bleiben Teil der Aussage. Dieses Gerüst trägt mehrere präzise Auslesungen. Die volle Materiespur zählt [formula in source] Komponenten; die Ladungsspur ergibt mit dem Higgs [formula in source] . Die ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die gemeinsame Mechanik in fünf Schritten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":1296,"byte_start":0,"id":"section:7514bf27f8aa443b5c7d","kind":"subsection","labels":[],"line_end":5,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/003-subsection-wo-die-ergebnisse-der-sitzung-in-dieses-bild-.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Wo die Ergebnisse der Sitzung in dieses Bild gehören","topic_suggestions":[]},{"byte_end":2666,"byte_start":1296,"id":"section:d7bed9da952b67b42a66","kind":"subsection","labels":[],"line_end":10,"line_start":6,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:fa2009f47b063e9dc0ed"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/003-subsection-wo-die-ergebnisse-der-sitzung-in-dieses-bild-.tex","status_markers_as_written":[],"summary_excerpt":"Eine Lösung muss zugleich die vollständige Quelle aus den ursprünglichen Bedingungen auswählen, ihre gemeinsame Wirkungs- und Zustandsregel konstruieren und die vorhandenen physikalischen Auslesungen in einer konsistenten lokalen Raumzeit realisieren. Dabei müssen auch Kopplungen, Neutrinosektor, Gravitation und kosmologische Anfangs-/Transferbedingungen am selben Objekt hängen. Ein metrologischer Maßstab darf ausdrü","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was als vollständige Lösung zählen würde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"}]},{"byte_end":2734,"byte_start":2666,"id":"section:f06383b64d11dd7ee85b","kind":"section","labels":[],"line_end":12,"line_start":11,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/003-subsection-wo-die-ergebnisse-der-sitzung-in-dieses-bild-.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Der Ursprung: P1, P2 und die rekursive Rückbestätigung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"}]},{"byte_end":4135,"byte_start":2734,"id":"section:c6156d05817971251fd2","kind":"subsection","labels":[],"line_end":23,"line_start":13,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/003-subsection-wo-die-ergebnisse-der-sitzung-in-dieses-bild-.tex","status_markers_as_written":[],"summary_excerpt":"P1 beginnt mit einem orientierten Seam und einem positiven beziehungsweise reflexionspositiven Kern. Die primitive Windung fixiert im verwendeten TFPT-Vertrag die topologische Normierung Eine positive Antwort bedeutet bildlich: Die aus der Quelle berechneten Normen dürfen nicht negativ werden. Orientierung bedeutet, dass Hin- und Rückweg sowie eine umgekehrte Windung nicht einfach dieselbe markierte Operation sind. `","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"P1: Orientierung, Rückkehr und positive Antworten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":5025,"byte_start":4135,"id":"section:54828569b5740b3e932b","kind":"subsection","labels":[],"line_end":32,"line_start":24,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/003-subsection-wo-die-ergebnisse-der-sitzung-in-dieses-bild-.tex","status_markers_as_written":[],"summary_excerpt":"P2 stellt die markierte Aufteilung des fünfdimensionalen Trägers bereit. Auf der fundamentalen Darstellung wird der Generator als geschrieben. Die Spurfreiheit ist exakt: [formula in source] . Bei der entsprechenden Trägernormierung entstehen [formula in source] und die bekannte Hochskalenrelation [formula in source] . Das sind Aussagen an der markierten Trägerstruktur. Ihre Identifikation mit laufenden, renormierten","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"P2: Die markierte Aufteilung [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"}]},{"byte_end":6821,"byte_start":5025,"id":"section:d533d2261775544cb5b9","kind":"subsection","labels":[],"line_end":51,"line_start":33,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/003-subsection-wo-die-ergebnisse-der-sitzung-in-dieses-bild-.tex","status_markers_as_written":[],"summary_excerpt":"Die ursprüngliche Ankerstruktur verwendet Damit ergeben sich Diese Zahlen passen zur Wurzelzahl, zum Rang und zur Dimension von [formula in source] . Die tragfähige Identifikation kommt jedoch aus der tatsächlich konstruierten Gitter- und Gruppenwirkung, nicht allein aus diesen Gleichheiten.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Anker, Familiengeometrie und Bootstrap","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"}]},{"byte_end":10291,"byte_start":6821,"id":"section:f771351de25bd70c1da6","kind":"subsection","labels":["sec:originproofaudit"],"line_end":66,"line_start":52,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:03154a8dc0327237f86e","relation:aa135482c9860977f6d7"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/003-subsection-wo-die-ergebnisse-der-sitzung-in-dieses-bild-.tex","status_markers_as_written":[],"summary_excerpt":"Die stärkste archivierte Fassung minimiert auf zulässigen einseitigen spektralen Bordismen den Defekt Die Wohlordnung dieser diskreten Werte liefert bei nichtleerer Klasse einen minimalen Wert. Sie beweist nicht, dass genau ein vollständiger Operator diesen Wert annimmt. Das Original benennt die dafür notwendige Klassifikation der minimalen Faser selbst, führt sie im anschließenden Eindeutigkeitsbeweis aber nicht aus","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was die erneute Prüfung des behaupteten Ursprungsabschlusses ergibt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":11755,"byte_start":10291,"id":"section:6269926806aae68e08f4","kind":"subsection","labels":[],"line_end":77,"line_start":67,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:291c51ac1bb320d9f5cc","relation:54503c963b86c6a15011","relation:731588c6dcfff65bb57f","relation:ae4cd970d941651f7b97","relation:e62e8ba047997f050fce","relation:eba256838803d0bd62bf"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/003-subsection-wo-die-ergebnisse-der-sitzung-in-dieses-bild-.tex","status_markers_as_written":[],"summary_excerpt":"Die Rückbestätigung des diskreten Gerüsts, der stationäre Zustand eines gegebenen Transfers und die Auswahl eines vollständigen physischen Gesetzes haben verschiedene Beweisgegenstände. Die erneute Originalprüfung macht die Verwechslung genau lokalisierbar: v56_unique_attractor.py setzt eine Matrix [formula in source] ein und prüft ihre führende Richtung sowie Konvergenz. Der erfolgreiche Test beweist keine Eindeutig","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Drei verschiedene Eindeutigkeitsfragen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":11824,"byte_start":11755,"id":"section:6823c34ef1a8dea5d267","kind":"section","labels":[],"line_end":79,"line_start":78,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/003-subsection-wo-die-ergebnisse-der-sitzung-in-dieses-bild-.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Vom Double Cover zum [formula in source] -Träger und zum Standardmodell","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":12892,"byte_start":11824,"id":"section:5c2d5c137768ad8548f3","kind":"subsection","labels":[],"line_end":94,"line_start":80,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/003-subsection-wo-die-ergebnisse-der-sitzung-in-dieses-bild-.tex","status_markers_as_written":[],"summary_excerpt":"Die alte Architektur benutzt die [formula in source] -Spinorstruktur und den [formula in source] -Registerpartner. Die Diskriminantengruppen der verwendeten Gitter tragen passende [formula in source] -Klassen. Die Normbeiträge [formula in source] und [formula in source] addieren sich zu [formula in source] . Die Index-vier-Verklebung liefert das gerade unimodulare Rang-acht-Gitter [formula in source] ; seine vier urs","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Verklebung ist eine konkrete Ladungsrechnung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":13726,"byte_start":12892,"id":"section:077dbeab4cbfaa2cad2f","kind":"subsection","labels":[],"line_end":99,"line_start":95,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/003-subsection-wo-die-ergebnisse-der-sitzung-in-dieses-bild-.tex","status_markers_as_written":[],"summary_excerpt":"Die Architektur liefert einen gemeinsamen Organisationsraum für interne Ladungen, Register und mögliche Materieblöcke. Anomaliefreiheit ist eine notwendige Konsistenzbedingung. Sie wählt nicht automatisch eine Wechselwirkung, entkoppelt keine Spiegelmaterie und präpariert keinen physischen Zustand.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was die Architektur liefert und was die Physik zusätzlich verlangt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":13797,"byte_start":13726,"id":"section:38a70245f636d0b354c2","kind":"section","labels":[],"line_end":101,"line_start":100,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/003-subsection-wo-die-ergebnisse-der-sitzung-in-dieses-bild-.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die verzahnten Clocks, Flavor und [formula in source] im Gesamtgefüge","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":14839,"byte_start":13797,"id":"section:4ee6daaa9dc2f790fafa","kind":"subsection","labels":[],"line_end":114,"line_start":102,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/003-subsection-wo-die-ergebnisse-der-sitzung-in-dieses-bild-.tex","status_markers_as_written":[],"summary_excerpt":"Die ursprünglichen Clock-Strukturen enthalten mit den Exponenten [formula in source] . Daneben steht die vierfache Markierung. [formula in source] ist keine Untergruppe eines zyklischen 30-Taktes. Der tatsächliche Anschluss verwendet unter anderem eine Wirkung der Form Die komplexe Reflexionsgruppe [formula in source] hat Ordnung [formula in source] , sechzig Reflexionen und Invariantengrade [formula in source] . Die","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Mehrere Uhren können dieselbe Struktur ablesen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":17143,"byte_start":14839,"id":"section:f5188df5e6a05ddf62a8","kind":"subsection","labels":["sec:physicalconstraints"],"line_end":132,"line_start":115,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/003-subsection-wo-die-ergebnisse-der-sitzung-in-dieses-bild-.tex","status_markers_as_written":[],"summary_excerpt":"Die Aussage ``Massen, Flavor, Yukawa und [formula in source] müssen noch hergeleitet werden'' war zu pauschal. Die Originale enthalten konkrete Formeln, Operatoren und Begründungen. Die präzise Frage lautet: Realisiert ein und derselbe ursprüngliche Quellprozess diese vorhandenen Gesetze mit denselben Markierungen, Normierungen und Zuständen?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die bereits vorhandene physikalische Herleitungskette","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":20642,"byte_start":17143,"id":"section:db553f90608e785ea4a8","kind":"subsection","labels":["eq:physicalleptonelimination"],"line_end":192,"line_start":133,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:0f5f33a0bb4fcb88455f","relation:16da6d18f9d9e558b2ee","relation:4358eef6afce3159d6a7","relation:ba31ae9ee092efbcfc4d","relation:c5a9aa2d08d1ac65612f"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/003-subsection-wo-die-ergebnisse-der-sitzung-in-dieses-bild-.tex","status_markers_as_written":[],"summary_excerpt":"Mit Zeilen [formula in source] lauten die ursprünglichen Operatoren beziehungsweise markierten Auslesetabellen Es gilt [formula in source] , [formula in source] und [formula in source] . Der Seed und das gemeinsame Yukawa-Gesetz sind Hüte kennzeichnen die Quellenwerte. Die Standard-RG-/Schwellenabbildung zu laufenden oder Polmassen ist ein eigener, benannter Rechenschritt. Sie macht die Quellenherleitung nicht wertlo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Massen und Yukawa-Kopplungen aus derselben markierten Struktur","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":23272,"byte_start":20642,"id":"section:e7f00fa0a0e13367f31d","kind":"subsection","labels":[],"line_end":228,"line_start":193,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:7e6966fffaad66df33a6"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/003-subsection-wo-die-ergebnisse-der-sitzung-in-dieses-bild-.tex","status_markers_as_written":[],"summary_excerpt":"Die Kopplung zwischen den beiden Herleitungswegen ist genauer als eine Zahlenähnlichkeit. Auf einer ursprünglichen Familie gilt Ungewichtet ergeben die drei Familien den Punkturnachtrag [formula in source] . Mit Fermion-/Skalargewicht und Eichnormierung folgt dagegen Der Higgs trägt den letzten Beitrag bei. Ein ungeladenes rechtshändiges Neutrino trägt nicht zur [formula in source] -Spur bei, gehört aber zum ungewich","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum [formula in source] , [formula in source] und [formula in source] eine gemeinsame Einschränkung sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":30004,"byte_start":23272,"id":"section:0cf51a01f0489758a3da","kind":"subsection","labels":["eq:flavorschur","sec:carriertraceclosure"],"line_end":317,"line_start":229,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:ef5196a3964c15e3b553"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/003-subsection-wo-die-ergebnisse-der-sitzung-in-dieses-bild-.tex","status_markers_as_written":[],"summary_excerpt":"Der ursprüngliche Flavorpol ist bereits aus einer gemeinsamen Wirkung hergeleitet. Die heutige Verbindung erklärt ihre genaue Einsetzung mit denselben [formula in source] -Ladungsdaten und dem vorhandenen gedoppelten Familienweg. Entscheidend sind die Art der Projektion und die Art der Spur.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Flavor-Determinant und die Eichspur aus gemeinsamen Ladungsdaten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":32641,"byte_start":30004,"id":"section:823c6857922270cc3ac8","kind":"subsection","labels":["eq:mixedvariation","sec:commonvariation"],"line_end":340,"line_start":318,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:592d959cb4f2dbd4418a","relation:62ad36823f2eefef0521","relation:a887cb8e7526ca05964d"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/003-subsection-wo-die-ergebnisse-der-sitzung-in-dieses-bild-.tex","status_markers_as_written":[],"summary_excerpt":"Eine bisher verfolgte Prüfroute untersucht die ursprüngliche gemeinsame Operatorfamilie [formula in source] mit [formula in source] . Die Masterformel in 02_carrier_source.tex:3021-3145 muss ihre verschiedenen Reduktionen aus dieser einen Familie erzeugen. Der heute bewiesene Trägeranschluss liefert die richtigen Räume und Spurgewichte; die bereits berechneten neutralen, geladenen und gemischten E8-Antworten liefern ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die gemeinsame Variationsidentität statt einzelner Extremwerte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"}]},{"byte_end":33870,"byte_start":32641,"id":"section:943b064e207b8a5356b0","kind":"subsection","labels":[],"line_end":360,"line_start":341,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/003-subsection-wo-die-ergebnisse-der-sitzung-in-dieses-bild-.tex","status_markers_as_written":[],"summary_excerpt":"Auf dem verwendeten kleinen Seedzweig folgt bereits Die ursprünglichen weiteren, jeweils bedingt physisch gelesenen Kanäle lauten Diese Gleichheiten verknüpfen dieselben Quellenformeln; sie sind kein heute neu ausgeführter globaler Fit an Beobachtungsdaten. Ihre Abhängigkeiten müssen mitgeführt werden, statt jede Auslesung als unabhängige Bestätigung zu zählen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die bekannten Formeln schränken den Ursprung rückwärts ein","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":2605,"byte_start":0,"id":"section:5bb78709ff4fd3f701e1","kind":"subsection","labels":["eq:physicalscalebridge"],"line_end":33,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:4e91fb234ccd4e62adfd","relation:83c7cb223f3e505e1e4e","relation:e055ffcf260444cc6584","relation:e7ea77219e205d4ddf70"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/004-subsection-auch-die-skalen-besitzen-einen-gemeinsamen-va.tex","status_markers_as_written":[],"summary_excerpt":"Im Metrologieoriginal ist die Planckfrage stärker formuliert als die bloße Wahl einer Einheit. Mit der ersten positiven Nahtfrequenz [formula in source] und [formula in source] lautet das Potential in Rand-Einheiten Unter [formula in source] , [formula in source] für [formula in source] und [formula in source] gibt es genau ein positives stationäres [formula in source] . Dann gilt Das ist ein wirklicher bedingter Ein","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Auch die Skalen besitzen einen gemeinsamen Variationsansatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"}]},{"byte_end":4101,"byte_start":2605,"id":"section:710a570bea7ab5171bf0","kind":"subsection","labels":[],"line_end":46,"line_start":34,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/004-subsection-auch-die-skalen-besitzen-einen-gemeinsamen-va.tex","status_markers_as_written":[],"summary_excerpt":"Der Flavoransatz schreibt tatsächlich auf dem zulässigen, invertierbaren Projektionsraum. Der Transportpol wird über das ursprüngliche Determinantenfunktional von [formula in source] bestimmt. Für die neue Quelle ist deshalb die konkrete Gleichheit [formula in source] mit denselben Familienlegs, [formula in source] -Gradierungen und derselben Norm zu zeigen. Die neue E8-Quelle enthält nicht automatisch die Flavorhier","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der gemeinsame Operator ist im Original bereits präzise vorgegeben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":14904,"byte_start":4101,"id":"section:3ededccfeac789055af3","kind":"subsection","labels":["eq:nuactualselection","eq:nujointmassnorm","eq:nuwashoutcp","sec:neutrinojoint"],"line_end":172,"line_start":47,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:5b2ab7e81da1a3fccdff","relation:9c1118bae89845d1447a","relation:b53b7b39210fd9bab667","relation:c38c1c536b413ab734ff","relation:cb62f4f7aae16c0993f9","relation:f12fb307777efb09c60b"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/004-subsection-auch-die-skalen-besitzen-einen-gemeinsamen-va.tex","status_markers_as_written":[],"summary_excerpt":"Der Originalbestand liefert einen endlichen Diracoperator mit Dirac- und Majoranablock, den tatsächlichen Seesaw-Ausdruck und konkrete PMNS-Kanäle. Auf dem ursprünglichen Zweig stehen unter anderem [formula in source] , [formula in source] und die hexagonale Phasenlesart [formula in source] . Der spätere Pentagonzweig aus FLAV.NUSCALE.06 benutzt dagegen eine andere Mischung und Phase; er ist ein ausdrücklich bedingte","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neutrinos: Die vorhandenen Herleitungen gemeinsam lösen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":16359,"byte_start":14904,"id":"section:7779d02d30f1856735de","kind":"subsection","labels":[],"line_end":177,"line_start":173,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:02bd097817cd4a2f2aab","relation:0882f5a7c622f1a5e15d","relation:0f652d3b7fca7b100aa8","relation:1a4d2507feff1fac12e6","relation:1c0eff9671b49a053ae0","relation:2da9b1e3504c6dccb207","relation:42dfc016744f120fe953","relation:7a92dbe206ec837cb44a","relation:934d79ee470c301f077d","relation:9a046edc47cb353be0dd","relation:b829bf58dbbe6525d203","relation:bbcafe9c98aaad74832a","relation:bfbf92dc00a190a8a2c4","relation:d0fce665fb42a7c9617a","relation:d49243c04d4d668b642f","relation:d7a8972c9824f04ff40e","relation:d89628ff7fe416c2ca97","relation:dd48178ab99c217f1399","relation:dda9ada6db8e018b1da0","relation:f1f9ced5323f72d6b4c2"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/004-subsection-auch-die-skalen-besitzen-einen-gemeinsamen-va.tex","status_markers_as_written":[],"summary_excerpt":"Die Originalkennungen sind insbesondere FLAV.LEPTONC.01, FLAV.RIGID.01/02, FLAV.CKM.01, FLAV.PMNS.02, FLAV.NUSCALE.05/06, EM.WARD.01 und ALPHA.QUILLEN.EXACT.01. Neu ausgeführt wurden v20 (12/12), v71 (7/7), v118 (6/6), v88 (11/11), v3 (14/14) und v485 (5/5); diese Läufe prüfen ihre angegebenen Formeln und Operatorrechnungen. Eine neue Ausführung der gesamten Lean- oder Repository-Suite wird damit nicht behauptet.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Nachweise der erneuten Prüfung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":16996,"byte_start":16359,"id":"section:7f0a334934c934f50714","kind":"section","labels":["sec:operatorbridge"],"line_end":182,"line_start":178,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/004-subsection-auch-die-skalen-besitzen-einen-gemeinsamen-va.tex","status_markers_as_written":[],"summary_excerpt":"Die gemeinsame Verbindung ist konkreter geworden. Das ursprüngliche Fuchssystem liefert jetzt einen wirklichen Wegoperator, der exakt zum bereits verwendeten Sechsertransport äquivalent ist. Auf der anderen Seite liefert die ursprüngliche E8-Quelle eine konkrete neutrale Anregung mit Gewicht zwei und Normquadrat 48. Die gemeinsame Aufgabe ist dadurch keine Suche nach irgendeiner passenden Matrix mehr: Es ist die Herl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Fortsetzung: Der gemeinsame Flavor- und Nahtanschluss","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":18468,"byte_start":16996,"id":"section:7462e3e53c3e50ebcad8","kind":"subsection","labels":["eq:fullflavorintertwiner"],"line_end":202,"line_start":183,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:62d576454b1bcbfcfab5"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/004-subsection-auch-die-skalen-besitzen-einen-gemeinsamen-va.tex","status_markers_as_written":[],"summary_excerpt":"Der Originalvertrag source-native-clock-flavor-bridge-20260922/PROOF.md liefert eine feste invertierbare Matrix [formula in source] mit [formula in source] ist die dort ausgewählte positive Familienform, [formula in source] der ganzzahlige Dreierzyklus, [formula in source] die Familienmonodromie und [formula in source] die Vierteldrehung. Die Orientierungsgerade ist in [formula in source] ausdrücklich mitgeführt. Für","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der ganze endliche Operator besitzt bereits ein gemeinsames Wörterbuch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":25287,"byte_start":18468,"id":"section:fd793f72e342d1d06c7b","kind":"subsection","labels":["eq:flavorg2","eq:pointhexagon","sec:flavorcover"],"line_end":327,"line_start":203,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:641f5720c8de14056fa6","relation:fe24b37c7df3396b3d8f"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/004-subsection-auch-die-skalen-besitzen-einen-gemeinsamen-va.tex","status_markers_as_written":[],"summary_excerpt":"Zunächst lässt sich die bisher numerische Fuchs-Monodromie analytisch schließen. Das ursprüngliche System aus v117 ist [formula in source] , mit Die Substitution [formula in source] , [formula in source] liefert exakt und Die lokalen Exponenten bei [formula in source] sind somit [formula in source] , [formula in source] und [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Vierer- und Sechsergeometrie gehören zu demselben Überlagerungsproblem","topic_suggestions":[]},{"byte_end":29522,"byte_start":25287,"id":"section:72ed0cdd1ae27d7450eb","kind":"subsection","labels":["eq:pathT","eq:pathclockdictionary","sec:pathclock"],"line_end":380,"line_start":328,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/004-subsection-auch-die-skalen-besitzen-einen-gemeinsamen-va.tex","status_markers_as_written":[],"summary_excerpt":"Ein globaler Inversionsautomorphismus des einzelnen Flachbündels ist hierfür nicht nötig. Wähle einen regulären Ausgangspunkt [formula in source] und setze [formula in source] . Der Kreis mit Mittelpunkt [formula in source] und Radius [formula in source] erfüllt [formula in source] und ist unter [formula in source] invariant. Sein unterer Halbkreis [formula in source] führt von [formula in source] nach [formula in so","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Sechsertransport entsteht aus zwei ursprünglichen Halbwegen","topic_suggestions":[]},{"byte_end":1172,"byte_start":0,"id":"section:2c6b056596503b203150","kind":"subsection","labels":["sec:fuchswinding"],"line_end":14,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/005-subsection-die-urspr-ngliche-determinantenlinie-tr-gt-be.tex","status_markers_as_written":[],"summary_excerpt":"Hier liefert das Fuchssystem selbst eine weitere Herkunftsverbindung. Aus den ursprünglichen Residuen folgt Deshalb gilt exakt Die Phase [formula in source] besitzt auf dem oben konstruierten positiven Kreis um [formula in source] Windung [formula in source] . Die tatsächliche Fuchs-Determinantenlinie stellt somit dieselbe primitive [formula in source] -Klasse dar, die P1 verlangt. Der ganzzahlige Anteil stammt aus d","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die ursprüngliche Determinantenlinie trägt bereits primitive Windung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"}]},{"byte_end":4123,"byte_start":1172,"id":"section:e0756c547671392053a1","kind":"subsection","labels":[],"line_end":32,"line_start":15,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/005-subsection-die-urspr-ngliche-determinantenlinie-tr-gt-be.tex","status_markers_as_written":[],"summary_excerpt":"Die rekonstruierte Fermionenquelle enthält [formula in source] unter [formula in source] . Für [formula in source] gilt ausdrücklich Somit sind [formula in source] und [formula in source] wirkliche innere Symmetrien ihres Familienzweigs. Die vorhandenen sechs reellen Familienfermionen entsprechen drei komplexen Fermionen. Ihre Wirkung [formula in source] ist jedoch nicht [formula in source] . Das Original-Sechserregi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Familienoperationen wirken in der bereits vorhandenen Quelle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":6502,"byte_start":4123,"id":"section:f4ce3ea37f533d15c463","kind":"subsection","labels":[],"line_end":70,"line_start":33,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/005-subsection-die-urspr-ngliche-determinantenlinie-tr-gt-be.tex","status_markers_as_written":[],"summary_excerpt":"Die endliche Flavorgram-Matrix besitzt außerdem eine genaue Darstellung als Dirichlet-zu-Neumann-Antwort. Für [formula in source] , [formula in source] , einen zyklischen Shift [formula in source] und ist der Sprungoperator von [formula in source] auf den [formula in source] Kreisintervallen Die Gleichheit folgt durch Einsetzen von [formula in source] . Sie identifiziert eine Operatorfamilie; die Interpretation des i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine explizite gemeinsame Klasse von Randoperatoren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":9240,"byte_start":6502,"id":"section:6e7ca2de416ea191a5b9","kind":"subsection","labels":["eq:neutralselfenergy","sec:neutralport"],"line_end":114,"line_start":71,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/005-subsection-die-urspr-ngliche-determinantenlinie-tr-gt-be.tex","status_markers_as_written":[],"summary_excerpt":"Im Original-Mark-Greenoperator mit renormierter Diagonale null steht die dimensionslose Matrix Für den geometrischen Viererschritt [formula in source] liefert der Halbturn-gerade Projektor [formula in source] exakt Das benennt einen konkreten geometrischen Port. [formula in source] ist nicht die ursprüngliche Nahtinvolution; [formula in source] bleibt eine gesonderte Feldidentifikation.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der gemeinsame neutrale Port ist jetzt genauer bestimmt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"}]},{"byte_end":12512,"byte_start":9240,"id":"section:65038733291239a68723","kind":"subsection","labels":["eq:nativeresidual","sec:neutralfield"],"line_end":156,"line_start":115,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/005-subsection-die-urspr-ngliche-determinantenlinie-tr-gt-be.tex","status_markers_as_written":[],"summary_excerpt":"Die ursprüngliche Level-eins-E8-Quelle enthält die Spinorströme [formula in source] mit 64 Komponenten und ihre Gegenfelder. Unter der erklärten Familienauswahl [formula in source] zerfällt dieser Block in [formula in source] . Die erste Komponente ist der hier untersuchte 48er-Materiereadout. Seine Identifikation mit dem ursprünglichen topologischen Familienraum bleibt Teil des markierten Wörterbuchs; die Rechnung b","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die tatsächliche Quelle liefert einen bestimmten neutralen Kandidaten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"}]},{"byte_end":15118,"byte_start":12512,"id":"section:3d5b50cd8b3a0fb6b631","kind":"subsection","labels":["eq:actualheatport","eq:conditionalvertex","sec:heatport"],"line_end":188,"line_start":157,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/005-subsection-die-urspr-ngliche-determinantenlinie-tr-gt-be.tex","status_markers_as_written":[],"summary_excerpt":"Dieser Zustand liefert eine konkrete Realisierung der zuvor nur als Ziel formulierten Gleichung Definiert man den Quellenzugang und die euklidische Quellenfortsetzung durch so folgt auf der vollständigen Quelle exakt Damit liefert derselbe erklärte Port auch [formula in source] , einschließlich seiner höheren Logdet-Koeffizienten. Der Exponent zwei ist nun das Gewicht eines vorhandenen Feldzustands; die 48 ist dessen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein exakter Quellenport realisiert den Alpha-Rundlauf bedingt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"}]},{"byte_end":18432,"byte_start":15118,"id":"section:ce7e00748b1472c65dca","kind":"subsection","labels":["eq:defectRnorm","eq:jointRresponse","sec:jointneutralward"],"line_end":221,"line_start":189,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/005-subsection-die-urspr-ngliche-determinantenlinie-tr-gt-be.tex","status_markers_as_written":[],"summary_excerpt":"Der neue Kandidat lässt sich unmittelbar am ursprünglichen Flavor-Hintergrund prüfen. Dafür wird die normierte Riemann–Hilbert-Defektantwort derselben drei komplexen Familienfermionen verwendet, mit den ursprünglichen Residuen und dem vorgeschriebenen ausgehenden Sektor. In dieser Darstellung liefern die Fermionen-Wardidentitäten Die symmetrische Stressdefinition entfernt den Ableitungsterm; der verbundene [formula i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Flavor und neutrale Quelle besitzen bereits eine gemeinsame berechnete Antwort","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":22474,"byte_start":18432,"id":"section:0cfe9479b259eaa3ab37","kind":"subsection","labels":["eq:fullflavorRR","sec:fullflavorRR"],"line_end":300,"line_start":222,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:227b31266b781de974a9"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/005-subsection-die-urspr-ngliche-determinantenlinie-tr-gt-be.tex","status_markers_as_written":[],"summary_excerpt":"Die gemeinsame Einpunktantwort bestimmt bereits einen Teil der Verträglichkeit. Der vollständige verbundene Zweipunktkern liefert nun die tatsächliche Antwort zwischen zwei verschiedenen Einsetzungsorten. Entscheidend ist die unveränderte Feldkonvention des ursprünglichen Fuchs- und Riemann–Hilbert-Systems: [formula in source] Im normierten quasifreien Riemann–Hilbert-Defektmatrixelement folgt aus symmetrischer Fermi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die vollständige neutrale Antwort im ursprünglichen Flavorprozess","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":24773,"byte_start":22474,"id":"section:67ccc4df3b51f6dae230","kind":"paragraph","labels":["eq:originalportmatching"],"line_end":346,"line_start":301,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:21e8f4e2d19cdd31406d","relation:9b53d2eb6bc57932639d","relation:e06799989b96d73a707b","relation:f703f57b90e18ddd1e0f"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/005-subsection-die-urspr-ngliche-determinantenlinie-tr-gt-be.tex","status_markers_as_written":[],"summary_excerpt":"Die Originalverifikationen v484 und v485 enthalten den Viermarken-Kern und seinen logarithmischen Referenzabzug. Ihre Matrix lautet [formula in source] Hier bezeichnet [formula in source] bereits das Orbitmittel des ursprünglichen Mark-Greenkerns. Mit der zyklischen Markverschiebung [formula in source] , [formula in source] und [formula in source] folgt exakt [formula in source] Der gerade Markraum hat Dimension zwei","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der ursprüngliche Randport ist bereits berechenbar.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":4395,"byte_start":0,"id":"section:82e83c4166bce36b708d","kind":"subsection","labels":["eq:neutralchargegram","eq:twojointpairresponses","sec:chargeweightedsource"],"line_end":82,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:2fc412e9a6455b5f9418","relation:4233b69f28f9696bed6c","relation:77be247f5ab0cb251f64","relation:d37f1ce55d45c804c380"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/006-subsection-die-48-und-die-41-sind-zwei-antworten-derselb.tex","status_markers_as_written":[],"summary_excerpt":"Der neue neutrale Zustand [formula in source] trägt die ungewichtete Familienantwort. Die ursprüngliche Hyperladung ist dagegen durch die [formula in source] -Markierung bereits festgelegt: [formula in source] Es wird also keine neue Ladung gewählt. Auf den ursprünglichen 48 Wurzeln ergeben sich [formula in source] Die tatsächlichen Multiplizitäten sind [formula in source] Felder mit [formula in source] , jeweils [fo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die 48 und die 41 sind zwei Antworten derselben geladenen Quelle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":7951,"byte_start":4395,"id":"section:9d6f6d49259b95cd9a4e","kind":"subsection","labels":["eq:fullsourceschur"],"line_end":118,"line_start":83,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/006-subsection-die-48-und-die-41-sind-zwei-antworten-derselb.tex","status_markers_as_written":[],"summary_excerpt":"Für einen positiven Operator [formula in source] auf erhaltenen und eliminierten Zuständen gilt Der Komplementterm ist das genaue Gedächtnis der nicht angezeigten Zustände. Bei positiver invertierbarer Komplementresolvente würde die Gleichheit mit [formula in source] bereits [formula in source] erzwingen. Ein exakt abgeschlossener endlicher Block ist deshalb eine stärkere Annahme als eine antworttreue Reduktion mit G","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Welche gemeinsame Reduktion die vorhandenen Antworten wirklich erhält","topic_suggestions":[]},{"byte_end":9182,"byte_start":7951,"id":"section:e7294e8d8a250400195d","kind":"subsection","labels":[],"line_end":123,"line_start":119,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:3177178f1fce0e6177a0","relation:3b66daebb2223f48cb00","relation:53d6d930dae7540a8140","relation:5641827a242a8d2a8745","relation:6d4c55eb1fc13fca0197","relation:850352d45d43bdb7122c","relation:ab8d46b4aff12dd6494e","relation:d0ca27fff9d24b4391bb","relation:de2acab93fc0f00c7e98","relation:dea916a68de10e239d71"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/006-subsection-die-48-und-die-41-sind-zwei-antworten-derselb.tex","status_markers_as_written":[],"summary_excerpt":"tfpt_explorer/flavor_path_transport.py integriert die ursprüngliche Verbindung entlang beider Halbwege und unabhängig entlang des geschlossenen Kreises. Es berechnet die Determinantenwindung aus den integrierten Lösungen und vergleicht die vollständigen endlichen Greenmatrizen. tfpt_explorer/neutral_source_response.py benutzt die ursprünglichen E8-Wurzeln, ihre Stressmomentmatrizen und den tatsächlichen Heisenbergzus","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ausführbare Nachweise dieser Fortsetzung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":10490,"byte_start":9182,"id":"section:dd6ae75f0a051dc057b2","kind":"section","labels":["sec:spinliftsynthesis"],"line_end":130,"line_start":124,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/006-subsection-die-48-und-die-41-sind-zwei-antworten-derselb.tex","status_markers_as_written":[],"summary_excerpt":"Der neue positive Herkunftssatz: Die primitive Determinantenwindung des ursprünglichen Flavorprozesses bestimmt beim internen Spin-Lift ein zusätzliches Minuszeichen. In der vorhandenen E8-Verklebung ist dieses Zeichen genau die Involution, die den 120er-Tensorsektor vom 128er-Spinorsektor unterscheidet. Damit ist ein Sechserumlauf auf tatsächlichen geladenen Quellenfeldern konstruiert. Die Identifikation dieses inne","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Windung wirkt auf der ganzen Quelle: neuer Anschluss und gemeinsamer Massentest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":12320,"byte_start":10490,"id":"section:1f9e527982f2ecac11e7","kind":"subsection","labels":["eq:nativespinlift"],"line_end":151,"line_start":131,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/006-subsection-die-48-und-die-41-sind-zwei-antworten-derselb.tex","status_markers_as_written":[],"summary_excerpt":"Die Eigenwerte der lokalen ursprünglichen Residuen sind [formula in source] . Die Spurlosfassung [formula in source] hat dieselben exponentierten Eigenwerte. Ihre Verbindungspfade sind dennoch verschieden: Beide enden am gleichen [formula in source] -Element. Die Determinante des ersten Pfads windet sich einmal, die des zweiten keinmal. Genau die erste Klasse trägt der integrierte Originalkreis, weil [formula in sour","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine weggeworfene Windung wäre eine weggeworfene Quellenwirkung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":14661,"byte_start":12320,"id":"section:d74cb58447f8b5833b9e","kind":"subsection","labels":["eq:deckspinidentity","eq:fullsourcesix"],"line_end":184,"line_start":152,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/006-subsection-die-48-und-die-41-sind-zwei-antworten-derselb.tex","status_markers_as_written":[],"summary_excerpt":"Im Original gilt als wirkliche Untergruppe von E8 Die diagonale Vierergruppe ist der Kern dieser Darstellung: Sie wirkt auf E8 trivial. Die einzeln wirksamen Faktorzentren erfüllen dagegen Alle 240 Originalwurzeln bestätigen dieselbe Charaktergleichheit; die acht Cartanrichtungen gehören zum geraden 120er-Sektor. Die Vorzeichen respektieren die ursprünglichen Wurzelklammern und damit die ganze von ihnen erzeugte Quel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Spinrahmen trifft genau die ursprüngliche E8-Verklebung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"}]},{"byte_end":16733,"byte_start":14661,"id":"section:5d1bba979b8fcae72626","kind":"subsection","labels":[],"line_end":200,"line_start":185,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/006-subsection-die-48-und-die-41-sind-zwei-antworten-derselb.tex","status_markers_as_written":[],"summary_excerpt":"Der interessante Gedanke des Anhangs ist, zusätzlich eine vierdimensionale Spin- [formula in source] -Struktur mit [formula in source] zu verlangen. Für gleichorientierte Weylfermionen zählt deren Anomalie den Unterschied der [formula in source] - und [formula in source] -Zustände modulo 16 razamattong. Auf dem ursprünglichen Halbspinor gilt feldweise Alle 16 Komponenten tragen denselben [formula in source] -Charakte","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was der neue Anomalieselektor tatsächlich auswählt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":18892,"byte_start":16733,"id":"section:62da8d57db3260c78314","kind":"subsection","labels":["sec:spinmajorana"],"line_end":223,"line_start":201,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:dafa7b55a224ff2c3279"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/006-subsection-die-48-und-die-41-sind-zwei-antworten-derselb.tex","status_markers_as_written":[],"summary_excerpt":"Eine gemeinsame Lösung muss dieselbe Symmetrie auch auf den bereits verwendeten Higgs- und Neutrinofeldern realisieren. Das ursprüngliche Standardmodell-Paper benutzt, weil ein elementares [formula in source] im erklärten Hull fehlt, den Einsatz Quelle: tfpt_2_standard_model.tex, Zeilen 2003–2006, und verification/v488_majorana_clebsch_door.py. Unter einer gewöhnlichen internen [formula in source] ist der Einsatz neu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der ganze Massensektor entscheidet über die neue Zusatzannahme","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":23490,"byte_start":18892,"id":"section:1619e17fcf57340feb0f","kind":"subsection","labels":["eq:nativemajoranacoupling","sec:sourcepairs"],"line_end":273,"line_start":224,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/006-subsection-die-48-und-die-41-sind-zwei-antworten-derselb.tex","status_markers_as_written":[],"summary_excerpt":"Der Konflikt wurde unmittelbar in der bestehenden Quelle weiterverfolgt. Es wurde kein neues elementares Higgsfeld eingeführt. Die ursprünglichen vier Singletströme [formula in source] im markierten Spinorblock besitzen Wurzeln [formula in source] mit [formula in source] und [formula in source] sind die tatsächlichen Originalphasen und der ursprüngliche Gitterkokzyklus. Bei der Konvention [formula in source] trägt di","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der benötigte geladene Paarkanal ist in der tatsächlichen Quelle vorhanden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"}]},{"byte_end":26359,"byte_start":23490,"id":"section:af381de775ce2041dbf4","kind":"subsection","labels":["eq:majoranapairtransport"],"line_end":309,"line_start":274,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/006-subsection-die-48-und-die-41-sind-zwei-antworten-derselb.tex","status_markers_as_written":[],"summary_excerpt":"Der benutzte Spinlift wirkt auf Sein symmetrischer Familienpaarraum zerfällt daher als [formula in source] ; der konjugierte Kanal enthält [formula in source] . Der Sechserraum ist der Raum symmetrischer Matrizen für drei Familien. Seine Komponenten sind noch keine bestimmten Erwartungswerte.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der symmetrische Paartransport schließt an den ursprünglichen Flavorweg an","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":28760,"byte_start":26359,"id":"section:1b4dc6009cb25792e1b9","kind":"subsection","labels":["eq:neutralmajoranaward","sec:neutralpairward"],"line_end":331,"line_start":310,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/006-subsection-die-48-und-die-41-sind-zwei-antworten-derselb.tex","status_markers_as_written":[],"summary_excerpt":"Die neue Paarstruktur kann mit dem bereits bestimmten neutralen Feld [formula in source] in derselben Quelle geprüft werden. Verwende dieselbe Auswahl, in der [formula in source] der ausgelassene Familien-Singulettzugang und [formula in source] der Dreieranteil sind. Für einen reinen normierten Gitterzustand [formula in source] gilt mit der ursprünglichen Matrix [formula in source] Der symmetrische Paarzustand [formu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der neutrale Alpha-Kandidat antwortet auf diesen Neutrinokanal","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"}]},{"byte_end":30102,"byte_start":28760,"id":"section:0444ab0b0ae0c5cad185","kind":"subsection","labels":[],"line_end":344,"line_start":332,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:d0e1d6e2e60ca39d57c7","relation:e0e73a9327802487cbe9"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/006-subsection-die-48-und-die-41-sind-zwei-antworten-derselb.tex","status_markers_as_written":[],"summary_excerpt":"Für die tatsächliche chirale E8-Fermionisierung gelten Die E8-Decksymmetrie hat Zeichen [formula in source] ; Fermionparität in den neuen Sektoren hat Zeichen [formula in source] beziehungsweise [formula in source] boylesmith. Das sind verschiedene Operatoren auf verschiedenen Sektoren.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die vorhandene Fermionisierung den Statistikschritt nicht überspringt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":32835,"byte_start":30102,"id":"section:faadce3641621281c19b","kind":"subsection","labels":["sec:carpairdictionary"],"line_end":393,"line_start":345,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/006-subsection-die-48-und-die-41-sind-zwei-antworten-derselb.tex","status_markers_as_written":[],"summary_excerpt":"Die Sektorunterscheidung lässt einen konstruktiven gemeinsamen Anschluss zu. Die geraden Paaroperatoren liegen im gemeinsamen [formula in source] -Vakuummodul [formula in source] . Für die hier auftretenden ganzzahligen Impulse [formula in source] setze [formula in source] in wachsender Koordinatenfolge. Die ursprünglichen E8- und CAR-Kokzyklen auf [formula in source] sind durch die im Programm angegebene quadratisch","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Majoranapaare bleiben als lokale CAR-Komposite erhalten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"}]},{"byte_end":2554,"byte_start":0,"id":"section:59b50548b2eacea6e329","kind":"subsection","labels":["eq:massformencoding","eq:pairisometry","eq:pairtomography","sec:neutrinodictionary"],"line_end":47,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/007-subsection-die-vollst-ndige-neutrinomatrix-besitzt-ein-n.tex","status_markers_as_written":[],"summary_excerpt":"Die vorhandenen Neutrinoherleitungen liefern ganze komplexe Matrizen. Ihr Quellenanschluss darf sich deshalb nicht auf Massen, Spur oder Norm beschränken. Der bereits konstruierte symmetrische Sechserraum hat genau die dafür benötigte bilineare Struktur. Für eine komplex-symmetrische Koeffizientenmatrix [formula in source] sei Die 36 ursprünglichen affinen Paarungen ergeben Dabei haben diagonale Paare Normquadrat ein","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die vollständige Neutrinomatrix besitzt ein norm- und phasentreues Quellenwörterbuch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":4323,"byte_start":2554,"id":"section:6bc5f7df6561e72eadcc","kind":"paragraph","labels":[],"line_end":81,"line_start":48,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/007-subsection-die-vollst-ndige-neutrinomatrix-besitzt-ein-n.tex","status_markers_as_written":[],"summary_excerpt":"Der konkrete D5-Singulettpaarkanal besitzt [formula in source] und gehört zum [formula in source] - beziehungsweise konjugierten schweren Majorana-Anschluss. Sein direkter Familientensor ist die ursprüngliche schwere Form [formula in source] in der erklärten Q [formula in source] -Eigenbasis. Auch sie wird durch [formula in source] samt allen sechs Rückleseamplituden dargestellt. Für den dimensionslosen Tensor [formu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Schwere und leichte Neutrinos bleiben verschiedene physische Felder.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":5105,"byte_start":4323,"id":"section:9066906d14d53927649f","kind":"paragraph","labels":[],"line_end":95,"line_start":82,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/007-subsection-die-vollst-ndige-neutrinomatrix-besitzt-ein-n.tex","status_markers_as_written":[],"summary_excerpt":"Das Programm verwendet den ursprünglichen Operator [formula in source] und die eingefrorenen Eingaben von nu_scalaron_v3.yaml. Die bestehende gleichzeitige Bedingung aus größtem Dirac-Singularwert und [formula in source] aus Abschnitt [formula in source] Dies ist die bereits dokumentierte bedingte Konsistenzlösung, keine neue Massenprognose. Insbesondere bleiben die Kalibrierung von [formula in source] , der Washout-","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die bereits vorhandenen gemeinsamen Neutrinobedingungen bleiben erhalten.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":6470,"byte_start":5105,"id":"section:68206360dff9a21fa2a7","kind":"paragraph","labels":["eq:majoranaphaseresponse"],"line_end":119,"line_start":96,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/007-subsection-die-vollst-ndige-neutrinomatrix-besitzt-ein-n.tex","status_markers_as_written":[],"summary_excerpt":"Im ausdrücklich phasenoffenen Zweig mit [formula in source] verbleibt eine physische Majorana-Phase. Mit dem ursprünglichen [formula in source] lautet diese Familie Die unveränderten leichten Massen, PMNS-Winkel und Dirac-CP-Invariante, [formula in source] , die ungeflavorten schweren CP-Invarianten sowie [formula in source] wählen [formula in source] nicht aus. Mit [formula in source] , wobei [formula in source] die","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die verbleibende Phase wird nun zu einer konkreten Quellenantwort.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":8273,"byte_start":6470,"id":"section:32f4278cfa35e310cbcd","kind":"paragraph","labels":[],"line_end":155,"line_start":120,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/007-subsection-die-vollst-ndige-neutrinomatrix-besitzt-ein-n.tex","status_markers_as_written":[],"summary_excerpt":"Die beiden ursprünglichen markierten Generatoren liefern einen zusätzlichen exakten Test. In der zyklischen Darstellung seien sie [formula in source] und [formula in source] . Sie erfüllen [formula in source] . Für eine gemeinsame Charakterlinie des symmetrischen Paarraums folgen daraus [formula in source] , also [formula in source] . Eine [formula in source] -invariante symmetrische Matrix besitzt die Form [formula ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Welche Symmetrie die Matrix tatsächlich auswählen darf.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":9826,"byte_start":8273,"id":"section:5a20ac3d1660e5433ae5","kind":"paragraph","labels":[],"line_end":183,"line_start":156,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:87dd015089e82a4f9743"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/007-subsection-die-vollst-ndige-neutrinomatrix-besitzt-ein-n.tex","status_markers_as_written":[],"summary_excerpt":"Alle sechs Paare tragen [formula in source] , während die neutralen Felder und die Familien-Defekte diese D5-Ladung nicht kompensieren. Im ursprünglichen [formula in source] -invarianten Vakuum gilt folglich [formula in source] Eine Matrix als geladene Einsetzung zu berechnen ist damit etwas anderes als ihre Auswahl durch einen physisch realisierten Hintergrund. Der verschwindende Einpunktwert schließt einen eichinva","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der jetzt genau bestimmte Auswahlgegenstand.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":10433,"byte_start":9826,"id":"section:13e84caf3b741e5ef992","kind":"subsection","labels":["sec:masssourceconnection"],"line_end":192,"line_start":184,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/007-subsection-die-vollst-ndige-neutrinomatrix-besitzt-ein-n.tex","status_markers_as_written":[],"summary_excerpt":"Die Fortsetzung vom 29. September arbeitet unmittelbar am vorher benannten Anschluss. Die ursprüngliche Fuchsverbindung bestimmt nicht nur die Familienendphasen. Ihr tatsächlicher Spin-Lift induziert auf den sechs symmetrischen Paaren eine Verbindung, aus der sich die ganze ursprüngliche Verbindung wieder zurückgewinnen lässt. Auch die primitive Determinantenwindung und die bereits berechnete neutrale RHP-Antwort las","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein gemeinsamer Transport für primitive Windung, Massentensor und neutrale Antwort","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":11581,"byte_start":10433,"id":"section:518137b49ed8cfe0b1a2","kind":"paragraph","labels":["eq:massspinconnection"],"line_end":215,"line_start":193,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/007-subsection-die-vollst-ndige-neutrinomatrix-besitzt-ein-n.tex","status_markers_as_written":[],"summary_excerpt":"Setze [formula in source] , [formula in source] und [formula in source] . Die bereits an den tatsächlichen C-Strömen geprüfte Basisabbildung ist [formula in source] , wobei [formula in source] die native Reihenfolge [formula in source] in die Außenpotenzreihenfolge [formula in source] übersetzt und [formula in source] die dreidimensionale Hodge-Abbildung ist. Die Identität [formula in source] ergibt auf dem behaltene","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die ursprüngliche Dreierwirkung muss mit ihrem Spin-Lift eingehen.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":14331,"byte_start":11581,"id":"section:d0851fb9eda15730139e","kind":"paragraph","labels":["eq:massdeterminantcarry"],"line_end":267,"line_start":216,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/007-subsection-die-vollst-ndige-neutrinomatrix-besitzt-ein-n.tex","status_markers_as_written":[],"summary_excerpt":"Für einen symmetrischen Quellenkoeffizienten [formula in source] und eine duale symmetrische Massenform [formula in source] lautet der faserweise Transport Denn [formula in source] . Die beiden Vorzeichen sind daher keine wählbaren Konventionen innerhalb derselben Zuordnung: Die Paarzustände und ihre kontrahierenden Koeffizienten sind dual. Das skalare Matrixelement [formula in source] bleibt erhalten, wenn gleichzei","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zustand und Massenkoeffizient besitzen entgegengesetzte Orientierung.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":15490,"byte_start":14331,"id":"section:749f7c5e961e74c49def","kind":"paragraph","labels":["eq:pairtraces","eq:sixconnection"],"line_end":293,"line_start":268,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/007-subsection-die-vollst-ndige-neutrinomatrix-besitzt-ein-n.tex","status_markers_as_written":[],"summary_excerpt":"Die induzierte Verbindung auf [formula in source] ist Aus ihrer Wirkung auf [formula in source] liest man [formula in source] auf dem diagonalen Eintrag und [formula in source] auf dem Eintrag [formula in source] ab. Damit sind sämtliche neun komplexen Einträge von [formula in source] bekannt. Es folgt [formula in source] Die Abbildung der Verbindung ist daher injektiv. Eine beliebige [formula in source] -Matrix lieg","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die sechs Paarkanäle behalten die vollständige Verbindung.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":16524,"byte_start":15490,"id":"section:9ab6936ae3a6bdf50683","kind":"paragraph","labels":["eq:massRRconnection","eq:massRconnection"],"line_end":312,"line_start":294,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/007-subsection-die-vollst-ndige-neutrinomatrix-besitzt-ein-n.tex","status_markers_as_written":[],"summary_excerpt":"Im festgehaltenen ursprünglichen Fuchsrahmen und mit derselben symmetrischen RHP-Normalordnung wie in Abschnitt Die rechte Seite stimmt mit dem bereits berechneten vollständigen rationalen Flavor-Defektkern überein. Es wird keine zweite neutrale Quelle eingesetzt. Die Spuren einer Verbindungsform sind bei beliebigen lokalen Rahmenwechseln nicht für sich invariant; deren Ward-/Normalordnungsterme müssen dann ebenfalls","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die neutrale Antwort ist eine Kontraktion genau dieser Verbindung.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"}]},{"byte_end":21114,"byte_start":16524,"id":"section:5112bdd23a5ba88e3d14","kind":"paragraph","labels":["eq:covariantpairjet"],"line_end":392,"line_start":313,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:fa7043f7b8b1fcbd5345"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/007-subsection-die-vollst-ndige-neutrinomatrix-besitzt-ein-n.tex","status_markers_as_written":[],"summary_excerpt":"Eine faserweise Darstellung allein berechtigt noch nicht dazu, gewöhnliche Ableitungen von ortsabhängig gedrehten Feldern einzusetzen. Hier ist die Korrektur konkret. In einer Spaltenkonvention für die Feldkomponenten sei [formula in source] Der konstante Term fehlt wegen der tatsächlichen Nullrelation [formula in source] . [formula in source] ist der bereits vorhandene antisymmetrische Grad-drei-Kanal. Für eine Feld","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Auch der nötige lokale Ableitungsterm lässt sich aus derselben Quelle ergänzen.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":1004,"byte_start":0,"id":"section:cd6ae36102a9e34a7944","kind":"subsection","labels":["sec:wallaudit"],"line_end":5,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/008-subsection-die-wand-lesart-gemeinsamer-geometrischer-ans.tex","status_markers_as_written":[],"summary_excerpt":"Die Wand-Idee liefert einen bedingten geometrischen Anschluss, aber keinen Zwang zu Dirac-Neutrinos. Die volle ursprüngliche Quelle enthält bereits Standardmodell-Singuletts mit [formula in source] . Ein spezielles Spinorbündel verbindet außerdem Familienindex und Anomalieklasse. Die entscheidende gemeinsame Auswahl betrifft die Verbindung, den physischen Zustand und die Kopplung; sie folgt nicht aus dem Fehlen eines","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Wand-Lesart: gemeinsamer geometrischer Anschluss und korrigierte Neutrino-Weiche","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":3685,"byte_start":1004,"id":"section:013a70b2e26d694794e4","kind":"paragraph","labels":[],"line_end":27,"line_start":6,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/008-subsection-die-wand-lesart-gemeinsamer-geometrischer-ans.tex","status_markers_as_written":[],"summary_excerpt":"Die Konstruktion beginnt mit elfdimensionaler Supergravitation und zwei zehndimensionalen Randkomponenten. Deren chirale Anomalie verlangt unter diesen Voraussetzungen 248 Vektormultipletts pro Wand; die vollständige Faktorisierung und das heterotische Wörterbuch führen zu [formula in source] horavawittenorigin,horavawittenwall. Der relevante irreduzible Gravitationsanteil ist [formula in source] in einem Zwölfform-A","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was Hořava–Witten tatsächlich verbindet.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"}]},{"byte_end":6107,"byte_start":3685,"id":"section:bd7a49f6074daa4f3282","kind":"paragraph","labels":["eq:wallchern","eq:wallindex"],"line_end":54,"line_start":28,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/008-subsection-die-wand-lesart-gemeinsamer-geometrischer-ans.tex","status_markers_as_written":[],"summary_excerpt":"Sei [formula in source] eine geschlossene orientierte Spin-Sechsmannigfaltigkeit, und werde ausdrücklich [formula in source] gewählt. Für die formalen Krümmungswurzeln [formula in source] von [formula in source] sind die vier Spinorgewichte Die elementarsymmetrischen Polynome ergeben unmittelbar mit umgekehrtem Vorzeichen des letzten Terms bei vertauschter Chiralität. Da [formula in source] keinen Term vom Grad sechs","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die stärkste richtige geometrische Identität.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":8340,"byte_start":6107,"id":"section:4afbffc16768cc02264e","kind":"paragraph","labels":[],"line_end":67,"line_start":55,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/008-subsection-die-wand-lesart-gemeinsamer-geometrischer-ans.tex","status_markers_as_written":[],"summary_excerpt":"Braun–Candelas–Davies–Donagi verwenden einen bekannten Raum mit [formula in source] , [formula in source] und [formula in source] . Ihr Abschnitt 3 untersucht Deformationen von [formula in source] ; Anhang B skizziert die mögliche Rang-vier-Konstruktion als Hilfsargument; das ausgearbeitete Modell verwendet Rang fünf. Die Topologie bleibt dabei erhalten braundeformation. Für die Wand-Lesart ist deshalb der präzise Ka","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein konkreter Anschluss, ohne eine neue Innengeometrie zu erfinden.","topic_suggestions":[]},{"byte_end":10379,"byte_start":8340,"id":"section:487af21f89f692df50f3","kind":"paragraph","labels":[],"line_end":93,"line_start":68,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/008-subsection-die-wand-lesart-gemeinsamer-geometrischer-ans.tex","status_markers_as_written":[],"summary_excerpt":"Wir verwenden die bereits originale Normierung Für die linkshändigen [formula in source] gilt [formula in source] . Die zwei exemplarischen nativen Zustände haben [formula in source] , [formula in source] , [formula in source] . Alle acht positiven und negativen Wurzelgeneratoren von [formula in source] annihilieren sie im einfachen unitären Quotienten; auch ihre Cartan-Gewichte verschwinden. Dieselbe Rechnung wurde ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Herleitung eines Ausschlusses aus der 248 ist widerlegt.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"}]},{"byte_end":11994,"byte_start":10379,"id":"section:24b9a184e6a304cbf057","kind":"paragraph","labels":[],"line_end":115,"line_start":94,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/008-subsection-die-wand-lesart-gemeinsamer-geometrischer-ans.tex","status_markers_as_written":[],"summary_excerpt":"Bei einer exakt erhaltenen schützenden Rest- [formula in source] lauten die Auswahlregeln für hyperladungsneutrale Operatoren: lrl Operator & [formula in source] & Rest- [formula in source] \\\\ [formula in source] & [formula in source] & erlaubt\\\\ [formula in source] & [formula in source] & verboten\\\\ [formula in source] & [formula in source] & verboten\\\\ [formula in source] & [formula in source] & erlaubt\\\\ [formula ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was über Dirac oder Majorana wirklich entscheidet.","topic_suggestions":[]},{"byte_end":13669,"byte_start":11994,"id":"section:bcabca0edb49668c4ae3","kind":"paragraph","labels":[],"line_end":126,"line_start":116,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:ec413a174a72fdef956d"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/008-subsection-die-wand-lesart-gemeinsamer-geometrischer-ans.tex","status_markers_as_written":[],"summary_excerpt":"Alle zwölf ursprünglichen [formula in source] -Wurzeln besitzen [formula in source] ; seine Cartanoperatoren sind ebenfalls neutral. Der bisherige Familientransport und das neutrale [formula in source] erhalten diese Ladung. Im invarianten Quellvakuum folgt deshalb exakt während [formula in source] positiv ist. Die volle Transportgleichung aus Abschnitt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum der vorhandene Familienprozess die Phase noch nicht auswählt.","topic_suggestions":[]},{"byte_end":15469,"byte_start":13669,"id":"section:9873d8728c127f20b433","kind":"paragraph","labels":[],"line_end":133,"line_start":127,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/008-subsection-die-wand-lesart-gemeinsamer-geometrischer-ans.tex","status_markers_as_written":[],"summary_excerpt":"Die Wand-Lesart darf die vorhandenen [formula in source] -, Massen- und Flavorherleitungen nicht durch freie Kompaktifizierungsparameter ersetzen. Schon dimensionsanalytisch ist [formula in source] von der Dimension Länge hoch sechs, während [formula in source] dimensionslos ist. In einer unverwobenen Produktkompaktifizierung mit konstantem Hintergrund gilt schematisch [formula in source] ; Normierung, Schwellen und ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die gemeinsame Bedingung für den weiteren Lösungsweg.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":25154,"byte_start":15469,"id":"section:9621677b00fd57a555f8","kind":"subsection","labels":["eq:massmodeexact","eq:sourcemajoranaoperator","sec:masszeromode"],"line_end":325,"line_start":134,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:84dfd0dea9547df014d6"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/008-subsection-die-wand-lesart-gemeinsamer-geometrischer-ans.tex","status_markers_as_written":[],"summary_excerpt":"Der innere Operatoranschluss ist jetzt explizit geschlossen. Die zuvor konstruierten Paarfelder erzeugen durch ihre tatsächliche Modenwirkung genau die symmetrischen Matrixeinträge des ursprünglichen schweren Neutrinoblocks. Dieselbe Einsetzung liefert nach Eliminierung der schweren Zustände die vorhandene Seesaw-Matrix, einen Determinantenbeitrag und eine vollständige Gedächtnisantwort. Die Wahl der Einsetzung und i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vom Quellenfeld zum wirklichen Massenblock und zur gemeinsamen Vergröberung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":559,"byte_start":0,"id":"section:fb5a79ad28f8f85f979b","kind":"subsection","labels":["sec:stateactionclosure"],"line_end":9,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/009-subsection-zustand-und-wirkung-aus-derselben-r-ckwirkung.tex","status_markers_as_written":[],"summary_excerpt":"Die gemeinsame Information ist jetzt genauer bestimmt. Eine korrekte Vergröberung muss sowohl die dynamische Antwort als auch den reduzierten Zustand aus demselben vollständigen Kern gewinnen. Am ursprünglichen Neutrinooperator ist diese Verbindung nun berechnet. Der aus einer Momentaufnahme rekonstruierte Operator ist im Allgemeinen nicht die ruhende Massenantwort. Unter passender Trennung der schweren und leichten ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zustand und Wirkung aus derselben Rückwirkung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"}]},{"byte_end":3386,"byte_start":559,"id":"section:8957ddff03f7cb92b048","kind":"paragraph","labels":["eq:commonsourcekms"],"line_end":70,"line_start":10,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:222e199bf2a8c0c87e4e","relation:7e17a2e9f0c735d50065"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/009-subsection-zustand-und-wirkung-aus-derselben-r-ckwirkung.tex","status_markers_as_written":[],"summary_excerpt":"verification/v258_dirac_covariance_induction.py verwendet bereits die Fermi-Dirac-Kovarianz und ihre Logit-Inversion. Für einen vollständigen endlichen Operator gilt diese Inversion exakt. Das erklärt jedoch noch nicht die stärkere Kompressionsgleichung [formula in source] : Die Inversion einer komprimierten Kovarianz ist im Allgemeinen weder [formula in source] noch deren statisches Schurkomplement. Die neue Rechnun","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Anschluss an die ursprünglichen Verifikationen.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":4568,"byte_start":3386,"id":"section:d4bc29433ac83d3ded4c","kind":"paragraph","labels":["eq:sourcekmsaction"],"line_end":95,"line_start":71,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/009-subsection-zustand-und-wirkung-aus-derselben-r-ckwirkung.tex","status_markers_as_written":[],"summary_excerpt":"Für den endlichen komplexen CAR-Vergleich gilt [formula in source] . Sei [formula in source] der entkoppelte Vergleich. Da beide Operatoren dieselbe Spur haben, folgt aus dem Produkt für den hyperbolischen Kosinus und derselben Schuridentität Die Realteile sind als Logarithmen der Beträge unabhängig von einer Phasenwahl des komplexen Logarithmus. Die ungekoppelte schwere Determinante kürzt sich; ihre Wirkung auf den ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum derselbe Kern auch die Wirkung trägt.","topic_suggestions":[]},{"byte_end":7286,"byte_start":4568,"id":"section:f4fc0af10aaac064b21c","kind":"paragraph","labels":["eq:kmswindow","eq:sourcekmsfilter"],"line_end":159,"line_start":96,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/009-subsection-zustand-und-wirkung-aus-derselben-r-ckwirkung.tex","status_markers_as_written":[],"summary_excerpt":"Für schwache schwere–leichte Mischung liefert die Entwicklung in [formula in source] bei festem [formula in source] in zweiter Ordnung Das Vorzeichen folgt bereits aus der zweiten geteilten Differenz der Fermi-Funktion bei [formula in source] . Gegenüber dem statischen Beitrag [formula in source] erhält jeder schwere Eigenkanal den Faktor Die Annäherung ist somit algebraisch in [formula in source] , nicht exponentiel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wann die Zustandsauswertung die leichte Massenmatrix wiedergibt.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":9177,"byte_start":7286,"id":"section:e164803d6ba9a40009be","kind":"paragraph","labels":[],"line_end":192,"line_start":160,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:0e3e24804496ee3a9f8f","relation:2b11b7f3d1bb23cf1701"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/009-subsection-zustand-und-wirkung-aus-derselben-r-ckwirkung.tex","status_markers_as_written":[],"summary_excerpt":"Die ursprüngliche Zustandsinduktion und der konkrete Seesaw-Anschluss sind miteinander verträglich, aber nicht durch unbeschränkte Gleichsetzung der beiden Operatoren. Ihre gemeinsame Realisierung muss den vollständigen Kern und seine Zustandsgewichte erhalten. Die Universalraum-Regel, spätere Antworten zu erhalten, betrifft daher ebenso die reduzierte Momentaufnahme und das variierte Funktional. Eine reine Massentab","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was damit für die Auswahlregel gewonnen ist.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12218,"byte_start":9177,"id":"section:0bbe263d0373acf1f39e","kind":"subsection","labels":[],"line_end":216,"line_start":193,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/009-subsection-zustand-und-wirkung-aus-derselben-r-ckwirkung.tex","status_markers_as_written":[],"summary_excerpt":"Am tatsächlichen 30-dimensionalen Blochoperator des markierten [formula in source] -Netzes wurden die Bandbefunde unabhängig bestätigt. Auf dem zehn-dimensionalen Eigenraum zum Bandniveau [formula in source] hat die erste Richtungsableitung die charakteristischen Polynome Nach Normierung der zweiten Richtung folgen die positiven Steigungsquadrate [formula in source] und [formula in source] . Diese Bandsteigungen sind","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was die Raum- und Literaturbefunde für dieselbe Kette beitragen","topic_suggestions":[]},{"byte_end":16083,"byte_start":12218,"id":"section:5d8e70422b19a84f2af5","kind":"subsection","labels":[],"line_end":259,"line_start":217,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:9a1cdfd7c732464983f1","relation:ba2f6c31584ef951f666"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/009-subsection-zustand-und-wirkung-aus-derselben-r-ckwirkung.tex","status_markers_as_written":[],"summary_excerpt":"Die Rechnung ersetzt eine Vermutung durch die exakten Gleichungen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das gemeinsame Feldwörterbuch und seine noch herzuleitende Auswahl","topic_suggestions":[]},{"byte_end":16666,"byte_start":16083,"id":"section:1539804273e8f60da49c","kind":"section","labels":["sec:orientationaudit"],"line_end":263,"line_start":260,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/009-subsection-zustand-und-wirkung-aus-derselben-r-ckwirkung.tex","status_markers_as_written":[],"summary_excerpt":"Der eingefügte Vorschlag vom 29. September mit der Kennung 9df45383-826d-4f53-8687-bf615454c26c enthält relevante Ergänzungen. Die folgenden algebraischen Aussagen wurden unabhängig neu berechnet; die angegebenen wissenschaftlichen Arbeiten wurden am Original geprüft. Die im Text verlinkten externen Rechnerpakete standen hier nicht zur Verfügung. Ihre QWZ-Tabellen und Ausführungsprotokolle werden deshalb nicht als ei","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Geprüfter Anhang: Orientierung und mehrteilige Antworten erhalten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"}]},{"byte_end":17939,"byte_start":16666,"id":"section:ad37ece4b94ccad75c39","kind":"subsection","labels":[],"line_end":275,"line_start":264,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/009-subsection-zustand-und-wirkung-aus-derselben-r-ckwirkung.tex","status_markers_as_written":[],"summary_excerpt":"Die ursprünglichen vier C-Wurzeln erfüllen [formula in source] . 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Sie liefert jedoch keine getreue Einbettung derselben ursprünglichen Operationen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das vorgeschlagene Carry ändert die kohärente Kompositionsregel","topic_suggestions":[]},{"byte_end":21128,"byte_start":19450,"id":"section:5e5ac9ef76208ec98a5b","kind":"subsection","labels":[],"line_end":328,"line_start":295,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/009-subsection-zustand-und-wirkung-aus-derselben-r-ckwirkung.tex","status_markers_as_written":[],"summary_excerpt":"Setze auf drei Qubits und Beide Zustände besitzen die Eigenwerte [formula in source] , jeweils vierfach. Ihre sämtlichen Ein- und Zweiteilreduktionen sind gleich: Trotzdem liefert dieselbe zugelassene Paaroperation [formula in source] Die anfänglichen Steigungen sind [formula in source] und [formula in source] . Gleiche Paaransichten und gleiche globale Spektren bestimmen somit nicht alle zukünftigen Paarantworten.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein exakter Zeuge gegen Kompression auf Paaransichten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":23454,"byte_start":21128,"id":"section:a4621408bc230f19ea9a","kind":"subsection","labels":[],"line_end":361,"line_start":329,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/009-subsection-zustand-und-wirkung-aus-derselben-r-ckwirkung.tex","status_markers_as_written":[],"summary_excerpt":"Für einen vollrangigen exakten Quanten-Markovzustand gilt Der letzte Schritt folgt durch zyklische Spur und [formula in source] . Eine nichtverschwindende solche Antwort darf daher nicht durch vollständige Entfernung der betreffenden räumlichen bedingten Korrelationen ausgelöscht werden. Dies verbietet keine zeitliche Markov- oder GKLS-Dynamik.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Chirale Diagnostik: bestätigte Literatur, ausdrücklich bedingte Übertragung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":2354,"byte_start":0,"id":"section:98a4a2e5a2b1c9c2845e","kind":"subsection","labels":["sec:chiralselector"],"line_end":25,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/010-subsection-der-st-rkste-neue-selektor-verbindet-orientie.tex","status_markers_as_written":[],"summary_excerpt":"Für dieselbe geeignete Bulk-/Randquelle sei der chirale Zusammenhang [formula in source] begründet. Für die Vakuum-Intervallentropie ihrer Rand-CFT auf der Linie gilt bei festem Regulator- und Lorentzrahmen castroentropy Dann ergibt sich Die Schranke folgt aus Unitarität, [formula in source] . Ihre Sättigung schließt gegenläufige gaplose CFT-Beiträge aus. Insbesondere Mit tatsächlich vorhandenen unitären affinen E8-S","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der stärkste neue Selektor verbindet Orientierung und gesamten Randinhalt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":2466,"byte_start":2354,"id":"section:ef90586ee8ea19b75a4c","kind":"section","labels":["sec:source"],"line_end":27,"line_start":26,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/010-subsection-der-st-rkste-neue-selektor-verbindet-orientie.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die wichtigste neue Verbindung: Die ursprünglichen 24 Felder erzeugen eine Quelle","topic_suggestions":[]},{"byte_end":4164,"byte_start":2466,"id":"section:0c79cc1eb6af26352be4","kind":"subsection","labels":[],"line_end":46,"line_start":28,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:13354283475c6851a928","relation:14d1aa9366966d5d4dc5","relation:6978341490bbd97088e7","relation:78dd5e71143296af7b00","relation:aac07ed08c7f37edef62","relation:e23c8402d5f68c7881d4"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/010-subsection-der-st-rkste-neue-selektor-verbindet-orientie.tex","status_markers_as_written":[],"summary_excerpt":"Aus dem positiven geraden unimodularen [formula in source] -Ladungsgitter und einem kompatiblen Kokzyklus entsteht in der erklärten Level-1-Gitterquantisierung Die grundlegenden geladenen Vertexantworten haben die Form Ladungsneutralität, Kokzyklus und Gitterpaarung bestimmen hier gemeinsam die Antwort. Die Unimodularität begründet die Holomorphie der Gitter-VOA; sie muss nicht als zusätzliche freie Auswahl erneut ei","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die direkte Konstruktion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":6052,"byte_start":4164,"id":"section:c5dd82e40e5d77e84b22","kind":"subsection","labels":[],"line_end":77,"line_start":47,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/010-subsection-der-st-rkste-neue-selektor-verbindet-orientie.tex","status_markers_as_written":[],"summary_excerpt":"Die ursprünglichen Felder sind zusammen mit ihren Adjungierten. Dabei transformiert [formula in source] als [formula in source] , [formula in source] als [formula in source] . In der ursprünglichen Wurzelbasis ist P2 diagonal; in der nativen Prozessbasis muss derselbe Generator passend transformiert werden. Seine Wirkung ist Die Sitzung hat diese Zuordnung auf allen 24 ursprünglichen Feldern geprüft.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[formula in source] : Der kleine Erzeugersatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"}]},{"byte_end":7286,"byte_start":6052,"id":"section:d123cc3080fd9939e11d","kind":"subsection","labels":[],"line_end":92,"line_start":78,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/010-subsection-der-st-rkste-neue-selektor-verbindet-orientie.tex","status_markers_as_written":[],"summary_excerpt":"Mit ursprünglichen [formula in source] -Wurzeln lässt sich eine einfache [formula in source] -Basis konkret schreiben: Hier bezeichnet [formula in source] in der Gleichung den Ladungsvektor des entsprechenden Feldes. Die Gramdeterminante ist [formula in source] ; die Smith-Normalform der Inklusion besitzt sieben Einträge [formula in source] und einen Eintrag [formula in source] . Der Gitterquotient ist deshalb [formu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die [formula in source] -Erweiterung und ihre Grenzen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"}]},{"byte_end":7386,"byte_start":7286,"id":"section:cbd32f900e1910556428","kind":"section","labels":["sec:finite"],"line_end":94,"line_start":93,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/010-subsection-der-st-rkste-neue-selektor-verbindet-orientie.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Code, Quartik und Rekursion: Was die endlichen Modelle wirklich zeigen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"}]},{"byte_end":8809,"byte_start":7386,"id":"section:06bf238bf954fdd90ee6","kind":"subsection","labels":[],"line_end":117,"line_start":95,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/010-subsection-der-st-rkste-neue-selektor-verbindet-orientie.tex","status_markers_as_written":[],"summary_excerpt":"Der verwendete binäre Code ist Unter der Gaussian- [formula in source] -Wirkung werden die 240 reellen [formula in source] -Wurzeln zu sechzig komplexen Strahlen. Ihre Projektoren lassen sich als gemeinsame Pauli-Eigenprojektoren darstellen. Die fünfzehn primitiven Kontexte enthalten je vier Strahlen. Andere orthogonale Gruppierungen erzeugen dadurch nicht automatisch neue primitive Kontexte.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vom Binärcode zu den 60 Ereignissen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"}]},{"byte_end":10346,"byte_start":8809,"id":"section:602328f3593f817933b6","kind":"subsection","labels":[],"line_end":137,"line_start":118,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/010-subsection-der-st-rkste-neue-selektor-verbindet-orientie.tex","status_markers_as_written":[],"summary_excerpt":"Für die konkrete Pauli-Gruppe der Ordnung 64 wurde der Molien-Ausdruck ausgewertet. Die Dimensionen in den Graden [formula in source] sind [formula in source] . Somit ist der Fünfer der erste nichtkonstante Pauli-invariante Polynomraum, wenn der kleinste positive Grad als Auswahlregel verlangt wird. Die Auswahlregel selbst ist eine zusätzliche Annahme, solange ihre Herkunft nicht gezeigt ist.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die Quartik einen Fünfer erzeugt","topic_suggestions":[]},{"byte_end":10966,"byte_start":10346,"id":"section:5a4ce879e1149f24e7e9","kind":"subsection","labels":[],"line_end":148,"line_start":138,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/010-subsection-der-st-rkste-neue-selektor-verbindet-orientie.tex","status_markers_as_written":[],"summary_excerpt":"Der symmetrische Delta-Tensor [formula in source] und der ursprüngliche Simplextensor [formula in source] liefern Die normierten Richtungen [formula in source] und [formula in source] sind orthogonal, und Die 60/40-Aussage bezeichnet also die quadrierten Normanteile dieser beiden Richtungen. Sie ist keine universelle Zerlegung physischer Energien. Als [formula in source] -Matrix gelesen liefert [formula in source] de","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Vierertensor und die 60/40-Zerlegung","topic_suggestions":[]},{"byte_end":12715,"byte_start":10966,"id":"section:b0a738e155ebe97b3505","kind":"subsection","labels":[],"line_end":174,"line_start":149,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/010-subsection-der-st-rkste-neue-selektor-verbindet-orientie.tex","status_markers_as_written":[],"summary_excerpt":"Die ältere gemeinsame Ereignisbindung ist Sie besitzt das Spektrum [formula in source] und den eindeutigen neutralen Zustand [formula in source] . Werden die beiden Ereignislabels unabhängig gezogen, entsteht stattdessen die skalare Energie [formula in source] . Die gemeinsame Ereignisidentität ist deshalb eine reale Voraussetzung.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei unterschiedliche, jeweils sinnvolle Rekursionen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":13898,"byte_start":12715,"id":"section:6171c45cbf97f6993b7c","kind":"subsection","labels":[],"line_end":188,"line_start":175,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/010-subsection-der-st-rkste-neue-selektor-verbindet-orientie.tex","status_markers_as_written":[],"summary_excerpt":"Die positive Neun-Port-Vervollständigung erfüllt in beiden Orientierungen Auf einem vorgegebenen endlichen Blockgraphen bleibt das Produkt der Codes daher unter einer Summe solcher Links invariant: [formula in source] . Die ursprünglichen einzelnen schwachen Restlinks haben dagegen Leakage. Die Neun-Port-Regel ist somit eine zusätzliche, ausdrücklich benannte Kompositionsregel. Wenn die Graphstruktur selbst dynamisch","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was bei der Blockkomposition erhalten bleibt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"}]},{"byte_end":16136,"byte_start":13898,"id":"section:be693a153851ecff8533","kind":"section","labels":[],"line_end":226,"line_start":189,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/010-subsection-der-st-rkste-neue-selektor-verbindet-orientie.tex","status_markers_as_written":[],"summary_excerpt":"Die beiden Beschreibungen [formula in source] und [formula in source] sind jetzt am gleichen achtfachen Heisenbergraum verbunden. Mit [formula in source] als Fünfermatrix aus lauter Einsen lauten die Projektoren Sie summieren sich zu [formula in source] , und [formula in source] . Deshalb ist der tatsächliche Virasorovektor in beiden Zerlegungen gleich. Damit gilt auf dieser Quelle Die Zentralzahlen erfüllen [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die gemeinsame Zeit: Der alte und der neue Quellblock passen wirklich zusammen","topic_suggestions":[]},{"byte_end":16217,"byte_start":16136,"id":"section:a0ca1397c1417bbe1b15","kind":"section","labels":["sec:ward"],"line_end":228,"line_start":227,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/010-subsection-der-st-rkste-neue-selektor-verbindet-orientie.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Das ausführbare Quellgesetz und die echte Hyperkante","topic_suggestions":[]},{"byte_end":17329,"byte_start":16217,"id":"section:ef9c1f087733d2593dd4","kind":"subsection","labels":["eq:ward"],"line_end":240,"line_start":229,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/010-subsection-der-st-rkste-neue-selektor-verbindet-orientie.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] bestimmt die affine Ward-Rekursion Im zweiten Term wird [formula in source] durch [formula in source] ersetzt. Alle Zwischenströme bleiben in der wirklichen 248-dimensionalen Wurzel-/Cartanalgebra. Die Implementierung nutzt exakte rationale Positionen und rationale Arithmetik; sie ist keine Näherung durch Gaußpaarungen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine Regel für alle endlichen Stromwörter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"}]},{"byte_end":19519,"byte_start":17329,"id":"section:09b6d0ae0fd4a58b5e28","kind":"subsection","labels":["eq:hex"],"line_end":269,"line_start":241,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:c217535d6762f5c631bc","relation:d04d613a8cd322c0252a","relation:e54f3ffc66bdd3146575"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/010-subsection-der-st-rkste-neue-selektor-verbindet-orientie.tex","status_markers_as_written":[],"summary_excerpt":"Für die Folge ist die Gesamtladung null. Jede der [formula in source] echten nichtleeren Teilmengen besitzt dagegen eine nichtverschwindende Gesamtladung. Alle ihre Vakuumkorrelatoren verschwinden, ebenso alle fünfzehn vollständigen Zweierpaarungsprodukte. Die ganze Antwort ist trotzdem Bei [formula in source] ist der Wert exakt [formula in source] . Er wurde unter allen 720 gleichzeitigen Permutationen von Feldern u","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine vollständig verbundene Sechserantwort","topic_suggestions":[]},{"byte_end":21437,"byte_start":19519,"id":"section:e81fed1404f40d4771d8","kind":"subsection","labels":[],"line_end":292,"line_start":270,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/010-subsection-der-st-rkste-neue-selektor-verbindet-orientie.tex","status_markers_as_written":[],"summary_excerpt":"An den harmonischen Marken [formula in source] ergibt der vollständige [formula in source] -Vierertensor Definiert man so ist [formula in source] . Nach der passenden Anordnung der Tensorfaktoren folgt Der mittlere Faktor ist jeweils konjugiert. Alle 8000 Ausgabetripel der dünn besetzten Abbildung wurden geprüft. Bei festem Familienindex wird derselbe Vierertensor zu [formula in source] . Mit der tatsächlichen reflex","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die [formula in source] -Rekursion ist eine besondere Antwort dieses Gesetzes","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":22307,"byte_start":21437,"id":"section:fb0905b1a03866d36598","kind":"subsection","labels":[],"line_end":297,"line_start":293,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/010-subsection-der-st-rkste-neue-selektor-verbindet-orientie.tex","status_markers_as_written":[],"summary_excerpt":"Die betrachtete [formula in source] -Level-1-KZ-Verbindung ist flach, obwohl überlappende Residuen nicht miteinander kommutieren. Zwei klassische Tensorkoordinaten bedeuten dabei nicht zwei unabhängige physische Level-1-Fusionsblöcke. Die Partnersektoren des vollständigen [formula in source] -Feldes kompensieren die gebrochenen Phasen des isolierten Faktors.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"KZ, Fusionsbäume und echte Komposition","topic_suggestions":[]},{"byte_end":22401,"byte_start":22307,"id":"section:afec65d6f247eac024e1","kind":"section","labels":[],"line_end":299,"line_start":298,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/010-subsection-der-st-rkste-neue-selektor-verbindet-orientie.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die Quellen- und Clockprüfungen: Welche Alternativen wirklich ausgeschlossen sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":23590,"byte_start":22401,"id":"section:086862a0caf12d0df49b","kind":"subsection","labels":[],"line_end":313,"line_start":300,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/010-subsection-der-st-rkste-neue-selektor-verbindet-orientie.tex","status_markers_as_written":[],"summary_excerpt":"Eine frühe Phase der Sitzung betrachtete die endliche Familie [formula in source] , [formula in source] . Ihr Populationsschatten bleibt gleich, während eine Kohärenz den Eigenwert besitzt. Damit ist die reine Populationsauslese in dieser Klasse unzureichend, um den Kanal zu bestimmen. Die Familie ist kein Gegenmodell zu sämtlichen TFPT-Prinzipien, weil nicht alle ursprünglichen Markierungen und höheren Antworten in ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die frühe Kanalfamilie und die vollständige Normierung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":25441,"byte_start":23590,"id":"section:cfd578b68dd4260cb765","kind":"subsection","labels":[],"line_end":332,"line_start":314,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:6f8289248d20265716d5"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/010-subsection-der-st-rkste-neue-selektor-verbindet-orientie.tex","status_markers_as_written":[],"summary_excerpt":"Der v487-Survivaloperator lautet Hier ist [formula in source] der Decktausch von Ordnung zwei, während [formula in source] die Familienmarkierung von Ordnung drei bezeichnet. Seine Eindeutigkeit gilt in der ursprünglichen treuen markierten Dreierklasse. Die Fortsetzung [formula in source] auf den Trimer setzt zusätzliche Identifikationen voraus und bestimmt außerhalb des Seedsektors nicht automatisch alles.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die ursprüngliche Clock ist ein konkreter markierter Operator","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":26766,"byte_start":25441,"id":"section:b70c123f9c6e03a68f97","kind":"subsection","labels":[],"line_end":344,"line_start":333,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:0b26e361a798623a0de5"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/010-subsection-der-st-rkste-neue-selektor-verbindet-orientie.tex","status_markers_as_written":[],"summary_excerpt":"Native Reflexionswörter realisieren die registrierte v976-Faser Die GNS-Antwort mit linken Einsetzungen ist [formula in source] . Die ältere Vorgabe [formula in source] wählt deshalb [formula in source] , sofern ihre unabhängige Quellenidentifikation gilt. Dies ist eine konkrete Möglichkeit, wie eine zusätzliche ursprüngliche Antwort eine zuvor offene Faser auswählt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die korrekt markierte Ereignisfaser","topic_suggestions":[]},{"byte_end":27962,"byte_start":26766,"id":"section:ad9c5fd97a1521850773","kind":"subsection","labels":[],"line_end":353,"line_start":345,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/010-subsection-der-st-rkste-neue-selektor-verbindet-orientie.tex","status_markers_as_written":[],"summary_excerpt":"Die Phasenkanalprüfung betrachtete eine ausdrücklich beschränkte Klasse zufälliger unitärer Generatoren Die nichttrivialen Charakterorbits haben Größen [formula in source] . Ein Deckorbit und ein Braidorbit liefern bei derselben gesamten Sprungrate auf allen 240 Wurzelströmen dieselbe Zerfallsrate [formula in source] . Auf einem Grad-zwei-Vertex mit [formula in source] und [formula in source] unterscheiden sie sich d","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Höhere Antworten unterscheiden sogar gleiche Wurzelzerfallsraten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":28075,"byte_start":27962,"id":"section:6166a715f43d3f2285b5","kind":"section","labels":["sec:carry"],"line_end":355,"line_start":354,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/010-subsection-der-st-rkste-neue-selektor-verbindet-orientie.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Hecke, Double Cover und geladener Carry: Was bei einer Vergröberung mitwandern muss","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":29552,"byte_start":28075,"id":"section:56e099fb105d3398ec51","kind":"subsection","labels":[],"line_end":375,"line_start":356,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/010-subsection-der-st-rkste-neue-selektor-verbindet-orientie.tex","status_markers_as_written":[],"summary_excerpt":"Mit [formula in source] gilt im verwendeten Gaussian-Gitter Alle sechzig nativen Ereignisse wurden tatsächlich auf die fünfzehn Marken abgebildet, einschließlich der Äquivarianzprüfung. Vier Ereignisse pro Marke bleiben dennoch verschiedene Operationen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die fünfzehn Marken sind an die ursprünglichen Ereignisse angeschlossen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"}]},{"byte_end":2183,"byte_start":0,"id":"section:c684190d139e9bd39c14","kind":"subsection","labels":[],"line_end":38,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/011-subsection-bei-gr-erer-tiefe-reichen-vorzeichen-nicht-au.tex","status_markers_as_written":[],"summary_excerpt":"Für eine ganzzahlige Inklusion [formula in source] und einen Kindcharakter [formula in source] ergibt eine Fortsetzung auf derselben Quelle. Dabei können Phasenordnungen [formula in source] auftreten. Für Ordnung vier ist [formula in source] kein Projektor. Der richtige Sektorprojektor lautet bei Ordnung [formula in source] Die kohärente Speicherung ist isometrisch. Für [formula in source] mit [formula in source] ist","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bei größerer Tiefe reichen Vorzeichen nicht aus","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"}]},{"byte_end":3836,"byte_start":2183,"id":"section:9cfb1413e99ad6d8416a","kind":"subsection","labels":[],"line_end":50,"line_start":39,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/011-subsection-bei-gr-erer-tiefe-reichen-vorzeichen-nicht-au.tex","status_markers_as_written":[],"summary_excerpt":"Auf dem unverdrehten Cartanraum wird die native Reflexion durch [formula in source] realisiert. Die gleiche Pauli-/Heisenberg-Paarung eines verdrehten Moduls reicht dagegen nicht: Die native Reflexion hat eine [formula in source] -Aufteilung mit [formula in source] , während die untersuchten Pauli-ambigen Cliffordimplementer [formula in source] oder [formula in source] und [formula in source] oder [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Lift muss die wirkliche Operatorwirkung erhalten","topic_suggestions":[]},{"byte_end":4199,"byte_start":3836,"id":"section:719a40f627f48f3e350a","kind":"section","labels":["sec:universal"],"line_end":54,"line_start":51,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/011-subsection-bei-gr-erer-tiefe-reichen-vorzeichen-nicht-au.tex","status_markers_as_written":[],"summary_excerpt":"Zwei Vorgeschichten gehören genau dann zum selben wirksamen Zustand, wenn keine zugelassene spätere Handlung oder Messung sie unterscheiden kann. Welcher Universalraum gemeint ist, hängt deshalb vom tatsächlichen Operations- und Auslesesystem ab.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Universalraum: Der Raum dessen, was eine Zukunft noch unterscheiden kann","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5202,"byte_start":4199,"id":"section:1db225225405f3828e54","kind":"subsection","labels":[],"line_end":68,"line_start":55,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/011-subsection-bei-gr-erer-tiefe-reichen-vorzeichen-nicht-au.tex","status_markers_as_written":[],"summary_excerpt":"Für eine festgelegte Klasse zulässiger Zukunftstests [formula in source] ist Wenn das Gewicht der vorbereitenden Geschichte relevant ist, müssen unnormierte gemeinsame Antworten verglichen werden. Wenn kohärente Referenzen und Interferenz zulässig sind, gehören auch diese zum Testsystem. Eine Aussage über alle Zukunftstests darf nicht auf die gerade sichtbare Bildschirmablesung verkürzt werden.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Operationale Äquivalenz und lineare Vorhersage","topic_suggestions":[]},{"byte_end":6510,"byte_start":5202,"id":"section:5d74fca3bf251d06b4a4","kind":"subsection","labels":[],"line_end":82,"line_start":69,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/011-subsection-bei-gr-erer-tiefe-reichen-vorzeichen-nicht-au.tex","status_markers_as_written":[],"summary_excerpt":"Für Operatorwörter [formula in source] ist der kohärente Kern Er enthält Kreuzterme zwischen Geschichten. Auf einer unitalen [formula in source] -Algebra mit normiertem positivem Zustand liefert die GNS-Konstruktion Das Nullideal ist unter Linksmultiplikation stabil; die zyklische Darstellung ist bis auf unitäre Äquivalenz eindeutig segal. Bei einer allgemeinen Algebra unbeschränkter Felder sind gemeinsame Domänen un","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die positive kohärente Rekonstruktion","topic_suggestions":[]},{"byte_end":7579,"byte_start":6510,"id":"section:0e4bd8b4a1914009b787","kind":"subsection","labels":[],"line_end":93,"line_start":83,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/011-subsection-bei-gr-erer-tiefe-reichen-vorzeichen-nicht-au.tex","status_markers_as_written":[],"summary_excerpt":"Das implementierte Instrument [formula in source] ergibt bei alleiniger Beobachtung seiner Ereignislabels Die zugehörige klassische Wort-Hankelmatrix hat Rang eins. Für denselben Operatorprozess mit [formula in source] besitzt der kohärente Kern dagegen den berechneten GNS-Rang 25, weil die Operatorwörter [formula in source] aufspannen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein Beispiel, das die drei Ebenen sofort trennt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":8305,"byte_start":7579,"id":"section:1c70dd5202607cbfb06e","kind":"subsection","labels":["eq:quotient"],"line_end":102,"line_start":94,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/011-subsection-bei-gr-erer-tiefe-reichen-vorzeichen-nicht-au.tex","status_markers_as_written":[],"summary_excerpt":"Eine Reduktion [formula in source] ist unter einer Fortsetzung [formula in source] geschlossen, wenn Im linearen Fall ist insbesondere [formula in source] erforderlich. Zusätzlich müssen alle relevanten Auslesungen durch [formula in source] faktorisieren. Dann folgt durch Induktion die Gleichheit der Antworten für beliebig lange zulässige Operationswörter.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die exakte Bedingung für eine verlustfreie Rekodierung","topic_suggestions":[]},{"byte_end":9660,"byte_start":8305,"id":"section:3b80067c3acf4dd0ac25","kind":"subsection","labels":[],"line_end":116,"line_start":103,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/011-subsection-bei-gr-erer-tiefe-reichen-vorzeichen-nicht-au.tex","status_markers_as_written":[],"summary_excerpt":"Ein primitiver positiver Operator kann unter passenden endlichen Voraussetzungen einen eindeutigen normierten Fixpunkt besitzen. Doch P1-Primitivität ist nicht automatisch diese Operatorprimitivität; auch ein endlicher Satz darf nicht ohne Grenzwertkontrolle auf einen unendlichen Raum übertragen werden.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum ein Fixpunkt des Gesetzes keine universelle Vergessensmaschine ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"}]},{"byte_end":9730,"byte_start":9660,"id":"section:86817d7bf16ae5a77ef0","kind":"section","labels":[],"line_end":118,"line_start":117,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/011-subsection-bei-gr-erer-tiefe-reichen-vorzeichen-nicht-au.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Raum, Topologie und Ausbreitung: Was aus dem Graphen folgt","topic_suggestions":[]},{"byte_end":10737,"byte_start":9730,"id":"section:222f3c97c6e6a31c787f","kind":"subsection","labels":[],"line_end":127,"line_start":119,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/011-subsection-bei-gr-erer-tiefe-reichen-vorzeichen-nicht-au.tex","status_markers_as_written":[],"summary_excerpt":"Die Tutte–Coxeter-Zelle besitzt dreißig Knotentypen, fünfundvierzig Kanten, Grad drei und Zyklusrang sechzehn. Der verwendete markierte periodische [formula in source] -Cover wählt daraus einen Rang-drei-Periodenquotienten. In der benutzten Normierung ergibt die kleine Blochwelle Dies ist ein konkreter dreidimensionaler Ausbreitungszweig. Die Dimension stammt aus der gewählten Periodenmarkierung, weder aus den sechze","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die räumliche Konstruktion ist markiert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":12007,"byte_start":10737,"id":"section:f473bc405e8e7cea25b4","kind":"subsection","labels":[],"line_end":139,"line_start":128,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/011-subsection-bei-gr-erer-tiefe-reichen-vorzeichen-nicht-au.tex","status_markers_as_written":[],"summary_excerpt":"Ein naiver Ausdruck aus lokalen zweiten Sprungmomenten, [formula in source] , muss noch keine globale effektive Metrik ergeben. An einzelnen Knoten ist er sogar singulär. Der interne harmonische Korrektor beschreibt, wie sich die Knotentypen einer ganzen Periode gemeinsam einstellen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die effektive Metrikantwort braucht die gesamte Zelle","topic_suggestions":[]},{"byte_end":12820,"byte_start":12007,"id":"section:1b7b8367dc194d85c806","kind":"subsection","labels":[],"line_end":144,"line_start":140,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/011-subsection-bei-gr-erer-tiefe-reichen-vorzeichen-nicht-au.tex","status_markers_as_written":[],"summary_excerpt":"Die ältere thermodynamische Dynamikarbeit enthält bereits Lieb–Robinson-Schranken, Zeitentwicklung, Gauss-Kompatibilität sowie Grundzustands-/KMS-Existenz für die dort spezifizierte lokale Hamiltonklasse mit endlichen Faktoren auf [formula in source] . Diese Ergebnisse werden hier nicht erneut als ungelöste reine Existenzfragen behandelt. Sie begründen aber auch nicht von selbst die ausgewählte räumliche [formula in ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Existenzsätze erhalten, ihre Reichweite nicht ausweiten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":15739,"byte_start":12820,"id":"section:0bfcea019d55740cad6f","kind":"section","labels":[],"line_end":166,"line_start":145,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/011-subsection-bei-gr-erer-tiefe-reichen-vorzeichen-nicht-au.tex","status_markers_as_written":[],"summary_excerpt":"Zuses Rechnender Raum motiviert den Gedanken, physische Entwicklung als lokale regelhafte Verarbeitung zu beschreiben. Für diese Sitzung ist die nützliche Konsequenz: Eine Theorie muss sagen, was einen Zustand ausmacht, welcher lokale Schritt erlaubt ist und wie große Strukturen aus wiederholter Komposition entstehen zuse. Die konkrete TFPT-Quelle liefert dafür eine reichere Algebra als ein bloßes Bitgitter; daraus f","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zuse und Wolfram: Der produktive gemeinsame Kern und die nötigen Unterschiede","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":16245,"byte_start":15739,"id":"section:53768a51c6f4d4743186","kind":"section","labels":["sec:levelselection"],"line_end":170,"line_start":167,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/011-subsection-bei-gr-erer-tiefe-reichen-vorzeichen-nicht-au.tex","status_markers_as_written":[],"summary_excerpt":"Ein positiver Auswahlsatz ist jetzt verfügbar. Innerhalb einer unitären positiven affinen [formula in source] -Quelle genügt entweder eine unabhängig begründete Zentralzahl höchstens acht oder die Nullrelation eines einzigen echten langen Wurzelstroms, um Level eins zu erzwingen. Das verbleibende Problem ist die Herkunft dieser konkreten Eigenschaft aus der ursprünglichen Quelle.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Fortsetzung: Die Auswahl von Level eins ist auf einen Ursprungssatz reduziert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"}]},{"byte_end":18356,"byte_start":16245,"id":"section:11f0aaa5ae524e3b1e36","kind":"subsection","labels":[],"line_end":189,"line_start":171,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/011-subsection-bei-gr-erer-tiefe-reichen-vorzeichen-nicht-au.tex","status_markers_as_written":[],"summary_excerpt":"Die Vergleichsklasse ist ausdrücklich festgelegt: eine einfache unitäre Vertexoperatoralgebra vom CFT-Typ, mit positivem Energiegrad, eindeutigem Vakuum im Grad null und einer tatsächlichen kompakten [formula in source] -Stromalgebra im Grad eins. Lange Wurzeln haben Normquadrat zwei. Der affine Level ist dann eine positive ganze Zahl [formula in source] ; die von den Strömen erzeugte Algebra ist [formula in source] ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was Zentralzahl acht tatsächlich erzwingt","topic_suggestions":[]},{"byte_end":21011,"byte_start":18356,"id":"section:c216f14cdf31c479ed5b","kind":"subsection","labels":["eq:rootnull"],"line_end":224,"line_start":190,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/011-subsection-bei-gr-erer-tiefe-reichen-vorzeichen-nicht-au.tex","status_markers_as_written":[],"summary_excerpt":"Für einen normierten langen Wurzelstrom und sein wirkliches Adjungiertes gilt Anwendung auf das Vakuum ergibt Somit erzwingen [formula in source] und [formula in source] den Level eins. Die zweite Gleichung ist eine Aussage über einen vollständigen affinen Modus. Die Nilpotenz irgendeiner endlichen Pauli-Matrix würde dafür nicht genügen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein einziger tatsächlicher Wurzelstrom genügt","topic_suggestions":[]},{"byte_end":23135,"byte_start":21011,"id":"section:4acf4f6a0389df835430","kind":"subsection","labels":[],"line_end":253,"line_start":225,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/011-subsection-bei-gr-erer-tiefe-reichen-vorzeichen-nicht-au.tex","status_markers_as_written":[],"summary_excerpt":"Die tatsächliche Chevalley-Ward-Rechnung lässt sich ohne Level-eins-Vorentscheidung ausführen. Für die Felder [formula in source] an [formula in source] folgt exakt mit Bei festem Familienindex bleibt [formula in source] . Nach Gesamtnormierung ist der Fünfertensor daher für alle positiven [formula in source] derselbe. Die normierte Fünferrekursion bestätigt ihre Form, sieht aber diese Levelalternative nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die bisherige Fünferrekursion den Level nicht auswählt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"}]},{"byte_end":24111,"byte_start":23135,"id":"section:ea5eaa026e815e2b5782","kind":"subsection","labels":[],"line_end":258,"line_start":254,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:09f5775cd4fc5c37b3e4","relation:39933dceefb908e91430"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/011-subsection-bei-gr-erer-tiefe-reichen-vorzeichen-nicht-au.tex","status_markers_as_written":[],"summary_excerpt":"Die alte Rechnung v470_alpha_inflow_level.py identifiziert [formula in source] mit dem primitiven [formula in source] -Inflow und dem betreffenden Koeffizienten der [formula in source] -Gleichung. Sie identifiziert nicht ohne zusätzlichen Abbildungssatz den affinen [formula in source] -Level.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Primitive Windung und Determinanten haben unterschiedliche Normierungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"}]},{"byte_end":24667,"byte_start":24111,"id":"section:0351679cbd8a9e6547af","kind":"section","labels":["sec:constructive"],"line_end":262,"line_start":259,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/011-subsection-bei-gr-erer-tiefe-reichen-vorzeichen-nicht-au.tex","status_markers_as_written":[],"summary_excerpt":"Die Quelle hat jetzt eine zweite vollständige, ausführbare Darstellung. Die [formula in source] -Felder sind explizite Fermionbilineare; die [formula in source] -Felder sind die erforderlichen geladenen Erweiterungsfelder. Mit dem ursprünglichen Kokzyklus ergibt sich eine geschlossene Formel für sämtliche endlichen C/X-Wörter. Dieselbe Formel liefert einen positiven Geschichtskern und eine exakte Darstellung ihres ge","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Konstruktiver Abschluss innerhalb der Quelle: Felder, Antworten und Gedächtnis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":26684,"byte_start":24667,"id":"section:12f7bd3abc963276d358","kind":"subsection","labels":["eq:Csu9"],"line_end":297,"line_start":263,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/011-subsection-bei-gr-erer-tiefe-reichen-vorzeichen-nicht-au.tex","status_markers_as_written":[],"summary_excerpt":"Die aus den ursprünglichen Wurzeln gebaute [formula in source] -Isometrie bildet alle 20 X-Wurzeln exakt auf im neundimensionalen Nullsummenraum ab. Neun komplexe chirale Hilfsfermionen realisieren deshalb die [formula in source] -Ströme durch Der gemeinsame [formula in source] -Anteil wird abgespalten: [formula in source] . Die tatsächlichen 8000 Tripelklammern erfüllen Die ursprünglichen Phasen passen also zu den M","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die neun Hilfsfermionen und die vier Erweiterungsfelder","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":28081,"byte_start":26684,"id":"section:e625aa3d48af41ebd1d4","kind":"subsection","labels":[],"line_end":308,"line_start":298,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/011-subsection-bei-gr-erer-tiefe-reichen-vorzeichen-nicht-au.tex","status_markers_as_written":[],"summary_excerpt":"Für den bekannten Sechserzeugen gibt es in der Liste der zwölf elementaren Fermionfelder genau eine zulässige Wick-Paarung. Ihr Gesamtvorzeichen ist positiv. Sie liefert unabhängig von der Strom-Ward-Rekursion an den bisherigen sechs Positionen. Alle 15 Paarungen ganzer Ströme bleiben null. Damit ist eine wichtige falsche Schlussfolgerung behoben: Nichtgaußische Stromantworten schließen eine zugrunde liegende Gaußdar","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Sechser-Hyperkante ist ein elementarer Fermionring","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"}]},{"byte_end":29993,"byte_start":28081,"id":"section:8ddad323fc1ac299db2f","kind":"subsection","labels":["eq:latticeoracle"],"line_end":330,"line_start":309,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/011-subsection-bei-gr-erer-tiefe-reichen-vorzeichen-nicht-au.tex","status_markers_as_written":[],"summary_excerpt":"Jedes Originalfeld ist ein phasenmarkierter Wurzelvertex [formula in source] . 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B","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die volle C/X-Regel als geschlossenes Produkt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"}]},{"byte_end":34086,"byte_start":29993,"id":"section:3cfa1bee767d714545e2","kind":"subsection","labels":["eq:fullhistory","eq:historyexact","eq:momentmemory"],"line_end":381,"line_start":331,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/011-subsection-bei-gr-erer-tiefe-reichen-vorzeichen-nicht-au.tex","status_markers_as_written":[],"summary_excerpt":"Es sei Das ist eine radiale Feldgeschichte, keine bereits normierte Folge von Detektormessungen. Definiere und den Vorfaktor [formula in source] als das Produkt rechts in Die Überlappung zweier solcher Geschichten ist daher Die Positivität folgt aus der tatsächlichen Hilbertraumdarstellung. Sie wurde zusätzlich an einer exakten Gram-Matrix und unabhängig über radial adjungierte Original-Ward-Wörter geprüft. Die imple","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein expliziter Universalraum für radiale Quellgeschichten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":105,"byte_start":0,"id":"section:2bfca1ebcbdfbebbdc33","kind":"section","labels":["sec:mobius"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/012-section-die-quelle-bewegt-sich-wirklich-eine-exakte-zeit.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die Quelle bewegt sich wirklich: Eine exakte Zeitentwicklung mit ihrem Rest","topic_suggestions":[]},{"byte_end":1571,"byte_start":105,"id":"section:c1ef86961d400fe2a934","kind":"subsection","labels":["eq:mobiustower"],"line_end":27,"line_start":3,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/012-section-die-quelle-bewegt-sich-wirklich-eine-exakte-zeit.tex","status_markers_as_written":[],"summary_excerpt":"Der bisherige Einwand [formula in source] auf allen Stromzuständen vom Grad eins ist richtig, aber er bedeutet nicht, dass die Quelle keine nichttriviale geometrische Zeit besitzt. Mit der positiven Hermiteschen Strommetrik und tatsächlichem Adjungieren bilden einen normierten Nachfahrenturm. Aus [formula in source] folgen die Leiterkoeffizienten [formula in source] und [formula in source] . Der antihermitesche Gener","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die höheren Moden gehören zur Bewegung","topic_suggestions":[]},{"byte_end":3079,"byte_start":1571,"id":"section:db796bce86ab27e87184","kind":"subsection","labels":[],"line_end":40,"line_start":28,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/012-section-die-quelle-bewegt-sich-wirklich-eine-exakte-zeit.tex","status_markers_as_written":[],"summary_excerpt":"Für den Projektor [formula in source] auf die anfänglichen Grad-eins-Ströme folgt Bei [formula in source] ist diese Amplitude [formula in source] . Die ununterbrochene Bewegung bis [formula in source] hat Amplitude [formula in source] , während zweimaliges Projizieren [formula in source] ergibt. Die scheinbare endliche Dynamik komponiert somit nicht wie der volle Prozess. Sie hat Anteile entfernt, die später zurückwi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum eine endliche Projektion Gedächtnis verliert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":3544,"byte_start":3079,"id":"section:5df19755110bca13958b","kind":"section","labels":["sec:physicalfollow"],"line_end":44,"line_start":41,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/012-section-die-quelle-bewegt-sich-wirklich-eine-exakte-zeit.tex","status_markers_as_written":[],"summary_excerpt":"Die Quelle, ihre vollständigen Wurzelantworten, ihr positiver Geschichtskern und ihre geometrische Bewegung passen jetzt in einer Konstruktion zusammen. Die physische Aufgabe ist die Abbildung dieser Konstruktion auf tatsächlich realisierte Raumzeitfelder. Ein bloßer Ersatz durch eine passende Kovarianz würde bereits die berechneten höheren Antworten verändern.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der physikalische Anschluss nach diesen Rechnungen","topic_suggestions":[]},{"byte_end":5349,"byte_start":3544,"id":"section:2bcbb431d1bad8712643","kind":"subsection","labels":[],"line_end":56,"line_start":45,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:7e4d5937f5f3a810ab29","relation:dad2bd69ac7b2e2e6779"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/012-section-die-quelle-bewegt-sich-wirklich-eine-exakte-zeit.tex","status_markers_as_written":[],"summary_excerpt":"Die ursprüngliche v258_dirac_covariance_induction.py verwendet Dabei ist [formula in source] der geometrische Maßstab und [formula in source] die Projektion auf den chiraliätsungeraden Anteil. Im ausgeführten chiralen Beispiel ist [formula in source] ; die Projektion ändert den eingesetzten Operator nicht. Die Rekonstruktion setzt neun Massen in [formula in source] ein, erzeugt daraus [formula in source] und gewinnt ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die Massenrekonstruktion noch keine Massenherkunft ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":6321,"byte_start":5349,"id":"section:6d6494c465792be08ad9","kind":"subsection","labels":[],"line_end":65,"line_start":57,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:9e8fe4d47cf61af3acf8"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/012-section-die-quelle-bewegt-sich-wirklich-eine-exakte-zeit.tex","status_markers_as_written":[],"summary_excerpt":"Die originale Vierintervallrechnung v480_multilocal_four_interval.py verwendet vier echte Teilintervalle mit Lücken eines freien fermionischen Rings: 256 Orte, jeweils 48 gewählte Orte im Abstand 64. Vier markierte Punkte allein wählen diese Lücken nicht aus. Im stark additiven vollen Netz erzeugen nur durch Punkte getrennte anstoßende Bögen wieder die globale Algebra; das ist nicht derselbe reduzierte Zustand.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der räumliche Ausschnitt ist ein Teil der Herleitung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":8014,"byte_start":6321,"id":"section:6cb57e5a831173cd1acf","kind":"subsection","labels":[],"line_end":77,"line_start":66,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/012-section-die-quelle-bewegt-sich-wirklich-eine-exakte-zeit.tex","status_markers_as_written":[],"summary_excerpt":"Für eine behauptete physische Realisierung wird ein Feldtransfer [formula in source] benötigt, so dass für alle zugelassenen Quellwörter gilt, mit verträglicher Lokalisation, P2-Ladung, Statistik, Adjungierung und Zeit. Die neue Produktformel macht die rechte Seite für beliebig lange endliche C/X-Wörter direkt berechenbar. Der positive Kernel prüft zusätzlich den gemeinsamen Zustand; die Möbiusformel prüft seine geom","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Welche gemeinsame Abbildung jetzt wirklich geprüft werden kann","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"}]},{"byte_end":8601,"byte_start":8014,"id":"section:066f82dc04e96e333c2c","kind":"section","labels":["sec:jointclosure"],"line_end":81,"line_start":78,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/012-section-die-quelle-bewegt-sich-wirklich-eine-exakte-zeit.tex","status_markers_as_written":[],"summary_excerpt":"Ergebnis dieser Fortsetzung: Die stärkste zusammenhängende Route hat zwei noch nicht ausgefüllte Eingänge: die Auswahl der gemeinsamen Quelle und die Auswahl ihrer physischen Lokalisation. Dazwischen liegen echte Konstruktions- und Rekonstruktionssätze. Diese unterscheiden wir von den Eingängen, die sie voraussetzen. Dadurch wird sichtbar, welche zusätzliche Herleitung mehrere bisher getrennte Probleme gleichzeitig v","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gesamtprüfung: Ursprung, Universalraum, Raumzeit und Materie an einem Objekt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13588,"byte_start":8601,"id":"section:f03ad4dd64724fcfb725","kind":"subsection","labels":["eq:forgetspin","eq:gravextension","sec:bordism16"],"line_end":130,"line_start":82,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:18cf1a88cb8ac25fe7e9","relation:34f0f11b0a9e7887b09d","relation:429553823224c1e712ec","relation:54cf6dacdaab981fb7a4","relation:bf955082e060c238c8d6","relation:e2b153afd05ea376cdae","relation:e7817c3552039b1fca3e","relation:ff16315ab4979cce09cc"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/012-section-die-quelle-bewegt-sich-wirklich-eine-exakte-zeit.tex","status_markers_as_written":[],"summary_excerpt":"Die originale Kummer-/K3-Konstruktion besitzt einen präzisen Anschluss an die Quantisierung einer gravitativen Antwort. Er beruht auf den Gruppen glatter geschlossener Viermannigfaltigkeiten modulo Bordismus: K3 erzeugt die erste Gruppe, [formula in source] die zweite, jeweils bis auf Orientierung. Die Signaturen sind [formula in source] und [formula in source] . Beim Vergessen der Spinstruktur gilt daher Für die gan","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein wirklicher topologischer Zusammenhang: Warum der Faktor 16 erscheint","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":16530,"byte_start":13588,"id":"section:08b27e005c6187df0faf","kind":"subsection","labels":[],"line_end":153,"line_start":131,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:113b008377d11653ce85","relation:39baa0fa1065518fe1b5","relation:a4b14484291283a68e7c"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/012-section-die-quelle-bewegt-sich-wirklich-eine-exakte-zeit.tex","status_markers_as_written":[],"summary_excerpt":"Der Anschluss benutzt die ursprüngliche markierte Struktur: Ihre [formula in source] irreduziblen invertiblen Sektoren sind [formula in source] . Die Twistphasen sind Die diagonale Untergruppe [formula in source] hat vier Elemente. Ihre tatsächlichen niedrigsten Gewichte sind [formula in source] ; insbesondere sind alle Twistphasen eins. Wird die entsprechende lokale einfache Stromerweiterung realisiert, gilt Die Ori","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie dieser Auswahlpfeil an die schon vorhandene E8-Verklebung anschließt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"}]},{"byte_end":18531,"byte_start":16530,"id":"section:00a7f568f81007a46d9f","kind":"subsection","labels":["sec:localmodular"],"line_end":169,"line_start":154,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/012-section-die-quelle-bewegt-sich-wirklich-eine-exakte-zeit.tex","status_markers_as_written":[],"summary_excerpt":"Das folgt unmittelbar: Sei [formula in source] , [formula in source] und [formula in source] . Für gilt [formula in source] , aber [formula in source] . Die Vorschrift [formula in source] wäre folglich nicht wohldefiniert. [formula in source] ist global nicht separierend. Dies ist eine Aussage über den gegebenen reinen irreduziblen Vakuumzustand; sie betrifft nicht alle GNS-Darstellungen oder gemischten Zustände.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum der Universalraum die lokale Zuordnung braucht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":19965,"byte_start":18531,"id":"section:8338c34af8374331e2f6","kind":"subsection","labels":[],"line_end":180,"line_start":170,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/012-section-die-quelle-bewegt-sich-wirklich-eine-exakte-zeit.tex","status_markers_as_written":[],"summary_excerpt":"Betrachtet man genau die bislang konstruierten geometrischen Möbiusbewegungen und die mit ihnen kommutierende kompakte interne E8-Wirkung, ist ihre zusammenhängende Liealgebra Aus diesen Symmetrien allein lässt sich keine nichttriviale Wirkung der Lorentzalgebra [formula in source] durch eine Liealgebraabbildung in dieses Produkt bilden.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was die bisherigen Symmetrien gemeinsam leisten – und was sie nicht erzeugen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"}]},{"byte_end":23055,"byte_start":19965,"id":"section:589f8309cc97a97f3b8c","kind":"subsection","labels":["eq:localizationtarget"],"line_end":202,"line_start":181,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/012-section-die-quelle-bewegt-sich-wirklich-eine-exakte-zeit.tex","status_markers_as_written":[],"summary_excerpt":"Die vorhandene chiral-konforme Theorie hat bereits einen echten holographischen Anschluss. Rehrens Konstruktion setzt Dabei übersetzt [formula in source] AdS-Keile in Randgebiete. Für das vorhandene schwach additive chirale Netz entsteht so ein AdS [formula in source] -Netz; Vakuum und positive Energie werden übertragen. Eine entsprechende AdS [formula in source] -Konstruktion benötigt bereits einen [formula in sourc","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der konstruktive gemeinsame Anschluss: Lokalisation bestimmt Bewegung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":24470,"byte_start":23055,"id":"section:186be605c9fda2c80784","kind":"subsection","labels":[],"line_end":217,"line_start":203,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:12274a5f91a4f3fca566"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/012-section-die-quelle-bewegt-sich-wirklich-eine-exakte-zeit.tex","status_markers_as_written":[],"summary_excerpt":"Für eine normale unital injektive Einbettung [formula in source] einer ganzen von-Neumann-Quellenalgebra und eine exakt autonome Zeitwirkung durch Automorphismen gilt notwendig Jedes Zeitbild ist dieselbe Algebra; ihre Vereinigung erzeugt keine größere. Eine schon abgeschlossene autonome Quelle wächst durch Wiederholung ihrer eigenen Zeit deshalb nicht zu einer größeren Algebra.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die ursprüngliche Prime Completion bleibt brauchbar, wenn die Algebren richtig gewählt sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":25962,"byte_start":24470,"id":"section:3b69eb3f67db33aa6c7d","kind":"subsection","labels":[],"line_end":225,"line_start":218,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/012-section-die-quelle-bewegt-sich-wirklich-eine-exakte-zeit.tex","status_markers_as_written":[],"summary_excerpt":"Die archivierte dreiteilige Gesamtkonstruktion wurde an ihren entscheidenden Eingangssätzen erneut geprüft. Ihr Defektvektor liegt in [formula in source] ; ein lexikographischer Minimalwert ist unter den genannten Nichtleerheitsannahmen auswählbar. Daraus folgt jedoch noch keine Eindeutigkeit des Operators, der diesen Wert besitzt. Mehrere nichtäquivalente Operatoren können denselben Defektvektor haben. Benötigt wird","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die älteren Gesamtvariationen die Auswahl noch nicht ersetzen","topic_suggestions":[]},{"byte_end":28733,"byte_start":25962,"id":"section:27468667b1845bc65e85","kind":"subsection","labels":[],"line_end":246,"line_start":226,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/012-section-die-quelle-bewegt-sich-wirklich-eine-exakte-zeit.tex","status_markers_as_written":[],"summary_excerpt":"Die gestrichelten Übergänge sind nicht durch das Diagramm bewiesen. Der erste verlangt die tatsächliche Antwortberechnung des ursprünglichen Operators. Der zweite verlangt eine aus den Markierungen ausgewählte lokale Algebraordnung. Danach werden Standardmodell, Kopplungen und Gravitation weiterhin an denselben Antworten geprüft; sie werden durch das Wort Rekonstruktion nicht vorweggenommen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die zusammenhängende Schlusskette und ihre genaue Reichweite","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"}]},{"byte_end":29426,"byte_start":28733,"id":"section:b39310dcc456f6c13c62","kind":"section","labels":["sec:nativeclosure"],"line_end":251,"line_start":247,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/012-section-die-quelle-bewegt-sich-wirklich-eine-exakte-zeit.tex","status_markers_as_written":[],"summary_excerpt":"Fortsetzung vom 29. September: Drei zuvor getrennte Teile greifen konkret ineinander. Die gemeinsame Verklebung beseitigt die Spin-Obstruktion des ursprünglichen Trägers. Die vier Quadratmarken wählen zwei getrennte Nahtabschnitte ohne zusätzliche Abstandsparameter. Dieselbe vollständige E8-Quelle bestimmt deren Korrelation, eine nichttriviale modulare Mischung und eine exakt berechenbare Zweifach-Replica-Antwort. Di","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die neue gemeinsame Verbindung: Originalträger, vier Marken und dieselbe Antwortquelle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":31737,"byte_start":29426,"id":"section:03bdf0418898c7948692","kind":"subsection","labels":["eq:nativeV16"],"line_end":283,"line_start":252,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/012-section-die-quelle-bewegt-sich-wirklich-eine-exakte-zeit.tex","status_markers_as_written":[],"summary_excerpt":"Das ursprüngliche Rang-fünf-Bündel [formula in source] und die Familienverklebung liefern den reellen Träger Hier ist [formula in source] die reelle Struktur der selbstdualen SU(4)-Darstellung. Die tatsächliche Darstellung lautet [formula in source] . Der komplexe Spin(10)-Halbspinor mit 16 komplexen Komponenten ist ein anderes Objekt; er darf nicht als dieser reelle Einteilchenträger eingesetzt werden.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der ursprüngliche gemeinsame Träger hebt wirklich nach Spin(16)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":34670,"byte_start":31737,"id":"section:0b5951aaee5a4b1cf5bf","kind":"subsection","labels":["eq:nativeI4","eq:nativelambda","sec:nativeanomaly"],"line_end":325,"line_start":284,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/012-section-die-quelle-bewegt-sich-wirklich-eine-exakte-zeit.tex","status_markers_as_written":[],"summary_excerpt":"Die charakteristische Klasse des Trägers lässt sich für alle ursprünglichen Lifts berechnen: Denn [formula in source] und [formula in source] bei [formula in source] . Ganzzahligkeit folgt aus [formula in source] ; das Minimum [formula in source] erreichen genau die Permutationen von [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine gemeinsame Formel für Eich- und Gravitationsantwort","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"}]},{"byte_end":40747,"byte_start":34670,"id":"section:94fef20a1bc42bcf715c","kind":"subsection","labels":["eq:originalmultiplicitybridge"],"line_end":378,"line_start":326,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:7b2d546ff6168977b39d"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/012-section-die-quelle-bewegt-sich-wirklich-eine-exakte-zeit.tex","status_markers_as_written":[],"summary_excerpt":"Der neue Bündelsatz liefert die rechte Seite der gesuchten Identifikation. Für einen wirklichen Diracoperator [formula in source] müsste sein Clifford-Multiplizitätsbündel mit [formula in source] identifiziert werden, einschließlich Basisgeometrie, Realität, Chiraliät und ursprünglicher Markierung. Ein lediglich elliptischer Operator erster Ordnung erfüllt nicht automatisch die Cliffordrelation seines Hauptsymbols ba","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Ursprungspfeil wird auf einen konkreten Operator- und Feldanschluss verdichtet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":3434,"byte_start":0,"id":"section:d4f3d81558d2dfd8be34","kind":"subsection","labels":["eq:nativequarter","sec:nativemodular"],"line_end":64,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/013-subsection-die-vier-urspr-nglichen-marken-w-hlen-eine-ec.tex","status_markers_as_written":[],"summary_excerpt":"Die erklärte Quadrat-Markierung wird jetzt konkret benutzt: Gemeint sind die positiv orientierten offenen Kreisbögen. Die beiden Komponenten von [formula in source] haben disjunkte Abschlüsse; ihre Zwischenräume sind genau die Komponenten von [formula in source] . Es wird keine zusätzliche Gapbreite gewählt. Die Quadratgestalt selbst bleibt eine ursprüngliche Rahmenvoraussetzung: Die Anzahl vier allein erzwingt die K","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die vier ursprünglichen Marken wählen eine echte lokale Zweiteilung","topic_suggestions":[]},{"byte_end":7478,"byte_start":3434,"id":"section:a8013ef7d9bc0f8d8baf","kind":"subsection","labels":["eq:nativecocycle"],"line_end":106,"line_start":65,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/013-subsection-die-vier-urspr-nglichen-marken-w-hlen-eine-ec.tex","status_markers_as_written":[],"summary_excerpt":"Setze [formula in source] und [formula in source] . Die Split-Eigenschaft liefert [formula in source] . Die Vakuummodulargruppe kann [formula in source] nicht für alle Zeiten erhalten.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Quelle bestimmt einen neutralen Mischer der geladenen lokalen Felder","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":11083,"byte_start":7478,"id":"section:bcc25114adee444feb32","kind":"subsection","labels":["eq:clockreplicaequality","eq:replicarational","sec:nativereplica"],"line_end":166,"line_start":107,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/013-subsection-die-vier-urspr-nglichen-marken-w-hlen-eine-ec.tex","status_markers_as_written":[],"summary_excerpt":"Die vier geordneten Quadratmarken besitzen die Kreuzratio [formula in source] . Für allgemeine geordnete [formula in source] ist die an den vier Endpunkten verzweigte doppelte Überlagerung ein Torus mit [formula in source] bezeichnet das vollständige elliptische Integral mit Parameter [formula in source] . Das Quadrat entspricht [formula in source] . Dieses Replica-Double-Cover wird aus der Intervallantwort konstruie","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die exakte Replica-Antwort verbindet die Viermarkengeometrie mit der Clockzahl","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":13161,"byte_start":11083,"id":"section:8e725711049edd68ed47","kind":"subsection","labels":["eq:replicaclockamplitudes"],"line_end":199,"line_start":167,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/013-subsection-die-vier-urspr-nglichen-marken-w-hlen-eine-ec.tex","status_markers_as_written":[],"summary_excerpt":"Die Antwort lässt sich auch unmittelbar auf Operatoren zurückführen. Die zwei Kopien besitzen die konforme Zerlegung Entscheidend ist nicht die Zentralzahlgleichheit, sondern die tatsächliche Verzweigung des verdrehten Sektors collazuolmelnikov: Der eindeutige Replica-Twistgrundzustand [formula in source] ist ein affiner [formula in source] -Singulett mit Ising-Gewicht [formula in source] . Sein Vierpunkt ist der fer","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dahinter steht tatsächlich ein Fermionfeld derselben replizierten Quelle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":15471,"byte_start":13161,"id":"section:e9ee831b73445d2d858c","kind":"subsection","labels":["eq:nativeclockmap"],"line_end":227,"line_start":200,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:bb84fcd4985b6fa1455d","relation:ce34f4a391c1dd08f1f4"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/013-subsection-die-vier-urspr-nglichen-marken-w-hlen-eine-ec.tex","status_markers_as_written":[],"summary_excerpt":"Die Replica-Verbindung identifiziert eine konkrete gemeinsame Quellantwort, aber noch keinen alten Transferoperator. Das lässt sich direkt am vollständigen Clockpaar prüfen. Der ursprüngliche Einzelschritt auf den drei Cusp-Populationen ist Die Moden sind [formula in source] , [formula in source] und [formula in source] ; der registrierte Sechsschritt ist [formula in source] . Die Originalverifikation v486_transfer_f","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der zweite Clockwert entscheidet über die noch fehlende Prozessidentität","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":17460,"byte_start":15471,"id":"section:79399e3c68c13e8a32ae","kind":"subsection","labels":[],"line_end":249,"line_start":228,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/013-subsection-die-vier-urspr-nglichen-marken-w-hlen-eine-ec.tex","status_markers_as_written":[],"summary_excerpt":"Der Universalraum enthält innerhalb der erklärten Quelle nun auch die Operationen in zwei ursprünglichen Nahtabschnitten, ihr Komplement, ihre modulare Mischung und ihre Replica-Antwort. Auf der Ursprungsseite ist der gemeinsame globale Spin-Träger konstruiert; seine charakteristische Antwort ist für die ganze natürliche Liftfamilie bekannt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was diese Verbindung am Gesamtbild ändert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18868,"byte_start":17460,"id":"section:f30b6ecba1ba7b4c8a5f","kind":"section","labels":["sec:pairingcompletion"],"line_end":264,"line_start":250,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/013-subsection-die-vier-urspr-nglichen-marken-w-hlen-eine-ec.tex","status_markers_as_written":[],"summary_excerpt":"Der neue Vorschlag enthält eine tragfähige zusätzliche Verbindung. Die drei Replica-Paarungen liefern exakt normierte positive Gewichte. Zusammen mit den bereits vorhandenen nativen Reflexionen entsteht daraus eine konkrete Operation, deren Erwartungswerttransfer die gesamte historische Matrix [formula in source] ergibt. Dafür muss kein Clockeigenwert eingesetzt werden. Dieselbe Rechnung zeigt, welche Information bei","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Prüfung des neuen Gesamtvorschlags: Die Clock als Auslese mit Gedächtnis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":20760,"byte_start":18868,"id":"section:0fc7a791bab64b641bc4","kind":"subsection","labels":["eq:pairingnorm","eq:pairingweights"],"line_end":299,"line_start":265,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/013-subsection-die-vier-urspr-nglichen-marken-w-hlen-eine-ec.tex","status_markers_as_written":[],"summary_excerpt":"Verwende die Reihenfolge der Paarungen [formula in source] , [formula in source] , [formula in source] und setze Für [formula in source] gilt mit [formula in source] exakt Damit sind die Gewichte positiv und durch die gewählte reale Viermarkengeometrie festgelegt. Am Quadrat ist [formula in source] . Hier wird kein Nenner nachträglich auf die Clock angepasst.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die normierten Paarungsgewichte folgen tatsächlich aus der Quelle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":23699,"byte_start":20760,"id":"section:17c06220c5ac857ad446","kind":"subsection","labels":["eq:pairingtransfer","eq:replicaluders"],"line_end":342,"line_start":300,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/013-subsection-die-vier-urspr-nglichen-marken-w-hlen-eine-ec.tex","status_markers_as_written":[],"summary_excerpt":"Der Anhang setzt zunächst [formula in source] an und bestimmt [formula in source] aus [formula in source] . Diese Gleichsetzung ist im ursprünglichen Vorschlag noch eine zusätzliche Prozessannahme. Sie lässt sich durch eine genau benannte Operation ersetzen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Halbierung erhält eine konkrete operative Bedeutung","topic_suggestions":[]},{"byte_end":24648,"byte_start":23699,"id":"section:ed073ba6c9cd1654b7eb","kind":"subsection","labels":[],"line_end":361,"line_start":343,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/013-subsection-die-vier-urspr-nglichen-marken-w-hlen-eine-ec.tex","status_markers_as_written":[],"summary_excerpt":"Die drei nativen Effekte sind eine Trine auf [formula in source] : [formula in source] mit Rang-eins-Projektoren [formula in source] . Sie kommutieren nicht. Die Aussage des Anhangs, sie bildeten bereits eine kommutative Dreierauslesealgebra, ist auf diesem ursprünglichen Träger deshalb falsch.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine Anzeige ist noch keine Kette gemessener Ausgänge","topic_suggestions":[]},{"byte_end":1961,"byte_start":0,"id":"section:a4c8379d4cb9f2244aa4","kind":"subsection","labels":[],"line_end":34,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/014-subsection-der-neue-anschluss-trifft-einen-bereits-bekan.tex","status_markers_as_written":[],"summary_excerpt":"Die exakte ursprüngliche [formula in source] -Wortfamilie hat in der Reihenfolge [formula in source] die Gewichte Alle diese Prozesse besitzen dieselbe Matrix [formula in source] auf den Anzeigen. Auf dem vollständigen markierten Operatorsystem [formula in source] ist jedoch Die neue Replica-Lüderskonstruktion wählt genau [formula in source] , also [formula in source] . Sie ist damit an die vorhandene Quellenrechnung","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der neue Anschluss trifft einen bereits bekannten Punkt der ganzen Prozessfamilie","topic_suggestions":[]},{"byte_end":6197,"byte_start":1961,"id":"section:954fda607130bae47d38","kind":"subsection","labels":["eq:recordrecovery","sec:replicacarry"],"line_end":78,"line_start":35,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/014-subsection-der-neue-anschluss-trifft-einen-bereits-bekan.tex","status_markers_as_written":[],"summary_excerpt":"Die letzte Aussage beendet die Verbindung nicht. Sie bestimmt, was die vollständige Fortschreibung zusätzlich behalten muss.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die konstruktive Fortsetzung: Derselbe Anzeigenübergang mit erhaltenem Ereignisrecord","topic_suggestions":[]},{"byte_end":8895,"byte_start":6197,"id":"section:4a527ec75bd112cdda07","kind":"subsection","labels":[],"line_end":100,"line_start":79,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/014-subsection-der-neue-anschluss-trifft-einen-bereits-bekan.tex","status_markers_as_written":[],"summary_excerpt":"Der neue Text schlägt vor, primitive Windung durch eine primitive reelle K-Homologie- oder Dirac-Symbolklasse zu ersetzen. Dafür sind zunächst die Typen festzulegen. Auf dem Nahtkreis besitzt die unverdrehte Fundamentalklasse einen primitiven freien Anteil. Ein orientiertes reelles [formula in source] ist als Bündel auf dem Kreis trivial; die Verdrehung mit Rang 16 vervielfacht diesen freien Anteil mit 16. Eine primi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"P1 als primitive Symbolklasse: sinnvolle Präzisierung, keine automatische Operatorwahl","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"}]},{"byte_end":11298,"byte_start":8895,"id":"section:2e95020e0b18f0df04c5","kind":"subsection","labels":[],"line_end":132,"line_start":101,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/014-subsection-der-neue-anschluss-trifft-einen-bereits-bekan.tex","status_markers_as_written":[],"summary_excerpt":"Setze [formula in source] für die vier zyklischen Marken. Die ersten beiden Paarungen geben die bereits vorhandenen komplementären Mengen Ihre modularen Daten sind miteinander verknüpft; sie sind keine zwei unabhängigen räumlichen Richtungen. Insbesondere [formula in source] ist auf dem nichttrivialen Vakuumraum kein zyklischer Schnitt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Drei Paarungen liefern keine drei räumlichen Achsen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":13439,"byte_start":11298,"id":"section:b030b7f042baa9618e25","kind":"subsection","labels":[],"line_end":145,"line_start":133,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/014-subsection-der-neue-anschluss-trifft-einen-bereits-bekan.tex","status_markers_as_written":[],"summary_excerpt":"Die Gesamtidee des Anhangs wird präziser, wenn sie dieselben Operatoren und dasselbe Gedächtnis durch alle Auslesungen verfolgt: Die ursprünglichen Daten wählen einen konkreten Nahtoperator samt Markierung und Verbindungsdaten. Eine bloße Symbolklasse genügt dafür nicht. Dieser Operator trägt die bereits konstruierte [formula in source] -Realstruktur und liefert die tatsächliche CAR-Polarisation; ihre gerade Algebra ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was der gemeinsame Abschluss jetzt tatsächlich verlangen muss","topic_suggestions":[]},{"byte_end":14620,"byte_start":13439,"id":"section:ffa9c0662611b0fadcd0","kind":"section","labels":["sec:anchorfibre"],"line_end":154,"line_start":146,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/014-subsection-der-neue-anschluss-trifft-einen-bereits-bekan.tex","status_markers_as_written":[],"summary_excerpt":"Die nächste Verbindung ist eine Identität für die ganze Vierpunktfamilie. Die ursprünglichen Replica-Paarungen und der neue Anker-Phasenschritt erzeugen exakt dieselben Matrizen [formula in source] . Am Quadrat liefert dies den ursprünglichen Anker [formula in source] . Der kohärente Schritt besitzt eine ausdrückliche Einbettung in die markierte C-Quelle. Die ältere Trine-Auslese besitzt wiederum eine genaue orthogon","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Anker, Viertelphase und Ladungsfasern: dieselbe Clockfamilie in zwei Darstellungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":16940,"byte_start":14620,"id":"section:b18a0a4e09025653273e","kind":"subsection","labels":["eq:anchorreplicajoint","eq:wholeclockfamily"],"line_end":207,"line_start":155,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/014-subsection-der-neue-anschluss-trifft-einen-bereits-bekan.tex","status_markers_as_written":[],"summary_excerpt":"Benutze dieselben normierten signierten Beiträge wie zuvor, Definiere daraus Dann folgen ohne Zahlenanpassung Für die letzte Gleichung benutzt man [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die beiden Clockvorschläge stimmen für alle reellen Viermarkengeometrien überein","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":19475,"byte_start":16940,"id":"section:8eefe4ac051e4d3884b5","kind":"subsection","labels":[],"line_end":242,"line_start":208,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/014-subsection-der-neue-anschluss-trifft-einen-bereits-bekan.tex","status_markers_as_written":[],"summary_excerpt":"Die im Originalvertrag bereits bewiesenen Charaktere sind Ihre Wirkung wird aus den tatsächlichen ursprünglichen C-Wurzeln ausgelesen. In der Reihenfolge [formula in source] folgt Der Drei-Unterraum [formula in source] ist unter [formula in source] invariant. Für eine orthogonale Matrix [formula in source] mit [formula in source] und die natürliche Inklusion [formula in source] setze [formula in source] . Dann Eine e","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die vorhandene markierte Quelle trägt die Viertelbewegung tatsächlich","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"}]},{"byte_end":21145,"byte_start":19475,"id":"section:9d843b27b8b2cc85e91f","kind":"subsection","labels":[],"line_end":268,"line_start":243,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/014-subsection-der-neue-anschluss-trifft-einen-bereits-bekan.tex","status_markers_as_written":[],"summary_excerpt":"Die bereits vorhandenen nativen Effekte auf [formula in source] sind genau Es gilt Damit ist die Trine eine Einschränkung der orthogonalen Dreierauslese, eine konkrete minimale Naimark-Erweiterung. Die Effekte sind aus den ursprünglichen Strahlen 13, 14 und 59 nachgerechnet, nicht durch passend gewählte neue Projektoren ersetzt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die alte Trine und die neue Dreiermessung haben einen exakten gemeinsamen Anschluss","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"}]},{"byte_end":24426,"byte_start":21145,"id":"section:2c12ac1245201d6d7ef1","kind":"subsection","labels":["eq:anchormemory"],"line_end":317,"line_start":269,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/014-subsection-der-neue-anschluss-trifft-einen-bereits-bekan.tex","status_markers_as_written":[],"summary_excerpt":"Für die erklärte orthogonale Auslese ist das Instrument vollständig angegeben. Seine Krausoperatoren [formula in source] erfüllen [formula in source] und Wird diese Dephasierung zwischen jedem Schritt tatsächlich vollzogen, folgen die Populationen [formula in source] . Sechs Anwendungen ergeben die bekannten Clocklücken; ihre physische Zuordnung zu genau sechs ursprünglichen Ereignissen bleibt gesondert zu zeigen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die ausgeschlossenen Kohärenzen liefern den Gedächtniskern ausdrücklich","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":26785,"byte_start":24426,"id":"section:46b56dcf50e9b9510e0d","kind":"subsection","labels":[],"line_end":353,"line_start":318,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/014-subsection-der-neue-anschluss-trifft-einen-bereits-bekan.tex","status_markers_as_written":[],"summary_excerpt":"In den ursprünglichen [formula in source] -Koordinaten ist Der Kern besteht aus ganzzahligen Fünfervektoren gerader Summe. Für jede ganzzahlige oder gleichmäßig halbganzzahlige Dreierkoordinate kann die Parität der fünf anderen Koordinaten passend ergänzt werden; die Projektion ist surjektiv. Jede Faser ist ein bestimmter [formula in source] -Koset. Die Folge zerfällt als Folge freier abelscher Gruppen, aber nicht au","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Dreier-Gitterbeschreibung ist eine exakte Ladungsfaserung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"}]},{"byte_end":28234,"byte_start":26785,"id":"section:79524980b0020f3d94ea","kind":"subsection","labels":[],"line_end":372,"line_start":354,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/014-subsection-der-neue-anschluss-trifft-einen-bereits-bekan.tex","status_markers_as_written":[],"summary_excerpt":"Die gleiche Faserbeschreibung zeigt eine bisher nur implizite Grenze: Die vorhandene markierte Clock und die konforme Zeit verschieben die Dreierkoordinate nicht. Die C/X-Felder können sie verschieben; daraus folgt aber noch keine ausgewählte Zeitentwicklung, die diese Einsetzungen mit bestimmten Raten ausführt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was für physische Bewegung und Lokalität noch fehlt, ist direkt prüfbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":2384,"byte_start":0,"id":"section:99f70dafece41d9c72e8","kind":"subsection","labels":["eq:rationalsewing"],"line_end":46,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/015-subsection-der-uniforme-sewing-test-wird-zu-einem-exakt-.tex","status_markers_as_written":[],"summary_excerpt":"Innerhalb der unitären affinen E8-Vakuumklasse gilt Die erste affine Integrabilitäts-Nullrelation tritt bei Grad [formula in source] auf; deshalb ist der Grad-zwei-Raum für [formula in source] noch [formula in source] . Für die erklärte Vakuumblock-Sewinggröße folgt wegen [formula in source] und positiver weiterer Koeffizienten die im Anhang angegebene Schranke Eine gröbere, vollständig rationale Zertifizierung genüg","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der uniforme Sewing-Test wird zu einem exakt zertifizierten Auswahlsatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"}]},{"byte_end":4895,"byte_start":2384,"id":"section:d5c22828992283675845","kind":"subsection","labels":[],"line_end":66,"line_start":47,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/015-subsection-der-uniforme-sewing-test-wird-zu-einem-exakt-.tex","status_markers_as_written":[],"summary_excerpt":"Die neuen Rechnungen verbinden jetzt ausdrücklich vier Ebenen: Die gleiche Viermarkengeometrie liefert die Paarungsgewichte; diese liefern einen Viertelphasen-Anker; die markierte Quelle trägt dessen kohärente Wirkung; eine konkret definierte Auslese erzeugt die alte Clockmatrix. Derselbe vollständige Quellenraum enthält außerdem die Ladungsfasern und das auf geschlossenen projizierten Wegen verbleibende Gedächtnis.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der verbundene nächste Herkunftsschritt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":6294,"byte_start":4895,"id":"section:f53c4a499ab4660a5205","kind":"section","labels":["sec:sharedtime"],"line_end":73,"line_start":67,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/015-subsection-der-uniforme-sewing-test-wird-zu-einem-exakt-.tex","status_markers_as_written":[],"summary_excerpt":"Der neue Anhang verbindet die richtige Frage mit einer noch zu engen Ereignisklasse. Die gemeinsame Clockhierarchie lässt sich exakt ausführen. Ihre kontinuierliche Markovfortsetzung ist jetzt für die ganze erklärte Klasse entschieden. Gleichzeitig zeigt die tatsächliche Quellenalgebra, warum diese Hierarchie allein keine wechselwirkende Welt beschreibt und warum der vorgeschlagene räumliche Lauf nicht unverändert au","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gemeinsame Zeit, wirkliche Übertragung und die Auswahl des Quellprozesses","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":9097,"byte_start":6294,"id":"section:7300c871735b76c1b717","kind":"subsection","labels":["eq:sharedhierarchy","eq:sharedweights"],"line_end":120,"line_start":74,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/015-subsection-der-uniforme-sewing-test-wird-zu-einem-exakt-.tex","status_markers_as_written":[],"summary_excerpt":"Auf der tatsächlichen markierten Zweierebene gilt in der Pauli-Reihenfolge [formula in source] Die ursprüngliche Trine erfüllt [formula in source] . Am historischen, weiterhin bedingt ausgewählten Punkt [formula in source] ist Der partiell transponierte normierte Choioperator hat den Eigenwert [formula in source] . Dieser Kanal kann also Verschränkung mit einer Referenz erhalten. Die dreidimensionale vollständige Dep","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der ganze Quantenkanal und die gemeinsame Ereignisregel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":15034,"byte_start":9097,"id":"section:126c069568addb605cf9","kind":"subsection","labels":[],"line_end":194,"line_start":121,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/015-subsection-der-uniforme-sewing-test-wird-zu-einem-exakt-.tex","status_markers_as_written":[],"summary_excerpt":"Zunächst bestätigt sich der einfache Endpunktzeuge des Anhangs. Für [formula in source] ist Die sechs [formula in source] sind unabhängig. Ihre Gram-Matrix ist Daher ist der Choi-Rang nach einem Schritt fünf und nach zwei Schritten sechs. Alle Tensorpotenzen [formula in source] mit [formula in source] enthalten die drei irreduziblen [formula in source] -Darstellungen; der gleiche Rangsprung gilt für sämtliche dieser ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die gemeinsame kontinuierliche Zeit ist für die ganze Klasse entschieden","topic_suggestions":[]},{"byte_end":16995,"byte_start":15034,"id":"section:d0b806be86d5e9615ef9","kind":"subsection","labels":["eq:nosupportgrowth"],"line_end":209,"line_start":195,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/015-subsection-der-uniforme-sewing-test-wird-zu-einem-exakt-.tex","status_markers_as_written":[],"summary_excerpt":"Der Bellzustand [formula in source] besitzt unter einem gemeinsamen Ereignis Rückkehrwahrscheinlichkeit eins; unter unabhängigen Ereignissen beträgt sie [formula in source] . Diese im Anhang behaupteten Werte stimmen. Die Ursache ist eine geschützte gemeinsame Symmetrie.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die gemeinsame Ereignisregel transportiert noch keine Wirkung zwischen Registern","topic_suggestions":[]},{"byte_end":18689,"byte_start":16995,"id":"section:a64ffa59c53c508ec739","kind":"subsection","labels":["eq:vacuumweightblind"],"line_end":225,"line_start":210,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/015-subsection-der-uniforme-sewing-test-wird-zu-einem-exakt-.tex","status_markers_as_written":[],"summary_excerpt":"Die tatsächlichen komplexen Reflexionen sind Produkte zweier reeller E8-Weylreflexionen: Für die drei verwendeten Strahlen wurde dies an der ursprünglichen Wurzelwirkung geprüft. Solche Gitterisometrien besitzen passende Vakuum-erhaltende Lifts zur Gitterquelle dongnagjoint. Der Lift samt Kokzyklus gehört zu den Daten: Eine [formula in source] -Wortgleichheit auf der markierten Zweierebene ist nicht automatisch eine ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum weitere simultane Symmetrieprüfungen die Ereignisgewichte nicht auswählen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"}]},{"byte_end":22014,"byte_start":18689,"id":"section:9d635765ee2f2d3c53ed","kind":"subsection","labels":["eq:nativehopfailure"],"line_end":273,"line_start":226,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/015-subsection-der-uniforme-sewing-test-wird-zu-einem-exakt-.tex","status_markers_as_written":[],"summary_excerpt":"Die neue Faserenergie ist korrekt: Sie folgt durch Minimieren der ersten fünf Ladungskoordinaten unter der E8-Parität. Ein energieerhaltender homogener Ortstransport lässt sich daher nicht einfach mit beliebig großen Familienladungen und unverändertem [formula in source] identifizieren.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der vorgeschlagene Raumlauf scheitert bei direkter Übertragung auf die Quelle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"}]},{"byte_end":24887,"byte_start":22014,"id":"section:f5c00e086d665ecae8a5","kind":"subsection","labels":["eq:localcausalresponse"],"line_end":313,"line_start":274,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/015-subsection-der-uniforme-sewing-test-wird-zu-einem-exakt-.tex","status_markers_as_written":[],"summary_excerpt":"Der stärkste nächste Ansatz verwendet die vorhandene lokale E8-Quelle selbst. Betrachte einen normierten Cartan-Strom mit Dies sind ihre bestehenden Level-eins- und Zeitrelationen. Für reelle glatte Kreisfunktionen seien Dann gilt [formula in source] und unter der bereits vorhandenen Quellenzeit Die zugrunde liegende lokale Stromnetzstruktur ist Standard tanimotojoint; die folgende Rechnung ist ihre direkte Anwendung","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein positiver gemeinsamer Prozess ist bereits in der vollständigen Quelle vorhanden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"}]},{"byte_end":27481,"byte_start":24887,"id":"section:72e39a66e3a00825ee65","kind":"subsection","labels":[],"line_end":332,"line_start":314,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/015-subsection-der-uniforme-sewing-test-wird-zu-einem-exakt-.tex","status_markers_as_written":[],"summary_excerpt":"Die Arbeit am fundamentalen Abschluss wird daher auf zwei gekoppelte Herkunftsgleichungen konzentriert: Der tatsächliche ursprüngliche Nahtoperator muss die erklärte Quelle samt Zustand und Instrument liefern; die räumliche Realisierung muss deren vollständige lokale Antwortstruktur erhalten und daraus die geforderten gemeinsamen physikalischen Ausgaben gewinnen. Die lokalen Impulsantworten, die gemeinsame Clockschra","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die fundamentale Auswahlfrage ist jetzt eine gemeinsame Antwortgleichung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":28153,"byte_start":27481,"id":"section:44aec848b52488e5fbde","kind":"section","labels":["sec:inverseorigin"],"line_end":336,"line_start":333,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/015-subsection-der-uniforme-sewing-test-wird-zu-einem-exakt-.tex","status_markers_as_written":[],"summary_excerpt":"Die entscheidende Verdichtung der Ursprungsfrage. Die bereits gewählte, markierte E8-Level-1-Quelle lässt sich zu genau ihrer passenden Theorie mit sechzehn reellen Fermionen zurückverfolgen. Dabei werden Vakuum, vollständige Feldantworten und Konformalzeit gemeinsam rekonstruiert. Der Herkunftsnachweis muss deshalb nicht vier unabhängig gewählte Zutaten rechtfertigen. Er muss einen bestimmten lokalen Feldkeim im urs","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der konstruktive Rückweg: Eine lokale Feldregel bestimmt Quelle, Zustand und Zeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":31910,"byte_start":28153,"id":"section:3edbdf9f2ab4bb8b4365","kind":"subsection","labels":["eq:inverseZ8"],"line_end":369,"line_start":337,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/015-subsection-der-uniforme-sewing-test-wird-zu-einem-exakt-.tex","status_markers_as_written":[],"summary_excerpt":"Die ursprüngliche Verklebung enthält die Zwischenstufe Sie wird nicht nachträglich ausgesucht: Im ursprünglichen [formula in source] -Glue sind es die beiden geraden Klassen. Dessen Charakter [formula in source] hat auf den Klassen [formula in source] den Wert [formula in source] ; der Fixpunkt von [formula in source] ist die [formula in source] -Gitteralgebra. In den ursprünglichen verdoppelten Wurzelkoordinaten [fo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das vorhandene E8 enthält den Rückweg bereits in seiner Markierung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"}]},{"byte_end":2866,"byte_start":0,"id":"section:6abb2035d8cd61ed5f6d","kind":"subsection","labels":["eq:inverseinternalglue"],"line_end":27,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/016-subsection-die-zur-ckgewonnene-darstellung-ist-der-urspr.tex","status_markers_as_written":[],"summary_excerpt":"Die sechzehn Gewichte zerfallen entlang der ursprünglichen ersten fünf und letzten drei Gitterrichtungen als Jede der [formula in source] ursprünglichen [formula in source] -Wurzeln verbindet tatsächlich zwei Gewichtspaare dieser Darstellung. Auf P2 lauten ihre Ladungen Das rekonstruiert die vorher geometrisch gewonnene Darstellung mitsamt ihrer Wirkung. Es identifiziert diese Richtungen weiterhin nicht mit sechzehn ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die zurückgewonnene Darstellung ist der ursprüngliche Träger","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"}]},{"byte_end":5617,"byte_start":2866,"id":"section:e2074517da153b4df025","kind":"subsection","labels":["eq:inverseL0","eq:inversekernel"],"line_end":60,"line_start":28,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/016-subsection-die-zur-ckgewonnene-darstellung-ist-der-urspr.tex","status_markers_as_written":[],"summary_excerpt":"Für die rekonstruierte Neveu–Schwarz-Darstellung sind die Moden und das Vakuum durch festgelegt. Der gemeinsame geerbte Stress-Tensor gibt Die Realisierung des geraden CAR-Netzes, seiner Sektoren und der Virasorowirkung ist in bockenhauercar explizit konstruiert. Hier wird sie an die ursprüngliche TFPT-Markierung angeschlossen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vakuum und Konformalzeit folgen zusammen","topic_suggestions":[]},{"byte_end":8432,"byte_start":5617,"id":"section:1b1bc4c9f6cda2b536b1","kind":"subsection","labels":["sec:originkernelcriterion"],"line_end":76,"line_start":61,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/016-subsection-die-zur-ckgewonnene-darstellung-ist-der-urspr.tex","status_markers_as_written":[],"summary_excerpt":"Der Rückweg liefert ein scharfes hinreichendes Ursprungskriterium. Angenommen, der ursprüngliche Prozess erzeugt eine unitäre, positiv graduierte chirale Vertexsuperalgebra mit eindeutigem Vakuumraum [formula in source] und sechzehn reellen, gegenseitig graduiert lokalen Primärfeldern [formula in source] vom Gewicht [formula in source] . Ihr positives Zweipunktprodukt sei nicht ausgeartet und in einer orthonormalen B","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der lokale Rekonstruktionssatz: Was am Ursprung tatsächlich genügt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":12672,"byte_start":8432,"id":"section:4249794f30d9e841e88a","kind":"subsection","labels":["eq:rawmixwitness"],"line_end":105,"line_start":77,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:a1f86a802c0c3ec02329"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/016-subsection-die-zur-ckgewonnene-darstellung-ist-der-urspr.tex","status_markers_as_written":[],"summary_excerpt":"Der Vertrag microscopic-charged-car-limit/README.md konstruiert am tatsächlich verwendeten QWZ-Zylinder einen lokalen geladenen CAR-Kanal mit beiden Adjungierten, seinem gefüllten Quellvakuum und kontrolliertem Zeitgrenzwert. Die tragende ursprüngliche Operatoridentität lautet für die obere Randzeile Sie liefert den chiralen linearen Anteil und einen quadratisch kleinen Mischterm. Daraus werden im Original alle feste","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der mikroskopische Ausgangspunkt ist im Originalbestand bereits vorhanden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":14814,"byte_start":12672,"id":"section:79016bccd8abf8d4047d","kind":"subsection","labels":[],"line_end":119,"line_start":106,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/016-subsection-die-zur-ckgewonnene-darstellung-ist-der-urspr.tex","status_markers_as_written":[],"summary_excerpt":"Der Rücklauf ist innerhalb der gewählten Quellenklasse geschlossen. Die schon vorhandene rekursive Rückbestätigung erhält damit ein Feld-, Vakuum- und Zeitgegenstück. Dieser Rücklauf liefert ein präzises Ziel für die Herkunftsherleitung; er ersetzt sie logisch nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie das den Weg zur fundamentalen Lösung verändert","topic_suggestions":[]},{"byte_end":15929,"byte_start":14814,"id":"section:60743534176690650663","kind":"subsection","labels":[],"line_end":124,"line_start":120,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/016-subsection-die-zur-ckgewonnene-darstellung-ist-der-urspr.tex","status_markers_as_written":[],"summary_excerpt":"Die bestehende Quellenimplementierung wurde um reconstruct_marked_fermion_source ergänzt. Sie benutzt die originalen E8-Wurzeln und Feldmarkierungen, berechnet den geraden Glue-Fixpunkt, die [formula in source] -Wirkung und die P2-Ladungen. Die Tests prüfen die Glue-Graduierung an sämtlichen ursprünglichen Wurzelklammern und die tatsächliche Wirkung der [formula in source] -Wurzeln auf den sechzehn Gewichten.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ausführbare Prüfung und ihr genauer Umfang","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":16573,"byte_start":15929,"id":"section:bcfebec440b871f179fc","kind":"section","labels":["sec:completion"],"line_end":128,"line_start":125,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/016-subsection-die-zur-ckgewonnene-darstellung-ist-der-urspr.tex","status_markers_as_written":[],"summary_excerpt":"Die Aufgabe bleibt die gemeinsame Herkunft, Prozessrekursion und physische Realisierung. Die vorhandenen physikalischen Herleitungen aus Abschnitt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie die Gesamtlösung konkret erreichbar würde","topic_suggestions":[]},{"byte_end":19788,"byte_start":16573,"id":"section:ce829034c574b9a3f18d","kind":"subsection","labels":[],"line_end":141,"line_start":129,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/016-subsection-die-zur-ckgewonnene-darstellung-ist-der-urspr.tex","status_markers_as_written":[],"summary_excerpt":"Die Zielaussage lautet: Die ursprünglichen P1/P2-Daten samt den tatsächlich schon begründeten Markierungen erzwingen oder charakterisieren die minimale positive lokale Level-1-Vakuumquantisierung des markierten Gitters innerhalb einer ausdrücklich definierten Vergleichsklasse.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Erste Brücke: Die Quantisierung aus dem Ursprung auswählen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"}]},{"byte_end":21448,"byte_start":19788,"id":"section:cae407dbd332fb1f0c9d","kind":"subsection","labels":[],"line_end":152,"line_start":142,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/016-subsection-die-zur-ckgewonnene-darstellung-ist-der-urspr.tex","status_markers_as_written":[],"summary_excerpt":"Die Zielgleichungen sind für die gemeinsam zugelassenen geladenen Operationen und die tatsächlich identifizierte Zeit. Die vorhandenen [formula in source] -Intertwiner, Hecke-Sektorprojektoren und geladenen Carry-Verbraucher sind konkrete Bausteine. Der Nachfahrenturm und die bei endlichen Abständen sichtbaren Restsektoren dürfen dabei nicht abgeschnitten werden, wenn die Behauptung vollständige Antworttreue lautet.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zweite Brücke: Ein vollständiger Prozess unter Rekursion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":22528,"byte_start":21448,"id":"section:75b58004727c9b28d8aa","kind":"subsection","labels":["eq:physical"],"line_end":170,"line_start":153,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:4d03b3278a80721cc5b2","relation:e93d327838cf167d6983","relation:f188d2a971e95932b402"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/016-subsection-die-zur-ckgewonnene-darstellung-ist-der-urspr.tex","status_markers_as_written":[],"summary_excerpt":"Die Originalverträge benennen bereits den richtigen gemeinsamen Prüfgegenstand. In passender Notation lautet er zusammen mit Zu spezifizieren sind die Einsetzungs- und Restriktionsabbildung, die zulässigen Quellen [formula in source] , die Feldnormalisierung, P2-Ladungen, Clockmarkierungen, Zustand, Zeit und analytischen Gebiete. Die Gleichheit eines ausgewählten Zahlenwertes oder bloßer Determinantenbeträge reicht n","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dritte Brücke: Dieselbe Quelle in der physischen Raumzeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":24518,"byte_start":22528,"id":"section:952b416f13f48444aea9","kind":"subsection","labels":[],"line_end":183,"line_start":171,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:1d6dfc681a490764bd97"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/016-subsection-die-zur-ckgewonnene-darstellung-ist-der-urspr.tex","status_markers_as_written":["[A]"],"summary_excerpt":"Der stärkere Originalvertrag BULK.PRIME_COMPLETION.01 verlangt ausdrücklich eine durch die Randoperationen erzeugte Realisierung ohne unsichtbaren Zusatzsektor. Unter dieser Bedingung dürfen beliebige angehängte Zuschauer nicht als Gegenbeweis gegen Eindeutigkeit verwendet werden. Sind auf einer zyklisch erzeugenden Wortalgebra sämtliche Antworten gegeben, wobei [formula in source] eine [formula in source] -Automorph","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der gemeinsame Prozess bestimmt noch nicht seine räumliche Zuordnung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":27708,"byte_start":24518,"id":"section:766267a43ff907cfc61f","kind":"subsection","labels":["sec:physicaltimeaudit"],"line_end":204,"line_start":184,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:4e8d02a8acde1172fda3"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/016-subsection-die-zur-ckgewonnene-darstellung-ist-der-urspr.tex","status_markers_as_written":[],"summary_excerpt":"Auch die Formulierung, der vorhandenen Konformalzeit fehle lediglich eine physische Einheit, wäre für den exakten Poincar\\'e-Vertrag zu schwach. Auf dem E8-Vakuumraum gilt [formula in source] . Jede affine Wahl [formula in source] mit [formula in source] besitzt daher eine skalare Periode. Beim fermionischen Cover verdoppelt sich die Periode; das Argument bleibt bestehen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Konforme Kreiszeit und physische Translation müssen getrennt werden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":28926,"byte_start":27708,"id":"section:757c21407c3158f0a902","kind":"subsection","labels":[],"line_end":211,"line_start":205,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/016-subsection-die-zur-ckgewonnene-darstellung-ist-der-urspr.tex","status_markers_as_written":[],"summary_excerpt":"Die 24 ursprünglichen Felder zusammen mit ihren Adjungierten erzeugen die gesamte Stromalgebra. Wenn eine physische Realisierung ihre vollständigen Level-1-Relationen, ein gemeinsames positives zyklisches Vakuum, analytische Lokalität und lokale Erzeugung nachweist, ist der erzeugte Vakuumsektor dadurch stark festgelegt. Unter den passenden Rekonstruktionsvoraussetzungen bestimmen diese Daten dieselben höheren Randan","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die 24 Felder die Aufgabe wesentlich verkleinern","topic_suggestions":[]},{"byte_end":30307,"byte_start":28926,"id":"section:ca0e8a58f305ec8e7376","kind":"subsection","labels":[],"line_end":225,"line_start":212,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/016-subsection-die-zur-ckgewonnene-darstellung-ist-der-urspr.tex","status_markers_as_written":[],"summary_excerpt":"L0.21 L0.38 L0.33 Zweig & Gemeinsames Objekt & Entscheidende noch benötigte Identifikation\\\\ Eichstruktur & Geladene Ströme, Wardidentitäten, lokale Gauss-Wirkung & Interne Symmetrie als tatsächliche lokale Eichwirkung\\\\ Chirale Materie & Physische Feldoperatoren und ihre Spektren & Chirale Raumzeitwirkung und Spiegelentkopplung\\\\ Flavor/Massen & Pole und Mischungsantworten derselben Mehrpunktfunktionen & Yukawa-Dyna","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Welche physikalischen Zweige danach am selben Objekt hängen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"}]},{"byte_end":32994,"byte_start":30307,"id":"section:c5f360ad2fb9aadfb107","kind":"subsection","labels":[],"line_end":234,"line_start":226,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/016-subsection-die-zur-ckgewonnene-darstellung-ist-der-urspr.tex","status_markers_as_written":[],"summary_excerpt":"Die Suche setzt am jetzt bewiesenen Rekonstruktionskriterium aus Abschnitt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was nach diesen Prüfungen tatsächlich herzuleiten bleibt","topic_suggestions":[]},{"byte_end":35932,"byte_start":32994,"id":"section:108dad8ee28a3ec8ae88","kind":"section","labels":[],"line_end":254,"line_start":235,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/016-subsection-die-zur-ckgewonnene-darstellung-ist-der-urspr.tex","status_markers_as_written":[],"summary_excerpt":"``Neu'' hat hier zwei verschiedene Bedeutungen. Eine Anwendung kann für TFPT neu sein, obwohl das mathematische Verfahren bekannt ist. Wissenschaftliche Erstmaligkeit oder ein bahnbrechender Leistungssprung verlangt zusätzlich einen Vergleich mit der einschlägigen Literatur und den stärksten vorhandenen Verfahren. Die folgenden Anwendungen ergeben sich konkret aus den Sitzungsbefunden.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neue Anwendungen: Wo die Verbindung bereits produktiv wird","topic_suggestions":[]},{"byte_end":36779,"byte_start":35932,"id":"section:f79b6eae212d93fa320f","kind":"section","labels":["sec:algorithms"],"line_end":260,"line_start":255,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/016-subsection-die-zur-ckgewonnene-darstellung-ist-der-urspr.tex","status_markers_as_written":[],"summary_excerpt":"Der stärkste gemeinsame Algorithmusgedanke ist ein Compiler für zukünftiges Verhalten: Er gewinnt aus tatsächlichen Antworten die nötigen Zustandsunterschiede, speichert sie in einer geeigneten Struktur und übersetzt zulässige Operationen in ein kleines, nachweislich antworttreues Programm.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Welche Algorithmen daraus entstehen könnten – und was daran bahnbrechend wäre","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"}]},{"byte_end":39590,"byte_start":36779,"id":"section:222149512147d545dd35","kind":"subsection","labels":[],"line_end":284,"line_start":261,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/016-subsection-die-zur-ckgewonnene-darstellung-ist-der-urspr.tex","status_markers_as_written":[],"summary_excerpt":"Zustände durch zukünftige Tests zu definieren ist bekannt. Aktive Automatenlerner, Predictive State Representations, Observable Operator Models und gewichtete Automaten verfolgen verwandte Ziele. Auch Verbindungen zu Tensor-Netzen sind publiziert littman,thon,adhikary,lsharp. Die bloße Zusammenführung dieser Begriffe ist daher kein neuer Universalalgorithmus.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Neuheitsmaßstab und ein bereits vorhandener Gegenvergleich","topic_suggestions":[]},{"byte_end":41984,"byte_start":39590,"id":"section:f0dd53913de552f866da","kind":"subsection","labels":[],"line_end":295,"line_start":285,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/016-subsection-die-zur-ckgewonnene-darstellung-ist-der-urspr.tex","status_markers_as_written":[],"summary_excerpt":"Die Forschungsfortsetzung hat hierfür bereits einen konkreten Teil umgesetzt: Für sämtliche endlichen C/X-Wurzelwörter wertet evaluate_lattice_word das ursprüngliche Gesetz durch quadratisch viele exakte Paaroperationen aus. Die tatsächlichen Kokzyklusphasen und geladenen Erweiterungssektoren bleiben erhalten. Die Ward-Rekursion ist der unabhängige Vergleich. Das ist eine im TFPT-Rechner nutzbare Anwendung einer beka","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Baustein 1: Ein schneller Compiler für das vollständige Quellgesetz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"}]},{"byte_end":45141,"byte_start":41984,"id":"section:11da13aac90475d2e0cd","kind":"subsection","labels":["eq:compiler"],"line_end":328,"line_start":296,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/016-subsection-die-zur-ckgewonnene-darstellung-ist-der-urspr.tex","status_markers_as_written":[],"summary_excerpt":"Für bekannte endliche lineare Dynamiken sind die Bedingungen konkret. Ein Encoder [formula in source] erhält sämtliche Antworten, wenn für jede erlaubte Aktion [formula in source] Dann folgt durch Induktion für jedes endliche Wort. Dies ist ein wirklicher Vertrag über die Zukunft, keine Ähnlichkeit nur des momentanen Zustands.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Baustein 2: Ein aktionsabhängiger Gedächtniscompiler","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"}]},{"byte_end":46588,"byte_start":45141,"id":"section:e33bbd3edc264ad389d4","kind":"subsection","labels":[],"line_end":339,"line_start":329,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/016-subsection-die-zur-ckgewonnene-darstellung-ist-der-urspr.tex","status_markers_as_written":[],"summary_excerpt":"Eine Symmetriedarstellung zerlegt sich als Die Darstellung [formula in source] beschreibt die Symmetriewirkung; die Multiplizitätsräume [formula in source] tragen weitere tatsächlich veränderliche Information. Geladene Operationen können zwischen Sektoren wechseln. Ein korrektes Kompressionsverfahren muss deshalb sowohl die Sektoren als auch die relevanten Multiplizitäten gegenüber der ganzen Aktionsfamilie erhalten.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Baustein 3: Symmetriekompression mit erhaltenen Multiplizitäten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"}]},{"byte_end":48237,"byte_start":46588,"id":"section:90c0d7bc6cef9e53866e","kind":"subsection","labels":[],"line_end":348,"line_start":340,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/016-subsection-die-zur-ckgewonnene-darstellung-ist-der-urspr.tex","status_markers_as_written":[],"summary_excerpt":"Der Sechserzeuge legt eine konkrete Suchregel nahe: Suche zuerst minimal ladungsneutrale Gruppen, deren echte Teilgruppen ladungsungleichgewichtig sind. Prüfe dann ihre vollständige und verbundene Antwort. So findet man Fälle, die eine rein niedrige Antwortbeschreibung übersehen kann. Minimalität der Ladungsneutralität ist eine hinreichende Auswahlhilfe für diese Zeugenklasse, keine vollständige Liste aller verbunden","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Baustein 4: Gezielte Suche nach höheren gemeinsamen Antworten","topic_suggestions":[]},{"byte_end":50116,"byte_start":48237,"id":"section:151d4a64c44e72c6b2c0","kind":"subsection","labels":[],"line_end":368,"line_start":349,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/016-subsection-die-zur-ckgewonnene-darstellung-ist-der-urspr.tex","status_markers_as_written":[],"summary_excerpt":"Lean besitzt bereits eine Programmiersprache und Codegenerierung lean. Die sinnvolle automatische Übernahme hängt von der Art des Originals ab: L0.30 Y Original in Lean & Nutzbarer Anschluss\\\\ Berechenbare Definition & Direkt ausführbarer Rechenkern oder Export\\\\ Konstruktiver Wert mit Eigenschaft & Algorithmus samt formalem Vertrag\\\\ Gleichheits-/Erhaltungssatz & Zulässige Optimierungsregel mit Voraussetzungen\\\\ Kla","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Baustein 5: Lean als Quelle ausführbarer, überprüfbarer Regeln","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":1194,"byte_start":0,"id":"section:eb197b3b56811f72be4d","kind":"subsection","labels":[],"line_end":13,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/017-subsection-ein-gemeinsamer-algorithmus-statt-f-nf-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"Der ambitionierte, messbare Anspruch lautet: Ein System gewinnt aus den Folgen seiner Handlungen ein kleines wiederverwendbares Programm und nutzt es nachweislich besser als bestehende Verfahren. Eine solche Leistung wäre ein möglicher Durchbruch. Die vorliegende Sitzung hat seine mathematischen Bausteine und Gegenfälle geschärft; sie hat die Überlegenheit noch nicht gezeigt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein gemeinsamer Algorithmus statt fünf neuer Architekturen","topic_suggestions":[]},{"byte_end":4247,"byte_start":1194,"id":"section:43487a83a2e041a3f672","kind":"section","labels":["sec:hylaean"],"line_end":34,"line_start":14,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/017-subsection-ein-gemeinsamer-algorithmus-statt-f-nf-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"Der Anwendungsteil nimmt vorläufig an, dass mit ``hallieren'' Hylæan beziehungsweise Field Intelligence gemeint ist. Sein aktueller Produktionsstand wurde für dieses Dokument nicht neu geprüft. Die folgenden Aussagen sind ein konkreter Integrations- und Forschungsentwurf, keine Behauptung über bereits gelandete Fähigkeiten.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was das für Hylæan konkret bedeuten würde","topic_suggestions":[]},{"byte_end":4701,"byte_start":4247,"id":"section:0a82087fd3ce6765d02d","kind":"section","labels":["sec:verification"],"line_end":38,"line_start":35,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/017-subsection-ein-gemeinsamer-algorithmus-statt-f-nf-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"Die historischen Ergebnisse dieses Abschnitts wurden aus den gespeicherten Originalprotokollen der Sitzung gelesen. Die Fortsetzung hat die neuen Herkunfts- und Realisierungsrechnungen gezielt frisch ausgeführt. Der gesamte tausendteilige Bestand wurde dafür nicht erneut ausgeführt; die folgenden Prüfstände bleiben voneinander unterscheidbar.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verifikation, Lean und Experimente: Der tatsächliche Sitzungsstand","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":10040,"byte_start":4701,"id":"section:f00907fc4211c508b9c9","kind":"subsection","labels":[],"line_end":55,"line_start":39,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:0b07f47858679dd303b3","relation:174a7306240d7817c4d1","relation:6d0773c2d6c1acfe4319","relation:9d9b4ce2b723f18af884","relation:b50b898a665a6f195ca8","relation:d9c9268a7fd0a0ad29cb"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/017-subsection-ein-gemeinsamer-algorithmus-statt-f-nf-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"Die früheren gezielten Läufe bestanden 45 beziehungsweise 58 Tests. Nach Integration des Anker-/Faservorschlags bestand der neue gemeinsame Lauf 67 Tests. Zusammen geprüft wurden test_source_selection.py, test_source_realization.py, test_source_program.py und test_marked_source_process.py. Die Zahlen werden nicht addiert; die früheren Testmengen sind enthalten. Die anschließende Prüfung der gemeinsamen Ereignishierar","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Frisch ausgeführte Forschungsfortsetzung","topic_suggestions":[]},{"byte_end":11396,"byte_start":10040,"id":"section:809bcf8f43b79f65fce9","kind":"paragraph","labels":[],"line_end":74,"line_start":56,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/017-subsection-ein-gemeinsamer-algorithmus-statt-f-nf-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"Die Fortsetzung integriert die tatsächliche Hyperladungsantwort, den expliziten CAR-Paaranschluss, das vollständige schwere Majorana-Tensorwörterbuch mit anschließender bestehender Seesaw-Rechnung sowie den gesamten neutralen Flavor-Defektkern. Nach Korrektur der linken/rechten RHP-Feldkonvention bestand im gemeinsamen gezielten Lauf 72 Tests in den acht betroffenen Testdateien. Der neu gestartete Explorer liefert 24","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gemeinsames Quellenwörterbuch, vorheriger Stand vom 29. September.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":12345,"byte_start":11396,"id":"section:89a0d8d2dcd61565328a","kind":"paragraph","labels":[],"line_end":88,"line_start":75,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/017-subsection-ein-gemeinsamer-algorithmus-statt-f-nf-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"Abschnitt Determinantenwindung mit dem vollständigen Paartransport und der neutralen Antwort. Im gemeinsamen gezielten Lauf bestanden 82 Tests in neun Dateien, einschließlich zehn neuer Prüfungen des Massentransports. Geprüft wurden die tatsächlichen C-Gewichte, allgemeine nichtkommutierende Verbindungen, die Umkehrabbildung, die endliche Zusammensetzung, die duale Massenform samt Metrik und die lokale kovariante Pun","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gemeinsamer Massentransport, anschließender Stand vom 29. September.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":13957,"byte_start":12345,"id":"section:bc6756e023a102c03053","kind":"paragraph","labels":[],"line_end":107,"line_start":89,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":["relation:1f9714812bf2acf5c5d8"],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/017-subsection-ein-gemeinsamer-algorithmus-statt-f-nf-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"Die neue Prüfung in Abschnitt Paarzustände und ihre zehn Gegenladungen an sämtlichen acht nichtdiagonalen SM-Generatoren, den drei nichtabelschen Cartan-Gewichten und der Hyperladung. Ein farbgeladener Strom dient als Gegenkontrolle: Er wird nicht annihiliert. Die Quelle besitzt die behaupteten Ladung-zwei-Operatoren; eine physische Skalarabbildung oder Kondensation wird dadurch nicht behauptet. Die zugehörigen neun ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wand-Lesart und vollständiger geladener Quellenkanal, aktueller Stand.","topic_suggestions":[]},{"byte_end":18302,"byte_start":13957,"id":"section:39ba3e74ad26f769c9c4","kind":"subsection","labels":[],"line_end":161,"line_start":108,"occurrence":1,"owner_documents":["document:tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/017-subsection-ein-gemeinsamer-algorithmus-statt-f-nf-neuer-.tex","status_markers_as_written":[],"summary_excerpt":"Fortsetzung vom 29. 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This is the actual bridge from compiler to physics — everything in CELEST.SEAM.01 is preparation for it. It is a research contract \\ (ledger row WOIT.OS.TWISTOR.01: Open, research contract), not a claim; nothing below asserts that the construction exists. The external programme it engages — Woit's Euclidean Twistor Unification ( arXiv:2104.05099) — is a named reference frame for the shape of the target, never","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — WOIT.OS.TWISTOR.01 (the Osterwalder–Schrader twistor bridge)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6698,"byte_start":0,"id":"section:17538bc5f76786fa0bbe","kind":"frontmatter","labels":[],"line_end":81,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_research_contracts"],"relation_ids":["relation:01534d12ba396b58ed0a","relation:0eac03c6cddbddc89720","relation:10cbe14d07a1257d704f","relation:129c2d83cdce96602254","relation:23a5ed76637625f93c7b","relation:36f018310268740d1eeb","relation:42a502f8f48244d38fd4","relation:5336df0ac32dcc5bb706","relation:57efc23fc1d4c0e1baa5","relation:60fd7a6d69c2155d7518","relation:69fe19b2c71c10a77bf7","relation:708431a8c81cc4398a7b","relation:7ca7c6bd175f56327f51","relation:7e459cd0e5ebf5e22f3f","relation:7ec6a2971eebd5c93024","relation:83701f541fb545af1701","relation:8dd7c4fd8e25751beaff","relation:91efaa83e1ca4a09b168","relation:a83d9b07da0afe8f69a3","relation:d27c2d227beeeedff6f2","relation:d9e8be14168a665eab1b","relation:f2c627cabbe686b48d74","relation:f9b2d221fd2f70d9647b","relation:ffd442b54e584263cc4a"],"semantic_review":false,"source":"documents/tfpt_research_contracts/sections/014-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"The [formula in source] / [formula in source] roadmap (named milestones, each with success and kill criteria). 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A research contract \\ (ledger row CCC.SEAM.CROSSOVER.01: Open, research contract), not a claim. It engages Penrose's Conformal Cyclic Cosmology (Tod, arXiv:1309.7248; Penrose–Meissner, arXiv:2503.24263) as a named reference frame for the shape of the target — never a confirmation in either direction. The cyclic reading of origin_theory stays \\ regardless of this contract's fate; nothing below asserts that CCC","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — CCC.SEAM.CROSSOVER.01 (the conformal-cyclic crossover on the seam geometry)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":19991,"byte_start":15455,"id":"section:580c8e5b415ac9b79cec","kind":"section","labels":[],"line_end":244,"line_start":183,"occurrence":1,"owner_documents":["document:tfpt_research_contracts"],"relation_ids":["relation:086fd0df6c4d107d1cef","relation:1ee9826fb1196d859b92","relation:4e52eedbc86d0f2c9461","relation:4f7a1e8bd0bbeb8c14cd","relation:542b6a50223c3f5e7f6c","relation:77339d82f2587bb7ad50","relation:81ef6318992dec02bc51","relation:a45454d4659f4faf5e48","relation:b015384aab042f9b9ea8","relation:f2dde22a16e837f36602"],"semantic_review":false,"source":"documents/tfpt_research_contracts/sections/014-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO","\\mX"],"summary_excerpt":"Typing. A standing discipline rule, in force immediately (ledger row DIMENSION.UPLIFT.FIREWALL.01); the uplift theorems it names are separate \\ contracts. It formalizes the core diagnosis of the 2026-08-27 external deep review: a chiral [formula in source] D seam net does not imply a local, interacting [formula in source] D quantum world. 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A research contract \\ (ledger row SEAM.BULK4D.RECON.01: Open, research contract), not a claim. It makes explicit the theorem that was previously only implicit between the SEAM.EQUIV.01 conclusion (a chiral [formula in source] boundary object) and the WOIT.OS.TWISTOR.01 goal statement (a Poincar\\'e-covariant, causal, chiral 4D theory): the missing seam [formula in source] bulk reconstruction is a theorem of it","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — SEAM.BULK4D.RECON.01 (from seam data to a 4D local quantum theory)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":26818,"byte_start":23996,"id":"section:c61a0a05c77babe52899","kind":"section","labels":[],"line_end":337,"line_start":299,"occurrence":1,"owner_documents":["document:tfpt_research_contracts"],"relation_ids":["relation:0e696302276b7bfaadf2","relation:292ed8513936b2f5dd3d","relation:a686e7f0d822ff8f3944","relation:dc3375ff34e8a3907102"],"semantic_review":false,"source":"documents/tfpt_research_contracts/sections/014-source.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row BULK.PRIME_COMPLETION.01: Open, research contract), not a claim. Registered 2026-09-04 from the r644 audit harvest; it replaces the ``unique from seam data alone'' reading of SEAM.BULK4D.RECON.01/B7 by uniqueness in the category of seam-generated (prime) completions. Dimension typing ( DIMENSION.UPLIFT.FIREWALL.01 F2): the hypothesis is [formula in source] D free-fermion, the","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — BULK.PRIME_COMPLETION.01 (prime/seam-generated completions, no spectator)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":11573,"byte_start":0,"id":"section:a3401d23c565056512c5","kind":"section","labels":[],"line_end":143,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_research_contracts"],"relation_ids":["relation:0a4df5710464e34133b8","relation:159a467ae7a84e41f5cb","relation:18ad78be5f3bd8807429","relation:219521b2b4153de64fe6","relation:2208c5dbe1eda15944a5","relation:2f24a74a946862dfa664","relation:3211a630b629c0210f00","relation:34667d175b0ab3db1288","relation:360cecd5b5ed64d6afc1","relation:3e37226502f0b50621bb","relation:41e23b50c5d02925a380","relation:56cc2ed41509b51de09e","relation:60cf226c2697ca8e90d2","relation:902bba22716bda4fe962","relation:91691dde17df0705f11f","relation:b33c02c966aea7fcfd99","relation:d1db277a253b86531245","relation:e18e07931cab22d4b9a4","relation:e2bb3402be1749c7d165","relation:e430f47f21494d729821","relation:e8435dfadbcd78e7b64f","relation:f07b7c219a41dcbc9179"],"semantic_review":false,"source":"documents/tfpt_research_contracts/sections/015-source.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"tocsectionResearch Contracts: DYN.MARKOV.EMBED.01 / DYN.UNITARY.DILATION.01","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contracts — DYN.MARKOV.EMBED.01 / DYN.UNITARY.DILATION.01 (the three meanings of ``dynamics'')","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":18083,"byte_start":11573,"id":"section:80661f09e2cb1c15bc8e","kind":"section","labels":[],"line_end":234,"line_start":144,"occurrence":1,"owner_documents":["document:tfpt_research_contracts"],"relation_ids":["relation:2887b32e9eb37a7a9f95","relation:4bdc22b49977b74674c1","relation:5296c730fa8cf5b00437","relation:5eaa784b11f5ac1309e6","relation:831fe02aea9354e36a03","relation:922c5142f2e1c094ab25","relation:925c0bf629f4138231be","relation:c9bf19fbb9e2ac7f6039","relation:fc6d7617ae82ce57a66b"],"semantic_review":false,"source":"documents/tfpt_research_contracts/sections/015-source.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row QFT4D.OS.RECON.01: Open, research contract), not a claim. This is step (3) of the DIMENSION.UPLIFT.FIREWALL.01 route ordering: the nonperturbative 4D existence statement that no perturbative or seam-level result can substitute for.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — QFT4D.OS.RECON.01 (the genuine 4D Euclidean lattice package)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":23254,"byte_start":18083,"id":"section:7b481ee095ad252819f8","kind":"section","labels":[],"line_end":303,"line_start":235,"occurrence":1,"owner_documents":["document:tfpt_research_contracts"],"relation_ids":["relation:2cec8c5d7522af70df53","relation:56b13aa9cb98db00a6d8","relation:7e1a5017c402334872f1","relation:ae76c7e643cf9b3429a2","relation:b5d4c434016c8715d3c6","relation:b8ded0468a97ccb729f3","relation:bb4ab583579ab92b1ee8","relation:dff2ec91691aea322787","relation:fe15a802bbe4ad7311f4"],"semantic_review":false,"source":"documents/tfpt_research_contracts/sections/015-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row CHIRAL4D.NOMIRROR.01: Open, research contract), not a claim. Step (4) of the firewall route ordering: chirality and mirror decoupling must be proven in the same 4D model that QFT4D.OS.RECON.01 constructs — the seam's [formula in source] and Chern/inflow structure are a boundary- anomaly signal, not yet 4D matter.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — CHIRAL4D.NOMIRROR.01 (the chiral 4D lattice matter theorem)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":27204,"byte_start":23254,"id":"section:f989f7674214352c43f6","kind":"section","labels":[],"line_end":366,"line_start":304,"occurrence":1,"owner_documents":["document:tfpt_research_contracts"],"relation_ids":["relation:2819e19ae451a234e6db","relation:3edfc98c36c18dcfdf8e","relation:47d8e60bbcb4e884e962","relation:840d9ff2956197e8621a","relation:b5b3ea214967e147fa13","relation:d91641dad0207604d6a3","relation:e7e99e5968ad099c0110"],"semantic_review":false,"source":"documents/tfpt_research_contracts/sections/015-source.tex","status_markers_as_written":["[N]","\\mC","\\mO"],"summary_excerpt":"Typing. A candidate \\ (ledger row CHIRAL4D.MIRROR.DET16.01), registered 2026-08-29 from review wave 5. ( v1002_ spin10_ mirror_ projector.py.) Content. Exact finite-cluster gapping on the full chiral [formula in source] Fock space via the number-violating determinant vertex, as executed above. Open. Dynamical gauge fields, domain-wall geometry, and a [formula in source] D volume theorem — this is not a [formula in so","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — CHIRAL4D.MIRROR.DET16.01 (DET16 rank-one projector, finite cluster)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":3764,"byte_start":0,"id":"section:8f5691e12b337bb463ce","kind":"section","labels":[],"line_end":50,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_research_contracts"],"relation_ids":["relation:1c7f8001971e24993510","relation:2ef105322fa869a276ad","relation:3410c22608b7154d637a","relation:3cd52f2a8701394cd830","relation:3fdf2452ce2184189839","relation:41ee0d00f93ab4d7b241","relation:5ef3a903c7a4c59ef36c","relation:6579714b7ebd26296ca8","relation:678964074245adb8cbda","relation:69dddb5184c17fa1c858","relation:6d0e0ebd29f87381c82a","relation:78198545e1bafdca67a9","relation:8b93d33c2f2ed5100683","relation:8b9dd372dce3bfc160a3","relation:983002a2d47b1c52e520","relation:a501acf9587fcaeede7d","relation:bb3fd9224de03a31a6c2","relation:c32a351faf7b6593c77b","relation:c937b658a605d75d031b","relation:d2ca6deb64c50c5882ee","relation:deaa7d75c5ce966e4bdf","relation:ded35ce2f9d4cf985fe4","relation:e1dac1f72a66873c967e","relation:e558df963496473dce2a","relation:e9472f39520ea8249366","relation:f4f9b1ecbed57c8d6067","relation:ff89bff87f80a75c4135"],"semantic_review":false,"source":"documents/tfpt_research_contracts/sections/016-source.tex","status_markers_as_written":["\\mC"],"summary_excerpt":"Typing. A standing discipline rule, in force immediately (ledger row GRAV.NONCIRCULAR.01), with an audit census at registration. Bisognano–Wichmann (BW) is a theorem within an already-local, Poincar\\'e-covariant QFT with a suitable vacuum: the modular flow of a wedge algebra acts as the boost. It is not a device that generates Lorentz spacetime from an arbitrary modular flow — there exist Poincar\\'e-covariant nets vi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Firewall Contract — GRAV.NONCIRCULAR.01 (the Bisognano–Wichmann direction discipline)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6758,"byte_start":3764,"id":"section:23d0347707f6a415af40","kind":"section","labels":[],"line_end":96,"line_start":51,"occurrence":1,"owner_documents":["document:tfpt_research_contracts"],"relation_ids":["relation:353017acdf654afc4e05","relation:85238dbc675db219a6ec","relation:a826bf7a8f42c4f50390"],"semantic_review":false,"source":"documents/tfpt_research_contracts/sections/016-source.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"Typing. A research contract (ledger row OBS.TRANSDUCTION.01); the principle is machine-checked on the minimal model at exploration level, the per-bundle transduction proofs are . It elevates the S15 typing rule to a named principle: [formula in source] Without the middle arrow, neither a non-observation falsifies nor an observation confirms. The minimal model is machine-checked in experiments/ theory-contracts/ fo01_","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — OBS.TRANSDUCTION.01 (the transduction principle: eigenvalue, projection, coupling)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":10336,"byte_start":6758,"id":"section:a45f6a79690639df5aa5","kind":"section","labels":[],"line_end":144,"line_start":97,"occurrence":1,"owner_documents":["document:tfpt_research_contracts"],"relation_ids":["relation:0d1714606d72d0088bf7","relation:3f26a7c67dc09974a78c","relation:682374c65e7c3b7f56cc","relation:6bd16683cc03de0a7ba5","relation:8fa1cf7f5282e0cb3452","relation:b1176c2526d46eca2d35","relation:bb2229beb8cbe746d434","relation:d7387e7304a42149d808","relation:dff50b353e9c4f943b33","relation:f6c3b8fd1bec0811bfbb","relation:fac3e4274c0cdd97d7fe"],"semantic_review":false,"source":"documents/tfpt_research_contracts/sections/016-source.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row PRED.JOINTLIKELIHOOD.01: Open, statistics-construction contract), not a claim. The [formula in source] individually matched values all descend from the same few atoms ( [formula in source] , [formula in source] , [formula in source] , [formula in source] ) and are therefore statistically correlated: counting hits overstates independent evidence. The evidence is to be reorgani","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — PRED.JOINTLIKELIHOOD.01 (from hit-counting to overdetermined relations)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":17947,"byte_start":10336,"id":"section:c8d53f7c2e20223e312d","kind":"section","labels":[],"line_end":247,"line_start":145,"occurrence":1,"owner_documents":["document:tfpt_research_contracts"],"relation_ids":["relation:229f2cff682c8830b368","relation:237aa8e9de3a1a8e281f","relation:330537aa774654cfd929","relation:3ed3aa4735f77fd3d75e","relation:4b41db40493aebdacbf3","relation:56bf8a831348fd324314","relation:6a890f7969cc01f4968f","relation:6b5ec92c7ca9ee4a6b57","relation:83c909363c1284c1c159","relation:ac16ea25cba261c88a20","relation:ad3fc0de278645ead18b","relation:bd90362246e2fae3c487","relation:bddcaebdcae7d776542c","relation:c5d281c9c3712e5e6e06","relation:c82a0df92ce1626d6279","relation:cfc91b42c551a306144e","relation:d570864b957cc2f6533f","relation:d5fa0b94b09622acd7d8","relation:d697625b2f25b38910be","relation:d6a8c3627e6cbb846b22","relation:e34b48923fe5f0f18fa9","relation:f1ccd6b58e6854f5f7c9","relation:f68358c086baf2e1459b","relation:febf3a5ac413eddc4f3f"],"semantic_review":false,"source":"documents/tfpt_research_contracts/sections/016-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Typing. A programme section (registered 2026-08-27 from the external bird's-eye review), not a claim: it organizes the existing 4D contracts and the four new ones below into one route and moves no marker. The organizing observation: TFPT is probably not missing twenty independent formulas; it is missing one mathematical growth principle that unfolds the discrete structure into a local, unitary, reflection-positive 4D","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Programme — the TFPT4D master route (one 4D transfer object instead of twenty formulas)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":20680,"byte_start":17947,"id":"section:0081d7d2be956c5e25a3","kind":"section","labels":[],"line_end":282,"line_start":248,"occurrence":1,"owner_documents":["document:tfpt_research_contracts"],"relation_ids":["relation:355234910dcf43c3ff30","relation:fb72c9cd141c39b1d449"],"semantic_review":false,"source":"documents/tfpt_research_contracts/sections/016-source.tex","status_markers_as_written":["\\mC","\\mO"],"summary_excerpt":"Typing. A conditional identity \\ (ledger row DIMENSION.SELECTOR.4D.01), machine-checked in v975_dimension_selector_4d.py ( [formula in source] , sympy-exact). The [formula in source] structure of the compiler must not be read as a proof of four spacetime dimensions ( DIMENSION.UPLIFT.FIREWALL.01); what is checkable is a selector theorem under a named axiom set. Statement. Under A1 [formula in source] (propagating loc","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verified Selector — DIMENSION.SELECTOR.4D.01 (why [formula in source] , conditionally)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":12058,"byte_start":0,"id":"section:aeb16d254373e2e88a13","kind":"section","labels":[],"line_end":152,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_research_contracts"],"relation_ids":["relation:0198e01b3146de8d1810","relation:0d05c7f54ae84c831070","relation:0db0210755be9523cb3e","relation:12d66567d6e3f5a24791","relation:248eadf14348229fa57d","relation:2fbf0e2840f347926597","relation:3bdc835aeb7bdb08140c","relation:3e786359f109ed5a0850","relation:432779dcf9774206c3da","relation:479c91b90f96e1892244","relation:49b44a7af559ebfcce90","relation:4d0b6c38771e7ec8a604","relation:501711beb392dcc79451","relation:52a7847949fb436ac478","relation:548d03a8f754392f344e","relation:55c39e73cf2da1d94844","relation:5906657309527008cef9","relation:596baf38a15efb067b91","relation:6abbf3ae0ceb7e3fac5d","relation:7bd773ed9ca20b993e6b","relation:7e706707404475a88b24","relation:8e7b5a46c8a172ffd010","relation:952dff0bad5e1b569dc4","relation:998bdefe47c58676d5b7","relation:a1b9744d24636909bfc5","relation:a5f5ba247e29aa8eba1a","relation:a63d379d8435fee6c258","relation:a7cb00dc8738c25d0cbb","relation:b316f5d02114e7215892","relation:bdb4117573a506b23e8b","relation:c203fea65ed2f3c48704","relation:c227eaa75300e7ec00ab","relation:c9bbb84a9e2cd33f3e27","relation:ca77ea731c1e603a0dda","relation:cc89e9b98f65a6b55498","relation:e064660d4f068f1e0c0c","relation:e4b1e863cf3ed8ad9fbb","relation:f3b771403fd696eb4741"],"semantic_review":false,"source":"documents/tfpt_research_contracts/sections/017-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row SEAM.SIMPLECURRENT.GENERATOR.01), not a claim. Context. The seam coverage carve ( v973_seam_route_narrowing.py) shows the [formula in source] fermion-bilinear half of the seam target is covered by the cited scaling-limit theorem; the named residual is N1 (the [formula in source] /GSO extension [formula in source] as a net statement — the 128 spinor currents are not bilinears)","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — SEAM.SIMPLECURRENT.GENERATOR.01 (one generator instead of 128 currents)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":18255,"byte_start":12058,"id":"section:c95b2cf8842af3a6603a","kind":"section","labels":[],"line_end":238,"line_start":153,"occurrence":1,"owner_documents":["document:tfpt_research_contracts"],"relation_ids":["relation:1392d8126dae6bf7dd16","relation:413b5b37f7d5573858c6","relation:63068763c3bef9a4ac1a","relation:7aaef407cfa8fbc34420","relation:8f9ead51d1e79beb427f","relation:8ff29d96c0b723220583","relation:b10684e1a656d00b459d","relation:c4e8d0b99c9508c7125c","relation:da233d25da4712e14535","relation:e29bb0c6958b6c54646e","relation:fa1e6f3706138a652609"],"semantic_review":false,"source":"documents/tfpt_research_contracts/sections/017-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row TFPT4D.LATTICE.ACTION.01); route step (2) of the DIMENSION.UPLIFT.FIREWALL.01 ordering made concrete — the single object on which nearly all open 4D questions become simultaneously testable. Demand. Exhibit one fully explicit finite family of 4D Euclidean lattice theories [formula in source] where [formula in source] are the fundamental holonomies (TFPT fixes representation c","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — TFPT4D.LATTICE.ACTION.01 (the explicit finite 4D lattice action and its seven finite gates)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":21766,"byte_start":18255,"id":"section:d4448dbe559362fa014a","kind":"section","labels":[],"line_end":285,"line_start":239,"occurrence":1,"owner_documents":["document:tfpt_research_contracts"],"relation_ids":["relation:0f40bb70ae42d09c385e","relation:48f32bcf423719344cb9","relation:58f5f074b2e9ecdc66d2","relation:685969400a86701dded0","relation:8c290c4c8d3df0079294","relation:aa98866b2dec048bd787","relation:ecc9b6b4a112495ff67c","relation:fafb9208373c2eaa1752"],"semantic_review":false,"source":"documents/tfpt_research_contracts/sections/017-source.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"Typing. A research hypothesis contract \\ (ledger row SEAM.DETLINE.UNIFICATION.01) — a precise conjecture, not a result. Observation. Three separately open structures may be projections of one geometric object: (1) the seam extension is described by a Q-system/simple current ( SEAM.SIMPLECURRENT.GENERATOR.01); (2) the chiral fermion measure lives on a determinant line ( CHIRAL4D.NOMIRROR.01 demand C1); (3) anomalies a","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — SEAM.DETLINE.UNIFICATION.01 (the determinant-line unification hypothesis)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":24502,"byte_start":21766,"id":"section:7e48439cd9f5f65a12df","kind":"section","labels":[],"line_end":319,"line_start":286,"occurrence":1,"owner_documents":["document:tfpt_research_contracts"],"relation_ids":["relation:66f82bcf3fb349b89ae7","relation:7b404729939004170f8a","relation:87c7dbf8e80748881da7","relation:924a940cdd7f54b2558e","relation:a497d6bbc01f5f56a139","relation:a93063639ecfd6fbad8c","relation:bb3b084fb75660c7e6bf","relation:bbcac00ec8289cef64e3","relation:bc689fa9160d28e9c3da","relation:d4000830fbf6393189aa","relation:dca5adae5c9946f33fa2"],"semantic_review":false,"source":"documents/tfpt_research_contracts/sections/017-source.tex","status_markers_as_written":["\\mC","\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row FTRANSFER.GENERATING.01); the constructive successor named by the FR.TRANSFER.01 typing guard. The four continuous-transfer interfaces ( [formula in source] : source masses [formula in source] pole, v183; [formula in source] : CP source [formula in source] , v169/ v184; [formula in source] : [formula in source] , v185; [formula in source] : [formula in source] , v164) are cur","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — FTRANSFER.GENERATING.01 (four transfer bridges from one generating functional)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":29037,"byte_start":24502,"id":"section:ed0b0591b41cd937120a","kind":"section","labels":[],"line_end":378,"line_start":320,"occurrence":1,"owner_documents":["document:tfpt_research_contracts"],"relation_ids":["relation:0524f9e7422658770cae","relation:182c2f82322461581bed","relation:4fdcfd23b9948885a612","relation:62105a2430a35e4449d2","relation:938c1b7e49d455aba14d","relation:96aa6ee851a041a5cba4","relation:9e2fdb97366b373806f7","relation:fb12931624f76f52c2df"],"semantic_review":false,"source":"documents/tfpt_research_contracts/sections/017-source.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row GAUGE.DETLINE.FIXPOINT.01), registered 2026-08-28 from review wave 3. Demand. All three gauge couplings ( [formula in source] / equivalently [formula in source] , [formula in source] , [formula in source] ) arise as stationary points of one nonabelian zeta-det / inflow functional on the determinant line — the nonabelian upgrade of the [formula in source] face ALPHA.QUILLEN.EX","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — GAUGE.DETLINE.FIXPOINT.01 (all three gauge couplings from one zeta-det functional)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":4792,"byte_start":0,"id":"section:65138c298db225aabbae","kind":"section","labels":[],"line_end":68,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_research_contracts"],"relation_ids":["relation:0de0e02581d3d824fa3a","relation:1137a97feef0aad7d2b7","relation:13f66a480d4455e39c4c","relation:26cd2af4adb9d5ad2426","relation:41f8378d4f9f4015680f","relation:5702e4f7157736f81995","relation:6733311655f95a89c3c8","relation:a2e9acaaab19b8f14b10","relation:cb73c12d40e0fa06f2fe","relation:d2ac1f98eadc4ca350ac","relation:d48e985d2b9c236d3fc2","relation:d717c6ce831dc7881176","relation:e2bc8131a8e026ea2dea"],"semantic_review":false,"source":"documents/tfpt_research_contracts/sections/018-source.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row GRAV.SPIN2.EMERGENCE.01), registered 2026-08-28 from review wave 3. Demand. From the same spectral determinant that carries the gauge fixpoints, a massless transversal spin-2 pole with two helicities, universal [formula in source] coupling, diffeomorphism Ward identities, and positive Hessian / reflection-positive transfer. Relation. The entanglement-equilibrium Einstein equa","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — GRAV.SPIN2.EMERGENCE.01 (massless transversal spin-2 from the same spectral determinant)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":9775,"byte_start":4792,"id":"section:0510f986f3f8ee9a5656","kind":"section","labels":[],"line_end":137,"line_start":69,"occurrence":1,"owner_documents":["document:tfpt_research_contracts"],"relation_ids":["relation:0cb34d3aa0288a0f39b4","relation:25f56d26298969d11200","relation:39deaeb3ca2c2a16f504","relation:6f7698b7f92504188fe5","relation:88551eb3e0f5be7eaabb","relation:88b49347d886b6fb2317","relation:8d4e8b2c1f5c6df80d12","relation:a3ff258396c92b4f5ca1","relation:e9a2bda4cafeabc20a30"],"semantic_review":false,"source":"documents/tfpt_research_contracts/sections/018-source.tex","status_markers_as_written":["\\mC","\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row FTRANSFER.SK.RHO0.01), registered 2026-08-28 from review wave 3; mechanism executed 2026-08-29. Demand. Cosmological transfers ( [formula in source] , [formula in source] , and any nonequilibrium 4D readout) need the pair [formula in source] , not [formula in source] alone — the Euclidean-cap / KMS initial state. Typed candidate. The [formula in source] saddle [formula in sou","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — FTRANSFER.SK.RHO0.01 (Schwinger–Keldysh completion: cosmological transfers need [formula in source] )","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":13144,"byte_start":9775,"id":"section:eed3aaec663e71b02dd1","kind":"section","labels":[],"line_end":180,"line_start":138,"occurrence":1,"owner_documents":["document:tfpt_research_contracts"],"relation_ids":["relation:03dff65d57c298b75d85","relation:1fa1848f48f145565a56","relation:506c17d9c4aa02b9138e","relation:7b89d058f6bb26c56f3c","relation:7f66f5a946a256ba82ce","relation:80733819cf24d05e7b0e","relation:9700cdbff2626b5e1d5d","relation:d68416dfdd126b5d5b40"],"semantic_review":false,"source":"documents/tfpt_research_contracts/sections/018-source.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row SEAM.MMST.TYPEIII.CHARGED.01), registered 2026-08-29 from review wave 5. Demand. One scaling-limit theorem [formula in source] strongly on the finite-energy core [formula in source] crossed-product continuity, from which [formula in source] , [formula in source] , type III [formula in source] , unique rotational KMS, unique conditional expectation, deck equidistribution and m","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — SEAM.MMST.TYPEIII.CHARGED.01 (one scaling-limit theorem)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":21930,"byte_start":13144,"id":"section:6b698096745880841f4c","kind":"subsection","labels":[],"line_end":347,"line_start":181,"occurrence":1,"owner_documents":["document:tfpt_research_contracts"],"relation_ids":["relation:139c3b4cd9bfcb8c0db1","relation:1a8cc1abccd29eaf6883","relation:309ec39303637111f81b","relation:483f310434c72ff489c5","relation:529dec2c5a51b8693545","relation:53e38443d74f2d471a0e","relation:a146e2980b3b995d1d93","relation:aa48623097c140c06592","relation:bb761c14dee6fcf63e84","relation:be9fa4783ac5a1bede8f","relation:c2c38388cf9a6f334899","relation:d75074e1dd86db17056b","relation:f8411ebc399c23b2425b"],"semantic_review":false,"source":"documents/tfpt_research_contracts/sections/018-source.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"The residual TEL-B-EXTERNAL is restated below. The earlier scalar dyadic increment [formula in source] with [formula in source] sufficient for [formula in source] is superseded — [formula in source] was measured [formula in source] (r645) but is no longer the route. Numerically closed ( [formula in source] ; conditional analytic [formula in source] with [formula in source] ); round 3 closed C1, C2a and the interval-T","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TEL-B reduction (2026-09-04)","topic_suggestions":[]},{"byte_end":8632,"byte_start":0,"id":"section:ae01aeb2bb0e5a5a8b6f","kind":"section","labels":[],"line_end":136,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_research_contracts"],"relation_ids":["relation:0260b2958a3c97533017","relation:0eca38ad772b0257b8fc","relation:121bbb8eb52e298bece3","relation:1a4eaa09a83e72a96dde","relation:22b5bd6dd5234b263eb7","relation:3b5258afafc1da480218","relation:3e848237c2c91c52cd11","relation:41eecdd00c596f107826","relation:45b8a6d9ec9e37a3ec6a","relation:4923eb61265e55381b6c","relation:4a30604c365be90918a3","relation:4b3547303c32e676c4a6","relation:4bd89adbb30feeda3f91","relation:4ed5430daea5e207af54","relation:536265812e9b0802639c","relation:5dbd06af920dcb44dfa0","relation:5f6df1fade22139ca9e3","relation:68810003a50dedf58084","relation:71c01ec7e780cc4aafdb","relation:849cee651e9bf1e8883a","relation:9acc8e0f8936be1d2445","relation:9ad8da42b5fcb4da0b62","relation:9cedb2bced07be9d3411","relation:9fc75596005b4ab27f21","relation:a319d4c104597a1ec511","relation:a87ea09802f5a8421ac8","relation:ae783404d08c45a504d5","relation:af7a36b85db239510344","relation:b62180270045e5f3b1ab","relation:b992db5cdfecb154519c","relation:c1885daedd5a490e6f5f","relation:c87fbf1aaaf4c3647f97","relation:c881ef0f28230fa21dd5","relation:f15be8b4391f28bc0e6d","relation:f4408b179213c14e1cf1","relation:f65691c49afa69356f16","relation:f745f0ba0476a8ab109c","relation:f792a8184afc6cd92cf6","relation:fb566f60cede232f2296","relation:fca65ee322847237e2d7"],"semantic_review":false,"source":"documents/tfpt_research_contracts/sections/019-source.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row TFPT.TOE.COMPLETE.01), registered 2026-08-29 from review wave 4. This row names the AND of eight gates; it does not close any of them and it does not upgrade a marker. Dual rest: the compiler residual [formula in source] sits beside [formula in source] ; this contract is the named AND, not a closure of either.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — TFPT.TOE.COMPLETE.01 (the named AND of eight completeness gates)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":9907,"byte_start":8632,"id":"section:a90932e0959fcdb17e02","kind":"section","labels":[],"line_end":154,"line_start":137,"occurrence":1,"owner_documents":["document:tfpt_research_contracts"],"relation_ids":["relation:06cdb3ad2b6e46a0b880","relation:08ca66393f0cd60dc43d","relation:2c6eaadd8f6d1546908e","relation:3052f2726644502d40e7","relation:930280979af7f9310da5","relation:aa0276f1ebaf0f082816","relation:b2642885e41fd51dfb36","relation:b750448177a454085ddb","relation:c4782423a2357c045fc2"],"semantic_review":false,"source":"documents/tfpt_research_contracts/sections/019-source.tex","status_markers_as_written":["\\mC","\\mO"],"summary_excerpt":"Typing. A candidate \\ (ledger row FLAV.NUSCALE.06); mechanism [formula in source] the [formula in source] -to-flavor operator . No seesaw closure; FLAV.NUSCALE.05 unmoved. ( v1001_ nu_ pentagon_ chain.py.)","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — FLAV.NUSCALE.06 (pentagon-class misalignment candidate)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":12983,"byte_start":9907,"id":"section:d9cc974e2c40e49f2071","kind":"section","labels":[],"line_end":200,"line_start":155,"occurrence":1,"owner_documents":["document:tfpt_research_contracts"],"relation_ids":["relation:0370e5d54445ef6d735f","relation:0d55a3c9afa79304753b","relation:12374b51566e8fc166f7","relation:9f32b37927e9bcdc9d5e","relation:e5a67582e2d13a0e335f","relation:eb6f9e9eb559257e936a"],"semantic_review":false,"source":"documents/tfpt_research_contracts/sections/019-source.tex","status_markers_as_written":["\\mE","\\mO","\\mX"],"summary_excerpt":"Typing. A research contract \\ (ledger row FLAV.NU.TEXTURE.MECHANISM.01), registered 2026-08-29 from review wave 5. ( v1003_ nu_ structural_ nulls.py.) Executed content. Charged-sector data [formula in source] , [formula in source] (coset min-norms all [formula in source] ) . Schur-texture NULL : all [formula in source] preregistered [formula in source] combinations fail; D4 reflection forces [formula in source] ; hie","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — FLAV.NU.TEXTURE.MECHANISM.01 (both structural nulls as binding constraints)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":18671,"byte_start":12983,"id":"section:83df5fee438149d3054f","kind":"section","labels":[],"line_end":279,"line_start":201,"occurrence":1,"owner_documents":["document:tfpt_research_contracts"],"relation_ids":["relation:216d2e4ed8defa177ea1","relation:228f38ac4d5839fef21a","relation:32afb6ba30061d2a0385","relation:37bd444540d728fa2f15","relation:3ca6a07604e44331b5a2","relation:40f0cbb5bc5acec72579","relation:4ba9806fe1f516886ec8","relation:67bf0f3b08ef849b03c5","relation:68d43cad625f316173a3","relation:6a5edebe07e7e857d4bb","relation:743a82488da166b160ea","relation:82848e73136440c4e804","relation:853bca0d445ebd1810b7","relation:8b72b8041fd9726ed424","relation:9ee8bcbb6616a8e6d1bd","relation:bd5a87528d1e3fc1f31e","relation:d47fda818c10588e2995"],"semantic_review":false,"source":"documents/tfpt_research_contracts/sections/019-source.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row SEAM.MILNOR.LOCALRING.01), registered 2026-08-30 from review wave 6. ( v1004_ milnor_ frobenius_ gray.py.) Demand. A canonical identification between the raw seam collar / [formula in source] transition bus and the reduced Milnor algebra [formula in source] preserving simultaneously the dual-number action, the Frobenius pairing, the Gray torsor, the deck action and CP. Accept","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — SEAM.MILNOR.LOCALRING.01 (canonical identification of the seam collar with the reduced Milnor algebra)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":19909,"byte_start":18671,"id":"section:39377efb0bba1d30e784","kind":"section","labels":[],"line_end":295,"line_start":280,"occurrence":1,"owner_documents":["document:tfpt_research_contracts"],"relation_ids":["relation:ab6e223643840c3c6663","relation:b38fb4d79a932158b4bb"],"semantic_review":false,"source":"documents/tfpt_research_contracts/sections/019-source.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row GRAV.WEINBERG.WITTEN.01), registered 2026-08-30 from review wave 6. Child of TOE gate T7; cross-link GRAV.SPIN2.EMERGENCE.01 (listed here, not back — that would cycle). Demand. 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TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Certifiability and recommended order","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":1742,"byte_start":0,"id":"section:0ca69d60f3542f22224a","kind":"frontmatter","labels":[],"line_end":43,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_safeguards"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_safeguards/preamble.tex","status_markers_as_written":[],"summary_excerpt":"-1.2cm TFPT — Safeguards against Coincidence and Numerology\\\\[2mm] The verification discipline: how every load-bearing claim is defended against chance, fitting and over-reading","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"-1.2cm TFPT — Safeguards against Coincidence and Numerology\\\\[2mm] The verification discipline: how every load-bearing claim is defended against chance, fitting and over-reading","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; 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It introduces no new physics; it make","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":3052,"byte_start":2202,"id":"section:cc5f9496b281c326cfda","kind":"section","labels":["fig:layers"],"line_end":43,"line_start":31,"occurrence":1,"owner_documents":["document:tfpt_safeguards"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_safeguards/sections/001-section-the-risk-and-the-shape-of-the-answer.tex","status_markers_as_written":[],"summary_excerpt":"The honest danger for TFPT is not that an individual number is wrong — the arithmetic is usually clean — but closure inflation: that an exact, discrete compiler closure is read, or worded, as a physical closure. 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The frozen registry ( v84_frozen_registry.py, REG.FREEZE.01) fixes every dimensionless prediction at [formula in source] digits, re-derived from the two axioms each run (a formula [formula in source] value lock). The null model then runs an exact census of the full declared formula grammar over the [formula in","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Layer 5 — frozen predictions, the null model, and the [formula in source] uniqueness scan","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":18381,"byte_start":17336,"id":"section:5df76a46cd1834f8c8c0","kind":"section","labels":[],"line_end":230,"line_start":216,"occurrence":1,"owner_documents":["document:tfpt_safeguards"],"relation_ids":["relation:3f9fdd009e42b429d5b4","relation:5d3ac0e5fd2a4df301f5","relation:870fe48fe635c090f40e","relation:908905fddae24c3a659f","relation:93d7f12def987f95bc79"],"semantic_review":false,"source":"documents/tfpt_safeguards/sections/001-section-the-risk-and-the-shape-of-the-answer.tex","status_markers_as_written":[],"summary_excerpt":"A single implementation can share a single bug; TFPT therefore re-derives the exact core twice more, independently. An independent Wolfram engine ( GATE.WOLFRAM.01/ GATE.WOLFRAM.02): [formula in source] base checks plus a [formula in source] extension mirror every exact algebraic / identity / lattice result in a different computer-algebra system, ending ALL WOLFRAM CHECKS PASSED. (Numerical ODE/PDE results are Python","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Layer 6 — two independent reproduction paths","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":19159,"byte_start":18381,"id":"section:5029b8017fd33afc480d","kind":"section","labels":[],"line_end":240,"line_start":231,"occurrence":1,"owner_documents":["document:tfpt_safeguards"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_safeguards/sections/001-section-the-risk-and-the-shape-of-the-answer.tex","status_markers_as_written":[],"summary_excerpt":"The adversarial audit (companion tfpt_5_redteam) does not defend; it attacks. It declares six targets — A (the seam [formula in source] identification), B (the carrier truncation [formula in source] ), C (the [formula in source] area law), D (the ratios [formula in source] reduction), E (whether one scale carries the theory), F (the perturbative 4D-QFT round) — states what survives each, and reduces every survivor to","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Layer 7 — the red team","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":20262,"byte_start":19159,"id":"section:4cda0736bf43dbd624d7","kind":"section","labels":[],"line_end":253,"line_start":241,"occurrence":1,"owner_documents":["document:tfpt_safeguards"],"relation_ids":["relation:185e85d611db6a7c6951","relation:23ef38f427b2f2e8a846","relation:69470d7868e5e9f21c45","relation:7ad1a92095bd8115c398","relation:bc23d4ae32a1eb97338f","relation:c3e3e99bc7028600019e","relation:c61cf542a31de995d9df","relation:cebc01750e1232def2f2","relation:debbfcd661a8503dcaa4"],"semantic_review":false,"source":"documents/tfpt_safeguards/sections/001-section-the-risk-and-the-shape-of-the-answer.tex","status_markers_as_written":[],"summary_excerpt":"The safeguards are only credible with explicit kill tests (companion ``How to kill TFPT''). Among the frozen ones: a fourth chiral generation (breaks [formula in source] ); a genuinely free fundamental constant that is not an [formula in source] -closure fixed point; a seam denominator [formula in source] ; [formula in source] away from the fixed-point root; a stable [formula in source] far from [formula in source] a","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"What would still falsify TFPT","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":21502,"byte_start":20262,"id":"section:d59ca752d5e1a51b75b5","kind":"section","labels":[],"line_end":274,"line_start":254,"occurrence":1,"owner_documents":["document:tfpt_safeguards"],"relation_ids":["relation:1af8a34a57e3f54a43f5","relation:2adb26b33b70f16f083e","relation:3968e60bda8c80a8025a","relation:57182fa5a364229a7a1f","relation:5954a919dc780688fa7f","relation:7146211b38019f4e2e03","relation:81a50eb831ab5b692d52","relation:825d637860c02e82d151","relation:969b5dbe93eff9330f57","relation:9806756f5c656d9ab374","relation:ac9c0ad980cdc602e960","relation:b5e820977b4c17c0f1d9","relation:bfac71dd892ce767a077","relation:c00d5e700b7d21337b0b","relation:ca81fe842a1fd6a75cf7","relation:cb7df6fb72bf10219cda","relation:d7a025af0b01ff5e89a7","relation:db3632da3aaccdb4d9aa","relation:e84630190030e3588f70","relation:f0c7ce1f5256aa7a8e14","relation:f2af6e0fba0d0420ba50","relation:f3648232272f632a1064"],"semantic_review":false,"source":"documents/tfpt_safeguards/sections/001-section-the-risk-and-the-shape-of-the-answer.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"@lYl@ Layer & What it defends against & Artefact \\\\ Status calculus & a \\ claim read as & ledger [formula in source] audit_sync.py \\\\ No free pattern [formula in source] reverse audit & cherry-picking, decorative identities & v305/ v100/ v431/ E8.REVERSE.AUDIT.01 \\\\ Over-determination map & rhetorical ``everything multiplies'' (incl.\\ our own miscount) & v427/ v428/ v432/ v436 \\\\ Firewall [formula in source] No-Unit ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Summary — the layered defense","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":568,"byte_start":0,"id":"section:3d04f5998baadb914979","kind":"frontmatter","labels":[],"line_end":14,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_universalraum_einfach_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_universalraum_einfach_2026-09-12/preamble.tex","status_markers_as_written":[],"summary_excerpt":"Der Universalraum\\ , Instrument und fehlende Spielregel Verständliche Forschungszusammenfassung 12. September 2026","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Universalraum\\ , Instrument und fehlende Spielregel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":243,"byte_start":0,"id":"section:0169478bd797ed083762","kind":"frontmatter","labels":[],"line_end":6,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_universalraum_einfach_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_universalraum_einfach_2026-09-12/sections/001-section-ein-instrument-ist-mehr-als-seine-teile.tex","status_markers_as_written":[],"summary_excerpt":"Wir haben mehrere funktionierende mathematische Verbindungen gefunden. Was fehlt, ist die ursprüngliche Regel, die daraus genau eine physikalische Welt auswählt. Die vollständige TOE ist nicht gelöst.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":803,"byte_start":243,"id":"section:36cfa8688f27f5e3964a","kind":"section","labels":[],"line_end":17,"line_start":7,"occurrence":1,"owner_documents":["document:tfpt_universalraum_einfach_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_universalraum_einfach_2026-09-12/sections/001-section-ein-instrument-ist-mehr-als-seine-teile.tex","status_markers_as_written":[],"summary_excerpt":"Stell dir ein Musikinstrument vor. Wir kennen viele seiner Teile, ihre Verbindungen und erlaubte Bewegungen. Manche lassen sich in mehreren mathematischen Sprachen exakt beschreiben. Darin liegt eine Stärke des Universalraum-Gedankens.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein Instrument ist mehr als seine Teile","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1532,"byte_start":803,"id":"section:0c3d79c3f2859c8e05a5","kind":"section","labels":[],"line_end":30,"line_start":18,"occurrence":1,"owner_documents":["document:tfpt_universalraum_einfach_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_universalraum_einfach_2026-09-12/sections/001-section-ein-instrument-ist-mehr-als-seine-teile.tex","status_markers_as_written":[],"summary_excerpt":"Vier andere ChatGPT-Aufgaben berichten präzise Fortschritte: In einer eng festgelegten Vergleichsfamilie kann ein geeigneter Quantenzustand das Bewegungsgesetz bis auf Maßstab und Energienullpunkt bestimmen. Öffnet man weitere zulässige Richtungen, können mehrere Gesetze zum selben Zustand passen. Zusätzliche thermische Antworten können diese Mehrdeutigkeit wieder verringern.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Aus Antworten lässt sich viel zurücklesen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2130,"byte_start":1532,"id":"section:03230abea23279cc7e17","kind":"section","labels":[],"line_end":41,"line_start":31,"occurrence":1,"owner_documents":["document:tfpt_universalraum_einfach_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_universalraum_einfach_2026-09-12/sections/001-section-ein-instrument-ist-mehr-als-seine-teile.tex","status_markers_as_written":[],"summary_excerpt":"Zwei Zustände können dieselben durchschnittlichen Besetzungen und dieselben Einteilchendaten haben, aber unterschiedliche gemeinsame Korrelationen und elektrische Energie. Ein Foto der durchschnittlichen Saitenlage zeigt nicht unbedingt, wie die Saiten gemeinsam schwingen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein Durchschnittsfoto verliert Beziehungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2981,"byte_start":2130,"id":"section:8f5eef615c5cdb5f6112","kind":"section","labels":[],"line_end":57,"line_start":42,"occurrence":1,"owner_documents":["document:tfpt_universalraum_einfach_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_universalraum_einfach_2026-09-12/sections/001-section-ein-instrument-ist-mehr-als-seine-teile.tex","status_markers_as_written":[],"summary_excerpt":"In unserer endlichen Kandidatenquelle sind vom Rand zunächst zehn von sechzehn mathematischen Richtungen zugänglich. Sechs bleiben verborgen. Eine einzelne von sechs vorhandenen Kopplungen könnte diesen Zugang öffnen, wenn sie einzeln ansprechbar wäre.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Verbindung existiert, der Zugriff fehlt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3518,"byte_start":2981,"id":"section:f7f27dbed3cc984cb273","kind":"section","labels":[],"line_end":67,"line_start":58,"occurrence":1,"owner_documents":["document:tfpt_universalraum_einfach_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_universalraum_einfach_2026-09-12/sections/001-section-ein-instrument-ist-mehr-als-seine-teile.tex","status_markers_as_written":[],"summary_excerpt":"Die neueste Gegenprobe zeigt: Der übertragende Ereignismechanismus besitzt mehrere stationäre Zustände. Ein Teil des Systems bleibt unberührt. Er wählt also noch keine eindeutige Weltkonfiguration aus und erzeugt aus dem leeren Vakuum keine Teilchen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein Durchgang ist noch keine Weltwahl","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4119,"byte_start":3518,"id":"section:b722da4dc2d84678755a","kind":"section","labels":[],"line_end":86,"line_start":68,"occurrence":1,"owner_documents":["document:tfpt_universalraum_einfach_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_universalraum_einfach_2026-09-12/sections/001-section-ein-instrument-ist-mehr-als-seine-teile.tex","status_markers_as_written":[],"summary_excerpt":"c Primitive Regeln\\\\ [formula in source] Herkunft noch zu beweisen\\\\ Schritte, Phasen, Zusammensetzung und Gewichte\\\\ [formula in source] \\\\ Konkreter Prozess\\\\ [formula in source] \\\\ Ausgewählter Zustand Bewegungsgesetz\\\\ [formula in source] \\\\ Zugängliche Antworten\\\\ [formula in source] weitere Beweise erforderlich\\\\ Raumzeit, Materie, Gravitation und Arithmetik Wir besitzen bedingte Brücken in der Mitte. Die erste","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das gemeinsame Bild","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":5128,"byte_start":4119,"id":"section:4d1d1c02894cf1cf8c24","kind":"section","labels":[],"line_end":105,"line_start":87,"occurrence":1,"owner_documents":["document:tfpt_universalraum_einfach_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_universalraum_einfach_2026-09-12/sections/001-section-ein-instrument-ist-mehr-als-seine-teile.tex","status_markers_as_written":[],"summary_excerpt":"Nur die ursprünglichen TFPT-Regeln hineingeben: nicht den gewünschten Hamiltonoperator, seine Zustände oder die gesuchten Kopplungen. Daraus müssen die elementaren Operationen, ihre Gewichte und die passenden Zustandsantworten folgen. Erst danach prüfen wir, welches Gesetz herauskommt, ob es eindeutig ist und ob seine Antworten zugänglich sind.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der nächste wirklich entscheidende Versuch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6146,"byte_start":5128,"id":"section:4b2f28daf2dcda896045","kind":"section","labels":[],"line_end":124,"line_start":106,"occurrence":1,"owner_documents":["document:tfpt_universalraum_einfach_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_universalraum_einfach_2026-09-12/sections/001-section-ein-instrument-ist-mehr-als-seine-teile.tex","status_markers_as_written":[],"summary_excerpt":"1. Den Baukasten überprüfen. Welche Teile sind ursprünglich, welche nur zusammengebaute Abläufe? Die Quelle muss diese Unterscheidung liefern, nicht unser Wunsch nach einem eindeutigen Ergebnis. Gleichzeitig müssen die entscheidenden Rechenzertifikate der anderen Aufgaben unabhängig reproduziert werden.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Drei konkrete nächste Versuche","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7837,"byte_start":6146,"id":"section:bf8b5e3cf08b661eba43","kind":"section","labels":[],"line_end":155,"line_start":125,"occurrence":1,"owner_documents":["document:tfpt_universalraum_einfach_2026-09-12"],"relation_ids":["relation:1ae1aeb597deb7e2a752","relation:c8c9bf289e68b471dd33"],"semantic_review":false,"source":"documents/tfpt_universalraum_einfach_2026-09-12/sections/001-section-ein-instrument-ist-mehr-als-seine-teile.tex","status_markers_as_written":[],"summary_excerpt":"Ein eindeutig bester Kompromiss statt perfekter Widerspruchsfreiheit. Die Stärke der einzelnen Anforderungen müsste aus der Quelle folgen. Ein direkt aus der Quelle gewonnenes Verbindungsmaß, das Zustand und Bewegung gemeinsam bestimmt, statt beide getrennt einzusetzen. Eine interne Referenz durch tatsächlich vorhandene Wechselwirkungen, statt einen äußeren Schalter nachträglich hinzuzufügen. Zusätzliche thermische o","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Welche kreativen Richtungen bleiben offen?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":605,"byte_start":0,"id":"section:a2cddeb907b991d3c854","kind":"frontmatter","labels":[],"line_end":15,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_universalraum_synthesis_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_universalraum_synthesis_2026-09-12/preamble.tex","status_markers_as_written":[],"summary_excerpt":"=3em TFPT and the Universalraum\\ selection, reconstruction and accessible dynamics Research consolidation 12 September 2026","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TFPT and the Universalraum\\ selection, reconstruction and accessible dynamics","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":608,"byte_start":0,"id":"section:97350e78c0c544ac5220","kind":"frontmatter","labels":[],"line_end":13,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_universalraum_synthesis_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"documents/tfpt_universalraum_synthesis_2026-09-12/sections/001-source.tex","status_markers_as_written":[],"summary_excerpt":"We consolidate finite algebraic and analytic controls, four attributed research-task reports on state-to-generator reconstruction, and new exact tests of covariant edge operations. The latter yield an original-boundary signal under an explicitly additional event channel, but their fixed algebra is not one-dimensional. 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Man erhält stattdessen [formula in source] , wobei [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3.3 Aufzeichnungen müssen die richtige Interferenz erhalten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3242,"byte_start":1300,"id":"section:cf0a4e7ba173acc0bee7","kind":"section","labels":["die-viertruxe4gerzelle-und-die-grenze-lokaler-modellluxf6sungen"],"line_end":82,"line_start":33,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/002-subsection-3-3-aufzeichnungen-m-ssen-die-richtige-interf.tex","status_markers_as_written":[],"summary_excerpt":"ist ein [formula in source] -Singulett. 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Die Vierträgerzelle und die Grenze lokaler Modelllösungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3382,"byte_start":3242,"id":"section:bd3dfef7087316cffc9c","kind":"section","labels":["die-native-bank-festgelegte-dynamik-und-gesicherte-antwort"],"line_end":85,"line_start":83,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/002-subsection-3-3-aufzeichnungen-m-ssen-die-richtige-interf.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"5. 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Am Betriebspunkt [formula in source] geben die bisherigen Zertifikate","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5.2 Grundzustand und Entnahmelinie","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6536,"byte_start":5553,"id":"section:07c5dddbfe3a0877263f","kind":"subsection","labels":["weshalb-eine-schwuxe4chere-sonde-den-stuxe4rkeren-satz-nicht-widerlegt"],"line_end":164,"line_start":144,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/002-subsection-3-3-aufzeichnungen-m-ssen-die-richtige-interf.tex","status_markers_as_written":[],"summary_excerpt":"Ein paralleler Arbeitsstand konnte den Grundzustand mit seinen eigenen gröberen Schranken bei [formula in source] nicht isolieren. 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Ein auf jedem Grad konstanter ganzzahliger Lift der betrachteten Z4-Klammern müsste","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5.6 Die Z4-Erweiterung: erlaubte Dynamik und echte neue Parameter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13139,"byte_start":13003,"id":"section:c78e4a99759fd56abcc3","kind":"section","labels":["der-neueste-stand-v1.6.7-die-richtige-kleine-rechenkette"],"line_end":313,"line_start":311,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/002-subsection-3-3-aufzeichnungen-m-ssen-die-richtige-interf.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"6. 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Bei [formula in source] Bosonen gibt es im [formula in source] -Sektor [formula in source] Löcher. Der invariante Teil liegt in","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6.1 Vier Singuletts auf der zweiten Bosonstufe","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1442,"byte_start":0,"id":"section:6a23af50e62c70be7377","kind":"subsection","labels":["lanczos-zuxe4hlt-hamiltonschritte-nicht-bosonen"],"line_end":40,"line_start":1,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/003-subsection-6-2-lanczos-z-hlt-hamiltonschritte-nicht.tex","status_markers_as_written":[],"summary_excerpt":"Die einfache Kette entsteht aus [formula in source] durch Orthogonalisierung:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6.2 Lanczos zählt Hamiltonschritte, nicht Bosonen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2107,"byte_start":1442,"id":"section:d0ecabd24dcc432365a8","kind":"subsection","labels":["ein-exakter-nachweis-fehlender-auswahl"],"line_end":55,"line_start":41,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/003-subsection-6-2-lanczos-z-hlt-hamiltonschritte-nicht.tex","status_markers_as_written":[],"summary_excerpt":"Das ergibt [formula in source] bei [formula in source] , aber [formula in source] bei [formula in source] . Beide Modelle besitzen dasselbe [formula in source] , dieselben inneren Symmetrien und denselben kommutierenden Clock. Die dimensionslose Differenz ist keine Einheitenfrage. Damit ist belegt, dass diese Grunddaten allein die physikalische Dynamik nicht eindeutig auswählen. 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Sein Tensor, Lochbild, Kommutantenstufen und Nichtschlussbefund sind deshalb bereits berücksichtigt. Seine Priorität „den Zwei-Boson-Singulettraum ausschreiben`` ist in v1.6.7 inzwischen durch die vier exp","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6.4 Nachgereichter Text: die interessante Fortsetzung liegt in Matrixmomenten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5613,"byte_start":5483,"id":"section:b70dc3cb92dc794af317","kind":"section","labels":["pruxe4paration-restantwort-und-die-herkunft-von-teilen"],"line_end":125,"line_start":123,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/003-subsection-6-2-lanczos-z-hlt-hamiltonschritte-nicht.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"7. Präparation, Restantwort und die Herkunft von Teilen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6578,"byte_start":5613,"id":"section:f2bfcdef2ae17f2d3ecf","kind":"subsection","labels":["ein-kontrollierter-weg-in-den-nativen-grundzustand"],"line_end":148,"line_start":126,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/003-subsection-6-2-lanczos-z-hlt-hamiltonschritte-nicht.tex","status_markers_as_written":[],"summary_excerpt":"im festen [formula in source] -Sektor. Der Startzustand [formula in source] ist dort bei [formula in source] eindeutig. 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Sei [formula in source] die Menge endlicher Wörter aus einem ausdrücklich festgelegten Alphabet von Operationen und ihren Adjungierten. Auf einem gemeinsamen Startzustand [formula in source] definiere","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.1 Die zentrale Vereinfachung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13105,"byte_start":9832,"id":"section:6eeb0e204a0bb4750a77","kind":"subsection","labels":["satz-rekonstruktion-aus-einem-vollstuxe4ndigen-positiven-wortkern"],"line_end":289,"line_start":229,"numbered_or_version_tokens_as_written":["B5.3"],"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/003-subsection-6-2-lanczos-z-hlt-hamiltonschritte-nicht.tex","status_markers_as_written":[],"summary_excerpt":"Voraussetzungen. Gegeben seien eine unital abgeschlossene [formula in source] -Algebra [formula in source] der zulässigen Wörter, ihre Relationen und ein normiertes positives Funktional [formula in source] mit [formula in source] . Für eine Darstellung durch beschränkte Operationen werde zusätzlich für jeden Generator [formula in source] eine Schranke","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.2 Satz: Rekonstruktion aus einem vollständigen positiven Wortkern","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14387,"byte_start":13105,"id":"section:2f1f653fd727ce417736","kind":"subsection","labels":["zustandswahl-und-dynamik-lassen-sich-nicht-durch-rekonstruktion-erschleichen"],"line_end":314,"line_start":290,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/003-subsection-6-2-lanczos-z-hlt-hamiltonschritte-nicht.tex","status_markers_as_written":[],"summary_excerpt":"Der Satz konstruiert aus vorhandenen Prozessdaten eine gemeinsame Darstellung. Er erzeugt diese Daten nicht aus E8 allein. Die Familie [formula in source] aus Abschnitt 6 zeigt ausdrücklich, dass gleiche Grammatik verschiedene positive Prozesskerne zulässt. Ebenso können verschiedene Anfangszustände auf derselben Algebra verschiedene Funktionale liefern.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.3 Zustandswahl und Dynamik lassen sich nicht durch Rekonstruktion erschleichen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15570,"byte_start":14387,"id":"section:82197e6f9d7c23cc0882","kind":"subsection","labels":["kompatibilituxe4tssatz-fuxfcr-verschiedene-arbeitsstuxe4nde"],"line_end":339,"line_start":315,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/003-subsection-6-2-lanczos-z-hlt-hamiltonschritte-nicht.tex","status_markers_as_written":[],"summary_excerpt":"Angenommen, zwei Konstruktionen verwenden dasselbe Wortalphabet und besitzen für alle zulässigen Wörter denselben Gramkern. Dann sind ihre zyklischen Ausführungen unitär äquivalent und die entsprechende Unitäre verschränkt sämtliche Generatoren. Gleichheit nur von [formula in source] oder wenigen Wahrscheinlichkeiten genügt nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.4 Kompatibilitätssatz für verschiedene Arbeitsstände","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16690,"byte_start":15570,"id":"section:df49b6497d3c4553a46a","kind":"subsection","labels":["ein-endlicher-fehlervertrag-fuxfcr-adapter"],"line_end":365,"line_start":340,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/003-subsection-6-2-lanczos-z-hlt-hamiltonschritte-nicht.tex","status_markers_as_written":[],"summary_excerpt":"Sei [formula in source] eine Isometrie, [formula in source] und","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.5 Ein endlicher Fehlervertrag für Adapter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16842,"byte_start":16690,"id":"section:6407fe9d1bb5a655e778","kind":"section","labels":["eigene-verbindung-ii-transfer-mit-mitgerechneter-ladungsreferenz"],"line_end":368,"line_start":366,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/003-subsection-6-2-lanczos-z-hlt-hamiltonschritte-nicht.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"9. 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Mit den sieben Pauli-Blockern","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9.1 Was der vorhandene Vierzustandszeuge bereits leistet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3504,"byte_start":1239,"id":"section:b0f1e958b3cad564293f","kind":"subsection","labels":["explizite-ladungserhaltende-erweiterung"],"line_end":97,"line_start":40,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/004-subsection-9-1-was-der-vorhandene-vierzustandszeuge-bere.tex","status_markers_as_written":[],"summary_excerpt":"Neue Konstruktion, bedingt. Ergänze eine zweidimensionale Referenz mit Zuständen [formula in source] und","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9.2 Explizite ladungserhaltende Erweiterung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4851,"byte_start":3504,"id":"section:e7c18a392a2a78f16882","kind":"subsection","labels":["was-damit-fundamental-geluxf6st-wird-und-was-nicht"],"line_end":123,"line_start":98,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/004-subsection-9-1-was-der-vorhandene-vierzustandszeuge-bere.tex","status_markers_as_written":[],"summary_excerpt":"Gelöst ist die konkrete mathematische Frage, ob die festgestellte Cartan-Schranke einen Transfer auch bei mitgeführtem Ladungsausgleich grundsätzlich verbietet. Das tut sie nicht: Die Erweiterung liefert einen expliziten positiven Zeugen. Sie bewahrt die betrachtete Gesamt-Cartanladung, ohne den ursprünglichen isolierten Mischer als bereits verfügbar auszugeben.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9.3 Was damit fundamental gelöst wird – und was nicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6124,"byte_start":4851,"id":"section:9ed40f3ccbbd4c34f486","kind":"subsection","labels":["die-referenz-wird-verbraucht-ein-einfacher-unmuxf6glichkeitssatz"],"line_end":147,"line_start":124,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/004-subsection-9-1-was-der-vorhandene-vierzustandszeuge-bere.tex","status_markers_as_written":[],"summary_excerpt":"Beginnt die Referenz in einer scharfen Ladung [formula in source] und erhöht sich die Systemladung in einem erfolgreichen Zweig um [formula in source] , muss die Referenz oder eine weitere Umgebung im selben Zweig ihre Ladung um [formula in source] ändern. Ein vollständiger Rücklauf zur exakt gleichen scharfen Referenzladung bei sonst unverändertem Außenraum ist wegen Gesamtladungserhaltung unmöglich.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9.4 Die Referenz wird verbraucht: ein einfacher Unmöglichkeitssatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6292,"byte_start":6124,"id":"section:7897ed5c0a5d0c0beee1","kind":"section","labels":["eigene-verbindung-iii-uxfcberlappung-dynamik-und-geometrische-kruxfcmmung"],"line_end":151,"line_start":148,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/004-subsection-9-1-was-der-vorhandene-vierzustandszeuge-bere.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"10. 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Dann","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10.1 Eine gemeinsame Quelle ist nicht automatisch Bewegung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8349,"byte_start":7389,"id":"section:243b5d62a2d3781f116e","kind":"subsection","labels":["zeitabhuxe4ngige-rahmen-brauchen-einen-verbindungsterm"],"line_end":197,"line_start":178,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/004-subsection-9-1-was-der-vorhandene-vierzustandszeuge-bere.tex","status_markers_as_written":[],"summary_excerpt":"Für einen glatten isometrischen Rahmen [formula in source] und [formula in source] ergibt die projizierte Schrödingergleichung","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10.2 Zeitabhängige Rahmen brauchen einen Verbindungsterm","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9839,"byte_start":8349,"id":"section:9a4af7227a90945e5417","kind":"subsection","labels":["feste-vollstuxe4ndige-rahmen-und-bewegte-projektoren-unterscheiden-sich"],"line_end":234,"line_start":198,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/004-subsection-9-1-was-der-vorhandene-vierzustandszeuge-bere.tex","status_markers_as_written":[],"summary_excerpt":"Sind [formula in source] bloße Basiswechsel vollständiger unitärer Rahmen, teleskopiert eine geschlossene Schleife:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10.3 Feste vollständige Rahmen und bewegte Projektoren unterscheiden sich","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11889,"byte_start":9839,"id":"section:02e17b42187cfba3ca75","kind":"subsection","labels":["ein-vollstuxe4ndig-gerechneter-kleiner-zeuge"],"line_end":285,"line_start":235,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/004-subsection-9-1-was-der-vorhandene-vierzustandszeuge-bere.tex","status_markers_as_written":[],"summary_excerpt":"Aus demselben Projektor folgt die reelle Quantenmetrik","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10.4 Ein vollständig gerechneter kleiner Zeuge","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13159,"byte_start":11889,"id":"section:05819f6b323f4dcebc38","kind":"subsection","labels":["ein-bedingter-dynamischer-parent"],"line_end":312,"line_start":286,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/004-subsection-9-1-was-der-vorhandene-vierzustandszeuge-bere.tex","status_markers_as_written":[],"summary_excerpt":"hat bei festem Parameter eine Lücke [formula in source] und einen Rang-eins-Grundraum [formula in source] . Bei kontrollierter langsamer Parameteränderung liefert er die bekannte geometrische Phase, mit separat zu kontrollierendem adiabatischem Fehler. Er zeigt konstruktiv, dass ein bewegter ausgewählter Unterraum die falsche „alles teleskopiert``-Abkürzung umgehen kann.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10.5 Ein bedingter dynamischer Parent","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13273,"byte_start":13159,"id":"section:680a0b81d0e77825bb00","kind":"section","labels":["wo-raum-und-echte-wirkung-entstehen-kuxf6nnten"],"line_end":315,"line_start":313,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/004-subsection-9-1-was-der-vorhandene-vierzustandszeuge-bere.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"11. Wo Raum und echte Wirkung entstehen könnten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14542,"byte_start":13273,"id":"section:34bc3b5a93b475fa6bef","kind":"subsection","labels":["innere-darstellung-und-multiplizituxe4t"],"line_end":346,"line_start":316,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/004-subsection-9-1-was-der-vorhandene-vierzustandszeuge-bere.tex","status_markers_as_written":[],"summary_excerpt":"Unter einer kompakten inneren Gruppe zerfällt ein endlicher Hilbertraum als","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"11.1 Innere Darstellung und Multiplizität","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15798,"byte_start":14542,"id":"section:d7e56075d1566e971fcf","kind":"subsection","labels":["zwei-verschiedene-kommutanten"],"line_end":379,"line_start":347,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/004-subsection-9-1-was-der-vorhandene-vierzustandszeuge-bere.tex","status_markers_as_written":[],"summary_excerpt":"Der Kommutant der inneren Gruppe beschreibt die mit ihr verträgliche Dynamik. Der Kommutant des verfügbaren Operationsalphabets beschreibt dagegen Unterschiede, die dieses Alphabet nicht auflösen kann. Diese Bezugsalgebren sind verschieden.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"11.2 Zwei verschiedene Kommutanten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1907,"byte_start":0,"id":"section:4af2b54f60ef4f74fa6d","kind":"subsection","labels":["wirkung-durch-einen-kontrollierten-eingriff"],"line_end":40,"line_start":1,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Ein nichtverschwindender Korrelator kann aus anfänglicher Überlappung stammen. Ein aussagekräftiger Test vergleicht deshalb dieselbe Quelle und denselben Eingang einmal mit und einmal ohne einen zugelassenen Eingriff in A. Für gerade Observablen und [formula in source] gilt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"11.3 Wirkung durch einen kontrollierten Eingriff","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2905,"byte_start":1907,"id":"section:7451c8f285bbed2895b8","kind":"subsection","labels":["weshalb-die-raumdimension-offen-bleibt"],"line_end":58,"line_start":41,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Aus demselben inneren Baustein kann man zunächst viele räumliche Wiederholungen definieren. Ein gewählter Graph ist eine zusätzliche Kompositionsregel. Weder seine Existenz noch die innere Zahl fünf wählt automatisch ein dreidimensionales Kontinuum aus. Die Quellen enthalten ausdrücklich alternative Verklebungen mit verschiedenen Dimensionen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"11.4 Weshalb die Raumdimension offen bleibt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3054,"byte_start":2905,"id":"section:5bd588ead746d8827ceb","kind":"section","labels":["relativistisches-feldwuxf6rterbuch-chiralituxe4t-und-gravitation"],"line_end":61,"line_start":59,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"12. Relativistisches Feldwörterbuch, Chiralität und Gravitation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3744,"byte_start":3054,"id":"section:b0abae1484d575850b67","kind":"subsection","labels":["derselbe-matrixraum-truxe4gt-eine-lorentz-kegelansicht"],"line_end":80,"line_start":62,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] erhält [formula in source] diese Determinante und den positiven Kegel. Das ist eine exakte Lorentzstruktur auf diesem Darstellungsraum. Die Verbindung zum kleinen Matrixkern ist deshalb mathematisch interessant. Sie identifiziert aber noch keine dynamischen Raumzeitereignisse, keine gemeinsamen Lichtgeschwindigkeiten verschiedener Sektoren und keine gravitative Wirkung. [S046, Kap. 11, 34–35]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"12.1 Derselbe Matrixraum trägt eine Lorentz-Kegelansicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5210,"byte_start":3744,"id":"section:9e01da0d157818e58095","kind":"subsection","labels":["der-grassmann-typentest-bleibt-unverzichtbar"],"line_end":110,"line_start":81,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Sei [formula in source] die antisymmetrische Fortsetzung einer W-Zeile und seien [formula in source] gleichhändige Weylfelder. Ein lokaler skalarer Ansatz mit Gesamtkoeffizient [formula in source] ist symmetrisch: antisymmetrisch mal antisymmetrisch. Ein symmetrischer Koeffizient kontrahiert mit zwei Grassmannfeldern zu null.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"12.2 Der Grassmann-Typentest bleibt unverzichtbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6453,"byte_start":5210,"id":"section:94eb324d064a27eb3c26","kind":"subsection","labels":["algebraisch-nicht-null-bedeutet-noch-nicht-stabile-feldtheorie"],"line_end":136,"line_start":111,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Der in S001 untersuchte freie geladene Zweitableitungsansatz für den [formula in source] -Tensor besitzt eine nach unten unbeschränkte Energie. Dieser konkrete Kandidat scheidet ohne zusätzliche Constraints aus. Daraus folgt kein Verbot sämtlicher Tensorfeldtheorien.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"12.3 Algebraisch nicht null bedeutet noch nicht stabile Feldtheorie","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7300,"byte_start":6453,"id":"section:a868ac09ccac1a065c2a","kind":"subsection","labels":["familien-und-spiegelmoden"],"line_end":153,"line_start":137,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Der innere Träger kann Familienzahlen und Anomaliesummen motivieren. Drei physikalische Familien benötigen jedoch einen chiralen Operator samt Darstellung, Maß und kontrollierter Spiegelentkopplung. Eine Faltung oder Umbenennung von Weylknoten entfernt keinen zusätzlichen dynamischen Freiheitsgrad. Im dokumentierten Walk treten mehrere Weylknoten auf; ihre Chiralitäten und Quasienergien müssen im tatsächlichen rezipr","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"12.4 Familien und Spiegelmoden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8344,"byte_start":7300,"id":"section:a0e3cf8d705d412e4bad","kind":"subsection","labels":["gravitation"],"line_end":174,"line_start":154,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Eine Metrik auf Zustandsparametern, eine Lorentz-Kegelform oder ein transversaler spurfreier Projektor ist noch kein dynamisches Graviton. Erforderlich sind ein positiver masseloser Spin-2-Sektor, zwei physische Helizitäten und eine konsistente universelle Kopplung im selben dynamischen Modell.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"12.5 Gravitation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8900,"byte_start":8344,"id":"section:d2207b85da372ad65e76","kind":"section","labels":["physikalische-zahlen-vorhersage-kalibrierung-und-gemeinsamer-test"],"line_end":185,"line_start":175,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Die frühen TFPT-Arbeiten enthalten zahlreiche Beziehungen für Kopplungen, Massenskalen und kosmologische Größen. Diese gehören in ein vollständiges Forschungspaper, müssen aber nach ihrem Transfervertrag gelesen werden. Ein präziser dimensionsloser Formelwert ist erst nach Zuordnung zur physikalischen Messgröße und Kontrolle der theoretischen Unsicherheit eine physikalische Vorhersage.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"13. Physikalische Zahlen: Vorhersage, Kalibrierung und gemeinsamer Test","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9670,"byte_start":8900,"id":"section:30a7b516412bef399651","kind":"subsection","labels":["feinstrukturkonstante"],"line_end":205,"line_start":186,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Die am Recherchetag abgerufene NIST-Tabelle enthält weiterhin die ausdrücklich bezeichnete CODATA-2022-Anpassung","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"13.1 Feinstrukturkonstante","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10693,"byte_start":9670,"id":"section:176e2a3c2a3d0ffec56f","kind":"subsection","labels":["kosmologie-und-gemeinsame-parameter"],"line_end":228,"line_start":206,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Für die im Hauptdokument untersuchte einfache Inflationsbranche gilt nach Eliminieren der E-Faltungszahl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"13.2 Kosmologie und gemeinsame Parameter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11531,"byte_start":10693,"id":"section:98b99b132d01e5146be9","kind":"subsection","labels":["was-ein-uxfcberzeugender-empirischer-anschluss-enthalten-muss"],"line_end":244,"line_start":229,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Ein prüfbarer Ausgabevertrag fixiert vor dem Vergleich: denselben Hamiltonoperator beziehungsweise dieselbe effektive Wirkung, dieselbe Zustandsregel, eine endliche Menge unabhängiger Parameter, die Abbildung auf Messgrößen, systematische Näherungsfehler und die verwendete Datenversion. Werden Eingaben kalibriert, müssen die verbleibenden unabhängigen Vorhersagen ausgewiesen werden.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"13.3 Was ein überzeugender empirischer Anschluss enthalten muss","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11626,"byte_start":11531,"id":"section:bfe6c9bb03a5c642d631","kind":"section","labels":["arithmetik-rh-und-rechenfuxe4higkeit"],"line_end":247,"line_start":245,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"14. Arithmetik, RH und Rechenfähigkeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12640,"byte_start":11626,"id":"section:2658414c0e1c58e1f034","kind":"subsection","labels":["der-gemeinsame-begriff-spektrum-genuxfcgt-nicht"],"line_end":266,"line_start":248,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Ein Hamiltonspektrum, ein endlicher Markovoperator und eine arithmetische explizite Formel sind verschiedene mathematische Objekte. Eine Brücke zur Riemannschen Vermutung benötigt eine exakte, phasen- und normierungstreue Identität mit dem vollständigen erforderlichen Weil-Ausdruck oder ein anderes vollständig bewiesenes RH-Kriterium. Positivität einiger Matrizen, einzelne Spektrallinien und die lokale Focklücke reic","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"14.1 Der gemeinsame Begriff „Spektrum`` genügt nicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":13551,"byte_start":12640,"id":"section:07e5e4944b53db97a406","kind":"subsection","labels":["grenze-der-aktuellen-quellenpruxfcfung"],"line_end":284,"line_start":267,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Der aktuelle RH-Quellencheck stoppte mit SOURCE_UNAVAILABLE für den referenzierten Forschungsordner 2026-09-04/scha-2/research. Der bestehende Index enthält hilfreiche routebezogene Hinweise, aber seine vollständige Aktualität konnte dadurch nicht bestätigt werden. Die Unterbrechung ist kein mathematischer Gegenbeweis; sie verhindert eine Behauptung, sämtliche arithmetischen Arbeitsstände seien frisch vollständig gep","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"14.2 Grenze der aktuellen Quellenprüfung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":14439,"byte_start":13551,"id":"section:351dacbabdfb9b6562a5","kind":"subsection","labels":["faktorisierung-und-universalituxe4t"],"line_end":301,"line_start":285,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Ein kohärenter Gattervertrag kann algorithmische Universalität besitzen. Das ist nicht identisch mit der physischen Verfügbarkeit seiner Register, Kontrolloperationen, Resets und Messungen. Ein klassischer Simulator eines Quantenschaltkreises hat auch dann keine automatisch polynomiellen klassischen Kosten, wenn der ideale Quantenschaltkreis eine effiziente Faktorisierung beschreibt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"14.3 Faktorisierung und Universalität","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14591,"byte_start":14439,"id":"section:0597eefde7d407e9a53c","kind":"section","labels":["die-fundamentale-gesamtluxf6sung-als-pruxe4ziser-forschungsauftrag"],"line_end":304,"line_start":302,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"15. Die fundamentale Gesamtlösung als präziser Forschungsauftrag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15812,"byte_start":14591,"id":"section:de97b14e0d8b6695ea6c","kind":"subsection","labels":["was-sich-auf-einen-gemeinsamen-gegenstand-reduzieren-luxe4sst"],"line_end":331,"line_start":305,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Die eigenen Herleitungen legen folgende Organisation nahe:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"15.1 Was sich auf einen gemeinsamen Gegenstand reduzieren lässt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16861,"byte_start":15812,"id":"section:9c6b0a82019d5d0027a9","kind":"subsection","labels":["warum-maximale-einfachheit-allein-nicht-auswuxe4hlt"],"line_end":350,"line_start":332,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Ein Minimalitätsprinzip benötigt eine Vergleichsklasse und ein Maß für Einfachheit. Ein minimaler Hilbertraum kann verschiedene Kernelphasen tragen. Ein festes Symmetriealphabet lässt verschiedene Kopplungsverhältnisse zu. Ein minimaler Referenzträger kann eine mathematische Ladungsbilanz lösen und trotzdem keinen nativen Ursprung haben. Ohne festgelegte physikalische Unterscheidbarkeit kann Minimalität sogar beobach","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"15.2 Warum „maximale Einfachheit`` allein nicht auswählt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18992,"byte_start":16861,"id":"section:2073decd4338b6cf34cb","kind":"subsection","labels":["drei-priorisierte-beweisaufgaben"],"line_end":389,"line_start":351,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"A. Ein ursprünglicher relationaler Übergang. Gesucht ist ein aus dem tatsächlich begründeten Alphabet erzeugtes Instrument, das den neuen neutralen Kopplungstyp oder einen äquivalenten Gesamtprozess realisiert. Zu liefern sind sämtliche inneren Ladungen, Referenzzustand, Energie und Auslesung. Erfolg bedeutet Transfer auf dem gemeinsamen Träger bei vollständiger Bilanz. Der oben bewiesene Ein-Cartan-Zeuge dient als Z","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"15.3 Drei priorisierte Beweisaufgaben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":2594,"byte_start":0,"id":"section:01b780896bdc28ad3ebd","kind":"section","labels":["t1t8-aktueller-gesamtstatus"],"line_end":54,"line_start":1,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/006-section-16-t1-t8-aktueller.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333@ Tor & Vorliegende Bausteine & Fehlender vollständiger Nachweis \\\\ T1 – Ursprung und Auswahl & Markierter Compiler, konkrete Tensoren, Clock in Spin(10), Unterbestimmtheitszeuge & Auswahl des tatsächlichen Prozesskerns, der Primitive und der physisch unterscheidbaren Parameter \\\\ T2 – Half-Charge und E8-Feld & Endliche Typen, geladene native Antwort, abstr","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"16. T1–T8: aktueller Gesamtstatus","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":4038,"byte_start":2594,"id":"section:a84a3daadaac0b001b02","kind":"section","labels":["schluss"],"line_end":80,"line_start":55,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/006-section-16-t1-t8-aktueller.tex","status_markers_as_written":[],"summary_excerpt":"Der neueste TFPT-/Universalraum-Stand ist mathematisch substanzieller und strukturell klarer als eine Sammlung von Analogien. Der markierte Matrixkern, die native Paarregel, die Grundzustandsantwort und die korrigierte Singulett-/Lanczos-Struktur sind konkrete Gegenstände. Die Fortschritte verbinden jedoch bislang verschiedene Ebenen unter zusätzlichen Verträgen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"17. Schluss","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5776,"byte_start":4038,"id":"section:19197b8af8b5280709f1","kind":"section","labels":["anhang-a.-notation-und-modellgrenzen"],"line_end":122,"line_start":81,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/006-section-16-t1-t8-aktueller.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 2 ) * 0.5000 > p( - 2 ) * 0.5000@ Symbol & Bedeutung \\\\ [formula in source] & antisymmetrisches Vierer-Singulett im Tetramermodell \\\\ [formula in source] & übernommener nativer Grundzustand bei [formula in source] \\\\ [formula in source] & voll besetzte native Fermionreferenz ohne Bosonen \\\\ [formula in source] & native Teilchenladung [formula in source] \\\\ [formula in source] & einzelne innere Cartanladung d","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Anhang A. Notation und Modellgrenzen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8232,"byte_start":5776,"id":"section:889803a13f9fbfa376ff","kind":"section","labels":["anhang-b.-reproduzierbarkeit-und-grenzen-der-neuen-pruxfcfung"],"line_end":166,"line_start":123,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/006-section-16-t1-t8-aktueller.tex","status_markers_as_written":[],"summary_excerpt":"Das begleitende Prüfpaket enthält den neuen Prüfer, den tatsächlich verwendeten Tensor, beide Ergebnisdateien, den isolierten H-Ketten-Replay, die Diagrammquellen, das Dokumentmanifest und die eingefrorenen Quellen. Die 57 Bedingungen zählen Prüfbedingungen, keine 57 unabhängigen Theoreme. Die analytischen Beweise in den Abschnitten 8–10 sind Bestandteil der wissenschaftlichen Begründung; sie sind nicht in einem form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Anhang B. Reproduzierbarkeit und Grenzen der neuen Prüfung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10671,"byte_start":8232,"id":"section:ac56751f6c2268a0f707","kind":"section","labels":["anhang-c.-zentrale-lokale-quellen"],"line_end":221,"line_start":167,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/006-section-16-t1-t8-aktueller.tex","status_markers_as_written":[],"summary_excerpt":"Die vollständigen Pfade, Hashes und Zeitstempel aller inventarisierten Dokumente stehen im Quellenmanifest. Die Kennungen im Haupttext beziehen sich auf die folgenden eingefrorenen Dateien:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Anhang C. Zentrale lokale Quellen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13907,"byte_start":10671,"id":"section:ce8c9e773cf1bcc43839","kind":"section","labels":["anhang-d.-externe-literatur-und-referenzdaten"],"line_end":290,"line_start":222,"occurrence":1,"owner_documents":["document:universal_room/new-2/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-2--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/006-section-16-t1-t8-aktueller.tex","status_markers_as_written":[],"summary_excerpt":"Die folgenden Arbeiten liefern etablierte Methoden oder datierte Vergleichsdaten. Sie beweisen nicht die TFPT-spezifische Herkunft der jeweiligen Eingaben. URLs wurden während dieser Synthese geprüft; bei einzelnen Arbeiten wurde nur die offizielle bibliographische Seite beziehungsweise Zusammenfassung konsultiert, soweit der Haupttext keine weitergehende Behauptung daraus übernimmt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Anhang D. Externe Literatur und Referenzdaten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":4355,"byte_start":0,"id":"section:97aaf5ce676d9e7811a5","kind":"frontmatter","labels":[],"line_end":128,"line_start":1,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/preamble.tex","status_markers_as_written":["[L]"],"summary_excerpt":"unicodehyperref hyphensurl dvipsnames,svgnames,x11namesxcolor ngerman, 11pt, a4paper, ]article Scale=MatchLowercase Ligatures=TeX,Scale=1","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TFPT und Universalraum","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":75,"byte_start":0,"id":"section:c0f04e54196baa564b3a","kind":"frontmatter","labels":[],"line_end":7,"line_start":1,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/001-section-zusammenfassung-label-zusammenfassung.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3997,"byte_start":75,"id":"section:3ceede5112aab6746372","kind":"section","labels":["zusammenfassung"],"line_end":73,"line_start":8,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/001-section-zusammenfassung-label-zusammenfassung.tex","status_markers_as_written":[],"summary_excerpt":"Die Topological Fixed-Point Theory (TFPT) verbindet eine markierte algebraische Ausgangsstruktur mit Darstellungen, Gitterdaten und Kandidaten für physikalische Größen. Der Universalraum bezeichnet das weitergehende Ziel, Zustände, erlaubte Operationen, Aufzeichnungen und beobachtbare Entwicklung als Teile einer gemeinsamen Konstruktion zu verstehen. Die vorliegende Arbeit synthetisiert die bis zum 15. September 2026","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zusammenfassung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4139,"byte_start":3997,"id":"section:c3d17008b42775b6cc41","kind":"section","labels":["fragestellung-quellenstand-und-wissenschaftliche-reichweite"],"line_end":76,"line_start":74,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/001-section-zusammenfassung-label-zusammenfassung.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"1. Fragestellung, Quellenstand und wissenschaftliche Reichweite","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5706,"byte_start":4139,"id":"section:281f98ceb421019c30cf","kind":"subsection","labels":["was-ganzheitlich-hier-bedeutet"],"line_end":107,"line_start":77,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/001-section-zusammenfassung-label-zusammenfassung.tex","status_markers_as_written":[],"summary_excerpt":"Eine ganzheitliche Theorie benötigt mehr als Ergebnisse mit ähnlichen Dimensionszahlen. Sie muss zeigen, dass ihre Algebra, ihr Zustand, ihre Dynamik und ihre Messungen zusammenpassen. Wenn ein Grundzustand in Modell A, ein Transport in Modell B und ein chirales Feld in Modell C berechnet werden, entsteht daraus erst dann eine gemeinsame Physik, wenn explizite Abbildungen die jeweiligen Annahmen und beobachtbaren Pro","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1.1 Was „ganzheitlich`` hier bedeutet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":8337,"byte_start":5706,"id":"section:0b9455e2f6dcab42783c","kind":"subsection","labels":["quellenhierarchie-und-stichtag"],"line_end":167,"line_start":108,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/001-section-zusammenfassung-label-zusammenfassung.tex","status_markers_as_written":[],"summary_excerpt":"Der Ausgangskorpus umfasst 74 eingefrorene Dokumentdateien einschließlich des nachgereichten Texts. Darunter befinden sich elf PDFs mit zusammen 830 Seiten; ihre Texte wurden extrahiert. Die zentralen und neu geänderten Abschnitte wurden gezielt gelesen, repräsentative Ausgangsseiten visuell kontrolliert. 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Auf einem gemeinsamen Startzustand [formula in source] definiere","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.1 Die zentrale Vereinfachung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13105,"byte_start":9832,"id":"section:f63457f2f0e017797bd6","kind":"subsection","labels":["satz-rekonstruktion-aus-einem-vollstuxe4ndigen-positiven-wortkern"],"line_end":289,"line_start":229,"numbered_or_version_tokens_as_written":["B5.3"],"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/003-subsection-6-2-lanczos-z-hlt-hamiltonschritte-nicht.tex","status_markers_as_written":[],"summary_excerpt":"Voraussetzungen. 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Für eine Darstellung durch beschränkte Operationen werde zusätzlich für jeden Generator [formula in source] eine Schranke","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.2 Satz: Rekonstruktion aus einem vollständigen positiven Wortkern","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14387,"byte_start":13105,"id":"section:71e71212608cf9b8776b","kind":"subsection","labels":["zustandswahl-und-dynamik-lassen-sich-nicht-durch-rekonstruktion-erschleichen"],"line_end":314,"line_start":290,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/003-subsection-6-2-lanczos-z-hlt-hamiltonschritte-nicht.tex","status_markers_as_written":[],"summary_excerpt":"Der Satz konstruiert aus vorhandenen Prozessdaten eine gemeinsame Darstellung. Er erzeugt diese Daten nicht aus E8 allein. Die Familie [formula in source] aus Abschnitt 6 zeigt ausdrücklich, dass gleiche Grammatik verschiedene positive Prozesskerne zulässt. Ebenso können verschiedene Anfangszustände auf derselben Algebra verschiedene Funktionale liefern.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.3 Zustandswahl und Dynamik lassen sich nicht durch Rekonstruktion erschleichen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15570,"byte_start":14387,"id":"section:e8ee789b77585df48af4","kind":"subsection","labels":["kompatibilituxe4tssatz-fuxfcr-verschiedene-arbeitsstuxe4nde"],"line_end":339,"line_start":315,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/003-subsection-6-2-lanczos-z-hlt-hamiltonschritte-nicht.tex","status_markers_as_written":[],"summary_excerpt":"Angenommen, zwei Konstruktionen verwenden dasselbe Wortalphabet und besitzen für alle zulässigen Wörter denselben Gramkern. 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Gleichheit nur von [formula in source] oder wenigen Wahrscheinlichkeiten genügt nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.4 Kompatibilitätssatz für verschiedene Arbeitsstände","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16690,"byte_start":15570,"id":"section:6bbbd227f8da4c69ccb1","kind":"subsection","labels":["ein-endlicher-fehlervertrag-fuxfcr-adapter"],"line_end":365,"line_start":340,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/003-subsection-6-2-lanczos-z-hlt-hamiltonschritte-nicht.tex","status_markers_as_written":[],"summary_excerpt":"Sei [formula in source] eine Isometrie, [formula in source] und","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8.5 Ein endlicher Fehlervertrag für Adapter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16842,"byte_start":16690,"id":"section:0fde3ce2bc84747a3045","kind":"section","labels":["eigene-verbindung-ii-transfer-mit-mitgerechneter-ladungsreferenz"],"line_end":368,"line_start":366,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/003-subsection-6-2-lanczos-z-hlt-hamiltonschritte-nicht.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"9. 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Mit den sieben Pauli-Blockern","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9.1 Was der vorhandene Vierzustandszeuge bereits leistet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3504,"byte_start":1239,"id":"section:0ae0647c95cba6b2b768","kind":"subsection","labels":["explizite-ladungserhaltende-erweiterung"],"line_end":97,"line_start":40,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/004-subsection-9-1-was-der-vorhandene-vierzustandszeuge-bere.tex","status_markers_as_written":[],"summary_excerpt":"Neue Konstruktion, bedingt. Ergänze eine zweidimensionale Referenz mit Zuständen [formula in source] und","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9.2 Explizite ladungserhaltende Erweiterung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4851,"byte_start":3504,"id":"section:341cd6b4054b64666583","kind":"subsection","labels":["was-damit-fundamental-geluxf6st-wird-und-was-nicht"],"line_end":123,"line_start":98,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/004-subsection-9-1-was-der-vorhandene-vierzustandszeuge-bere.tex","status_markers_as_written":[],"summary_excerpt":"Gelöst ist die konkrete mathematische Frage, ob die festgestellte Cartan-Schranke einen Transfer auch bei mitgeführtem Ladungsausgleich grundsätzlich verbietet. Das tut sie nicht: Die Erweiterung liefert einen expliziten positiven Zeugen. Sie bewahrt die betrachtete Gesamt-Cartanladung, ohne den ursprünglichen isolierten Mischer als bereits verfügbar auszugeben.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9.3 Was damit fundamental gelöst wird – und was nicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6124,"byte_start":4851,"id":"section:754d08c3e551a92d1934","kind":"subsection","labels":["die-referenz-wird-verbraucht-ein-einfacher-unmuxf6glichkeitssatz"],"line_end":147,"line_start":124,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/004-subsection-9-1-was-der-vorhandene-vierzustandszeuge-bere.tex","status_markers_as_written":[],"summary_excerpt":"Beginnt die Referenz in einer scharfen Ladung [formula in source] und erhöht sich die Systemladung in einem erfolgreichen Zweig um [formula in source] , muss die Referenz oder eine weitere Umgebung im selben Zweig ihre Ladung um [formula in source] ändern. Ein vollständiger Rücklauf zur exakt gleichen scharfen Referenzladung bei sonst unverändertem Außenraum ist wegen Gesamtladungserhaltung unmöglich.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"9.4 Die Referenz wird verbraucht: ein einfacher Unmöglichkeitssatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6292,"byte_start":6124,"id":"section:54c7566a461bcea6a9e6","kind":"section","labels":["eigene-verbindung-iii-uxfcberlappung-dynamik-und-geometrische-kruxfcmmung"],"line_end":151,"line_start":148,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/004-subsection-9-1-was-der-vorhandene-vierzustandszeuge-bere.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"10. Eigene Verbindung III: Überlappung, Dynamik und geometrische Krümmung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7389,"byte_start":6292,"id":"section:e9f4568715350e1d2978","kind":"subsection","labels":["eine-gemeinsame-quelle-ist-nicht-automatisch-bewegung"],"line_end":177,"line_start":152,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/004-subsection-9-1-was-der-vorhandene-vierzustandszeuge-bere.tex","status_markers_as_written":[],"summary_excerpt":"Sei [formula in source] ein Adapter, dessen Spalten die betrachteten Zustände sind. Dann","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10.1 Eine gemeinsame Quelle ist nicht automatisch Bewegung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8349,"byte_start":7389,"id":"section:e83e1b5691c43e1ff6d5","kind":"subsection","labels":["zeitabhuxe4ngige-rahmen-brauchen-einen-verbindungsterm"],"line_end":197,"line_start":178,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/004-subsection-9-1-was-der-vorhandene-vierzustandszeuge-bere.tex","status_markers_as_written":[],"summary_excerpt":"Für einen glatten isometrischen Rahmen [formula in source] und [formula in source] ergibt die projizierte Schrödingergleichung","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10.2 Zeitabhängige Rahmen brauchen einen Verbindungsterm","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9839,"byte_start":8349,"id":"section:ae105be7998042450a05","kind":"subsection","labels":["feste-vollstuxe4ndige-rahmen-und-bewegte-projektoren-unterscheiden-sich"],"line_end":234,"line_start":198,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/004-subsection-9-1-was-der-vorhandene-vierzustandszeuge-bere.tex","status_markers_as_written":[],"summary_excerpt":"Sind [formula in source] bloße Basiswechsel vollständiger unitärer Rahmen, teleskopiert eine geschlossene Schleife:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10.3 Feste vollständige Rahmen und bewegte Projektoren unterscheiden sich","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11889,"byte_start":9839,"id":"section:2b88220849ae1015e84b","kind":"subsection","labels":["ein-vollstuxe4ndig-gerechneter-kleiner-zeuge"],"line_end":285,"line_start":235,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/004-subsection-9-1-was-der-vorhandene-vierzustandszeuge-bere.tex","status_markers_as_written":[],"summary_excerpt":"Aus demselben Projektor folgt die reelle Quantenmetrik","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10.4 Ein vollständig gerechneter kleiner Zeuge","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13159,"byte_start":11889,"id":"section:4ec06540b8c273ec0116","kind":"subsection","labels":["ein-bedingter-dynamischer-parent"],"line_end":312,"line_start":286,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/004-subsection-9-1-was-der-vorhandene-vierzustandszeuge-bere.tex","status_markers_as_written":[],"summary_excerpt":"hat bei festem Parameter eine Lücke [formula in source] und einen Rang-eins-Grundraum [formula in source] . Bei kontrollierter langsamer Parameteränderung liefert er die bekannte geometrische Phase, mit separat zu kontrollierendem adiabatischem Fehler. Er zeigt konstruktiv, dass ein bewegter ausgewählter Unterraum die falsche „alles teleskopiert``-Abkürzung umgehen kann.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"10.5 Ein bedingter dynamischer Parent","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13273,"byte_start":13159,"id":"section:cc116004170e1c187143","kind":"section","labels":["wo-raum-und-echte-wirkung-entstehen-kuxf6nnten"],"line_end":315,"line_start":313,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/004-subsection-9-1-was-der-vorhandene-vierzustandszeuge-bere.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"11. Wo Raum und echte Wirkung entstehen könnten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14542,"byte_start":13273,"id":"section:af3d4587a56b74b5d995","kind":"subsection","labels":["innere-darstellung-und-multiplizituxe4t"],"line_end":346,"line_start":316,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/004-subsection-9-1-was-der-vorhandene-vierzustandszeuge-bere.tex","status_markers_as_written":[],"summary_excerpt":"Unter einer kompakten inneren Gruppe zerfällt ein endlicher Hilbertraum als","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"11.1 Innere Darstellung und Multiplizität","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15798,"byte_start":14542,"id":"section:40f598c0ac7a501ad284","kind":"subsection","labels":["zwei-verschiedene-kommutanten"],"line_end":379,"line_start":347,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/004-subsection-9-1-was-der-vorhandene-vierzustandszeuge-bere.tex","status_markers_as_written":[],"summary_excerpt":"Der Kommutant der inneren Gruppe beschreibt die mit ihr verträgliche Dynamik. Der Kommutant des verfügbaren Operationsalphabets beschreibt dagegen Unterschiede, die dieses Alphabet nicht auflösen kann. Diese Bezugsalgebren sind verschieden.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"11.2 Zwei verschiedene Kommutanten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1907,"byte_start":0,"id":"section:a8e550a195d5486e5f83","kind":"subsection","labels":["wirkung-durch-einen-kontrollierten-eingriff"],"line_end":40,"line_start":1,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Ein nichtverschwindender Korrelator kann aus anfänglicher Überlappung stammen. Ein aussagekräftiger Test vergleicht deshalb dieselbe Quelle und denselben Eingang einmal mit und einmal ohne einen zugelassenen Eingriff in A. Für gerade Observablen und [formula in source] gilt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"11.3 Wirkung durch einen kontrollierten Eingriff","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2905,"byte_start":1907,"id":"section:bba313c4dd5e5d142e0b","kind":"subsection","labels":["weshalb-die-raumdimension-offen-bleibt"],"line_end":58,"line_start":41,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Aus demselben inneren Baustein kann man zunächst viele räumliche Wiederholungen definieren. Ein gewählter Graph ist eine zusätzliche Kompositionsregel. Weder seine Existenz noch die innere Zahl fünf wählt automatisch ein dreidimensionales Kontinuum aus. Die Quellen enthalten ausdrücklich alternative Verklebungen mit verschiedenen Dimensionen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"11.4 Weshalb die Raumdimension offen bleibt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3054,"byte_start":2905,"id":"section:4f1af58741cba87200dd","kind":"section","labels":["relativistisches-feldwuxf6rterbuch-chiralituxe4t-und-gravitation"],"line_end":61,"line_start":59,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"12. Relativistisches Feldwörterbuch, Chiralität und Gravitation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3744,"byte_start":3054,"id":"section:8d9a2128dd5c1062550a","kind":"subsection","labels":["derselbe-matrixraum-truxe4gt-eine-lorentz-kegelansicht"],"line_end":80,"line_start":62,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] erhält [formula in source] diese Determinante und den positiven Kegel. Das ist eine exakte Lorentzstruktur auf diesem Darstellungsraum. Die Verbindung zum kleinen Matrixkern ist deshalb mathematisch interessant. Sie identifiziert aber noch keine dynamischen Raumzeitereignisse, keine gemeinsamen Lichtgeschwindigkeiten verschiedener Sektoren und keine gravitative Wirkung. [S046, Kap. 11, 34–35]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"12.1 Derselbe Matrixraum trägt eine Lorentz-Kegelansicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5210,"byte_start":3744,"id":"section:c93e1c218b0a0bca40b0","kind":"subsection","labels":["der-grassmann-typentest-bleibt-unverzichtbar"],"line_end":110,"line_start":81,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Sei [formula in source] die antisymmetrische Fortsetzung einer W-Zeile und seien [formula in source] gleichhändige Weylfelder. Ein lokaler skalarer Ansatz mit Gesamtkoeffizient [formula in source] ist symmetrisch: antisymmetrisch mal antisymmetrisch. Ein symmetrischer Koeffizient kontrahiert mit zwei Grassmannfeldern zu null.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"12.2 Der Grassmann-Typentest bleibt unverzichtbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6453,"byte_start":5210,"id":"section:ef4c2cff1c68d7e9c81e","kind":"subsection","labels":["algebraisch-nicht-null-bedeutet-noch-nicht-stabile-feldtheorie"],"line_end":136,"line_start":111,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Der in S001 untersuchte freie geladene Zweitableitungsansatz für den [formula in source] -Tensor besitzt eine nach unten unbeschränkte Energie. Dieser konkrete Kandidat scheidet ohne zusätzliche Constraints aus. Daraus folgt kein Verbot sämtlicher Tensorfeldtheorien.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"12.3 Algebraisch nicht null bedeutet noch nicht stabile Feldtheorie","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7300,"byte_start":6453,"id":"section:e867ffbbdc6a2af9e820","kind":"subsection","labels":["familien-und-spiegelmoden"],"line_end":153,"line_start":137,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Der innere Träger kann Familienzahlen und Anomaliesummen motivieren. Drei physikalische Familien benötigen jedoch einen chiralen Operator samt Darstellung, Maß und kontrollierter Spiegelentkopplung. Eine Faltung oder Umbenennung von Weylknoten entfernt keinen zusätzlichen dynamischen Freiheitsgrad. Im dokumentierten Walk treten mehrere Weylknoten auf; ihre Chiralitäten und Quasienergien müssen im tatsächlichen rezipr","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"12.4 Familien und Spiegelmoden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8344,"byte_start":7300,"id":"section:bdbf83dde7fc91df381b","kind":"subsection","labels":["gravitation"],"line_end":174,"line_start":154,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Eine Metrik auf Zustandsparametern, eine Lorentz-Kegelform oder ein transversaler spurfreier Projektor ist noch kein dynamisches Graviton. Erforderlich sind ein positiver masseloser Spin-2-Sektor, zwei physische Helizitäten und eine konsistente universelle Kopplung im selben dynamischen Modell.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"12.5 Gravitation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8900,"byte_start":8344,"id":"section:031fbc7baba367fbe1bc","kind":"section","labels":["physikalische-zahlen-vorhersage-kalibrierung-und-gemeinsamer-test"],"line_end":185,"line_start":175,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Die frühen TFPT-Arbeiten enthalten zahlreiche Beziehungen für Kopplungen, Massenskalen und kosmologische Größen. Diese gehören in ein vollständiges Forschungspaper, müssen aber nach ihrem Transfervertrag gelesen werden. Ein präziser dimensionsloser Formelwert ist erst nach Zuordnung zur physikalischen Messgröße und Kontrolle der theoretischen Unsicherheit eine physikalische Vorhersage.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"13. Physikalische Zahlen: Vorhersage, Kalibrierung und gemeinsamer Test","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9670,"byte_start":8900,"id":"section:b2d116adce4bfa470396","kind":"subsection","labels":["feinstrukturkonstante"],"line_end":205,"line_start":186,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Die am Recherchetag abgerufene NIST-Tabelle enthält weiterhin die ausdrücklich bezeichnete CODATA-2022-Anpassung","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"13.1 Feinstrukturkonstante","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10693,"byte_start":9670,"id":"section:cf645a434f2b0961ea9f","kind":"subsection","labels":["kosmologie-und-gemeinsame-parameter"],"line_end":228,"line_start":206,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Für die im Hauptdokument untersuchte einfache Inflationsbranche gilt nach Eliminieren der E-Faltungszahl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"13.2 Kosmologie und gemeinsame Parameter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11531,"byte_start":10693,"id":"section:3558bb7b725bf31b37d7","kind":"subsection","labels":["was-ein-uxfcberzeugender-empirischer-anschluss-enthalten-muss"],"line_end":244,"line_start":229,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Ein prüfbarer Ausgabevertrag fixiert vor dem Vergleich: denselben Hamiltonoperator beziehungsweise dieselbe effektive Wirkung, dieselbe Zustandsregel, eine endliche Menge unabhängiger Parameter, die Abbildung auf Messgrößen, systematische Näherungsfehler und die verwendete Datenversion. Werden Eingaben kalibriert, müssen die verbleibenden unabhängigen Vorhersagen ausgewiesen werden.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"13.3 Was ein überzeugender empirischer Anschluss enthalten muss","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11626,"byte_start":11531,"id":"section:7ff2a883865df44088fc","kind":"section","labels":["arithmetik-rh-und-rechenfuxe4higkeit"],"line_end":247,"line_start":245,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"14. Arithmetik, RH und Rechenfähigkeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12640,"byte_start":11626,"id":"section:9101002f7c02fbb45824","kind":"subsection","labels":["der-gemeinsame-begriff-spektrum-genuxfcgt-nicht"],"line_end":266,"line_start":248,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Ein Hamiltonspektrum, ein endlicher Markovoperator und eine arithmetische explizite Formel sind verschiedene mathematische Objekte. Eine Brücke zur Riemannschen Vermutung benötigt eine exakte, phasen- und normierungstreue Identität mit dem vollständigen erforderlichen Weil-Ausdruck oder ein anderes vollständig bewiesenes RH-Kriterium. Positivität einiger Matrizen, einzelne Spektrallinien und die lokale Focklücke reic","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"14.1 Der gemeinsame Begriff „Spektrum`` genügt nicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":13551,"byte_start":12640,"id":"section:f9506900664b6ff061aa","kind":"subsection","labels":["grenze-der-aktuellen-quellenpruxfcfung"],"line_end":284,"line_start":267,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Der aktuelle RH-Quellencheck stoppte mit SOURCE_UNAVAILABLE für den referenzierten Forschungsordner 2026-09-04/scha-2/research. Der bestehende Index enthält hilfreiche routebezogene Hinweise, aber seine vollständige Aktualität konnte dadurch nicht bestätigt werden. Die Unterbrechung ist kein mathematischer Gegenbeweis; sie verhindert eine Behauptung, sämtliche arithmetischen Arbeitsstände seien frisch vollständig gep","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"14.2 Grenze der aktuellen Quellenprüfung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":14439,"byte_start":13551,"id":"section:5b3123d582078bfc75a9","kind":"subsection","labels":["faktorisierung-und-universalituxe4t"],"line_end":301,"line_start":285,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Ein kohärenter Gattervertrag kann algorithmische Universalität besitzen. Das ist nicht identisch mit der physischen Verfügbarkeit seiner Register, Kontrolloperationen, Resets und Messungen. Ein klassischer Simulator eines Quantenschaltkreises hat auch dann keine automatisch polynomiellen klassischen Kosten, wenn der ideale Quantenschaltkreis eine effiziente Faktorisierung beschreibt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"14.3 Faktorisierung und Universalität","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14591,"byte_start":14439,"id":"section:fc86579dbb003c50e897","kind":"section","labels":["die-fundamentale-gesamtluxf6sung-als-pruxe4ziser-forschungsauftrag"],"line_end":304,"line_start":302,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"15. Die fundamentale Gesamtlösung als präziser Forschungsauftrag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15812,"byte_start":14591,"id":"section:f9fe3ba465e6fb3043c5","kind":"subsection","labels":["was-sich-auf-einen-gemeinsamen-gegenstand-reduzieren-luxe4sst"],"line_end":331,"line_start":305,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Die eigenen Herleitungen legen folgende Organisation nahe:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"15.1 Was sich auf einen gemeinsamen Gegenstand reduzieren lässt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16861,"byte_start":15812,"id":"section:8774da682be1a977592c","kind":"subsection","labels":["warum-maximale-einfachheit-allein-nicht-auswuxe4hlt"],"line_end":350,"line_start":332,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"Ein Minimalitätsprinzip benötigt eine Vergleichsklasse und ein Maß für Einfachheit. Ein minimaler Hilbertraum kann verschiedene Kernelphasen tragen. Ein festes Symmetriealphabet lässt verschiedene Kopplungsverhältnisse zu. Ein minimaler Referenzträger kann eine mathematische Ladungsbilanz lösen und trotzdem keinen nativen Ursprung haben. Ohne festgelegte physikalische Unterscheidbarkeit kann Minimalität sogar beobach","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"15.2 Warum „maximale Einfachheit`` allein nicht auswählt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18992,"byte_start":16861,"id":"section:b917ef8e255e12c5f0b8","kind":"subsection","labels":["drei-priorisierte-beweisaufgaben"],"line_end":389,"line_start":351,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/005-subsection-11-3-wirkung-durch-einen-kontrollierten.tex","status_markers_as_written":[],"summary_excerpt":"A. Ein ursprünglicher relationaler Übergang. Gesucht ist ein aus dem tatsächlich begründeten Alphabet erzeugtes Instrument, das den neuen neutralen Kopplungstyp oder einen äquivalenten Gesamtprozess realisiert. Zu liefern sind sämtliche inneren Ladungen, Referenzzustand, Energie und Auslesung. Erfolg bedeutet Transfer auf dem gemeinsamen Träger bei vollständiger Bilanz. Der oben bewiesene Ein-Cartan-Zeuge dient als Z","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"15.3 Drei priorisierte Beweisaufgaben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":2594,"byte_start":0,"id":"section:d59ba489a4e53e810376","kind":"section","labels":["t1t8-aktueller-gesamtstatus"],"line_end":54,"line_start":1,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/006-section-16-t1-t8-aktueller.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333 > p( - 4 ) * 0.3333@ Tor & Vorliegende Bausteine & Fehlender vollständiger Nachweis \\\\ T1 – Ursprung und Auswahl & Markierter Compiler, konkrete Tensoren, Clock in Spin(10), Unterbestimmtheitszeuge & Auswahl des tatsächlichen Prozesskerns, der Primitive und der physisch unterscheidbaren Parameter \\\\ T2 – Half-Charge und E8-Feld & Endliche Typen, geladene native Antwort, abstr","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"16. T1–T8: aktueller Gesamtstatus","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":4038,"byte_start":2594,"id":"section:3772ab014bae8f026aa5","kind":"section","labels":["schluss"],"line_end":80,"line_start":55,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/006-section-16-t1-t8-aktueller.tex","status_markers_as_written":[],"summary_excerpt":"Der neueste TFPT-/Universalraum-Stand ist mathematisch substanzieller und strukturell klarer als eine Sammlung von Analogien. Der markierte Matrixkern, die native Paarregel, die Grundzustandsantwort und die korrigierte Singulett-/Lanczos-Struktur sind konkrete Gegenstände. Die Fortschritte verbinden jedoch bislang verschiedene Ebenen unter zusätzlichen Verträgen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"17. Schluss","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5776,"byte_start":4038,"id":"section:e9fe7ab9562ef47d1ea1","kind":"section","labels":["anhang-a.-notation-und-modellgrenzen"],"line_end":122,"line_start":81,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/006-section-16-t1-t8-aktueller.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 2 ) * 0.5000 > p( - 2 ) * 0.5000@ Symbol & Bedeutung \\\\ [formula in source] & antisymmetrisches Vierer-Singulett im Tetramermodell \\\\ [formula in source] & übernommener nativer Grundzustand bei [formula in source] \\\\ [formula in source] & voll besetzte native Fermionreferenz ohne Bosonen \\\\ [formula in source] & native Teilchenladung [formula in source] \\\\ [formula in source] & einzelne innere Cartanladung d","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Anhang A. Notation und Modellgrenzen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8232,"byte_start":5776,"id":"section:e5a5a2770785da09eaac","kind":"section","labels":["anhang-b.-reproduzierbarkeit-und-grenzen-der-neuen-pruxfcfung"],"line_end":166,"line_start":123,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/006-section-16-t1-t8-aktueller.tex","status_markers_as_written":[],"summary_excerpt":"Das begleitende Prüfpaket enthält den neuen Prüfer, den tatsächlich verwendeten Tensor, beide Ergebnisdateien, den isolierten H-Ketten-Replay, die Diagrammquellen, das Dokumentmanifest und die eingefrorenen Quellen. Die 57 Bedingungen zählen Prüfbedingungen, keine 57 unabhängigen Theoreme. Die analytischen Beweise in den Abschnitten 8–10 sind Bestandteil der wissenschaftlichen Begründung; sie sind nicht in einem form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Anhang B. Reproduzierbarkeit und Grenzen der neuen Prüfung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10671,"byte_start":8232,"id":"section:7fc9d250cf5eb70c3c23","kind":"section","labels":["anhang-c.-zentrale-lokale-quellen"],"line_end":221,"line_start":167,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/006-section-16-t1-t8-aktueller.tex","status_markers_as_written":[],"summary_excerpt":"Die vollständigen Pfade, Hashes und Zeitstempel aller inventarisierten Dokumente stehen im Quellenmanifest. Die Kennungen im Haupttext beziehen sich auf die folgenden eingefrorenen Dateien:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Anhang C. Zentrale lokale Quellen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13907,"byte_start":10671,"id":"section:c8b55651ea0f190499c8","kind":"section","labels":["anhang-d.-externe-literatur-und-referenzdaten"],"line_end":290,"line_start":222,"occurrence":1,"owner_documents":["document:universal_room/new-3/TFPT_Universalraum_Forschungspaper_2026-09-15/TFPT_Universalraum_Forschungspaper_2026-09-15"],"relation_ids":[],"semantic_review":false,"source":"documents/universal_room--new-3--TFPT_Universalraum_Forschungspaper_2026-09-15--TFPT_Universalraum_Forschungspaper_2026-09-15/sections/006-section-16-t1-t8-aktueller.tex","status_markers_as_written":[],"summary_excerpt":"Die folgenden Arbeiten liefern etablierte Methoden oder datierte Vergleichsdaten. Sie beweisen nicht die TFPT-spezifische Herkunft der jeweiligen Eingaben. URLs wurden während dieser Synthese geprüft; bei einzelnen Arbeiten wurde nur die offizielle bibliographische Seite beziehungsweise Zusammenfassung konsultiert, soweit der Haupttext keine weitergehende Behauptung daraus übernimmt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Anhang D. Externe Literatur und Referenzdaten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":1691,"byte_start":0,"id":"section:da15d5f86b98127575ae","kind":"frontmatter","labels":[],"line_end":39,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/ftransfer-clocks/ftransfer_clocks_contract"],"relation_ids":["relation:7ff457b8da99deed4425"],"semantic_review":false,"source":"experiments/ftransfer-clocks/ftransfer_clocks_contract.tex","status_markers_as_written":["[X]"],"summary_excerpt":"-1.4cm FTRANSFER.CLOCKS.01 — the frozen external-clock contract\\ the [formula in source] jets\\\\[1mm] Preregistration companion (design, type [X]); frozen 2026-08-04","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"-1.4cm FTRANSFER.CLOCKS.01 — the frozen external-clock contract\\ the [formula in source] jets\\\\[1mm] Preregistration companion (design, type [X]); frozen 2026-08-04","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":3095,"byte_start":1691,"id":"section:0aa531691d44e875db34","kind":"section","labels":["eq:quadruple"],"line_end":60,"line_start":40,"occurrence":1,"owner_documents":["document:experiments/ftransfer-clocks/ftransfer_clocks_contract"],"relation_ids":["relation:101304bb16929e9980f5","relation:5a7131de4cb3dda683b6","relation:6cc4f87b1ac400f34e0c","relation:7bbe4211ce46229ae965","relation:de265d88dbbe46d67322","relation:e5f76967e1200480af6e"],"semantic_review":false,"source":"experiments/ftransfer-clocks/ftransfer_clocks_contract.tex","status_markers_as_written":[],"summary_excerpt":"The [formula in source] interface ( CONTRACT.F.01) has its PGL [formula in source] syntax closed: one common parabolic action on the discrete half, and on the native continuous half the classified degeneration [formula in source] (hyperbolic, forced identical by the single-flow theorem v425), [formula in source] parabolic and exactly conjugate to the base translation, [formula in source] the identity ( v632_ftransfer","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Where the contract starts","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":5280,"byte_start":3095,"id":"section:1d19ef4ba26a6869c8f3","kind":"section","labels":[],"line_end":92,"line_start":61,"occurrence":1,"owner_documents":["document:experiments/ftransfer-clocks/ftransfer_clocks_contract"],"relation_ids":["relation:12b7a9daddd01e4d3ab5","relation:59cfe25d478a221b4883"],"semantic_review":false,"source":"experiments/ftransfer-clocks/ftransfer_clocks_contract.tex","status_markers_as_written":[],"summary_excerpt":"@llll@ Solver & Clock & Operational definition & Chart / gauge (frozen) \\\\ [formula in source] (Koide) & proper time [formula in source] & @l@rest-frame proper time of the lepton\\ -particle state [formula in source] the phase clock of\\ propagator pole, [formula in source] (on-shell\\ ; PDG pole masses) & @l@ [formula in source] ;\\ v99 seam tick [formula in source] \\ proper-phase e-fold \\\\[8.5mm] [formula in source] ( ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. The four frozen clocks (one per solver, no residual freedom)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":7465,"byte_start":5280,"id":"section:e828f1dd74126d18e139","kind":"section","labels":[],"line_end":124,"line_start":93,"occurrence":1,"owner_documents":["document:experiments/ftransfer-clocks/ftransfer_clocks_contract"],"relation_ids":["relation:1f0153fdb36061327022"],"semantic_review":false,"source":"experiments/ftransfer-clocks/ftransfer_clocks_contract.tex","status_markers_as_written":[],"summary_excerpt":"The common projective connection lives on the log-scale line [formula in source] . The four dictionaries are affine in their log charts with slopes [formula in source] frozen; every dimensionful anchor ( [formula in source] , [formula in source] , [formula in source] , [formula in source] , the thermal matching constant [formula in source] ) enters as an affine offset only and drops out of every Schwarzian and every ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Transport and the preregistered prediction","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":8476,"byte_start":7465,"id":"section:36af8b2797de31eabfc8","kind":"section","labels":[],"line_end":139,"line_start":125,"occurrence":1,"owner_documents":["document:experiments/ftransfer-clocks/ftransfer_clocks_contract"],"relation_ids":[],"semantic_review":false,"source":"experiments/ftransfer-clocks/ftransfer_clocks_contract.tex","status_markers_as_written":[],"summary_excerpt":"2pt no-common-connection: with the clocks and dictionaries exactly as frozen, the transported Schwarzians differ (symbolic inequality, no tolerance). On kill, the executor must exhibit the reparametrization that would be needed per failing pair, documenting the forbidden freedom. free-reparam-needed: a pass is achievable only by a post-freeze, per-channel change of gauge or dictionary (re-sloped or non-affine diction","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Kill criteria (frozen)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"}]},{"byte_end":10384,"byte_start":8476,"id":"section:c160f54e23592ab7f2ef","kind":"section","labels":[],"line_end":166,"line_start":140,"occurrence":1,"owner_documents":["document:experiments/ftransfer-clocks/ftransfer_clocks_contract"],"relation_ids":["relation:92de8840e9f118a3b868","relation:cf85cb5cf036c822d5b0"],"semantic_review":false,"source":"experiments/ftransfer-clocks/ftransfer_clocks_contract.tex","status_markers_as_written":[],"summary_excerpt":"Data (pin base points and dictionary validity only): PDG 2024 pole masses ( [formula in source] MeV dominates; frozen tolerance [formula in source] , [formula in source] ); FIRAS [formula in source] + Saikawa–Shirai [formula in source] table + Planck [formula in source] for the [formula in source] chart; [formula in source] (PDG world average) with the frozen 1-loop chain [formula in source] and a [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Decision rules and executor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"}]},{"byte_end":11561,"byte_start":10384,"id":"section:9d09ec84cd28113d6184","kind":"section","labels":[],"line_end":182,"line_start":167,"occurrence":1,"owner_documents":["document:experiments/ftransfer-clocks/ftransfer_clocks_contract"],"relation_ids":["relation:16c69bfe3033357e7e3b","relation:4eb2ddb630553bd86daa","relation:91204d3d11c0ca53f93e"],"semantic_review":false,"source":"experiments/ftransfer-clocks/ftransfer_clocks_contract.tex","status_markers_as_written":[],"summary_excerpt":"Stated before execution (the v723 precedent: preregistering the expected kill is house style). The expected verdict is K1: all four frozen dictionaries are affine on the log-scale chart, affine transport scales a Schwarzian by [formula in source] and cannot move [formula in source] (the QCD value) onto [formula in source] (the seam value) — the v578 split survives every slope, and the no-diagonalizable-logarithm kill","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Honest priors","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":1655,"byte_start":0,"id":"section:6c91787ee447b25a2d36","kind":"frontmatter","labels":[],"line_end":41,"line_start":1,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-common-process-20260915/pdf-header.tex","status_markers_as_written":["[L]"],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4621,"byte_start":0,"id":"section:afbe6dbaa8eae0532a04","kind":"frontmatter","labels":[],"line_end":118,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Einfach_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Einfach_2026-09-15_v1.6.8.tex","status_markers_as_written":["[L]"],"summary_excerpt":"unicodehyperref hyphensurl dvipsnames,svgnames,x11namesxcolor ngerman, 10pt, a4paper, ]article Scale=MatchLowercase Ligatures=TeX,Scale=1","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4824,"byte_start":4621,"id":"section:bd19ef83d33cfb587205","kind":"section","labels":["tfpt-universalraum-einfach-erkluxe4rt-dieselbe-maschine-mehrere-ansichten"],"line_end":124,"line_start":119,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Einfach_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Einfach_2026-09-15_v1.6.8.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"TFPT / Universalraum einfach erklärt: dieselbe Maschine, mehrere Ansichten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6083,"byte_start":4824,"id":"section:ca3a2427d2279e3dc2d7","kind":"subsection","labels":["wo-wir-stehen"],"line_end":149,"line_start":125,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Einfach_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Einfach_2026-09-15_v1.6.8.tex","status_markers_as_written":[],"summary_excerpt":"Wir haben noch keine vollständige Theorie des Universums. Aber wir können jetzt an einem kleinen Teil des ursprünglichen TFPT-Modells drei Dinge genauer zusammenbringen: Was passiert darin? Was lässt sich davon sehen? Und verändert ein gezielter Eingriff tatsächlich etwas anderes?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wo wir stehen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7147,"byte_start":6083,"id":"section:c27f8722cd7bbc5c17f7","kind":"subsection","labels":["was-die-neu-zugeschickte-arbeit-beitruxe4gt"],"line_end":171,"line_start":150,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Einfach_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Einfach_2026-09-15_v1.6.8.tex","status_markers_as_written":[],"summary_excerpt":"Sie schlägt vor, alle erlaubten Handlungsfolgen mitsamt ihren Überlappungen als gemeinsame Beschreibung zu verwenden. Das ist ein brauchbarer Ordnungsrahmen: Zwei vermeintliche Teillösungen müssen dieselben Handlungen und Antworten wiedergeben, nicht bloß ähnliche Zahlen enthalten.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was die neu zugeschickte Arbeit beiträgt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7232,"byte_start":7147,"id":"section:aa4bce288e28570eca81","kind":"subsection","labels":["drei-neue-ergebnisse-in-bildern"],"line_end":174,"line_start":172,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Einfach_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Einfach_2026-09-15_v1.6.8.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Drei neue Ergebnisse in Bildern","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7816,"byte_start":7232,"id":"section:3b5855c44eabd50f8a67","kind":"subsubsection","labels":["ein-kleines-pendel-statt-eines-unuxfcbersichtlichen-zustandsbergs"],"line_end":186,"line_start":175,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Einfach_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Einfach_2026-09-15_v1.6.8.tex","status_markers_as_written":[],"summary_excerpt":"Im ursprünglichen Modell gibt es zwei vollständig symmetrische Zustände, die ausschließlich ineinander umgewandelt werden. Alle anderen denkbaren Ausgänge heben sich exakt auf. Der ganze Vorgang passt deshalb in eine Zweizustandsrechnung.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein kleines Pendel statt eines unübersichtlichen Zustandsbergs","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8578,"byte_start":7816,"id":"section:61622ee69695bc6ac797","kind":"subsubsection","labels":["die-richtigen-fenster-zeigen-mehr-als-immer-mehr-fotos-desselben-fensters"],"line_end":201,"line_start":187,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Einfach_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Einfach_2026-09-15_v1.6.8.tex","status_markers_as_written":[],"summary_excerpt":"Einzelne Besetzungsanzeigen sehen nur einen kleinen Teil der inneren Information. Auch beliebig viele einfache Einzelteilchenmessungen lassen viel unsichtbar. Geeignet gedrehte gemeinsame Paarmessungen reichen dagegen für eine vollständige innere Zustandsbeschreibung.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die richtigen Fenster zeigen mehr als immer mehr Fotos desselben Fensters","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9507,"byte_start":8578,"id":"section:08567e0f461869965023","kind":"subsubsection","labels":["ein-gezielter-anstouxdf-veruxe4ndert-wirklich-einen-anderen-ausgang"],"line_end":219,"line_start":202,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Einfach_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Einfach_2026-09-15_v1.6.8.tex","status_markers_as_written":[],"summary_excerpt":"Wir lassen ein bestimmtes Fermionpaar kurz unter den ursprünglichen Regeln laufen. Dann ändern wir an einer einzigen Mode nur das Vorzeichen ihrer Amplitude. Nach weiterer Entwicklung hat eine andere Mode eine andere Besetzungswahrscheinlichkeit als ohne den Eingriff.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein gezielter Anstoß verändert wirklich einen anderen Ausgang","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10357,"byte_start":9507,"id":"section:b157ba7c4e4d2e2a38b0","kind":"subsubsection","labels":["die-beiden-aufgaben-passen-sogar-in-denselben-dreierbaustein"],"line_end":235,"line_start":220,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Einfach_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Einfach_2026-09-15_v1.6.8.tex","status_markers_as_written":[],"summary_excerpt":"Für genau diesen Versuch reichen drei Zustände: das Anfangspaar, eine gemeinsame Schwingung der sieben anderen Paare und ein Boson. Wir können auf diesem selben kleinen Baustein sowohl seinen Zustand auslesen als auch die Wirkung des Anstoßes berechnen. Das ist die direkteste neue Verbindung zwischen Schatten und Dynamik.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die beiden Aufgaben passen sogar in denselben Dreierbaustein","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11050,"byte_start":10357,"id":"section:4f776f6fcbd3b609855f","kind":"subsection","labels":["was-die-schattenidee-leistet---und-was-nicht"],"line_end":249,"line_start":236,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Einfach_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Einfach_2026-09-15_v1.6.8.tex","status_markers_as_written":[],"summary_excerpt":"Deine Idee trifft hier einen prüfbaren Punkt: Verschiedene Ansichten können gemeinsam verraten, was im Hintergrund passiert. Dafür müssen wir wissen, wie jede Ansicht aus derselben Maschine entsteht. Dann kann die eine Ansicht eine fehlende Information der anderen ergänzen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was die Schattenidee leistet - und was nicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12399,"byte_start":11050,"id":"section:0a945a48437493720c9b","kind":"subsection","labels":["was-die-letzten-nachtruxe4ge-noch-veruxe4ndert-haben"],"line_end":273,"line_start":250,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Einfach_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Einfach_2026-09-15_v1.6.8.tex","status_markers_as_written":[],"summary_excerpt":"Ein zusätzlicher exakt geprüfter Rechenbaustein erlaubt eine stärkere Untergrenze für die Energie der bekannten niedrigen Entnahmeanregung. Ihre genaue Energie kennen wir weiter nicht. Wichtig war dabei das Sortieren: Einige Zahlen im zugeschickten Text gehören zu einem kleineren Näherungszustand, andere zu einem größeren. Zusammengeschoben ergeben sie kein einziges berechnetes Teilchen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was die letzten Nachträge noch verändert haben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13609,"byte_start":12399,"id":"section:9b84a303f59067cb1bfa","kind":"subsection","labels":["der-jetzt-wichtigste-nuxe4chste-schritt"],"line_end":305,"line_start":274,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Einfach_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Einfach_2026-09-15_v1.6.8.tex","status_markers_as_written":[],"summary_excerpt":"Nicht noch mehr mögliche Bauteile sammeln, sondern einen dieser kleinen Versuche vollständig aus dem Compiler herleiten:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der jetzt wichtigste nächste Schritt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5074,"byte_start":0,"id":"section:101033e893dd010fd2ea","kind":"frontmatter","labels":[],"line_end":129,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Update_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Update_2026-09-15_v1.6.8.tex","status_markers_as_written":["[L]"],"summary_excerpt":"unicodehyperref hyphensurl dvipsnames,svgnames,x11namesxcolor ngerman, 10pt, a4paper, ]article Scale=MatchLowercase Ligatures=TeX,Scale=1","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5427,"byte_start":5074,"id":"section:8b9c99adbe1d7954e134","kind":"section","labels":["tfpt-universalraum-kurzupdate-v1.6.8"],"line_end":142,"line_start":130,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Update_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Update_2026-09-15_v1.6.8.tex","status_markers_as_written":[],"summary_excerpt":"September 2026. Nur neue Befunde und Änderungen gegenüber v1.6.7. Vollständige Herleitungen und bewahrte Vorfassung stehen im Hauptdokument.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TFPT / Universalraum: Kurzupdate v1.6.8","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6663,"byte_start":5427,"id":"section:20e9e3f0db8a57a06547","kind":"subsection","labels":["die-neue-forschungssynthese-ist-nuxfctzlich-aber-nicht-fehlerfrei"],"line_end":169,"line_start":143,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Update_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Update_2026-09-15_v1.6.8.tex","status_markers_as_written":[],"summary_excerpt":"Alle 74 archivierten Quellenhashes stimmen. 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Die große Grundzustandsprüfung und die gesamte alte 822er-Suite wurden nicht erneut ausgeführt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die neue Forschungssynthese ist nützlich, aber nicht fehlerfrei","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10178,"byte_start":6663,"id":"section:11a525022da40d37663a","kind":"subsection","labels":["drei-parallele-fortschritte"],"line_end":257,"line_start":170,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Update_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Update_2026-09-15_v1.6.8.tex","status_markers_as_written":[],"summary_excerpt":"1. 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Das ist keine geschlossene Siebener-Lanczoskette und kein Polzentralwert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Noch nachgereicht: zwei zusätzliche wichtige Befunde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12225,"byte_start":11779,"id":"section:814ffd8d713a9a88bb6a","kind":"subsection","labels":["was-sich-nicht-geuxe4ndert-hat"],"line_end":297,"line_start":288,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Update_2026-09-15_v1.6.8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-common-process-20260915/tmp/pdfs/TFPT_Universalraum_Gemeinsamer_Prozess_Update_2026-09-15_v1.6.8.tex","status_markers_as_written":[],"summary_excerpt":"Die neuen N=2-/N=4-Zeugen ersetzen nicht den N=64-Grundzustand oder seinen geladenen Pol. 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Jetzt ist aber ein konkreter kleiner Instrumentenvertrag vorhanden, an dem sich der nächste Herkunftsnachweis entscheiden lässt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was sich nicht geändert hat","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic 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They do not identify a single complete physical [formula in source] D parent. All T1–T8 and TFPT.TOE.COMPLETE.01 remain . The finite regressions are checks of the proofs below, not substitutes for their quantifiers.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Round 4: proved subgates and binding residuals (2026-09-05)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":1080,"byte_start":475,"id":"section:83c8266dcbf844e64c6b","kind":"paragraph","labels":[],"line_end":22,"line_start":9,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:251318dfece8c4b10ffb","relation:73fa83975a5e3374f3f0","relation:cf1a9746eee150f210b1","relation:e6e941a4b793ac0e89d9"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tex-artefacts/toe_round4_proofs.tex","status_markers_as_written":[],"summary_excerpt":"SEAM.MMST.TELB.NORM.01. For the frozen [formula in source] , [formula in source] collar, the original remainder obeys [formula in source] The interval inputs are v1022 (TV and potential), v1025 (C1/C2a), and v1026_ telb_ round4_ closure.py (CF, DG, signed CROSS, validated Fourier core and all-volume aliases). This is not a proof of the historical sharper [formula in source] or Bound-B target [formula in source] . In ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T2: uniform relaxed TEL-B theorem.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4937,"byte_start":1080,"id":"section:e6789663704e1e5cda55","kind":"paragraph","labels":[],"line_end":113,"line_start":23,"numbered_or_version_tokens_as_written":["R4.1","R4.2"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tex-artefacts/toe_round4_proofs.tex","status_markers_as_written":[],"summary_excerpt":"Put [formula in source] , [formula in source] , [formula in source] , [formula in source] and let bars denote normalized means over [formula in source] . Define [formula in source] Partial fractions give [formula in source] , [formula in source] , [formula in source] , [formula in source] and [formula in source] , with [formula in source] . The identities used are the standard cotangent and polygamma identities https","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"CF: cell covariance and the periodic corner.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6110,"byte_start":4937,"id":"section:e383ef5a5e1f2ec28db8","kind":"paragraph","labels":[],"line_end":142,"line_start":114,"numbered_or_version_tokens_as_written":["R4.3","R4.4"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tex-artefacts/toe_round4_proofs.tex","status_markers_as_written":[],"summary_excerpt":"The csc-squared finite product identity and trigamma recurrence for the original remainder give, for [formula in source] , [formula in source] where [formula in source] and [formula in source] . 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Direct polynomial algebra gives [formula in source] The four constraint","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T7: local constraints and zero-mode removal.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":21941,"byte_start":19967,"id":"section:0c057e20a3b1322e45f5","kind":"paragraph","labels":[],"line_end":457,"line_start":423,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:010b462728ed4ccf30de","relation:434d4e70e841401abe7b","relation:814f95dd10fd4a42410d"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tex-artefacts/toe_round4_proofs.tex","status_markers_as_written":[],"summary_excerpt":"SEAM.MMST.ALG2.FRAME.01. v1030_ alg2_ sector_ frame.py does not restore the refuted Vandermonde implication. 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A compact synthesis of this contract's executed work packages (WP1–WP5d, both WP5d stages, [formula in source] the WP5e [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] and [formula in source] stages [formula in source] the three back-reaction milestones M1–M3) — the narrative arc from the [formula in source] clock to the [formula in source] bo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — CELEST.SEAM.01 (the celestial and twistor continuum route)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":861553,"byte_start":833944,"id":"section:2db6bd35ce5c578613f3","kind":"section","labels":[],"line_end":12469,"line_start":12137,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:0044eae7751b83cc89d6","relation:02382c1e76a2a73a637e","relation:0a5630c2d67a2180fc31","relation:1ad9e5669ff269fe136a","relation:340bbe382d507535417f","relation:39836ce3c1d8283e35f5","relation:41fcaedc4a942170d3dd","relation:42256793e4d2445c9bfd","relation:48a6ba2ebf4c41828f97","relation:4cdfc22cab01cd15e4e3","relation:4f38759681e5e6478761","relation:4fe1b422aa244e69a845","relation:579fe96a1394338c61a1","relation:59cca0ce18b9c765cb29","relation:5eb1d079a7f0d9dc6e9b","relation:6642c13d7378a9d81a14","relation:6d52dd1eae1c0aa93fa7","relation:6dc011ddbcc7796bbd87","relation:712116379ddb92e2855e","relation:71952c5bf473a640f67d","relation:720c495b8132b0a36735","relation:7f04901eae278dd97b6f","relation:817ab81969f9f23d8302","relation:82df5e1aeb52f52bbff3","relation:832e144fdf3cf8a37196","relation:92396bf5f36962fa4888","relation:96e07e20ec36a7442505","relation:976af482ea55c33621d4","relation:9aca79cd6bada4ccd0f6","relation:9d8c048ca2d74f0134c8","relation:9faa84ab4b64406eee5f","relation:a072619a37548e5ecf94","relation:a1b21cd05cae290c74a5","relation:a229c7ee2ce2eaf088aa","relation:a7a2fa798bcbd8f8a3ef","relation:a7cbce0547a6c291ccfc","relation:b8f2b48dc14aa9db3895","relation:b927ed19ae87c37e07b6","relation:b97a0cb0cb17a48c7af2","relation:bc3b50789bb477803a8c","relation:bd06c719ec7a1649beea","relation:bdaab0352040b32fd282","relation:d2e84706eaf66f4e0231","relation:d50c33232f50d954f5b5","relation:d8d819a87b8a556c21d9","relation:d9a1cd5123b569b730e6","relation:e03a094144887dbe1c8d","relation:ed5fb97d4c5427ab3786","relation:f0a7dc36e3916393bb2b","relation:f4b1e6d1de07f8e2c545","relation:fe89176c18618d34244f"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Typing. This is the actual bridge from compiler to physics — everything in CELEST.SEAM.01 is preparation for it. It is a research contract \\ (ledger row WOIT.OS.TWISTOR.01: Open, research contract), not a claim; nothing below asserts that the construction exists. The external programme it engages — Woit's Euclidean Twistor Unification ( arXiv:2104.05099) — is a named reference frame for the shape of the target, never","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — WOIT.OS.TWISTOR.01 (the Osterwalder–Schrader twistor bridge)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":870310,"byte_start":861553,"id":"section:2a4b108348409f980f6d","kind":"section","labels":[],"line_end":12570,"line_start":12470,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:02119f7a13007e10e378","relation:050a850037b59fc940d7","relation:0704744e1b98c458b1ec","relation:137e854218bcdef94b02","relation:16eb3f14ee6d87aad5e4","relation:56517fcc94e73d8455e1","relation:5b9fff6ef78432c28c9f","relation:71ecb88d448636969995","relation:98862ebfb97478f013f7","relation:d276c7a432b2eabd240a","relation:d27b86f44dc84921e32b","relation:d325ccab3b8cca702749","relation:e7edc7128c649188fd1d","relation:e9e7d81174cae9b69d88","relation:f06a65f846fa09ba3b8f","relation:f568a4a1a5213029fbf5"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row CCC.SEAM.CROSSOVER.01: Open, research contract), not a claim. It engages Penrose's Conformal Cyclic Cosmology (Tod, arXiv:1309.7248; Penrose–Meissner, arXiv:2503.24263) as a named reference frame for the shape of the target — never a confirmation in either direction. The cyclic reading of origin_theory stays \\ regardless of this contract's fate; nothing below asserts that CCC","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — CCC.SEAM.CROSSOVER.01 (the conformal-cyclic crossover on the seam geometry)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":874846,"byte_start":870310,"id":"section:fd8a259cd96f2b7b4df5","kind":"section","labels":[],"line_end":12632,"line_start":12571,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:0f70f25f65ccc2b6d4fa","relation:27f5500cb487cb40be06","relation:2d8105469b7dfe919c0d","relation:4f24ce63bec33f35498c","relation:65c4e043e9198b257fc3","relation:7d72f8b4bace4cff2274","relation:87ce8e7590b669a3f723","relation:cba55909dee81ba2d509","relation:e8b8161f4d15fde8043e","relation:edf15cfc953d9a3cbece"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mC","\\mE","\\mO","\\mX"],"summary_excerpt":"Typing. A standing discipline rule, in force immediately (ledger row DIMENSION.UPLIFT.FIREWALL.01); the uplift theorems it names are separate \\ contracts. It formalizes the core diagnosis of the 2026-08-27 external deep review: a chiral [formula in source] D seam net does not imply a local, interacting [formula in source] D quantum world. The corpus's strongest finite results are boundary/kinematic building blocks — ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Firewall Contract — DIMENSION.UPLIFT.FIREWALL.01 (no [formula in source] D theorem closes a [formula in source] D claim)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":878851,"byte_start":874846,"id":"section:73dd631de817637ce12d","kind":"section","labels":[],"line_end":12686,"line_start":12633,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:024f6d77c019c6e493c7","relation:0ab634505b8f1ed7dfa9","relation:0db0a23b34aadb8767c5","relation:19cb8ddf439e3b5d4f2c","relation:1e2457830144e7e0b927","relation:289805e33ed7a8df7926","relation:4471437d8bf5c8fe53a9","relation:506f62e185c01c50e326","relation:58bf5472b8a4e4449e48","relation:5de7c7ca05b6fbf08310","relation:60cabdd741eea41c9e1a","relation:6d7160f48e10fa6ac7e3","relation:6fc58a1cdd26d0292384","relation:7fbdbd047c41a7d29655","relation:9239704a5e06acae4298","relation:9a79fbd453cfdb624533","relation:a03fb8f6efc77f75442b","relation:ab0e4fffe336ffa6d2a0","relation:b7d465ad8a1966bf15ab","relation:d4373faeb1e7ca6e127b","relation:ee3978d4bbdaa2dd70a8","relation:f13e3f20dee41a291816","relation:f5a160c72c2df4df8655","relation:fba0455fcaf9e3144825"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row SEAM.BULK4D.RECON.01: Open, research contract), not a claim. It makes explicit the theorem that was previously only implicit between the SEAM.EQUIV.01 conclusion (a chiral [formula in source] boundary object) and the WOIT.OS.TWISTOR.01 goal statement (a Poincar\\'e-covariant, causal, chiral 4D theory): the missing seam [formula in source] bulk reconstruction is a theorem of it","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — SEAM.BULK4D.RECON.01 (from seam data to a 4D local quantum theory)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":881673,"byte_start":878851,"id":"section:f287beabd75c01fb7360","kind":"section","labels":[],"line_end":12725,"line_start":12687,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:5322725e0ec973a0df12","relation:733c18740e20cbc61193","relation:e4573fdd5df06fcf4175","relation:fb8278fa23d956c22e2d"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row BULK.PRIME_COMPLETION.01: Open, research contract), not a claim. Registered 2026-09-04 from the r644 audit harvest; it replaces the ``unique from seam data alone'' reading of SEAM.BULK4D.RECON.01/B7 by uniqueness in the category of seam-generated (prime) completions. Dimension typing ( DIMENSION.UPLIFT.FIREWALL.01 F2): the hypothesis is [formula in source] D free-fermion, the","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — BULK.PRIME_COMPLETION.01 (prime/seam-generated completions, no spectator)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":893246,"byte_start":881673,"id":"section:98cf6dab6e992992d2c9","kind":"section","labels":[],"line_end":12868,"line_start":12726,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:002d379bf468da6279c9","relation:0db33b09c8e8a2580c52","relation:10f875341caf2bfa70bb","relation:27b2fe913ec50d184438","relation:291e69a55bbaea7c9be1","relation:393573182292b2463dd4","relation:4c1af63095e194c977de","relation:5207091d339d7d338d9d","relation:56dff0c4ef376563466a","relation:77cbc27f82e3cf1ce93b","relation:7efa7973944a94515c19","relation:9513fd7bb30c6c5c82c7","relation:9969835430b6ece19213","relation:9bede06acf4be8c59c04","relation:a8374e7a46df2bbde2cf","relation:b49ed6a16b3c17da86d4","relation:d107ca24608c42ce349f","relation:d23ef6a9d9826c1d47b8","relation:d8ed65ecc30d25c8ef20","relation:e623ca16afb389280261","relation:e937182e0f4834a76b7c","relation:f4c56a18e4d11a25220c"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"tocsectionResearch Contracts: DYN.MARKOV.EMBED.01 / DYN.UNITARY.DILATION.01","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contracts — DYN.MARKOV.EMBED.01 / DYN.UNITARY.DILATION.01 (the three meanings of ``dynamics'')","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":899756,"byte_start":893246,"id":"section:c01350c4771209b4c9e1","kind":"section","labels":[],"line_end":12959,"line_start":12869,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:244ba105c4de2dbcaeca","relation:4c516cd2eacc4fcdb9bd","relation:4d6553d0b64d25a6b309","relation:4ed3e8c4a552a9fbfc22","relation:6a96617c81b9a807280e","relation:7fd0ca58a7552454217e","relation:a2016c6b2026c89e0c24","relation:bf5cfde5020fdc341cb2","relation:eaa7fb97beb32d1384eb"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row QFT4D.OS.RECON.01: Open, research contract), not a claim. This is step (3) of the DIMENSION.UPLIFT.FIREWALL.01 route ordering: the nonperturbative 4D existence statement that no perturbative or seam-level result can substitute for.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — QFT4D.OS.RECON.01 (the genuine 4D Euclidean lattice package)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":904927,"byte_start":899756,"id":"section:11cf2220db595f7b5339","kind":"section","labels":[],"line_end":13028,"line_start":12960,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:40a5854ca73ceee6537a","relation:730540c9449eddf9fdc0","relation:74364f30b4b2840505da","relation:77b354f07a96ea058486","relation:857c72214d9db8c90426","relation:a6bfd015abe37ecec12a","relation:c89cf2aad73bef60579e","relation:fbc30945f27e8b4956d3","relation:fcd636662f904fdd015f"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row CHIRAL4D.NOMIRROR.01: Open, research contract), not a claim. Step (4) of the firewall route ordering: chirality and mirror decoupling must be proven in the same 4D model that QFT4D.OS.RECON.01 constructs — the seam's [formula in source] and Chern/inflow structure are a boundary- anomaly signal, not yet 4D matter.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — CHIRAL4D.NOMIRROR.01 (the chiral 4D lattice matter theorem)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":908877,"byte_start":904927,"id":"section:6ce553746490f88b0988","kind":"section","labels":[],"line_end":13091,"line_start":13029,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:05f783db6e529e64f4fb","relation:0b74f4edc44fcfbd59e3","relation:35ddc238a7ae1d903e61","relation:3a8c853de4d4b882bd05","relation:91350926d50e846510c2","relation:bf623970dde127c5c7aa","relation:e578ef8bbac7fd952822"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["[N]","\\mC","\\mO"],"summary_excerpt":"Typing. A candidate \\ (ledger row CHIRAL4D.MIRROR.DET16.01), registered 2026-08-29 from review wave 5. ( v1002_ spin10_ mirror_ projector.py.) Content. Exact finite-cluster gapping on the full chiral [formula in source] Fock space via the number-violating determinant vertex, as executed above. Open. Dynamical gauge fields, domain-wall geometry, and a [formula in source] D volume theorem — this is not a [formula in so","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — CHIRAL4D.MIRROR.DET16.01 (DET16 rank-one projector, finite cluster)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":912641,"byte_start":908877,"id":"section:136a1e576865c1424f29","kind":"section","labels":[],"line_end":13141,"line_start":13092,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:0afdd94d91a8257bc581","relation:11e4816460293a162f04","relation:1259f964cadd5ceea3f2","relation:167091fa03be24654ffe","relation:189fc741278efa513ce7","relation:1996cacff1e12b93978c","relation:204b3aef0f2ab1946aed","relation:328c4df033a536c56127","relation:4800a8ce2ed271e5e8f1","relation:5f085b1143b393cfbaf6","relation:64ee90f52849cc2a300d","relation:6a8a614c04dcecc93896","relation:719d1b33686a01984a35","relation:7204544e0fde4575fe40","relation:770603870cd3a1678fb2","relation:78ff73dde8695da4acbe","relation:8e1a242e5a57c78ed688","relation:9369882f71a5d8b34223","relation:9ff86f4a3851bd3d6673","relation:ac3632cc82225bb9800a","relation:be7353ae0f54d358830d","relation:c85d1a382367254a3265","relation:cf96e1eae2a88e4cc64a","relation:d11bac328d156935dca1","relation:d92cdf3ed12e3f0cb88f","relation:e31962768b21deab0c9c","relation:f7a2f2283feacf599af1"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mC"],"summary_excerpt":"Typing. A standing discipline rule, in force immediately (ledger row GRAV.NONCIRCULAR.01), with an audit census at registration. Bisognano–Wichmann (BW) is a theorem within an already-local, Poincar\\'e-covariant QFT with a suitable vacuum: the modular flow of a wedge algebra acts as the boost. It is not a device that generates Lorentz spacetime from an arbitrary modular flow — there exist Poincar\\'e-covariant nets vi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Firewall Contract — GRAV.NONCIRCULAR.01 (the Bisognano–Wichmann direction discipline)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":915635,"byte_start":912641,"id":"section:e37df96de6e66060644b","kind":"section","labels":[],"line_end":13187,"line_start":13142,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:2b468f1dd67def853af2","relation:59dccf8ea35e1b0b2c59","relation:a8a13899b8affabfa792"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"Typing. A research contract (ledger row OBS.TRANSDUCTION.01); the principle is machine-checked on the minimal model at exploration level, the per-bundle transduction proofs are . It elevates the S15 typing rule to a named principle: [formula in source] Without the middle arrow, neither a non-observation falsifies nor an observation confirms. The minimal model is machine-checked in experiments/ theory-contracts/ fo01_","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — OBS.TRANSDUCTION.01 (the transduction principle: eigenvalue, projection, coupling)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":919213,"byte_start":915635,"id":"section:66ed6033e537375adb6f","kind":"section","labels":[],"line_end":13235,"line_start":13188,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:0ab9975f7e0f0ba9d08f","relation:474a5c2f5aba4f209038","relation:68025d2bbed9f55730c8","relation:72001080829dbd695275","relation:98c6c40162400d7d965e","relation:9c7d62401cef936a7b72","relation:b21fffc456840b398488","relation:e1ebdf8b7c4ca374f55a","relation:e25a9d93fb2e31dd2c30","relation:ed3760698dcde6961432","relation:fb0692dc9c72ac8ad780"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row PRED.JOINTLIKELIHOOD.01: Open, statistics-construction contract), not a claim. The [formula in source] individually matched values all descend from the same few atoms ( [formula in source] , [formula in source] , [formula in source] , [formula in source] ) and are therefore statistically correlated: counting hits overstates independent evidence. The evidence is to be reorgani","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — PRED.JOINTLIKELIHOOD.01 (from hit-counting to overdetermined relations)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":927211,"byte_start":919213,"id":"section:39807bac57329dd11bcf","kind":"section","labels":[],"line_end":13342,"line_start":13236,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:080db2ff328a8046c0d4","relation:09cd71b4fdc72e5309f8","relation:22de94b4cb224ed98755","relation:25a6632edace59a27578","relation:2612bb2402dabd88acb0","relation:28f081e333812e8cc9bf","relation:324b959a0f76dd94d9d0","relation:4424c51d1d8f3b8264a0","relation:6a272529929680e3ad5f","relation:76d179ae2e46663f68a6","relation:7703b42d07343b9a0e75","relation:775f24424146a48eed7e","relation:7da2a70eaa9e9d9fbed7","relation:89dbed709e54f861f42f","relation:909025abbf1df65df5cc","relation:940ec7e0df9689f14d00","relation:9a05871151424772e8f5","relation:beba797a7eeea291679f","relation:c7c8879c84e85fe95b98","relation:d84fd8be174868167d53","relation:df0deb09a64ca25c1561","relation:e251dbead7706667d109","relation:e98a30d18bd8d3a0ed5e","relation:efe4d952f11bed12012e"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Typing. A programme section (registered 2026-08-27 from the external bird's-eye review), not a claim: it organizes the existing 4D contracts and the four new ones below into one route and moves no marker. The organizing observation: TFPT is probably not missing twenty independent formulas; it is missing one mathematical growth principle that unfolds the discrete structure into a local, unitary, reflection-positive 4D","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Programme — the TFPT4D master route (one 4D transfer object instead of twenty formulas)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":929944,"byte_start":927211,"id":"section:ccf4833d317bae46eaf7","kind":"section","labels":[],"line_end":13377,"line_start":13343,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:3901c918b5a855c06a7d","relation:8dbe85948d664c24b94d"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mC","\\mO"],"summary_excerpt":"Typing. A conditional identity \\ (ledger row DIMENSION.SELECTOR.4D.01), machine-checked in v975_dimension_selector_4d.py ( [formula in source] , sympy-exact). The [formula in source] structure of the compiler must not be read as a proof of four spacetime dimensions ( DIMENSION.UPLIFT.FIREWALL.01); what is checkable is a selector theorem under a named axiom set. Statement. Under A1 [formula in source] (propagating loc","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verified Selector — DIMENSION.SELECTOR.4D.01 (why [formula in source] , conditionally)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":942002,"byte_start":929944,"id":"section:c9d9fdab1f8620914792","kind":"section","labels":[],"line_end":13529,"line_start":13378,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:0456ad0cea373982f112","relation:10fce1d6d146a2c910f9","relation:12f85952fad364246cf7","relation:1d75775d371ec9296ba0","relation:1db0dbbae82e548ab458","relation:2632f044623b55eb288e","relation:2d735d05014d3f7f5315","relation:2ecc112965cfe7785baa","relation:3c4d31d140bd7e31e3f0","relation:3c7b70eb8863c07ca59f","relation:540f0eae5b4a43cd0edd","relation:5cc28084416bb194b683","relation:628be4b5717e0e9b9a03","relation:62bcc7fbd33c90daabe9","relation:6c5ad35473149aafc991","relation:769e9e3f2fff5ec942d9","relation:7bac5c09c0811f5db846","relation:7cbf4e35529e1f36e0e1","relation:7ecac44b5f5bd858b48e","relation:7ff9c69a67b7d92a38a6","relation:87556a8d839f8d5fc53f","relation:88833025632faee629fe","relation:89afcd704e4587e93933","relation:8b8be24b15478a3b17fc","relation:90e6abfca9a934c85e22","relation:9c06b2aa0eabb3a0e7a1","relation:aabb0c58cc3d00724666","relation:abcf0a71592f4f70c3e4","relation:afd5676a9bab91f23e14","relation:b0a4b00dc73fa5013e92","relation:b180553055a6b0c12387","relation:cb9742c130f1d7ff0b67","relation:d001beed0d8db45e615c","relation:d152b076b5f87b628104","relation:d3fb79df7a8fa1b067bb","relation:dccc245f15eef90fca58","relation:dfffa3d0184c35179ceb","relation:ebdd4f919e1713433fe0"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row SEAM.SIMPLECURRENT.GENERATOR.01), not a claim. Context. The seam coverage carve ( v973_seam_route_narrowing.py) shows the [formula in source] fermion-bilinear half of the seam target is covered by the cited scaling-limit theorem; the named residual is N1 (the [formula in source] /GSO extension [formula in source] as a net statement — the 128 spinor currents are not bilinears)","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — SEAM.SIMPLECURRENT.GENERATOR.01 (one generator instead of 128 currents)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":948199,"byte_start":942002,"id":"section:0a835f45f6d36c79eb46","kind":"section","labels":[],"line_end":13615,"line_start":13530,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:162ed9cee8f2431f1dc2","relation:1ad53b10cc77ff722330","relation:1b50b903c6dec9fa7a7e","relation:6b190c714fdeed82754b","relation:745415d8337570ab2c8b","relation:8791dc141bab0ed99487","relation:a4143107c11383013ba2","relation:caa9792c06264b8fc1fc","relation:de827289a5e01118dcad","relation:eb077f916cdb33fe51ad","relation:fb220c52a3a0557462d7"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row TFPT4D.LATTICE.ACTION.01); route step (2) of the DIMENSION.UPLIFT.FIREWALL.01 ordering made concrete — the single object on which nearly all open 4D questions become simultaneously testable. Demand. Exhibit one fully explicit finite family of 4D Euclidean lattice theories [formula in source] where [formula in source] are the fundamental holonomies (TFPT fixes representation c","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — TFPT4D.LATTICE.ACTION.01 (the explicit finite 4D lattice action and its seven finite gates)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":951710,"byte_start":948199,"id":"section:ce12b2c64758813c083c","kind":"section","labels":[],"line_end":13662,"line_start":13616,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:04e96a16d58ece2328e5","relation:7bd9716a32e94663b2a5","relation:7f8b4a7a96be27a7c4be","relation:c2e27e899a355b2a90bf","relation:e8974b27bd905e8b3130","relation:ed6c3f1b9b842f57547c","relation:ef528aa427cb94eb4005","relation:f7d6380e118b6138df40"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"Typing. A research hypothesis contract \\ (ledger row SEAM.DETLINE.UNIFICATION.01) — a precise conjecture, not a result. Observation. Three separately open structures may be projections of one geometric object: (1) the seam extension is described by a Q-system/simple current ( SEAM.SIMPLECURRENT.GENERATOR.01); (2) the chiral fermion measure lives on a determinant line ( CHIRAL4D.NOMIRROR.01 demand C1); (3) anomalies a","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — SEAM.DETLINE.UNIFICATION.01 (the determinant-line unification hypothesis)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":954446,"byte_start":951710,"id":"section:1fc598d7241c419069ab","kind":"section","labels":[],"line_end":13696,"line_start":13663,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:1144ae7d29c5aa42c4c4","relation:4cc75d535235c286fb2a","relation:679e0153d0b152475ff8","relation:7c45dab0c6cda9fcc767","relation:8cfdb4b3fe051e04ffd9","relation:8d2c78fa8e10a713f6cc","relation:949503505cbfab66d39a","relation:9ddc4503a14dcf50cbda","relation:d72e99c64fcb39213d83","relation:ee7eec94f5727a97f75b","relation:f98a285123c881437da1"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mC","\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row FTRANSFER.GENERATING.01); the constructive successor named by the FR.TRANSFER.01 typing guard. The four continuous-transfer interfaces ( [formula in source] : source masses [formula in source] pole, v183; [formula in source] : CP source [formula in source] , v169/ v184; [formula in source] : [formula in source] , v185; [formula in source] : [formula in source] , v164) are cur","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — FTRANSFER.GENERATING.01 (four transfer bridges from one generating functional)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":958981,"byte_start":954446,"id":"section:d5ab0f60059af6a8fe27","kind":"section","labels":[],"line_end":13755,"line_start":13697,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:07ec06faa9e8b06024d5","relation:3addf6766656e92b67da","relation:6900c073f2f843c32639","relation:9c7a1c22448b1ede84ac","relation:ad931696b904e0088c5b","relation:dfeced0d5d69684119a2","relation:eb9ec80934e9837743fb","relation:f02e15916e27487e000f"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row GAUGE.DETLINE.FIXPOINT.01), registered 2026-08-28 from review wave 3. Demand. All three gauge couplings ( [formula in source] / equivalently [formula in source] , [formula in source] , [formula in source] ) arise as stationary points of one nonabelian zeta-det / inflow functional on the determinant line — the nonabelian upgrade of the [formula in source] face ALPHA.QUILLEN.EX","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — GAUGE.DETLINE.FIXPOINT.01 (all three gauge couplings from one zeta-det functional)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":963773,"byte_start":958981,"id":"section:e4bb9a238c9f340ff5d1","kind":"section","labels":[],"line_end":13823,"line_start":13756,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:01980111511a31504214","relation:09289a083e2dcb6cd40b","relation:261d9943691dea316fb2","relation:450d24a5fbb5c9570f97","relation:62b46d64b7738d1086cb","relation:78eebe1e43020cbcd03c","relation:7dd550e02022aaa93f79","relation:7f60dfc7816a889a1fb2","relation:89dabc0bab9e27bd1eef","relation:99bace174201cacda657","relation:a7ac5fa8897df25958d3","relation:c9674f923352c531015d","relation:d4f2046df814492852aa"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row GRAV.SPIN2.EMERGENCE.01), registered 2026-08-28 from review wave 3. Demand. From the same spectral determinant that carries the gauge fixpoints, a massless transversal spin-2 pole with two helicities, universal [formula in source] coupling, diffeomorphism Ward identities, and positive Hessian / reflection-positive transfer. Relation. The entanglement-equilibrium Einstein equa","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — GRAV.SPIN2.EMERGENCE.01 (massless transversal spin-2 from the same spectral determinant)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":968756,"byte_start":963773,"id":"section:d8ed1f80544bebc4760c","kind":"section","labels":[],"line_end":13892,"line_start":13824,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:12d4d8a4583a9f229b65","relation:1c095d5f98189969a691","relation:3a274e42e2b921e3ff0c","relation:77ad36c5e846bf490caa","relation:7e56cce06b708d05d507","relation:8de47049571a3eccc05d","relation:9a2df2982dff51616a09","relation:b111c09085b9826cd790","relation:f254085bbbb20b017222"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mC","\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row FTRANSFER.SK.RHO0.01), registered 2026-08-28 from review wave 3; mechanism executed 2026-08-29. Demand. Cosmological transfers ( [formula in source] , [formula in source] , and any nonequilibrium 4D readout) need the pair [formula in source] , not [formula in source] alone — the Euclidean-cap / KMS initial state. Typed candidate. The [formula in source] saddle [formula in sou","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — FTRANSFER.SK.RHO0.01 (Schwinger–Keldysh completion: cosmological transfers need [formula in source] )","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":972125,"byte_start":968756,"id":"section:2465208e294a3178e3e1","kind":"section","labels":[],"line_end":13935,"line_start":13893,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:0c76eff266966406d64d","relation:2d1dbb1dc71797ea8154","relation:4b1bdc64d3214803ff9f","relation:5128ecbc09776d2465cd","relation:875344bcca032e147069","relation:9ffb960b81cd2f644225","relation:a6fe92f1d7979c8e1a40","relation:ced5c6e5408d5c567eb2"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row SEAM.MMST.TYPEIII.CHARGED.01), registered 2026-08-29 from review wave 5. Demand. One scaling-limit theorem [formula in source] strongly on the finite-energy core [formula in source] crossed-product continuity, from which [formula in source] , [formula in source] , type III [formula in source] , unique rotational KMS, unique conditional expectation, deck equidistribution and m","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — SEAM.MMST.TYPEIII.CHARGED.01 (one scaling-limit theorem)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":980911,"byte_start":972125,"id":"section:ace8f6c66089bf3029b9","kind":"subsection","labels":[],"line_end":14102,"line_start":13936,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:08b8a8712a4d020829b7","relation:0a956cb928745b6214d5","relation:1033cc5415411f8615d3","relation:11218dce3874b4d9f9aa","relation:4a98212999209a697550","relation:67e8dab89dddcdbf626c","relation:72a52d8ec771be895311","relation:7fffdfca8fa0e91a34ec","relation:b70ea976ddd9effff82d","relation:daa46fe6d2bc82777321","relation:dc7b2d1d65f249f9b73c","relation:f6b13e90e833b083639b","relation:f9ca198e97573c7cb416"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"The residual TEL-B-EXTERNAL is restated below. The earlier scalar dyadic increment [formula in source] with [formula in source] sufficient for [formula in source] is superseded — [formula in source] was measured [formula in source] (r645) but is no longer the route. Numerically closed ( [formula in source] ; conditional analytic [formula in source] with [formula in source] ); round 3 closed C1, C2a and the interval-T","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TEL-B reduction (2026-09-04)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":989480,"byte_start":980911,"id":"section:b9be0eca5eee141eabc7","kind":"section","labels":[],"line_end":14237,"line_start":14103,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:0567bdf39080a17eed62","relation:05d1004564725337b139","relation:05f42253cdca72d888b8","relation:07b600af276ed5244e41","relation:0c9cba9d6c8d64aaa5fa","relation:0ee4bcdd9efb2511c3f4","relation:12c4eecc6cecefcdc5d9","relation:144e7995d3697a89198e","relation:1ede48e354bcccd9e898","relation:2107e045d3b48d84f381","relation:2d580083961c70644d4d","relation:369f980df3db2a20b51c","relation:3ee82d6ec578fdaaed44","relation:4a4fee4e3235d829b8ca","relation:544d7cafec5480a75d29","relation:5667a2d0719f9b04afeb","relation:60ea4eb627d3cd56ec0b","relation:67c565087c2c65109e3f","relation:73eb191bb663f72dc7b8","relation:7581ed6ec558784170ca","relation:797e01b9c8dafa75b32d","relation:89b0d266a2b6b9e95479","relation:8eac6a65cfd4ff2f881f","relation:8ff870530040c7f276ce","relation:93358d95e87ae40061ce","relation:a40547aaa5d2675c75d9","relation:ae55991a4521cf94f18a","relation:bceb5e976e4660c56ee9","relation:c43337f27ac447058ddf","relation:c480f216db5fafec59af","relation:cf7937610d9759b5f007","relation:d46d3e2681a0dbba5ad6","relation:dc565502006d5291593c","relation:de94a13130f2597b1173","relation:eb3913f5e78098c55a2a","relation:ebd5a0bdb27b90d835c9","relation:ec21a283cc8d844e2d17","relation:ec9e8af0fb839f35b832","relation:f3dc2a0521cab9fe2b4b","relation:fbffa972b5b8b0475aec"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row TFPT.TOE.COMPLETE.01), registered 2026-08-29 from review wave 4. This row names the AND of eight gates; it does not close any of them and it does not upgrade a marker. Dual rest: the compiler residual [formula in source] sits beside [formula in source] ; this contract is the named AND, not a closure of either.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — TFPT.TOE.COMPLETE.01 (the named AND of eight completeness gates)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":990755,"byte_start":989480,"id":"section:12feef6a28eadbb9a373","kind":"section","labels":[],"line_end":14255,"line_start":14238,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:3d9d0c12fce4c31fcdad","relation:67e65bff49c621dd6a93","relation:775d64fc895f6f51f7d1","relation:7927af4ba8613bb5c4c2","relation:7eb9c8cec6a752be4b81","relation:7edbf279660eb6b819ae","relation:8dba7dc45ef367748af4","relation:d498049b5fc0d88544be","relation:ea395bd84bdae48da4fa"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mC","\\mO"],"summary_excerpt":"Typing. A candidate \\ (ledger row FLAV.NUSCALE.06); mechanism [formula in source] the [formula in source] -to-flavor operator . No seesaw closure; FLAV.NUSCALE.05 unmoved. ( v1001_ nu_ pentagon_ chain.py.)","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — FLAV.NUSCALE.06 (pentagon-class misalignment candidate)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":993831,"byte_start":990755,"id":"section:11b8cd7b32010b22189d","kind":"section","labels":[],"line_end":14301,"line_start":14256,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:004a9df5e5ccc1c6c53e","relation:76acadc318d25c51218a","relation:bd4143ae61f062b188fa","relation:c39918ceb8b3fefae641","relation:c57a395bab3acbddb639","relation:faf1b7d4bb5f888f7307"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mE","\\mO","\\mX"],"summary_excerpt":"Typing. A research contract \\ (ledger row FLAV.NU.TEXTURE.MECHANISM.01), registered 2026-08-29 from review wave 5. ( v1003_ nu_ structural_ nulls.py.) Executed content. Charged-sector data [formula in source] , [formula in source] (coset min-norms all [formula in source] ) . Schur-texture NULL : all [formula in source] preregistered [formula in source] combinations fail; D4 reflection forces [formula in source] ; hie","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — FLAV.NU.TEXTURE.MECHANISM.01 (both structural nulls as binding constraints)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":999519,"byte_start":993831,"id":"section:2cbe5d1807cd76c5e04d","kind":"section","labels":[],"line_end":14380,"line_start":14302,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:42ba7d977c83c6a98ab8","relation:459ee1d346f686eebff6","relation:6085f66c68d301121133","relation:66aa067ce5925a45b030","relation:757664021cf140001a60","relation:a131b076f4e48c8ed83c","relation:a3e11005894ff748c1b0","relation:a6b8cd8cd7d13f09abd0","relation:abc2c82c8696dd6e0840","relation:bd0f2736cf22948b2d2b","relation:beec31e2e761fbc33fba","relation:c00b93fb6b64b862e226","relation:d5926e37a22cda84079c","relation:d9c2a3c6b791e23b9963","relation:e53390dfb857f06f694f","relation:ec7e056e0e816107a876","relation:f1dcef2b1189e6d4f125"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row SEAM.MILNOR.LOCALRING.01), registered 2026-08-30 from review wave 6. ( v1004_ milnor_ frobenius_ gray.py.) Demand. A canonical identification between the raw seam collar / [formula in source] transition bus and the reduced Milnor algebra [formula in source] preserving simultaneously the dual-number action, the Frobenius pairing, the Gray torsor, the deck action and CP. Accept","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — SEAM.MILNOR.LOCALRING.01 (canonical identification of the seam collar with the reduced Milnor algebra)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":1000757,"byte_start":999519,"id":"section:b83de37eb381c3c07bbe","kind":"section","labels":[],"line_end":14396,"line_start":14381,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:7967e8bd01e97fa5b795","relation:98ebe4242f24cb15d830"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row GRAV.WEINBERG.WITTEN.01), registered 2026-08-30 from review wave 6. Child of TOE gate T7; cross-link GRAV.SPIN2.EMERGENCE.01 (listed here, not back — that would cycle). Demand. 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The minimal additive refinement is the eight-bit symplectic space [formula in source] , with four-dimensional kernel [formula in source] . There are 64 quadratic-form-preserving sections, four compatible with the family marking; the deck exchanges complementary sections. The full target on [formula in source] has charge shifts, cocycle and [fo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. What the compiler, Clock and lattice audits actually decide","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":11486,"byte_start":9986,"id":"section:85e15aaab937d77dc57c","kind":"subsection","labels":[],"line_end":215,"line_start":193,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tex-artefacts/toe_research_20260909.tex","status_markers_as_written":[],"summary_excerpt":"The integer charged CAR field is substantial progress beyond neutral determinants, but is not yet the half-charged [formula in source] spin field. 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They extend the positive matter/constraint constructions to an interacting scalar/charge model, local charge transport, exact scalar elimination and controlled signed history sums. Additional off-shell fields, sel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Non-RH research through Round 27: a full-reference control theorem","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2158,"byte_start":957,"id":"section:f7f91042aebe0550677a","kind":"paragraph","labels":[],"line_end":35,"line_start":18,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tex-artefacts/toe_round27_full_reference.tex","status_markers_as_written":[],"summary_excerpt":"The geometry branch realizes the proposed elliptic boundary data but exposes its unselected markings and symmetry enlargement; it supplies neither physical dimension selection nor a selected chiral measure. The local positive and constraint-domain branches distinguish the separated completion from the first-vertex-preserving completion, including their different off-shell terms and form domains. The charge branch ret","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"What the intermediate contracts establish.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3392,"byte_start":2158,"id":"section:c392c9bdc8fbf53f4d83","kind":"paragraph","labels":[],"line_end":65,"line_start":36,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tex-artefacts/toe_round27_full_reference.tex","status_markers_as_written":[],"summary_excerpt":"Fix [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] , a time step [formula in source] , [formula in source] and [formula in source] . Every site's charge remains in [formula in source] . The original signed hopping and potential are [formula in source] The [formula in source] directed elementary shifts include their original phases. Thus [formula in source] ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The common reference.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5828,"byte_start":3392,"id":"section:f6a4452580c2f7e16d7b","kind":"paragraph","labels":["eq:r27-reference"],"line_end":113,"line_start":66,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tex-artefacts/toe_round27_full_reference.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the sum of moduli before cancellation, resolved into elementary hopping words, initial charge profiles and scalar integrals. Then Every elementary hop changes the complete profile, hence [formula in source] . Scalar spectral Jensen gives [formula in source] . Pinching [formula in source] into its charge blocks [formula in source] contracts the Schatten [formula in source] norm, so [formula ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Full-reference theorem and proof.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":7766,"byte_start":5828,"id":"section:972f686fdb36adfb7228","kind":"paragraph","labels":[],"line_end":154,"line_start":114,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tex-artefacts/toe_round27_full_reference.tex","status_markers_as_written":[],"summary_excerpt":"The exact Gram inverse satisfies [formula in source] , so [formula in source] , [formula in source] . On the neutral sector define [formula in source] Let [formula in source] bound all charge coordinates at sampled slice boundaries and [formula in source] bound total elementary hopping order. If [formula in source] , [formula in source] For the first estimate, insert the boundary projection [formula in source] in the","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Three explicit error budgets.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9744,"byte_start":7766,"id":"section:1c0230b25e478f83c79c","kind":"paragraph","labels":[],"line_end":187,"line_start":155,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:0d2deae5cbb96068aa49","relation:5e3aff88083935c8e1dd"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tex-artefacts/toe_round27_full_reference.tex","status_markers_as_written":[],"summary_excerpt":"The planner uses integers and fractions, with upward roots, [formula in source] , [formula in source] and [formula in source] for [formula in source] . At [formula in source] , full memory and a [formula in source] omission target, the published Round 26 [formula in source] improve to [formula in source] . Applying the same first-passing-integer search to the old inequalities gives [formula in source] : the gain is n","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproducible certificates and actual remaining cost.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10461,"byte_start":9744,"id":"section:717dd035381c3c6c8617","kind":"paragraph","labels":[],"line_end":198,"line_start":188,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tex-artefacts/toe_round27_full_reference.tex","status_markers_as_written":[],"summary_excerpt":"For overlapping original hops [formula in source] and [formula in source] , the word [formula in source] closes with phase [formula in source] because [formula in source] . Its actual hopping matrix-element product is [formula in source] for [formula in source] . Diagonal configuration rephasing telescopes around this loop and cannot remove it. This excludes that particular stoquastic rephasing, not all bases, regrou","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The original sign obstruction and physical frontier remain.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4944,"byte_start":0,"id":"section:5c02cd7e8c43ae65228b","kind":"frontmatter","labels":[],"line_end":117,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8.tex","status_markers_as_written":[],"summary_excerpt":"arrows.meta,positioning,calc,fit,backgrounds,shapes.geometric,shapes.misc,decorations.pathmorphing,decorations.pathreplacing,patterns,angles,quotes,matrix =3.5em","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"-1.2cm TFPT — Architecture and the [formula in source] Compiler\\\\[2mm] The two axioms [formula in source] , the derivation map, and the Coxeter–cyclotomic [formula in source] construction","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7187,"byte_start":4944,"id":"section:9ca5a033bd4f9f33b3aa","kind":"part","labels":[],"line_end":146,"line_start":118,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8.tex","status_markers_as_written":["[C]","\\mC","\\mE","\\mO"],"summary_excerpt":"This document develops the architecture layer of TFPT: the two axioms, the derivation map, and the explicit [formula in source] construction. 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We write [formula in source] for the root-lattice direct sum (used in the glue/lattice statements: discriminant forms, [formula in source] glue, [formula in source] as an even unimodular lattice), and [formula in source] for the group/representation branching (used for subalgebra embeddings and [formula in source] -rep decompositions). 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Proof of uniqueness. Direct evaluation gives [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] ; so [formula in source] is the only root in [formula in source] . For [formula in source] the forward difference is ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[formula in source] as the Pascal closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":109554,"byte_start":108713,"id":"section:38538ebfe54ea1f0dd1c","kind":"subsection","labels":[],"line_end":1796,"line_start":1781,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8"],"relation_ids":["relation:9ea9a8b95a673fde6fc0"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"With [formula in source] , the quadratic hypercharge trace on one family is [formula in source] , and it generates the whole integer chain: The flavor budget, the [formula in source] budget, the [formula in source] count and the second seam defect all hang on the second hypercharge moment [formula in source] . \\ Round-22 sharpening: the moment itself is one symbolic identity, [formula in source] — the Coxeter number ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"One master moment generates [formula in source] , [formula in source] , [formula in source] , [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":110167,"byte_start":109554,"id":"section:917a1cfd95ec48bd78c1","kind":"subsection","labels":[],"line_end":1808,"line_start":1797,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"with [formula in source] and [formula in source] . . 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The whole content is consolidated and verified in the standalone companion note ``The Even Carrier Code and the [formula in source] Coxeter Compiler.'' 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Writing [formula in source] , So [formula in source] is the exact leading value (the inverse of the [formula in source] family/gauge compression that sits in the seed [formula in source] , so [formula in source] ), and the deviation is precisely the small topological seed correction [formula in source] , i.e.\\ [formula in source] . Gravity","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Einstein normaliser as a corrected tree value","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":272004,"byte_start":267761,"id":"section:ec8585de3650da47eb97","kind":"section","labels":[],"line_end":4282,"line_start":4211,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8"],"relation_ids":["relation:02a6c2ae6fe3411ebfd4","relation:1d7308a09354fede9a12"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Machine checks for this section: v60_ lambda_ metrology_ branch.py","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[formula in source] -anchored metrology closure, and two anchors","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":273462,"byte_start":272004,"id":"section:553342d17f28cf01ed99","kind":"section","labels":[],"line_end":4308,"line_start":4283,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8"],"relation_ids":["relation:33a0133c7c1ebad9bab9","relation:380dd222f505658ebf69","relation:4bc30ed110c6970088c8"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mC"],"summary_excerpt":"Machine checks for this section: v6_ bootstrap.py v14_ carrier_ uniqueness.py","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The landscape: [formula in source] is overdetermined","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":273910,"byte_start":273462,"id":"section:de8c36913e171d46bc64","kind":"section","labels":["sec:e8"],"line_end":4317,"line_start":4309,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8"],"relation_ids":["relation:9f10d534bfe48620b355","relation:c7bba8127ab8af4dba57","relation:d71641faf19473309d12"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8.tex","status_markers_as_written":[],"summary_excerpt":"In the series [formula in source] is a downstream scale grammar, not a primitive cause: the boundary kernel fixes [formula in source] , the carrier rank, families and admissibility without [formula in source] upstream. Three levels.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The [formula in source] carrier atlas — stated unambiguously","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":275076,"byte_start":273910,"id":"section:9cd02b2b0f5af263291c","kind":"subsection","labels":[],"line_end":4334,"line_start":4318,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"Coxeter/gauge typing of the lcm–gcd pair. Writing [formula in source] and [formula in source] , the relations become [formula in source] and [formula in source] : the local SM algebra is the gcd of the Coxeter double-period and the [formula in source] rank-occupancy, and the [formula in source] root count is their lcm. Likewise the EW exponent reads [formula in source] (Coxeter principal part plus a rank singlet). \\ ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Level 1 — original [formula in source] data of the series ( )","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":275610,"byte_start":275076,"id":"section:9dd5fb9305edd0b08bff","kind":"subsection","labels":[],"line_end":4343,"line_start":4335,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"with [formula in source] the number of non-empty occupation words of the [formula in source] carrier code.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Level 2 — new exact counting identities ( )","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":280141,"byte_start":275610,"id":"section:5e1509353325b787484d","kind":"subsection","labels":[],"line_end":4404,"line_start":4344,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8"],"relation_ids":["relation:059054515ef9ffaf93ca","relation:3b96b61a3b6647dac336","relation:5580b9042aefc88419c9","relation:57e495bc7a4c52dacd8b","relation:834207034ccf83737b88","relation:add53eba2a7b8678f6cc","relation:beae3d022cd541505820","relation:e0b1126a6828ab823c1f"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"Identify [formula in source] with the even-weight binary code on five bits. A transition [formula in source] has flip [formula in source] , even and nonempty, so [formula in source] ; per state there are [formula in source] flips, giving and the [formula in source] undirected flips match the [formula in source] [formula in source] root pairs ( , counting). This makes the atlas conjecture testable: a genuine root map ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Level 2.5 — the even-flip transition atlas (a falsifiable program)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":281523,"byte_start":280141,"id":"section:911b129fc3e3dd46c69d","kind":"subsection","labels":[],"line_end":4425,"line_start":4405,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"Use the universal root-system identity [formula in source] (Coxeter number [formula in source] ). 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The whole integer chain then reads off [formula in source] : The [formula in source] slice is then [formula in source] : one [formula in source] phase slice of the [formula in source] root atlas is exactly the full flavor transport budget. \\ (arithmeti","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Level 2.8 — positive-root moment: [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":283838,"byte_start":282306,"id":"section:ef6b3386018f18c6b0d4","kind":"subsection","labels":[],"line_end":4467,"line_start":4442,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"The three hard carrier atoms — weak rank [formula in source] , color rank / family count [formula in source] , carrier rank [formula in source] — generate the [formula in source] data cyclotomically, without taking [formula in source] as input. Set where [formula in source] is the Coxeter number and [formula in source] the rank. 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The one-generation spinor packet is the even exterior algebra, equivalently the even-weight binary code The two carrier roots [formula in source] , [formula in source] generate all hypercharges ( [formula in source] , [formula in source] , [formula in","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Theorem 1 — the even carrier code","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":321249,"byte_start":317452,"id":"section:8a4b44500953ff638855","kind":"section","labels":[],"line_end":5006,"line_start":4948,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8"],"relation_ids":["relation:1ba8bc4db06586d6e4fb","relation:d62d7796fbf4139b3418"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"tocsectionTheorem 2 On [formula in source] the flip [formula in source] is even, so [formula in source] . The three relations [formula in source] form a symmetric association scheme (the even Hamming scheme on five bits) with The eigenvalues (computed directly) are [formula in source] and [formula in source] , with [formula in source] . The two graphs are named objects: The Standard-Model family is the valency side [","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Theorem 2 — Exterior–Action Duality","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":321962,"byte_start":321249,"id":"section:f571553ff2e9f9a3c71c","kind":"section","labels":[],"line_end":5019,"line_start":5007,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"tocsectionTheorem 3 Requiring the even family to equal the action truncation through pair degree, [formula in source] , i.e. the unique positive-integer solution. At [formula in source] the two sides equal [formula in source] , so carrier exhaustion [formula in source] and the Coxeter period [formula in source] coincide only at five slots: [formula in source] and [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Theorem 3 — the Coxeter closure equation selects [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":322965,"byte_start":321962,"id":"section:e9e51ef45afec3ba4ffb","kind":"section","labels":[],"line_end":5038,"line_start":5020,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"tocsectionTheorem 4 From the three atoms [formula in source] , with [formula in source] and [formula in source] : The [formula in source] exponents are the primitive residues modulo [formula in source] , and [formula in source] . The local SM algebra and the root atlas are the two arithmetic projections of [formula in source] :","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Theorem 4 — the [formula in source] cyclotomic Coxeter compiler","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":324832,"byte_start":322965,"id":"section:ec1ffa8eecd05cd52454","kind":"section","labels":[],"line_end":5064,"line_start":5039,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"tocsectionTheorem 5 The directed even-flips of [formula in source] are the complete graph [formula in source] : ( [formula in source] .) So the positive [formula in source] roots are the unordered transitions of one family; the second hypercharge moment, the positive-root count and the sum of the [formula in source] exponents coincide at [formula in source] . The CP pairing [formula in source] of the exponents gives ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Theorem 5 — the root transition atlas and the positive-edge moment","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":329615,"byte_start":324832,"id":"section:3bdc8876b2b4284f0227","kind":"section","labels":[],"line_end":5140,"line_start":5065,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8"],"relation_ids":["relation:344ec2055bf03c8d320b","relation:828c7b50717789511a10","relation:c02035c88957d0b76149","relation:c928354fcfb67d414ac3"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"tocsectionTheorem 6 All discrete budgets and the seam seed are functions of [formula in source] : Two-graph product table. With the carrier-pair graph [formula in source] ( [formula in source] ) and the family-corner graph [formula in source] on [formula in source] ( [formula in source] , [formula in source] ), every large budget is a product of the two graphs: i.e.\\ ( [formula in source] , [formula in source] , [for","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Theorem 6 — downstream readouts from [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":346301,"byte_start":329615,"id":"section:f9b30725993b14c4ee95","kind":"section","labels":[],"line_end":5388,"line_start":5141,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8"],"relation_ids":["relation:01084314d45cc1d2f0de","relation:078c532ab010152682dc","relation:0dff749cbdf0fb19eb2b","relation:0fa8b459a5a5e16ee65d","relation:17c13e74c3f09f5a6bf2","relation:17deddc2c25c0fbd7c89","relation:19377cd8ea91b454fccf","relation:1ae34d1f57a3fb1b733c","relation:1df4033bcb5ee21030f9","relation:1e0579818a1a3d388878","relation:1ef0919a9799a98b4c85","relation:2856c346428ad0b32297","relation:293d75a20b6caa5a4894","relation:2b25d72439b68ffd4d96","relation:372910a2f2de61cbb7dd","relation:46cd7b9b9ca90d0292d3","relation:555fdf647b3a35a3a45b","relation:586842c80260bcbdb413","relation:64289f1fa836932754f6","relation:6c1e2f1ed7f7e726311f","relation:6de8ced8e5c2109aa7a2","relation:723aada9061fc2ac3478","relation:87e9af887c0ad2b93aa1","relation:8ed0492cc4e0d639d241","relation:9a12335a899465b31c3a","relation:9add84e61d8c20527c95","relation:9b11d79d94b59b27f872","relation:9b80d2728ead0e60d4ea","relation:a0020ec2b8d5acce0a5b","relation:a4020d27fa43b26e0ee3","relation:a9bd52e771ae602d2a28","relation:b767b8be80d0fa44feb9","relation:c0f08e33250c29f947bb","relation:cbb3ebf2b3be7893cd10","relation:edd0194f4e45120a62f4","relation:f68c68ee3b86d5344c0c","relation:f76a3b0feea0fedb0442","relation:f804b79c91e08f90ab70","relation:fbcba58e7525f71cde46","relation:fce1d7374025783575b8"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"tocsectionTheorem 7 Since [formula in source] , one has the standard chain [formula in source] , with the exact branching (verified dimensions and root/weight counts): The adjoint [formula in source] of [formula in source] is [formula in source] and its spinor [formula in source] is [formula in source] . The TFPT dictionary makes each summand a known object: @llY@ piece & value & TFPT reading \\\\ [formula in source] &","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Theorem 7 — the [formula in source] lift of the [formula in source] atlas","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":350385,"byte_start":346301,"id":"section:ef3ac63aa9e6dcddf33d","kind":"section","labels":[],"line_end":5445,"line_start":5389,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8"],"relation_ids":["relation:03fa999da0d10ae2994d","relation:7e96f6fd039bb2a80f9f","relation:86b5557e16d08fe37c5d","relation:c6d377fe49d4f0aa88c0","relation:d36d503f44f688368c02","relation:e4111622097aa6260751"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"tocsectionTheorem 8 — anchor microcode The parabolic flavor bundle [formula in source] on [formula in source] has splitting type [formula in source] , whose power sums [formula in source] generate the whole compiler budget:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Theorem 8 — the [formula in source] anchor microcode and the [formula in source] -ladder","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":354145,"byte_start":350385,"id":"section:8ab1f0d3c74dd8b84247","kind":"section","labels":[],"line_end":5495,"line_start":5446,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"tocsectionMaster statement Five carrier slots give [formula in source] ,\\ four family corners give [formula in source] ,\\ and [formula in source] gives the [formula in source] atlas. Equivalently: [formula in source] , [formula in source] , [formula in source] ; [formula in source] , [formula in source] , the [formula in source] Coxeter structure and the action ladder read the same five-slot pair-decuple. The Standar","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Master statement and status","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":356885,"byte_start":354145,"id":"section:9dbcdb3b5820985270ed","kind":"section","labels":[],"line_end":5542,"line_start":5496,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"The lift is reproducible by a short script (all entries below verified exactly).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Appendix: machine-checkable [formula in source] construction","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":360513,"byte_start":356885,"id":"section:e398e2b82404aee49434","kind":"part","labels":["fig:ablation","sec:ablation"],"line_end":5614,"line_start":5543,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8"],"relation_ids":["relation:b7fd093ff589c38e8c4c"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"The single sharpest reviewer test is: was the closure [formula in source] engineered so that [formula in source] comes out? The honest answer is an ablation — vary each input and see which actually move the root. Three one-parameter scans (all others held at their compiler values) separate the load-bearing integers from the fine last-digit selector.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Appendix: ablation of the EM fixed point","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":361775,"byte_start":360513,"id":"section:1b936c4aa48ef2007937","kind":"section","labels":[],"line_end":5634,"line_start":5615,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8"],"relation_ids":["relation:18edbd359d6c61f603fc","relation:33be13e96d05af72a19f","relation:379eb0fa2c0550a378a4","relation:55d1314d94ab1020aa04","relation:6b7727185828dd411224","relation:849eb8066fa7f437b5d1","relation:aff22cb97af8e1bef2cb","relation:b42ab5f01b8e0dc01359","relation:b6fb7f765b86bcf49517","relation:cf2fdebbf3e309747c62","relation:de0d873cad28752d80a6","relation:dfa7d6b69d0cf955d683"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"The load-bearing identities of this document (marked , , ) are re-derived from [formula in source] alone and machine-checked by the suite in the repository folder verification/; the inline tags [verification/ [formula in source] ] point to the exact script. Relevant here: v1_e8_glue.py — the [formula in source] glue ( [formula in source] , [formula in source] , [formula in source] ). v2_carrier_pascal.py — [formula i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Appendix: computational verification","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":5116,"byte_start":0,"id":"section:20442cfa54b4f5fd00ed","kind":"frontmatter","labels":[],"line_end":118,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":[],"summary_excerpt":"arrows.meta,positioning,calc,fit,backgrounds,shapes.geometric,shapes.misc,decorations.pathmorphing,decorations.pathreplacing,patterns,angles,quotes,matrix =3.5em","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"-1.2cm TFPT — The Standard Model from the Compiler\\\\[2mm] The [formula in source] -ladder, the flavor block from parabolic transport, and the worked closures ( [formula in source] , quark [formula in source] , the gap, Starobinsky [formula in source] )","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6067,"byte_start":5116,"id":"section:c8c3dc1157054638d4ef","kind":"part","labels":[],"line_end":130,"line_start":119,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":["relation:0b7ff198cea3f4b8a659","relation:0d2591ab885e638dd374","relation:392a80450239526c7629","relation:c6fbdcc0238736a2f5a3","relation:edd2f6ba6fa11dc9b0d3"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":["\\mC","\\mE","\\mO","\\mX"],"summary_excerpt":"In one sentence. The fermion spectrum — masses, Yukawa structure, CKM, the PMNS skeleton and the neutrinos — follows from one master formula with three ingredients: the seed [formula in source] , the carrier base [formula in source] and the residue matrix of the compiler. No free Yukawa exponents remain; the charged-lepton amplitudes are closed, the quark mass ratios are closed too (integer Pl\\\"ucker readouts, v49/ v","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Standard Model in one master formula","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7907,"byte_start":6067,"id":"section:610e7b9e8a68e0834305","kind":"section","labels":[],"line_end":160,"line_start":131,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":["relation:1279cad77634d6f6bb82","relation:cbfdb2c7772a1d9cba5e"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":[],"summary_excerpt":"In the source-layer construction each fermion mass arises through a Yukawa coupling [formula in source] built as a transport word-length [formula in source] on a hexagon ( [formula in source] ) times a holonomy amplitude. In the compiler picture this is one line:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The principle: one master formula instead of many Yukawa numbers","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9398,"byte_start":7907,"id":"section:a1d77fa3b349dfff922c","kind":"section","labels":[],"line_end":185,"line_start":161,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":[],"summary_excerpt":"A single seed drives four independent low-energy observables. 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two derived variants in the named box & [formula in source] (NuFIT 6.0 [formula in source] ) ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neutrinos","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":153247,"byte_start":151294,"id":"section:2ffaaee2ce19180008ab","kind":"section","labels":[],"line_end":2117,"line_start":2091,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":["relation:35793204a5227a2222e6","relation:486d77b1a8f3a36f6097","relation:99486c6663be84fe05bc","relation:9a5501cfe5004b544707","relation:9de0ef87d8adc2ee6226","relation:9e6d714ea4dd36929a76","relation:e3b8f1072fcff953184c"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"@p0.7cmp3.5cmY@ layer & before & in the compiler picture \\\\ 1 & boundary [formula in source] & axiom (P1), unchanged; 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Three layers:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Is the entire Standard Model thereby derived?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":158216,"byte_start":157751,"id":"section:1a2458f59412a5e4396c","kind":"section","labels":[],"line_end":2175,"line_start":2169,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":[],"summary_excerpt":"For each question the entry is typed honestly as closed, reduced or conditional: the proof chain isolating one sharply named remainder — and, where possible, a reduction that makes the problem smaller than previously thought. This is a resolution map, not a claim that all five are fully solved.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Closure status of the five former open questions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":160916,"byte_start":158216,"id":"section:2546f93b78129f0fded4","kind":"subsection","labels":[],"line_end":2205,"line_start":2176,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":["relation:0682122579a706bbfa98","relation:093c5d024570b2c6005e","relation:2e7956993a46d25ab5c0","relation:32ee99465e301e73b76f","relation:37a899c8d79ebeac6dd3","relation:45cbaa4267c150927432","relation:5afae3ae3e6e36989219","relation:6bb385e833e0f2481c1f","relation:70303eeb75a50f16f6ce","relation:74711db2464170bcfee3","relation:8e55e2dadf9c0bc4e3e7","relation:e6bfddd23ddcd8006826","relation:f5c211a9de6a460ae054"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"Mehta–Seshadri supplies the equivalence-class framework — stable parabolic bundles [formula in source] irreducible unitary representations — but it does not by itself give ``parabolic-stable [formula in source] transport-minimal'' or the hexagonal word-lengths; that is the TFPT-specific step. The family connection [formula in source] provides the representation, its weights are the cusp exponents, the stable degree i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"(1) Flavor residual — ratios closed combinatorially; only the absolute scale is the wall-selection [formula in source] /","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":164772,"byte_start":160916,"id":"section:2e4923f3fd42adc44e3d","kind":"subsection","labels":[],"line_end":2255,"line_start":2206,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":["relation:023bc29bfb2c256ea59c","relation:62a78750b34e16f19a68","relation:644332d56208803a5a10","relation:7b8159b1ff8c9cee3eca","relation:ad013bbaaddcf81906f0","relation:af1d45ffbf58b121fe00","relation:b1134f7713c9d2e63258","relation:ca3e823720dfafcc9122"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"The metric-sector field equation itself carries no free dimensionless Newton coupling under those premises: fixed- volume entanglement equilibrium (Jacobson 2015) forces the full covariant Einstein equation [formula in source] with both coefficients fixed ( [formula in source] , [formula in source] from [formula in source] ; v358/ v359). What this subsection details is the complementary spectral-action / inflation la","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"(2) Gravity — the classical covariant field equation carries no free dimensionless Newton coupling under the named QFT/entanglement premises ; the [formula in source] inflation layer up to one truncation /","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":167831,"byte_start":164772,"id":"section:2d043e484362d7a8bd90","kind":"subsection","labels":[],"line_end":2296,"line_start":2256,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":["relation:cc5182d2a018e2f78313"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"The key reduction: [formula in source] needs neither the full OS package nor the mass gap. It follows from three purely structural facts plus reflection positivity on the admissible branch:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"(3) Strong CP — decoupled from the mass-gap problem /","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":175296,"byte_start":167831,"id":"section:eef94f3ff4627b2515d5","kind":"subsection","labels":[],"line_end":2384,"line_start":2297,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":["relation:06ac71b1fb8e1635c5ad","relation:081a25da953a291032ef","relation:14312beab73debf5a2e6","relation:14ff93d0f874945eacef","relation:179c628766ee3743b52c","relation:19d290cce57512567fa0","relation:25302bea0cdb8ee32913","relation:2a2d0e19ffa7b07952df","relation:33807832fd906894979f","relation:36736b069d4c76b45126","relation:50d6176f550a59b32d2d","relation:76f2b436869dd069e018","relation:805d2669270aaf607065","relation:a6b8b63aac6dd80df44a","relation:b0f93fa25c0c0a461f0b","relation:b5aad0953b0ac758ae8d","relation:c5baf2c0b5095e425f0a","relation:d268b50b4b4cff641f33","relation:d83e7133fc84f6cc1de1","relation:dc5063bacb02fb2e49c3","relation:e0ae3f904956233644a8","relation:e6be3c7c9bb68a496dd6","relation:ec2e77227a8ff84d8c85","relation:f6a8eb191cdfca4e01f9"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"This is the constructive QFT closure of the admissible physical sector — not the unprojected ambient theory: the unprojected ambient metric measure is not constructed here and remains the [formula in source] frontier item ( ambient QG). On the admissible sector, the input previously listed as ``open'' — the parent-domination / mass-gap lemma from (3) — is not analytically open: it is computed by the explicit discrete","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"(4) Constructive QFT closure of the admissible physical sector /","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":179723,"byte_start":175296,"id":"section:c80612b5b357f44d318a","kind":"subsection","labels":[],"line_end":2448,"line_start":2385,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":["relation:354ceee1cc220261e679","relation:8123c7438a9d4a5fe839","relation:b0d317db34e36df88fbf","relation:baf1955d376aa4dc7993","relation:c0742d2801c30fda355a","relation:e0e468bb3df420857012","relation:e4b363a2f03baaf03a54"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Here the hardening is empirical and concrete. The Lean 4 proof ( lean4-carrier-rigidity, toolchain v4.29.1 [formula in source] Mathlib) builds cleanly: @lY@ Verified (Lean, 0 sorry) & Content \\\\ Polarization.sixY_carrier_polynomial & [formula in source] as a corollary of orthogonal idempotents \\\\ Rigidity.unique_carrier_pair & [formula in source] unique (integer rigidity) \\\\ Hypercharge.trace_Y, _carrier_polynomial &","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"(5) Axioms P1/P2 — P2 machine-verified, P1 as an interface /","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":182069,"byte_start":179723,"id":"section:ac645a098a5f04c5bc5d","kind":"section","labels":[],"line_end":2483,"line_start":2449,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":[],"summary_excerpt":"The same numbers, now as closed expressions instead of distributed theorems:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"How the original-paper predictions simplify","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":184387,"byte_start":182069,"id":"section:f55a4eb54f833ae02970","kind":"section","labels":[],"line_end":2509,"line_start":2484,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":["relation:1e4b2a979f479ac9e4da","relation:43ed4bfa3a8da7d4df54","relation:555e16b9b8bb8cb0bf1c","relation:850f0431537ed0635a15","relation:88330e06ba3791825e22","relation:b317f9bf94f6005775f1","relation:b6d6de5a71e9143cb8e2","relation:b7b1ef9b64e54833f0b0","relation:d40a38d04d6b4c5d121a","relation:ed5157c70c24085c8b95"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":["\\mC"],"summary_excerpt":"tocsectionConclusion The simplification is substantial: the discrete Standard-Model structure (charges, families, flavor operators) is derived under the axioms; [formula in source] D existence, chiral measure, mirror gap, couplings and neutrino dynamics are open. The [formula in source] -ladder formula [formula in source] with one seed [formula in source] and one fixed residue matrix whose spectral invariants ( [form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conclusion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":187865,"byte_start":184387,"id":"section:fbfb03a6f6363aec86a1","kind":"part","labels":[],"line_end":2554,"line_start":2510,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"This note closes the last structural gap of the [formula in source] compiler by deriving the charged-fermion transport word-lengths [formula in source] , [formula in source] , [formula in source] — equivalently the residue triple [formula in source] and its [formula in source] orbit — from first principles, rather than from the legacy resolvent construction. The correct framework is parabolic Higgs/bundle theory on t","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The flavor block: parabolic weights and the transport theorem","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":190950,"byte_start":187865,"id":"section:d5c622aa93b612fe2842","kind":"section","labels":[],"line_end":2603,"line_start":2555,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"The family curve is the rigid four-punctured sphere [formula in source] , [formula in source] (the flavor construction above). The flavor bundle is a rank- [formula in source] parabolic bundle [formula in source] on [formula in source] . At each puncture the local monodromy is the order- [formula in source] cusp class with eigenvalues [formula in source] , [formula in source] ; by the Mehta–Seshadri dictionary the co","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The setup: parabolic data on the family curve","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":193077,"byte_start":190950,"id":"section:8bd8676e11910b28336f","kind":"section","labels":[],"line_end":2640,"line_start":2604,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"For a unitary (flat) family local system, [formula in source] is parabolic-polystable of parabolic degree zero (Mehta–Seshadri). With full flags and weights [formula in source] at each of the four punctures, The balanced (stable) underlying splitting is therefore [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Exact scaffolding (proved)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":195097,"byte_start":193077,"id":"section:04d13a0d2894f95a8c21","kind":"section","labels":[],"line_end":2668,"line_start":2641,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"Constructing the rigid [formula in source] -symmetric local system explicitly (four monodromies [formula in source] , [formula in source] , [formula in source] ), the closure [formula in source] is solvable to machine precision, and the unique rotation [formula in source] has eigenvalues [formula in source] : the [formula in source] Coxeter element. \\ This independently reproduces the corner-rotation [formula in sour","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Riemann–Hilbert side (what the monodromy fixes)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":199432,"byte_start":195097,"id":"section:10dfd6e9f65946a0b7ff","kind":"section","labels":[],"line_end":2726,"line_start":2669,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":["relation:2ac131eb5f61ef5c5f62","relation:7ae384a3a8eea19e8e84","relation:868b622f142d1e955ee2","relation:c9435a23ece33daad5f4"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"Status (no drift). The splitting type is now closed: the unique partition [formula in source] fixes the anchor and [formula in source] fixes the residue branch (verified, below and v4_flavor_matrix.py), and the solar texture is built ( v9_neutrino_texture.py). The roadmap below is kept as the derivation record of how [formula in source] is obtained; it is no longer an open project. The only residual is the parabolic ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The parabolic-weight computation (resolved this round)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":206530,"byte_start":199432,"id":"section:ffb3c952b2d4af559d34","kind":"section","labels":[],"line_end":2826,"line_start":2727,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":["relation:04bb97837371fc343fe8","relation:0c3867e99c5811791962","relation:0cc8568db5a2f5baac01","relation:156224647d79bea90ed4","relation:2877ba41162409ca6d31","relation:3e12fcacb393e1478108","relation:426f9684db7179fb0d6c","relation:4290f897a345cd4669a8","relation:4c8808a86a5e183d6bdc","relation:532b7e7f4acc2bb9218b","relation:622a9603756958369d41","relation:67a4b72384e10a22e740","relation:7043ce6aca1ab23f1da6","relation:9bedbb4f47c852d43547","relation:a5c77a42a6f13ea9d851","relation:aef93a2ca89daaa2dde0","relation:af66fe0cb1546365dc9c","relation:b3336626f4185e02f7a8","relation:b429030c83bfa4b90abc","relation:bba0ff6b66d39cd84a72","relation:bc9a1b69c1c250452c26","relation:bea250ed6070e76b49e3","relation:c20536c7837ef8f3456e","relation:c441d71e7c2a277fad2f","relation:c53a61a062cd7df4fa9b","relation:c8d5bf8852692f4d8724","relation:cb67269ccc25fe500efd","relation:cea94d7b52aa43152230","relation:e01331b2a9fc7eef2fb2","relation:e10985a540fa20995d1e","relation:e3a7fc78a5f4c7c88347","relation:ed791fbd67050ae06ac1"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"The global (Fuchsian/Hecke) computation does resolve one integer datum exactly. Work in the rotation eigenbasis [formula in source] and take the [formula in source] -symmetric Fuchsian residues [formula in source] with [formula in source] (the cusp exponents). Then the symmetrisation collapses exactly, because [formula in source] for [formula in source] (off-diagonal terms are summed fourth roots of unity). The expon","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Global computation: the anchor multiset is derived","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":208708,"byte_start":206530,"id":"section:ffed8b3e60556b248cbb","kind":"subsection","labels":[],"line_end":2870,"line_start":2827,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"Every residue decomposes uniquely into a cusp index [formula in source] (the [formula in source] family phase, [formula in source] ) and a sheet parity [formula in source] (the [formula in source] deck involution), via the bijection [formula in source] : [formula in source] The full transport table in these parabolic coordinates is l|ccc|ccc & 3c|cusp index [formula in source] (g1,g2,g3) & 3csheet [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Part (ii): the [formula in source] structure of the residues, and the frontier","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":212775,"byte_start":208708,"id":"section:8747a372d96eb69beb0d","kind":"subsection","labels":["thm:flavor"],"line_end":2932,"line_start":2871,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"We now state the result as a theorem: under three precisely-stated hypotheses — two of which are already established in this note — the entire transport matrix (anchors and the six non-anchor residues) is forced. The combinatorial core is proved by complete enumeration.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The flavor transport theorem","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":213453,"byte_start":212775,"id":"section:2c70d6b249ff31626bca","kind":"section","labels":[],"line_end":2945,"line_start":2933,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"The anchor vector [formula in source] — the absolute value of the splitting type [formula in source] — is the smallest parabolic object that encodes the three operative structures at once: The [formula in source] norm is the glue/anti-degree, the [formula in source] norm [formula in source] is the [formula in source] positive-root hexagon, and the product is the sheet parity.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Parabolic Anchor Compiler","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":214240,"byte_start":213453,"id":"section:4fd5a4b18f4ba9a372b6","kind":"subsection","labels":[],"line_end":2959,"line_start":2946,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"With [formula in source] fixed by parabolic degree zero, the entire integer landscape collapses: So [formula in source] and the spinor block [formula in source] are all functions of [formula in source] with the single new ingredient [formula in source] derived from parabolic degree zero (not posited).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Budget master table: everything is [formula in source] times a Coxeter datum","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":215602,"byte_start":214240,"id":"section:da9fd7c73cc9015647dc","kind":"subsection","labels":[],"line_end":2982,"line_start":2960,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":["relation:5c6c9ccbd67a23cc586e"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"The flavor budget splits into anchor [formula in source] two equal Coxeter copies: The residue row sums and full row sums read named objects, and the generation (column) sums are [formula in source] . \\ Finally the scalaron exponent is the parabolic anti-degree plus the family rank, linking the stable family bundle [formula in source] directly to the inflation scale. The [formula in source] residue sum is the project","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Flavor budget split, row sums, scalaron deficit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":218544,"byte_start":215602,"id":"section:24936ed30d94da69b871","kind":"subsection","labels":[],"line_end":3031,"line_start":2983,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"/ / in 0/-2/blue!60!black, 1/-1/green!50!black, 2/-1/green!45!black (0,- 0.62) rectangle (2.6,- 0.62+0.5); at (1.3,- 0.62+0.25) [formula in source] ; at (1.3,0.95) splitting type\\\\[-1pt] [formula in source] ; at (1.3,-2.05) degrees [formula in source] anchor [formula in source] \\\\[-1pt] [formula in source] ;","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The anchor power compiler","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":225348,"byte_start":218544,"id":"section:b76309fbfced7aff0c43","kind":"subsection","labels":[],"line_end":3129,"line_start":3032,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":["relation:1512ab3c491b4deae847","relation:41cbaea83f3cfc445f3f","relation:44fc04ecd17a88f0cf6a","relation:7b578f4d081705309a0f","relation:90b201f210f43dcb3b0f","relation:9fbe9e994e097a30b362","relation:a1ed813b188f5901b6f6","relation:ae85642521a8e2c0b345","relation:d230d5db68176a7ea9cd","relation:dc749a42b2cb4f7790b3","relation:dc82334d5fd474115894"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Hypotheses (H1),(H3) plus the unique sum- [formula in source] set fix the up and lepton sectors and reduce (H2) to a single binary choice in the down sector: [formula in source] versus its distinct-distance sibling [formula in source] (both contain the anchor [formula in source] , both have row sum [formula in source] , so sum rules do not separate them). The residue matrix [formula in source] (rows [formula in sourc","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Residue-matrix spectral selector — sharpening (H2)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":233942,"byte_start":225348,"id":"section:de1edf5378afcd852d3e","kind":"section","labels":["lem:dd","prop:equiv","thm:h2","thm:ms"],"line_end":3248,"line_start":3130,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":["relation:189aa81094df827b5bee","relation:32176a85cf224fbde463","relation:46d957f7e80ca7da5098","relation:5b9eea8c0cdddc5df745","relation:7be092f611c0de8c5bdf","relation:9bad074a4e0eba614816","relation:baae68f784fc82c33ca9","relation:c05536847334a69b3672","relation:d465a0b60782bcb316b8","relation:d88e8a8dcb4145b06131"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"We promote the two genericity/equivalence steps to proved statements.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Closing the flavor block: two theorems","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":237369,"byte_start":233942,"id":"section:35abcdeb3c5b2946d464","kind":"section","labels":[],"line_end":3293,"line_start":3249,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"tocsectionStatus @p0.56 p0.08 Y@ Statement & Status & Note \\\\ weights [formula in source] from cusps [formula in source] data & & Mehta–Seshadri \\\\ [formula in source] & & exact \\\\ balanced bundle [formula in source] & & stable splitting \\\\ [formula in source] , [formula in source] degree, [formula in source] & & winding/residue split \\\\ [formula in source] , [formula in source] & & budget bookkeeping \\\\ rigid [formu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Status","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":238323,"byte_start":237369,"id":"section:0fbf9d0da4afc6e6a3e8","kind":"part","labels":[],"line_end":3305,"line_start":3294,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":["relation:910dbc5c259df28464aa","relation:a542dbfb07644d998643"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":["\\mC"],"summary_excerpt":"Scope and honesty. This note discharges the items that were flagged ``standard but not written out,'' and now also carries the closures previously collected in the research-sprints note: the seam-fixed Starobinsky mass, the derived solar angle [formula in source] , the H2 splitting type, and the quark [formula in source] amplitude band. It does not force the items that stay typed transfer targets, never compiler powe","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Closing computations and proofs","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":248720,"byte_start":238323,"id":"section:e8967e47143a0fba6b23","kind":"section","labels":["lem:gap","prop:qftmeasure"],"line_end":3465,"line_start":3306,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":["relation:2b87398d2aa3fae08669","relation:56e6824a511aa6c38bf2","relation:b2299d84176f64df49a6","relation:decaa32783e11939bd26","relation:e882dfbf068d12ac203c","relation:f1bc84a9c067f93d751b"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"unique limit state and exponential clustering] The admissible [formula in source] transport transfer operator has the closed spectrum [formula in source] (the cusp cubic). Hence [formula in source] The contraction ratio [formula in source] satisfies the Dobrushin uniqueness condition for a finite-range (range- [formula in source] , cyclic) transfer operator; therefore the thermodynamic limit has a unique Gibbs/vacuum","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The explicit mass gap closes dynamics and clustering","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":250257,"byte_start":248720,"id":"section:86b980859caf8db336e6","kind":"section","labels":["lem:aps"],"line_end":3488,"line_start":3466,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"Compactify the oriented two-dimensional normal slice [formula in source] to [formula in source] . 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Higher curvature terms [formula in source] , [formula in source] , enter with [formula in source] , so their contribution to the observables is [formula in source] . With [formula in source] this is [formula in source] ( [formula in source] ), and the leading predictions are [formula in source] matching Planck. The","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The [formula in source] truncation is [formula in source] -bounded","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":264485,"byte_start":254954,"id":"section:33f8ca97d5f5599b425b","kind":"section","labels":["prop:ambient","prop:metricrp"],"line_end":3713,"line_start":3578,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model"],"relation_ids":["relation:0c190cf0cfe81e900ed7","relation:245d895ad16211ec15e9","relation:365ee0ca52c843df935b","relation:3cec8b8841be4266dcce","relation:549fc8f926154b486598","relation:5bcfa180e5f68e7404aa","relation:621a965de57691ea215d","relation:68c759ad45fa372b2447","relation:7739a060e594dddc0d89","relation:778a536c9b5607c9904e","relation:7af322a6bbddd8e58b76","relation:7afb113dd5f284c56209","relation:9945722c2e634f2d60ce","relation:a01798589e702f9a171f","relation:a5cfc7ef5fb18e400ce1","relation:aa3fc5cfe4a823201765","relation:d1df60d1cea7ea5c9660","relation:d59dbc2688129bf06049","relation:dad385f21c2543892404","relation:f251ad98a69837d0bdbb","relation:fcce87158d5241640a04"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"The two formerly-hardest items — the ambient (unprojected) QFT measure beyond the selector [formula in source] , and full quantum gravity beyond the [formula in source] scalaron — are not two separate problems. They are one object: the relative spectral-action measure [formula in source] with [formula in source] the matter/gauge Dirac operator and the gravitational data in the same trace. 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A compact synthesis of this contract's executed work packages (WP1–WP5d, both WP5d stages, [formula in source] the WP5e [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] and [formula in source] stages [formula in source] the three back-reaction milestones M1–M3) — the narrative arc from the [formula in source] clock to the [formula in source] bo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — CELEST.SEAM.01 (the celestial and twistor continuum route)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":861553,"byte_start":833944,"id":"section:b191b0a66e5bacdc1a0e","kind":"section","labels":[],"line_end":12469,"line_start":12137,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:0bb8d6367864ddef799d","relation:0e9e38cf247f61a1ff5b","relation:0ebb66f7938c6bb2d2a9","relation:18a733bf0af3463049c3","relation:192d7bb8c09effea38e7","relation:1cb4daf01d13181d2140","relation:2bba9c2b40b6f99ae9a2","relation:3302c277f64196cb06a9","relation:41f3cc7b2a15981d1aac","relation:4b4010bd1569b3d2834c","relation:4b66f4c5d528f18c046e","relation:4d2d9c646531877e908d","relation:50c1b065cfb64e44ee45","relation:519fa7a1ef11550cd10c","relation:5a176024d7444d59ffa8","relation:712f828729ec302a5760","relation:737daae6c8dd4a240186","relation:7baf58ede63e9feda225","relation:82d3bb379578985c1550","relation:83702286ada560ceacc2","relation:889497750b38fe3a26c0","relation:8da4bf2eb66e413e4d5c","relation:8e0bf924e6e1790260fd","relation:945faa79d19dd49fd60e","relation:94f6df1630ad5c832112","relation:953a0abfe3d42f58102c","relation:9e9a035289658a839b15","relation:a22d400714740c52e1ab","relation:a29e969c2e1a4744459d","relation:a99e4bfebc8a2d28b07b","relation:b3254fdc81a46dc584b3","relation:b99ae1994999baae8360","relation:be03c26208dd03bc55d8","relation:be32d9d807bc6f88bace","relation:c1c9236b28a5381f43f3","relation:c2b0cb96f481817ccd65","relation:c894ec0044f89ee36ba5","relation:c8fbc089b130e4e994c0","relation:c90df630b4f5afd022b2","relation:c968c9386ac757acfb52","relation:c992c47eea2e0cdeb8db","relation:ceec4dfdba97d7343ef8","relation:ddf3119005440701a162","relation:e2a7905a54597d27badb","relation:e89c2b16ee2a2f45463b","relation:ebf2b1ba363f508c5462","relation:ef389802bc41512728c6","relation:f17687f53a57f6282b71","relation:f2b8d39c9b57c709b62e","relation:f7351deb72d09c53f327","relation:ff70cbea14b541d0af86"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Typing. This is the actual bridge from compiler to physics — everything in CELEST.SEAM.01 is preparation for it. It is a research contract \\ (ledger row WOIT.OS.TWISTOR.01: Open, research contract), not a claim; nothing below asserts that the construction exists. The external programme it engages — Woit's Euclidean Twistor Unification ( arXiv:2104.05099) — is a named reference frame for the shape of the target, never","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — WOIT.OS.TWISTOR.01 (the Osterwalder–Schrader twistor bridge)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":870310,"byte_start":861553,"id":"section:f8ad9138e39428999ab9","kind":"section","labels":[],"line_end":12570,"line_start":12470,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:03cb16abcfbec3daa499","relation:1d0c62a8fd0aa82bf464","relation:21ac40908f55ef135f95","relation:249b4bdd9118af814657","relation:2f02621c0934e7561241","relation:4d626bc7476f2af82405","relation:6ce544158c9f66d84327","relation:7881672f0ba35183f934","relation:78908dcc22a2ca7ab4f6","relation:949393234c3ea48a1cba","relation:a75bad2996a3020f7cc8","relation:aa06d4fec91f70fd0767","relation:aaeea6954bea59c4076d","relation:b3077c827e2cee443924","relation:c897fff40647e071963b","relation:e543bd02681ead06e1f9"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row CCC.SEAM.CROSSOVER.01: Open, research contract), not a claim. It engages Penrose's Conformal Cyclic Cosmology (Tod, arXiv:1309.7248; Penrose–Meissner, arXiv:2503.24263) as a named reference frame for the shape of the target — never a confirmation in either direction. The cyclic reading of origin_theory stays \\ regardless of this contract's fate; nothing below asserts that CCC","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — CCC.SEAM.CROSSOVER.01 (the conformal-cyclic crossover on the seam geometry)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":874846,"byte_start":870310,"id":"section:ea28e660b1549c41a88a","kind":"section","labels":[],"line_end":12632,"line_start":12571,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:12e0676a8c5009a073e1","relation:39fc3973be8844053ea3","relation:5bd3ea3b261e6ee78e1a","relation:73bf36ae1caf71426834","relation:782800c03e3d17073d42","relation:86b2af50ff0c4df91fd8","relation:8a77607e19bea5ca35d6","relation:d3b11476e11fd4bb5649","relation:e56ec8c91b8a03a78521","relation:f45ad4a8646f4e24edf3"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mC","\\mE","\\mO","\\mX"],"summary_excerpt":"Typing. A standing discipline rule, in force immediately (ledger row DIMENSION.UPLIFT.FIREWALL.01); the uplift theorems it names are separate \\ contracts. It formalizes the core diagnosis of the 2026-08-27 external deep review: a chiral [formula in source] D seam net does not imply a local, interacting [formula in source] D quantum world. The corpus's strongest finite results are boundary/kinematic building blocks — ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Firewall Contract — DIMENSION.UPLIFT.FIREWALL.01 (no [formula in source] D theorem closes a [formula in source] D claim)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":878851,"byte_start":874846,"id":"section:fbf67a6377a333f71dff","kind":"section","labels":[],"line_end":12686,"line_start":12633,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:00f106d0f6f54e934fa0","relation:1145e10482413d649686","relation:14e2ea4cf94247b9a00b","relation:2366da33e567cafb5c57","relation:35883dd393e1a92d95a5","relation:38875da7c7ce7f5523c2","relation:38b6d46b9c3b45e80bdc","relation:3f5d66226812916d7959","relation:479aaebc17fea2369ae7","relation:4aed910f3624d338d5fb","relation:5834b6a5d3d4720a7ce9","relation:5e435dc1f5d226674272","relation:72a02bf0ff4f998b7503","relation:7d152b32df3cdf36f0be","relation:8554e576fe2451fbefc0","relation:978b01d8307d2e96e718","relation:9ab48af4548814c63d02","relation:9ebaa9bd0611a6de9319","relation:a3387f9b3fc7147425f8","relation:bf29b5c2ea42641eb26e","relation:cd674e9f06cb05651d7c","relation:e387efa0a5933b34f5dc","relation:edf8263671d7418b3b47","relation:f70acfbcc5e0d8b185a9"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row SEAM.BULK4D.RECON.01: Open, research contract), not a claim. It makes explicit the theorem that was previously only implicit between the SEAM.EQUIV.01 conclusion (a chiral [formula in source] boundary object) and the WOIT.OS.TWISTOR.01 goal statement (a Poincar\\'e-covariant, causal, chiral 4D theory): the missing seam [formula in source] bulk reconstruction is a theorem of it","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — SEAM.BULK4D.RECON.01 (from seam data to a 4D local quantum theory)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":881673,"byte_start":878851,"id":"section:9541b674d713737f6e7f","kind":"section","labels":[],"line_end":12725,"line_start":12687,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:1d0f58e7c381536c90b1","relation:2bbb0c053bffa83dec99","relation:97634702a61cad8c4035","relation:ccae775dab892bb0aa81"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row BULK.PRIME_COMPLETION.01: Open, research contract), not a claim. Registered 2026-09-04 from the r644 audit harvest; it replaces the ``unique from seam data alone'' reading of SEAM.BULK4D.RECON.01/B7 by uniqueness in the category of seam-generated (prime) completions. Dimension typing ( DIMENSION.UPLIFT.FIREWALL.01 F2): the hypothesis is [formula in source] D free-fermion, the","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — BULK.PRIME_COMPLETION.01 (prime/seam-generated completions, no spectator)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":893246,"byte_start":881673,"id":"section:5c7b501c80f2e5816761","kind":"section","labels":[],"line_end":12868,"line_start":12726,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:0981ae603ff388bd4a11","relation:0a49424419b962d3152b","relation:14f866194ea14398cba3","relation:1c1dbf7b9651ce81538f","relation:239c38699588bd423a62","relation:30d1daa83fa03f4f1b0e","relation:4fe002e2322dacac895a","relation:51ab641552ab4d540f48","relation:54b9378474e8ecdbdb1d","relation:5a77476195c57bde5d70","relation:6427c7c03b8f0408ba09","relation:6b31f2f60d578f183320","relation:8d8853c717bfc786ba6d","relation:a67594134d34360fd55c","relation:ac7c23a2533263201fcf","relation:b058a6b3c02722f469f7","relation:ca37e4a60e604bc84169","relation:d6ed12eca5def62c5287","relation:d8a3527637c287ee3dab","relation:e938b1654874f53b5a49","relation:ed0c926fb9f58dc38522","relation:f5cf65d10d48aa1d43d3"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"tocsectionResearch Contracts: DYN.MARKOV.EMBED.01 / DYN.UNITARY.DILATION.01","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contracts — DYN.MARKOV.EMBED.01 / DYN.UNITARY.DILATION.01 (the three meanings of ``dynamics'')","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":899756,"byte_start":893246,"id":"section:44a203d3c701b05d1360","kind":"section","labels":[],"line_end":12959,"line_start":12869,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:026c8595585c5f203069","relation:41f5621170ccf73f6bbc","relation:7546bc91e27f70e1b5ea","relation:97c0bf156994a8262d42","relation:982d2beb7af9532c41c1","relation:a42ab5e95645e2968072","relation:a8a4b62c5aa8bf3b013a","relation:d6764ce998e284c0aa67","relation:f38c174383e0733ae6d3"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row QFT4D.OS.RECON.01: Open, research contract), not a claim. This is step (3) of the DIMENSION.UPLIFT.FIREWALL.01 route ordering: the nonperturbative 4D existence statement that no perturbative or seam-level result can substitute for.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — QFT4D.OS.RECON.01 (the genuine 4D Euclidean lattice package)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":904927,"byte_start":899756,"id":"section:f0556283246eaeda72b3","kind":"section","labels":[],"line_end":13028,"line_start":12960,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:010d513898c217d507ad","relation:27f5aa70ad019c4370af","relation:34ea10bc1f81d498d86f","relation:6b742120f88594b90e8c","relation:8059fc1bc5bcc1469272","relation:840bf05bef3ada4f4ff5","relation:b556f4016abed77503d1","relation:d6b4c5de9e6f9236a821","relation:f414968e366dc4c423eb"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row CHIRAL4D.NOMIRROR.01: Open, research contract), not a claim. Step (4) of the firewall route ordering: chirality and mirror decoupling must be proven in the same 4D model that QFT4D.OS.RECON.01 constructs — the seam's [formula in source] and Chern/inflow structure are a boundary- anomaly signal, not yet 4D matter.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — CHIRAL4D.NOMIRROR.01 (the chiral 4D lattice matter theorem)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":908877,"byte_start":904927,"id":"section:845ed867739988332e9e","kind":"section","labels":[],"line_end":13091,"line_start":13029,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:014c413cc033e592577a","relation:610a6759451fca22dba7","relation:677a3e727935da164db4","relation:816088bcb5cc80010078","relation:97e7157067d21f2b29b2","relation:cd321abb151a96986ed6","relation:d8c384b8f416e282c578"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["[N]","\\mC","\\mO"],"summary_excerpt":"Typing. A candidate \\ (ledger row CHIRAL4D.MIRROR.DET16.01), registered 2026-08-29 from review wave 5. ( v1002_ spin10_ mirror_ projector.py.) Content. Exact finite-cluster gapping on the full chiral [formula in source] Fock space via the number-violating determinant vertex, as executed above. Open. Dynamical gauge fields, domain-wall geometry, and a [formula in source] D volume theorem — this is not a [formula in so","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — CHIRAL4D.MIRROR.DET16.01 (DET16 rank-one projector, finite cluster)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":912641,"byte_start":908877,"id":"section:9f2ef8163653328e6c3e","kind":"section","labels":[],"line_end":13141,"line_start":13092,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:18fb33c669ddcab8751a","relation:2d987d9fc25f1839f539","relation:2dcb3f50538382b71de9","relation:30dad872ff230342e0f8","relation:35d172e682aeab5668c6","relation:418281b336fce77791c7","relation:4869b1e321f754a9bb20","relation:49f425ee3718e327a327","relation:4a01c97fa17fb96c3830","relation:5311e534674e2dc5bdd9","relation:55a7162f6bf39b934af8","relation:57c433df3944934be90e","relation:5a4a6e04449254655c1c","relation:6105180380e4150abf23","relation:82e9110c4840edb13148","relation:85603aaea5051e3f19f1","relation:8ab73c52447d9ec0d257","relation:960ab777d2dd6d32441c","relation:9e644fa9ca21dccb65ec","relation:a40863e0b3c23ddbde31","relation:a536bbf3ae9812f5db3a","relation:bf0f1e6a30419072081f","relation:c4917f9d7d2fad8d5745","relation:d39cb3f6f3d2b61e3aad","relation:e25d7360ba3590bbbbf0","relation:e3a1565e44190ee85a71","relation:f16d92feaea7a6c03fbd"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mC"],"summary_excerpt":"Typing. A standing discipline rule, in force immediately (ledger row GRAV.NONCIRCULAR.01), with an audit census at registration. Bisognano–Wichmann (BW) is a theorem within an already-local, Poincar\\'e-covariant QFT with a suitable vacuum: the modular flow of a wedge algebra acts as the boost. It is not a device that generates Lorentz spacetime from an arbitrary modular flow — there exist Poincar\\'e-covariant nets vi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Firewall Contract — GRAV.NONCIRCULAR.01 (the Bisognano–Wichmann direction discipline)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":915635,"byte_start":912641,"id":"section:1a140dd2e54c1f43c055","kind":"section","labels":[],"line_end":13187,"line_start":13142,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:6ff809bf663c65284c0e","relation:779547593fad24233df8","relation:786552df9a9b5765b63b"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"Typing. A research contract (ledger row OBS.TRANSDUCTION.01); the principle is machine-checked on the minimal model at exploration level, the per-bundle transduction proofs are . It elevates the S15 typing rule to a named principle: [formula in source] Without the middle arrow, neither a non-observation falsifies nor an observation confirms. The minimal model is machine-checked in experiments/ theory-contracts/ fo01_","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — OBS.TRANSDUCTION.01 (the transduction principle: eigenvalue, projection, coupling)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":919213,"byte_start":915635,"id":"section:f08abc84c0e5893cbfe5","kind":"section","labels":[],"line_end":13235,"line_start":13188,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:295e56273be54ef895b7","relation:2eb9032e7db4c3a71aa1","relation:7ba32fa24678e2e3c0bf","relation:803b7676278708dacbb8","relation:83e12627cb8dadf99124","relation:90c8326f8b4c11cc93bd","relation:911b36677c65fb4cd009","relation:93d6b5ea94fab5e91884","relation:dad5fb92fa914e0da9ed","relation:dd328ff4d6ffb5dd339d","relation:f7e1a06336e3b742ffd1"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row PRED.JOINTLIKELIHOOD.01: Open, statistics-construction contract), not a claim. The [formula in source] individually matched values all descend from the same few atoms ( [formula in source] , [formula in source] , [formula in source] , [formula in source] ) and are therefore statistically correlated: counting hits overstates independent evidence. The evidence is to be reorgani","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — PRED.JOINTLIKELIHOOD.01 (from hit-counting to overdetermined relations)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":927211,"byte_start":919213,"id":"section:10eb7a1a008b9b2bbd4b","kind":"section","labels":[],"line_end":13342,"line_start":13236,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:128a43c2fb914e4457a4","relation:3577e1909f0fa8eace8c","relation:4af0b6b9935f22272f0d","relation:4de5c99961567fea3687","relation:546503c93fdea5c74193","relation:5632cf49dfe57b5fd8e1","relation:59f68c71521b44719d77","relation:6059c1105744973ef74d","relation:6adb8ca0aaeb801f4c9c","relation:6dafbd097fdf1caaba6e","relation:803d2fffc36189855059","relation:84b375fa1413a7d3f74f","relation:91071c947ff8cb67f8f6","relation:971e48d0042e2397bbff","relation:9eb337e0e82088bb44ea","relation:abc219918dd8f81a5214","relation:b0830b4e4f7dffc032d0","relation:b73139329668b964b42a","relation:c51233ed451122bcc607","relation:d07a163b584cd45d54bd","relation:d73bcad5438a7d1b971e","relation:e465c72c8152c20f7514","relation:f5c78a19f3be3b1c7597","relation:fc4da087cce1f2539606"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Typing. A programme section (registered 2026-08-27 from the external bird's-eye review), not a claim: it organizes the existing 4D contracts and the four new ones below into one route and moves no marker. The organizing observation: TFPT is probably not missing twenty independent formulas; it is missing one mathematical growth principle that unfolds the discrete structure into a local, unitary, reflection-positive 4D","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Programme — the TFPT4D master route (one 4D transfer object instead of twenty formulas)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":929944,"byte_start":927211,"id":"section:8af62b489904198afb19","kind":"section","labels":[],"line_end":13377,"line_start":13343,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:71226dcab948d5b02b5f","relation:c1d76c0620b4e96194e2"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mC","\\mO"],"summary_excerpt":"Typing. A conditional identity \\ (ledger row DIMENSION.SELECTOR.4D.01), machine-checked in v975_dimension_selector_4d.py ( [formula in source] , sympy-exact). The [formula in source] structure of the compiler must not be read as a proof of four spacetime dimensions ( DIMENSION.UPLIFT.FIREWALL.01); what is checkable is a selector theorem under a named axiom set. Statement. Under A1 [formula in source] (propagating loc","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verified Selector — DIMENSION.SELECTOR.4D.01 (why [formula in source] , conditionally)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":942002,"byte_start":929944,"id":"section:daecafc150c9651ad391","kind":"section","labels":[],"line_end":13529,"line_start":13378,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:0a50a140e49ca576f423","relation:0b7f7a40894bc1fb3c41","relation:13a8f6206a716b21d32c","relation:16e1dc8da37e62ff865c","relation:1f334cca0491d0dca804","relation:1f9835565e478a1f91f1","relation:276646636830ad976770","relation:2a9401be4eb58be0aafa","relation:30e51a678f44fcfb32a4","relation:41e437279503ee771ebb","relation:42ca04328488321dac24","relation:5068edf709af4d4b6784","relation:507787672bf88f153556","relation:5f6124a88daa684213d6","relation:5f780e1fb4230de32fbc","relation:5fd6c2b1ec6741fa6f39","relation:69aa9d01a0bc01a1210a","relation:6f05c7a928ad24c7cf3e","relation:6fc499c48590eac32281","relation:71d380ddadd8a8f5c225","relation:79bd280b4da9a506a85e","relation:7efb1646ffdea11d6b97","relation:85d5d59a954dbfdfe745","relation:8a1506f921b5a240e735","relation:a5bff3798aefeacf64b5","relation:b33b40ff632eba70a88a","relation:c424f2a7fa368cedf801","relation:c8bcc0277d911dc954d9","relation:d71b69ed4cb75f7543a5","relation:d86f6818f0b194d034d2","relation:d9d6fa3edb0620bb6fee","relation:dafe19dc3b5d70029547","relation:df8414087ac771bf3d73","relation:e155fadedff836859a8c","relation:e15d4b219548c6e326a6","relation:e3992669c1e682629f0b","relation:eafc01a0882a8b7dbfd2","relation:eb95a32175b7ae31dcad"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row SEAM.SIMPLECURRENT.GENERATOR.01), not a claim. Context. The seam coverage carve ( v973_seam_route_narrowing.py) shows the [formula in source] fermion-bilinear half of the seam target is covered by the cited scaling-limit theorem; the named residual is N1 (the [formula in source] /GSO extension [formula in source] as a net statement — the 128 spinor currents are not bilinears)","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — SEAM.SIMPLECURRENT.GENERATOR.01 (one generator instead of 128 currents)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":948199,"byte_start":942002,"id":"section:17f2d15b7cbfb816c548","kind":"section","labels":[],"line_end":13615,"line_start":13530,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:2645e0ea3d980f35bf58","relation:3153ba02bef3cc1375b0","relation:5420a2bf3741dbe6be1c","relation:87ffe654d45f99b55042","relation:8f6dea54d3044766d70a","relation:adbe3eef0eaf12b8ad85","relation:bad5f4895caccab9c500","relation:c0b49ba8305d1437e094","relation:d1d26b745fa492388eb4","relation:d381296278cd44c86696","relation:f1d1056231db00a853c4"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row TFPT4D.LATTICE.ACTION.01); route step (2) of the DIMENSION.UPLIFT.FIREWALL.01 ordering made concrete — the single object on which nearly all open 4D questions become simultaneously testable. Demand. Exhibit one fully explicit finite family of 4D Euclidean lattice theories [formula in source] where [formula in source] are the fundamental holonomies (TFPT fixes representation c","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — TFPT4D.LATTICE.ACTION.01 (the explicit finite 4D lattice action and its seven finite gates)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":951710,"byte_start":948199,"id":"section:203b4eaaede7d9249190","kind":"section","labels":[],"line_end":13662,"line_start":13616,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:641096a9a0a651349f37","relation:77681a34c6f492b97c21","relation:895e53fec3995255bf52","relation:b3abdf6f23dc5c1de399","relation:bb7b22de3b2b62e614a6","relation:c5814a160c3a9dab0a71","relation:c7049c05e56f805c6cd7","relation:c7c6e820faf2267cd897"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"Typing. A research hypothesis contract \\ (ledger row SEAM.DETLINE.UNIFICATION.01) — a precise conjecture, not a result. Observation. Three separately open structures may be projections of one geometric object: (1) the seam extension is described by a Q-system/simple current ( SEAM.SIMPLECURRENT.GENERATOR.01); (2) the chiral fermion measure lives on a determinant line ( CHIRAL4D.NOMIRROR.01 demand C1); (3) anomalies a","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — SEAM.DETLINE.UNIFICATION.01 (the determinant-line unification hypothesis)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":954446,"byte_start":951710,"id":"section:6f0af99769531bda7e90","kind":"section","labels":[],"line_end":13696,"line_start":13663,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:04b29da262308ce5af3d","relation:1f115f7fec290c9db2d5","relation:3faf4a9790fee5ef3903","relation:3fe5e44deaa660674726","relation:8676bad063175f9c086f","relation:8ccb6c092ae9986ca198","relation:941ebe5ca8e0e39e1134","relation:99a82faf2d4ce96cf35f","relation:c0f275737a492fab9276","relation:f8a6cc1a9cb4eb1524a6","relation:f8fe02fcca185847be3b"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mC","\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row FTRANSFER.GENERATING.01); the constructive successor named by the FR.TRANSFER.01 typing guard. The four continuous-transfer interfaces ( [formula in source] : source masses [formula in source] pole, v183; [formula in source] : CP source [formula in source] , v169/ v184; [formula in source] : [formula in source] , v185; [formula in source] : [formula in source] , v164) are cur","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — FTRANSFER.GENERATING.01 (four transfer bridges from one generating functional)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":958981,"byte_start":954446,"id":"section:2256a2d99fd8e09d2837","kind":"section","labels":[],"line_end":13755,"line_start":13697,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:1700d1c0c86a12ce07f6","relation:1f2ad2ef516366599819","relation:24a295439b6ad3fc9d99","relation:2b3f73049200bfd25faf","relation:8d8160dcdba101b73f62","relation:b7f1cb837dc1113d5c4a","relation:d610183cb8afa36f4625","relation:e4aa48749a397fea696e"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row GAUGE.DETLINE.FIXPOINT.01), registered 2026-08-28 from review wave 3. Demand. All three gauge couplings ( [formula in source] / equivalently [formula in source] , [formula in source] , [formula in source] ) arise as stationary points of one nonabelian zeta-det / inflow functional on the determinant line — the nonabelian upgrade of the [formula in source] face ALPHA.QUILLEN.EX","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — GAUGE.DETLINE.FIXPOINT.01 (all three gauge couplings from one zeta-det functional)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":963773,"byte_start":958981,"id":"section:3ef64d782ddc411f1754","kind":"section","labels":[],"line_end":13823,"line_start":13756,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:194136254796855e55cf","relation:30161fdcb263357819f1","relation:34df4978b1383f4ada73","relation:3f9dc2c58734f6b0609c","relation:460c94d4c76afda3eb0b","relation:5132141e93910d38f9e3","relation:8d5c478b00d89b791d9e","relation:b4e045d2013b2f860d56","relation:d25f2a62c9aded5ac01b","relation:d98b9a149657afbab99c","relation:e6b2089b62cbf7e726ab","relation:f3a0aa2e7aa74260bbf4","relation:ff070994f229539ec1a5"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row GRAV.SPIN2.EMERGENCE.01), registered 2026-08-28 from review wave 3. Demand. From the same spectral determinant that carries the gauge fixpoints, a massless transversal spin-2 pole with two helicities, universal [formula in source] coupling, diffeomorphism Ward identities, and positive Hessian / reflection-positive transfer. Relation. The entanglement-equilibrium Einstein equa","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — GRAV.SPIN2.EMERGENCE.01 (massless transversal spin-2 from the same spectral determinant)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":968756,"byte_start":963773,"id":"section:16a3dfffba2175d45b88","kind":"section","labels":[],"line_end":13892,"line_start":13824,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:1d84e39165130e738345","relation:261cb84c1090866a679e","relation:42a212332f29d34c31e2","relation:4c952cfc204558a15ef1","relation:83d050b8eb8105ea7c44","relation:92974f60ea5d66c555df","relation:a383ad034978ba145483","relation:ee8fb303e7887722e641","relation:fb31a2aa6290a23992da"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mC","\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row FTRANSFER.SK.RHO0.01), registered 2026-08-28 from review wave 3; mechanism executed 2026-08-29. Demand. Cosmological transfers ( [formula in source] , [formula in source] , and any nonequilibrium 4D readout) need the pair [formula in source] , not [formula in source] alone — the Euclidean-cap / KMS initial state. Typed candidate. The [formula in source] saddle [formula in sou","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — FTRANSFER.SK.RHO0.01 (Schwinger–Keldysh completion: cosmological transfers need [formula in source] )","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":972125,"byte_start":968756,"id":"section:d185199a34886354d525","kind":"section","labels":[],"line_end":13935,"line_start":13893,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:2ca36daee530ebc0ed0b","relation:367b13552b00741f803c","relation:52fa87dd096ceabbf81c","relation:64cf37d1679d9fd921e2","relation:65a0079cf93cea725b08","relation:73feb9c9e112f80f8e9c","relation:e5e0ad0fc8a30f4b23a1","relation:e67e3f12e1912b779592"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row SEAM.MMST.TYPEIII.CHARGED.01), registered 2026-08-29 from review wave 5. Demand. One scaling-limit theorem [formula in source] strongly on the finite-energy core [formula in source] crossed-product continuity, from which [formula in source] , [formula in source] , type III [formula in source] , unique rotational KMS, unique conditional expectation, deck equidistribution and m","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — SEAM.MMST.TYPEIII.CHARGED.01 (one scaling-limit theorem)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":980911,"byte_start":972125,"id":"section:be838d1d0321f5b1e358","kind":"subsection","labels":[],"line_end":14102,"line_start":13936,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:04c852d77129319deaa4","relation:1d151c95bfc82c55db78","relation:29b929dad2cb0a026177","relation:3578d7b55329215573ab","relation:3f8dfe00eee956bfe2e9","relation:4ebda45910aa1449cf29","relation:57283befa424c7ac15a6","relation:601063064ac34b4f741d","relation:624a462f8eb3a0cf61af","relation:829a20089daf0fa29a91","relation:8cdd2e062fc3fd534d2c","relation:942bfc49bfc02d467797","relation:c9b8d56cbcf42b1454a0"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"The residual TEL-B-EXTERNAL is restated below. The earlier scalar dyadic increment [formula in source] with [formula in source] sufficient for [formula in source] is superseded — [formula in source] was measured [formula in source] (r645) but is no longer the route. Numerically closed ( [formula in source] ; conditional analytic [formula in source] with [formula in source] ); round 3 closed C1, C2a and the interval-T","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TEL-B reduction (2026-09-04)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":989480,"byte_start":980911,"id":"section:14713793ccdcb9ca035e","kind":"section","labels":[],"line_end":14237,"line_start":14103,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:094fe983db34a6a6d6f1","relation:0a5f8c07bd9ed9150d69","relation:15b45268f649c5f5a66b","relation:15ffdf00807ddd51bcff","relation:1717a0b8f2960baae155","relation:1ba27af960ed6df916d9","relation:24d4d3e380a8eac135da","relation:3b628ad8e3c3cedcf4f5","relation:3eb6cf23c5aa8a4a2dbb","relation:3f5242016cec06cc97d6","relation:413d6af74da9eb3ed4e6","relation:45718ade61c1370a0e63","relation:64593dd6724070f28d6d","relation:7386dac6455bcdb0ec90","relation:7b027133241eb99d134c","relation:7d6b6ea6ede42dbf1814","relation:7ffab11a7395fc6de885","relation:86bd9a55b165623fa989","relation:8873f6df4ab729a0af32","relation:89c7e53e9a1026a91e4f","relation:8b6579db0fb44be7ccb3","relation:9c95683c618e0df8dc83","relation:9ddd6b2a1488f1e9f2fa","relation:a2f90107ae9e0b2c5e1e","relation:a5141cf5f8d72dd7e009","relation:a77032cabf5fcfaac068","relation:a9c43f0265af7c854209","relation:aa56020839dee733b799","relation:ab9f78bf5d5f6a0aa1f1","relation:af7da9d639583557feb1","relation:c84682e2ef91b008558d","relation:c986fb4599f89b2086e7","relation:d890d22e9690cf0d373f","relation:dad7f579e1215f4f79c7","relation:dd9c61bc4972a8e7cb47","relation:dfde60102b488bea36e8","relation:e814654276149cd6f76f","relation:eac8c85b1288d283485a","relation:f7eb40b1f538adce4175","relation:f8172e439f425cad9997"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row TFPT.TOE.COMPLETE.01), registered 2026-08-29 from review wave 4. This row names the AND of eight gates; it does not close any of them and it does not upgrade a marker. Dual rest: the compiler residual [formula in source] sits beside [formula in source] ; this contract is the named AND, not a closure of either.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — TFPT.TOE.COMPLETE.01 (the named AND of eight completeness gates)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":990755,"byte_start":989480,"id":"section:f66120aaaa353a653001","kind":"section","labels":[],"line_end":14255,"line_start":14238,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:047430ab6ba3cb564bca","relation:0ae4d5ca14846afd14df","relation:2ae8c59493265d09ca1d","relation:4232563b799ab3a7acfd","relation:6bf101a5c004629365ea","relation:907fb0d699d0dd8619a2","relation:aace21aadb1c1913f756","relation:b5d0da2c564092162099","relation:e45d087aef3c09a35bab"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mC","\\mO"],"summary_excerpt":"Typing. A candidate \\ (ledger row FLAV.NUSCALE.06); mechanism [formula in source] the [formula in source] -to-flavor operator . No seesaw closure; FLAV.NUSCALE.05 unmoved. ( v1001_ nu_ pentagon_ chain.py.)","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — FLAV.NUSCALE.06 (pentagon-class misalignment candidate)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":993831,"byte_start":990755,"id":"section:b26740716a2d0cca0ac3","kind":"section","labels":[],"line_end":14301,"line_start":14256,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:31ab81e652be5fa7b7f3","relation:6c4ae42e7d953addec06","relation:8238b2d091c26f694b70","relation:93583942082581cf8c03","relation:b17d9746611655984edb","relation:e614b7ea40d98409ece0"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mE","\\mO","\\mX"],"summary_excerpt":"Typing. A research contract \\ (ledger row FLAV.NU.TEXTURE.MECHANISM.01), registered 2026-08-29 from review wave 5. ( v1003_ nu_ structural_ nulls.py.) Executed content. Charged-sector data [formula in source] , [formula in source] (coset min-norms all [formula in source] ) . Schur-texture NULL : all [formula in source] preregistered [formula in source] combinations fail; D4 reflection forces [formula in source] ; hie","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — FLAV.NU.TEXTURE.MECHANISM.01 (both structural nulls as binding constraints)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":999519,"byte_start":993831,"id":"section:789583ec50a9f61cdf33","kind":"section","labels":[],"line_end":14380,"line_start":14302,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:16d6aa8ee448d9281d0c","relation:182bc77558ef562c52b5","relation:1a2771bf4c3924c3822b","relation:22fb104bd734ed10b93d","relation:25f6892cdbaa475616a3","relation:2bcb00b5c7b89822af8c","relation:45edf9a57bbd9ec82327","relation:4aa2a221973d5f7a07b4","relation:6dded99a91c79019f5be","relation:7718aa028b9c08e8d59f","relation:b514d3eb6d891b25d237","relation:bab8e52bdb38f8cddebf","relation:cef8c8654e9dc39f71d6","relation:de3e5c2feb8349147f52","relation:f0c40880a824cb5bf2a1","relation:f52c3315477c5f2d579c","relation:f8dfaaa2bf58e8af569b"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row SEAM.MILNOR.LOCALRING.01), registered 2026-08-30 from review wave 6. ( v1004_ milnor_ frobenius_ gray.py.) Demand. A canonical identification between the raw seam collar / [formula in source] transition bus and the reduced Milnor algebra [formula in source] preserving simultaneously the dual-number action, the Frobenius pairing, the Gray torsor, the deck action and CP. Accept","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Research Contract — SEAM.MILNOR.LOCALRING.01 (canonical identification of the seam collar with the reduced Milnor algebra)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":1000757,"byte_start":999519,"id":"section:8a4e51786c63605a14f0","kind":"section","labels":[],"line_end":14396,"line_start":14381,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts"],"relation_ids":["relation:2acab06453e61d0796a3","relation:c3494406c85cc02c238f"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"Typing. A research contract \\ (ledger row GRAV.WEINBERG.WITTEN.01), registered 2026-08-30 from review wave 6. Child of TOE gate T7; cross-link GRAV.SPIN2.EMERGENCE.01 (listed here, not back — that would cycle). Demand. 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Eine Bühne mit Entfernungen und einer Uhr entsteht erst, wenn viele dieser Beziehungen ein beständiges Muster bilden.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kein zusätzlicher Behälter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3208,"byte_start":1381,"id":"section:d3794006a1d3bb5eae1a","kind":"section","labels":[],"line_end":33,"line_start":10,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Eine ausreichend konkrete Fassung benötigt mindestens: Zustände: Was ist gegeben, einschließlich relevanter Korrelationen? Operationen: Welche Veränderungen sind erlaubt? Zusammensetzung: Wie dürfen Vorgänge hintereinander und nebeneinander verbunden werden? Aufzeichnungen: Welche Spuren bleiben erhalten und dürfen später erneut benutzt werden? Auslesung: Welche Ergebnisse sind mit welchen Wahrscheinlichkeiten beobac","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die fünf Bestandteile","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4343,"byte_start":3208,"id":"section:604362b8bab92d196a33","kind":"section","labels":["eq:op"],"line_end":46,"line_start":34,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Zwei Uhren können jetzt beide zwölf anzeigen und trotzdem verschieden weiterlaufen. Eine ist aufgezogen, die andere steht kurz vor dem Stillstand. Wer nur das Zifferblatt betrachtet, sieht den Unterschied noch nicht. Ein späterer Blick unterscheidet sie.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wann zwei Beschreibungen wirklich dasselbe sagen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5759,"byte_start":4343,"id":"section:7f51ad41a315a914969f","kind":"section","labels":["eq:vorwaerts"],"line_end":60,"line_start":47,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"TFPT liefert eine reichhaltige Grammatik: Träger, Darstellungen, Gitter, markierte Symmetrien, Projektoren und kurze wiederverwendete Zahlenformeln. 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Zuerst fällt auf, dass kleine geometrische und algebraische Daten in verschiedenen Rechnungen wiederkehren. Der Fünferträger führt zu einem 16-dimensionalen Spinor; die passenden Gitterfaktoren führen zu [formula in source] ; ein komplexer Viererträger zeigt 60 besondere Strahlen. Clocks, Ladungszuordnungen und Fl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vom Wiedererkennen zur gemeinsamen Ursache","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7642,"byte_start":6733,"id":"section:53cd7350646974a52932","kind":"section","labels":[],"line_end":71,"line_start":67,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Die älteren, in S09 zusammengefassten Untersuchungen fanden mehrere Räume, die man nicht einfach gleichsetzen darf: eine Kommutantenalgebra, einen Majorana-/Fockraum, einen festen Teilchensektor, eine verdoppelte Familienbeschreibung und eingeschränkte Kanalmodelle. Manche lokalen Ansichten ließen verschiedene gemeinsame Dynamiken zu. Andere Tests konnten unter engeren Voraussetzungen ausgewählte Zustände bestimmen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum Spektren und Einzelbilder nicht genügten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9498,"byte_start":7642,"id":"section:9e09442fc2b56a8dbcb7","kind":"section","labels":[],"line_end":86,"line_start":72,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"L30mmL55mmL65mm Etappe& Erkenntnis& Neue Frage\\\\ Vorarbeiten, in S09 rückblickend beschrieben&Mehrere algebraische Ansichten, Lorentzkegel, verborgene Richtungen, lokale und gemeinsame Kanäle.&Welche Informationen gehen beim Auslesen verloren?\\\\ 13. September: Compiler-Manuskript S09&60 Strahlen, 15 Kontexte, zwei Schatten desselben Prozesses; explizite Vormessung mit Register.&Wer wählt Kreuzkopplung, Kontextgewicht","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die dokumentierte Entwicklung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10684,"byte_start":9498,"id":"section:4bc79237555b7b40c52c","kind":"section","labels":[],"line_end":94,"line_start":87,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Der eingefügte Gesprächstext spricht von einem Regelwerk mit Logbuch und von Raum und Materie als Mustern seiner Spuren. Das trifft die Forschungsintuition. Die Formulierung „TFPT ist die Grammatik, der Universalraum die Ausführung“ ist als Einstieg hilfreich.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was von der anschaulichen Ursprungserzählung bleibt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":66,"byte_start":0,"id":"section:878a5f3a5cac7f12967e","kind":"chapter","labels":["ch:algebra"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die mathematischen Bauteile von TFPT","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1113,"byte_start":66,"id":"section:185051c6a24906465080","kind":"section","labels":[],"line_end":12,"line_start":3,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Die historische Kurzfassung nennt [formula in source] und einen fünfteiligen Träger. Vollständig gelesen setzt P1 einen orientierten Rand beziehungsweise eine Naht, einen geeigneten positiven Kern und eine Normierung voraus. P2 setzt Art und Struktur des Trägers voraus; die spätere [formula in source] -Lesart wird mit Farb- und schwachen Richtungen verbunden. Orientierung, Positivität, komplexe Struktur und Markierun","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Ausgangsannahmen enthalten mehr als zwei Zahlen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2337,"byte_start":1113,"id":"section:4d28369773fe1e5e6d55","kind":"section","labels":[],"line_end":26,"line_start":13,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Bei fünf komplexen Richtungen kann man antisymmetrische Kombinationen von null, zwei und vier Richtungen bilden. Zusammen erhält man Das ist die gerade Spinorstruktur von [formula in source] . „Antisymmetrisch“ heißt hier: Beim Vertauschen zweier Plätze wechselt ein Vorzeichen. Es ist eine genaue Bauvorschrift, keine bildliche Ähnlichkeit.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vom Fünferträger zum Spinor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4400,"byte_start":2337,"id":"section:dc570a18f524ed8c9083","kind":"section","labels":[],"line_end":57,"line_start":27,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Die beiden positiven Wurzelgitter [formula in source] und [formula in source] besitzen Determinante vier und Diskriminantengruppe [formula in source] . Eine Diskriminantengruppe beschreibt hier die möglichen Restklassen, mit denen man das Gitter ohne Verlust der Ganzzahligkeit ergänzen kann. Für passende Generatoren gilt modulo eins Diagonal gekoppelt ist die Summe [formula in source] ganzzahlig. Die vier gemeinsamen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die Verklebung wirklich zu E [formula in source] 8 führt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6023,"byte_start":4400,"id":"section:16e8821413eeadbb7954","kind":"section","labels":["eq:branch"],"line_end":83,"line_start":58,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Die 240 Wurzeln sind besondere Vektoren in einem acht-dimensionalen Raum. Hinzu kommen acht Cartanrichtungen, sodass die Lie-Algebra 248 Dimensionen besitzt. Unter [formula in source] lautet ihre komplexe Zerlegung L47mmrY Sektor& Wurzeln& Generatoren einschließlich Cartan\\\\ [formula in source] &40& [formula in source] \\\\ [formula in source] &12& [formula in source] \\\\ Gemischter Vektorsektor&60& [formula in source] ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wurzeln und Generatoren sind verschiedene Zählungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7221,"byte_start":6023,"id":"section:4f3b7c29cf7a3cce86dd","kind":"section","labels":[],"line_end":90,"line_start":84,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Ein Strahl ist ein reiner Zustand ohne seine insgesamt irrelevante globale Phase. Ein Kontext ist eine vollständige orthogonale Viererbasis: vier mögliche Ausgänge einer scharfen Messung. Im markierten komplexen Viererträger ergeben sich 60 besondere Strahlen in 15 solchen Kontexten. In der gewählten Kodierung sind dies die reinen Zwei-Qubit-Stabilizerzustände und ihre vollständigen Pauli-Kontexte. S09, Kap. 3 und 9","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das endliche Fenster: 60 Strahlen und 15 Kontexte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8754,"byte_start":7221,"id":"section:f7bb81d0c7d16a0ad2bc","kind":"section","labels":[],"line_end":106,"line_start":91,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"L45mmL31mmL74mm Objekt& Größe& Was die Zahl zählt\\\\ [formula in source] -Wurzeln&240&Besondere Vektoren, keine 240 unabhängigen Raumrichtungen.\\\\ [formula in source] &248&Dimension der Generatoralgebra.\\\\ Ein Viererträger& [formula in source] &Zustände eines Ququarts, hier als zwei Qubits kodiert.\\\\ Vier solche Träger& [formula in source] &Komplexe Hilbertraumdimension der Zelle.\\\\ 15 allgemeine CQ-Blöcke& [formula i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Räume im Größenvergleich","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":71,"byte_start":0,"id":"section:03f297517948c833cb3f","kind":"chapter","labels":["ch:prozess"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Ein gemeinsamer Prozess mit zwei Schatten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1558,"byte_start":71,"id":"section:857d7f1b54632b57d3c7","kind":"section","labels":["eq:T"],"line_end":19,"line_start":3,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Man beginnt mit einem Strahl [formula in source] : Kontext [formula in source] , Ergebnis [formula in source] . Dann wählt man einen nächsten Kontext [formula in source] und misst in dessen Basis. Die Quellkonstruktion benutzt [formula in source] ist eine [formula in source] -Inzidenzmatrix. Sie erlaubt den aktuellen Kontext und sechs andere, mit ihm inzidente Kontexte. Jeder erlaubte Nachfolger erhält in dieser spez","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine einzelne Messrunde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3449,"byte_start":1558,"id":"section:07562212c420bc603ab7","kind":"section","labels":["eq:D","eq:shadows"],"line_end":55,"line_start":20,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Die Matrix [formula in source] summiert die vier Ergebnisgewichte jedes Kontexts. Die Matrix [formula in source] liest die 15 nichttrivialen Pauli-Erwartungswerte aus. Mit [formula in source] lauten ihre Einträge Für [formula in source] und [formula in source] ergibt sich exakt Der Systemschatten entwickelt sich somit als depolarisierender Kanal Die Dämpfung [formula in source] entsteht aus der Kontextkombinatorik. B","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kontext und Quantenzustand als zwei Auslesungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4623,"byte_start":3449,"id":"section:2f9359226392971fd8ab","kind":"section","labels":["eq:Tfactor"],"line_end":74,"line_start":56,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Die in S01 ausgearbeitete Faktorisierung lautet Hier gelten [formula in source] , [formula in source] und [formula in source] . Die beiden Zeilenräume sind orthogonal. Im selben Kontext haben die Pauli-Vorzeichenvektoren Skalarprodukt drei für denselben Strahl und minus eins für verschiedene Strahlen; bei inzidenten Kontexten bleibt eine gemeinsame Pauli-Richtung. Diese Werte ergeben genau die Einträge von","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die genaue Kompression auf 30 Koordinaten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6433,"byte_start":4623,"id":"section:afbf3fadca58bdf36ba7","kind":"section","labels":[],"line_end":96,"line_start":75,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Aus [formula in source] mit Permutationsmatrizen folgt beim gleichgewichteten Mitteln unmittelbar [formula in source] . Zusätzliche Konjugation durch die Symmetriegruppe [formula in source] ändert das nicht: S07 berichtet 5040 Terme über 4500 verschiedene Matchings, gegenüber 24\\,601\\,472 insgesamt möglichen perfekten Matchings des bipartiten Inzidenzbildes. Diese kombinatorische Realisierung ist konkret. Die Gleichg","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum Symmetrie die Gewichte noch nicht auswählt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7204,"byte_start":6433,"id":"section:73c8ccccad805521ee94","kind":"section","labels":[],"line_end":111,"line_start":97,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Für die Kontextmatrix gilt Ihre Determinante ist negativ. Eine reelle Matrixexponentialfunktion hat jedoch [formula in source] . Deshalb ist [formula in source] auf diesem 15-dimensionalen Raum kein [formula in source] mit reellem [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein Schritt ist nicht dasselbe wie zwei halbe Schritte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7280,"byte_start":7204,"id":"section:09b2a19a3b43221cd73e","kind":"chapter","labels":["ch:memory"],"line_end":113,"line_start":112,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Gedächtnis: Was ein einzelnes Bild verschweigt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9410,"byte_start":7280,"id":"section:9338f49c76995a6c1078","kind":"section","labels":[],"line_end":147,"line_start":114,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Ein klassisch-quantenmechanischer Zustand, kurz CQ-Zustand, besitzt 15 positive [formula in source] -Blöcke [formula in source] . Zusammen haben sie 240 reelle lineare Koordinaten und Gesamtspur eins. Die feste Regel macht jeden Ausgangsblock in seinem Kontext diagonal. Deshalb gilt Es ist also nicht richtig, 240 Koordinaten pauschal als kleinste dauerhaft autonome Hülle dieser festen Ausführung auszugeben.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Allgemeine Kontextblöcke brauchen eine andere Beschreibung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10711,"byte_start":9410,"id":"section:7b0a02a0a71423be858b","kind":"section","labels":["eq:record"],"line_end":168,"line_start":148,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Für die vier Projektoren eines Kontexts sind [formula in source] Spiegelungen. In Dimension vier gilt Allgemein in Dimension [formula in source] wäre die linke Seite [formula in source] . Der kurze Auslöschungseffekt ist hier also tatsächlich viererspezifisch.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie die Aufzeichnung gebaut wird","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12540,"byte_start":10711,"id":"section:742def90427665ea060c","kind":"section","labels":[],"line_end":182,"line_start":169,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Für einen gleichförmigen reinen Eingang in der gewählten Kontextbasis erzeugt eine Vormessung maximale Verschränkung. Ohne Registerblick ist der Systemzustand [formula in source] . Nun gibt es zwei Ausführungen: Derselbe kohärente Speicher wird nochmals gekoppelt: [formula in source] stellt den reinen Eingang wieder her. Ein neuer Speicher wird benutzt: Im reduzierten System wird die Dephasierung wiederholt; [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das Echo des behaltenen Registers","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13348,"byte_start":12540,"id":"section:8f8ef2bc44182898f3d3","kind":"section","labels":[],"line_end":192,"line_start":183,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Bei frischen Registern trägt eine Folge von Kontexten den kohärenten Zustand Das Weglassen des Registers summiert Dichteoperatorbeiträge. Eine kohärente Projektion auf eine Registersuperposition summiert Amplituden und beschreibt ein anderes Experiment, einschließlich seiner Erfolgswahrscheinlichkeit.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reihenfolge bleibt wichtig","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15023,"byte_start":13348,"id":"section:63347caf89772f988e6e","kind":"section","labels":[],"line_end":205,"line_start":193,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Eine nichtverschwindende Beobachtungsfolge eines geschlossenen endlichen Systems mit festem unitärem Schritt ist eine endliche Summe von Phasenfaktoren. Nach Zusammenfassung gleicher Frequenzen besitzt ihr mittleres Betragsquadrat einen positiven Cesàro-Grenzwert. Sie kann daher nicht für alle [formula in source] exakt wie [formula in source] abklingen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Endliches Gedächtnis und scheinbares Vergessen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":72,"byte_start":0,"id":"section:c4ccbe0327b52a8995ae","kind":"chapter","labels":["ch:zelle"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die Vierträgerzelle: ein gemeinsames Muster","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1404,"byte_start":72,"id":"section:b6f998b1c0cd688874c9","kind":"section","labels":["eq:omega"],"line_end":24,"line_start":3,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Vier Träger mit je vier Basiswerten besitzen den total antisymmetrischen Zustand Jedes Basiswort verwendet alle vier Werte genau einmal. Die 24 Permutationen erhalten passende Vorzeichen. Das Ergebnis ist ein reiner gemeinsamer Zustand. Jeder einzelne Träger sieht für sich trotzdem maximal gemischt aus: Die Paarreduktion hat Rang sechs und sechs gleich große Eigenwerte [formula in source] . Die Ordnung steckt in den ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein Zustand, dessen Teile allein nichts verraten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2609,"byte_start":1404,"id":"section:832b78a30b5ba8bd9db5","kind":"section","labels":[],"line_end":38,"line_start":25,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Sei [formula in source] der Projektor auf den symmetrischen Paarraum. Wenn für alle Paare [formula in source] gilt, dann hat jeder Swap Eigenwert minus eins. Da Transpositionen alle Permutationen erzeugen, folgt Für [formula in source] ist dieser Raum eindimensional, für [formula in source] null. Auch gemischte Zustände mit entsprechender Trägerbedingung erfüllen die Aussage. Für [formula in source] existieren aber e","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Hüllensatz und seine genaue Voraussetzung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3902,"byte_start":2609,"id":"section:bc9c74dbb2c87642015e","kind":"section","labels":["eq:tet-spec"],"line_end":54,"line_start":39,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Das vollständige Tetramermodell lautet Es besitzt das exakte Spektrum Der Grundzustand ist [formula in source] , die Lücke [formula in source] . Die hochgestellten Zahlen zählen die Zustände pro Energiewert und summieren sich zu 256.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine weiche Energiebedingung erlaubt Bewegung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5057,"byte_start":3902,"id":"section:876f3bafcba620663924","kind":"section","labels":[],"line_end":68,"line_start":55,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Der vollständige Graph, ein Stern und ein Pfad besitzen auf vier Trägern denselben antisymmetrischen Grundzustand, aber verschiedene Anregungen. Für gleiche Sterngewichte ist die Lücke [formula in source] statt [formula in source] . S01 nennt für einen Pfad mit Gewichten [formula in source] etwa [formula in source] ; S06 für sechs Gewichte [formula in source] etwa [formula in source] . Die letzten Werte werden hier a","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was ein Zustand über seinen Generator verrät","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5655,"byte_start":5057,"id":"section:0b688b82ab8e8eef5c30","kind":"section","labels":[],"line_end":73,"line_start":69,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Der Projektor [formula in source] kommutiert mit allen Swaps. Daher erhält jede rein zellinterne Austauschentwicklung, auch mit zeitabhängigen Gewichten, den Anteil [formula in source] . Kollektive [formula in source] -Drehungen tun dasselbe. Ein Grundzustand kann also bekannt sein, ohne dass der vorhandene Ablauf einen beliebigen Eingang dorthin bringt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum Austausch allein die Zelle nicht herstellt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5734,"byte_start":5655,"id":"section:5fdc43c1e9d11b47f1eb","kind":"chapter","labels":["ch:fugen"],"line_end":75,"line_start":74,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Vermittlung und Graph: die Prüfung der fünf Fugen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7886,"byte_start":5734,"id":"section:891b2fdc1936c2c62fa3","kind":"section","labels":[],"line_end":103,"line_start":76,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Der gewünschte positive Austausch lässt sich in einem kleinen Modell genau erklären. Man ergänzt den Paarraum [formula in source] durch einen sechsdimensionalen Vermittler mit Energie [formula in source] . Die partielle Isometrie [formula in source] erfüllt Für bleiben die zehn symmetrischen Zustände bei null; die antisymmetrischen Zustände koppeln paarweise an den Vermittler. Die unteren Energien sind Nach Identifik","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie ein virtueller Zwischenzustand bindet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9877,"byte_start":7886,"id":"section:d4caab38fff3da8c5ab2","kind":"section","labels":[],"line_end":125,"line_start":104,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"S11 macht die zusätzliche Zuordnung: Ein [formula in source] -Spinorgewicht [formula in source] ist ein Ort; das [formula in source] -Gewicht [formula in source] ist der lokale Viererzustand. Die 64 Gewichte von [formula in source] werden somit als 16 Orte mit je vier inneren Zuständen gelesen. Das ist eine konkrete bedingte Interpretation, keine bloße Umbenennung einer bereits gegebenen räumlichen Geometrie.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Clebsch-Vorschlag: eine genaue neue Graphlesart","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11916,"byte_start":9877,"id":"section:e8ca7f66afa7e0c7aec4","kind":"section","labels":[],"line_end":134,"line_start":126,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Die Graphkombinatorik folgt aus der angegebenen Ortslesart. Um daraus einen Vielteilchen-Hamiltonoperator zu erhalten, braucht man außerdem eine Fock- oder Tensorproduktstruktur, Besetzungsbedingungen, die Bedeutung der virtuellen Zustände und ihre Energien. Betragsgleiche Chevalley-Strukturkonstanten wählen noch keine physikalischen Kopplungsstärken in normierten Mehrteilchenzuständen aus. Gleiche [formula in source","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Welche Auswahl hier noch hinzukommt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13528,"byte_start":11916,"id":"section:36b4c6cbfd02672cdd07","kind":"section","labels":[],"line_end":153,"line_start":135,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"L74mmY Clebsch-Cluster bei [formula in source] , nach S11& Berichteter Wert\\\\ Grundenergie& [formula in source] \\\\ Grundzustand&Eindeutiges [formula in source] -Singulett, Form [formula in source] \\\\ Erster angeregter Singulettwert& [formula in source] ; mindestens vier orthogonale Moden, Gap etwa [formula in source] \\\\ Erste adjungierte Anregung& [formula in source] , Gap etwa [formula in source] \\\\ Weitere Multiple","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die berichteten Clusterzahlen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14709,"byte_start":13528,"id":"section:a7608634204de12353e6","kind":"section","labels":[],"line_end":169,"line_start":154,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"S11 behauptet für den vollständigen Graphen mit [formula in source] einen eindeutigen Grundzustand bei [formula in source] und Gap [formula in source] . Energie und Gap stimmen; die Eindeutigkeit stimmt ab acht Trägern nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neue Korrektur: Singulett heißt nicht eindeutig","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16989,"byte_start":14709,"id":"section:5d3eedfde8ebe570d54e","kind":"section","labels":[],"line_end":191,"line_start":170,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Operatoren unterscheiden (v1.3): Das folgende [formula in source] beschreibt eine gleichkontextige Vierer-Aufzeichnung. Das neue binäre Austauschregister [formula in source] ist ein anderer Operator und nachweislich nicht Clifford. Seine zusätzliche Ressourcenanforderung widerspricht der folgenden Darstellbarkeit von [formula in source] nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neue Präzisierung: Aufzeichnung ist nicht durch die 248 verboten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":66,"byte_start":0,"id":"section:4358385250c3165a4dd3","kind":"chapter","labels":["ch:two"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Zwei Zellen: aus Verbindung wird Dynamik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":839,"byte_start":66,"id":"section:b48be491ca3293694d6c","kind":"section","labels":[],"line_end":7,"line_start":3,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Ist eine reduzierte Dichtematrix [formula in source] rein, so muss der gemeinsame Zustand bezüglich [formula in source] und seinem Rest faktorisiert sein. Sein Träger liegt in [formula in source] . Sind alle disjunkten Zellmarginalien unverändert rein, ist der Gesamtzustand ein Produkt über die Zellen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die Zellen beim Verbinden ihre Reinheit verlieren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1875,"byte_start":839,"id":"section:e11a7313a455e05077d3","kind":"section","labels":["eq:Hred"],"line_end":28,"line_start":8,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Zwei vollständige Tetramerzellen mit genau einer Brücke haben Der volle Raum besitzt [formula in source] Dimensionen. Trotzdem bleibt die Entwicklung des Produktzustands in einem zweidimensionalen invarianten Unterraum: Die beiden Vektoren sind orthonormal; [formula in source] und [formula in source] . Es folgt Die Brücke koppelt den Produktgrundzustand an eine gemeinsame adjungierte Anregung. Beide Zellhälften verwe","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein kleiner exakter Raum in einem großen Hilbertraum","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4244,"byte_start":1875,"id":"section:fc591aea070ffbf90ca9","kind":"section","labels":["eq:alllambda13","eq:gapbound"],"line_end":73,"line_start":29,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Mit lauten die beiden Eigenwerte Die negative Korrektur beschreibt die Absenkung gegenüber dem einfachen Produktwert [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Energie und ein wirklicher Grundzustandsnachweis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5445,"byte_start":4244,"id":"section:24a64e5e33618f73a9fb","kind":"section","labels":[],"line_end":95,"line_start":74,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Der niedrige Eigenzustand lässt sich schreiben als Seine Zellreduktion besitzt das Spektrum Die Entropie in natürlichen Logarithmen ist Bei [formula in source] sind [formula in source] und [formula in source] ; bei [formula in source] gilt [formula in source] . Schon eine endliche einzelne Brücke macht die lokale Zelle gemischt. Energieabsenkung und Verschränkung sind hier keine unabhängig eingesetzten Zusätze.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verschränkung aus derselben Kopplung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6560,"byte_start":5445,"id":"section:91ff5141bf20d181c974","kind":"section","labels":["eq:two-clock"],"line_end":111,"line_start":96,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Starte im Produkt [formula in source] und lasse denselben konstanten gekoppelten Hamiltonoperator wirken. Dann gilt Bei [formula in source] vereinfacht sich dies zu [formula in source] . Der Energieinhalt beider Zellen pulsiert in einem messbaren Muster.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein Uhrsignal ohne zusätzlich gewählten lokalen Tick","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7528,"byte_start":6560,"id":"section:c0f2a2dfb49d5566a92d","kind":"section","labels":[],"line_end":120,"line_start":112,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Ein einzelner eindeutiger Singulettgrundraum besitzt keine logische Zustandsvielfalt. Das Produkt solcher Grundräume bleibt eindimensional. Wer alles auf diese Grundräume projiziert, erhält nur eine skalare Energie. Nichttriviale effektive Dynamik muss Anregungen, Randzustände, Multiplizitäten oder zusätzliche Vakuumsektoren behalten.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum viele Zellen noch ein eigener Schritt sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":71,"byte_start":0,"id":"section:9e00ecb925c20a1741b1","kind":"chapter","labels":["ch:zeit"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Zeit: Takt, Uhrwerk und lesbare Veränderung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1193,"byte_start":71,"id":"section:4d18be97a0f76b18da6a","kind":"section","labels":[],"line_end":15,"line_start":3,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Eine zyklische Matrix ist zunächst ein Taktmuster. Eine Dynamik sagt, wann welcher Zustand entsteht. Eine Uhr braucht zusätzlich eine beobachtbare Anzeige und eine Kalibrierung. Diese drei Ebenen müssen zusammenpassen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Drei Bedeutungen des Wortes Clock","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2069,"byte_start":1193,"id":"section:35bfac0bdfd197b60694","kind":"section","labels":[],"line_end":20,"line_start":16,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Der vollständige gleichgewichtete Tetramer-Hamiltonoperator ist eine zentrale Transpositionssumme. Deshalb kommutiert er mit jedem [formula in source] und jedem [formula in source] . Die Paarenergien ändern sich unter seiner freien Entwicklung nicht. Eine Tabelle, die nacheinander einen lokalen [formula in source] -Tick anwendet, ist somit kein Beweis, dass genau diese Anzeige unter [formula in source] von selbst läu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die Paarenergien unter dem Tetramer stillstehen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":3008,"byte_start":2069,"id":"section:65aec690e67a6cf72e4c","kind":"section","labels":[],"line_end":38,"line_start":21,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Ein präparierter nichtstationärer Zustand kann dennoch unter demselben Tetramer laufen. Für einen lokalen spurfreien hermiteschen Pauli [formula in source] mit [formula in source] setze Da [formula in source] , folgt Die lokalen Anzeigen oszillieren gegeneinander; ihre Summe bleibt null. Die Periode ist [formula in source] . Präparation, Ausleserichtung und die Kalibrierung von [formula in source] sind weitere Eingab","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine laufende lokale Anzeige im gesetzten Modell","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4494,"byte_start":3008,"id":"section:c6cf9af897d87aca9c02","kind":"section","labels":[],"line_end":57,"line_start":39,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Zerlege [formula in source] . Die vier [formula in source] sind orthonormal. Wähle zusätzlich Weil jedes Wort von [formula in source] jedes Energielabel einmal enthält, gilt [formula in source] . Für erhält man [formula in source] . Die Zeiten [formula in source] liefern vier orthogonale Anzeigen. Global ist der Zustand stationär, bedingt auf die Uhranzeige entwickelt sich das System. Das ist eine konkrete Page-Woott","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine relationale Viereruhr ist konstruierbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":5172,"byte_start":4494,"id":"section:205f9626334b2508e7c4","kind":"section","labels":[],"line_end":62,"line_start":58,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Aus [formula in source] folgt [formula in source] . Die historischen Größen [formula in source] und [formula in source] beschreiben deshalb sechsfach wiederholte Faktoren [formula in source] und [formula in source] . Eine physikalische Rate ist erst [formula in source] für einen festgelegten Schritt [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum ein Logarithmus noch keine Sekunde ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5883,"byte_start":5172,"id":"section:95cd53a239ce47b30384","kind":"chapter","labels":["ch:echo"],"line_end":67,"line_start":63,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Verschiedene Präparationsverträge bleiben getrennt Dieses Kapitel bewahrt die ursprüngliche endliche Schaltung mit Erfolg [formula in source] aus dem vorausgesetzten Zweisingulett-Eingang. Der neue Stern-Spektralfilter erreicht [formula in source] aus demselben Eingang, setzt aber kontrollierte kontinuierliche Pulse voraus. Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die ausführbare Präparation und der Mehrzeittest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7250,"byte_start":5883,"id":"section:613a11f99cd6aeeee686","kind":"section","labels":[],"line_end":89,"line_start":68,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Die Präparationsnotiz S02 geht über den abstrakten Satz „ [formula in source] existiert“ hinaus. Sie beschreibt eine konkrete Schaltung, die aus einem einfachen Eingang den Zustand mit Erfolgsanzeige herstellt, anschließend ein Register schreibt und die Rückkehr ausliest. Laut Quelle wurde die Schaltung exakt simuliert, nicht auf Hardware ausgeführt. Ihr Zugriff auf zusätzliche Hilfssysteme und Nicht-Clifford-Operati","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was S02 tatsächlich geschlossen hat","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8727,"byte_start":7250,"id":"section:fe86732634e908eb107f","kind":"section","labels":[],"line_end":104,"line_start":90,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Der benötigte Zustand [formula in source] ist in der Acht-Qubit-Kodierung kein Stabilizerzustand. Schon für einen nichttrivialen lokalen Pauli gilt während reine Qubit-Stabilizerzustände für Pauli-Observablen nur [formula in source] liefern. Ebenso ist der Paarreduktionsrang sechs keine Zweierpotenz. Eine exakte Präparation aus einem Stabilizer-Eingang benötigt deshalb eine zusätzliche Ressource, etwa einen passenden","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die zusätzliche Ressource bleibt sichtbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9859,"byte_start":8727,"id":"section:27bd82a253284fef95cb","kind":"section","labels":[],"line_end":126,"line_start":105,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Der einfache Eingang lautet Er ist mit dem in S02 angenommenen Clifford-Baukasten präparierbar und besitzt [formula in source] -Anteil [formula in source] . Der Antisymmetrisierer ist Die konkrete Schaltung erzeugt 32 Kontrollzweige, von denen 24 die Permutationen tragen. Acht ungültige Zweige werden markiert. Nach Interferenz und Erfolgsselektion ist der implementierte Operator Somit gilt Der erfolgreiche Zweig ist ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie der Filter den Zustand erzeugt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11835,"byte_start":9859,"id":"section:20986e0ad5f888baa3ec","kind":"section","labels":["eq:originalecho"],"line_end":163,"line_start":127,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] schreibe [formula in source] . Dann Ein ignorierter frischer Pointer erzeugt Diese binäre Swap-Aufzeichnung ist ein anderer Kanal als die 15-Kontext-Mischung mit Faktor [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das ursprüngliche Echo: eins gegen siebzehn Zweiunddreißigstel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13337,"byte_start":11835,"id":"section:d89912a7ac0133fb1c55","kind":"section","labels":[],"line_end":183,"line_start":164,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Der Endfilter hat den Effekt [formula in source] . Seine beobachtbare Erfolgsrate ist deshalb [formula in source] , nicht [formula in source] selbst. L68mmY Y Statistik& Behalten& Frisch\\\\ [formula in source] -Rückkehr, bedingt auf Präparation& [formula in source] & [formula in source] \\\\ Endfilter erfolgreich, bedingt auf Präparation& [formula in source] & [formula in source] \\\\ Beide Filter erfolgreich, je begonnen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die wirklichen Erfolgswahrscheinlichkeiten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15734,"byte_start":13337,"id":"section:62d624c29c301bb761ec","kind":"section","labels":["eq:optimal"],"line_end":210,"line_start":184,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Eigene exakte Ergänzung dieser Synthese. Man kann die gleiche Messfrage für einen beliebigen lokalen unitären Tick [formula in source] ausrechnen. Setze Die beiden Swap-Gewichte sind [formula in source] . Daher Der Kontrast dieser Rückkehrstatistik ist maximal, wenn [formula in source] , also [formula in source] . Ein einzelnes CNOT innerhalb des Viererträgers erfüllt [formula in source] . Es permutiert dieselbe Meng","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neue Fortsetzung: der maximal ausgeglichene Echovergleich","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17149,"byte_start":15734,"id":"section:59617a673609f0732add","kind":"section","labels":[],"line_end":218,"line_start":211,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Y r Ressource nach S02& Anzahl\\\\ Systemqubits&8\\ , wiederverwendet&10\\ ätze&2\\ reservierte Qubits&20\\ Erfolgsbits beider Filter&12\\ -Gatter&574\\ CNOT vor Toffoliauflösung&382\\ &26\\ - [formula in source] / Pauli- [formula in source] &276 / 26\\\\T/T^ [formula in source] T-Varianten waren durch lokale Matrixidentität und Ersetzung zertifiziert, nicht zusätzlich als komplette komplexe 20-Qubit-Vektoren simuliert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ressourcen und Beweisgrenze der Originalschaltung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":75,"byte_start":0,"id":"section:2582b01b75519dced337","kind":"chapter","labels":["ch:seam"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Von der Kette zur E [formula in source] 8-Naht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1943,"byte_start":75,"id":"section:c0ec8b39410b8acd72a7","kind":"section","labels":[],"line_end":28,"line_start":3,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Das Zweizellenmodell benutzt zwei vollständige Vierergraphen mit einer Brücke. Die Vielzellenrechnung in S08 benutzt dagegen Vierersegmente mit nächster Nachbarschaft. Bei [formula in source] wird erst dieses zweite Modell eine uniforme Kette. Derselbe isolierte Singulettzustand garantiert keine identischen Anregungen und keinen identischen Grenzwert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein wichtiger Modellwechsel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3203,"byte_start":1943,"id":"section:368f61fe798ea76a2005","kind":"section","labels":[],"line_end":44,"line_start":29,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Für den uniformen periodischen Austauschring liefern die Quellen [formula in source] bei acht und [formula in source] bei zwölf Trägern. Der bekannte Vergleich lautet Die Sutherland-Grundenergie pro Träger ist für [formula in source] . S08 nennt die Extrapolation [formula in source] und [formula in source] . Diese endlichen Zahlen passen zur [formula in source] -WZW-Beschreibung des Kettenmodells. Die allgemeine Verb","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die SU(4)-WZW-Theorie hier plausibel ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4699,"byte_start":3203,"id":"section:67e571744e99ca5b1bfd","kind":"section","labels":[],"line_end":70,"line_start":45,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Die zentrale Ladung ist eine Kennzahl einer konformen Feldtheorie. Für die chiralen Niveau-1-Faktoren gilt Das Produkt hat also schon vor einer Kopplung [formula in source] . Ein später gefundener Wert acht allein ist kein Beweis einer [formula in source] -Erweiterung und kein Beweis eines Kondo-Flusses.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Naht braucht mehr als die Zahl acht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6584,"byte_start":4699,"id":"section:77f5c13e9bd28b16530d","kind":"section","labels":[],"line_end":92,"line_start":71,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"S11 ersetzt die frühere Kondo-Zielbeschreibung sinnvoll durch eine konkrete Erweiterungsaufgabe. Die Kurzschreibweise eines Quotienten durch [formula in source] kann jedoch verschiedene Operationen meinen. Nur auf invariante Zustände des ursprünglichen Produkts zu projizieren ist nicht dasselbe wie eine Simple-Current-Erweiterung mit den nötigen zusätzlichen beziehungsweise entsprechend gekoppelten Sektoren.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum „Z [formula in source] 4-Eichung“ präzisiert werden muss","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7319,"byte_start":6584,"id":"section:4446e5ee7f4d8fda03fe","kind":"section","labels":[],"line_end":97,"line_start":93,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Eine gewöhnliche kritische SU(4)-Kette hat links- und rechtslaufende Sektoren, mit [formula in source] . Die übliche Kennzahl heißt dabei [formula in source] , nicht sechs. Die chirale Differenz ist null. Eine rein chirale [formula in source] -Naht hat dagegen Differenz acht. Ein zusätzliches ebenfalls nichtchirales [formula in source] -Modell ändert daran nichts.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Chiralitätslücke","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8698,"byte_start":7319,"id":"section:c4ffd1636c079cfb84f5","kind":"section","labels":[],"line_end":103,"line_start":98,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Die innere Glue- [formula in source] wirkt auf den 248 Strömen mit Phasen [formula in source] auf Sektoren der Größen [formula in source] . Ihre Spur ist null. Die geometrische Vierteldrehung [formula in source] hat auf Stufe eins dagegen Spur [formula in source] . Die Operatoren sind somit nicht identisch. Eine Clock kann eine geometrische Drehung mit innerem Twist kombinieren; die beiden Faktoren bleiben getrennt. ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei Vierteldrehungen und der Index","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":551,"byte_start":0,"id":"section:1a7480015728ee840200","kind":"chapter","labels":["ch:recon"],"line_end":5,"line_start":1,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Fortschritt v1.3 Ein gemeinsamer endlicher Träger realisiert nun Aufzeichnung, Näherungspräparation, Reset und Mehrzeitantwort unter einem ausdrücklich angegebenen Ressourcenvertrag. Das beantwortet eine bedingte Existenzfrage. Es wählt weder den Vertrag aus TFPT allein noch ein universelles positives Zustandsfunktional aus. Die nachfolgenden Anforderungen bleiben deshalb nötig; die Konstruktion steht in Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie eine vollständige Rekonstruktion aussehen könnte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1946,"byte_start":551,"id":"section:fc25f58e9a7dc0dcf5a3","kind":"section","labels":[],"line_end":17,"line_start":6,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Eine endliche Liste von Schatten bestimmt im Allgemeinen mehrere Prozesse. Man kann sogar jeden Kandidaten um einen ungekoppelten unsichtbaren Hilfsfaktor ergänzen, auf den alle erlaubten Experimente trivial wirken. Alle Antworten bleiben gleich. Eindeutigkeit ist daher zunächst nur für die minimal beobachtbare Darstellung erreichbar.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vom Wunsch nach Eindeutigkeit zu einer prüfbaren Frage","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2535,"byte_start":1946,"id":"section:cebce08434f8e26b59d8","kind":"section","labels":[],"line_end":24,"line_start":18,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Eine Projektion kann wichtige Wahrscheinlichkeiten erhalten und trotzdem die Multiplikation zerstören. S03 gibt einen einfachen Gegenbeleg: Projiziere [formula in source] auf [formula in source] und definiere [formula in source] . Dann Die neue Multiplikation ist nicht assoziativ. Eine nützliche reduzierte Vorhersagebeschreibung darf also nicht ohne zusätzlichen Nachweis als geschlossene physische Operationsalgebra v","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine kleinere Beschreibung ist nicht automatisch eine Algebra","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4676,"byte_start":2535,"id":"section:2e3f061bf06de652dec8","kind":"section","labels":[],"line_end":52,"line_start":25,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Eine phasentreue Rekonstruktion braucht mehr als eine Tabelle einzelner Wahrscheinlichkeiten. Ein passender Ausgangspunkt ist eine komplexe Algebra [formula in source] mit Einheit, Multiplikation, Adjunktion und einem positiven normierten Zustandsfunktional [formula in source] : Für Operationswörter [formula in source] definiert einen positiven semidefiniten Korrelationskern. Er enthält die relativen komplexen Phasen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was vollständige Phaseninformation zusätzlich bringt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5967,"byte_start":4676,"id":"section:19f379a516d5cb56e965","kind":"section","labels":[],"line_end":65,"line_start":53,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Ein Prozesstensor beziehungsweise Quantenkamm ordnet einer Folge von Instrumenten gemeinsame Ergebniswahrscheinlichkeiten zu. Positivität und kausale Normierungsregeln sichern die Konsistenz. Eine tomographisch vollständige Eingriffsfamilie bestimmt einen endlichen Prozesstensor; sie bestimmt nicht automatisch eine eindeutige verborgene Umgebung oder sämtliche unendlichen Horizonte.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Mehrzeitdaten statt einer einzigen Dichtematrix","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7082,"byte_start":5967,"id":"section:786ca4411f3bceeb259e","kind":"section","labels":[],"line_end":72,"line_start":66,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"S05 schlägt eine nützliche endliche Vorgehensweise vor: Man fixiert zulässige Operationswörter bis Länge [formula in source] , ihre Relationen, Symmetrien und die belegten Auslesungen. Die unbekannten Momente müssen eine positive Momentenmatrix bilden. Dann minimiert und maximiert man eine noch offene Ausgabe [formula in source] über alle kompatiblen Modelle.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein konkreter Auswahltest für offene Größen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9427,"byte_start":7082,"id":"section:01c6c30834f6c5a6b7e0","kind":"section","labels":[],"line_end":106,"line_start":73,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Die in S03 vorgeschlagene Alternative verwendet als lokalen Viererverknüpfungstensor. An orientierten Verbindungen werden Trägerräume mit ihren dualen Räumen kontrahiert. So verbindet man Amplituden, ohne jede physische Zellreduktion als unverändert reines [formula in source] festzuschreiben.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Zelle als Verknüpfungsamplitude","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10340,"byte_start":9427,"id":"section:8359367399e8a90aac4e","kind":"section","labels":[],"line_end":111,"line_start":107,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Paarweise kommutierende volle Matrixunteralgebren, die gemeinsam die Gesamtalgebra erzeugen, bestimmen im endlichen Fall eine Tensorproduktstruktur bis auf lokale Basiswechsel und Umbenennungen. Bei nichttrivialem Zentrum können stattdessen Sektoren übrigbleiben. Die Auswahl der privilegierten Unteralgebren aus den Wechselwirkungen ist der eigentliche inverse Schritt. https://arxiv.org/abs/quant-ph/0308043Zanardi, Li","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Teilsysteme aus Beziehungen erkennen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11809,"byte_start":10340,"id":"section:47189ac60e0950e803ad","kind":"section","labels":[],"line_end":122,"line_start":112,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"S08 untersucht einen neutralen Sektor aus 70 Materiemasken und Schleifenfluss, insgesamt 1190 Zuständen. In einer festgehaltenen lokalen Operatorliste wird über der Generator rekonstruiert. Nach Entfernen trivialer Identitätsrichtungen reproduziert der Grundzustand die Koeffizienten [formula in source] , [formula in source] , [formula in source] und [formula in source] . Ein zusätzlicher angeregter Zustand verbessert","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was das Zustandsgate am Rotor/CAR-Ring prüft","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":85,"byte_start":0,"id":"section:8ff51b30b976931b2254","kind":"chapter","labels":["ch:physik"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Raumzeit, Materie und Gravitation aus demselben Ursprung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1976,"byte_start":85,"id":"section:08708dbb4ec8d7a955a5","kind":"section","labels":[],"line_end":30,"line_start":3,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Ein markierter [formula in source] -Block trägt die hermitesche Matrix Ihre Determinante ist exakt Die Eigenwerte sind [formula in source] . Deshalb entspricht [formula in source] dem Zukunftskegel [formula in source] . Die Kongruenz [formula in source] mit [formula in source] erhält die Determinante und den positiven Kegel.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Lorentzkegel: eine echte, aber begrenzte Brücke","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3724,"byte_start":1976,"id":"section:dedd8a4bbe15bd2621f8","kind":"section","labels":[],"line_end":47,"line_start":31,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"S03 formuliert eine nützliche bedingte Brücke. Angenommen, derselbe Prozess liefert einen lokalen kohärenten Zweikomponentensektor mit inverser Zweipunktfunktion Dann folgt Für invertierbares [formula in source] ist dies eine Lorentzform. Jetzt wäre der Kegel aus einem tatsächlichen Propagator gewonnen. Vorausgesetzt sind jedoch ein sinnvoller Impulsraum, ein kontrollierter lokaler Grenzprozess, ein kohärenter Pol un","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der präzise nächste Schritt: den Kegel aus der Ausbreitung gewinnen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4823,"byte_start":3724,"id":"section:07dc23517e043e00255e","kind":"section","labels":[],"line_end":58,"line_start":48,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Eine mögliche Materieanregung muss stabil oder kontrolliert propagierend sein. Man benötigt ihr Spektrum, ihre Ladungen, chirale Ausbreitung, erlaubte Vertizes und das Verschwinden unerwünschter Spiegelpartner. Eine vorkommende Darstellung allein erfüllt das nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Materie ist mehr als eine Ladungstabelle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5811,"byte_start":4823,"id":"section:d45294c0b031dc6a416f","kind":"section","labels":[],"line_end":67,"line_start":59,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Eine Algebra mit Darstellung und geeignetem Diracoperator kann Geometrie kodieren. Beispielsweise macht die Distanzformel sichtbar, warum nicht nur Eigenwerte, sondern die Relation zwischen [formula in source] und den Observablen zählt. Connes' kommutativer Rekonstruktionssatz benötigt starke Spektralaxiome und liefert eine kompakte glatte Riemannsche Mannigfaltigkeit. Er erzeugt keine lorentzsche 3+1D-Welt aus einer","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spektrale Geometrie hilft, ersetzt aber keine fehlenden Daten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":7020,"byte_start":5811,"id":"section:ee1dbc31f09b69e1f767","kind":"section","labels":[],"line_end":80,"line_start":68,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Die Identität [formula in source] passt zu einer bekannten Normierung. Sie liefert nicht das Feld [formula in source] , einen masselosen quantisierten Spin-2-Pol, zwei physische Helizitäten oder universelle Kopplung.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was für Gravitation noch wirklich fehlen würde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7111,"byte_start":7020,"id":"section:b71a2143cbcffd5976aa","kind":"chapter","labels":["ch:zahlen"],"line_end":82,"line_start":81,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die Zahlenprogramme: Nähe, Spannungen und offene Übertragung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8020,"byte_start":7111,"id":"section:31973b40d1e3c3bd92c9","kind":"section","labels":[],"line_end":97,"line_start":83,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Die [formula in source] -Zerlegung benutzt Hyperladungen [formula in source] auf den drei Farbplätzen und [formula in source] auf den zwei schwachen Plätzen. In der Konvention ausschließlich linkshändiger Weylfelder ergibt eine Familie: lccr Feld& [formula in source] & [formula in source] &Komponenten\\\\ [formula in source] & [formula in source] & [formula in source] &6\\\\ [formula in source] & [formula in source] & [f","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Standardmodell-Ladungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9595,"byte_start":8020,"id":"section:bca0e5ae4d9a413def0a","kind":"section","labels":[],"line_end":119,"line_start":98,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Der eingefrorene Flavor-Seed lautet Er organisiert mehrere Ausgaben gemeinsam. Eine Änderung an ihm verschiebt daher mehrere Zahlen; das macht den Ansatz prüfbarer als unabhängig eingestellte Einzelwerte.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der gemeinsame kleine Seed und die Kopplungsgleichung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11924,"byte_start":9595,"id":"section:4dc71a57d9f707c818de","kind":"section","labels":[],"line_end":145,"line_start":120,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Der historische Quellmassenansatz lautet Die sektorabhängigen [formula in source] sind nicht automatisch eins. Die Restklassenmatrix mit Zeilen [formula in source] , [formula in source] , [formula in source] hat Determinante acht und charakteristisches Polynom [formula in source] . Das sind interne Daten, keine direkte Massenmessung.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Flavor und Massenschemata","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14391,"byte_start":11924,"id":"section:c2decebe3ece212dcb18","kind":"section","labels":[],"line_end":165,"line_start":146,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"L36mmL49mmL65mm Größe& Formel / Quellwert& Zusätzliche Bedingung\\\\ Birefringenz [formula in source] & [formula in source] &Rotationstransfer, Kalibrierung und Vordergründe.\\\\ Baryonenanteil [formula in source] & [formula in source] &Nicht mit [formula in source] gleichsetzen.\\\\ Skalarer Index [formula in source] & [formula in source] & [formula in source] und Reheatinggeschichte.\\\\ Tensorverhältnis [formula in source","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kosmologie und große Hierarchien","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16077,"byte_start":14391,"id":"section:1ce347ba9067944a60fa","kind":"section","labels":[],"line_end":181,"line_start":166,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"L41mmL46mmL63mm Zweig& Historischer Quellwert& Offener Anteil\\\\ Starke CP-Phase& [formula in source] im Pfaffian-Zweig&Positives physisches Maß und nichtperturbativer Transfer.\\\\ Elektrische Dipolmomente&Führend null oder stark unterdrückt&Keine pauschale Null sämtlicher SM-Beiträge.\\\\ Axion& [formula in source] GeV; [formula in source] eV&Externe Planckskala und QCD-Massenrelation.\\\\ Neutrinomassen&Summe um [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die übrigen Zweige bleiben Teil des Bildes","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":18538,"byte_start":16077,"id":"section:63e565d2eda8fc6fe3d3","kind":"section","labels":[],"line_end":202,"line_start":182,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"S08 untersucht einen zweistufigen Lauf mit quellenseitig ausgewähltem Skalarinhalt, aber in einer eingeschränkten gauge-only-Zweischleifennäherung. Die Nähe von [formula in source] zu [formula in source] GeV bleibt ungefähr bestehen. 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Übertragung un","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Frühere Nebenstränge, die im Gesamtbild erhalten bleiben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10041,"byte_start":5908,"id":"section:93bc9b620759b83cccba","kind":"chapter","labels":[],"line_end":74,"line_start":38,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"L34mmL116mm Begriff& Bedeutung in diesem Dokument\\\\ Adjungierte&Die Darstellung einer Lie-Algebra auf ihren eigenen Generatoren durch die Klammer; nicht automatisch der gesamte Raum physischer Zustände.\\\\ Adjunktion [formula in source] &Komplex konjugierte Transposition beziehungsweise die passende Operatoradjunktion. 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Die vollständigen Originalpfade und SHA-256-Werte stehen im beiliegenden Manifest. Hier werden die Dateinamen und inhaltlichen Rollen aufgeführt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die elf Eingabedokumente","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":12676,"byte_start":10437,"id":"section:b4815cdd94ca25a7545f","kind":"section","labels":[],"line_end":96,"line_start":80,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Der eigenständige Prüfer importiert keinen Code des ursprünglichen TFPT-Repositoriums. Die Standard-Zwei-Qubit-Kontexte wurden aus den üblichen Pauli-Matrizen rekonstruiert. Das kontrolliert die endlichen im Text angegebenen Beziehungen, ist aber kein erneuter phasentreuer Import des nativen Gauß- [formula in source] -Adapters.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was neu geprüft wurde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13823,"byte_start":12676,"id":"section:665c3efa018681437595","kind":"section","labels":[],"line_end":108,"line_start":97,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"L16mmL41mmY Quelle& Berichtete Prüfung& Reichweite\\\\ S09&11214 Bedingungen pro Modus, elf Negativvarianten&Ursprungsaudits und Zahlenprüfungen; kein vollständiger Lean-/RH-Neubau.\\\\ S07&325 + 147 Bedingungen, 19 Tests&Inversion und Follow-ups; mehrere spätere Minimalitätskorrekturen erforderlich.\\\\ S06&86 eigene Bedingungen sowie ausgewählte Originalreplays&45-/30-Quotienten, Uhr und Herkunftskontrollen; begrenzte Ke","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie die Quellen ihre eigenen Prüfungen beschreiben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":14798,"byte_start":13823,"id":"section:273da674408e7ae07e31","kind":"section","labels":[],"line_end":113,"line_start":109,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Das Paket enthält die vollständige LaTeX-Quelle, Kapiteldateien, Vektordiagramme, den eigenständigen Prüfer, die Ergebnisdatei und das Eingabemanifest. Mit einer LaTeX-Installation einschließlich LuaLaTeX, TikZ und den verwendeten Standardpaketen lässt sich das Buch durch zwei Läufe von lualatex main.tex im Quellverzeichnis bauen. Für die endlichen Gegenrechnungen werden Python, NumPy, SymPy, mpmath und Matplotlib be","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproduktionspaket dieser Synthese","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18166,"byte_start":14798,"id":"section:92d73a7a445e79c179ba","kind":"section","labels":[],"line_end":135,"line_start":114,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Die folgenden Quellen wurden zur fachlichen Einordnung beziehungsweise für den datierten Konstantenvergleich aufgerufen. Sie bestätigen die allgemeinen Werkzeuge, nicht die physikalische Richtigkeit von TFPT. Die spezifischen langen Herleitungen dieses Buches beruhen auf den Anhängen und den ausgeschriebenen Gegenrechnungen. F. A. Pollock et al.: Non-Markovian quantum processes: complete framework and efficient chara","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Externe Primärliteratur und Referenzdaten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18523,"byte_start":18166,"id":"section:2680a492f927836c7224","kind":"section","labels":[],"line_end":137,"line_start":136,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Die Anhänge wurden unverändert gelesen; ihre tatsächlichen Dateiinhalte sind durch SHA-256 dokumentiert. Dieses Buch aktualisiert keinen ursprünglichen Theorievertrag und keinen Abschlussmarker. Es liefert eine neue, zusammenhängende und prüfbare Darstellung mit ausdrücklich abgegrenzten eigenen Fortsetzungen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Abschluss der Dokumentation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":968,"byte_start":0,"id":"section:b13cd23c524e58ba0554","kind":"chapter","labels":["ch:shadow-arithmetic"],"line_end":8,"line_start":1,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Was uns ein Schatten verraten kann Wenn wir nur den Schatten eines Rades sehen, erkennen wir vielleicht einen Kreis. Erst wenn wir das Rad drehen, belasten und mit einem zweiten Rad verbinden, erkennen wir seine Achse, seine Zähne und seine Übersetzung. Genau so lesen wir hier Primzahlen, Quanteneffekte und Raumzeit: als verschiedene Antworten, die eine mögliche gemeinsame Struktur gleichzeitig erklären müsste.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Primzahlen, RH und die Musik hinter den Schatten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":2819,"byte_start":968,"id":"section:6f0221a764011d9595c1","kind":"section","labels":["eq:primon-partition"],"line_end":25,"line_start":9,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Jede natürliche Zahl [formula in source] zerfällt eindeutig in Primfaktoren: Die erste Gleichung beschreibt ein Zusammensetzen durch Multiplikation; die zweite übersetzt dieses Zusammensetzen in Addition. Zum Beispiel ist [formula in source] , also [formula in source] . Die Primzahlen sind die unabhängigen Bausteine dieses multiplikativen Systems. Das ist ein Satz über natürliche Zahlen. Es ist noch kein Satz darüber","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"In welchem Sinn Primzahlen Bausteine sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":4018,"byte_start":2819,"id":"section:3da3131701887f7eb677","kind":"subsection","labels":[],"line_end":36,"line_start":26,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Warum gerade [formula in source] ? Aus [formula in source] allein folgt das noch nicht: Man darf jeder Primzahl zunächst einen beliebigen Wert [formula in source] geben. Eine zusätzliche Ordnungsregel schließt die Lücke. Ist [formula in source] monoton in der natürlichen Zahl [formula in source] , so gilt notwendig Der Beweis ist kurz. Setze [formula in source] . Aus [formula in source] folgen [formula in source] Div","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine bedingte Auswahlregel für die logarithmische Energie","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":7179,"byte_start":4018,"id":"section:87457f62c9c8bddcc27a","kind":"section","labels":["eq:prime-trace"],"line_end":64,"line_start":37,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die häufig verkürzte Aussage Primzahlen tauchen als Quantenenergien auf umfasst verschiedene Sachverhalte. Beim klassischen Zeta–Quantenchaos-Vergleich entsprechen Nullstellenhöhen den Energien eines gesuchten Spektrums. Die Primzahlen spielen auf der anderen Seite die Rolle primitiver periodischer Bahnen; Primzahlpotenzen sind deren Wiederholungen. Eine Bahn wird einmal durchlaufen, zweimal, dreimal. Ihr logarithmis","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was Primzahlen mit Quantenchaos verbindet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":10149,"byte_start":7179,"id":"section:0e0127eb403eab74d49e","kind":"section","labels":[],"line_end":81,"line_start":65,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die Unterlagen und der zusätzlich eingesehene Forschungsbestand ergeben keine abgeschlossene RH-Lösung. Sie ergeben jedoch eine ungewöhnlich präzise Landkarte aus positiven Bausteinen und bereits ausgeschlossenen Abkürzungen. Die folgende Verdichtung ordnet die inhaltlichen Familien; sie behauptet keine erneute Prüfung jedes Katalogeintrags.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was unser RH-Zweig tatsächlich beigetragen hat","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11189,"byte_start":10149,"id":"section:cbeb85103b892f3b7d1b","kind":"subsection","labels":[],"line_end":96,"line_start":82,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die ersten sechs Werte sind [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] und [formula in source] . Daraus folgt für [formula in source] Hier ist der Primzahlbezug wirklich vorhanden. Die Selbstdualität des Gitters schließt die Poisson-Transformation auf dasselbe Gitter. Poisson-Summation gilt auch für nichtselbstduale Gitter und verbindet dann Gitter und ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der genaue Ertrag der [formula in source] -Schalen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":12659,"byte_start":11189,"id":"section:45a96a6680ce801ae38e","kind":"subsection","labels":[],"line_end":108,"line_start":97,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die entscheidende arithmetische Form enthält eine Differenz: vereinfacht [formula in source] . Zwei positive Matrizen können eine indefinite Differenz besitzen; schon [formula in source] hat die Eigenwerte [formula in source] und [formula in source] . Entsprechend löst ein beliebiger positiver Born- oder Gramkern die signierte Aufgabe noch nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die fehlende Positivität so hartnäckig ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14262,"byte_start":12659,"id":"section:8a28c8e255701869b4f0","kind":"subsection","labels":[],"line_end":115,"line_start":109,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Der Jensen/Coxeter-Test r618 findet eine starre [formula in source] -Struktur auf der [formula in source] -Seite, während die verglichenen Jensen-Polynome mit ihrem Index variieren. Die gewählte Identifikation scheitert. Der Selberg-Kontakttest r638 besitzt im untersuchten Fall weiterhin einen negativen kleinsten Eigenwert von ungefähr [formula in source] ; eine Quadratvervollständigung hat die falsche signierte Form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was die negativen Routen konkret lehren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15958,"byte_start":14262,"id":"section:59a7503fae8d46cd884e","kind":"section","labels":[],"line_end":126,"line_start":116,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die vorhandene freie fermionische Naht hat bei fester Größe eine endliche Zustandssumme. Das Primonmodell verlangt eine unbegrenzte Primfamilie und andere Besetzungsdaten. Schon für [formula in source] gilt [formula in source] und [formula in source] : Der Pol bei [formula in source] entsteht erst in der unendlichen Familie. Eine endliche Demonstration kann ihn nicht besitzen. Der vorhandene Nahtvergleich findet ents","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Naht braucht mehr als ein paar zusätzliche Takte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16501,"byte_start":15958,"id":"section:640b4c8884718ee299f9","kind":"section","labels":[],"line_end":129,"line_start":127,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Wei und Mitautoren verbinden in zwei gezielt konstruierten Quantensystemen Nullstellen mit dynamischen Phasenübergängen. Berichtet werden ein Fünf-Qubit-NMR-Prinzipversuch und weitergehende numerische Untersuchungen. Die verwendeten Hamiltonoperatoren und Zustandsgewichte sind so gewählt, dass sie Zeta-Daten kodieren. Das macht den Zusammenhang experimentell bearbeitbar; eine Ableitung dieser Wahl aus TFPT oder ein R","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die neue Quantenphasen-Arbeit von 2026","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":18843,"byte_start":16501,"id":"section:8052fbf017c8c33b46c5","kind":"subsection","labels":["eq:eta-readout"],"line_end":150,"line_start":130,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Unabhängig vom vollständigen Ressourcenbeweis dieser Arbeit untersuchen wir den folgenden einfachen thermischen Eta-Auslesekanal: Er entsteht durch einen Gibbszustand für [formula in source] und eine diagonal ausgelesene Paritätsphase. Bei festem [formula in source] und [formula in source] konvergiert der Zähler gegen [formula in source] , während [formula in source] Also geht das Rohsignal [formula in source] an jed","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eigene Anschlussrechnung: Ein verschwindendes Signal ist mehrdeutig","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":541,"byte_start":0,"id":"section:ee58bfc31dd3e8c61148","kind":"chapter","labels":["ch:shadow-quantum"],"line_end":6,"line_start":1,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Nicht nur die Anzahl der Kugeln zählt Zwei Kästen können dieselben möglichen Messergebnisse enthalten und doch verschieden reagieren, wenn wir zuerst an einer anderen Stelle messen oder zwei Teile zusammenführen. Die Quantenphänomene sagen uns deshalb vor allem etwas über die Regeln des Zusammensetzens, über relative Phasen und über erlaubte Eingriffe. Genau diese Daten verliert ein einfacher Schatten leicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was Quantenphänomene über den verborgenen Aufbau sagen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1925,"byte_start":541,"id":"section:f9cfce01017c01eaf445","kind":"section","labels":[],"line_end":21,"line_start":7,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Für zwei Alternativen mit Amplituden [formula in source] und [formula in source] lautet die Born-Regel [formula in source] Der letzte Term kann verstärken oder auslöschen. Wer ausschließlich die beiden Einzelwahrscheinlichkeiten aufbewahrt, kann ihn nicht rekonstruieren. Das erklärt im Kleinen, warum die behaltenen Register und Echoexperimente der früheren Kapitel mehr verraten als der erste sichtbare Markovschritt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Interferenz verlangt eine Information vor den Wahrscheinlichkeiten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4273,"byte_start":1925,"id":"section:5b84ba757f4fb37831c1","kind":"section","labels":[],"line_end":40,"line_start":22,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Die 15 Zwei-Qubit-Pauli-Kontexte der Synthese enthalten das folgende Mermin–Peres-Quadrat. Hier bedeutet [formula in source] und entsprechend für die anderen Einträge: Jede Zeile und jede Spalte ist gemeinsam messbar. Alle Zeilenprodukte sind positiv, aber das letzte Spaltenprodukt ist negativ. Diese sechs Kontexte gehören zum bereits verwendeten Pauli-System.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der vorhandene Baukasten enthält bereits Kontextualität","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5718,"byte_start":4273,"id":"section:a0804599d91d3f14538d","kind":"section","labels":[],"line_end":52,"line_start":41,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Für zwei räumlich getrennte Messstellen hat die CHSH-Kombination [formula in source] in einem lokalen Modell mit unabhängiger Wahl der Einstellungen die Grenze [formula in source] . Quantenmechanik erreicht [formula in source] . Mit [formula in source] , [formula in source] und [formula in source] ist der zugehörige Operator [formula in source] ; seine Eigenwerte sind [formula in source] . Beides wurde hier exakt nac","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verschränkung legt die Zusammensetzung fest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6899,"byte_start":5718,"id":"section:07c7d34b0a87efd64285","kind":"section","labels":[],"line_end":68,"line_start":53,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Wähle bei festgehaltenen Labor-Teilsystemen [formula in source] Beide Hamiltonoperatoren haben exakt die Energien [formula in source] . Der Grundzustand von [formula in source] ist ein Produktzustand, der von [formula in source] ein Bell-Zustand. Die Reinheit [formula in source] eines lokalen Teils beträgt entsprechend 1 beziehungsweise [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gleiche Energien können verschiedene Welten beschreiben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8198,"byte_start":6899,"id":"section:ae4e2b5c3305f6020812","kind":"section","labels":[],"line_end":75,"line_start":69,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Die komplexe Vierdimensionalität ist für den bestehenden Pauli-/Spinorbaukasten passend. Eine direkte Ableitung der komplexen Zahlen aus einem einzelnen Quantenphänomen wäre trotzdem zu stark. Renou und Mitautoren untersuchen Quantennetzwerke, in denen die übliche reale und komplexe Theorie unter einer bestimmten Unabhängigkeits- und Kompositionsannahme verschiedene Vorhersagen machen. F10","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was komplexe Zahlen verraten und was offenbleibt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9556,"byte_start":8198,"id":"section:54eadd1112a5751773d2","kind":"section","labels":[],"line_end":81,"line_start":76,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Die bisherigen Registerbeispiele erklären, wie ein global kohärenter Ablauf nach eingeschränktem Zugriff wie ein irreversibler Prozess aussehen kann. Sie liefern noch keine eindeutige Lösung des Messproblems: Insbesondere folgt aus einer diagonalen reduzierten Dichtematrix allein keine Auswahl eines einzelnen Ereignisses. Eine zusätzliche Kollapsdynamik müsste messbare Abweichungen angeben; eine unitäre Beschreibung ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Messung, Zeitpfeil und Statistik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":900,"byte_start":0,"id":"section:d9fc8650a1acd3183405","kind":"chapter","labels":["ch:shadow-dimension"],"line_end":8,"line_start":1,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"Dimension ist die Antwort auf eine Frage Eine Ameise auf einer dünnen Schnur kann entlang einer Richtung laufen. Auf einem Blatt kann sie außerdem ausweichen. In einem Zimmer kann sie auch über ein Hindernis hinweg. Eine Dimension zählt solche unabhängigen Möglichkeiten. Die Zahl der inneren Zustandskomponenten oder der Knöpfe eines Geräts ist etwas anderes.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Drei Raumrichtungen und eine Zeit: Welche Bedingungen bleiben?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2245,"byte_start":900,"id":"section:f2428b29d35438721755","kind":"section","labels":[],"line_end":23,"line_start":9,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"Ein traceloses hermitesches [formula in source] -Objekt hat genau drei reelle Komponenten: [formula in source] Ergänzt man [formula in source] , ergibt die Determinante [formula in source] Der positive Kegel erfüllt [formula in source] . Das ist die präzise Lorentz-Brücke aus dem Ursprungsteil. Sie zeigt eine passende lokale algebraische Form. Noch fehlen ihre Interpretation als Ereignisse, die Verklebung zu einer Ra","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Drei unterschiedliche Hinweise führen zur Zahl drei","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4446,"byte_start":2245,"id":"section:049384dfe146a60b52d8","kind":"section","labels":[],"line_end":47,"line_start":24,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"Für einen Graph-Laplaceoperator [formula in source] definieren wir die mittlere Rückkehrfunktion und eine skalenabhängige Dimension durch Auf einem großen regelmäßigen dreidimensionalen Gitter entsteht zwischen der Gitter- und der endlichen Systemskala ein Bereich mit [formula in source] , also [formula in source] . Bei einem endlichen zusammenhängenden Graphen geht [formula in source] sowohl für sehr kleine als auch","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine neue Gegenprobe am Clebsch-Vorschlag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5395,"byte_start":4446,"id":"section:64d3bcd11949ac9afd46","kind":"section","labels":[],"line_end":52,"line_start":48,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"In einer gewöhnlichen hyperbolischen Wellengleichung werden lokale Anfangsdaten auf einer räumlichen Fläche vorgegeben und entlang einer ausgezeichneten Zeitrichtung entwickelt. Mehrere Zeitkoordinaten verändern das Anfangswertproblem grundlegend. Unter zusätzlichen nichtlokalen Beschränkungen existieren dennoch wohldefinierte Mehrzeit-Probleme; ein pauschaler Unmöglichkeitssatz wäre falsch. F14","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine Zeitrichtung ist mehr als ein weiterer Zahlenplatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6488,"byte_start":5395,"id":"section:e5651bdb979b38c2b790","kind":"section","labels":[],"line_end":64,"line_start":53,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"Ein elementares mechanisches Beispiel illustriert die Rolle von Constraints. Nimmt man in [formula in source] Raumdimensionen eine Newtonsche Punktkraft mit Gaußgesetz an, lautet das effektive Radialpotential [formula in source] An einer Kreisbahn ergibt sich [formula in source] Unter diesen Voraussetzungen sind solche Kreisbahnen bei [formula in source] stabil, bei [formula in source] instabil und bei [formula in so","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was Stabilität zusätzlich einschränkt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":397,"byte_start":0,"id":"section:908e023504ad147ceff6","kind":"chapter","labels":["ch:shadow-open"],"line_end":4,"line_start":1,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Offene Physik ist kein freier Platz, in den jede neue Idee hineinpasst. Sie ist oft durch viele bekannte Eigenschaften eng begrenzt. Der nützliche Schritt lautet deshalb: Welcher Teil des Phänomens ist beobachtet, welcher Mechanismus fehlt, und welche Antwort müsste unser Modell zusätzlich liefern?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Schwer verstandene Phänomene als zusätzliche Prüfsteine","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1423,"byte_start":397,"id":"section:69fb1992defe83a815c3","kind":"section","labels":[],"line_end":9,"line_start":5,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Gravitationslinsen und die Verteilung sichtbarer Materie in kollidierenden Haufen liefern eine wichtige Beobachtung: Der aus der Gravitation erschlossene Beitrag muss nicht dem heißen sichtbaren Gas folgen. Die Bullet-Cluster-Analyse ist ein prominentes Beispiel. Sie identifiziert damit noch kein bestimmtes mikroskopisches Teilchen. Zusammen mit anderen kosmologischen Daten ist sie eine starke Anforderung an jede Erk","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dunkle Materie: unsichtbar heißt nicht frei wählbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2590,"byte_start":1423,"id":"section:48e0900f24a2758c8033","kind":"section","labels":[],"line_end":16,"line_start":10,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Die beschleunigte kosmische Expansion verlangt eine konsistente Erklärung im Gesamtmodell. Für TFPT ist besonders schwierig, eine passende effektive Vakuumwirkung zu erhalten, ohne sie bei jedem neuen Beitrag nachzujustieren. Der Mechanismus müsste seine Größe und Stabilität gegenüber Korrekturen erklären.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dunkle Energie: ein kleiner Rest mit großen Folgen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3656,"byte_start":2590,"id":"section:69f6ca5efc76b0149468","kind":"section","labels":[],"line_end":21,"line_start":17,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Die Schwarzlochfrage verbindet Quanteninformation, Gravitation und die Wahl zugänglicher Teilsysteme besonders eng. In bestimmten berechenbaren Modellen verändern Quanteneffekte die extremale Fläche und damit die Zuordnung rekonstruierbarer Information. Die verallgemeinerte Entropie enthält einen Flächenbeitrag und einen Quantenfeldbeitrag. Das ist erheblicher theoretischer Fortschritt in diesen Modellen, aber noch k","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Schwarze Löcher: Information kann die Aufteilung selbst betreffen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4418,"byte_start":3656,"id":"section:9e3235a407b6da02ec9a","kind":"section","labels":[],"line_end":26,"line_start":22,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Äquivalenztests wie MICROSCOPE prüfen die Universalität des freien Falls für unterschiedliche Materialien mit hoher Genauigkeit. Eine neue Quelle für Raumzeit muss daher erklären, warum verschiedene innere Zusammensetzungen auf dieselbe effektive Geometrie reagieren. F18","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gravitation muss sehr verschiedene Inhalte gleich behandeln","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6966,"byte_start":4418,"id":"section:2ed06791fbfcca01ddab","kind":"section","labels":[],"line_end":43,"line_start":27,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"L32mmL56mmL60mm Thema& Was den Ansatz einschränkt& Was eine Erklärung liefern müsste\\\\ Zeitpfeil&Beständige Aufzeichnungen und irreversible Makroprozesse bei oft reversiblen Grundgleichungen.&Zustandsauswahl, Anfangskorrelationen, Zugriff und Entropiefluss; keine bloße Benennung eines inneren Parameters als Zeit.\\\\ Messproblem&Interferenz und stabile Messergebnisse müssen zusammen beschrieben werden.&Ein vollständige","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Weitere offene Stellen mit unterschiedlicher Beweiskraft","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":947,"byte_start":0,"id":"section:fba84e492af73aa131de","kind":"chapter","labels":["ch:shadow-synthesis"],"line_end":7,"line_start":1,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Die zusammengetragenen Schatten sprechen am stärksten für eine Struktur von Zusammensetzungen und gemeinsamen Antworten. Arithmetik verlangt eindeutig kombinierbare primitive Faktoren. Quantenphänomene verlangen Phasen, Kontexte und eine besondere Zusammensetzung von Teilsystemen. Raumzeit verlangt eine skalenstabile Ordnung von Nachbarschaften, Signalwegen und Anfangsdaten. Keine dieser Forderungen wird durch die Za","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein engeres Bild und ein neues berechenbares Puzzleteil","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2397,"byte_start":947,"id":"section:b2d074e38d5bf173f713","kind":"section","labels":[],"line_end":20,"line_start":8,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Die bildhafte Aussage Alles ist aus Primzahlen gebaut lässt sich zu einer brauchbareren Hypothese präzisieren: Ein möglicher gemeinsamer Ursprung besitzt elementare, zusammensetzbare Operationen. In einem kommutativen arithmetischen Schatten erscheinen primitive Faktoren. Vor dieser Auslesung bleiben zusätzliche Phasen, Kontexte und Aufzeichnungen erhalten. Räumliche Nachbarschaft und Zeitordnung müssten aus den erla","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine engere Arbeitshypothese","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":4907,"byte_start":2397,"id":"section:d6fdfff2e2bf15c9f6f7","kind":"section","labels":["eq:arithmetic-projective"],"line_end":61,"line_start":21,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Die folgenden Formeln sind eine neue Anschlusskonstruktion für dieses Buch. Ihre Zutaten sind Standardoperatoren; sie beanspruchen keine neue allgemeine mathematische Entdeckung. Sie zeigen jedoch exakt, dass ein gemeinsamer arithmetischer Endpunkt unterschiedliche kohärente Geschichten besitzen kann.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein konstruktiver Versuch: gleiche Zahl, verschiedene Phasen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5784,"byte_start":4907,"id":"section:eaebe86b1b48bd258291","kind":"subsection","labels":[],"line_end":69,"line_start":62,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Ein Kontrollqubit speichert kohärent, welcher der beiden Wege durchlaufen wurde. Setze [formula in source] und [formula in source] . Nach einer Hadamard-Auslesung des Kontrollqubits gelten [formula in source] Ohne die lokalen [formula in source] -Markierungen wäre [formula in source] und damit [formula in source] . Die neue Rechnung kontrolliert dies im Zahlfenster [formula in source] exakt. Die benutzten Wege ab [fo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine vollständig bestimmte Vorhersage im Modell","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7119,"byte_start":5784,"id":"section:ade9484eb6f023080774","kind":"subsection","labels":[],"line_end":76,"line_start":70,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Gelöst ist eine kleine Kompatibilitätsfrage: Unbegrenzte arithmetische Zusammensetzung und ein endlicher lokaler Quantenbaukasten lassen sich in einem expliziten gemeinsamen Modell verbinden. Der rein arithmetische Schatten kann kommutativ sein, während kohärent zugängliche Wegrelationen eine nichttriviale Phase behalten. Das passt genau zum Motiv der vorherigen Echoexperimente.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was damit gelöst ist und was nicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9085,"byte_start":7119,"id":"section:dc01066ffa8b5e6d9e14","kind":"section","labels":[],"line_end":97,"line_start":77,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Man könnte einen arithmetischen Raum, ein Quantensystem und ein geometrisches Modell einfach nebeneinanderstellen: [formula in source] Bei Produktzustand und unabhängig wirkenden Operationen passen dann vielleicht alle Einzelstatistiken. Der gemeinsame Ursprung wäre dadurch nicht erklärt. Nötig sind gemeinsame Relationen und überprüfbare Antworten auf gemischte Eingriffe. Die oben konstruierte Wegphase ist ein kleine","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum getrennte passende Modelle noch keine gemeinsame Quelle sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11082,"byte_start":9085,"id":"section:700da1e5ca27a31c58c4","kind":"section","labels":[],"line_end":111,"line_start":98,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"L37mmL60mmL51mm Gewonnene Präzisierung& Konkretes Ergebnis& Nächste fehlende Bedingung\\\\ Logarithmische Skala&Multiplikative Additivität plus Monotonie erzwingen [formula in source] .&Native Begründung der Ordnung und Energieskala.\\\\ Unbegrenzte Primfamilie&Endlich viele additive Grundtakte tragen nicht alle [formula in source] .&Eine passende wachsende Familie oder reichere Dynamik.\\\\ Arithmetik und Phase&Zwei Multi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Welche Puzzleteile jetzt enger gefasst sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":82,"byte_start":0,"id":"section:bd62efb9562d7c019b77","kind":"chapter","labels":["app:shadow-sources"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Erweiterung: Quellen und genaue Prüfgrenzen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4118,"byte_start":82,"id":"section:1315342ad619cf8c4410","kind":"section","labels":[],"line_end":29,"line_start":3,"occurrence":1,"owner_documents":[],"relation_ids":["relation:be34722831ca1719aa27"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"Die Erweiterung wurde am 14. September 2026 gegen verfügbare Originalabschnitte im lokalen Repository tfpt-theoryv4 abgeglichen. Der gelesene Git-Stand war 66b91e40e245569f06ab440ead80f446c9be0ee5. Dies identifiziert den Checkout; es behauptet keinen frischen vollständigen Beweis- oder Testlauf. Die tatsächlich verwendeten Dateiinhalte sind zusätzlich mit SHA-256 im Paket erfasst, auch soweit der Arbeitsbaum von Git ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zusätzlicher Einblick in den RH-Forschungsbestand","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6033,"byte_start":4118,"id":"section:506f3fb05137a3b6a269","kind":"section","labels":[],"line_end":38,"line_start":30,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"Der separate Prüfer verify_shadows.py importiert keinen ursprünglichen TFPT- oder RH-Code und keine Nullstellentabellen. Er enthält 126 exakte beziehungsweise symbolische Bedingungen und zwei numerische Kontrollen. Die Nummer der ersten Nullstelle im Eta-Diagramm ist ein ausdrücklich eingesetzter Referenzwert; das Diagramm ist kein eigener Nullstellensuchlauf.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die 128 zusätzlichen Bedingungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10751,"byte_start":6033,"id":"section:f9c6e2a2015d0919b430","kind":"section","labels":[],"line_end":62,"line_start":39,"occurrence":1,"owner_documents":[],"relation_ids":["relation:32cd69e69b89ffbd3a94","relation:959f61a348d9dff44afb"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"Die folgenden Quellen wurden zur Erweiterung aufgerufen. Es handelt sich um gezielte Literaturauswahl, nicht um einen vollständigen systematischen Review aller Veröffentlichungen bis September 2026. Eigene Formeln, Gegenbeispiele und Illustrationen sind im Haupttext als solche bezeichnet. Neue Preprints bleiben als Preprints kenntlich. M. V. Berry, J. P. Keating: The Riemann Zeros and Eigenvalue Asymptotics. SIAM Rev","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zusätzliche Primärliteratur","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":11375,"byte_start":10751,"id":"section:036124efa58580d85bcc","kind":"section","labels":[],"line_end":64,"line_start":63,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"Das aktualisierte Quellpaket enthält beide unabhängigen Prüfer, beide Ergebnisdateien, die zusätzlichen drei Vektorplots, die LaTeX-Diagramme, das RH-Quellenmanifest und die ausgewählten Katalogeinträge. Die fünf neuen Hauptkapitel sind in dieselbe LaTeX-Datei eingebunden; ursprüngliche Textteile wurden nur um Versionshinweise und Querverweise ergänzt. Das fertige PDF wird weiterhin mit LuaLaTeX gebaut. Die beiliegen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproduktion der erweiterten Fassung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":76,"byte_start":0,"id":"section:5db26c5c342537bd32e7","kind":"chapter","labels":["ch:audit13"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die sechs neuen Quellen: geprüfte Korrekturen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":593,"byte_start":76,"id":"section:866e9030194940799837","kind":"section","labels":[],"line_end":5,"line_start":3,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Die sechs zusätzlichen Unterlagen heißen im neuen Quellenregister N1 bis N6; die ursprünglichen S01 bis S11 bleiben unverändert. Ihr Audit trennt exakte endliche Identitäten, numerische Spektren und zusätzliche Modellannahmen. 100 eigene Bedingungen bestanden: 78 exakte beziehungsweise Integritätsprüfungen und 22 numerische. Die anschließende gemeinsame Ausführung hat einen eigenen 231-Bedingungen-Vertrag. Diese Zähl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was gegenüber v1.1 neu ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":2635,"byte_start":593,"id":"section:a736ece557b95fcb2fb0","kind":"section","labels":[],"line_end":28,"line_start":6,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Setze [formula in source] und [formula in source] . Der Wedge-Kanal besitzt Für [formula in source] verschwindet [formula in source] . Beide geordneten Wege enden im gleichen virtuellen Zustand und interferieren. Orthogonale Records für [formula in source] und [formula in source] ersetzen dies durch [formula in source] : Der antisymmetrische Rang-6-Kanal wird zum Rang-12-Kanal. Bei gleichem Energienenner entsteht ein","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die zentrale Reparatur: Wege nicht zu früh unterscheiden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":3264,"byte_start":2635,"id":"section:d1d7ed4cb3c96e4c4450","kind":"section","labels":[],"line_end":35,"line_start":29,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Mit [formula in source] und [formula in source] ist auf [formula in source] unitär und kollektiv [formula in source] -kovariant. Alle [formula in source] liefern für Materieeingänge denselben ersten blockdephasierten Schatten. Dennoch wirkt [formula in source] dort als [formula in source] , während [formula in source] als [formula in source] wirkt: [formula in source] kehrt als [formula in source] oder als [formula i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der erste Schatten wählt die Fortsetzung noch nicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":5090,"byte_start":3264,"id":"section:e07d8c03006c9d14ca6b","kind":"section","labels":[],"line_end":59,"line_start":36,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für genau zwei vollständige [formula in source] -Zellen und eine positive Brücke gelten die Formeln aus Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der allkopplige Zweizellenbeweis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6474,"byte_start":5090,"id":"section:7fb3252a78c653eb2745","kind":"section","labels":[],"line_end":77,"line_start":60,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Im ausgewiesenen harmonischen Modell eines geteilten Vermittlers lautet der symmetrische aktive Block Sein niedriger Zweig beginnt mit [formula in source] ; der antisymmetrische mit [formula in source] . Deshalb ist auf dem aktiven [formula in source] -Raum Nach Abzug beider Einzelbondkorrekturen [formula in source] bleibt Beide Schreibweisen sind kompatibel. Eine Konstante auf dem aktiven Sektor ist außerhalb davon ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vierte Ordnung und unterschiedliche Subtraktionskonventionen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":7332,"byte_start":6474,"id":"section:bea80f21dc081fa7db7a","kind":"section","labels":[],"line_end":90,"line_start":78,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] gilt Mit [formula in source] und [formula in source] folgen Ein kohärentes Achtzweigregister liefert aus dem früheren Zweisingulett-Eingang [formula in source] Erfolg [formula in source] . Alle acht Ausgänge haben Gewichte [formula in source] . Dies ist eine exakte Alternative zur alten 32-Zweigschaltung. Kontrollierte kontinuierliche Sternpulse und Register bleiben zusätzliche Ressourcen. Erz","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein exakter Stern-Spektralfilter unter zusätzlichen Ressourcen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":8009,"byte_start":7332,"id":"section:e30a6bb8dbb241e8f3a0","kind":"section","labels":[],"line_end":98,"line_start":91,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"In der Inzidenzfamilie [formula in source] sind die beiden relevanten Entropien Strikte Konkavität liefert verschiedene Maxima: [formula in source] für Kontexte und [formula in source] für Strahlen. Letzterer Prozess hat Rang 60. Erweitert man den Nachfolgerträger, entstehen symmetrieverträgliche Ränge 15 und 16. Weder maximale Entropie noch minimale Rangzahl wählt die Regel ohne erklärte Klasse. Die passive separate","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Einfachheit braucht einen Auslesevertrag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10096,"byte_start":8009,"id":"section:811ec4cbb4e28436f29e","kind":"section","labels":[],"line_end":113,"line_start":99,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Zwei Singulettläufe finden mindestens vier orthogonale Moden bei [formula in source] über [formula in source] , Residuen unter [formula in source] . Das Dublett ist widerlegt; ein exakter oberer Multiplizitätsbeweis fehlt. -Typen.] 960 gleichgradige Wurzelsummen gehen nach [formula in source] ; gemischt ergeben sich 640 und 192 Summen nach Grad null sowie 64 Cartanfälle. Der vorgeschlagene gemischte Kanal nach [formu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Weitere architektonisch wichtige Korrekturen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":100,"byte_start":0,"id":"section:55dd0d31212a068ec9ec","kind":"chapter","labels":["ch:execution13"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Eine gemeinsame Ausführung für Record, Präparation und Mehrzeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":798,"byte_start":100,"id":"section:02c40d1d14d26ee40c5e","kind":"section","labels":[],"line_end":7,"line_start":3,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Dieselbe korrigierte Vermittlungsoperation erzeugt jetzt Aufzeichnung, kontrollierte Näherungspräparation und Mehrzeitantwort. Die tatsächlichen Quellprojektoren, Paulioperationen und die Dreierclock wurden benutzt. Ein bereits präpariertes [formula in source] oder ein separater Präparations-Hamiltonoperator wird nicht benötigt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine Konstruktion, aber ein ausdrücklich zusätzlicher Ressourcenvertrag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1605,"byte_start":798,"id":"section:656855f929c1182fc4ff","kind":"section","labels":[],"line_end":27,"line_start":8,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Mit [formula in source] , [formula in source] und [formula in source] gilt Kopiere nur die Vermittlerbelegung, nicht das geordnete Farbwort: Dann ist auf allen 44 Dimensionen Der Vermittler kehrt zurück. Auf Materie und Pointer bleibt [formula in source] , [formula in source] , mit Beide Krausoperatoren gehören zum Instrument; ihre Effekte summieren sich zu [formula in source] . Ein ungemessener Pointer bleibt kohäre","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die vollständige Recordoperation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2895,"byte_start":1605,"id":"section:92eca1026135a98351c4","kind":"section","labels":[],"line_end":43,"line_start":28,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für vier Materieträger und höchstens einen aktiven Vermittler sei Alle sechs [formula in source] wurden auf dem vollen Materieraum rekonstruiert: [formula in source] , [formula in source] , [formula in source] . Andere Vermittlersektoren bleiben bei einer adressierten Operation unverändert. Die Kanten haben orthogonale Ausgänge; verschränkte Zuschauer sind eingeschlossen. Dies ist ein vollständiges sequenzielles Prot","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein gemeinsamer Träger und ein fester Schritt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3576,"byte_start":2895,"id":"section:06c1c30824178df7fc5b","kind":"section","labels":[],"line_end":55,"line_start":44,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Rechenbasis- und uniformer Projektor gehören zu den 60 tatsächlichen Quellprojektoren. Die Swap-Identität verwendet dieselben 16 Quell-Paulis: Für Messausgang [formula in source] und Ziel [formula in source] liefert die Bitverschiebung Damit ist [formula in source] . Vier lokale Resets erzeugen [formula in source] sogar aus verschränktem Eingang. Messung und Feedback bleiben Ressourcen, keine hergeleitete kosmologisc","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Quellseitiger Reset ohne vorpräpariertes Zielreservoir","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5624,"byte_start":3576,"id":"section:94350fb2ff235ff57c7a","kind":"section","labels":[],"line_end":84,"line_start":56,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Akzeptiere in jeder Sternrunde die Recordfolge 111: Alle acht ersten Recordfolgen haben Wahrscheinlichkeit [formula in source] . [formula in source] wird erst zur Zielprüfung definiert. Im 24-dimensionalen Raum der verschiedenen Farbanordnungen gilt exakt Dieser Raum trägt die treue reguläre Darstellung von [formula in source] . Die polynomialen Identitäten der Gruppenalgebra gelten daher auch auf allen 256 Materiedi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wiederholung präpariert den Viererzustand kontrolliert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7259,"byte_start":5624,"id":"section:ca00fae1038eba17c369","kind":"section","labels":[],"line_end":106,"line_start":85,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Nach erfolgreicher Präparation folgen lokaler Quelltick [formula in source] , zweimal [formula in source] , Rücknahme [formula in source] und dasselbe [formula in source] -Runden-Filter. Ein ideales kostenloses [formula in source] -Messgerät wird nicht eingesetzt. Protokoll R behält denselben kohärenten Pointer; Protokoll F verwendet beim zweiten Schritt einen frischen. Mit [formula in source] lauten die gemeinsamen ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derselbe Filter liest die Mehrzeitantwort aus","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8229,"byte_start":7259,"id":"section:40dafc4839dc4fcdc6ef","kind":"section","labels":[],"line_end":115,"line_start":107,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Das neue Register ist nicht Clifford: Ein vierqubitiger Pauli hat Spur null oder [formula in source] . Noch konkreter erzeugt der Quellinput [formula in source] genau 13 nichtverschwindende Rechenbasisamplituden. Das ist kein reiner Stabilizerzustand, dessen Trägergröße eine Zweierpotenz ist. Nur Cliffordoperationen, Stabilizer-Hilfszustände und Pauli-Messungen reichen auch mit Feedback nicht aus. Andere Kodierungen ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was für eine native Implementierung noch fehlt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9018,"byte_start":8229,"id":"section:beadcaa3eb3e13a484be","kind":"section","labels":[],"line_end":122,"line_start":116,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Alle [formula in source] kommutieren mit [formula in source] ; der ungelesene Kanal erhält das Zielgewicht. Seine einzelnen Dephasierungen sind orthogonale Hilbert–Schmidt-Projektionen. Ein Fixpunkt ihres Zyklus kann bei keinem Schritt Norm verlieren und liegt deshalb im Schnitt der Fixräume: in der Kommutante der [formula in source] -Wirkung. Deren Dimension ist Die spurlose Dimension 3875 identifiziert keinen gleic","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ungelesener Austausch ist keine Kühlung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10000,"byte_start":9018,"id":"section:62d7b1f43455d28352a8","kind":"section","labels":[],"line_end":126,"line_start":123,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Ein nativer Adapter muss [formula in source] , [formula in source] , Kern und Belegung gemeinsam liefern, beim Half-Charge-Feld zusätzlich mit Domänen- und Energiekontrolle. Er muss den 13-Amplituden-Eingang, beide Recordzweige und die Acht-Runden-Echos reproduzieren, einschließlich Hilfszuständen und Fehlerausgängen. Erst anschließend ist eine skalierende Zellfamilie sinnvoll auf Geometrie, Chiralität und Spin 2 zu ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Abnahmetests und T1–T8-Grenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":87,"byte_start":0,"id":"section:6dc5d0ada8fea4cda44e","kind":"chapter","labels":["app:release13"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Versionspaar v1.3: Quellen, Abdeckung und Reproduktion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":812,"byte_start":87,"id":"section:3ead1e8d98eaa710874f","kind":"section","labels":[],"line_end":7,"line_start":3,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"Diese Ausgabe führt das 90-seitige Hauptbuch v1.1 vollständig fort; die kompakte 35-seitige Compiler-Fassung v1.2 ist nicht ihre Basis. Alle ursprünglichen 21 Hauptkapitel und vier Anhänge bleiben zugänglich. Hinzu kommen drei neue Hauptkapitel und dieses Quellenregister.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei Dokumente mit unterschiedlichen Aufgaben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2181,"byte_start":812,"id":"section:c8a495d9c5a7fb3066d0","kind":"section","labels":[],"line_end":18,"line_start":8,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"Die alten IDs S01–S11 bleiben unverändert. N1–N6 bezeichnen die sechs bereits archivierten Konsolidierungen: Fable-Konsolidierung, Sol-Rekonstruktion, kurze Universalraum-Konsolidierung, Q-Audit/U-Regel, TFPT-Rekonstruktion und Sechs-Prüfpunkte-Analyse, jeweils vom 14. September 2026. Originaltexte und Hashes stehen im Sechs-Quellen-Auditpaket.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neue Quellen und unveränderte Originale","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":3389,"byte_start":2181,"id":"section:73540c32f1ed46362317","kind":"section","labels":[],"line_end":30,"line_start":19,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"L37mmL30mmL83mm Paket&Umfang&Prüfgrenze\\\\ Basisbuch v1.1&210 Bedingungen&Historische Basisprüfung; nicht erneut vollständig ausgeführt.\\\\ Schatten v1.1&128 Bedingungen&Historische Erweiterung; alte RH-Aktualitätsgrenze bleibt sichtbar.\\\\ Sechs-Quellen-Audit&100 eigene&78 exakt/Integrität, 22 numerisch; in dieser Ausgabe redaktionell integriert.\\\\ Gemeinsame Ausführung&231 eigene exakte&Für diese Ausgabe erneut ausgef","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Evidenz nicht durch Addition aufwerten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4020,"byte_start":3389,"id":"section:47bf3fe5625d7a0afd16","kind":"section","labels":[],"line_end":39,"line_start":31,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"Die wissenschaftlichen Pakete liegen unter experiments/theory-contracts/universalraum-six-source-audit-20260914 experiments/theory-contracts/compiler-single-execution-20260914 experiments/theory-contracts/universalraum-paired-release-20260914/new-input-audit Das dritte enthält den neuen endlichen Prüfer, seine Normal-/Optimierungsausgaben und die gesonderte Singulettrechnung. Das Releaseverzeichnis enthält LaTeX, all","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Rechen- und Dokumentpakete","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":4865,"byte_start":4020,"id":"section:a729f039a5b180c20b7f","kind":"section","labels":[],"line_end":43,"line_start":40,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"Der RH-Aktualitätslauf scheiterte an einem fehlenden referenzierten Quellenordner. Der konfigurierte separate Faktorgraph ist nicht verfügbar. Die ausgewählte Originalroute r647 und die verfügbaren Beweise wurden gelesen; keine vollständige globale Aktualität wird behauptet. Es wurde kein RH-Abschlussmarker geändert und keine neue arithmetische Kampagne gestartet.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Aktualität und ausdrücklich fehlende Prüfungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":103,"byte_start":0,"id":"section:92253fea23cc3fd41179","kind":"chapter","labels":["ch:newinputs13"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Zwei weitere Eingaben: Mikrodynamik und deterministische Präparation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":929,"byte_start":103,"id":"section:dccda1ad7edab6a755fe","kind":"section","labels":[],"line_end":7,"line_start":3,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Die während der Konsolidierung zusätzlich eingereichten Texte N7 und N8 enthalten neue Resultate, nicht nur Zusammenfassungen. N7 berichtet die vollständige vierte Ordnung eines harten CAR-Referenzmodells, einen mikroskopischen Stern und einen Relaxationskanal. N8 konstruiert einen harten Tensorproduktkandidaten mit globaler Bandschranke und eine deterministische ideale Präparation.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Prüfurteil und Modellgrenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2213,"byte_start":929,"id":"section:b79e1b799141b58fde7d","kind":"section","labels":[],"line_end":28,"line_start":8,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"N7 verwendet Dieser Operator ist unitär, aber im Gegensatz zu [formula in source] aus Kapitel Das ist kein Widerspruch, sondern eine verschiedene Phase des Rückwegs. Beim Recordaufbau ist der tatsächliche Adjungierte nötig: [formula in source] reproduziert dieselbe Materie-Aufzeichnung wie [formula in source] , unter Einschluss der Pointertensorfaktoren. Blindes Ersetzen beider [formula in source] durch [formula in s","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei richtige unitäre Vertizes, aber nicht derselbe Schritt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4264,"byte_start":2213,"id":"section:77d48448191919d320c0","kind":"section","labels":[],"line_end":50,"line_start":29,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] lautet der eingereichte Referenzoperator [formula in source] vertauscht die beiden vollständigen Paare. Die 40 Clebsch-Kanten ergeben 40 Einzelkanten-, 160 überlappende und 60 gleichlabelige disjunkte Beiträge. Jede Labelklasse ist ein Matching; gleiche Labels teilen keinen Endpunkt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der vollständige vierte-Ordnungs-Operator","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5715,"byte_start":4264,"id":"section:404f59829a78c929d674","kind":"section","labels":[],"line_end":74,"line_start":51,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Der gesamte 24024-dimensionale Singulett-Multiplizitätsraum wurde aus Youngs orthogonaler Darstellung aufgebaut. Ein neuer Lauf mit zwölf niedrigen Eigenvektoren ergab Beim zweiten Niveau wurden vier orthogonale Moden gefunden. Die größte Eigenvektorresiduen-Norm des Laufs liegt unter [formula in source] . Das ist eine hochgenaue endliche Rechnung, kein algebraischer oberer Multiplizitätsbeweis.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die neue Singulettantwort ist unabhängig reproduziert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6794,"byte_start":5715,"id":"section:b99ed3d63c515e4c707a","kind":"section","labels":[],"line_end":88,"line_start":75,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"N8 definiert 16 harte Ortsfaktoren [formula in source] und sechs Bosonmoden pro Vektorlabel. Bei Gesamtladung [formula in source] ist der Sektor endlich. Für gilt [formula in source] . Denn der antisymmetrische Umwandlungsblock [formula in source] erfüllt [formula in source] und [formula in source] . Die selbstadjungierte Offdiagonalblocknorm ist dieselbe. Daher Der führende Austausch ist dann [formula in source] . D","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine globale Bandschranke, aber kein genauer Niedrigenergiefehler","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8548,"byte_start":6794,"id":"section:f78066974c06b3eb31ee","kind":"section","labels":[],"line_end":105,"line_start":89,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] gilt [formula in source] . Definiere [formula in source] mit [formula in source] . Dann In der Basis [formula in source] ist [formula in source] , [formula in source] , [formula in source] . Die unerwünschte Amplitude ist Sie verschwindet für die angegebene Wurzel exakt. Die ideale Phase ist [formula in source] . Es ist eine konkrete Anwendung bekannter https://arxiv.org/abs/quant-ph/0005055Am","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Deterministische Präparation im idealen erweiterten Gattermodell","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9815,"byte_start":8548,"id":"section:b2134f2be1db2a7dab42","kind":"section","labels":[],"line_end":126,"line_start":106,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Gewöhnliche Vermittlerverluste [formula in source] lassen vollständig symmetrische Farbzustände mit Vermittlervakuum dunkel. Auf 16 Trägern hat [formula in source] Dimension [formula in source] . Dieser Raum verhindert einen eindeutigen globalen Attraktor dieser Verlustdynamik.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Relaxation: konstruktiv möglich, aber nicht durch Bosonenverlust allein","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10862,"byte_start":9815,"id":"section:98c7b8298425ebf4849d","kind":"section","labels":[],"line_end":143,"line_start":127,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Nach einem Paarabbau am Stern ist sein gemeinsamer Mittelpunkt leer; ein zweiter Paarabbau ist unmöglich. Für den geschlossenen Block aus 256 Materie- und 288 Vermittlerzuständen gilt Die untere effektive Matrix ist deshalb exakt Der volle 544-dimensionale Block wurde unabhängig gebaut und diagonalisiert. Bei [formula in source] , [formula in source] sind die niedrige Lücke [formula in source] und das nackte Materieg","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der isolierte mikroskopische Stern: vollständiger kleiner Block","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11905,"byte_start":10862,"id":"section:d92bec0f3713fa14afaf","kind":"section","labels":["eq:matched-general"],"line_end":160,"line_start":144,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für beliebige bekannte Zielüberlappung [formula in source] ist die Fehleramplitude nach zwei angepassten Schritten proportional zu Sie verschwindet bei Die Polynomidentität wurde symbolisch geprüft. Für den angekleideten Stern-Grundzustand und nackten Eingang [formula in source] gilt [formula in source] . Daraus folgt die angepasste Phase Verwendet man bei idealem Zugriff auf den angekleideten Zielprojektor dennoch d","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Begonnenes Follow-up: die Präparation an das Mikromodell anpassen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13190,"byte_start":11905,"id":"section:7e4ad4265b2a24c9a33d","kind":"section","labels":[],"line_end":171,"line_start":161,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Bereits der detunierte isolierte Paarblock hat maximale Transferwahrscheinlichkeit Bei [formula in source] , [formula in source] sind das nur [formula in source] . Eine einzelne freie Entwicklung dieses Blocks realisiert daher keinen vollständigen Materie-Vermittler-Tausch [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Begonnenes Follow-up: warum ein einziger fester Puls nicht genügt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14612,"byte_start":13190,"id":"section:27bcb2dc3cca069732e9","kind":"section","labels":[],"line_end":190,"line_start":172,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Das Einzelpuls-Hindernis legt einen konkreten Ausweg nahe, sofern zusätzliche Kontrollen zugelassen werden. Im isolierten resonanten Paar, also bei auf null gesetzter Verstimmung, sei Dann lautet seine exakte Entwicklung Mit dem relativen Viertelphasenpuls [formula in source] gilt Die volle 22-dimensionale Identität ist symbolisch geprüft. Zwei Belegungsphasen und ein resonanter Transfer genügen somit unter diesem Ko","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein kurzer positiver Kontrollkandidat für die nächste Revision","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16745,"byte_start":14612,"id":"section:315305988bfc4b872ffb","kind":"section","labels":[],"line_end":203,"line_start":191,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Der singuläre Schur-Satz für [formula in source] benötigt [formula in source] , [formula in source] und [formula in source] . Das Gegenbeispiel [formula in source] , [formula in source] , [formula in source] hat negatives Determinant trotz positivem Schurrest. Kompatible positive Blöcke ergeben eine positive dichte Fortsetzung nur für alle Stufen, die tatsächliche Form und passende Stetigkeit. Die Identität der volls","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Arithmetik: bestätigt ist der Vertrag, nicht die offene Lösung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18707,"byte_start":16745,"id":"section:4a93cb57561a6eba4262","kind":"section","labels":[],"line_end":219,"line_start":204,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/baseline-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Kann die echte kleine Maschine die nötigen Handgriffe ausführen? Gesucht ist eine kontrollierte Kopplung, die Vermittler hin- und zurückführt und Aufzeichnung erhält. Ein fester freier Puls reicht im geprüften Stern nicht. Abnahme: beide Recordzweige und alle Eingänge, keine versteckten Zielzustände. Können wir den richtigen, angekleideten Zustand auswählen? Die passende Verstärkungsphase ist jetzt berechnet. Es fehl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die wichtigsten nächsten Fragen, einfach ausgedrückt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":60,"byte_start":0,"id":"section:f849bd85aa8f7207ad95","kind":"chapter","labels":["ch:idee"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Was mit Universalraum gemeint ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1381,"byte_start":60,"id":"section:760c987952a04df7a7a8","kind":"section","labels":[],"line_end":9,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Wenn wir gewöhnlich von Raum sprechen, denken wir an eine Bühne: Hier steht ein Tisch, dort fliegt ein Teilchen, und die Uhr läuft im Hintergrund. Die Universalraum-Idee dreht diese Reihenfolge um. Vielleicht sind zuerst Beziehungen und mögliche Veränderungen da. Eine Bühne mit Entfernungen und einer Uhr entsteht erst, wenn viele dieser Beziehungen ein beständiges Muster bilden.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kein zusätzlicher Behälter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3208,"byte_start":1381,"id":"section:c0ae8a96a50b1c96036d","kind":"section","labels":[],"line_end":33,"line_start":10,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Eine ausreichend konkrete Fassung benötigt mindestens: Zustände: Was ist gegeben, einschließlich relevanter Korrelationen? Operationen: Welche Veränderungen sind erlaubt? Zusammensetzung: Wie dürfen Vorgänge hintereinander und nebeneinander verbunden werden? Aufzeichnungen: Welche Spuren bleiben erhalten und dürfen später erneut benutzt werden? Auslesung: Welche Ergebnisse sind mit welchen Wahrscheinlichkeiten beobac","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die fünf Bestandteile","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4343,"byte_start":3208,"id":"section:3e81c23fb3ef7b3b8c90","kind":"section","labels":["eq:op"],"line_end":46,"line_start":34,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Zwei Uhren können jetzt beide zwölf anzeigen und trotzdem verschieden weiterlaufen. Eine ist aufgezogen, die andere steht kurz vor dem Stillstand. Wer nur das Zifferblatt betrachtet, sieht den Unterschied noch nicht. Ein späterer Blick unterscheidet sie.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wann zwei Beschreibungen wirklich dasselbe sagen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5759,"byte_start":4343,"id":"section:47b31f7d1c0cb37d2f3c","kind":"section","labels":["eq:vorwaerts"],"line_end":60,"line_start":47,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"TFPT liefert eine reichhaltige Grammatik: Träger, Darstellungen, Gitter, markierte Symmetrien, Projektoren und kurze wiederverwendete Zahlenformeln. Die Metapher vom Compiler meint eine Übersetzung zwischen diesen Beschreibungen. Sie sagt nicht, dass bereits ein kosmisches Computerprogramm identifiziert ist.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TFPT als Grammatik und als Übersetzung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5797,"byte_start":5759,"id":"section:5fb778df0f761c1b03f1","kind":"chapter","labels":[],"line_end":61,"line_start":61,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Wie die Idee entstanden ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6733,"byte_start":5797,"id":"section:3fd2f1193cda98918e0c","kind":"section","labels":[],"line_end":66,"line_start":62,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Die Anhänge zeigen keine einzige plötzliche Entdeckung, sondern eine Folge von Verschiebungen der Frage. Zuerst fällt auf, dass kleine geometrische und algebraische Daten in verschiedenen Rechnungen wiederkehren. Der Fünferträger führt zu einem 16-dimensionalen Spinor; die passenden Gitterfaktoren führen zu [formula in source] ; ein komplexer Viererträger zeigt 60 besondere Strahlen. Clocks, Ladungszuordnungen und Fl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vom Wiedererkennen zur gemeinsamen Ursache","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7642,"byte_start":6733,"id":"section:0b76809263422bcd5d62","kind":"section","labels":[],"line_end":71,"line_start":67,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Die älteren, in S09 zusammengefassten Untersuchungen fanden mehrere Räume, die man nicht einfach gleichsetzen darf: eine Kommutantenalgebra, einen Majorana-/Fockraum, einen festen Teilchensektor, eine verdoppelte Familienbeschreibung und eingeschränkte Kanalmodelle. Manche lokalen Ansichten ließen verschiedene gemeinsame Dynamiken zu. Andere Tests konnten unter engeren Voraussetzungen ausgewählte Zustände bestimmen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum Spektren und Einzelbilder nicht genügten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9498,"byte_start":7642,"id":"section:c392b7fbfd3c35057972","kind":"section","labels":[],"line_end":86,"line_start":72,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"L30mmL55mmL65mm Etappe& Erkenntnis& Neue Frage\\\\ Vorarbeiten, in S09 rückblickend beschrieben&Mehrere algebraische Ansichten, Lorentzkegel, verborgene Richtungen, lokale und gemeinsame Kanäle.&Welche Informationen gehen beim Auslesen verloren?\\\\ 13. September: Compiler-Manuskript S09&60 Strahlen, 15 Kontexte, zwei Schatten desselben Prozesses; explizite Vormessung mit Register.&Wer wählt Kreuzkopplung, Kontextgewicht","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die dokumentierte Entwicklung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10684,"byte_start":9498,"id":"section:ea23d7b379a42be071fc","kind":"section","labels":[],"line_end":94,"line_start":87,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Der eingefügte Gesprächstext spricht von einem Regelwerk mit Logbuch und von Raum und Materie als Mustern seiner Spuren. Das trifft die Forschungsintuition. Die Formulierung „TFPT ist die Grammatik, der Universalraum die Ausführung“ ist als Einstieg hilfreich.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was von der anschaulichen Ursprungserzählung bleibt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":66,"byte_start":0,"id":"section:a78019756e65a9c9d2cf","kind":"chapter","labels":["ch:algebra"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die mathematischen Bauteile von TFPT","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1113,"byte_start":66,"id":"section:0b66b511703173d3aaa8","kind":"section","labels":[],"line_end":12,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Die historische Kurzfassung nennt [formula in source] und einen fünfteiligen Träger. Vollständig gelesen setzt P1 einen orientierten Rand beziehungsweise eine Naht, einen geeigneten positiven Kern und eine Normierung voraus. P2 setzt Art und Struktur des Trägers voraus; die spätere [formula in source] -Lesart wird mit Farb- und schwachen Richtungen verbunden. Orientierung, Positivität, komplexe Struktur und Markierun","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Ausgangsannahmen enthalten mehr als zwei Zahlen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2337,"byte_start":1113,"id":"section:23f8dda7d7d0ed1489b4","kind":"section","labels":[],"line_end":26,"line_start":13,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Bei fünf komplexen Richtungen kann man antisymmetrische Kombinationen von null, zwei und vier Richtungen bilden. Zusammen erhält man Das ist die gerade Spinorstruktur von [formula in source] . „Antisymmetrisch“ heißt hier: Beim Vertauschen zweier Plätze wechselt ein Vorzeichen. Es ist eine genaue Bauvorschrift, keine bildliche Ähnlichkeit.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vom Fünferträger zum Spinor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4400,"byte_start":2337,"id":"section:f35bf55f811b5f489d7c","kind":"section","labels":[],"line_end":57,"line_start":27,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Die beiden positiven Wurzelgitter [formula in source] und [formula in source] besitzen Determinante vier und Diskriminantengruppe [formula in source] . Eine Diskriminantengruppe beschreibt hier die möglichen Restklassen, mit denen man das Gitter ohne Verlust der Ganzzahligkeit ergänzen kann. Für passende Generatoren gilt modulo eins Diagonal gekoppelt ist die Summe [formula in source] ganzzahlig. Die vier gemeinsamen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die Verklebung wirklich zu E [formula in source] 8 führt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6023,"byte_start":4400,"id":"section:48285b53f03c038bd0d0","kind":"section","labels":["eq:branch"],"line_end":83,"line_start":58,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Die 240 Wurzeln sind besondere Vektoren in einem acht-dimensionalen Raum. Hinzu kommen acht Cartanrichtungen, sodass die Lie-Algebra 248 Dimensionen besitzt. Unter [formula in source] lautet ihre komplexe Zerlegung L47mmrY Sektor& Wurzeln& Generatoren einschließlich Cartan\\\\ [formula in source] &40& [formula in source] \\\\ [formula in source] &12& [formula in source] \\\\ Gemischter Vektorsektor&60& [formula in source] ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wurzeln und Generatoren sind verschiedene Zählungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7221,"byte_start":6023,"id":"section:42e9fa355e14dd4915f9","kind":"section","labels":[],"line_end":90,"line_start":84,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Ein Strahl ist ein reiner Zustand ohne seine insgesamt irrelevante globale Phase. Ein Kontext ist eine vollständige orthogonale Viererbasis: vier mögliche Ausgänge einer scharfen Messung. Im markierten komplexen Viererträger ergeben sich 60 besondere Strahlen in 15 solchen Kontexten. In der gewählten Kodierung sind dies die reinen Zwei-Qubit-Stabilizerzustände und ihre vollständigen Pauli-Kontexte. S09, Kap. 3 und 9","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das endliche Fenster: 60 Strahlen und 15 Kontexte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8754,"byte_start":7221,"id":"section:cb01493d6bd2c9971249","kind":"section","labels":[],"line_end":106,"line_start":91,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"L45mmL31mmL74mm Objekt& Größe& Was die Zahl zählt\\\\ [formula in source] -Wurzeln&240&Besondere Vektoren, keine 240 unabhängigen Raumrichtungen.\\\\ [formula in source] &248&Dimension der Generatoralgebra.\\\\ Ein Viererträger& [formula in source] &Zustände eines Ququarts, hier als zwei Qubits kodiert.\\\\ Vier solche Träger& [formula in source] &Komplexe Hilbertraumdimension der Zelle.\\\\ 15 allgemeine CQ-Blöcke& [formula i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Räume im Größenvergleich","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":71,"byte_start":0,"id":"section:bbffcd21d38b35592a6b","kind":"chapter","labels":["ch:prozess"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Ein gemeinsamer Prozess mit zwei Schatten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1558,"byte_start":71,"id":"section:9ca11ccd95d1bdb1043d","kind":"section","labels":["eq:T"],"line_end":19,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Man beginnt mit einem Strahl [formula in source] : Kontext [formula in source] , Ergebnis [formula in source] . Dann wählt man einen nächsten Kontext [formula in source] und misst in dessen Basis. Die Quellkonstruktion benutzt [formula in source] ist eine [formula in source] -Inzidenzmatrix. Sie erlaubt den aktuellen Kontext und sechs andere, mit ihm inzidente Kontexte. Jeder erlaubte Nachfolger erhält in dieser spez","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine einzelne Messrunde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3449,"byte_start":1558,"id":"section:3332f27e384e8c9f3a98","kind":"section","labels":["eq:D","eq:shadows"],"line_end":55,"line_start":20,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Die Matrix [formula in source] summiert die vier Ergebnisgewichte jedes Kontexts. Die Matrix [formula in source] liest die 15 nichttrivialen Pauli-Erwartungswerte aus. Mit [formula in source] lauten ihre Einträge Für [formula in source] und [formula in source] ergibt sich exakt Der Systemschatten entwickelt sich somit als depolarisierender Kanal Die Dämpfung [formula in source] entsteht aus der Kontextkombinatorik. B","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kontext und Quantenzustand als zwei Auslesungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4623,"byte_start":3449,"id":"section:03cdd306d5645b7e609a","kind":"section","labels":["eq:Tfactor"],"line_end":74,"line_start":56,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Die in S01 ausgearbeitete Faktorisierung lautet Hier gelten [formula in source] , [formula in source] und [formula in source] . Die beiden Zeilenräume sind orthogonal. Im selben Kontext haben die Pauli-Vorzeichenvektoren Skalarprodukt drei für denselben Strahl und minus eins für verschiedene Strahlen; bei inzidenten Kontexten bleibt eine gemeinsame Pauli-Richtung. Diese Werte ergeben genau die Einträge von","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die genaue Kompression auf 30 Koordinaten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6433,"byte_start":4623,"id":"section:f1310ed45265beb22120","kind":"section","labels":[],"line_end":96,"line_start":75,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Aus [formula in source] mit Permutationsmatrizen folgt beim gleichgewichteten Mitteln unmittelbar [formula in source] . Zusätzliche Konjugation durch die Symmetriegruppe [formula in source] ändert das nicht: S07 berichtet 5040 Terme über 4500 verschiedene Matchings, gegenüber 24\\,601\\,472 insgesamt möglichen perfekten Matchings des bipartiten Inzidenzbildes. Diese kombinatorische Realisierung ist konkret. Die Gleichg","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum Symmetrie die Gewichte noch nicht auswählt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7204,"byte_start":6433,"id":"section:f978c9461040cde8d0bf","kind":"section","labels":[],"line_end":111,"line_start":97,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Für die Kontextmatrix gilt Ihre Determinante ist negativ. Eine reelle Matrixexponentialfunktion hat jedoch [formula in source] . Deshalb ist [formula in source] auf diesem 15-dimensionalen Raum kein [formula in source] mit reellem [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein Schritt ist nicht dasselbe wie zwei halbe Schritte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7280,"byte_start":7204,"id":"section:ebebdcb53dff5794747a","kind":"chapter","labels":["ch:memory"],"line_end":113,"line_start":112,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Gedächtnis: Was ein einzelnes Bild verschweigt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9410,"byte_start":7280,"id":"section:79d205736f1576c2fbaa","kind":"section","labels":[],"line_end":147,"line_start":114,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Ein klassisch-quantenmechanischer Zustand, kurz CQ-Zustand, besitzt 15 positive [formula in source] -Blöcke [formula in source] . Zusammen haben sie 240 reelle lineare Koordinaten und Gesamtspur eins. Die feste Regel macht jeden Ausgangsblock in seinem Kontext diagonal. Deshalb gilt Es ist also nicht richtig, 240 Koordinaten pauschal als kleinste dauerhaft autonome Hülle dieser festen Ausführung auszugeben.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Allgemeine Kontextblöcke brauchen eine andere Beschreibung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10711,"byte_start":9410,"id":"section:0faa9bebf8cccbb7f7a2","kind":"section","labels":["eq:record"],"line_end":168,"line_start":148,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Für die vier Projektoren eines Kontexts sind [formula in source] Spiegelungen. In Dimension vier gilt Allgemein in Dimension [formula in source] wäre die linke Seite [formula in source] . Der kurze Auslöschungseffekt ist hier also tatsächlich viererspezifisch.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie die Aufzeichnung gebaut wird","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12540,"byte_start":10711,"id":"section:45d7c84bffed313c0ee7","kind":"section","labels":[],"line_end":182,"line_start":169,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Für einen gleichförmigen reinen Eingang in der gewählten Kontextbasis erzeugt eine Vormessung maximale Verschränkung. Ohne Registerblick ist der Systemzustand [formula in source] . Nun gibt es zwei Ausführungen: Derselbe kohärente Speicher wird nochmals gekoppelt: [formula in source] stellt den reinen Eingang wieder her. Ein neuer Speicher wird benutzt: Im reduzierten System wird die Dephasierung wiederholt; [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das Echo des behaltenen Registers","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13348,"byte_start":12540,"id":"section:f3590221e63cedbff1ec","kind":"section","labels":[],"line_end":192,"line_start":183,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Bei frischen Registern trägt eine Folge von Kontexten den kohärenten Zustand Das Weglassen des Registers summiert Dichteoperatorbeiträge. Eine kohärente Projektion auf eine Registersuperposition summiert Amplituden und beschreibt ein anderes Experiment, einschließlich seiner Erfolgswahrscheinlichkeit.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reihenfolge bleibt wichtig","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15023,"byte_start":13348,"id":"section:0d2b31d49cad9d65475b","kind":"section","labels":[],"line_end":205,"line_start":193,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Eine nichtverschwindende Beobachtungsfolge eines geschlossenen endlichen Systems mit festem unitärem Schritt ist eine endliche Summe von Phasenfaktoren. Nach Zusammenfassung gleicher Frequenzen besitzt ihr mittleres Betragsquadrat einen positiven Cesàro-Grenzwert. Sie kann daher nicht für alle [formula in source] exakt wie [formula in source] abklingen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Endliches Gedächtnis und scheinbares Vergessen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":72,"byte_start":0,"id":"section:7a5797059683582e297a","kind":"chapter","labels":["ch:zelle"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die Vierträgerzelle: ein gemeinsames Muster","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1404,"byte_start":72,"id":"section:e97c3b05b1c2b1da7f12","kind":"section","labels":["eq:omega"],"line_end":24,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Vier Träger mit je vier Basiswerten besitzen den total antisymmetrischen Zustand Jedes Basiswort verwendet alle vier Werte genau einmal. Die 24 Permutationen erhalten passende Vorzeichen. Das Ergebnis ist ein reiner gemeinsamer Zustand. Jeder einzelne Träger sieht für sich trotzdem maximal gemischt aus: Die Paarreduktion hat Rang sechs und sechs gleich große Eigenwerte [formula in source] . Die Ordnung steckt in den ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein Zustand, dessen Teile allein nichts verraten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2609,"byte_start":1404,"id":"section:28c47965c47783b59f91","kind":"section","labels":[],"line_end":38,"line_start":25,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Sei [formula in source] der Projektor auf den symmetrischen Paarraum. Wenn für alle Paare [formula in source] gilt, dann hat jeder Swap Eigenwert minus eins. Da Transpositionen alle Permutationen erzeugen, folgt Für [formula in source] ist dieser Raum eindimensional, für [formula in source] null. Auch gemischte Zustände mit entsprechender Trägerbedingung erfüllen die Aussage. Für [formula in source] existieren aber e","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Hüllensatz und seine genaue Voraussetzung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3902,"byte_start":2609,"id":"section:39c0f8ae7dfc981118ed","kind":"section","labels":["eq:tet-spec"],"line_end":54,"line_start":39,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Das vollständige Tetramermodell lautet Es besitzt das exakte Spektrum Der Grundzustand ist [formula in source] , die Lücke [formula in source] . Die hochgestellten Zahlen zählen die Zustände pro Energiewert und summieren sich zu 256.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine weiche Energiebedingung erlaubt Bewegung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5057,"byte_start":3902,"id":"section:91a2e20eefb7b5e389df","kind":"section","labels":[],"line_end":68,"line_start":55,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Der vollständige Graph, ein Stern und ein Pfad besitzen auf vier Trägern denselben antisymmetrischen Grundzustand, aber verschiedene Anregungen. Für gleiche Sterngewichte ist die Lücke [formula in source] statt [formula in source] . S01 nennt für einen Pfad mit Gewichten [formula in source] etwa [formula in source] ; S06 für sechs Gewichte [formula in source] etwa [formula in source] . Die letzten Werte werden hier a","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was ein Zustand über seinen Generator verrät","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5655,"byte_start":5057,"id":"section:95f6471ad59bcf836941","kind":"section","labels":[],"line_end":73,"line_start":69,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Der Projektor [formula in source] kommutiert mit allen Swaps. Daher erhält jede rein zellinterne Austauschentwicklung, auch mit zeitabhängigen Gewichten, den Anteil [formula in source] . Kollektive [formula in source] -Drehungen tun dasselbe. Ein Grundzustand kann also bekannt sein, ohne dass der vorhandene Ablauf einen beliebigen Eingang dorthin bringt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum Austausch allein die Zelle nicht herstellt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5734,"byte_start":5655,"id":"section:bd1aee607a140d031adc","kind":"chapter","labels":["ch:fugen"],"line_end":75,"line_start":74,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Vermittlung und Graph: die Prüfung der fünf Fugen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7886,"byte_start":5734,"id":"section:3d43024ce3e08a68ef3d","kind":"section","labels":[],"line_end":103,"line_start":76,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Der gewünschte positive Austausch lässt sich in einem kleinen Modell genau erklären. Man ergänzt den Paarraum [formula in source] durch einen sechsdimensionalen Vermittler mit Energie [formula in source] . Die partielle Isometrie [formula in source] erfüllt Für bleiben die zehn symmetrischen Zustände bei null; die antisymmetrischen Zustände koppeln paarweise an den Vermittler. Die unteren Energien sind Nach Identifik","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie ein virtueller Zwischenzustand bindet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9877,"byte_start":7886,"id":"section:5bd703cb9a0ceca6ea92","kind":"section","labels":[],"line_end":125,"line_start":104,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"S11 macht die zusätzliche Zuordnung: Ein [formula in source] -Spinorgewicht [formula in source] ist ein Ort; das [formula in source] -Gewicht [formula in source] ist der lokale Viererzustand. Die 64 Gewichte von [formula in source] werden somit als 16 Orte mit je vier inneren Zuständen gelesen. Das ist eine konkrete bedingte Interpretation, keine bloße Umbenennung einer bereits gegebenen räumlichen Geometrie.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Clebsch-Vorschlag: eine genaue neue Graphlesart","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11916,"byte_start":9877,"id":"section:773ac1973617d1f62b0a","kind":"section","labels":[],"line_end":134,"line_start":126,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Die Graphkombinatorik folgt aus der angegebenen Ortslesart. Um daraus einen Vielteilchen-Hamiltonoperator zu erhalten, braucht man außerdem eine Fock- oder Tensorproduktstruktur, Besetzungsbedingungen, die Bedeutung der virtuellen Zustände und ihre Energien. Betragsgleiche Chevalley-Strukturkonstanten wählen noch keine physikalischen Kopplungsstärken in normierten Mehrteilchenzuständen aus. Gleiche [formula in source","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Welche Auswahl hier noch hinzukommt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13528,"byte_start":11916,"id":"section:5c4d64ff4f77dc2a2751","kind":"section","labels":[],"line_end":153,"line_start":135,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"L74mmY Clebsch-Cluster bei [formula in source] , nach S11& Berichteter Wert\\\\ Grundenergie& [formula in source] \\\\ Grundzustand&Eindeutiges [formula in source] -Singulett, Form [formula in source] \\\\ Erster angeregter Singulettwert& [formula in source] ; mindestens vier orthogonale Moden, Gap etwa [formula in source] \\\\ Erste adjungierte Anregung& [formula in source] , Gap etwa [formula in source] \\\\ Weitere Multiple","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die berichteten Clusterzahlen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14709,"byte_start":13528,"id":"section:16feda71dac7b670a5c4","kind":"section","labels":[],"line_end":169,"line_start":154,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"S11 behauptet für den vollständigen Graphen mit [formula in source] einen eindeutigen Grundzustand bei [formula in source] und Gap [formula in source] . Energie und Gap stimmen; die Eindeutigkeit stimmt ab acht Trägern nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neue Korrektur: Singulett heißt nicht eindeutig","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16989,"byte_start":14709,"id":"section:e8ef37a99436af46dd6f","kind":"section","labels":[],"line_end":191,"line_start":170,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Operatoren unterscheiden (v1.3): Das folgende [formula in source] beschreibt eine gleichkontextige Vierer-Aufzeichnung. Das neue binäre Austauschregister [formula in source] ist ein anderer Operator und nachweislich nicht Clifford. Seine zusätzliche Ressourcenanforderung widerspricht der folgenden Darstellbarkeit von [formula in source] nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neue Präzisierung: Aufzeichnung ist nicht durch die 248 verboten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":66,"byte_start":0,"id":"section:69b67e1cc7de91259470","kind":"chapter","labels":["ch:two"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Zwei Zellen: aus Verbindung wird Dynamik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":839,"byte_start":66,"id":"section:7a738c6a9e8e8f93fd77","kind":"section","labels":[],"line_end":7,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Ist eine reduzierte Dichtematrix [formula in source] rein, so muss der gemeinsame Zustand bezüglich [formula in source] und seinem Rest faktorisiert sein. Sein Träger liegt in [formula in source] . Sind alle disjunkten Zellmarginalien unverändert rein, ist der Gesamtzustand ein Produkt über die Zellen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die Zellen beim Verbinden ihre Reinheit verlieren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1875,"byte_start":839,"id":"section:bc5b6a78fd7cfbe7617b","kind":"section","labels":["eq:Hred"],"line_end":28,"line_start":8,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Zwei vollständige Tetramerzellen mit genau einer Brücke haben Der volle Raum besitzt [formula in source] Dimensionen. Trotzdem bleibt die Entwicklung des Produktzustands in einem zweidimensionalen invarianten Unterraum: Die beiden Vektoren sind orthonormal; [formula in source] und [formula in source] . Es folgt Die Brücke koppelt den Produktgrundzustand an eine gemeinsame adjungierte Anregung. Beide Zellhälften verwe","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein kleiner exakter Raum in einem großen Hilbertraum","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4244,"byte_start":1875,"id":"section:de700c7b5fe1c8e2c9bb","kind":"section","labels":["eq:alllambda13","eq:gapbound"],"line_end":73,"line_start":29,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Mit lauten die beiden Eigenwerte Die negative Korrektur beschreibt die Absenkung gegenüber dem einfachen Produktwert [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Energie und ein wirklicher Grundzustandsnachweis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5445,"byte_start":4244,"id":"section:a3607b9b698de6a70cb6","kind":"section","labels":[],"line_end":95,"line_start":74,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Der niedrige Eigenzustand lässt sich schreiben als Seine Zellreduktion besitzt das Spektrum Die Entropie in natürlichen Logarithmen ist Bei [formula in source] sind [formula in source] und [formula in source] ; bei [formula in source] gilt [formula in source] . Schon eine endliche einzelne Brücke macht die lokale Zelle gemischt. Energieabsenkung und Verschränkung sind hier keine unabhängig eingesetzten Zusätze.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verschränkung aus derselben Kopplung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6560,"byte_start":5445,"id":"section:8369db27d2852563df09","kind":"section","labels":["eq:two-clock"],"line_end":111,"line_start":96,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Starte im Produkt [formula in source] und lasse denselben konstanten gekoppelten Hamiltonoperator wirken. Dann gilt Bei [formula in source] vereinfacht sich dies zu [formula in source] . Der Energieinhalt beider Zellen pulsiert in einem messbaren Muster.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein Uhrsignal ohne zusätzlich gewählten lokalen Tick","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7528,"byte_start":6560,"id":"section:0022ac251e0b4d265fe2","kind":"section","labels":[],"line_end":120,"line_start":112,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Ein einzelner eindeutiger Singulettgrundraum besitzt keine logische Zustandsvielfalt. Das Produkt solcher Grundräume bleibt eindimensional. Wer alles auf diese Grundräume projiziert, erhält nur eine skalare Energie. Nichttriviale effektive Dynamik muss Anregungen, Randzustände, Multiplizitäten oder zusätzliche Vakuumsektoren behalten.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum viele Zellen noch ein eigener Schritt sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":71,"byte_start":0,"id":"section:9968c3b47cd33bac8903","kind":"chapter","labels":["ch:zeit"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Zeit: Takt, Uhrwerk und lesbare Veränderung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1193,"byte_start":71,"id":"section:b4cae7c86cc51c598e24","kind":"section","labels":[],"line_end":15,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Eine zyklische Matrix ist zunächst ein Taktmuster. Eine Dynamik sagt, wann welcher Zustand entsteht. Eine Uhr braucht zusätzlich eine beobachtbare Anzeige und eine Kalibrierung. Diese drei Ebenen müssen zusammenpassen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Drei Bedeutungen des Wortes Clock","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2069,"byte_start":1193,"id":"section:c8f39d51cf7690fc211c","kind":"section","labels":[],"line_end":20,"line_start":16,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Der vollständige gleichgewichtete Tetramer-Hamiltonoperator ist eine zentrale Transpositionssumme. Deshalb kommutiert er mit jedem [formula in source] und jedem [formula in source] . Die Paarenergien ändern sich unter seiner freien Entwicklung nicht. Eine Tabelle, die nacheinander einen lokalen [formula in source] -Tick anwendet, ist somit kein Beweis, dass genau diese Anzeige unter [formula in source] von selbst läu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die Paarenergien unter dem Tetramer stillstehen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":3008,"byte_start":2069,"id":"section:aa29cf5dc90bc183e0ee","kind":"section","labels":[],"line_end":38,"line_start":21,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Ein präparierter nichtstationärer Zustand kann dennoch unter demselben Tetramer laufen. Für einen lokalen spurfreien hermiteschen Pauli [formula in source] mit [formula in source] setze Da [formula in source] , folgt Die lokalen Anzeigen oszillieren gegeneinander; ihre Summe bleibt null. Die Periode ist [formula in source] . Präparation, Ausleserichtung und die Kalibrierung von [formula in source] sind weitere Eingab","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine laufende lokale Anzeige im gesetzten Modell","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4494,"byte_start":3008,"id":"section:4c03c8ef3e280532029e","kind":"section","labels":[],"line_end":57,"line_start":39,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Zerlege [formula in source] . Die vier [formula in source] sind orthonormal. Wähle zusätzlich Weil jedes Wort von [formula in source] jedes Energielabel einmal enthält, gilt [formula in source] . Für erhält man [formula in source] . Die Zeiten [formula in source] liefern vier orthogonale Anzeigen. Global ist der Zustand stationär, bedingt auf die Uhranzeige entwickelt sich das System. Das ist eine konkrete Page-Woott","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine relationale Viereruhr ist konstruierbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":5172,"byte_start":4494,"id":"section:4f2301304656920e0b55","kind":"section","labels":[],"line_end":62,"line_start":58,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Aus [formula in source] folgt [formula in source] . Die historischen Größen [formula in source] und [formula in source] beschreiben deshalb sechsfach wiederholte Faktoren [formula in source] und [formula in source] . Eine physikalische Rate ist erst [formula in source] für einen festgelegten Schritt [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum ein Logarithmus noch keine Sekunde ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5883,"byte_start":5172,"id":"section:63194486b668dfb0e3ff","kind":"chapter","labels":["ch:echo"],"line_end":67,"line_start":63,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Verschiedene Präparationsverträge bleiben getrennt Dieses Kapitel bewahrt die ursprüngliche endliche Schaltung mit Erfolg [formula in source] aus dem vorausgesetzten Zweisingulett-Eingang. Der neue Stern-Spektralfilter erreicht [formula in source] aus demselben Eingang, setzt aber kontrollierte kontinuierliche Pulse voraus. Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die ausführbare Präparation und der Mehrzeittest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7250,"byte_start":5883,"id":"section:440af4c150824cf93f2b","kind":"section","labels":[],"line_end":89,"line_start":68,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Die Präparationsnotiz S02 geht über den abstrakten Satz „ [formula in source] existiert“ hinaus. Sie beschreibt eine konkrete Schaltung, die aus einem einfachen Eingang den Zustand mit Erfolgsanzeige herstellt, anschließend ein Register schreibt und die Rückkehr ausliest. Laut Quelle wurde die Schaltung exakt simuliert, nicht auf Hardware ausgeführt. Ihr Zugriff auf zusätzliche Hilfssysteme und Nicht-Clifford-Operati","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was S02 tatsächlich geschlossen hat","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8727,"byte_start":7250,"id":"section:002f3cc3a4dd7cfd30c4","kind":"section","labels":[],"line_end":104,"line_start":90,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Der benötigte Zustand [formula in source] ist in der Acht-Qubit-Kodierung kein Stabilizerzustand. Schon für einen nichttrivialen lokalen Pauli gilt während reine Qubit-Stabilizerzustände für Pauli-Observablen nur [formula in source] liefern. Ebenso ist der Paarreduktionsrang sechs keine Zweierpotenz. Eine exakte Präparation aus einem Stabilizer-Eingang benötigt deshalb eine zusätzliche Ressource, etwa einen passenden","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die zusätzliche Ressource bleibt sichtbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9859,"byte_start":8727,"id":"section:1c35b764c8c0547b5a44","kind":"section","labels":[],"line_end":126,"line_start":105,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Der einfache Eingang lautet Er ist mit dem in S02 angenommenen Clifford-Baukasten präparierbar und besitzt [formula in source] -Anteil [formula in source] . Der Antisymmetrisierer ist Die konkrete Schaltung erzeugt 32 Kontrollzweige, von denen 24 die Permutationen tragen. Acht ungültige Zweige werden markiert. Nach Interferenz und Erfolgsselektion ist der implementierte Operator Somit gilt Der erfolgreiche Zweig ist ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie der Filter den Zustand erzeugt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11835,"byte_start":9859,"id":"section:84f2a66887a40239067a","kind":"section","labels":["eq:originalecho"],"line_end":163,"line_start":127,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] schreibe [formula in source] . Dann Ein ignorierter frischer Pointer erzeugt Diese binäre Swap-Aufzeichnung ist ein anderer Kanal als die 15-Kontext-Mischung mit Faktor [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das ursprüngliche Echo: eins gegen siebzehn Zweiunddreißigstel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13337,"byte_start":11835,"id":"section:6c003dae94644fdbbf15","kind":"section","labels":[],"line_end":183,"line_start":164,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Der Endfilter hat den Effekt [formula in source] . Seine beobachtbare Erfolgsrate ist deshalb [formula in source] , nicht [formula in source] selbst. L68mmY Y Statistik& Behalten& Frisch\\\\ [formula in source] -Rückkehr, bedingt auf Präparation& [formula in source] & [formula in source] \\\\ Endfilter erfolgreich, bedingt auf Präparation& [formula in source] & [formula in source] \\\\ Beide Filter erfolgreich, je begonnen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die wirklichen Erfolgswahrscheinlichkeiten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15734,"byte_start":13337,"id":"section:f38240b9451910bd506f","kind":"section","labels":["eq:optimal"],"line_end":210,"line_start":184,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Eigene exakte Ergänzung dieser Synthese. Man kann die gleiche Messfrage für einen beliebigen lokalen unitären Tick [formula in source] ausrechnen. Setze Die beiden Swap-Gewichte sind [formula in source] . Daher Der Kontrast dieser Rückkehrstatistik ist maximal, wenn [formula in source] , also [formula in source] . Ein einzelnes CNOT innerhalb des Viererträgers erfüllt [formula in source] . Es permutiert dieselbe Meng","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neue Fortsetzung: der maximal ausgeglichene Echovergleich","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17149,"byte_start":15734,"id":"section:2f3033f4a4f3f92264bf","kind":"section","labels":[],"line_end":218,"line_start":211,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Y r Ressource nach S02& Anzahl\\\\ Systemqubits&8\\ , wiederverwendet&10\\ ätze&2\\ reservierte Qubits&20\\ Erfolgsbits beider Filter&12\\ -Gatter&574\\ CNOT vor Toffoliauflösung&382\\ &26\\ - [formula in source] / Pauli- [formula in source] &276 / 26\\\\T/T^ [formula in source] T-Varianten waren durch lokale Matrixidentität und Ersetzung zertifiziert, nicht zusätzlich als komplette komplexe 20-Qubit-Vektoren simuliert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ressourcen und Beweisgrenze der Originalschaltung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":75,"byte_start":0,"id":"section:107dd494ed9a72c68eef","kind":"chapter","labels":["ch:seam"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Von der Kette zur E [formula in source] 8-Naht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1943,"byte_start":75,"id":"section:49a79c21b1f53b68527d","kind":"section","labels":[],"line_end":28,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Das Zweizellenmodell benutzt zwei vollständige Vierergraphen mit einer Brücke. Die Vielzellenrechnung in S08 benutzt dagegen Vierersegmente mit nächster Nachbarschaft. Bei [formula in source] wird erst dieses zweite Modell eine uniforme Kette. Derselbe isolierte Singulettzustand garantiert keine identischen Anregungen und keinen identischen Grenzwert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein wichtiger Modellwechsel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3203,"byte_start":1943,"id":"section:9891dae87cbab6fe24ff","kind":"section","labels":[],"line_end":44,"line_start":29,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Für den uniformen periodischen Austauschring liefern die Quellen [formula in source] bei acht und [formula in source] bei zwölf Trägern. Der bekannte Vergleich lautet Die Sutherland-Grundenergie pro Träger ist für [formula in source] . S08 nennt die Extrapolation [formula in source] und [formula in source] . Diese endlichen Zahlen passen zur [formula in source] -WZW-Beschreibung des Kettenmodells. Die allgemeine Verb","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die SU(4)-WZW-Theorie hier plausibel ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4699,"byte_start":3203,"id":"section:9fb14a6eb1c23d87af5e","kind":"section","labels":[],"line_end":70,"line_start":45,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Die zentrale Ladung ist eine Kennzahl einer konformen Feldtheorie. Für die chiralen Niveau-1-Faktoren gilt Das Produkt hat also schon vor einer Kopplung [formula in source] . Ein später gefundener Wert acht allein ist kein Beweis einer [formula in source] -Erweiterung und kein Beweis eines Kondo-Flusses.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Naht braucht mehr als die Zahl acht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6584,"byte_start":4699,"id":"section:f0f07d810f959e8f3481","kind":"section","labels":[],"line_end":92,"line_start":71,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"S11 ersetzt die frühere Kondo-Zielbeschreibung sinnvoll durch eine konkrete Erweiterungsaufgabe. Die Kurzschreibweise eines Quotienten durch [formula in source] kann jedoch verschiedene Operationen meinen. Nur auf invariante Zustände des ursprünglichen Produkts zu projizieren ist nicht dasselbe wie eine Simple-Current-Erweiterung mit den nötigen zusätzlichen beziehungsweise entsprechend gekoppelten Sektoren.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum „Z [formula in source] 4-Eichung“ präzisiert werden muss","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7319,"byte_start":6584,"id":"section:8a1f20837110be451db6","kind":"section","labels":[],"line_end":97,"line_start":93,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Eine gewöhnliche kritische SU(4)-Kette hat links- und rechtslaufende Sektoren, mit [formula in source] . Die übliche Kennzahl heißt dabei [formula in source] , nicht sechs. Die chirale Differenz ist null. Eine rein chirale [formula in source] -Naht hat dagegen Differenz acht. Ein zusätzliches ebenfalls nichtchirales [formula in source] -Modell ändert daran nichts.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Chiralitätslücke","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8698,"byte_start":7319,"id":"section:3181c3942c8b50d2b8d9","kind":"section","labels":[],"line_end":103,"line_start":98,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Die innere Glue- [formula in source] wirkt auf den 248 Strömen mit Phasen [formula in source] auf Sektoren der Größen [formula in source] . Ihre Spur ist null. Die geometrische Vierteldrehung [formula in source] hat auf Stufe eins dagegen Spur [formula in source] . Die Operatoren sind somit nicht identisch. Eine Clock kann eine geometrische Drehung mit innerem Twist kombinieren; die beiden Faktoren bleiben getrennt. ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei Vierteldrehungen und der Index","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":551,"byte_start":0,"id":"section:7117bfd9cb5d310d205e","kind":"chapter","labels":["ch:recon"],"line_end":5,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Fortschritt v1.3 Ein gemeinsamer endlicher Träger realisiert nun Aufzeichnung, Näherungspräparation, Reset und Mehrzeitantwort unter einem ausdrücklich angegebenen Ressourcenvertrag. Das beantwortet eine bedingte Existenzfrage. Es wählt weder den Vertrag aus TFPT allein noch ein universelles positives Zustandsfunktional aus. Die nachfolgenden Anforderungen bleiben deshalb nötig; die Konstruktion steht in Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie eine vollständige Rekonstruktion aussehen könnte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1946,"byte_start":551,"id":"section:dadddd3462bd3aea80fb","kind":"section","labels":[],"line_end":17,"line_start":6,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Eine endliche Liste von Schatten bestimmt im Allgemeinen mehrere Prozesse. Man kann sogar jeden Kandidaten um einen ungekoppelten unsichtbaren Hilfsfaktor ergänzen, auf den alle erlaubten Experimente trivial wirken. Alle Antworten bleiben gleich. Eindeutigkeit ist daher zunächst nur für die minimal beobachtbare Darstellung erreichbar.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vom Wunsch nach Eindeutigkeit zu einer prüfbaren Frage","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2535,"byte_start":1946,"id":"section:70d3ebbf509c20a951f8","kind":"section","labels":[],"line_end":24,"line_start":18,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Eine Projektion kann wichtige Wahrscheinlichkeiten erhalten und trotzdem die Multiplikation zerstören. S03 gibt einen einfachen Gegenbeleg: Projiziere [formula in source] auf [formula in source] und definiere [formula in source] . Dann Die neue Multiplikation ist nicht assoziativ. Eine nützliche reduzierte Vorhersagebeschreibung darf also nicht ohne zusätzlichen Nachweis als geschlossene physische Operationsalgebra v","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine kleinere Beschreibung ist nicht automatisch eine Algebra","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4676,"byte_start":2535,"id":"section:24893998ec68c1b038a7","kind":"section","labels":[],"line_end":52,"line_start":25,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Eine phasentreue Rekonstruktion braucht mehr als eine Tabelle einzelner Wahrscheinlichkeiten. Ein passender Ausgangspunkt ist eine komplexe Algebra [formula in source] mit Einheit, Multiplikation, Adjunktion und einem positiven normierten Zustandsfunktional [formula in source] : Für Operationswörter [formula in source] definiert einen positiven semidefiniten Korrelationskern. Er enthält die relativen komplexen Phasen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was vollständige Phaseninformation zusätzlich bringt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5967,"byte_start":4676,"id":"section:c83f4cf8262818057a9a","kind":"section","labels":[],"line_end":65,"line_start":53,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Ein Prozesstensor beziehungsweise Quantenkamm ordnet einer Folge von Instrumenten gemeinsame Ergebniswahrscheinlichkeiten zu. Positivität und kausale Normierungsregeln sichern die Konsistenz. Eine tomographisch vollständige Eingriffsfamilie bestimmt einen endlichen Prozesstensor; sie bestimmt nicht automatisch eine eindeutige verborgene Umgebung oder sämtliche unendlichen Horizonte.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Mehrzeitdaten statt einer einzigen Dichtematrix","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7082,"byte_start":5967,"id":"section:e3d43c0f7612e8ad6bbe","kind":"section","labels":[],"line_end":72,"line_start":66,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"S05 schlägt eine nützliche endliche Vorgehensweise vor: Man fixiert zulässige Operationswörter bis Länge [formula in source] , ihre Relationen, Symmetrien und die belegten Auslesungen. Die unbekannten Momente müssen eine positive Momentenmatrix bilden. Dann minimiert und maximiert man eine noch offene Ausgabe [formula in source] über alle kompatiblen Modelle.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein konkreter Auswahltest für offene Größen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9427,"byte_start":7082,"id":"section:3bc5a4a90c83877a22f6","kind":"section","labels":[],"line_end":106,"line_start":73,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Die in S03 vorgeschlagene Alternative verwendet als lokalen Viererverknüpfungstensor. An orientierten Verbindungen werden Trägerräume mit ihren dualen Räumen kontrahiert. So verbindet man Amplituden, ohne jede physische Zellreduktion als unverändert reines [formula in source] festzuschreiben.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Zelle als Verknüpfungsamplitude","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10340,"byte_start":9427,"id":"section:b3644a3c4b9d4ac53d1a","kind":"section","labels":[],"line_end":111,"line_start":107,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Paarweise kommutierende volle Matrixunteralgebren, die gemeinsam die Gesamtalgebra erzeugen, bestimmen im endlichen Fall eine Tensorproduktstruktur bis auf lokale Basiswechsel und Umbenennungen. Bei nichttrivialem Zentrum können stattdessen Sektoren übrigbleiben. Die Auswahl der privilegierten Unteralgebren aus den Wechselwirkungen ist der eigentliche inverse Schritt. https://arxiv.org/abs/quant-ph/0308043Zanardi, Li","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Teilsysteme aus Beziehungen erkennen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11809,"byte_start":10340,"id":"section:91cac71ed105fffe601f","kind":"section","labels":[],"line_end":122,"line_start":112,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"S08 untersucht einen neutralen Sektor aus 70 Materiemasken und Schleifenfluss, insgesamt 1190 Zuständen. In einer festgehaltenen lokalen Operatorliste wird über der Generator rekonstruiert. Nach Entfernen trivialer Identitätsrichtungen reproduziert der Grundzustand die Koeffizienten [formula in source] , [formula in source] , [formula in source] und [formula in source] . Ein zusätzlicher angeregter Zustand verbessert","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was das Zustandsgate am Rotor/CAR-Ring prüft","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":547,"byte_start":0,"id":"section:9af53123bd430d104df8","kind":"chapter","labels":["ch:physik"],"line_end":5,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Raumzeit, Materie und Gravitation aus demselben Ursprung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2438,"byte_start":547,"id":"section:7ac32931cc6ab8623346","kind":"section","labels":[],"line_end":33,"line_start":6,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Ein markierter [formula in source] -Block trägt die hermitesche Matrix Ihre Determinante ist exakt Die Eigenwerte sind [formula in source] . Deshalb entspricht [formula in source] dem Zukunftskegel [formula in source] . Die Kongruenz [formula in source] mit [formula in source] erhält die Determinante und den positiven Kegel.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Lorentzkegel: eine echte, aber begrenzte Brücke","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4186,"byte_start":2438,"id":"section:894bcf530dc77b49c1a2","kind":"section","labels":[],"line_end":50,"line_start":34,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"S03 formuliert eine nützliche bedingte Brücke. Angenommen, derselbe Prozess liefert einen lokalen kohärenten Zweikomponentensektor mit inverser Zweipunktfunktion Dann folgt Für invertierbares [formula in source] ist dies eine Lorentzform. Jetzt wäre der Kegel aus einem tatsächlichen Propagator gewonnen. Vorausgesetzt sind jedoch ein sinnvoller Impulsraum, ein kontrollierter lokaler Grenzprozess, ein kohärenter Pol un","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der präzise nächste Schritt: den Kegel aus der Ausbreitung gewinnen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5285,"byte_start":4186,"id":"section:75f90c356903abbf93bf","kind":"section","labels":[],"line_end":61,"line_start":51,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Eine mögliche Materieanregung muss stabil oder kontrolliert propagierend sein. Man benötigt ihr Spektrum, ihre Ladungen, chirale Ausbreitung, erlaubte Vertizes und das Verschwinden unerwünschter Spiegelpartner. Eine vorkommende Darstellung allein erfüllt das nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Materie ist mehr als eine Ladungstabelle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6273,"byte_start":5285,"id":"section:7b46ffc81ee43868d9bd","kind":"section","labels":[],"line_end":70,"line_start":62,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Eine Algebra mit Darstellung und geeignetem Diracoperator kann Geometrie kodieren. Beispielsweise macht die Distanzformel sichtbar, warum nicht nur Eigenwerte, sondern die Relation zwischen [formula in source] und den Observablen zählt. Connes' kommutativer Rekonstruktionssatz benötigt starke Spektralaxiome und liefert eine kompakte glatte Riemannsche Mannigfaltigkeit. Er erzeugt keine lorentzsche 3+1D-Welt aus einer","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spektrale Geometrie hilft, ersetzt aber keine fehlenden Daten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":7482,"byte_start":6273,"id":"section:3cfe4ab368f0755a9a7b","kind":"section","labels":[],"line_end":83,"line_start":71,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Die Identität [formula in source] passt zu einer bekannten Normierung. Sie liefert nicht das Feld [formula in source] , einen masselosen quantisierten Spin-2-Pol, zwei physische Helizitäten oder universelle Kopplung.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was für Gravitation noch wirklich fehlen würde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7573,"byte_start":7482,"id":"section:9e77b44fff2ec29726c8","kind":"chapter","labels":["ch:zahlen"],"line_end":85,"line_start":84,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die Zahlenprogramme: Nähe, Spannungen und offene Übertragung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8482,"byte_start":7573,"id":"section:a324947f24e4dcba449a","kind":"section","labels":[],"line_end":100,"line_start":86,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Die [formula in source] -Zerlegung benutzt Hyperladungen [formula in source] auf den drei Farbplätzen und [formula in source] auf den zwei schwachen Plätzen. In der Konvention ausschließlich linkshändiger Weylfelder ergibt eine Familie: lccr Feld& [formula in source] & [formula in source] &Komponenten\\\\ [formula in source] & [formula in source] & [formula in source] &6\\\\ [formula in source] & [formula in source] & [f","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Standardmodell-Ladungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10057,"byte_start":8482,"id":"section:ba39e61927ccb5a266a1","kind":"section","labels":[],"line_end":122,"line_start":101,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Der eingefrorene Flavor-Seed lautet Er organisiert mehrere Ausgaben gemeinsam. Eine Änderung an ihm verschiebt daher mehrere Zahlen; das macht den Ansatz prüfbarer als unabhängig eingestellte Einzelwerte.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der gemeinsame kleine Seed und die Kopplungsgleichung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12386,"byte_start":10057,"id":"section:597060f5ce663fc8590c","kind":"section","labels":[],"line_end":148,"line_start":123,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Der historische Quellmassenansatz lautet Die sektorabhängigen [formula in source] sind nicht automatisch eins. Die Restklassenmatrix mit Zeilen [formula in source] , [formula in source] , [formula in source] hat Determinante acht und charakteristisches Polynom [formula in source] . Das sind interne Daten, keine direkte Massenmessung.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Flavor und Massenschemata","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":14853,"byte_start":12386,"id":"section:7bab748a420a8967681b","kind":"section","labels":[],"line_end":168,"line_start":149,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"L36mmL49mmL65mm Größe& Formel / Quellwert& Zusätzliche Bedingung\\\\ Birefringenz [formula in source] & [formula in source] &Rotationstransfer, Kalibrierung und Vordergründe.\\\\ Baryonenanteil [formula in source] & [formula in source] &Nicht mit [formula in source] gleichsetzen.\\\\ Skalarer Index [formula in source] & [formula in source] & [formula in source] und Reheatinggeschichte.\\\\ Tensorverhältnis [formula in source","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kosmologie und große Hierarchien","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16539,"byte_start":14853,"id":"section:0cb56bce05f74c1c714b","kind":"section","labels":[],"line_end":184,"line_start":169,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"L41mmL46mmL63mm Zweig& Historischer Quellwert& Offener Anteil\\\\ Starke CP-Phase& [formula in source] im Pfaffian-Zweig&Positives physisches Maß und nichtperturbativer Transfer.\\\\ Elektrische Dipolmomente&Führend null oder stark unterdrückt&Keine pauschale Null sämtlicher SM-Beiträge.\\\\ Axion& [formula in source] GeV; [formula in source] eV&Externe Planckskala und QCD-Massenrelation.\\\\ Neutrinomassen&Summe um [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die übrigen Zweige bleiben Teil des Bildes","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":19000,"byte_start":16539,"id":"section:c7806fa39ebb19848289","kind":"section","labels":[],"line_end":205,"line_start":185,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"S08 untersucht einen zweistufigen Lauf mit quellenseitig ausgewähltem Skalarinhalt, aber in einer eingeschränkten gauge-only-Zweischleifennäherung. Die Nähe von [formula in source] zu [formula in source] GeV bleibt ungefähr bestehen. Zugleich verschärft sich die Protonlebensdauerspannung, falls SO(10) oberhalb der Vereinigungsskala geeicht ist.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Pati-Salam-Vereinigung und die negative Protonzerfallsprobe","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":440,"byte_start":0,"id":"section:5670002b386b0e15cad8","kind":"chapter","labels":[],"line_end":4,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/10_ausblick.tex","status_markers_as_written":[],"summary_excerpt":"Aktueller Forschungsauftrag v1.4 Der folgende Ausblick bleibt als Grundrahmen erhalten. Die sechs inzwischen weiterbearbeiteten Fragen und die neuesten Ergebnisse stehen gesammelt in Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verwandte Ideen und mögliche Folgen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2723,"byte_start":440,"id":"section:423d4d8b3fa434f09d43","kind":"section","labels":[],"line_end":18,"line_start":5,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/10_ausblick.tex","status_markers_as_written":[],"summary_excerpt":"Der eingefügte Gesprächstext vergleicht den Universalraum mit Konrad Zuse und Stephen Wolfram. Zuses Werk heißt Rechnender Raum, nicht „denkender Raum“. In seinem Buch von 1969 untersucht er digitale Beschreibungen physikalischer Felder und Teilchen und die Rolle von Automaten. 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Daraus könnten irgendwann konkrete Material-, Mess- oder Rechenverfahren entstehen. 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Die folgende Gesamtkart","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was noch offen ist und wie es weitergehen sollte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8380,"byte_start":6957,"id":"section:39f56271a8cad4df5396","kind":"section","labels":[],"line_end":55,"line_start":45,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/10_ausblick.tex","status_markers_as_written":[],"summary_excerpt":"L31mmL62mmL57mm Fuge& Erreichter Stand& Verbleibende Herkunft\\\\ Kopplungsstärke&Exakter antisymmetrischer Vermittler; [formula in source] unter benannten Bedingungen; S11 liefert [formula in source] in seiner Normierung.&Energien, Amplituden, konkurrierende Kanäle und ihre gemeinsame Auswahl.\\\\ Kopplungsgraph&Clebsch-Graph exakt unter „Ort = Spinorgewicht“; Tetramer, Kette und Clebsch getrennt.&Ortslesart, Belegung, ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die fünf Fugen nach allen Korrekturen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10320,"byte_start":8380,"id":"section:26965ed2200cee435949","kind":"section","labels":[],"line_end":69,"line_start":56,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/10_ausblick.tex","status_markers_as_written":[],"summary_excerpt":"L9mmL62mmL79mm Tor& Was gemeinsam nachzuweisen ist& Was bisher dazu vorliegt\\\\ T1&Herkunft von P1/P2, Dimensionen, Markierungen und Auswahlregeln.&Exakte Konsequenzen festgelegter Daten; Gegenmodelle gegen Symmetrie-Eindeutigkeit. 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Erfolg ist ein ausführbarer Quellenvertrag; Scheitern ist eine noch frei wählbare Regel, die das Ergebnis verändert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein priorisiertes, entscheidbares Anschlussprogramm","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13860,"byte_start":12713,"id":"section:3358164c58a74f39a8d9","kind":"section","labels":[],"line_end":89,"line_start":83,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/10_ausblick.tex","status_markers_as_written":[],"summary_excerpt":"Der Kandidat, auf den die Dokumente gemeinsam zulaufen Es gibt eine phasentreue Kompositionsregel mit positivem Zustandsfunktional, deren endliche Auslesungen die markierte TFPT-Struktur tragen. Aus ihren gekoppelten Anregungen und Aufzeichnungen entsteht ein kontrollierter gemeinsamer Grenzprozess. Erst dieser Grenzprozess liefert Raumzeit, chirale Materie, Wechselwirkungen und gegebenenfalls Gravitation. 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Übertragung un","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Frühere Nebenstränge, die im Gesamtbild erhalten bleiben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10041,"byte_start":5908,"id":"section:7c7ac23eb17b9497694b","kind":"chapter","labels":[],"line_end":74,"line_start":38,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"L34mmL116mm Begriff& Bedeutung in diesem Dokument\\\\ Adjungierte&Die Darstellung einer Lie-Algebra auf ihren eigenen Generatoren durch die Klammer; nicht automatisch der gesamte Raum physischer Zustände.\\\\ Adjunktion [formula in source] &Komplex konjugierte Transposition beziehungsweise die passende Operatoradjunktion. 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Die vollständigen Originalpfade und SHA-256-Werte stehen im beiliegenden Manifest. Hier werden die Dateinamen und inhaltlichen Rollen aufgeführt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die elf Eingabedokumente","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":12676,"byte_start":10437,"id":"section:cfef1dcb810019c85353","kind":"section","labels":[],"line_end":96,"line_start":80,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Der eigenständige Prüfer importiert keinen Code des ursprünglichen TFPT-Repositoriums. Die Standard-Zwei-Qubit-Kontexte wurden aus den üblichen Pauli-Matrizen rekonstruiert. Das kontrolliert die endlichen im Text angegebenen Beziehungen, ist aber kein erneuter phasentreuer Import des nativen Gauß- [formula in source] -Adapters.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was neu geprüft wurde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13823,"byte_start":12676,"id":"section:efa5cc955cc30f1e2afd","kind":"section","labels":[],"line_end":108,"line_start":97,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"L16mmL41mmY Quelle& Berichtete Prüfung& Reichweite\\\\ S09&11214 Bedingungen pro Modus, elf Negativvarianten&Ursprungsaudits und Zahlenprüfungen; kein vollständiger Lean-/RH-Neubau.\\\\ S07&325 + 147 Bedingungen, 19 Tests&Inversion und Follow-ups; mehrere spätere Minimalitätskorrekturen erforderlich.\\\\ S06&86 eigene Bedingungen sowie ausgewählte Originalreplays&45-/30-Quotienten, Uhr und Herkunftskontrollen; begrenzte Ke","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie die Quellen ihre eigenen Prüfungen beschreiben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":14798,"byte_start":13823,"id":"section:b33a3197fe09295e8bed","kind":"section","labels":[],"line_end":113,"line_start":109,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Das Paket enthält die vollständige LaTeX-Quelle, Kapiteldateien, Vektordiagramme, den eigenständigen Prüfer, die Ergebnisdatei und das Eingabemanifest. Mit einer LaTeX-Installation einschließlich LuaLaTeX, TikZ und den verwendeten Standardpaketen lässt sich das Buch durch zwei Läufe von lualatex main.tex im Quellverzeichnis bauen. Für die endlichen Gegenrechnungen werden Python, NumPy, SymPy, mpmath und Matplotlib be","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproduktionspaket dieser Synthese","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18166,"byte_start":14798,"id":"section:16b3aab6b3479d8f02b9","kind":"section","labels":[],"line_end":135,"line_start":114,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Die folgenden Quellen wurden zur fachlichen Einordnung beziehungsweise für den datierten Konstantenvergleich aufgerufen. 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Pollock et al.: Non-Markovian quantum processes: complete framework and efficient chara","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Externe Primärliteratur und Referenzdaten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18523,"byte_start":18166,"id":"section:9b1b26ebbeb4989be900","kind":"section","labels":[],"line_end":137,"line_start":136,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Die Anhänge wurden unverändert gelesen; ihre tatsächlichen Dateiinhalte sind durch SHA-256 dokumentiert. Dieses Buch aktualisiert keinen ursprünglichen Theorievertrag und keinen Abschlussmarker. Es liefert eine neue, zusammenhängende und prüfbare Darstellung mit ausdrücklich abgegrenzten eigenen Fortsetzungen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Abschluss der Dokumentation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":968,"byte_start":0,"id":"section:9068796d291aed34ec4b","kind":"chapter","labels":["ch:shadow-arithmetic"],"line_end":8,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Was uns ein Schatten verraten kann Wenn wir nur den Schatten eines Rades sehen, erkennen wir vielleicht einen Kreis. Erst wenn wir das Rad drehen, belasten und mit einem zweiten Rad verbinden, erkennen wir seine Achse, seine Zähne und seine Übersetzung. Genau so lesen wir hier Primzahlen, Quanteneffekte und Raumzeit: als verschiedene Antworten, die eine mögliche gemeinsame Struktur gleichzeitig erklären müsste.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Primzahlen, RH und die Musik hinter den Schatten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":2819,"byte_start":968,"id":"section:c52b89225d1e130ada95","kind":"section","labels":["eq:primon-partition"],"line_end":25,"line_start":9,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Jede natürliche Zahl [formula in source] zerfällt eindeutig in Primfaktoren: Die erste Gleichung beschreibt ein Zusammensetzen durch Multiplikation; die zweite übersetzt dieses Zusammensetzen in Addition. Zum Beispiel ist [formula in source] , also [formula in source] . Die Primzahlen sind die unabhängigen Bausteine dieses multiplikativen Systems. Das ist ein Satz über natürliche Zahlen. Es ist noch kein Satz darüber","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"In welchem Sinn Primzahlen Bausteine sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":4018,"byte_start":2819,"id":"section:ce05eacf34a3e2d381fe","kind":"subsection","labels":[],"line_end":36,"line_start":26,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Warum gerade [formula in source] ? Aus [formula in source] allein folgt das noch nicht: Man darf jeder Primzahl zunächst einen beliebigen Wert [formula in source] geben. Eine zusätzliche Ordnungsregel schließt die Lücke. Ist [formula in source] monoton in der natürlichen Zahl [formula in source] , so gilt notwendig Der Beweis ist kurz. Setze [formula in source] . Aus [formula in source] folgen [formula in source] Div","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine bedingte Auswahlregel für die logarithmische Energie","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":7179,"byte_start":4018,"id":"section:5c8c08fd0632b2bfbfd8","kind":"section","labels":["eq:prime-trace"],"line_end":64,"line_start":37,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die häufig verkürzte Aussage Primzahlen tauchen als Quantenenergien auf umfasst verschiedene Sachverhalte. Beim klassischen Zeta–Quantenchaos-Vergleich entsprechen Nullstellenhöhen den Energien eines gesuchten Spektrums. Die Primzahlen spielen auf der anderen Seite die Rolle primitiver periodischer Bahnen; Primzahlpotenzen sind deren Wiederholungen. Eine Bahn wird einmal durchlaufen, zweimal, dreimal. Ihr logarithmis","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was Primzahlen mit Quantenchaos verbindet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":10149,"byte_start":7179,"id":"section:d0bf2b0b7bab9ba4313b","kind":"section","labels":[],"line_end":81,"line_start":65,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die Unterlagen und der zusätzlich eingesehene Forschungsbestand ergeben keine abgeschlossene RH-Lösung. Sie ergeben jedoch eine ungewöhnlich präzise Landkarte aus positiven Bausteinen und bereits ausgeschlossenen Abkürzungen. Die folgende Verdichtung ordnet die inhaltlichen Familien; sie behauptet keine erneute Prüfung jedes Katalogeintrags.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was unser RH-Zweig tatsächlich beigetragen hat","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11189,"byte_start":10149,"id":"section:a425abe30d729823057f","kind":"subsection","labels":[],"line_end":96,"line_start":82,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die ersten sechs Werte sind [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] und [formula in source] . Daraus folgt für [formula in source] Hier ist der Primzahlbezug wirklich vorhanden. Die Selbstdualität des Gitters schließt die Poisson-Transformation auf dasselbe Gitter. Poisson-Summation gilt auch für nichtselbstduale Gitter und verbindet dann Gitter und ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der genaue Ertrag der [formula in source] -Schalen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":12659,"byte_start":11189,"id":"section:01621b4011963608f898","kind":"subsection","labels":[],"line_end":108,"line_start":97,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die entscheidende arithmetische Form enthält eine Differenz: vereinfacht [formula in source] . Zwei positive Matrizen können eine indefinite Differenz besitzen; schon [formula in source] hat die Eigenwerte [formula in source] und [formula in source] . Entsprechend löst ein beliebiger positiver Born- oder Gramkern die signierte Aufgabe noch nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die fehlende Positivität so hartnäckig ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14262,"byte_start":12659,"id":"section:beecd8fbf1df986ac09d","kind":"subsection","labels":[],"line_end":115,"line_start":109,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Der Jensen/Coxeter-Test r618 findet eine starre [formula in source] -Struktur auf der [formula in source] -Seite, während die verglichenen Jensen-Polynome mit ihrem Index variieren. Die gewählte Identifikation scheitert. Der Selberg-Kontakttest r638 besitzt im untersuchten Fall weiterhin einen negativen kleinsten Eigenwert von ungefähr [formula in source] ; eine Quadratvervollständigung hat die falsche signierte Form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was die negativen Routen konkret lehren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15958,"byte_start":14262,"id":"section:ea13eaba133161cb3975","kind":"section","labels":[],"line_end":126,"line_start":116,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die vorhandene freie fermionische Naht hat bei fester Größe eine endliche Zustandssumme. Das Primonmodell verlangt eine unbegrenzte Primfamilie und andere Besetzungsdaten. Schon für [formula in source] gilt [formula in source] und [formula in source] : Der Pol bei [formula in source] entsteht erst in der unendlichen Familie. Eine endliche Demonstration kann ihn nicht besitzen. Der vorhandene Nahtvergleich findet ents","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Naht braucht mehr als ein paar zusätzliche Takte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16501,"byte_start":15958,"id":"section:e15ed6c5984971c699e4","kind":"section","labels":[],"line_end":129,"line_start":127,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Wei und Mitautoren verbinden in zwei gezielt konstruierten Quantensystemen Nullstellen mit dynamischen Phasenübergängen. Berichtet werden ein Fünf-Qubit-NMR-Prinzipversuch und weitergehende numerische Untersuchungen. Die verwendeten Hamiltonoperatoren und Zustandsgewichte sind so gewählt, dass sie Zeta-Daten kodieren. Das macht den Zusammenhang experimentell bearbeitbar; eine Ableitung dieser Wahl aus TFPT oder ein R","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die neue Quantenphasen-Arbeit von 2026","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":18843,"byte_start":16501,"id":"section:526967fb0c628e297e03","kind":"subsection","labels":["eq:eta-readout"],"line_end":150,"line_start":130,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Unabhängig vom vollständigen Ressourcenbeweis dieser Arbeit untersuchen wir den folgenden einfachen thermischen Eta-Auslesekanal: Er entsteht durch einen Gibbszustand für [formula in source] und eine diagonal ausgelesene Paritätsphase. Bei festem [formula in source] und [formula in source] konvergiert der Zähler gegen [formula in source] , während [formula in source] Also geht das Rohsignal [formula in source] an jed","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eigene Anschlussrechnung: Ein verschwindendes Signal ist mehrdeutig","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":541,"byte_start":0,"id":"section:94335c1a5434109fe7de","kind":"chapter","labels":["ch:shadow-quantum"],"line_end":6,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Nicht nur die Anzahl der Kugeln zählt Zwei Kästen können dieselben möglichen Messergebnisse enthalten und doch verschieden reagieren, wenn wir zuerst an einer anderen Stelle messen oder zwei Teile zusammenführen. Die Quantenphänomene sagen uns deshalb vor allem etwas über die Regeln des Zusammensetzens, über relative Phasen und über erlaubte Eingriffe. Genau diese Daten verliert ein einfacher Schatten leicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was Quantenphänomene über den verborgenen Aufbau sagen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1925,"byte_start":541,"id":"section:0314fa22df1a552af5f4","kind":"section","labels":[],"line_end":21,"line_start":7,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Für zwei Alternativen mit Amplituden [formula in source] und [formula in source] lautet die Born-Regel [formula in source] Der letzte Term kann verstärken oder auslöschen. Wer ausschließlich die beiden Einzelwahrscheinlichkeiten aufbewahrt, kann ihn nicht rekonstruieren. Das erklärt im Kleinen, warum die behaltenen Register und Echoexperimente der früheren Kapitel mehr verraten als der erste sichtbare Markovschritt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Interferenz verlangt eine Information vor den Wahrscheinlichkeiten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4273,"byte_start":1925,"id":"section:23d0159cc73bea3eba2a","kind":"section","labels":[],"line_end":40,"line_start":22,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Die 15 Zwei-Qubit-Pauli-Kontexte der Synthese enthalten das folgende Mermin–Peres-Quadrat. Hier bedeutet [formula in source] und entsprechend für die anderen Einträge: Jede Zeile und jede Spalte ist gemeinsam messbar. Alle Zeilenprodukte sind positiv, aber das letzte Spaltenprodukt ist negativ. Diese sechs Kontexte gehören zum bereits verwendeten Pauli-System.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der vorhandene Baukasten enthält bereits Kontextualität","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5718,"byte_start":4273,"id":"section:4c57abfd6b0e69b496a1","kind":"section","labels":[],"line_end":52,"line_start":41,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Für zwei räumlich getrennte Messstellen hat die CHSH-Kombination [formula in source] in einem lokalen Modell mit unabhängiger Wahl der Einstellungen die Grenze [formula in source] . Quantenmechanik erreicht [formula in source] . Mit [formula in source] , [formula in source] und [formula in source] ist der zugehörige Operator [formula in source] ; seine Eigenwerte sind [formula in source] . Beides wurde hier exakt nac","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verschränkung legt die Zusammensetzung fest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6899,"byte_start":5718,"id":"section:59420a81ae342d5d748d","kind":"section","labels":[],"line_end":68,"line_start":53,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Wähle bei festgehaltenen Labor-Teilsystemen [formula in source] Beide Hamiltonoperatoren haben exakt die Energien [formula in source] . Der Grundzustand von [formula in source] ist ein Produktzustand, der von [formula in source] ein Bell-Zustand. Die Reinheit [formula in source] eines lokalen Teils beträgt entsprechend 1 beziehungsweise [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gleiche Energien können verschiedene Welten beschreiben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8198,"byte_start":6899,"id":"section:2f70cda5339efb07d663","kind":"section","labels":[],"line_end":75,"line_start":69,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Die komplexe Vierdimensionalität ist für den bestehenden Pauli-/Spinorbaukasten passend. Eine direkte Ableitung der komplexen Zahlen aus einem einzelnen Quantenphänomen wäre trotzdem zu stark. Renou und Mitautoren untersuchen Quantennetzwerke, in denen die übliche reale und komplexe Theorie unter einer bestimmten Unabhängigkeits- und Kompositionsannahme verschiedene Vorhersagen machen. F10","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was komplexe Zahlen verraten und was offenbleibt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9556,"byte_start":8198,"id":"section:a797c057d92647ff05f4","kind":"section","labels":[],"line_end":81,"line_start":76,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Die bisherigen Registerbeispiele erklären, wie ein global kohärenter Ablauf nach eingeschränktem Zugriff wie ein irreversibler Prozess aussehen kann. Sie liefern noch keine eindeutige Lösung des Messproblems: Insbesondere folgt aus einer diagonalen reduzierten Dichtematrix allein keine Auswahl eines einzelnen Ereignisses. Eine zusätzliche Kollapsdynamik müsste messbare Abweichungen angeben; eine unitäre Beschreibung ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Messung, Zeitpfeil und Statistik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":900,"byte_start":0,"id":"section:f2fcec31b9d83fba6e18","kind":"chapter","labels":["ch:shadow-dimension"],"line_end":8,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"Dimension ist die Antwort auf eine Frage Eine Ameise auf einer dünnen Schnur kann entlang einer Richtung laufen. Auf einem Blatt kann sie außerdem ausweichen. In einem Zimmer kann sie auch über ein Hindernis hinweg. Eine Dimension zählt solche unabhängigen Möglichkeiten. Die Zahl der inneren Zustandskomponenten oder der Knöpfe eines Geräts ist etwas anderes.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Drei Raumrichtungen und eine Zeit: Welche Bedingungen bleiben?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2245,"byte_start":900,"id":"section:ef4d1354633cade02cc4","kind":"section","labels":[],"line_end":23,"line_start":9,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"Ein traceloses hermitesches [formula in source] -Objekt hat genau drei reelle Komponenten: [formula in source] Ergänzt man [formula in source] , ergibt die Determinante [formula in source] Der positive Kegel erfüllt [formula in source] . Das ist die präzise Lorentz-Brücke aus dem Ursprungsteil. Sie zeigt eine passende lokale algebraische Form. Noch fehlen ihre Interpretation als Ereignisse, die Verklebung zu einer Ra","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Drei unterschiedliche Hinweise führen zur Zahl drei","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4446,"byte_start":2245,"id":"section:1b966b6b2bfa4af0d57f","kind":"section","labels":[],"line_end":47,"line_start":24,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"Für einen Graph-Laplaceoperator [formula in source] definieren wir die mittlere Rückkehrfunktion und eine skalenabhängige Dimension durch Auf einem großen regelmäßigen dreidimensionalen Gitter entsteht zwischen der Gitter- und der endlichen Systemskala ein Bereich mit [formula in source] , also [formula in source] . Bei einem endlichen zusammenhängenden Graphen geht [formula in source] sowohl für sehr kleine als auch","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine neue Gegenprobe am Clebsch-Vorschlag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5395,"byte_start":4446,"id":"section:9384b793e9cfedd67e24","kind":"section","labels":[],"line_end":52,"line_start":48,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"In einer gewöhnlichen hyperbolischen Wellengleichung werden lokale Anfangsdaten auf einer räumlichen Fläche vorgegeben und entlang einer ausgezeichneten Zeitrichtung entwickelt. Mehrere Zeitkoordinaten verändern das Anfangswertproblem grundlegend. Unter zusätzlichen nichtlokalen Beschränkungen existieren dennoch wohldefinierte Mehrzeit-Probleme; ein pauschaler Unmöglichkeitssatz wäre falsch. F14","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine Zeitrichtung ist mehr als ein weiterer Zahlenplatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6488,"byte_start":5395,"id":"section:4107228d4ba30aa6089c","kind":"section","labels":[],"line_end":64,"line_start":53,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"Ein elementares mechanisches Beispiel illustriert die Rolle von Constraints. Nimmt man in [formula in source] Raumdimensionen eine Newtonsche Punktkraft mit Gaußgesetz an, lautet das effektive Radialpotential [formula in source] An einer Kreisbahn ergibt sich [formula in source] Unter diesen Voraussetzungen sind solche Kreisbahnen bei [formula in source] stabil, bei [formula in source] instabil und bei [formula in so","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was Stabilität zusätzlich einschränkt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":397,"byte_start":0,"id":"section:f7fb7cdbc3f9c6f05cbf","kind":"chapter","labels":["ch:shadow-open"],"line_end":4,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Offene Physik ist kein freier Platz, in den jede neue Idee hineinpasst. Sie ist oft durch viele bekannte Eigenschaften eng begrenzt. Der nützliche Schritt lautet deshalb: Welcher Teil des Phänomens ist beobachtet, welcher Mechanismus fehlt, und welche Antwort müsste unser Modell zusätzlich liefern?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Schwer verstandene Phänomene als zusätzliche Prüfsteine","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1423,"byte_start":397,"id":"section:c0580f322fcbb680ec8c","kind":"section","labels":[],"line_end":9,"line_start":5,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Gravitationslinsen und die Verteilung sichtbarer Materie in kollidierenden Haufen liefern eine wichtige Beobachtung: Der aus der Gravitation erschlossene Beitrag muss nicht dem heißen sichtbaren Gas folgen. Die Bullet-Cluster-Analyse ist ein prominentes Beispiel. Sie identifiziert damit noch kein bestimmtes mikroskopisches Teilchen. Zusammen mit anderen kosmologischen Daten ist sie eine starke Anforderung an jede Erk","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dunkle Materie: unsichtbar heißt nicht frei wählbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2590,"byte_start":1423,"id":"section:e9a41138cf02caae2c19","kind":"section","labels":[],"line_end":16,"line_start":10,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Die beschleunigte kosmische Expansion verlangt eine konsistente Erklärung im Gesamtmodell. Für TFPT ist besonders schwierig, eine passende effektive Vakuumwirkung zu erhalten, ohne sie bei jedem neuen Beitrag nachzujustieren. Der Mechanismus müsste seine Größe und Stabilität gegenüber Korrekturen erklären.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dunkle Energie: ein kleiner Rest mit großen Folgen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3656,"byte_start":2590,"id":"section:99b2bac778b1300133a5","kind":"section","labels":[],"line_end":21,"line_start":17,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Die Schwarzlochfrage verbindet Quanteninformation, Gravitation und die Wahl zugänglicher Teilsysteme besonders eng. In bestimmten berechenbaren Modellen verändern Quanteneffekte die extremale Fläche und damit die Zuordnung rekonstruierbarer Information. Die verallgemeinerte Entropie enthält einen Flächenbeitrag und einen Quantenfeldbeitrag. Das ist erheblicher theoretischer Fortschritt in diesen Modellen, aber noch k","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Schwarze Löcher: Information kann die Aufteilung selbst betreffen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4418,"byte_start":3656,"id":"section:0c77ee197316df430aff","kind":"section","labels":[],"line_end":26,"line_start":22,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Äquivalenztests wie MICROSCOPE prüfen die Universalität des freien Falls für unterschiedliche Materialien mit hoher Genauigkeit. Eine neue Quelle für Raumzeit muss daher erklären, warum verschiedene innere Zusammensetzungen auf dieselbe effektive Geometrie reagieren. F18","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gravitation muss sehr verschiedene Inhalte gleich behandeln","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6966,"byte_start":4418,"id":"section:26cd596dca0819265277","kind":"section","labels":[],"line_end":43,"line_start":27,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"L32mmL56mmL60mm Thema& Was den Ansatz einschränkt& Was eine Erklärung liefern müsste\\\\ Zeitpfeil&Beständige Aufzeichnungen und irreversible Makroprozesse bei oft reversiblen Grundgleichungen.&Zustandsauswahl, Anfangskorrelationen, Zugriff und Entropiefluss; keine bloße Benennung eines inneren Parameters als Zeit.\\\\ Messproblem&Interferenz und stabile Messergebnisse müssen zusammen beschrieben werden.&Ein vollständige","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Weitere offene Stellen mit unterschiedlicher Beweiskraft","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":947,"byte_start":0,"id":"section:6a5cc08d36f313834645","kind":"chapter","labels":["ch:shadow-synthesis"],"line_end":7,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Die zusammengetragenen Schatten sprechen am stärksten für eine Struktur von Zusammensetzungen und gemeinsamen Antworten. Arithmetik verlangt eindeutig kombinierbare primitive Faktoren. Quantenphänomene verlangen Phasen, Kontexte und eine besondere Zusammensetzung von Teilsystemen. Raumzeit verlangt eine skalenstabile Ordnung von Nachbarschaften, Signalwegen und Anfangsdaten. Keine dieser Forderungen wird durch die Za","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein engeres Bild und ein neues berechenbares Puzzleteil","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2397,"byte_start":947,"id":"section:4ebc26a9a2141adff5d4","kind":"section","labels":[],"line_end":20,"line_start":8,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Die bildhafte Aussage Alles ist aus Primzahlen gebaut lässt sich zu einer brauchbareren Hypothese präzisieren: Ein möglicher gemeinsamer Ursprung besitzt elementare, zusammensetzbare Operationen. In einem kommutativen arithmetischen Schatten erscheinen primitive Faktoren. Vor dieser Auslesung bleiben zusätzliche Phasen, Kontexte und Aufzeichnungen erhalten. Räumliche Nachbarschaft und Zeitordnung müssten aus den erla","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine engere Arbeitshypothese","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":4907,"byte_start":2397,"id":"section:3e5b0600410ea0abe735","kind":"section","labels":["eq:arithmetic-projective"],"line_end":61,"line_start":21,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Die folgenden Formeln sind eine neue Anschlusskonstruktion für dieses Buch. Ihre Zutaten sind Standardoperatoren; sie beanspruchen keine neue allgemeine mathematische Entdeckung. Sie zeigen jedoch exakt, dass ein gemeinsamer arithmetischer Endpunkt unterschiedliche kohärente Geschichten besitzen kann.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein konstruktiver Versuch: gleiche Zahl, verschiedene Phasen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5784,"byte_start":4907,"id":"section:f7edfeb5b3289dab53e0","kind":"subsection","labels":[],"line_end":69,"line_start":62,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Ein Kontrollqubit speichert kohärent, welcher der beiden Wege durchlaufen wurde. Setze [formula in source] und [formula in source] . Nach einer Hadamard-Auslesung des Kontrollqubits gelten [formula in source] Ohne die lokalen [formula in source] -Markierungen wäre [formula in source] und damit [formula in source] . Die neue Rechnung kontrolliert dies im Zahlfenster [formula in source] exakt. Die benutzten Wege ab [fo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine vollständig bestimmte Vorhersage im Modell","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7119,"byte_start":5784,"id":"section:45292ebdd9cde0b2cfa2","kind":"subsection","labels":[],"line_end":76,"line_start":70,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Gelöst ist eine kleine Kompatibilitätsfrage: Unbegrenzte arithmetische Zusammensetzung und ein endlicher lokaler Quantenbaukasten lassen sich in einem expliziten gemeinsamen Modell verbinden. Der rein arithmetische Schatten kann kommutativ sein, während kohärent zugängliche Wegrelationen eine nichttriviale Phase behalten. Das passt genau zum Motiv der vorherigen Echoexperimente.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was damit gelöst ist und was nicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9085,"byte_start":7119,"id":"section:437ec515ec9757f3bdec","kind":"section","labels":[],"line_end":97,"line_start":77,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Man könnte einen arithmetischen Raum, ein Quantensystem und ein geometrisches Modell einfach nebeneinanderstellen: [formula in source] Bei Produktzustand und unabhängig wirkenden Operationen passen dann vielleicht alle Einzelstatistiken. Der gemeinsame Ursprung wäre dadurch nicht erklärt. Nötig sind gemeinsame Relationen und überprüfbare Antworten auf gemischte Eingriffe. Die oben konstruierte Wegphase ist ein kleine","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum getrennte passende Modelle noch keine gemeinsame Quelle sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11082,"byte_start":9085,"id":"section:f08339ebb6e787938d4c","kind":"section","labels":[],"line_end":111,"line_start":98,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"L37mmL60mmL51mm Gewonnene Präzisierung& Konkretes Ergebnis& Nächste fehlende Bedingung\\\\ Logarithmische Skala&Multiplikative Additivität plus Monotonie erzwingen [formula in source] .&Native Begründung der Ordnung und Energieskala.\\\\ Unbegrenzte Primfamilie&Endlich viele additive Grundtakte tragen nicht alle [formula in source] .&Eine passende wachsende Familie oder reichere Dynamik.\\\\ Arithmetik und Phase&Zwei Multi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Welche Puzzleteile jetzt enger gefasst sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":82,"byte_start":0,"id":"section:fea20f4367f1a7b6f48c","kind":"chapter","labels":["app:shadow-sources"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Erweiterung: Quellen und genaue Prüfgrenzen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4118,"byte_start":82,"id":"section:fdb85c35eaeeff800a9c","kind":"section","labels":[],"line_end":29,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":["relation:98e5007ca087b68c0323"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"Die Erweiterung wurde am 14. September 2026 gegen verfügbare Originalabschnitte im lokalen Repository tfpt-theoryv4 abgeglichen. Der gelesene Git-Stand war 66b91e40e245569f06ab440ead80f446c9be0ee5. Dies identifiziert den Checkout; es behauptet keinen frischen vollständigen Beweis- oder Testlauf. Die tatsächlich verwendeten Dateiinhalte sind zusätzlich mit SHA-256 im Paket erfasst, auch soweit der Arbeitsbaum von Git ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zusätzlicher Einblick in den RH-Forschungsbestand","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6033,"byte_start":4118,"id":"section:b22a112d37255f0e61e8","kind":"section","labels":[],"line_end":38,"line_start":30,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"Der separate Prüfer verify_shadows.py importiert keinen ursprünglichen TFPT- oder RH-Code und keine Nullstellentabellen. Er enthält 126 exakte beziehungsweise symbolische Bedingungen und zwei numerische Kontrollen. Die Nummer der ersten Nullstelle im Eta-Diagramm ist ein ausdrücklich eingesetzter Referenzwert; das Diagramm ist kein eigener Nullstellensuchlauf.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die 128 zusätzlichen Bedingungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10751,"byte_start":6033,"id":"section:168b0c93d23b5df799ce","kind":"section","labels":[],"line_end":62,"line_start":39,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":["relation:d7c55757159e7fdecdb5","relation:fc10904c61399bda370c"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"Die folgenden Quellen wurden zur Erweiterung aufgerufen. Es handelt sich um gezielte Literaturauswahl, nicht um einen vollständigen systematischen Review aller Veröffentlichungen bis September 2026. Eigene Formeln, Gegenbeispiele und Illustrationen sind im Haupttext als solche bezeichnet. Neue Preprints bleiben als Preprints kenntlich. M. V. Berry, J. P. Keating: The Riemann Zeros and Eigenvalue Asymptotics. SIAM Rev","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zusätzliche Primärliteratur","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":11375,"byte_start":10751,"id":"section:13b158e81eca40684275","kind":"section","labels":[],"line_end":64,"line_start":63,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"Das aktualisierte Quellpaket enthält beide unabhängigen Prüfer, beide Ergebnisdateien, die zusätzlichen drei Vektorplots, die LaTeX-Diagramme, das RH-Quellenmanifest und die ausgewählten Katalogeinträge. Die fünf neuen Hauptkapitel sind in dieselbe LaTeX-Datei eingebunden; ursprüngliche Textteile wurden nur um Versionshinweise und Querverweise ergänzt. Das fertige PDF wird weiterhin mit LuaLaTeX gebaut. Die beiliegen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproduktion der erweiterten Fassung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":76,"byte_start":0,"id":"section:83e3f059b0c3653dd00d","kind":"chapter","labels":["ch:audit13"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die sechs neuen Quellen: geprüfte Korrekturen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":593,"byte_start":76,"id":"section:1435bf84f663ed464132","kind":"section","labels":[],"line_end":5,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Die sechs zusätzlichen Unterlagen heißen im neuen Quellenregister N1 bis N6; die ursprünglichen S01 bis S11 bleiben unverändert. Ihr Audit trennt exakte endliche Identitäten, numerische Spektren und zusätzliche Modellannahmen. 100 eigene Bedingungen bestanden: 78 exakte beziehungsweise Integritätsprüfungen und 22 numerische. Die anschließende gemeinsame Ausführung hat einen eigenen 231-Bedingungen-Vertrag. Diese Zähl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was gegenüber v1.1 neu ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":2635,"byte_start":593,"id":"section:2919c49f21edcc05b13f","kind":"section","labels":[],"line_end":28,"line_start":6,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Setze [formula in source] und [formula in source] . Der Wedge-Kanal besitzt Für [formula in source] verschwindet [formula in source] . Beide geordneten Wege enden im gleichen virtuellen Zustand und interferieren. Orthogonale Records für [formula in source] und [formula in source] ersetzen dies durch [formula in source] : Der antisymmetrische Rang-6-Kanal wird zum Rang-12-Kanal. Bei gleichem Energienenner entsteht ein","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die zentrale Reparatur: Wege nicht zu früh unterscheiden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":3264,"byte_start":2635,"id":"section:823a5e1c2814ba84786f","kind":"section","labels":[],"line_end":35,"line_start":29,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Mit [formula in source] und [formula in source] ist auf [formula in source] unitär und kollektiv [formula in source] -kovariant. Alle [formula in source] liefern für Materieeingänge denselben ersten blockdephasierten Schatten. Dennoch wirkt [formula in source] dort als [formula in source] , während [formula in source] als [formula in source] wirkt: [formula in source] kehrt als [formula in source] oder als [formula i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der erste Schatten wählt die Fortsetzung noch nicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":5090,"byte_start":3264,"id":"section:a908960efcbc419e22a7","kind":"section","labels":[],"line_end":59,"line_start":36,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für genau zwei vollständige [formula in source] -Zellen und eine positive Brücke gelten die Formeln aus Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der allkopplige Zweizellenbeweis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6474,"byte_start":5090,"id":"section:81d5a658495cbfd747d3","kind":"section","labels":[],"line_end":77,"line_start":60,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Im ausgewiesenen harmonischen Modell eines geteilten Vermittlers lautet der symmetrische aktive Block Sein niedriger Zweig beginnt mit [formula in source] ; der antisymmetrische mit [formula in source] . Deshalb ist auf dem aktiven [formula in source] -Raum Nach Abzug beider Einzelbondkorrekturen [formula in source] bleibt Beide Schreibweisen sind kompatibel. Eine Konstante auf dem aktiven Sektor ist außerhalb davon ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vierte Ordnung und unterschiedliche Subtraktionskonventionen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":7332,"byte_start":6474,"id":"section:8f26101903dc75ad88d9","kind":"section","labels":[],"line_end":90,"line_start":78,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] gilt Mit [formula in source] und [formula in source] folgen Ein kohärentes Achtzweigregister liefert aus dem früheren Zweisingulett-Eingang [formula in source] Erfolg [formula in source] . Alle acht Ausgänge haben Gewichte [formula in source] . Dies ist eine exakte Alternative zur alten 32-Zweigschaltung. Kontrollierte kontinuierliche Sternpulse und Register bleiben zusätzliche Ressourcen. Erz","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein exakter Stern-Spektralfilter unter zusätzlichen Ressourcen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":8009,"byte_start":7332,"id":"section:f03b8106425a501c4c80","kind":"section","labels":[],"line_end":98,"line_start":91,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"In der Inzidenzfamilie [formula in source] sind die beiden relevanten Entropien Strikte Konkavität liefert verschiedene Maxima: [formula in source] für Kontexte und [formula in source] für Strahlen. Letzterer Prozess hat Rang 60. Erweitert man den Nachfolgerträger, entstehen symmetrieverträgliche Ränge 15 und 16. Weder maximale Entropie noch minimale Rangzahl wählt die Regel ohne erklärte Klasse. Die passive separate","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Einfachheit braucht einen Auslesevertrag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10096,"byte_start":8009,"id":"section:6847a2aaf614a7b0ebff","kind":"section","labels":[],"line_end":113,"line_start":99,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Zwei Singulettläufe finden mindestens vier orthogonale Moden bei [formula in source] über [formula in source] , Residuen unter [formula in source] . Das Dublett ist widerlegt; ein exakter oberer Multiplizitätsbeweis fehlt. -Typen.] 960 gleichgradige Wurzelsummen gehen nach [formula in source] ; gemischt ergeben sich 640 und 192 Summen nach Grad null sowie 64 Cartanfälle. Der vorgeschlagene gemischte Kanal nach [formu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Weitere architektonisch wichtige Korrekturen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":100,"byte_start":0,"id":"section:098ac7db5f28c66d0b67","kind":"chapter","labels":["ch:execution13"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Eine gemeinsame Ausführung für Record, Präparation und Mehrzeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":798,"byte_start":100,"id":"section:b76141fdc2ca34e6a47d","kind":"section","labels":[],"line_end":7,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Dieselbe korrigierte Vermittlungsoperation erzeugt jetzt Aufzeichnung, kontrollierte Näherungspräparation und Mehrzeitantwort. Die tatsächlichen Quellprojektoren, Paulioperationen und die Dreierclock wurden benutzt. Ein bereits präpariertes [formula in source] oder ein separater Präparations-Hamiltonoperator wird nicht benötigt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine Konstruktion, aber ein ausdrücklich zusätzlicher Ressourcenvertrag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1605,"byte_start":798,"id":"section:6f603f3bf4e8f035aefc","kind":"section","labels":[],"line_end":27,"line_start":8,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Mit [formula in source] , [formula in source] und [formula in source] gilt Kopiere nur die Vermittlerbelegung, nicht das geordnete Farbwort: Dann ist auf allen 44 Dimensionen Der Vermittler kehrt zurück. Auf Materie und Pointer bleibt [formula in source] , [formula in source] , mit Beide Krausoperatoren gehören zum Instrument; ihre Effekte summieren sich zu [formula in source] . Ein ungemessener Pointer bleibt kohäre","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die vollständige Recordoperation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2895,"byte_start":1605,"id":"section:a4974a1abb95b7cbb9c8","kind":"section","labels":[],"line_end":43,"line_start":28,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für vier Materieträger und höchstens einen aktiven Vermittler sei Alle sechs [formula in source] wurden auf dem vollen Materieraum rekonstruiert: [formula in source] , [formula in source] , [formula in source] . Andere Vermittlersektoren bleiben bei einer adressierten Operation unverändert. Die Kanten haben orthogonale Ausgänge; verschränkte Zuschauer sind eingeschlossen. Dies ist ein vollständiges sequenzielles Prot","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein gemeinsamer Träger und ein fester Schritt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3576,"byte_start":2895,"id":"section:d77e9ee65153df81774b","kind":"section","labels":[],"line_end":55,"line_start":44,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Rechenbasis- und uniformer Projektor gehören zu den 60 tatsächlichen Quellprojektoren. Die Swap-Identität verwendet dieselben 16 Quell-Paulis: Für Messausgang [formula in source] und Ziel [formula in source] liefert die Bitverschiebung Damit ist [formula in source] . Vier lokale Resets erzeugen [formula in source] sogar aus verschränktem Eingang. Messung und Feedback bleiben Ressourcen, keine hergeleitete kosmologisc","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Quellseitiger Reset ohne vorpräpariertes Zielreservoir","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5624,"byte_start":3576,"id":"section:3b8994dbabd08c5bf175","kind":"section","labels":[],"line_end":84,"line_start":56,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Akzeptiere in jeder Sternrunde die Recordfolge 111: Alle acht ersten Recordfolgen haben Wahrscheinlichkeit [formula in source] . [formula in source] wird erst zur Zielprüfung definiert. Im 24-dimensionalen Raum der verschiedenen Farbanordnungen gilt exakt Dieser Raum trägt die treue reguläre Darstellung von [formula in source] . Die polynomialen Identitäten der Gruppenalgebra gelten daher auch auf allen 256 Materiedi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wiederholung präpariert den Viererzustand kontrolliert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7259,"byte_start":5624,"id":"section:bb3650b1e2ab66eebb29","kind":"section","labels":[],"line_end":106,"line_start":85,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Nach erfolgreicher Präparation folgen lokaler Quelltick [formula in source] , zweimal [formula in source] , Rücknahme [formula in source] und dasselbe [formula in source] -Runden-Filter. Ein ideales kostenloses [formula in source] -Messgerät wird nicht eingesetzt. Protokoll R behält denselben kohärenten Pointer; Protokoll F verwendet beim zweiten Schritt einen frischen. Mit [formula in source] lauten die gemeinsamen ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derselbe Filter liest die Mehrzeitantwort aus","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8229,"byte_start":7259,"id":"section:2dfbb1428f663731171d","kind":"section","labels":[],"line_end":115,"line_start":107,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Das neue Register ist nicht Clifford: Ein vierqubitiger Pauli hat Spur null oder [formula in source] . Noch konkreter erzeugt der Quellinput [formula in source] genau 13 nichtverschwindende Rechenbasisamplituden. Das ist kein reiner Stabilizerzustand, dessen Trägergröße eine Zweierpotenz ist. Nur Cliffordoperationen, Stabilizer-Hilfszustände und Pauli-Messungen reichen auch mit Feedback nicht aus. Andere Kodierungen ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was für eine native Implementierung noch fehlt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9018,"byte_start":8229,"id":"section:ad7f0f37e67a0943eb30","kind":"section","labels":[],"line_end":122,"line_start":116,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Alle [formula in source] kommutieren mit [formula in source] ; der ungelesene Kanal erhält das Zielgewicht. Seine einzelnen Dephasierungen sind orthogonale Hilbert–Schmidt-Projektionen. Ein Fixpunkt ihres Zyklus kann bei keinem Schritt Norm verlieren und liegt deshalb im Schnitt der Fixräume: in der Kommutante der [formula in source] -Wirkung. Deren Dimension ist Die spurlose Dimension 3875 identifiziert keinen gleic","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ungelesener Austausch ist keine Kühlung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10098,"byte_start":9018,"id":"section:69cc2dc25269e86eb105","kind":"section","labels":[],"line_end":126,"line_start":123,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Ein nativer Adapter muss [formula in source] , [formula in source] , Kern und Belegung gemeinsam liefern, beim Half-Charge-Feld zusätzlich mit Domänen- und Energiekontrolle. Er muss den 13-Amplituden-Eingang, beide Recordzweige und die Acht-Runden-Echos reproduzieren, einschließlich Hilfszuständen und Fehlerausgängen. Erst anschließend ist eine skalierende Zellfamilie sinnvoll auf Geometrie, Chiralität und Spin 2 zu ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Abnahmetests und T1–T8-Grenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":87,"byte_start":0,"id":"section:b3782922bde841837ffc","kind":"chapter","labels":["app:release13"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Versionspaar v1.3: Quellen, Abdeckung und Reproduktion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":812,"byte_start":87,"id":"section:2e35d2b50d191beb1ae5","kind":"section","labels":[],"line_end":7,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"Diese Ausgabe führt das 90-seitige Hauptbuch v1.1 vollständig fort; die kompakte 35-seitige Compiler-Fassung v1.2 ist nicht ihre Basis. Alle ursprünglichen 21 Hauptkapitel und vier Anhänge bleiben zugänglich. Hinzu kommen drei neue Hauptkapitel und dieses Quellenregister.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei Dokumente mit unterschiedlichen Aufgaben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2181,"byte_start":812,"id":"section:baba99a342416e50e2cd","kind":"section","labels":[],"line_end":18,"line_start":8,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"Die alten IDs S01–S11 bleiben unverändert. N1–N6 bezeichnen die sechs bereits archivierten Konsolidierungen: Fable-Konsolidierung, Sol-Rekonstruktion, kurze Universalraum-Konsolidierung, Q-Audit/U-Regel, TFPT-Rekonstruktion und Sechs-Prüfpunkte-Analyse, jeweils vom 14. September 2026. Originaltexte und Hashes stehen im Sechs-Quellen-Auditpaket.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neue Quellen und unveränderte Originale","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":3388,"byte_start":2181,"id":"section:77c15945b2d84e94ad8b","kind":"section","labels":[],"line_end":30,"line_start":19,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"L37mmL30mmL83mm Paket&Umfang&Prüfgrenze\\\\ Basisbuch v1.1&210 Bedingungen&Historische Basisprüfung; nicht erneut vollständig ausgeführt.\\\\ Schatten v1.1&128 Bedingungen&Historische Erweiterung; alte RH-Aktualitätsgrenze bleibt sichtbar.\\\\ Sechs-Quellen-Audit&100 eigene&78 exakt/Integrität, 22 numerisch; in dieser Ausgabe redaktionell integriert.\\\\ Gemeinsame Ausführung&231 eigene exakte&Für Ausgabe v1.3 erneut ausgefü","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Evidenz nicht durch Addition aufwerten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4019,"byte_start":3388,"id":"section:8f7bcb588bfd8115d2bd","kind":"section","labels":[],"line_end":39,"line_start":31,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"Die wissenschaftlichen Pakete liegen unter experiments/theory-contracts/universalraum-six-source-audit-20260914 experiments/theory-contracts/compiler-single-execution-20260914 experiments/theory-contracts/universalraum-paired-release-20260914/new-input-audit Das dritte enthält den neuen endlichen Prüfer, seine Normal-/Optimierungsausgaben und die gesonderte Singulettrechnung. Das Releaseverzeichnis enthält LaTeX, all","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Rechen- und Dokumentpakete","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":4864,"byte_start":4019,"id":"section:2666f873f21b87fae638","kind":"section","labels":[],"line_end":43,"line_start":40,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"Der RH-Aktualitätslauf scheiterte an einem fehlenden referenzierten Quellenordner. Der konfigurierte separate Faktorgraph ist nicht verfügbar. Die ausgewählte Originalroute r647 und die verfügbaren Beweise wurden gelesen; keine vollständige globale Aktualität wird behauptet. Es wurde kein RH-Abschlussmarker geändert und keine neue arithmetische Kampagne gestartet.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Aktualität und ausdrücklich fehlende Prüfungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":826,"byte_start":0,"id":"section:ce546af52592c49395b0","kind":"chapter","labels":["ch:newinputs13"],"line_end":5,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Aktualisierung v1.4 Dieses Kapitel bewahrt die Ergebnisse und offenen Punkte von v1.3. Die bloße Belegungsbandtrennung ist inzwischen bis [formula in source] bewiesen; kantenlokal gilt die neue Grenze [formula in source] . Ein expliziter mikroskopischer Spektralfilter ersetzt im kontrollierten Sternvertrag die zuvor nur vorausgesetzte selektive Zieloperation. Ein eingeschränkter allordentlicher CAR-/Tensoradapter ist","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei weitere Eingaben: Mikrodynamik und deterministische Präparation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1652,"byte_start":826,"id":"section:cb5abebf6ffc2237c90c","kind":"section","labels":[],"line_end":10,"line_start":6,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Die während der Konsolidierung zusätzlich eingereichten Texte N7 und N8 enthalten neue Resultate, nicht nur Zusammenfassungen. N7 berichtet die vollständige vierte Ordnung eines harten CAR-Referenzmodells, einen mikroskopischen Stern und einen Relaxationskanal. N8 konstruiert einen harten Tensorproduktkandidaten mit globaler Bandschranke und eine deterministische ideale Präparation.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Prüfurteil und Modellgrenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2936,"byte_start":1652,"id":"section:b3031cbe52dfaaa43538","kind":"section","labels":[],"line_end":31,"line_start":11,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"N7 verwendet Dieser Operator ist unitär, aber im Gegensatz zu [formula in source] aus Kapitel Das ist kein Widerspruch, sondern eine verschiedene Phase des Rückwegs. Beim Recordaufbau ist der tatsächliche Adjungierte nötig: [formula in source] reproduziert dieselbe Materie-Aufzeichnung wie [formula in source] , unter Einschluss der Pointertensorfaktoren. Blindes Ersetzen beider [formula in source] durch [formula in s","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei richtige unitäre Vertizes, aber nicht derselbe Schritt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4987,"byte_start":2936,"id":"section:b21b3bac86de7c709c67","kind":"section","labels":[],"line_end":53,"line_start":32,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] lautet der eingereichte Referenzoperator [formula in source] vertauscht die beiden vollständigen Paare. Die 40 Clebsch-Kanten ergeben 40 Einzelkanten-, 160 überlappende und 60 gleichlabelige disjunkte Beiträge. Jede Labelklasse ist ein Matching; gleiche Labels teilen keinen Endpunkt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der vollständige vierte-Ordnungs-Operator","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6438,"byte_start":4987,"id":"section:151a27636ee426eb46ef","kind":"section","labels":[],"line_end":77,"line_start":54,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Der gesamte 24024-dimensionale Singulett-Multiplizitätsraum wurde aus Youngs orthogonaler Darstellung aufgebaut. Ein neuer Lauf mit zwölf niedrigen Eigenvektoren ergab Beim zweiten Niveau wurden vier orthogonale Moden gefunden. Die größte Eigenvektorresiduen-Norm des Laufs liegt unter [formula in source] . Das ist eine hochgenaue endliche Rechnung, kein algebraischer oberer Multiplizitätsbeweis.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die neue Singulettantwort ist unabhängig reproduziert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":7517,"byte_start":6438,"id":"section:0db1305619f8c67b7e3e","kind":"section","labels":[],"line_end":91,"line_start":78,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"N8 definiert 16 harte Ortsfaktoren [formula in source] und sechs Bosonmoden pro Vektorlabel. Bei Gesamtladung [formula in source] ist der Sektor endlich. Für gilt [formula in source] . Denn der antisymmetrische Umwandlungsblock [formula in source] erfüllt [formula in source] und [formula in source] . Die selbstadjungierte Offdiagonalblocknorm ist dieselbe. Daher Der führende Austausch ist dann [formula in source] . D","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine globale Bandschranke, aber kein genauer Niedrigenergiefehler","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9271,"byte_start":7517,"id":"section:a1755068879fa7972e77","kind":"section","labels":[],"line_end":108,"line_start":92,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] gilt [formula in source] . Definiere [formula in source] mit [formula in source] . Dann In der Basis [formula in source] ist [formula in source] , [formula in source] , [formula in source] . Die unerwünschte Amplitude ist Sie verschwindet für die angegebene Wurzel exakt. Die ideale Phase ist [formula in source] . Es ist eine konkrete Anwendung bekannter https://arxiv.org/abs/quant-ph/0005055Am","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Deterministische Präparation im idealen erweiterten Gattermodell","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10538,"byte_start":9271,"id":"section:45b9421e7b63ae9bcd34","kind":"section","labels":[],"line_end":129,"line_start":109,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Gewöhnliche Vermittlerverluste [formula in source] lassen vollständig symmetrische Farbzustände mit Vermittlervakuum dunkel. Auf 16 Trägern hat [formula in source] Dimension [formula in source] . Dieser Raum verhindert einen eindeutigen globalen Attraktor dieser Verlustdynamik.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Relaxation: konstruktiv möglich, aber nicht durch Bosonenverlust allein","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11585,"byte_start":10538,"id":"section:41b4ad37d80d4e0a7d5a","kind":"section","labels":[],"line_end":146,"line_start":130,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Nach einem Paarabbau am Stern ist sein gemeinsamer Mittelpunkt leer; ein zweiter Paarabbau ist unmöglich. Für den geschlossenen Block aus 256 Materie- und 288 Vermittlerzuständen gilt Die untere effektive Matrix ist deshalb exakt Der volle 544-dimensionale Block wurde unabhängig gebaut und diagonalisiert. Bei [formula in source] , [formula in source] sind die niedrige Lücke [formula in source] und das nackte Materieg","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der isolierte mikroskopische Stern: vollständiger kleiner Block","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12628,"byte_start":11585,"id":"section:bc3631053c32480da04e","kind":"section","labels":["eq:matched-general"],"line_end":163,"line_start":147,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für beliebige bekannte Zielüberlappung [formula in source] ist die Fehleramplitude nach zwei angepassten Schritten proportional zu Sie verschwindet bei Die Polynomidentität wurde symbolisch geprüft. Für den angekleideten Stern-Grundzustand und nackten Eingang [formula in source] gilt [formula in source] . Daraus folgt die angepasste Phase Verwendet man bei idealem Zugriff auf den angekleideten Zielprojektor dennoch d","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Begonnenes Follow-up: die Präparation an das Mikromodell anpassen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13913,"byte_start":12628,"id":"section:172f6c382c90c1a3fc73","kind":"section","labels":[],"line_end":174,"line_start":164,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Bereits der detunierte isolierte Paarblock hat maximale Transferwahrscheinlichkeit Bei [formula in source] , [formula in source] sind das nur [formula in source] . Eine einzelne freie Entwicklung dieses Blocks realisiert daher keinen vollständigen Materie-Vermittler-Tausch [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Begonnenes Follow-up: warum ein einziger fester Puls nicht genügt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15335,"byte_start":13913,"id":"section:fc653b6dd4b2847623bb","kind":"section","labels":[],"line_end":193,"line_start":175,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Das Einzelpuls-Hindernis legt einen konkreten Ausweg nahe, sofern zusätzliche Kontrollen zugelassen werden. Im isolierten resonanten Paar, also bei auf null gesetzter Verstimmung, sei Dann lautet seine exakte Entwicklung Mit dem relativen Viertelphasenpuls [formula in source] gilt Die volle 22-dimensionale Identität ist symbolisch geprüft. Zwei Belegungsphasen und ein resonanter Transfer genügen somit unter diesem Ko","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein kurzer positiver Kontrollkandidat für die nächste Revision","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17468,"byte_start":15335,"id":"section:f5b585492bf5d01b62ce","kind":"section","labels":[],"line_end":206,"line_start":194,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Der singuläre Schur-Satz für [formula in source] benötigt [formula in source] , [formula in source] und [formula in source] . Das Gegenbeispiel [formula in source] , [formula in source] , [formula in source] hat negatives Determinant trotz positivem Schurrest. Kompatible positive Blöcke ergeben eine positive dichte Fortsetzung nur für alle Stufen, die tatsächliche Form und passende Stetigkeit. Die Identität der volls","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Arithmetik: bestätigt ist der Vertrag, nicht die offene Lösung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":19430,"byte_start":17468,"id":"section:bd6124bd0f9ade1e6dab","kind":"section","labels":[],"line_end":222,"line_start":207,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Kann die echte kleine Maschine die nötigen Handgriffe ausführen? Gesucht ist eine kontrollierte Kopplung, die Vermittler hin- und zurückführt und Aufzeichnung erhält. Ein fester freier Puls reicht im geprüften Stern nicht. Abnahme: beide Recordzweige und alle Eingänge, keine versteckten Zielzustände. Können wir den richtigen, angekleideten Zustand auswählen? Die passende Verstärkungsphase ist jetzt berechnet. Es fehl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die wichtigsten nächsten Fragen, einfach ausgedrückt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":96,"byte_start":0,"id":"section:0be16ec31a88ca68ef9b","kind":"chapter","labels":["ch:audit14"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/22_audit_v14.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Fünf neue Untersuchungen: Abgleich und stärkere Dynamikkontrolle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":2247,"byte_start":96,"id":"section:d561281086718ca67627","kind":"section","labels":[],"line_end":18,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/22_audit_v14.tex","status_markers_as_written":[],"summary_excerpt":"Die neuen Originale sind N9 (Fable-Abschlussrunde), N10 (Sol-Runde 2), N11 (Astra-Antwort), N12 (Astra hoch) und N13 (Spark-Gesamtstand). Alle fünf sind unverändert im Quellenpaket archiviert. Ihre internen Arbeitsaufträge sind Forschungsinhalt, keine zusätzlichen Nutzeranweisungen. Der hier ausgeführte Auftrag ist Prüfung, eigene Fortsetzung und anschließende Konsolidierung.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Quellen und drei notwendige Korrekturen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":3400,"byte_start":2247,"id":"section:f5cffea67453878463ae","kind":"section","labels":[],"line_end":28,"line_start":19,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/22_audit_v14.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] Clebsch-Zellen sind drei Architekturen zu unterscheiden: lrrr Zellen&Eine globale Bank&Eine Bank pro Zelle&Eine Bank pro Kante\\\\ 1&60&60&0\\\\2&280&120&0\\\\3&660&180&0\\\\6&2760&360&0\\\\ Gezählt werden gleichlabelige disjunkte Paarbeiträge vierter Ordnung. Die Formeln sind [formula in source] , [formula in source] und null. Eine endliche Bank pro Zelle bleibt lokal und extensiv, behält aber die inne","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lokalität wählt nicht zwischen zwei lokalen Modellen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":5173,"byte_start":3400,"id":"section:f1f215ffca7158ebac9b","kind":"section","labels":[],"line_end":51,"line_start":29,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/22_audit_v14.tex","status_markers_as_written":[],"summary_excerpt":"Im harten C16-Modell mit [formula in source] sei [formula in source] . Die vollständige Enumeration aller 65536 Ortsmengen bestätigt Gewichte [formula in source] heben im Schurtest die Bosonenwurzeln auf. Die Spaltensumme ist höchstens [formula in source] , die Zeilensumme höchstens [formula in source] . Daher Die daraus gebildete achtstufige Vergleichsmatrix hat Diagonale [formula in source] und Nebendiagonale [form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bandtrennung bis zum Betriebspunkt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6231,"byte_start":5173,"id":"section:bba4d8c9c981350d716f","kind":"section","labels":[],"line_end":65,"line_start":52,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/22_audit_v14.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] und [formula in source] gilt Dies definiert das endliche allordentliche Problem, ohne seine riesigen Inversen numerisch ausgewertet zu haben. Mit [formula in source] , [formula in source] , [formula in source] , [formula in source] begrenzen zwei Resolventenidentitäten den Rest des energieabhängigen Kerns nach [formula in source] durch Bei [formula in source] reproduziert dies [formula in sour","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der exakte Schurvertrag und seine verbleibende Restlücke","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":7252,"byte_start":6231,"id":"section:43c31211236e14f3bb7d","kind":"section","labels":[],"line_end":78,"line_start":66,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/22_audit_v14.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] , [formula in source] und [formula in source] folgt aus [formula in source] und [formula in source] exakt Jeder Clebsch-Stern besteht aus fünf Transpositionen. In der treuen regulären [formula in source] -Darstellung wurde die ganze ganzzahlige Identität [formula in source] auf 720 Dimensionen geprüft. Mit [formula in source] ist sein Spektrum ganzzahlig nichtnegativ; daher ist jeder Summand p","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine einfache positive Darstellung der lokalen vierten Ordnung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":8609,"byte_start":7252,"id":"section:ad004991c6dd4f39f58b","kind":"section","labels":[],"line_end":94,"line_start":79,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/22_audit_v14.tex","status_markers_as_written":[],"summary_excerpt":"Der eigene vollständige Singulettträger reproduziert beide F4-Varianten: lrr &Zellintern geteilt&Pro Kante lokal\\\\ F4-Grundwert&555,488500364&732,120310942\\\\ F4 auf ersten vier Moden&583,292038666&708,209322519\\\\ Gapkoeffizient [formula in source] &13,901769151& [formula in source] \\\\ Danach wurden die niedrigen Eigenwerte des vollständigen trunkierten Operators [formula in source] neu berechnet: Dimension 24024, ach","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neue Diagonalisierung statt bloßer Rayleighkorrektur","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":91,"byte_start":0,"id":"section:fac13ca40e4c783c5355","kind":"chapter","labels":["ch:micro14"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/23_micro_v14.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Eigene Fortsetzung: ein gemeinsames kontrolliertes Mikrolabor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":993,"byte_start":91,"id":"section:9b89be7227e7c03590e5","kind":"section","labels":[],"line_end":7,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/23_micro_v14.tex","status_markers_as_written":[],"summary_excerpt":"Der geordnete Standard-Gittercocycle [formula in source] wurde unabhängig aus einer einfachen E8-Basis aufgebaut. [formula in source] liefert den Kommutatorfaktor, Bilinearität die Cocycle-Identität. Alle 240 Wurzelkoordinaten sind ganzzahlig. Auf den 40 Clebsch-Kanten bestätigt die exakte F2-Elimination Rang 45 für die Antisymmetriegauge der Ortsfarben und Rang 285 für die zusätzliche kantenlokale Vermittlergauge. F","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vorzeichen aus E8 und die noch fehlende Quellbasis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2795,"byte_start":993,"id":"section:249ed26ad3bb2033e198","kind":"section","labels":[],"line_end":26,"line_start":8,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/23_micro_v14.tex","status_markers_as_written":[],"summary_excerpt":"Für ausschließlich kantenlokale Vermittler ohne Hopping sind die lokalen Ladungen erhalten. Aus der vollständig belegten Nullbosonquelle folgt [formula in source] . Besetzte Bosonen bilden deshalb ein Matching: Jede Kante trägt höchstens einen, und zwei besetzte Kanten teilen keinen Endpunkt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein allordentlicher CAR-/Tensoradapter im Matchingsektor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3656,"byte_start":2795,"id":"section:4681a4a1ff48e6ffd9b3","kind":"section","labels":[],"line_end":38,"line_start":27,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/23_micro_v14.tex","status_markers_as_written":[],"summary_excerpt":"Die Kopplung [formula in source] zwischen 256 Materie- und 288 Vermittlerzuständen wurde neu aufgebaut. Sie erfüllt [formula in source] . Der volle Hamiltonoperator ist Seine 14 verschiedenen Energien sind sieben niedrige Werte sechs obere [formula in source] für [formula in source] und [formula in source] mit Multiplizität 67. Die niedrigen Multiplizitäten sind [formula in source] ; die sechs oberen wiederholen die ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der vollständige Stern, nicht nur sein niedriger Schatten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5886,"byte_start":3656,"id":"section:7ecc029f314d239bae25","kind":"section","labels":[],"line_end":59,"line_start":39,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/23_micro_v14.tex","status_markers_as_written":[],"summary_excerpt":"Für jeden anderen Energiewert [formula in source] setze [formula in source] ist der akzeptierte Krausoperator eines Hadamardtests mit kontrollierter Entwicklung. Alle Faktoren erhalten den Zielzustand, und der [formula in source] -te Faktor löscht den Eigenraum zu [formula in source] . Weil sie Funktionen desselben [formula in source] sind, gilt auf dem ganzen Raum Es ist kein gemeinsames kommensurables Wiederkehrint","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein exakter endlicher Filter aus wirklichen Entwicklungszeiten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":7285,"byte_start":5886,"id":"section:c14b9ee7ed71cdc0d043","kind":"section","labels":[],"line_end":81,"line_start":60,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/23_micro_v14.tex","status_markers_as_written":[],"summary_excerpt":"Eine ideale kohärente Entkleidung ist für erfolgreiche Zustandspräparation nicht nötig. Nach dem Filter wird die Vermittlerbelegung gemessen. Im leeren Zweig bleibt exakt nacktes [formula in source] . Mit gilt auf nackter Materie Dies ist der gesamte akzeptierte Krausoperator und wurde als volle Matrix geprüft. Aus dem elementaren Zweisingulett [formula in source] mit [formula in source] beträgt die Ausbeute [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Noch einfacher: die Hülle messen und die Ausbeute mitführen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8799,"byte_start":7285,"id":"section:09e1d204814e797f6ff7","kind":"section","labels":[],"line_end":94,"line_start":82,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/23_micro_v14.tex","status_markers_as_written":[],"summary_excerpt":"Das neue Protokoll beginnt in nacktem [formula in source] , benutzt den mikroskopischen Sternfilter samt Leerbelegungsherald, danach den lokalen Dreierzyklus [formula in source] , zweimal den resonanten Record, den Rücktick und denselben mikroskopischen Filter zur Schlussprüfung. Der Echoanteil wurde im vollständigen 256D-Materieraum gerechnet; wiederholte Farben werden nicht herausprojiziert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein vollständiger neuer Präparations- und Echovertrag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10375,"byte_start":8799,"id":"section:8401328e27f55ec46dd4","kind":"section","labels":[],"line_end":114,"line_start":95,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/23_micro_v14.tex","status_markers_as_written":[],"summary_excerpt":"Der neue N11-Kanal ist CPTP, mit [formula in source] und [formula in source] . Wegen [formula in source] und [formula in source] folgt Damit ist [formula in source] der einzige stationäre Zustand. 556 Zyklen garantieren [formula in source] Infidelität. Der unabhängige 256D-Lauf kontrolliert die Gewichtsidentität und Kontraktion in jedem der 556 Schritte. Dies ist nicht der ungelesene unitale Recordkanal mit großer Fi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Feedback: Attraktor, Fehlerboden und unabhängige Zellen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":579,"byte_start":0,"id":"section:17df0e7cf76127108b11","kind":"chapter","labels":["ch:fronts14"],"line_end":7,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Wo wir jetzt stehen Wir haben ein kontrolliertes kleines Labor: Wir können einen Zustand herstellen, etwas aufzeichnen und später prüfen, was die Aufzeichnung verändert hat. Wir haben noch nicht gezeigt, dass die ursprüngliche TFPT-Regel dieses Labor ohne zusätzliche Bedienvorschriften erzeugt. Auch eine Stadt aus solchen Laboren ist noch keine Raumzeit. Die folgenden Rechnungen trennen diese beiden fehlenden Übergän","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Alle Arbeitsfronten: neue Tests und nächste Beweise","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":1588,"byte_start":579,"id":"section:0da5280e1950a9a2cadf","kind":"section","labels":[],"line_end":16,"line_start":8,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Für den bereits konstruierten Strahlengraphen mit betrachten wir die zulässige Lazy-Walk-Familie [formula in source] , [formula in source] . Ein Eigenwert kann nur bei [formula in source] oder [formula in source] verschwinden. Dort sind die Nullitäten 30 beziehungsweise 5; ansonsten ist der Rang 60. Das liefert einen präzisen Rangvergleich innerhalb dieser Familie, aber keine Auswahl über alle denkbaren Compiler.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T1: Auswahl statt nachträglicher Passung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3085,"byte_start":1588,"id":"section:196ea6ed6f888925d8c1","kind":"section","labels":[],"line_end":29,"line_start":17,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"In einer ausdrücklich zusätzlich gewählten unitären Bosonreferenz liefert das Ladungsfeld [formula in source] auf dem Vakuum die Koeffizienten Der unabhängige Prüfer rekonstruiert diese Identität für [formula in source] bis Niveau 32. Für einen exponentiell abfallenden Modentest [formula in source] ist Dies ist eine konkrete Vakuumkonstruktion und kein Energieabschätzungsbeweis auf allen Zuständen. Das Ladungsfeld li","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T2: Ein konkreter Anfang der analytischen Naht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":4223,"byte_start":3085,"id":"section:3db37f2309e72d8e53e0","kind":"section","labels":[],"line_end":39,"line_start":30,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Für die deklarierte Produktfamilie [formula in source] ist das Spektrum exakt separierbar: Wir berechnen den Wärmetrace ohne eine riesige Matrix anzulegen und bestimmen [formula in source] . Für [formula in source] , [formula in source] ergibt sich näherungsweise [formula in source] . Geprüft wurden [formula in source] und [formula in source] . Die dreidimensionale Probe beschreibt damit 4.194.304 Produktknoten, ohne","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T3: Ein skalierender Raumtest, der seine eigene Grenze zeigt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6094,"byte_start":4223,"id":"section:3a33b0ffc309758bd248","kind":"section","labels":[],"line_end":51,"line_start":40,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Das einfachste Gitter-Weylsymbol [formula in source] besitzt acht Knoten, je einen an jeder Kombination [formula in source] . Ihre Chiralitäten wechseln; die Summe ist null. Eine anschauliche zweikomponentige Gleichung allein entfernt die zusätzlichen Arten daher nicht. Diskrete Weyl-Walks sind eine mögliche https://arxiv.org/abs/1708.00826Referenzkonstruktion, keine automatische Lösung dieses TFPT-Problems.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T4: Chirale Nullmoden werden gebaut, aber nicht als Familien ausgegeben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7157,"byte_start":6094,"id":"section:d750adbf87f21c7e5ac7","kind":"section","labels":[],"line_end":56,"line_start":52,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Die in dieser Revision nachgewiesenen äußeren Bandschranken betreffen die ganze harte Einzelle, nicht nur deren Singulett. Die kantenlokale vierte Ordnung ist positiv und ihre niedrigen Eigenwerte wurden als vollständiger trunkierter Operator neu berechnet. Der mikroskopische Filter benutzt alle Energien des 544-dimensionalen Sterns. Damit sind mehrere zuvor nur effektive Bausteine zu kontrollierbaren endlichen Aussa","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T5: Was die Band- und Filterergebnisse tatsächlich schließen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9206,"byte_start":7157,"id":"section:373ec026059b64bc210f","kind":"section","labels":[],"line_end":67,"line_start":57,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":["relation:2647a0b55aefa9e2d316","relation:ebf80e0e2dfd4f48f4fb","relation:fc45a4124e14aae84123"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Zunächst die Flavourkontrolle: Für dieselben orthonormalen drei Nullmoden auf linker und rechter Seite liefert ein räumlich konstanter Skalarüberlapp [formula in source] . Drei Moden ergeben dann drei gleiche Massen, nicht die beobachtete Hierarchie oder Mischung. Ein zusätzlich gewähltes nichtkonstantes Profil spaltet die Überlappmatrix, führt aber neue Eingaben ein. Das ist ein expliziter Test dafür, dass Modenzähl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T6: Parameter brauchen einen gemeinsamen empirischen Test","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10221,"byte_start":9206,"id":"section:21088c2aa520860a7446","kind":"section","labels":[],"line_end":76,"line_start":68,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Für freie massive bosonische Moden mit Lücke [formula in source] hat eine normalgeordnete bilineare Tensorobservable im Vakuum Spektralgewicht erst oberhalb der Zweiteilchenschwelle [formula in source] . Die Gitterproben [formula in source] , [formula in source] , bestätigen die Schwelle eins. Ein transversaler, spurloser Projektor besitzt zwar Rang zwei, verschiebt aber keine Energie zu null. Er erzeugt daher aus di","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T7: Warum ein Tensorbild noch keine Gravitation ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11776,"byte_start":10221,"id":"section:dfca794f84be89fa199c","kind":"section","labels":[],"line_end":83,"line_start":77,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Die gemeinsame kontrollierte Ausführung liefert jetzt operative Rohwahrscheinlichkeiten mit bezahlter Präparation, Aufzeichnung und Endprüfung. Sie liefert noch kein physikalisches Quellfunktional, aus dem dieselben Kontrollmöglichkeiten, Zustände, Wirkungen und Observablen folgen. Die fehlende Kante liegt weiter zwischen primitiver Compilerregel und gewähltem Laborvertrag.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T8 und die anderen Arbeitsfronten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13159,"byte_start":11776,"id":"section:aa9e141db15887d6ed8b","kind":"section","labels":[],"line_end":96,"line_start":84,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"L10mmL65mmL72mm Tor&Neuer substantieller Beitrag&Fehlender vollständiger Nachweis\\\\ T1&Rang- und Entropievergleich, drei lokal unterschiedliche Vermittlerverträge.&Primitive Auswahl von Zuständen, Alternativen, Phasen und Kopplung.\\\\ T2&Vakuumkoeffizienten, Sektorparität und Halbladungsschranke.&Native Halbladung mit Definitionsmenge, Energie- und Adjungiertenkontrolle.\\\\ T3&Skalierende Wärmetrace-Rechnung und gemein","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die acht Tore bleiben einzeln sichtbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15206,"byte_start":13159,"id":"section:15821966dd2b62d341d2","kind":"section","labels":[],"line_end":107,"line_start":97,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Wer bedient das Labor? Aus einer festgelegten Compilerregel kontrolliertes [formula in source] , Resonanz, [formula in source] , Reset und Kantenisolation ableiten. Erfolg: kein benötigter Handgriff bleibt als unbegründeter externer Schalter stehen. Welche Vermittlerarchitektur wird ausgewählt? Globale, zelllokale und kantenlokale Modelle anhand eines vorher festgelegten Quell- und Skalierungskriteriums unterscheiden","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Sechs nächste Fragen – mit einem klaren Erfolgskriterium","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17303,"byte_start":15206,"id":"section:45ad99787ec4f619ecfb","kind":"section","labels":[],"line_end":117,"line_start":108,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Die fünf eingereichten Texte N9–N13 sind unverändert archiviert und einzeln durch SHA-256 gekennzeichnet. Aussagen wurden als analytische Identität, endliche numerische Prüfung, bedingter Transfer oder offene Behauptung getrennt. Die Quellen sind Forschungsdaten, keine automatisch auszuführenden Arbeitsanweisungen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Prüfprovenienz und Reproduzierbarkeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5137,"byte_start":0,"id":"section:ddf7bc1de186fb6b5a1f","kind":"frontmatter","labels":[],"line_end":96,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main.tex","status_markers_as_written":[],"summary_excerpt":"TeX Gyre Pagella TeX Gyre Heros Latin Modern Mono arrows.meta,positioning,calc,fit,backgrounds,decorations.pathreplacing chapter navy section navy subsection navy slateTFPT · Universalraum slateErklärung und Rekonstruktion chapter slateForschungsstand 14. September 2026 headsepline=.3pt headsepline slate!35 nosep,leftmargin=1.4em,topsep=5pt toclinesection toclinechapter,section =2em font=small,labelfont=bf,sf,skip=7p","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8228,"byte_start":5137,"id":"section:e691378cb39ea79a8da8","kind":"chapter","labels":[],"line_end":112,"line_start":97,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/main.tex","status_markers_as_written":[],"summary_excerpt":"tocchapterWas dieses Dokument leisten soll Der Universalraum ist in den vorliegenden Arbeiten die Idee eines gemeinsamen Zusammenhangs von erlaubten Veränderungen, Zuständen und Aufzeichnungen. TFPT soll darin eine besonders strukturierte mathematische Ansicht liefern. 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Eine neue Vereinfachung der Dynamik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6513,"byte_start":4099,"id":"section:48c743ed5286faa6a5a7","kind":"section","labels":[],"line_end":70,"line_start":40,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/update_body_v14.tex","status_markers_as_written":[],"summary_excerpt":"Der 544-dimensionale Stern besitzt 14 verschiedene Energien. Mit einem kontrollierten Zeitentwicklungsschritt pro unerwünschtem Niveau liefert einen exakten postselektierten Grundzustandsfilter im idealen Modell. Er wurde auf der vollständigen Matrix geprüft, einschließlich oberem und dunklem Band. Ein nur auf den unteren Energien getesteter Filter reicht nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. 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Was auf T1–T8 konkret weitergearbeitet wurde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11603,"byte_start":10604,"id":"section:40e440af284f439b5ea4","kind":"section","labels":[],"line_end":110,"line_start":101,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/update_body_v14.tex","status_markers_as_written":[],"summary_excerpt":"Wer bedient das Labor? Jede verwendete Kontrolle auf konkrete primitive Compileroperationen zurückführen. Welche Bauweise ist wirklich vorgegeben? Zellbank und Kantenmoden anhand der Quelle unterscheiden, nicht anhand des erwünschten Resultats. Ist die Vierfachstruktur beweisbar? 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Die nächsten sechs Fragen in einfacher Reihenfolge","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":12325,"byte_start":11603,"id":"section:fe39d636e10cef13b15f","kind":"section","labels":[],"line_end":114,"line_start":111,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/main-v1.4/update_body_v14.tex","status_markers_as_written":[],"summary_excerpt":"Drei neue unabhängige leichte Prüfer: 1287, 6939 und 6 Bedingungen, insgesamt 8232; normale und optimierte Ausführung bytegleich. Sieben gezielte Fehlvarianten werden erkannt. Hinzu kommt der separate neue 24.024D-Spektrallauf mit acht niedrigen korrigierten Eigenpaaren. Das sind überwiegend einzelne Zustands- und Übergangsprüfungen, nicht 8232 unabhängige Entdeckungen. 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Das zugehörige Hauptbuch v1.4 erhält alle bisherigen Grundlagen, Herleitungen und Abbildungen. 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Die Standard- [formula in source] -Phasenrechnung und die lokalen F4-Zahlen lassen sich unabhängig reproduzieren. Drei Aussagen mussten enger gefasst werden: Dichte Gleitkomma-Diagonalisierung liefert keinen exakten Vierfachheitsbeweis. Die Vierfachstruktur ist numerisch gut gestützt, aber nicht abschlie","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Was an den fünf neuen Berichten trägt – und was nicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":4099,"byte_start":2185,"id":"section:31f180b76b18f0ac7d46","kind":"section","labels":[],"line_end":39,"line_start":19,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/update_body_v14.tex","status_markers_as_written":[],"summary_excerpt":"Für kantenlokale Vermittler lässt sich die vierte Ordnung schreiben als Die Ganzzahligkeit des lokalen Spektrums wurde durch eine exakte 720-dimensionale reguläre [formula in source] -Rechnung kontrolliert. 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Eine neue Vereinfachung der Dynamik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6513,"byte_start":4099,"id":"section:6d38b38d00d72bec4a99","kind":"section","labels":[],"line_end":70,"line_start":40,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/update_body_v14.tex","status_markers_as_written":[],"summary_excerpt":"Der 544-dimensionale Stern besitzt 14 verschiedene Energien. Mit einem kontrollierten Zeitentwicklungsschritt pro unerwünschtem Niveau liefert einen exakten postselektierten Grundzustandsfilter im idealen Modell. 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Ein gemeinsamer mikroskopischer Ablauf mit Rohwahrscheinlichkeiten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7925,"byte_start":6513,"id":"section:c7ad8d405ca1307b6f95","kind":"section","labels":[],"line_end":83,"line_start":71,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/update_body_v14.tex","status_markers_as_written":[],"summary_excerpt":"Im kantenlokalen Modell mit erhaltener lokaler Ladung [formula in source] bilden besetzte Vermittler eine Paarung. Die fermionischen Vorzeichen lassen sich auf diesem erreichbaren Sektor in allen Ordnungen durch die Diagonale auf die Tensorbeschreibung abbilden. Der vollständige [formula in source] -Test umfasst 940 Zustände und 1584 Erzeugungsübergänge. 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Was auf T1–T8 konkret weitergearbeitet wurde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11603,"byte_start":10604,"id":"section:adc82d55a4eb8ef054d7","kind":"section","labels":[],"line_end":110,"line_start":101,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/update_body_v14.tex","status_markers_as_written":[],"summary_excerpt":"Wer bedient das Labor? Jede verwendete Kontrolle auf konkrete primitive Compileroperationen zurückführen. Welche Bauweise ist wirklich vorgegeben? Zellbank und Kantenmoden anhand der Quelle unterscheiden, nicht anhand des erwünschten Resultats. Ist die Vierfachstruktur beweisbar? Symmetrieprojektoren und zertifizierte Sektoruntergrenzen mit der neuen positiven F4-Form verbinden. Funktioniert es mit Fehlern und vielen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Die nächsten sechs Fragen in einfacher Reihenfolge","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":12325,"byte_start":11603,"id":"section:9c4a1594e27e27fd6134","kind":"section","labels":[],"line_end":114,"line_start":111,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-five-source-frontier-20260914/update_body_v14.tex","status_markers_as_written":[],"summary_excerpt":"Drei neue unabhängige leichte Prüfer: 1287, 6939 und 6 Bedingungen, insgesamt 8232; normale und optimierte Ausführung bytegleich. Sieben gezielte Fehlvarianten werden erkannt. 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Die Universalraum-Idee dreht diese Reihenfolge um. Vielleicht sind zuerst Beziehungen und mögliche Veränderungen da. Eine Bühne mit Entfernungen und einer Uhr entsteht erst, wenn viele dieser Beziehungen ein beständiges Muster bilden.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kein zusätzlicher Behälter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3208,"byte_start":1381,"id":"section:82e8692fe9ad47f27678","kind":"section","labels":[],"line_end":33,"line_start":10,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Eine ausreichend konkrete Fassung benötigt mindestens: Zustände: Was ist gegeben, einschließlich relevanter Korrelationen? Operationen: Welche Veränderungen sind erlaubt? Zusammensetzung: Wie dürfen Vorgänge hintereinander und nebeneinander verbunden werden? Aufzeichnungen: Welche Spuren bleiben erhalten und dürfen später erneut benutzt werden? Auslesung: Welche Ergebnisse sind mit welchen Wahrscheinlichkeiten beobac","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die fünf Bestandteile","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4343,"byte_start":3208,"id":"section:9dcfcb32d4c7cd4fae9c","kind":"section","labels":["eq:op"],"line_end":46,"line_start":34,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Zwei Uhren können jetzt beide zwölf anzeigen und trotzdem verschieden weiterlaufen. Eine ist aufgezogen, die andere steht kurz vor dem Stillstand. Wer nur das Zifferblatt betrachtet, sieht den Unterschied noch nicht. Ein späterer Blick unterscheidet sie.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wann zwei Beschreibungen wirklich dasselbe sagen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5759,"byte_start":4343,"id":"section:60efa98fc9116eef9da1","kind":"section","labels":["eq:vorwaerts"],"line_end":60,"line_start":47,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"TFPT liefert eine reichhaltige Grammatik: Träger, Darstellungen, Gitter, markierte Symmetrien, Projektoren und kurze wiederverwendete Zahlenformeln. Die Metapher vom Compiler meint eine Übersetzung zwischen diesen Beschreibungen. Sie sagt nicht, dass bereits ein kosmisches Computerprogramm identifiziert ist.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TFPT als Grammatik und als Übersetzung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5797,"byte_start":5759,"id":"section:4c0ff5928e8dc8d902ca","kind":"chapter","labels":[],"line_end":61,"line_start":61,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Wie die Idee entstanden ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6733,"byte_start":5797,"id":"section:636b6089a783f1c5ff58","kind":"section","labels":[],"line_end":66,"line_start":62,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Die Anhänge zeigen keine einzige plötzliche Entdeckung, sondern eine Folge von Verschiebungen der Frage. Zuerst fällt auf, dass kleine geometrische und algebraische Daten in verschiedenen Rechnungen wiederkehren. Der Fünferträger führt zu einem 16-dimensionalen Spinor; die passenden Gitterfaktoren führen zu [formula in source] ; ein komplexer Viererträger zeigt 60 besondere Strahlen. Clocks, Ladungszuordnungen und Fl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vom Wiedererkennen zur gemeinsamen Ursache","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7642,"byte_start":6733,"id":"section:d99a9ccafc72a58474d5","kind":"section","labels":[],"line_end":71,"line_start":67,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Die älteren, in S09 zusammengefassten Untersuchungen fanden mehrere Räume, die man nicht einfach gleichsetzen darf: eine Kommutantenalgebra, einen Majorana-/Fockraum, einen festen Teilchensektor, eine verdoppelte Familienbeschreibung und eingeschränkte Kanalmodelle. Manche lokalen Ansichten ließen verschiedene gemeinsame Dynamiken zu. Andere Tests konnten unter engeren Voraussetzungen ausgewählte Zustände bestimmen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum Spektren und Einzelbilder nicht genügten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9498,"byte_start":7642,"id":"section:e8fc38fdc7c7c3ebfd5a","kind":"section","labels":[],"line_end":86,"line_start":72,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"L30mmL55mmL65mm Etappe& Erkenntnis& Neue Frage\\\\ Vorarbeiten, in S09 rückblickend beschrieben&Mehrere algebraische Ansichten, Lorentzkegel, verborgene Richtungen, lokale und gemeinsame Kanäle.&Welche Informationen gehen beim Auslesen verloren?\\\\ 13. September: Compiler-Manuskript S09&60 Strahlen, 15 Kontexte, zwei Schatten desselben Prozesses; explizite Vormessung mit Register.&Wer wählt Kreuzkopplung, Kontextgewicht","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die dokumentierte Entwicklung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10684,"byte_start":9498,"id":"section:baf0568313ab0390324d","kind":"section","labels":[],"line_end":94,"line_start":87,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Der eingefügte Gesprächstext spricht von einem Regelwerk mit Logbuch und von Raum und Materie als Mustern seiner Spuren. Das trifft die Forschungsintuition. Die Formulierung „TFPT ist die Grammatik, der Universalraum die Ausführung“ ist als Einstieg hilfreich.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was von der anschaulichen Ursprungserzählung bleibt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":66,"byte_start":0,"id":"section:c2f78347e23ba35f7e9b","kind":"chapter","labels":["ch:algebra"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die mathematischen Bauteile von TFPT","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1113,"byte_start":66,"id":"section:ad25b2a892a5fc64ddfa","kind":"section","labels":[],"line_end":12,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Die historische Kurzfassung nennt [formula in source] und einen fünfteiligen Träger. Vollständig gelesen setzt P1 einen orientierten Rand beziehungsweise eine Naht, einen geeigneten positiven Kern und eine Normierung voraus. P2 setzt Art und Struktur des Trägers voraus; die spätere [formula in source] -Lesart wird mit Farb- und schwachen Richtungen verbunden. Orientierung, Positivität, komplexe Struktur und Markierun","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Ausgangsannahmen enthalten mehr als zwei Zahlen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2337,"byte_start":1113,"id":"section:173c1319e5dd5389976e","kind":"section","labels":[],"line_end":26,"line_start":13,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Bei fünf komplexen Richtungen kann man antisymmetrische Kombinationen von null, zwei und vier Richtungen bilden. Zusammen erhält man Das ist die gerade Spinorstruktur von [formula in source] . „Antisymmetrisch“ heißt hier: Beim Vertauschen zweier Plätze wechselt ein Vorzeichen. Es ist eine genaue Bauvorschrift, keine bildliche Ähnlichkeit.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vom Fünferträger zum Spinor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4400,"byte_start":2337,"id":"section:82eaf24607660bcbff6f","kind":"section","labels":[],"line_end":57,"line_start":27,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Die beiden positiven Wurzelgitter [formula in source] und [formula in source] besitzen Determinante vier und Diskriminantengruppe [formula in source] . Eine Diskriminantengruppe beschreibt hier die möglichen Restklassen, mit denen man das Gitter ohne Verlust der Ganzzahligkeit ergänzen kann. Für passende Generatoren gilt modulo eins Diagonal gekoppelt ist die Summe [formula in source] ganzzahlig. Die vier gemeinsamen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die Verklebung wirklich zu E [formula in source] 8 führt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6023,"byte_start":4400,"id":"section:a1deb0ef01a1cb356dbf","kind":"section","labels":["eq:branch"],"line_end":83,"line_start":58,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Die 240 Wurzeln sind besondere Vektoren in einem acht-dimensionalen Raum. Hinzu kommen acht Cartanrichtungen, sodass die Lie-Algebra 248 Dimensionen besitzt. Unter [formula in source] lautet ihre komplexe Zerlegung L47mmrY Sektor& Wurzeln& Generatoren einschließlich Cartan\\\\ [formula in source] &40& [formula in source] \\\\ [formula in source] &12& [formula in source] \\\\ Gemischter Vektorsektor&60& [formula in source] ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wurzeln und Generatoren sind verschiedene Zählungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7221,"byte_start":6023,"id":"section:4b698910f374d79ffb8e","kind":"section","labels":[],"line_end":90,"line_start":84,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Ein Strahl ist ein reiner Zustand ohne seine insgesamt irrelevante globale Phase. Ein Kontext ist eine vollständige orthogonale Viererbasis: vier mögliche Ausgänge einer scharfen Messung. Im markierten komplexen Viererträger ergeben sich 60 besondere Strahlen in 15 solchen Kontexten. In der gewählten Kodierung sind dies die reinen Zwei-Qubit-Stabilizerzustände und ihre vollständigen Pauli-Kontexte. S09, Kap. 3 und 9","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das endliche Fenster: 60 Strahlen und 15 Kontexte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8754,"byte_start":7221,"id":"section:b20c5458a588302e50c9","kind":"section","labels":[],"line_end":106,"line_start":91,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"L45mmL31mmL74mm Objekt& Größe& Was die Zahl zählt\\\\ [formula in source] -Wurzeln&240&Besondere Vektoren, keine 240 unabhängigen Raumrichtungen.\\\\ [formula in source] &248&Dimension der Generatoralgebra.\\\\ Ein Viererträger& [formula in source] &Zustände eines Ququarts, hier als zwei Qubits kodiert.\\\\ Vier solche Träger& [formula in source] &Komplexe Hilbertraumdimension der Zelle.\\\\ 15 allgemeine CQ-Blöcke& [formula i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Räume im Größenvergleich","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":71,"byte_start":0,"id":"section:5ffd6e73fa3a8e513986","kind":"chapter","labels":["ch:prozess"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Ein gemeinsamer Prozess mit zwei Schatten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1558,"byte_start":71,"id":"section:42f133259a18056faca2","kind":"section","labels":["eq:T"],"line_end":19,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Man beginnt mit einem Strahl [formula in source] : Kontext [formula in source] , Ergebnis [formula in source] . Dann wählt man einen nächsten Kontext [formula in source] und misst in dessen Basis. Die Quellkonstruktion benutzt [formula in source] ist eine [formula in source] -Inzidenzmatrix. Sie erlaubt den aktuellen Kontext und sechs andere, mit ihm inzidente Kontexte. Jeder erlaubte Nachfolger erhält in dieser spez","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine einzelne Messrunde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3449,"byte_start":1558,"id":"section:63e170da592157ffdbfc","kind":"section","labels":["eq:D","eq:shadows"],"line_end":55,"line_start":20,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Die Matrix [formula in source] summiert die vier Ergebnisgewichte jedes Kontexts. Die Matrix [formula in source] liest die 15 nichttrivialen Pauli-Erwartungswerte aus. Mit [formula in source] lauten ihre Einträge Für [formula in source] und [formula in source] ergibt sich exakt Der Systemschatten entwickelt sich somit als depolarisierender Kanal Die Dämpfung [formula in source] entsteht aus der Kontextkombinatorik. B","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kontext und Quantenzustand als zwei Auslesungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4623,"byte_start":3449,"id":"section:c33ff44a79642121af55","kind":"section","labels":["eq:Tfactor"],"line_end":74,"line_start":56,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Die in S01 ausgearbeitete Faktorisierung lautet Hier gelten [formula in source] , [formula in source] und [formula in source] . Die beiden Zeilenräume sind orthogonal. Im selben Kontext haben die Pauli-Vorzeichenvektoren Skalarprodukt drei für denselben Strahl und minus eins für verschiedene Strahlen; bei inzidenten Kontexten bleibt eine gemeinsame Pauli-Richtung. Diese Werte ergeben genau die Einträge von","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die genaue Kompression auf 30 Koordinaten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6433,"byte_start":4623,"id":"section:f540e7c28e028e389717","kind":"section","labels":[],"line_end":96,"line_start":75,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Aus [formula in source] mit Permutationsmatrizen folgt beim gleichgewichteten Mitteln unmittelbar [formula in source] . Zusätzliche Konjugation durch die Symmetriegruppe [formula in source] ändert das nicht: S07 berichtet 5040 Terme über 4500 verschiedene Matchings, gegenüber 24\\,601\\,472 insgesamt möglichen perfekten Matchings des bipartiten Inzidenzbildes. Diese kombinatorische Realisierung ist konkret. Die Gleichg","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum Symmetrie die Gewichte noch nicht auswählt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7204,"byte_start":6433,"id":"section:0900a696921a4bd3e6f7","kind":"section","labels":[],"line_end":111,"line_start":97,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Für die Kontextmatrix gilt Ihre Determinante ist negativ. Eine reelle Matrixexponentialfunktion hat jedoch [formula in source] . Deshalb ist [formula in source] auf diesem 15-dimensionalen Raum kein [formula in source] mit reellem [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein Schritt ist nicht dasselbe wie zwei halbe Schritte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7280,"byte_start":7204,"id":"section:a162f19357c7888ed065","kind":"chapter","labels":["ch:memory"],"line_end":113,"line_start":112,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Gedächtnis: Was ein einzelnes Bild verschweigt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9410,"byte_start":7280,"id":"section:aba8d612c52806af1ce4","kind":"section","labels":[],"line_end":147,"line_start":114,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Ein klassisch-quantenmechanischer Zustand, kurz CQ-Zustand, besitzt 15 positive [formula in source] -Blöcke [formula in source] . Zusammen haben sie 240 reelle lineare Koordinaten und Gesamtspur eins. Die feste Regel macht jeden Ausgangsblock in seinem Kontext diagonal. Deshalb gilt Es ist also nicht richtig, 240 Koordinaten pauschal als kleinste dauerhaft autonome Hülle dieser festen Ausführung auszugeben.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Allgemeine Kontextblöcke brauchen eine andere Beschreibung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10711,"byte_start":9410,"id":"section:16a589c8a6d8f0e8b937","kind":"section","labels":["eq:record"],"line_end":168,"line_start":148,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Für die vier Projektoren eines Kontexts sind [formula in source] Spiegelungen. In Dimension vier gilt Allgemein in Dimension [formula in source] wäre die linke Seite [formula in source] . Der kurze Auslöschungseffekt ist hier also tatsächlich viererspezifisch.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie die Aufzeichnung gebaut wird","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12540,"byte_start":10711,"id":"section:962c8533f9e454b6849c","kind":"section","labels":[],"line_end":182,"line_start":169,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Für einen gleichförmigen reinen Eingang in der gewählten Kontextbasis erzeugt eine Vormessung maximale Verschränkung. Ohne Registerblick ist der Systemzustand [formula in source] . Nun gibt es zwei Ausführungen: Derselbe kohärente Speicher wird nochmals gekoppelt: [formula in source] stellt den reinen Eingang wieder her. Ein neuer Speicher wird benutzt: Im reduzierten System wird die Dephasierung wiederholt; [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das Echo des behaltenen Registers","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13348,"byte_start":12540,"id":"section:589a946b56d666f34e73","kind":"section","labels":[],"line_end":192,"line_start":183,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Bei frischen Registern trägt eine Folge von Kontexten den kohärenten Zustand Das Weglassen des Registers summiert Dichteoperatorbeiträge. Eine kohärente Projektion auf eine Registersuperposition summiert Amplituden und beschreibt ein anderes Experiment, einschließlich seiner Erfolgswahrscheinlichkeit.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reihenfolge bleibt wichtig","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15023,"byte_start":13348,"id":"section:5981c70768451e09939b","kind":"section","labels":[],"line_end":205,"line_start":193,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Eine nichtverschwindende Beobachtungsfolge eines geschlossenen endlichen Systems mit festem unitärem Schritt ist eine endliche Summe von Phasenfaktoren. Nach Zusammenfassung gleicher Frequenzen besitzt ihr mittleres Betragsquadrat einen positiven Cesàro-Grenzwert. Sie kann daher nicht für alle [formula in source] exakt wie [formula in source] abklingen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Endliches Gedächtnis und scheinbares Vergessen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":72,"byte_start":0,"id":"section:64eb230ce5d04215696f","kind":"chapter","labels":["ch:zelle"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die Vierträgerzelle: ein gemeinsames Muster","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1404,"byte_start":72,"id":"section:f83bc6e9e579cac2a29a","kind":"section","labels":["eq:omega"],"line_end":24,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Vier Träger mit je vier Basiswerten besitzen den total antisymmetrischen Zustand Jedes Basiswort verwendet alle vier Werte genau einmal. Die 24 Permutationen erhalten passende Vorzeichen. Das Ergebnis ist ein reiner gemeinsamer Zustand. Jeder einzelne Träger sieht für sich trotzdem maximal gemischt aus: Die Paarreduktion hat Rang sechs und sechs gleich große Eigenwerte [formula in source] . Die Ordnung steckt in den ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein Zustand, dessen Teile allein nichts verraten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2609,"byte_start":1404,"id":"section:1038cd07236a648f2bef","kind":"section","labels":[],"line_end":38,"line_start":25,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Sei [formula in source] der Projektor auf den symmetrischen Paarraum. Wenn für alle Paare [formula in source] gilt, dann hat jeder Swap Eigenwert minus eins. Da Transpositionen alle Permutationen erzeugen, folgt Für [formula in source] ist dieser Raum eindimensional, für [formula in source] null. Auch gemischte Zustände mit entsprechender Trägerbedingung erfüllen die Aussage. Für [formula in source] existieren aber e","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Hüllensatz und seine genaue Voraussetzung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3902,"byte_start":2609,"id":"section:2db9128f701e274c12bc","kind":"section","labels":["eq:tet-spec"],"line_end":54,"line_start":39,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Das vollständige Tetramermodell lautet Es besitzt das exakte Spektrum Der Grundzustand ist [formula in source] , die Lücke [formula in source] . Die hochgestellten Zahlen zählen die Zustände pro Energiewert und summieren sich zu 256.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine weiche Energiebedingung erlaubt Bewegung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5057,"byte_start":3902,"id":"section:5296c496d0ba87b1f145","kind":"section","labels":[],"line_end":68,"line_start":55,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Der vollständige Graph, ein Stern und ein Pfad besitzen auf vier Trägern denselben antisymmetrischen Grundzustand, aber verschiedene Anregungen. Für gleiche Sterngewichte ist die Lücke [formula in source] statt [formula in source] . S01 nennt für einen Pfad mit Gewichten [formula in source] etwa [formula in source] ; S06 für sechs Gewichte [formula in source] etwa [formula in source] . Die letzten Werte werden hier a","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was ein Zustand über seinen Generator verrät","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5655,"byte_start":5057,"id":"section:884d456ca793fe643ce0","kind":"section","labels":[],"line_end":73,"line_start":69,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Der Projektor [formula in source] kommutiert mit allen Swaps. Daher erhält jede rein zellinterne Austauschentwicklung, auch mit zeitabhängigen Gewichten, den Anteil [formula in source] . Kollektive [formula in source] -Drehungen tun dasselbe. Ein Grundzustand kann also bekannt sein, ohne dass der vorhandene Ablauf einen beliebigen Eingang dorthin bringt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum Austausch allein die Zelle nicht herstellt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6196,"byte_start":5655,"id":"section:409ac0e605de7a30ff9a","kind":"chapter","labels":["ch:fugen"],"line_end":78,"line_start":74,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Aktualisierung v1.5: ein exakter kleinerer Spektralauftrag Der 80-dimensionale Standard-Multiplizitätsblock ist inzwischen explizit konstruiert und sein einfaches Spektrum exakt zertifiziert. Eine zusätzliche Tableau-Transposition reduziert die führenden Singulettprobleme auf höchstens 131-dimensionale quadrierte Singularwertprobleme. Das beweist noch keine globale Ordnung aller SU(4)-Sektoren. Siehe Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vermittlung und Graph: die Prüfung der fünf Fugen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":8348,"byte_start":6196,"id":"section:5909d8e2b5e1bf87b02a","kind":"section","labels":[],"line_end":106,"line_start":79,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Der gewünschte positive Austausch lässt sich in einem kleinen Modell genau erklären. Man ergänzt den Paarraum [formula in source] durch einen sechsdimensionalen Vermittler mit Energie [formula in source] . Die partielle Isometrie [formula in source] erfüllt Für bleiben die zehn symmetrischen Zustände bei null; die antisymmetrischen Zustände koppeln paarweise an den Vermittler. Die unteren Energien sind Nach Identifik","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie ein virtueller Zwischenzustand bindet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10339,"byte_start":8348,"id":"section:0160fe83f84851d29fa3","kind":"section","labels":[],"line_end":128,"line_start":107,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"S11 macht die zusätzliche Zuordnung: Ein [formula in source] -Spinorgewicht [formula in source] ist ein Ort; das [formula in source] -Gewicht [formula in source] ist der lokale Viererzustand. Die 64 Gewichte von [formula in source] werden somit als 16 Orte mit je vier inneren Zuständen gelesen. Das ist eine konkrete bedingte Interpretation, keine bloße Umbenennung einer bereits gegebenen räumlichen Geometrie.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Clebsch-Vorschlag: eine genaue neue Graphlesart","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12378,"byte_start":10339,"id":"section:d10949e60ab69b7f1911","kind":"section","labels":[],"line_end":137,"line_start":129,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Die Graphkombinatorik folgt aus der angegebenen Ortslesart. Um daraus einen Vielteilchen-Hamiltonoperator zu erhalten, braucht man außerdem eine Fock- oder Tensorproduktstruktur, Besetzungsbedingungen, die Bedeutung der virtuellen Zustände und ihre Energien. Betragsgleiche Chevalley-Strukturkonstanten wählen noch keine physikalischen Kopplungsstärken in normierten Mehrteilchenzuständen aus. Gleiche [formula in source","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Welche Auswahl hier noch hinzukommt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13990,"byte_start":12378,"id":"section:239070ae5747a9481922","kind":"section","labels":[],"line_end":156,"line_start":138,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"L74mmY Clebsch-Cluster bei [formula in source] , nach S11& Berichteter Wert\\\\ Grundenergie& [formula in source] \\\\ Grundzustand&Eindeutiges [formula in source] -Singulett, Form [formula in source] \\\\ Erster angeregter Singulettwert& [formula in source] ; mindestens vier orthogonale Moden, Gap etwa [formula in source] \\\\ Erste adjungierte Anregung& [formula in source] , Gap etwa [formula in source] \\\\ Weitere Multiple","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die berichteten Clusterzahlen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15171,"byte_start":13990,"id":"section:8363ffc68c1a1b2ebd31","kind":"section","labels":[],"line_end":172,"line_start":157,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"S11 behauptet für den vollständigen Graphen mit [formula in source] einen eindeutigen Grundzustand bei [formula in source] und Gap [formula in source] . Energie und Gap stimmen; die Eindeutigkeit stimmt ab acht Trägern nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neue Korrektur: Singulett heißt nicht eindeutig","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17451,"byte_start":15171,"id":"section:510cfbe0664258144ed1","kind":"section","labels":[],"line_end":194,"line_start":173,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Operatoren unterscheiden (v1.3): Das folgende [formula in source] beschreibt eine gleichkontextige Vierer-Aufzeichnung. Das neue binäre Austauschregister [formula in source] ist ein anderer Operator und nachweislich nicht Clifford. Seine zusätzliche Ressourcenanforderung widerspricht der folgenden Darstellbarkeit von [formula in source] nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neue Präzisierung: Aufzeichnung ist nicht durch die 248 verboten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":504,"byte_start":0,"id":"section:3c16bae1fb5a1fc604ce","kind":"chapter","labels":["ch:two"],"line_end":5,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Aktualisierung v1.5: der Übergang zu vielen Zellen ist genauer Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei Zellen: aus Verbindung wird Dynamik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1277,"byte_start":504,"id":"section:370253b895704d37693d","kind":"section","labels":[],"line_end":10,"line_start":6,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Ist eine reduzierte Dichtematrix [formula in source] rein, so muss der gemeinsame Zustand bezüglich [formula in source] und seinem Rest faktorisiert sein. Sein Träger liegt in [formula in source] . Sind alle disjunkten Zellmarginalien unverändert rein, ist der Gesamtzustand ein Produkt über die Zellen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die Zellen beim Verbinden ihre Reinheit verlieren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2313,"byte_start":1277,"id":"section:74848c2832d28c5d86fc","kind":"section","labels":["eq:Hred"],"line_end":31,"line_start":11,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Zwei vollständige Tetramerzellen mit genau einer Brücke haben Der volle Raum besitzt [formula in source] Dimensionen. Trotzdem bleibt die Entwicklung des Produktzustands in einem zweidimensionalen invarianten Unterraum: Die beiden Vektoren sind orthonormal; [formula in source] und [formula in source] . Es folgt Die Brücke koppelt den Produktgrundzustand an eine gemeinsame adjungierte Anregung. Beide Zellhälften verwe","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein kleiner exakter Raum in einem großen Hilbertraum","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4682,"byte_start":2313,"id":"section:b11e21b0535a0af588ea","kind":"section","labels":["eq:alllambda13","eq:gapbound"],"line_end":76,"line_start":32,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Mit lauten die beiden Eigenwerte Die negative Korrektur beschreibt die Absenkung gegenüber dem einfachen Produktwert [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Energie und ein wirklicher Grundzustandsnachweis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5883,"byte_start":4682,"id":"section:490b52b957973c8bfc05","kind":"section","labels":[],"line_end":98,"line_start":77,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Der niedrige Eigenzustand lässt sich schreiben als Seine Zellreduktion besitzt das Spektrum Die Entropie in natürlichen Logarithmen ist Bei [formula in source] sind [formula in source] und [formula in source] ; bei [formula in source] gilt [formula in source] . Schon eine endliche einzelne Brücke macht die lokale Zelle gemischt. Energieabsenkung und Verschränkung sind hier keine unabhängig eingesetzten Zusätze.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verschränkung aus derselben Kopplung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6998,"byte_start":5883,"id":"section:6c08fd93699a9461c956","kind":"section","labels":["eq:two-clock"],"line_end":114,"line_start":99,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Starte im Produkt [formula in source] und lasse denselben konstanten gekoppelten Hamiltonoperator wirken. Dann gilt Bei [formula in source] vereinfacht sich dies zu [formula in source] . Der Energieinhalt beider Zellen pulsiert in einem messbaren Muster.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein Uhrsignal ohne zusätzlich gewählten lokalen Tick","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7966,"byte_start":6998,"id":"section:88ef487d45bf0d4a1a49","kind":"section","labels":[],"line_end":123,"line_start":115,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Ein einzelner eindeutiger Singulettgrundraum besitzt keine logische Zustandsvielfalt. Das Produkt solcher Grundräume bleibt eindimensional. Wer alles auf diese Grundräume projiziert, erhält nur eine skalare Energie. Nichttriviale effektive Dynamik muss Anregungen, Randzustände, Multiplizitäten oder zusätzliche Vakuumsektoren behalten.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum viele Zellen noch ein eigener Schritt sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":71,"byte_start":0,"id":"section:175a9a60bc378701fc5d","kind":"chapter","labels":["ch:zeit"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Zeit: Takt, Uhrwerk und lesbare Veränderung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1193,"byte_start":71,"id":"section:b1a8e631d10d96b7513c","kind":"section","labels":[],"line_end":15,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Eine zyklische Matrix ist zunächst ein Taktmuster. Eine Dynamik sagt, wann welcher Zustand entsteht. Eine Uhr braucht zusätzlich eine beobachtbare Anzeige und eine Kalibrierung. Diese drei Ebenen müssen zusammenpassen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Drei Bedeutungen des Wortes Clock","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2069,"byte_start":1193,"id":"section:642ecbf0cfff9f9b2801","kind":"section","labels":[],"line_end":20,"line_start":16,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Der vollständige gleichgewichtete Tetramer-Hamiltonoperator ist eine zentrale Transpositionssumme. Deshalb kommutiert er mit jedem [formula in source] und jedem [formula in source] . Die Paarenergien ändern sich unter seiner freien Entwicklung nicht. Eine Tabelle, die nacheinander einen lokalen [formula in source] -Tick anwendet, ist somit kein Beweis, dass genau diese Anzeige unter [formula in source] von selbst läu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die Paarenergien unter dem Tetramer stillstehen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":3008,"byte_start":2069,"id":"section:dc69d61a116a7226008d","kind":"section","labels":[],"line_end":38,"line_start":21,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Ein präparierter nichtstationärer Zustand kann dennoch unter demselben Tetramer laufen. Für einen lokalen spurfreien hermiteschen Pauli [formula in source] mit [formula in source] setze Da [formula in source] , folgt Die lokalen Anzeigen oszillieren gegeneinander; ihre Summe bleibt null. Die Periode ist [formula in source] . Präparation, Ausleserichtung und die Kalibrierung von [formula in source] sind weitere Eingab","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine laufende lokale Anzeige im gesetzten Modell","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4494,"byte_start":3008,"id":"section:d5eecf92119433b9e645","kind":"section","labels":[],"line_end":57,"line_start":39,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Zerlege [formula in source] . Die vier [formula in source] sind orthonormal. Wähle zusätzlich Weil jedes Wort von [formula in source] jedes Energielabel einmal enthält, gilt [formula in source] . Für erhält man [formula in source] . Die Zeiten [formula in source] liefern vier orthogonale Anzeigen. Global ist der Zustand stationär, bedingt auf die Uhranzeige entwickelt sich das System. Das ist eine konkrete Page-Woott","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine relationale Viereruhr ist konstruierbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":5172,"byte_start":4494,"id":"section:11e557e98cb7d0b998fb","kind":"section","labels":[],"line_end":62,"line_start":58,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Aus [formula in source] folgt [formula in source] . Die historischen Größen [formula in source] und [formula in source] beschreiben deshalb sechsfach wiederholte Faktoren [formula in source] und [formula in source] . Eine physikalische Rate ist erst [formula in source] für einen festgelegten Schritt [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum ein Logarithmus noch keine Sekunde ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5883,"byte_start":5172,"id":"section:8afa07664a4dc0576c36","kind":"chapter","labels":["ch:echo"],"line_end":67,"line_start":63,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Verschiedene Präparationsverträge bleiben getrennt Dieses Kapitel bewahrt die ursprüngliche endliche Schaltung mit Erfolg [formula in source] aus dem vorausgesetzten Zweisingulett-Eingang. Der neue Stern-Spektralfilter erreicht [formula in source] aus demselben Eingang, setzt aber kontrollierte kontinuierliche Pulse voraus. Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die ausführbare Präparation und der Mehrzeittest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7250,"byte_start":5883,"id":"section:4786ea6bb60b615ff394","kind":"section","labels":[],"line_end":89,"line_start":68,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Die Präparationsnotiz S02 geht über den abstrakten Satz „ [formula in source] existiert“ hinaus. Sie beschreibt eine konkrete Schaltung, die aus einem einfachen Eingang den Zustand mit Erfolgsanzeige herstellt, anschließend ein Register schreibt und die Rückkehr ausliest. Laut Quelle wurde die Schaltung exakt simuliert, nicht auf Hardware ausgeführt. Ihr Zugriff auf zusätzliche Hilfssysteme und Nicht-Clifford-Operati","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was S02 tatsächlich geschlossen hat","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8727,"byte_start":7250,"id":"section:32cc9e8017bf955306f1","kind":"section","labels":[],"line_end":104,"line_start":90,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Der benötigte Zustand [formula in source] ist in der Acht-Qubit-Kodierung kein Stabilizerzustand. Schon für einen nichttrivialen lokalen Pauli gilt während reine Qubit-Stabilizerzustände für Pauli-Observablen nur [formula in source] liefern. Ebenso ist der Paarreduktionsrang sechs keine Zweierpotenz. Eine exakte Präparation aus einem Stabilizer-Eingang benötigt deshalb eine zusätzliche Ressource, etwa einen passenden","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die zusätzliche Ressource bleibt sichtbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9859,"byte_start":8727,"id":"section:9a970a42813ece21f107","kind":"section","labels":[],"line_end":126,"line_start":105,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Der einfache Eingang lautet Er ist mit dem in S02 angenommenen Clifford-Baukasten präparierbar und besitzt [formula in source] -Anteil [formula in source] . Der Antisymmetrisierer ist Die konkrete Schaltung erzeugt 32 Kontrollzweige, von denen 24 die Permutationen tragen. Acht ungültige Zweige werden markiert. Nach Interferenz und Erfolgsselektion ist der implementierte Operator Somit gilt Der erfolgreiche Zweig ist ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie der Filter den Zustand erzeugt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11835,"byte_start":9859,"id":"section:bab0d21ea7a07e325c0a","kind":"section","labels":["eq:originalecho"],"line_end":163,"line_start":127,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] schreibe [formula in source] . Dann Ein ignorierter frischer Pointer erzeugt Diese binäre Swap-Aufzeichnung ist ein anderer Kanal als die 15-Kontext-Mischung mit Faktor [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das ursprüngliche Echo: eins gegen siebzehn Zweiunddreißigstel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13337,"byte_start":11835,"id":"section:ae4dfc38ed84ad709e70","kind":"section","labels":[],"line_end":183,"line_start":164,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Der Endfilter hat den Effekt [formula in source] . Seine beobachtbare Erfolgsrate ist deshalb [formula in source] , nicht [formula in source] selbst. L68mmY Y Statistik& Behalten& Frisch\\\\ [formula in source] -Rückkehr, bedingt auf Präparation& [formula in source] & [formula in source] \\\\ Endfilter erfolgreich, bedingt auf Präparation& [formula in source] & [formula in source] \\\\ Beide Filter erfolgreich, je begonnen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die wirklichen Erfolgswahrscheinlichkeiten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15734,"byte_start":13337,"id":"section:86f7d74858e716121317","kind":"section","labels":["eq:optimal"],"line_end":210,"line_start":184,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Eigene exakte Ergänzung dieser Synthese. Man kann die gleiche Messfrage für einen beliebigen lokalen unitären Tick [formula in source] ausrechnen. Setze Die beiden Swap-Gewichte sind [formula in source] . Daher Der Kontrast dieser Rückkehrstatistik ist maximal, wenn [formula in source] , also [formula in source] . Ein einzelnes CNOT innerhalb des Viererträgers erfüllt [formula in source] . Es permutiert dieselbe Meng","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neue Fortsetzung: der maximal ausgeglichene Echovergleich","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17149,"byte_start":15734,"id":"section:a4c14923a6ac2bf772f6","kind":"section","labels":[],"line_end":218,"line_start":211,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Y r Ressource nach S02& Anzahl\\\\ Systemqubits&8\\ , wiederverwendet&10\\ ätze&2\\ reservierte Qubits&20\\ Erfolgsbits beider Filter&12\\ -Gatter&574\\ CNOT vor Toffoliauflösung&382\\ &26\\ - [formula in source] / Pauli- [formula in source] &276 / 26\\\\T/T^ [formula in source] T-Varianten waren durch lokale Matrixidentität und Ersetzung zertifiziert, nicht zusätzlich als komplette komplexe 20-Qubit-Vektoren simuliert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ressourcen und Beweisgrenze der Originalschaltung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":75,"byte_start":0,"id":"section:bc926767aaf26e92fbf1","kind":"chapter","labels":["ch:seam"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Von der Kette zur E [formula in source] 8-Naht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1943,"byte_start":75,"id":"section:b85f697716366fb5ab2c","kind":"section","labels":[],"line_end":28,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Das Zweizellenmodell benutzt zwei vollständige Vierergraphen mit einer Brücke. Die Vielzellenrechnung in S08 benutzt dagegen Vierersegmente mit nächster Nachbarschaft. Bei [formula in source] wird erst dieses zweite Modell eine uniforme Kette. Derselbe isolierte Singulettzustand garantiert keine identischen Anregungen und keinen identischen Grenzwert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein wichtiger Modellwechsel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3203,"byte_start":1943,"id":"section:cab18638441ec0851463","kind":"section","labels":[],"line_end":44,"line_start":29,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Für den uniformen periodischen Austauschring liefern die Quellen [formula in source] bei acht und [formula in source] bei zwölf Trägern. Der bekannte Vergleich lautet Die Sutherland-Grundenergie pro Träger ist für [formula in source] . S08 nennt die Extrapolation [formula in source] und [formula in source] . Diese endlichen Zahlen passen zur [formula in source] -WZW-Beschreibung des Kettenmodells. Die allgemeine Verb","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die SU(4)-WZW-Theorie hier plausibel ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4699,"byte_start":3203,"id":"section:2110583e4d72b7434b79","kind":"section","labels":[],"line_end":70,"line_start":45,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Die zentrale Ladung ist eine Kennzahl einer konformen Feldtheorie. Für die chiralen Niveau-1-Faktoren gilt Das Produkt hat also schon vor einer Kopplung [formula in source] . Ein später gefundener Wert acht allein ist kein Beweis einer [formula in source] -Erweiterung und kein Beweis eines Kondo-Flusses.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Naht braucht mehr als die Zahl acht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6584,"byte_start":4699,"id":"section:2151b0bd7a80e73d8153","kind":"section","labels":[],"line_end":92,"line_start":71,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"S11 ersetzt die frühere Kondo-Zielbeschreibung sinnvoll durch eine konkrete Erweiterungsaufgabe. Die Kurzschreibweise eines Quotienten durch [formula in source] kann jedoch verschiedene Operationen meinen. Nur auf invariante Zustände des ursprünglichen Produkts zu projizieren ist nicht dasselbe wie eine Simple-Current-Erweiterung mit den nötigen zusätzlichen beziehungsweise entsprechend gekoppelten Sektoren.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum „Z [formula in source] 4-Eichung“ präzisiert werden muss","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7319,"byte_start":6584,"id":"section:ffcdd3702c7947168b59","kind":"section","labels":[],"line_end":97,"line_start":93,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Eine gewöhnliche kritische SU(4)-Kette hat links- und rechtslaufende Sektoren, mit [formula in source] . Die übliche Kennzahl heißt dabei [formula in source] , nicht sechs. Die chirale Differenz ist null. Eine rein chirale [formula in source] -Naht hat dagegen Differenz acht. Ein zusätzliches ebenfalls nichtchirales [formula in source] -Modell ändert daran nichts.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Chiralitätslücke","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8698,"byte_start":7319,"id":"section:0d359d1ab7db2c14501d","kind":"section","labels":[],"line_end":103,"line_start":98,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Die innere Glue- [formula in source] wirkt auf den 248 Strömen mit Phasen [formula in source] auf Sektoren der Größen [formula in source] . Ihre Spur ist null. Die geometrische Vierteldrehung [formula in source] hat auf Stufe eins dagegen Spur [formula in source] . Die Operatoren sind somit nicht identisch. Eine Clock kann eine geometrische Drehung mit innerem Twist kombinieren; die beiden Faktoren bleiben getrennt. ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei Vierteldrehungen und der Index","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":551,"byte_start":0,"id":"section:2c7cb450b633cd506d08","kind":"chapter","labels":["ch:recon"],"line_end":5,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Fortschritt v1.3 Ein gemeinsamer endlicher Träger realisiert nun Aufzeichnung, Näherungspräparation, Reset und Mehrzeitantwort unter einem ausdrücklich angegebenen Ressourcenvertrag. Das beantwortet eine bedingte Existenzfrage. Es wählt weder den Vertrag aus TFPT allein noch ein universelles positives Zustandsfunktional aus. Die nachfolgenden Anforderungen bleiben deshalb nötig; die Konstruktion steht in Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie eine vollständige Rekonstruktion aussehen könnte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1946,"byte_start":551,"id":"section:fa3ab8dbe4dcf450e729","kind":"section","labels":[],"line_end":17,"line_start":6,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Eine endliche Liste von Schatten bestimmt im Allgemeinen mehrere Prozesse. Man kann sogar jeden Kandidaten um einen ungekoppelten unsichtbaren Hilfsfaktor ergänzen, auf den alle erlaubten Experimente trivial wirken. Alle Antworten bleiben gleich. Eindeutigkeit ist daher zunächst nur für die minimal beobachtbare Darstellung erreichbar.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vom Wunsch nach Eindeutigkeit zu einer prüfbaren Frage","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2535,"byte_start":1946,"id":"section:de1471cd8eba1af4f664","kind":"section","labels":[],"line_end":24,"line_start":18,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Eine Projektion kann wichtige Wahrscheinlichkeiten erhalten und trotzdem die Multiplikation zerstören. S03 gibt einen einfachen Gegenbeleg: Projiziere [formula in source] auf [formula in source] und definiere [formula in source] . Dann Die neue Multiplikation ist nicht assoziativ. Eine nützliche reduzierte Vorhersagebeschreibung darf also nicht ohne zusätzlichen Nachweis als geschlossene physische Operationsalgebra v","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine kleinere Beschreibung ist nicht automatisch eine Algebra","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4676,"byte_start":2535,"id":"section:8cbe023bd4a4ddb96135","kind":"section","labels":[],"line_end":52,"line_start":25,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Eine phasentreue Rekonstruktion braucht mehr als eine Tabelle einzelner Wahrscheinlichkeiten. Ein passender Ausgangspunkt ist eine komplexe Algebra [formula in source] mit Einheit, Multiplikation, Adjunktion und einem positiven normierten Zustandsfunktional [formula in source] : Für Operationswörter [formula in source] definiert einen positiven semidefiniten Korrelationskern. Er enthält die relativen komplexen Phasen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was vollständige Phaseninformation zusätzlich bringt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5967,"byte_start":4676,"id":"section:b8cc9e1770c19fbb494d","kind":"section","labels":[],"line_end":65,"line_start":53,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Ein Prozesstensor beziehungsweise Quantenkamm ordnet einer Folge von Instrumenten gemeinsame Ergebniswahrscheinlichkeiten zu. Positivität und kausale Normierungsregeln sichern die Konsistenz. Eine tomographisch vollständige Eingriffsfamilie bestimmt einen endlichen Prozesstensor; sie bestimmt nicht automatisch eine eindeutige verborgene Umgebung oder sämtliche unendlichen Horizonte.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Mehrzeitdaten statt einer einzigen Dichtematrix","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7082,"byte_start":5967,"id":"section:f1b30d30338806e459b6","kind":"section","labels":[],"line_end":72,"line_start":66,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"S05 schlägt eine nützliche endliche Vorgehensweise vor: Man fixiert zulässige Operationswörter bis Länge [formula in source] , ihre Relationen, Symmetrien und die belegten Auslesungen. Die unbekannten Momente müssen eine positive Momentenmatrix bilden. Dann minimiert und maximiert man eine noch offene Ausgabe [formula in source] über alle kompatiblen Modelle.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein konkreter Auswahltest für offene Größen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9427,"byte_start":7082,"id":"section:94f044dcb64af3ea43cf","kind":"section","labels":[],"line_end":106,"line_start":73,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Die in S03 vorgeschlagene Alternative verwendet als lokalen Viererverknüpfungstensor. An orientierten Verbindungen werden Trägerräume mit ihren dualen Räumen kontrahiert. So verbindet man Amplituden, ohne jede physische Zellreduktion als unverändert reines [formula in source] festzuschreiben.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Zelle als Verknüpfungsamplitude","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10340,"byte_start":9427,"id":"section:eedb751aeab395d0909e","kind":"section","labels":[],"line_end":111,"line_start":107,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Paarweise kommutierende volle Matrixunteralgebren, die gemeinsam die Gesamtalgebra erzeugen, bestimmen im endlichen Fall eine Tensorproduktstruktur bis auf lokale Basiswechsel und Umbenennungen. Bei nichttrivialem Zentrum können stattdessen Sektoren übrigbleiben. Die Auswahl der privilegierten Unteralgebren aus den Wechselwirkungen ist der eigentliche inverse Schritt. https://arxiv.org/abs/quant-ph/0308043Zanardi, Li","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Teilsysteme aus Beziehungen erkennen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11809,"byte_start":10340,"id":"section:d956a017e3686749e3cb","kind":"section","labels":[],"line_end":122,"line_start":112,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"S08 untersucht einen neutralen Sektor aus 70 Materiemasken und Schleifenfluss, insgesamt 1190 Zuständen. In einer festgehaltenen lokalen Operatorliste wird über der Generator rekonstruiert. Nach Entfernen trivialer Identitätsrichtungen reproduziert der Grundzustand die Koeffizienten [formula in source] , [formula in source] , [formula in source] und [formula in source] . Ein zusätzlicher angeregter Zustand verbessert","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was das Zustandsgate am Rotor/CAR-Ring prüft","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":547,"byte_start":0,"id":"section:aa293382fc4702acc1d6","kind":"chapter","labels":["ch:physik"],"line_end":5,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Raumzeit, Materie und Gravitation aus demselben Ursprung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2438,"byte_start":547,"id":"section:02b0fe20d51712c3d749","kind":"section","labels":[],"line_end":33,"line_start":6,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Ein markierter [formula in source] -Block trägt die hermitesche Matrix Ihre Determinante ist exakt Die Eigenwerte sind [formula in source] . Deshalb entspricht [formula in source] dem Zukunftskegel [formula in source] . Die Kongruenz [formula in source] mit [formula in source] erhält die Determinante und den positiven Kegel.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Lorentzkegel: eine echte, aber begrenzte Brücke","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4186,"byte_start":2438,"id":"section:b91bae28d4e5120f0a6f","kind":"section","labels":[],"line_end":50,"line_start":34,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"S03 formuliert eine nützliche bedingte Brücke. Angenommen, derselbe Prozess liefert einen lokalen kohärenten Zweikomponentensektor mit inverser Zweipunktfunktion Dann folgt Für invertierbares [formula in source] ist dies eine Lorentzform. Jetzt wäre der Kegel aus einem tatsächlichen Propagator gewonnen. Vorausgesetzt sind jedoch ein sinnvoller Impulsraum, ein kontrollierter lokaler Grenzprozess, ein kohärenter Pol un","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der präzise nächste Schritt: den Kegel aus der Ausbreitung gewinnen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5285,"byte_start":4186,"id":"section:29b4c634e41cea6041bd","kind":"section","labels":[],"line_end":61,"line_start":51,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Eine mögliche Materieanregung muss stabil oder kontrolliert propagierend sein. Man benötigt ihr Spektrum, ihre Ladungen, chirale Ausbreitung, erlaubte Vertizes und das Verschwinden unerwünschter Spiegelpartner. Eine vorkommende Darstellung allein erfüllt das nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Materie ist mehr als eine Ladungstabelle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6273,"byte_start":5285,"id":"section:ea9cd485fcdc64a4e239","kind":"section","labels":[],"line_end":70,"line_start":62,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Eine Algebra mit Darstellung und geeignetem Diracoperator kann Geometrie kodieren. Beispielsweise macht die Distanzformel sichtbar, warum nicht nur Eigenwerte, sondern die Relation zwischen [formula in source] und den Observablen zählt. Connes' kommutativer Rekonstruktionssatz benötigt starke Spektralaxiome und liefert eine kompakte glatte Riemannsche Mannigfaltigkeit. Er erzeugt keine lorentzsche 3+1D-Welt aus einer","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spektrale Geometrie hilft, ersetzt aber keine fehlenden Daten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":7482,"byte_start":6273,"id":"section:ea23a854ee28f910ebb9","kind":"section","labels":[],"line_end":83,"line_start":71,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Die Identität [formula in source] passt zu einer bekannten Normierung. 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Aus ihren gekoppelten Anregungen und Aufzeichnungen entsteht ein kontrollierter gemeinsamer Grenzprozess. Erst dieser Grenzprozess liefert Raumzeit, chirale Materie, Wechselwirkungen und gegebenenfalls Gravitation. Die erste ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die präziseste gemeinsame Hypothese","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4033,"byte_start":0,"id":"section:fc73e2085e6949b5d171","kind":"chapter","labels":["app:corrections"],"line_end":28,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"L46mmL77mmL27mm Frühere Formulierung& Konsolidierte Aussage& Herkunft\\\\ Aus zwei Zahlen folgt der ganze Aufbau.&P1/P2 enthalten Orientierung, Positivität, Trägerart und Markierungen. Ihre Konsequenzen sind von ihrer Auswahl verschieden.&S09; S05/S06\\\\ Die Kontextregel ist symmetrieerzwungen.& [formula in source] ist eine konkrete gleichgewichtete Realisierung; die kovariante Familie [formula in source] bleibt ein Geg","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Korrekturregister und ergänzende Details","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5908,"byte_start":4033,"id":"section:af78983c46ac4a3cd20a","kind":"section","labels":[],"line_end":37,"line_start":29,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"S09 berichtet für ein früheres Majoranamodell zehn zugängliche und sechs verborgene reelle Richtungen, entsprechend einer [formula in source] -Zerlegung auf Fockebene. Verschränkung allein macht einen verborgenen Zustand nicht am Rand lesbar; eine geeignete Kopplung oder erweiterte Messung ist nötig. Ein dort gebauter Ereigniskanal übertrug Besetzung, besaß aber weiterhin eine nichttriviale Fixalgebra. Übertragung un","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Frühere Nebenstränge, die im Gesamtbild erhalten bleiben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10041,"byte_start":5908,"id":"section:0086f47a322276a12361","kind":"chapter","labels":[],"line_end":74,"line_start":38,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"L34mmL116mm Begriff& Bedeutung in diesem Dokument\\\\ Adjungierte&Die Darstellung einer Lie-Algebra auf ihren eigenen Generatoren durch die Klammer; nicht automatisch der gesamte Raum physischer Zustände.\\\\ Adjunktion [formula in source] &Komplex konjugierte Transposition beziehungsweise die passende Operatoradjunktion. Nicht dasselbe Wort wie adjungierte Darstellung.\\\\ Algebra&Ein Raum von Objekten mit Regeln für Addi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Begriffe in einfachen Worten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10087,"byte_start":10041,"id":"section:b495c162b77c546b556e","kind":"chapter","labels":[],"line_end":75,"line_start":75,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Quellen, Abdeckung und Reproduktion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10437,"byte_start":10087,"id":"section:a0969530910194e174f1","kind":"section","labels":[],"line_end":79,"line_start":76,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Die Quellenkürzel S01 bis S11 gelten durchgängig für dieses Buch und sind von den jeweils eigenen Kürzeln der Anhänge zu unterscheiden. Die vollständigen Originalpfade und SHA-256-Werte stehen im beiliegenden Manifest. Hier werden die Dateinamen und inhaltlichen Rollen aufgeführt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die elf Eingabedokumente","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":12676,"byte_start":10437,"id":"section:248068d71fd6ffb1550a","kind":"section","labels":[],"line_end":96,"line_start":80,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Der eigenständige Prüfer importiert keinen Code des ursprünglichen TFPT-Repositoriums. Die Standard-Zwei-Qubit-Kontexte wurden aus den üblichen Pauli-Matrizen rekonstruiert. Das kontrolliert die endlichen im Text angegebenen Beziehungen, ist aber kein erneuter phasentreuer Import des nativen Gauß- [formula in source] -Adapters.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was neu geprüft wurde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13823,"byte_start":12676,"id":"section:1450cf85beb9400a1170","kind":"section","labels":[],"line_end":108,"line_start":97,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"L16mmL41mmY Quelle& Berichtete Prüfung& Reichweite\\\\ S09&11214 Bedingungen pro Modus, elf Negativvarianten&Ursprungsaudits und Zahlenprüfungen; kein vollständiger Lean-/RH-Neubau.\\\\ S07&325 + 147 Bedingungen, 19 Tests&Inversion und Follow-ups; mehrere spätere Minimalitätskorrekturen erforderlich.\\\\ S06&86 eigene Bedingungen sowie ausgewählte Originalreplays&45-/30-Quotienten, Uhr und Herkunftskontrollen; begrenzte Ke","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie die Quellen ihre eigenen Prüfungen beschreiben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":14798,"byte_start":13823,"id":"section:be2586a1c78ba44f7cbb","kind":"section","labels":[],"line_end":113,"line_start":109,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Das Paket enthält die vollständige LaTeX-Quelle, Kapiteldateien, Vektordiagramme, den eigenständigen Prüfer, die Ergebnisdatei und das Eingabemanifest. Mit einer LaTeX-Installation einschließlich LuaLaTeX, TikZ und den verwendeten Standardpaketen lässt sich das Buch durch zwei Läufe von lualatex main.tex im Quellverzeichnis bauen. Für die endlichen Gegenrechnungen werden Python, NumPy, SymPy, mpmath und Matplotlib be","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproduktionspaket dieser Synthese","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18166,"byte_start":14798,"id":"section:4452596e4ecd2bdad3f8","kind":"section","labels":[],"line_end":135,"line_start":114,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Die folgenden Quellen wurden zur fachlichen Einordnung beziehungsweise für den datierten Konstantenvergleich aufgerufen. Sie bestätigen die allgemeinen Werkzeuge, nicht die physikalische Richtigkeit von TFPT. Die spezifischen langen Herleitungen dieses Buches beruhen auf den Anhängen und den ausgeschriebenen Gegenrechnungen. F. A. Pollock et al.: Non-Markovian quantum processes: complete framework and efficient chara","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Externe Primärliteratur und Referenzdaten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18523,"byte_start":18166,"id":"section:cbe673e559c730b8f4b8","kind":"section","labels":[],"line_end":137,"line_start":136,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Die Anhänge wurden unverändert gelesen; ihre tatsächlichen Dateiinhalte sind durch SHA-256 dokumentiert. Dieses Buch aktualisiert keinen ursprünglichen Theorievertrag und keinen Abschlussmarker. Es liefert eine neue, zusammenhängende und prüfbare Darstellung mit ausdrücklich abgegrenzten eigenen Fortsetzungen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Abschluss der Dokumentation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":968,"byte_start":0,"id":"section:4c2a9c38af42ca6b2152","kind":"chapter","labels":["ch:shadow-arithmetic"],"line_end":8,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Was uns ein Schatten verraten kann Wenn wir nur den Schatten eines Rades sehen, erkennen wir vielleicht einen Kreis. Erst wenn wir das Rad drehen, belasten und mit einem zweiten Rad verbinden, erkennen wir seine Achse, seine Zähne und seine Übersetzung. Genau so lesen wir hier Primzahlen, Quanteneffekte und Raumzeit: als verschiedene Antworten, die eine mögliche gemeinsame Struktur gleichzeitig erklären müsste.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Primzahlen, RH und die Musik hinter den Schatten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":2819,"byte_start":968,"id":"section:da730ec8ae73a090903a","kind":"section","labels":["eq:primon-partition"],"line_end":25,"line_start":9,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Jede natürliche Zahl [formula in source] zerfällt eindeutig in Primfaktoren: Die erste Gleichung beschreibt ein Zusammensetzen durch Multiplikation; die zweite übersetzt dieses Zusammensetzen in Addition. Zum Beispiel ist [formula in source] , also [formula in source] . Die Primzahlen sind die unabhängigen Bausteine dieses multiplikativen Systems. Das ist ein Satz über natürliche Zahlen. Es ist noch kein Satz darüber","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"In welchem Sinn Primzahlen Bausteine sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":4018,"byte_start":2819,"id":"section:0f1ec001600bf88582ad","kind":"subsection","labels":[],"line_end":36,"line_start":26,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Warum gerade [formula in source] ? Aus [formula in source] allein folgt das noch nicht: Man darf jeder Primzahl zunächst einen beliebigen Wert [formula in source] geben. Eine zusätzliche Ordnungsregel schließt die Lücke. Ist [formula in source] monoton in der natürlichen Zahl [formula in source] , so gilt notwendig Der Beweis ist kurz. Setze [formula in source] . Aus [formula in source] folgen [formula in source] Div","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine bedingte Auswahlregel für die logarithmische Energie","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":7179,"byte_start":4018,"id":"section:b770260df0637ffb332e","kind":"section","labels":["eq:prime-trace"],"line_end":64,"line_start":37,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die häufig verkürzte Aussage Primzahlen tauchen als Quantenenergien auf umfasst verschiedene Sachverhalte. Beim klassischen Zeta–Quantenchaos-Vergleich entsprechen Nullstellenhöhen den Energien eines gesuchten Spektrums. Die Primzahlen spielen auf der anderen Seite die Rolle primitiver periodischer Bahnen; Primzahlpotenzen sind deren Wiederholungen. Eine Bahn wird einmal durchlaufen, zweimal, dreimal. Ihr logarithmis","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was Primzahlen mit Quantenchaos verbindet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":10149,"byte_start":7179,"id":"section:26956be24fffddcda5b5","kind":"section","labels":[],"line_end":81,"line_start":65,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die Unterlagen und der zusätzlich eingesehene Forschungsbestand ergeben keine abgeschlossene RH-Lösung. Sie ergeben jedoch eine ungewöhnlich präzise Landkarte aus positiven Bausteinen und bereits ausgeschlossenen Abkürzungen. Die folgende Verdichtung ordnet die inhaltlichen Familien; sie behauptet keine erneute Prüfung jedes Katalogeintrags.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was unser RH-Zweig tatsächlich beigetragen hat","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11189,"byte_start":10149,"id":"section:171e1728c5ae88592388","kind":"subsection","labels":[],"line_end":96,"line_start":82,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die ersten sechs Werte sind [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] und [formula in source] . Daraus folgt für [formula in source] Hier ist der Primzahlbezug wirklich vorhanden. Die Selbstdualität des Gitters schließt die Poisson-Transformation auf dasselbe Gitter. Poisson-Summation gilt auch für nichtselbstduale Gitter und verbindet dann Gitter und ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der genaue Ertrag der [formula in source] -Schalen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":12659,"byte_start":11189,"id":"section:756c734e7952f2013537","kind":"subsection","labels":[],"line_end":108,"line_start":97,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die entscheidende arithmetische Form enthält eine Differenz: vereinfacht [formula in source] . Zwei positive Matrizen können eine indefinite Differenz besitzen; schon [formula in source] hat die Eigenwerte [formula in source] und [formula in source] . Entsprechend löst ein beliebiger positiver Born- oder Gramkern die signierte Aufgabe noch nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die fehlende Positivität so hartnäckig ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14262,"byte_start":12659,"id":"section:8cb1d5b7919591505357","kind":"subsection","labels":[],"line_end":115,"line_start":109,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Der Jensen/Coxeter-Test r618 findet eine starre [formula in source] -Struktur auf der [formula in source] -Seite, während die verglichenen Jensen-Polynome mit ihrem Index variieren. Die gewählte Identifikation scheitert. Der Selberg-Kontakttest r638 besitzt im untersuchten Fall weiterhin einen negativen kleinsten Eigenwert von ungefähr [formula in source] ; eine Quadratvervollständigung hat die falsche signierte Form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was die negativen Routen konkret lehren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15958,"byte_start":14262,"id":"section:a4eb9473130b9bffa859","kind":"section","labels":[],"line_end":126,"line_start":116,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die vorhandene freie fermionische Naht hat bei fester Größe eine endliche Zustandssumme. Das Primonmodell verlangt eine unbegrenzte Primfamilie und andere Besetzungsdaten. Schon für [formula in source] gilt [formula in source] und [formula in source] : Der Pol bei [formula in source] entsteht erst in der unendlichen Familie. Eine endliche Demonstration kann ihn nicht besitzen. Der vorhandene Nahtvergleich findet ents","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Naht braucht mehr als ein paar zusätzliche Takte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16501,"byte_start":15958,"id":"section:1566ade42f1d0d96b052","kind":"section","labels":[],"line_end":129,"line_start":127,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Wei und Mitautoren verbinden in zwei gezielt konstruierten Quantensystemen Nullstellen mit dynamischen Phasenübergängen. Berichtet werden ein Fünf-Qubit-NMR-Prinzipversuch und weitergehende numerische Untersuchungen. Die verwendeten Hamiltonoperatoren und Zustandsgewichte sind so gewählt, dass sie Zeta-Daten kodieren. Das macht den Zusammenhang experimentell bearbeitbar; eine Ableitung dieser Wahl aus TFPT oder ein R","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die neue Quantenphasen-Arbeit von 2026","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":18843,"byte_start":16501,"id":"section:9c5ccc554a5399f9f61f","kind":"subsection","labels":["eq:eta-readout"],"line_end":150,"line_start":130,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Unabhängig vom vollständigen Ressourcenbeweis dieser Arbeit untersuchen wir den folgenden einfachen thermischen Eta-Auslesekanal: Er entsteht durch einen Gibbszustand für [formula in source] und eine diagonal ausgelesene Paritätsphase. Bei festem [formula in source] und [formula in source] konvergiert der Zähler gegen [formula in source] , während [formula in source] Also geht das Rohsignal [formula in source] an jed","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eigene Anschlussrechnung: Ein verschwindendes Signal ist mehrdeutig","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":541,"byte_start":0,"id":"section:ecf0937122f3ad0cc280","kind":"chapter","labels":["ch:shadow-quantum"],"line_end":6,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Nicht nur die Anzahl der Kugeln zählt Zwei Kästen können dieselben möglichen Messergebnisse enthalten und doch verschieden reagieren, wenn wir zuerst an einer anderen Stelle messen oder zwei Teile zusammenführen. Die Quantenphänomene sagen uns deshalb vor allem etwas über die Regeln des Zusammensetzens, über relative Phasen und über erlaubte Eingriffe. Genau diese Daten verliert ein einfacher Schatten leicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was Quantenphänomene über den verborgenen Aufbau sagen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1925,"byte_start":541,"id":"section:fb59ffd3d84aa0361292","kind":"section","labels":[],"line_end":21,"line_start":7,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Für zwei Alternativen mit Amplituden [formula in source] und [formula in source] lautet die Born-Regel [formula in source] Der letzte Term kann verstärken oder auslöschen. Wer ausschließlich die beiden Einzelwahrscheinlichkeiten aufbewahrt, kann ihn nicht rekonstruieren. Das erklärt im Kleinen, warum die behaltenen Register und Echoexperimente der früheren Kapitel mehr verraten als der erste sichtbare Markovschritt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Interferenz verlangt eine Information vor den Wahrscheinlichkeiten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4273,"byte_start":1925,"id":"section:f1bbb9286ac3f168e216","kind":"section","labels":[],"line_end":40,"line_start":22,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Die 15 Zwei-Qubit-Pauli-Kontexte der Synthese enthalten das folgende Mermin–Peres-Quadrat. Hier bedeutet [formula in source] und entsprechend für die anderen Einträge: Jede Zeile und jede Spalte ist gemeinsam messbar. Alle Zeilenprodukte sind positiv, aber das letzte Spaltenprodukt ist negativ. Diese sechs Kontexte gehören zum bereits verwendeten Pauli-System.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der vorhandene Baukasten enthält bereits Kontextualität","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5718,"byte_start":4273,"id":"section:1e96871d2668be2eb3d5","kind":"section","labels":[],"line_end":52,"line_start":41,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Für zwei räumlich getrennte Messstellen hat die CHSH-Kombination [formula in source] in einem lokalen Modell mit unabhängiger Wahl der Einstellungen die Grenze [formula in source] . Quantenmechanik erreicht [formula in source] . Mit [formula in source] , [formula in source] und [formula in source] ist der zugehörige Operator [formula in source] ; seine Eigenwerte sind [formula in source] . Beides wurde hier exakt nac","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verschränkung legt die Zusammensetzung fest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6899,"byte_start":5718,"id":"section:8d276ecbad5d1d11dba8","kind":"section","labels":[],"line_end":68,"line_start":53,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Wähle bei festgehaltenen Labor-Teilsystemen [formula in source] Beide Hamiltonoperatoren haben exakt die Energien [formula in source] . Der Grundzustand von [formula in source] ist ein Produktzustand, der von [formula in source] ein Bell-Zustand. Die Reinheit [formula in source] eines lokalen Teils beträgt entsprechend 1 beziehungsweise [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gleiche Energien können verschiedene Welten beschreiben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8198,"byte_start":6899,"id":"section:315124bd61c39deb2072","kind":"section","labels":[],"line_end":75,"line_start":69,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Die komplexe Vierdimensionalität ist für den bestehenden Pauli-/Spinorbaukasten passend. Eine direkte Ableitung der komplexen Zahlen aus einem einzelnen Quantenphänomen wäre trotzdem zu stark. Renou und Mitautoren untersuchen Quantennetzwerke, in denen die übliche reale und komplexe Theorie unter einer bestimmten Unabhängigkeits- und Kompositionsannahme verschiedene Vorhersagen machen. F10","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was komplexe Zahlen verraten und was offenbleibt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9556,"byte_start":8198,"id":"section:472b8e12ec7e00a99875","kind":"section","labels":[],"line_end":81,"line_start":76,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Die bisherigen Registerbeispiele erklären, wie ein global kohärenter Ablauf nach eingeschränktem Zugriff wie ein irreversibler Prozess aussehen kann. Sie liefern noch keine eindeutige Lösung des Messproblems: Insbesondere folgt aus einer diagonalen reduzierten Dichtematrix allein keine Auswahl eines einzelnen Ereignisses. Eine zusätzliche Kollapsdynamik müsste messbare Abweichungen angeben; eine unitäre Beschreibung ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Messung, Zeitpfeil und Statistik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":900,"byte_start":0,"id":"section:c0b927e75326f3d76f7f","kind":"chapter","labels":["ch:shadow-dimension"],"line_end":8,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"Dimension ist die Antwort auf eine Frage Eine Ameise auf einer dünnen Schnur kann entlang einer Richtung laufen. Auf einem Blatt kann sie außerdem ausweichen. In einem Zimmer kann sie auch über ein Hindernis hinweg. Eine Dimension zählt solche unabhängigen Möglichkeiten. Die Zahl der inneren Zustandskomponenten oder der Knöpfe eines Geräts ist etwas anderes.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Drei Raumrichtungen und eine Zeit: Welche Bedingungen bleiben?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2245,"byte_start":900,"id":"section:11bb356a9b3353e59fbd","kind":"section","labels":[],"line_end":23,"line_start":9,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"Ein traceloses hermitesches [formula in source] -Objekt hat genau drei reelle Komponenten: [formula in source] Ergänzt man [formula in source] , ergibt die Determinante [formula in source] Der positive Kegel erfüllt [formula in source] . Das ist die präzise Lorentz-Brücke aus dem Ursprungsteil. Sie zeigt eine passende lokale algebraische Form. Noch fehlen ihre Interpretation als Ereignisse, die Verklebung zu einer Ra","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Drei unterschiedliche Hinweise führen zur Zahl drei","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4446,"byte_start":2245,"id":"section:57f7b37aa0bf6c8f74f2","kind":"section","labels":[],"line_end":47,"line_start":24,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"Für einen Graph-Laplaceoperator [formula in source] definieren wir die mittlere Rückkehrfunktion und eine skalenabhängige Dimension durch Auf einem großen regelmäßigen dreidimensionalen Gitter entsteht zwischen der Gitter- und der endlichen Systemskala ein Bereich mit [formula in source] , also [formula in source] . Bei einem endlichen zusammenhängenden Graphen geht [formula in source] sowohl für sehr kleine als auch","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine neue Gegenprobe am Clebsch-Vorschlag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5395,"byte_start":4446,"id":"section:458426875e0e24a297e2","kind":"section","labels":[],"line_end":52,"line_start":48,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"In einer gewöhnlichen hyperbolischen Wellengleichung werden lokale Anfangsdaten auf einer räumlichen Fläche vorgegeben und entlang einer ausgezeichneten Zeitrichtung entwickelt. Mehrere Zeitkoordinaten verändern das Anfangswertproblem grundlegend. Unter zusätzlichen nichtlokalen Beschränkungen existieren dennoch wohldefinierte Mehrzeit-Probleme; ein pauschaler Unmöglichkeitssatz wäre falsch. F14","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine Zeitrichtung ist mehr als ein weiterer Zahlenplatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6488,"byte_start":5395,"id":"section:ccff0765bada49857e57","kind":"section","labels":[],"line_end":64,"line_start":53,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"Ein elementares mechanisches Beispiel illustriert die Rolle von Constraints. Nimmt man in [formula in source] Raumdimensionen eine Newtonsche Punktkraft mit Gaußgesetz an, lautet das effektive Radialpotential [formula in source] An einer Kreisbahn ergibt sich [formula in source] Unter diesen Voraussetzungen sind solche Kreisbahnen bei [formula in source] stabil, bei [formula in source] instabil und bei [formula in so","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was Stabilität zusätzlich einschränkt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":397,"byte_start":0,"id":"section:eb66f0e90673df753567","kind":"chapter","labels":["ch:shadow-open"],"line_end":4,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Offene Physik ist kein freier Platz, in den jede neue Idee hineinpasst. Sie ist oft durch viele bekannte Eigenschaften eng begrenzt. Der nützliche Schritt lautet deshalb: Welcher Teil des Phänomens ist beobachtet, welcher Mechanismus fehlt, und welche Antwort müsste unser Modell zusätzlich liefern?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Schwer verstandene Phänomene als zusätzliche Prüfsteine","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1423,"byte_start":397,"id":"section:435391771b60611caf61","kind":"section","labels":[],"line_end":9,"line_start":5,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Gravitationslinsen und die Verteilung sichtbarer Materie in kollidierenden Haufen liefern eine wichtige Beobachtung: Der aus der Gravitation erschlossene Beitrag muss nicht dem heißen sichtbaren Gas folgen. Die Bullet-Cluster-Analyse ist ein prominentes Beispiel. Sie identifiziert damit noch kein bestimmtes mikroskopisches Teilchen. Zusammen mit anderen kosmologischen Daten ist sie eine starke Anforderung an jede Erk","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dunkle Materie: unsichtbar heißt nicht frei wählbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2590,"byte_start":1423,"id":"section:39a2ec5b7e44919548bb","kind":"section","labels":[],"line_end":16,"line_start":10,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Die beschleunigte kosmische Expansion verlangt eine konsistente Erklärung im Gesamtmodell. Für TFPT ist besonders schwierig, eine passende effektive Vakuumwirkung zu erhalten, ohne sie bei jedem neuen Beitrag nachzujustieren. Der Mechanismus müsste seine Größe und Stabilität gegenüber Korrekturen erklären.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dunkle Energie: ein kleiner Rest mit großen Folgen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3656,"byte_start":2590,"id":"section:f8272c3828b9ae4bd6a7","kind":"section","labels":[],"line_end":21,"line_start":17,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Die Schwarzlochfrage verbindet Quanteninformation, Gravitation und die Wahl zugänglicher Teilsysteme besonders eng. In bestimmten berechenbaren Modellen verändern Quanteneffekte die extremale Fläche und damit die Zuordnung rekonstruierbarer Information. Die verallgemeinerte Entropie enthält einen Flächenbeitrag und einen Quantenfeldbeitrag. Das ist erheblicher theoretischer Fortschritt in diesen Modellen, aber noch k","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Schwarze Löcher: Information kann die Aufteilung selbst betreffen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4418,"byte_start":3656,"id":"section:cc7dd823692a938a29df","kind":"section","labels":[],"line_end":26,"line_start":22,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Äquivalenztests wie MICROSCOPE prüfen die Universalität des freien Falls für unterschiedliche Materialien mit hoher Genauigkeit. Eine neue Quelle für Raumzeit muss daher erklären, warum verschiedene innere Zusammensetzungen auf dieselbe effektive Geometrie reagieren. F18","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gravitation muss sehr verschiedene Inhalte gleich behandeln","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6966,"byte_start":4418,"id":"section:23c9adf9737ab94d2e3d","kind":"section","labels":[],"line_end":43,"line_start":27,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"L32mmL56mmL60mm Thema& Was den Ansatz einschränkt& Was eine Erklärung liefern müsste\\\\ Zeitpfeil&Beständige Aufzeichnungen und irreversible Makroprozesse bei oft reversiblen Grundgleichungen.&Zustandsauswahl, Anfangskorrelationen, Zugriff und Entropiefluss; keine bloße Benennung eines inneren Parameters als Zeit.\\\\ Messproblem&Interferenz und stabile Messergebnisse müssen zusammen beschrieben werden.&Ein vollständige","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Weitere offene Stellen mit unterschiedlicher Beweiskraft","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":947,"byte_start":0,"id":"section:5fe237cd6f5ee46c4c18","kind":"chapter","labels":["ch:shadow-synthesis"],"line_end":7,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Die zusammengetragenen Schatten sprechen am stärksten für eine Struktur von Zusammensetzungen und gemeinsamen Antworten. Arithmetik verlangt eindeutig kombinierbare primitive Faktoren. Quantenphänomene verlangen Phasen, Kontexte und eine besondere Zusammensetzung von Teilsystemen. Raumzeit verlangt eine skalenstabile Ordnung von Nachbarschaften, Signalwegen und Anfangsdaten. Keine dieser Forderungen wird durch die Za","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein engeres Bild und ein neues berechenbares Puzzleteil","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2397,"byte_start":947,"id":"section:ca0163d90aa0cb4aca58","kind":"section","labels":[],"line_end":20,"line_start":8,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Die bildhafte Aussage Alles ist aus Primzahlen gebaut lässt sich zu einer brauchbareren Hypothese präzisieren: Ein möglicher gemeinsamer Ursprung besitzt elementare, zusammensetzbare Operationen. In einem kommutativen arithmetischen Schatten erscheinen primitive Faktoren. Vor dieser Auslesung bleiben zusätzliche Phasen, Kontexte und Aufzeichnungen erhalten. Räumliche Nachbarschaft und Zeitordnung müssten aus den erla","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine engere Arbeitshypothese","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":4907,"byte_start":2397,"id":"section:f28d0c5ee3bad7085c8d","kind":"section","labels":["eq:arithmetic-projective"],"line_end":61,"line_start":21,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Die folgenden Formeln sind eine neue Anschlusskonstruktion für dieses Buch. Ihre Zutaten sind Standardoperatoren; sie beanspruchen keine neue allgemeine mathematische Entdeckung. Sie zeigen jedoch exakt, dass ein gemeinsamer arithmetischer Endpunkt unterschiedliche kohärente Geschichten besitzen kann.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein konstruktiver Versuch: gleiche Zahl, verschiedene Phasen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5784,"byte_start":4907,"id":"section:321ba28c1bac38e42872","kind":"subsection","labels":[],"line_end":69,"line_start":62,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Ein Kontrollqubit speichert kohärent, welcher der beiden Wege durchlaufen wurde. Setze [formula in source] und [formula in source] . Nach einer Hadamard-Auslesung des Kontrollqubits gelten [formula in source] Ohne die lokalen [formula in source] -Markierungen wäre [formula in source] und damit [formula in source] . Die neue Rechnung kontrolliert dies im Zahlfenster [formula in source] exakt. Die benutzten Wege ab [fo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine vollständig bestimmte Vorhersage im Modell","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7119,"byte_start":5784,"id":"section:96c3ea95f25e9f3e7e67","kind":"subsection","labels":[],"line_end":76,"line_start":70,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Gelöst ist eine kleine Kompatibilitätsfrage: Unbegrenzte arithmetische Zusammensetzung und ein endlicher lokaler Quantenbaukasten lassen sich in einem expliziten gemeinsamen Modell verbinden. Der rein arithmetische Schatten kann kommutativ sein, während kohärent zugängliche Wegrelationen eine nichttriviale Phase behalten. Das passt genau zum Motiv der vorherigen Echoexperimente.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was damit gelöst ist und was nicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9085,"byte_start":7119,"id":"section:ed1d5100a133f474179d","kind":"section","labels":[],"line_end":97,"line_start":77,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Man könnte einen arithmetischen Raum, ein Quantensystem und ein geometrisches Modell einfach nebeneinanderstellen: [formula in source] Bei Produktzustand und unabhängig wirkenden Operationen passen dann vielleicht alle Einzelstatistiken. Der gemeinsame Ursprung wäre dadurch nicht erklärt. Nötig sind gemeinsame Relationen und überprüfbare Antworten auf gemischte Eingriffe. Die oben konstruierte Wegphase ist ein kleine","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum getrennte passende Modelle noch keine gemeinsame Quelle sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11082,"byte_start":9085,"id":"section:c922c37435b133758c26","kind":"section","labels":[],"line_end":111,"line_start":98,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"L37mmL60mmL51mm Gewonnene Präzisierung& Konkretes Ergebnis& Nächste fehlende Bedingung\\\\ Logarithmische Skala&Multiplikative Additivität plus Monotonie erzwingen [formula in source] .&Native Begründung der Ordnung und Energieskala.\\\\ Unbegrenzte Primfamilie&Endlich viele additive Grundtakte tragen nicht alle [formula in source] .&Eine passende wachsende Familie oder reichere Dynamik.\\\\ Arithmetik und Phase&Zwei Multi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Welche Puzzleteile jetzt enger gefasst sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":82,"byte_start":0,"id":"section:4dc33ccb8369b2d8e57e","kind":"chapter","labels":["app:shadow-sources"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Erweiterung: Quellen und genaue Prüfgrenzen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4118,"byte_start":82,"id":"section:a2485b8d2638af1f1a23","kind":"section","labels":[],"line_end":29,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":["relation:8daa315fa0843987dcd9"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"Die Erweiterung wurde am 14. September 2026 gegen verfügbare Originalabschnitte im lokalen Repository tfpt-theoryv4 abgeglichen. Der gelesene Git-Stand war 66b91e40e245569f06ab440ead80f446c9be0ee5. Dies identifiziert den Checkout; es behauptet keinen frischen vollständigen Beweis- oder Testlauf. Die tatsächlich verwendeten Dateiinhalte sind zusätzlich mit SHA-256 im Paket erfasst, auch soweit der Arbeitsbaum von Git ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zusätzlicher Einblick in den RH-Forschungsbestand","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6033,"byte_start":4118,"id":"section:69cba93a03b1f8563949","kind":"section","labels":[],"line_end":38,"line_start":30,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"Der separate Prüfer verify_shadows.py importiert keinen ursprünglichen TFPT- oder RH-Code und keine Nullstellentabellen. Er enthält 126 exakte beziehungsweise symbolische Bedingungen und zwei numerische Kontrollen. Die Nummer der ersten Nullstelle im Eta-Diagramm ist ein ausdrücklich eingesetzter Referenzwert; das Diagramm ist kein eigener Nullstellensuchlauf.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die 128 zusätzlichen Bedingungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10751,"byte_start":6033,"id":"section:a33fc3b0678d541984ea","kind":"section","labels":[],"line_end":62,"line_start":39,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":["relation:2097e0f24daa4f2e18dd","relation:53591815c91846550348"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"Die folgenden Quellen wurden zur Erweiterung aufgerufen. Es handelt sich um gezielte Literaturauswahl, nicht um einen vollständigen systematischen Review aller Veröffentlichungen bis September 2026. Eigene Formeln, Gegenbeispiele und Illustrationen sind im Haupttext als solche bezeichnet. Neue Preprints bleiben als Preprints kenntlich. M. V. Berry, J. P. Keating: The Riemann Zeros and Eigenvalue Asymptotics. SIAM Rev","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zusätzliche Primärliteratur","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":11375,"byte_start":10751,"id":"section:42f0301010a5f2612275","kind":"section","labels":[],"line_end":64,"line_start":63,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"Das aktualisierte Quellpaket enthält beide unabhängigen Prüfer, beide Ergebnisdateien, die zusätzlichen drei Vektorplots, die LaTeX-Diagramme, das RH-Quellenmanifest und die ausgewählten Katalogeinträge. Die fünf neuen Hauptkapitel sind in dieselbe LaTeX-Datei eingebunden; ursprüngliche Textteile wurden nur um Versionshinweise und Querverweise ergänzt. Das fertige PDF wird weiterhin mit LuaLaTeX gebaut. Die beiliegen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproduktion der erweiterten Fassung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":76,"byte_start":0,"id":"section:fbe7f6a7b8da98be6e41","kind":"chapter","labels":["ch:audit13"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die sechs neuen Quellen: geprüfte Korrekturen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":593,"byte_start":76,"id":"section:2127d7c90c3a56279c19","kind":"section","labels":[],"line_end":5,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Die sechs zusätzlichen Unterlagen heißen im neuen Quellenregister N1 bis N6; die ursprünglichen S01 bis S11 bleiben unverändert. Ihr Audit trennt exakte endliche Identitäten, numerische Spektren und zusätzliche Modellannahmen. 100 eigene Bedingungen bestanden: 78 exakte beziehungsweise Integritätsprüfungen und 22 numerische. Die anschließende gemeinsame Ausführung hat einen eigenen 231-Bedingungen-Vertrag. Diese Zähl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was gegenüber v1.1 neu ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":2635,"byte_start":593,"id":"section:a7290cbe0022166809ba","kind":"section","labels":[],"line_end":28,"line_start":6,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Setze [formula in source] und [formula in source] . Der Wedge-Kanal besitzt Für [formula in source] verschwindet [formula in source] . Beide geordneten Wege enden im gleichen virtuellen Zustand und interferieren. Orthogonale Records für [formula in source] und [formula in source] ersetzen dies durch [formula in source] : Der antisymmetrische Rang-6-Kanal wird zum Rang-12-Kanal. Bei gleichem Energienenner entsteht ein","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die zentrale Reparatur: Wege nicht zu früh unterscheiden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":3264,"byte_start":2635,"id":"section:3a1c2f81662aefabc0eb","kind":"section","labels":[],"line_end":35,"line_start":29,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Mit [formula in source] und [formula in source] ist auf [formula in source] unitär und kollektiv [formula in source] -kovariant. Alle [formula in source] liefern für Materieeingänge denselben ersten blockdephasierten Schatten. Dennoch wirkt [formula in source] dort als [formula in source] , während [formula in source] als [formula in source] wirkt: [formula in source] kehrt als [formula in source] oder als [formula i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der erste Schatten wählt die Fortsetzung noch nicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":5090,"byte_start":3264,"id":"section:84b56c2bdde78ef24986","kind":"section","labels":[],"line_end":59,"line_start":36,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für genau zwei vollständige [formula in source] -Zellen und eine positive Brücke gelten die Formeln aus Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der allkopplige Zweizellenbeweis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6474,"byte_start":5090,"id":"section:fd239c991ed7e6c04dc9","kind":"section","labels":[],"line_end":77,"line_start":60,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Im ausgewiesenen harmonischen Modell eines geteilten Vermittlers lautet der symmetrische aktive Block Sein niedriger Zweig beginnt mit [formula in source] ; der antisymmetrische mit [formula in source] . Deshalb ist auf dem aktiven [formula in source] -Raum Nach Abzug beider Einzelbondkorrekturen [formula in source] bleibt Beide Schreibweisen sind kompatibel. Eine Konstante auf dem aktiven Sektor ist außerhalb davon ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vierte Ordnung und unterschiedliche Subtraktionskonventionen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":7332,"byte_start":6474,"id":"section:9e89eaea0f12a057a5e5","kind":"section","labels":[],"line_end":90,"line_start":78,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] gilt Mit [formula in source] und [formula in source] folgen Ein kohärentes Achtzweigregister liefert aus dem früheren Zweisingulett-Eingang [formula in source] Erfolg [formula in source] . Alle acht Ausgänge haben Gewichte [formula in source] . Dies ist eine exakte Alternative zur alten 32-Zweigschaltung. Kontrollierte kontinuierliche Sternpulse und Register bleiben zusätzliche Ressourcen. Erz","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein exakter Stern-Spektralfilter unter zusätzlichen Ressourcen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":8009,"byte_start":7332,"id":"section:2e832ed66bd735f33eab","kind":"section","labels":[],"line_end":98,"line_start":91,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"In der Inzidenzfamilie [formula in source] sind die beiden relevanten Entropien Strikte Konkavität liefert verschiedene Maxima: [formula in source] für Kontexte und [formula in source] für Strahlen. Letzterer Prozess hat Rang 60. Erweitert man den Nachfolgerträger, entstehen symmetrieverträgliche Ränge 15 und 16. Weder maximale Entropie noch minimale Rangzahl wählt die Regel ohne erklärte Klasse. Die passive separate","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Einfachheit braucht einen Auslesevertrag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10096,"byte_start":8009,"id":"section:27129c4ed1581dc50dfd","kind":"section","labels":[],"line_end":113,"line_start":99,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Zwei Singulettläufe finden mindestens vier orthogonale Moden bei [formula in source] über [formula in source] , Residuen unter [formula in source] . Das Dublett ist widerlegt; ein exakter oberer Multiplizitätsbeweis fehlt. -Typen.] 960 gleichgradige Wurzelsummen gehen nach [formula in source] ; gemischt ergeben sich 640 und 192 Summen nach Grad null sowie 64 Cartanfälle. Der vorgeschlagene gemischte Kanal nach [formu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Weitere architektonisch wichtige Korrekturen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":561,"byte_start":0,"id":"section:f7c7039c0e7d5a0fbf58","kind":"chapter","labels":["ch:execution13"],"line_end":5,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Aktualisierung v1.5: weniger zusätzliche Steuerung Die hier eingeführte gemeinsame Record-/Präparations-/Mehrzeitausführung lässt sich jetzt bei festem [formula in source] ohne negative Evolutionszeiten anschließen. Endliche Q-Gatezeiten sind unter einem ausdrücklich belegungserhaltenden Gatevertrag mitgerechnet. Wedge-Kopplung, Q, adressiertes An/aus und Reset bleiben zusätzliche Ressourcen; Details in Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine gemeinsame Ausführung für Record, Präparation und Mehrzeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1259,"byte_start":561,"id":"section:f22d9a4ae06eb4399e65","kind":"section","labels":[],"line_end":10,"line_start":6,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Dieselbe korrigierte Vermittlungsoperation erzeugt jetzt Aufzeichnung, kontrollierte Näherungspräparation und Mehrzeitantwort. Die tatsächlichen Quellprojektoren, Paulioperationen und die Dreierclock wurden benutzt. Ein bereits präpariertes [formula in source] oder ein separater Präparations-Hamiltonoperator wird nicht benötigt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine Konstruktion, aber ein ausdrücklich zusätzlicher Ressourcenvertrag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2066,"byte_start":1259,"id":"section:27cac20b1e46ba4e8419","kind":"section","labels":[],"line_end":30,"line_start":11,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Mit [formula in source] , [formula in source] und [formula in source] gilt Kopiere nur die Vermittlerbelegung, nicht das geordnete Farbwort: Dann ist auf allen 44 Dimensionen Der Vermittler kehrt zurück. Auf Materie und Pointer bleibt [formula in source] , [formula in source] , mit Beide Krausoperatoren gehören zum Instrument; ihre Effekte summieren sich zu [formula in source] . Ein ungemessener Pointer bleibt kohäre","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die vollständige Recordoperation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3356,"byte_start":2066,"id":"section:acdac835098c2eab9763","kind":"section","labels":[],"line_end":46,"line_start":31,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für vier Materieträger und höchstens einen aktiven Vermittler sei Alle sechs [formula in source] wurden auf dem vollen Materieraum rekonstruiert: [formula in source] , [formula in source] , [formula in source] . Andere Vermittlersektoren bleiben bei einer adressierten Operation unverändert. Die Kanten haben orthogonale Ausgänge; verschränkte Zuschauer sind eingeschlossen. Dies ist ein vollständiges sequenzielles Prot","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein gemeinsamer Träger und ein fester Schritt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4037,"byte_start":3356,"id":"section:c5ed04f11cd07e04a501","kind":"section","labels":[],"line_end":58,"line_start":47,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Rechenbasis- und uniformer Projektor gehören zu den 60 tatsächlichen Quellprojektoren. Die Swap-Identität verwendet dieselben 16 Quell-Paulis: Für Messausgang [formula in source] und Ziel [formula in source] liefert die Bitverschiebung Damit ist [formula in source] . Vier lokale Resets erzeugen [formula in source] sogar aus verschränktem Eingang. Messung und Feedback bleiben Ressourcen, keine hergeleitete kosmologisc","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Quellseitiger Reset ohne vorpräpariertes Zielreservoir","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6085,"byte_start":4037,"id":"section:e866a861d9172b6053c0","kind":"section","labels":[],"line_end":87,"line_start":59,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Akzeptiere in jeder Sternrunde die Recordfolge 111: Alle acht ersten Recordfolgen haben Wahrscheinlichkeit [formula in source] . [formula in source] wird erst zur Zielprüfung definiert. Im 24-dimensionalen Raum der verschiedenen Farbanordnungen gilt exakt Dieser Raum trägt die treue reguläre Darstellung von [formula in source] . Die polynomialen Identitäten der Gruppenalgebra gelten daher auch auf allen 256 Materiedi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wiederholung präpariert den Viererzustand kontrolliert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7720,"byte_start":6085,"id":"section:2f40225e7069ab9d24b9","kind":"section","labels":[],"line_end":109,"line_start":88,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Nach erfolgreicher Präparation folgen lokaler Quelltick [formula in source] , zweimal [formula in source] , Rücknahme [formula in source] und dasselbe [formula in source] -Runden-Filter. Ein ideales kostenloses [formula in source] -Messgerät wird nicht eingesetzt. Protokoll R behält denselben kohärenten Pointer; Protokoll F verwendet beim zweiten Schritt einen frischen. Mit [formula in source] lauten die gemeinsamen ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derselbe Filter liest die Mehrzeitantwort aus","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8690,"byte_start":7720,"id":"section:baaed08bb68077f9f164","kind":"section","labels":[],"line_end":118,"line_start":110,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Das neue Register ist nicht Clifford: Ein vierqubitiger Pauli hat Spur null oder [formula in source] . Noch konkreter erzeugt der Quellinput [formula in source] genau 13 nichtverschwindende Rechenbasisamplituden. Das ist kein reiner Stabilizerzustand, dessen Trägergröße eine Zweierpotenz ist. Nur Cliffordoperationen, Stabilizer-Hilfszustände und Pauli-Messungen reichen auch mit Feedback nicht aus. Andere Kodierungen ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was für eine native Implementierung noch fehlt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9479,"byte_start":8690,"id":"section:532be96ae7afd5770c64","kind":"section","labels":[],"line_end":125,"line_start":119,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Alle [formula in source] kommutieren mit [formula in source] ; der ungelesene Kanal erhält das Zielgewicht. Seine einzelnen Dephasierungen sind orthogonale Hilbert–Schmidt-Projektionen. Ein Fixpunkt ihres Zyklus kann bei keinem Schritt Norm verlieren und liegt deshalb im Schnitt der Fixräume: in der Kommutante der [formula in source] -Wirkung. Deren Dimension ist Die spurlose Dimension 3875 identifiziert keinen gleic","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ungelesener Austausch ist keine Kühlung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10559,"byte_start":9479,"id":"section:35b9994e51f9a1df159e","kind":"section","labels":[],"line_end":129,"line_start":126,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Ein nativer Adapter muss [formula in source] , [formula in source] , Kern und Belegung gemeinsam liefern, beim Half-Charge-Feld zusätzlich mit Domänen- und Energiekontrolle. Er muss den 13-Amplituden-Eingang, beide Recordzweige und die Acht-Runden-Echos reproduzieren, einschließlich Hilfszuständen und Fehlerausgängen. Erst anschließend ist eine skalierende Zellfamilie sinnvoll auf Geometrie, Chiralität und Spin 2 zu ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Abnahmetests und T1–T8-Grenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":87,"byte_start":0,"id":"section:420aa0bea4b113b77bbf","kind":"chapter","labels":["app:release13"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Versionspaar v1.3: Quellen, Abdeckung und Reproduktion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":812,"byte_start":87,"id":"section:06168931c74d0a886e90","kind":"section","labels":[],"line_end":7,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"Diese Ausgabe führt das 90-seitige Hauptbuch v1.1 vollständig fort; die kompakte 35-seitige Compiler-Fassung v1.2 ist nicht ihre Basis. Alle ursprünglichen 21 Hauptkapitel und vier Anhänge bleiben zugänglich. Hinzu kommen drei neue Hauptkapitel und dieses Quellenregister.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei Dokumente mit unterschiedlichen Aufgaben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2181,"byte_start":812,"id":"section:5bb5208f06d128844555","kind":"section","labels":[],"line_end":18,"line_start":8,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"Die alten IDs S01–S11 bleiben unverändert. N1–N6 bezeichnen die sechs bereits archivierten Konsolidierungen: Fable-Konsolidierung, Sol-Rekonstruktion, kurze Universalraum-Konsolidierung, Q-Audit/U-Regel, TFPT-Rekonstruktion und Sechs-Prüfpunkte-Analyse, jeweils vom 14. September 2026. Originaltexte und Hashes stehen im Sechs-Quellen-Auditpaket.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neue Quellen und unveränderte Originale","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":3388,"byte_start":2181,"id":"section:88dcee359b10187b7775","kind":"section","labels":[],"line_end":30,"line_start":19,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"L37mmL30mmL83mm Paket&Umfang&Prüfgrenze\\\\ Basisbuch v1.1&210 Bedingungen&Historische Basisprüfung; nicht erneut vollständig ausgeführt.\\\\ Schatten v1.1&128 Bedingungen&Historische Erweiterung; alte RH-Aktualitätsgrenze bleibt sichtbar.\\\\ Sechs-Quellen-Audit&100 eigene&78 exakt/Integrität, 22 numerisch; in dieser Ausgabe redaktionell integriert.\\\\ Gemeinsame Ausführung&231 eigene exakte&Für Ausgabe v1.3 erneut ausgefü","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Evidenz nicht durch Addition aufwerten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4019,"byte_start":3388,"id":"section:3904ce0a949b82547d65","kind":"section","labels":[],"line_end":39,"line_start":31,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"Die wissenschaftlichen Pakete liegen unter experiments/theory-contracts/universalraum-six-source-audit-20260914 experiments/theory-contracts/compiler-single-execution-20260914 experiments/theory-contracts/universalraum-paired-release-20260914/new-input-audit Das dritte enthält den neuen endlichen Prüfer, seine Normal-/Optimierungsausgaben und die gesonderte Singulettrechnung. Das Releaseverzeichnis enthält LaTeX, all","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Rechen- und Dokumentpakete","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":4864,"byte_start":4019,"id":"section:91f278abdec50dbaf60d","kind":"section","labels":[],"line_end":43,"line_start":40,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"Der RH-Aktualitätslauf scheiterte an einem fehlenden referenzierten Quellenordner. Der konfigurierte separate Faktorgraph ist nicht verfügbar. Die ausgewählte Originalroute r647 und die verfügbaren Beweise wurden gelesen; keine vollständige globale Aktualität wird behauptet. Es wurde kein RH-Abschlussmarker geändert und keine neue arithmetische Kampagne gestartet.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Aktualität und ausdrücklich fehlende Prüfungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":1268,"byte_start":0,"id":"section:1aef3b7b37972d7a9bff","kind":"chapter","labels":["ch:newinputs13"],"line_end":8,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Aktualisierung v1.5: ein fester Puls ist nicht ein festes Detuning Die unten gezeigte Schranke eines einzigen verstimmten Pulses bleibt richtig. Eine endliche Folge positiver Pulse mit diskreten Q-abgeleiteten Belegungs-Z-Kicks und zwei Off-Intervallen erreicht dagegen vollständigen phasenrichtigen Transfer. Der fehlende Einzelpuls beweist also kein Verbot einer Kompositfolge. Siehe Kapitel Aktualisierung v1.4 Dieses","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei weitere Eingaben: Mikrodynamik und deterministische Präparation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":2094,"byte_start":1268,"id":"section:e025e1c05da1bf37eaef","kind":"section","labels":[],"line_end":13,"line_start":9,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Die während der Konsolidierung zusätzlich eingereichten Texte N7 und N8 enthalten neue Resultate, nicht nur Zusammenfassungen. N7 berichtet die vollständige vierte Ordnung eines harten CAR-Referenzmodells, einen mikroskopischen Stern und einen Relaxationskanal. N8 konstruiert einen harten Tensorproduktkandidaten mit globaler Bandschranke und eine deterministische ideale Präparation.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Prüfurteil und Modellgrenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3378,"byte_start":2094,"id":"section:f2227ee7df166fbf3c52","kind":"section","labels":[],"line_end":34,"line_start":14,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"N7 verwendet Dieser Operator ist unitär, aber im Gegensatz zu [formula in source] aus Kapitel Das ist kein Widerspruch, sondern eine verschiedene Phase des Rückwegs. Beim Recordaufbau ist der tatsächliche Adjungierte nötig: [formula in source] reproduziert dieselbe Materie-Aufzeichnung wie [formula in source] , unter Einschluss der Pointertensorfaktoren. Blindes Ersetzen beider [formula in source] durch [formula in s","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei richtige unitäre Vertizes, aber nicht derselbe Schritt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5429,"byte_start":3378,"id":"section:ce34cb65552d14b77cdf","kind":"section","labels":[],"line_end":56,"line_start":35,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] lautet der eingereichte Referenzoperator [formula in source] vertauscht die beiden vollständigen Paare. Die 40 Clebsch-Kanten ergeben 40 Einzelkanten-, 160 überlappende und 60 gleichlabelige disjunkte Beiträge. Jede Labelklasse ist ein Matching; gleiche Labels teilen keinen Endpunkt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der vollständige vierte-Ordnungs-Operator","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6880,"byte_start":5429,"id":"section:d8d14c70c1bee43b5687","kind":"section","labels":[],"line_end":80,"line_start":57,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Der gesamte 24024-dimensionale Singulett-Multiplizitätsraum wurde aus Youngs orthogonaler Darstellung aufgebaut. Ein neuer Lauf mit zwölf niedrigen Eigenvektoren ergab Beim zweiten Niveau wurden vier orthogonale Moden gefunden. Die größte Eigenvektorresiduen-Norm des Laufs liegt unter [formula in source] . Das ist eine hochgenaue endliche Rechnung, kein algebraischer oberer Multiplizitätsbeweis.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die neue Singulettantwort ist unabhängig reproduziert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":7959,"byte_start":6880,"id":"section:c44056defc6395f45230","kind":"section","labels":[],"line_end":94,"line_start":81,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"N8 definiert 16 harte Ortsfaktoren [formula in source] und sechs Bosonmoden pro Vektorlabel. Bei Gesamtladung [formula in source] ist der Sektor endlich. Für gilt [formula in source] . Denn der antisymmetrische Umwandlungsblock [formula in source] erfüllt [formula in source] und [formula in source] . Die selbstadjungierte Offdiagonalblocknorm ist dieselbe. Daher Der führende Austausch ist dann [formula in source] . D","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine globale Bandschranke, aber kein genauer Niedrigenergiefehler","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9713,"byte_start":7959,"id":"section:9b4cf5f77a1728338407","kind":"section","labels":[],"line_end":111,"line_start":95,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] gilt [formula in source] . Definiere [formula in source] mit [formula in source] . Dann In der Basis [formula in source] ist [formula in source] , [formula in source] , [formula in source] . Die unerwünschte Amplitude ist Sie verschwindet für die angegebene Wurzel exakt. Die ideale Phase ist [formula in source] . Es ist eine konkrete Anwendung bekannter https://arxiv.org/abs/quant-ph/0005055Am","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Deterministische Präparation im idealen erweiterten Gattermodell","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10980,"byte_start":9713,"id":"section:f77d7a4e0a9f7c8c0f55","kind":"section","labels":[],"line_end":132,"line_start":112,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Gewöhnliche Vermittlerverluste [formula in source] lassen vollständig symmetrische Farbzustände mit Vermittlervakuum dunkel. Auf 16 Trägern hat [formula in source] Dimension [formula in source] . Dieser Raum verhindert einen eindeutigen globalen Attraktor dieser Verlustdynamik.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Relaxation: konstruktiv möglich, aber nicht durch Bosonenverlust allein","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12027,"byte_start":10980,"id":"section:4ae8950a2eb7b49d6f24","kind":"section","labels":[],"line_end":149,"line_start":133,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Nach einem Paarabbau am Stern ist sein gemeinsamer Mittelpunkt leer; ein zweiter Paarabbau ist unmöglich. Für den geschlossenen Block aus 256 Materie- und 288 Vermittlerzuständen gilt Die untere effektive Matrix ist deshalb exakt Der volle 544-dimensionale Block wurde unabhängig gebaut und diagonalisiert. Bei [formula in source] , [formula in source] sind die niedrige Lücke [formula in source] und das nackte Materieg","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der isolierte mikroskopische Stern: vollständiger kleiner Block","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13070,"byte_start":12027,"id":"section:62d288f5f0f2a5fb6e0d","kind":"section","labels":["eq:matched-general"],"line_end":166,"line_start":150,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für beliebige bekannte Zielüberlappung [formula in source] ist die Fehleramplitude nach zwei angepassten Schritten proportional zu Sie verschwindet bei Die Polynomidentität wurde symbolisch geprüft. Für den angekleideten Stern-Grundzustand und nackten Eingang [formula in source] gilt [formula in source] . Daraus folgt die angepasste Phase Verwendet man bei idealem Zugriff auf den angekleideten Zielprojektor dennoch d","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Begonnenes Follow-up: die Präparation an das Mikromodell anpassen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14355,"byte_start":13070,"id":"section:5b729f7cc6d33facb3ab","kind":"section","labels":[],"line_end":177,"line_start":167,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Bereits der detunierte isolierte Paarblock hat maximale Transferwahrscheinlichkeit Bei [formula in source] , [formula in source] sind das nur [formula in source] . Eine einzelne freie Entwicklung dieses Blocks realisiert daher keinen vollständigen Materie-Vermittler-Tausch [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Begonnenes Follow-up: warum ein einziger fester Puls nicht genügt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15777,"byte_start":14355,"id":"section:f17c9a32dc16b8fc0600","kind":"section","labels":[],"line_end":196,"line_start":178,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Das Einzelpuls-Hindernis legt einen konkreten Ausweg nahe, sofern zusätzliche Kontrollen zugelassen werden. Im isolierten resonanten Paar, also bei auf null gesetzter Verstimmung, sei Dann lautet seine exakte Entwicklung Mit dem relativen Viertelphasenpuls [formula in source] gilt Die volle 22-dimensionale Identität ist symbolisch geprüft. Zwei Belegungsphasen und ein resonanter Transfer genügen somit unter diesem Ko","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein kurzer positiver Kontrollkandidat für die nächste Revision","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17910,"byte_start":15777,"id":"section:0507b862ed9c6c11043a","kind":"section","labels":[],"line_end":209,"line_start":197,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Der singuläre Schur-Satz für [formula in source] benötigt [formula in source] , [formula in source] und [formula in source] . Das Gegenbeispiel [formula in source] , [formula in source] , [formula in source] hat negatives Determinant trotz positivem Schurrest. Kompatible positive Blöcke ergeben eine positive dichte Fortsetzung nur für alle Stufen, die tatsächliche Form und passende Stetigkeit. Die Identität der volls","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Arithmetik: bestätigt ist der Vertrag, nicht die offene Lösung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":19872,"byte_start":17910,"id":"section:28fba992ed9d0af987f6","kind":"section","labels":[],"line_end":225,"line_start":210,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Kann die echte kleine Maschine die nötigen Handgriffe ausführen? Gesucht ist eine kontrollierte Kopplung, die Vermittler hin- und zurückführt und Aufzeichnung erhält. Ein fester freier Puls reicht im geprüften Stern nicht. Abnahme: beide Recordzweige und alle Eingänge, keine versteckten Zielzustände. Können wir den richtigen, angekleideten Zustand auswählen? Die passende Verstärkungsphase ist jetzt berechnet. Es fehl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die wichtigsten nächsten Fragen, einfach ausgedrückt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":96,"byte_start":0,"id":"section:35178ee92b3384c8d8d2","kind":"chapter","labels":["ch:audit14"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/22_audit_v14.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Fünf neue Untersuchungen: Abgleich und stärkere Dynamikkontrolle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":2247,"byte_start":96,"id":"section:1d620f1078a114ad2e66","kind":"section","labels":[],"line_end":18,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/22_audit_v14.tex","status_markers_as_written":[],"summary_excerpt":"Die neuen Originale sind N9 (Fable-Abschlussrunde), N10 (Sol-Runde 2), N11 (Astra-Antwort), N12 (Astra hoch) und N13 (Spark-Gesamtstand). Alle fünf sind unverändert im Quellenpaket archiviert. Ihre internen Arbeitsaufträge sind Forschungsinhalt, keine zusätzlichen Nutzeranweisungen. Der hier ausgeführte Auftrag ist Prüfung, eigene Fortsetzung und anschließende Konsolidierung.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Quellen und drei notwendige Korrekturen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":3400,"byte_start":2247,"id":"section:225a31d171fae6dfcabc","kind":"section","labels":[],"line_end":28,"line_start":19,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/22_audit_v14.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] Clebsch-Zellen sind drei Architekturen zu unterscheiden: lrrr Zellen&Eine globale Bank&Eine Bank pro Zelle&Eine Bank pro Kante\\\\ 1&60&60&0\\\\2&280&120&0\\\\3&660&180&0\\\\6&2760&360&0\\\\ Gezählt werden gleichlabelige disjunkte Paarbeiträge vierter Ordnung. Die Formeln sind [formula in source] , [formula in source] und null. Eine endliche Bank pro Zelle bleibt lokal und extensiv, behält aber die inne","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lokalität wählt nicht zwischen zwei lokalen Modellen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":5173,"byte_start":3400,"id":"section:7f41a95c98984acbd571","kind":"section","labels":[],"line_end":51,"line_start":29,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/22_audit_v14.tex","status_markers_as_written":[],"summary_excerpt":"Im harten C16-Modell mit [formula in source] sei [formula in source] . Die vollständige Enumeration aller 65536 Ortsmengen bestätigt Gewichte [formula in source] heben im Schurtest die Bosonenwurzeln auf. Die Spaltensumme ist höchstens [formula in source] , die Zeilensumme höchstens [formula in source] . Daher Die daraus gebildete achtstufige Vergleichsmatrix hat Diagonale [formula in source] und Nebendiagonale [form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bandtrennung bis zum Betriebspunkt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6231,"byte_start":5173,"id":"section:afc19f6e8b7c4114d7e7","kind":"section","labels":[],"line_end":65,"line_start":52,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/22_audit_v14.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] und [formula in source] gilt Dies definiert das endliche allordentliche Problem, ohne seine riesigen Inversen numerisch ausgewertet zu haben. Mit [formula in source] , [formula in source] , [formula in source] , [formula in source] begrenzen zwei Resolventenidentitäten den Rest des energieabhängigen Kerns nach [formula in source] durch Bei [formula in source] reproduziert dies [formula in sour","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der exakte Schurvertrag und seine verbleibende Restlücke","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":7252,"byte_start":6231,"id":"section:af89b89867887a1acf04","kind":"section","labels":[],"line_end":78,"line_start":66,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/22_audit_v14.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] , [formula in source] und [formula in source] folgt aus [formula in source] und [formula in source] exakt Jeder Clebsch-Stern besteht aus fünf Transpositionen. In der treuen regulären [formula in source] -Darstellung wurde die ganze ganzzahlige Identität [formula in source] auf 720 Dimensionen geprüft. Mit [formula in source] ist sein Spektrum ganzzahlig nichtnegativ; daher ist jeder Summand p","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine einfache positive Darstellung der lokalen vierten Ordnung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":8609,"byte_start":7252,"id":"section:ac637377e3034bc06088","kind":"section","labels":[],"line_end":94,"line_start":79,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/22_audit_v14.tex","status_markers_as_written":[],"summary_excerpt":"Der eigene vollständige Singulettträger reproduziert beide F4-Varianten: lrr &Zellintern geteilt&Pro Kante lokal\\\\ F4-Grundwert&555,488500364&732,120310942\\\\ F4 auf ersten vier Moden&583,292038666&708,209322519\\\\ Gapkoeffizient [formula in source] &13,901769151& [formula in source] \\\\ Danach wurden die niedrigen Eigenwerte des vollständigen trunkierten Operators [formula in source] neu berechnet: Dimension 24024, ach","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neue Diagonalisierung statt bloßer Rayleighkorrektur","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":551,"byte_start":0,"id":"section:d550b187f712f0fa4352","kind":"chapter","labels":["ch:micro14"],"line_end":5,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/23_micro_v14.tex","status_markers_as_written":[],"summary_excerpt":"Aktualisierung v1.5: zwei gültige Präparationsverträge Der unten konstruierte exakt selektive Spektralfilter bleibt gültig unter seinen stärkeren Kontrollannahmen. Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eigene Fortsetzung: ein gemeinsames kontrolliertes Mikrolabor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1453,"byte_start":551,"id":"section:c1ff6a1ef440790cd257","kind":"section","labels":[],"line_end":10,"line_start":6,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/23_micro_v14.tex","status_markers_as_written":[],"summary_excerpt":"Der geordnete Standard-Gittercocycle [formula in source] wurde unabhängig aus einer einfachen E8-Basis aufgebaut. [formula in source] liefert den Kommutatorfaktor, Bilinearität die Cocycle-Identität. Alle 240 Wurzelkoordinaten sind ganzzahlig. Auf den 40 Clebsch-Kanten bestätigt die exakte F2-Elimination Rang 45 für die Antisymmetriegauge der Ortsfarben und Rang 285 für die zusätzliche kantenlokale Vermittlergauge. F","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vorzeichen aus E8 und die noch fehlende Quellbasis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3255,"byte_start":1453,"id":"section:cc7208034d70da448a63","kind":"section","labels":[],"line_end":29,"line_start":11,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/23_micro_v14.tex","status_markers_as_written":[],"summary_excerpt":"Für ausschließlich kantenlokale Vermittler ohne Hopping sind die lokalen Ladungen erhalten. Aus der vollständig belegten Nullbosonquelle folgt [formula in source] . Besetzte Bosonen bilden deshalb ein Matching: Jede Kante trägt höchstens einen, und zwei besetzte Kanten teilen keinen Endpunkt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein allordentlicher CAR-/Tensoradapter im Matchingsektor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4116,"byte_start":3255,"id":"section:2709ea9ff79d52d76649","kind":"section","labels":[],"line_end":41,"line_start":30,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/23_micro_v14.tex","status_markers_as_written":[],"summary_excerpt":"Die Kopplung [formula in source] zwischen 256 Materie- und 288 Vermittlerzuständen wurde neu aufgebaut. Sie erfüllt [formula in source] . Der volle Hamiltonoperator ist Seine 14 verschiedenen Energien sind sieben niedrige Werte sechs obere [formula in source] für [formula in source] und [formula in source] mit Multiplizität 67. Die niedrigen Multiplizitäten sind [formula in source] ; die sechs oberen wiederholen die ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der vollständige Stern, nicht nur sein niedriger Schatten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6346,"byte_start":4116,"id":"section:ea1f187e2805e78d56a6","kind":"section","labels":[],"line_end":62,"line_start":42,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/23_micro_v14.tex","status_markers_as_written":[],"summary_excerpt":"Für jeden anderen Energiewert [formula in source] setze [formula in source] ist der akzeptierte Krausoperator eines Hadamardtests mit kontrollierter Entwicklung. Alle Faktoren erhalten den Zielzustand, und der [formula in source] -te Faktor löscht den Eigenraum zu [formula in source] . Weil sie Funktionen desselben [formula in source] sind, gilt auf dem ganzen Raum Es ist kein gemeinsames kommensurables Wiederkehrint","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein exakter endlicher Filter aus wirklichen Entwicklungszeiten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":7745,"byte_start":6346,"id":"section:c6fa835bb619b94f3ebb","kind":"section","labels":[],"line_end":84,"line_start":63,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/23_micro_v14.tex","status_markers_as_written":[],"summary_excerpt":"Eine ideale kohärente Entkleidung ist für erfolgreiche Zustandspräparation nicht nötig. Nach dem Filter wird die Vermittlerbelegung gemessen. Im leeren Zweig bleibt exakt nacktes [formula in source] . Mit gilt auf nackter Materie Dies ist der gesamte akzeptierte Krausoperator und wurde als volle Matrix geprüft. Aus dem elementaren Zweisingulett [formula in source] mit [formula in source] beträgt die Ausbeute [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Noch einfacher: die Hülle messen und die Ausbeute mitführen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9259,"byte_start":7745,"id":"section:f10dfca6f9f78df7d5cd","kind":"section","labels":[],"line_end":97,"line_start":85,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/23_micro_v14.tex","status_markers_as_written":[],"summary_excerpt":"Das neue Protokoll beginnt in nacktem [formula in source] , benutzt den mikroskopischen Sternfilter samt Leerbelegungsherald, danach den lokalen Dreierzyklus [formula in source] , zweimal den resonanten Record, den Rücktick und denselben mikroskopischen Filter zur Schlussprüfung. Der Echoanteil wurde im vollständigen 256D-Materieraum gerechnet; wiederholte Farben werden nicht herausprojiziert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein vollständiger neuer Präparations- und Echovertrag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10835,"byte_start":9259,"id":"section:b9262636ae81f94e12e0","kind":"section","labels":[],"line_end":117,"line_start":98,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/23_micro_v14.tex","status_markers_as_written":[],"summary_excerpt":"Der neue N11-Kanal ist CPTP, mit [formula in source] und [formula in source] . Wegen [formula in source] und [formula in source] folgt Damit ist [formula in source] der einzige stationäre Zustand. 556 Zyklen garantieren [formula in source] Infidelität. Der unabhängige 256D-Lauf kontrolliert die Gewichtsidentität und Kontraktion in jedem der 556 Schritte. Dies ist nicht der ungelesene unitale Recordkanal mit großer Fi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Feedback: Attraktor, Fehlerboden und unabhängige Zellen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1075,"byte_start":0,"id":"section:49762c24dcc9bf580732","kind":"chapter","labels":["ch:fronts14"],"line_end":10,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Aktualisierung v1.5: die aktuelle Frontkarte steht weiter hinten Die folgenden Rechnungen bleiben als v1.4-Befunde erhalten. Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Alle Arbeitsfronten: neue Tests und nächste Beweise","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":2084,"byte_start":1075,"id":"section:24cf719af9697a628987","kind":"section","labels":[],"line_end":19,"line_start":11,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Für den bereits konstruierten Strahlengraphen mit betrachten wir die zulässige Lazy-Walk-Familie [formula in source] , [formula in source] . Ein Eigenwert kann nur bei [formula in source] oder [formula in source] verschwinden. Dort sind die Nullitäten 30 beziehungsweise 5; ansonsten ist der Rang 60. Das liefert einen präzisen Rangvergleich innerhalb dieser Familie, aber keine Auswahl über alle denkbaren Compiler.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T1: Auswahl statt nachträglicher Passung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3581,"byte_start":2084,"id":"section:7f139ecb669441ba1701","kind":"section","labels":[],"line_end":32,"line_start":20,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"In einer ausdrücklich zusätzlich gewählten unitären Bosonreferenz liefert das Ladungsfeld [formula in source] auf dem Vakuum die Koeffizienten Der unabhängige Prüfer rekonstruiert diese Identität für [formula in source] bis Niveau 32. Für einen exponentiell abfallenden Modentest [formula in source] ist Dies ist eine konkrete Vakuumkonstruktion und kein Energieabschätzungsbeweis auf allen Zuständen. Das Ladungsfeld li","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T2: Ein konkreter Anfang der analytischen Naht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":4719,"byte_start":3581,"id":"section:51324bbdc837cffa4297","kind":"section","labels":[],"line_end":42,"line_start":33,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Für die deklarierte Produktfamilie [formula in source] ist das Spektrum exakt separierbar: Wir berechnen den Wärmetrace ohne eine riesige Matrix anzulegen und bestimmen [formula in source] . Für [formula in source] , [formula in source] ergibt sich näherungsweise [formula in source] . Geprüft wurden [formula in source] und [formula in source] . Die dreidimensionale Probe beschreibt damit 4.194.304 Produktknoten, ohne","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T3: Ein skalierender Raumtest, der seine eigene Grenze zeigt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6590,"byte_start":4719,"id":"section:d963030ec878ae470c30","kind":"section","labels":[],"line_end":54,"line_start":43,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Das einfachste Gitter-Weylsymbol [formula in source] besitzt acht Knoten, je einen an jeder Kombination [formula in source] . Ihre Chiralitäten wechseln; die Summe ist null. Eine anschauliche zweikomponentige Gleichung allein entfernt die zusätzlichen Arten daher nicht. Diskrete Weyl-Walks sind eine mögliche https://arxiv.org/abs/1708.00826Referenzkonstruktion, keine automatische Lösung dieses TFPT-Problems.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T4: Chirale Nullmoden werden gebaut, aber nicht als Familien ausgegeben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7653,"byte_start":6590,"id":"section:502dd7a57b70f8e50430","kind":"section","labels":[],"line_end":59,"line_start":55,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Die in dieser Revision nachgewiesenen äußeren Bandschranken betreffen die ganze harte Einzelle, nicht nur deren Singulett. Die kantenlokale vierte Ordnung ist positiv und ihre niedrigen Eigenwerte wurden als vollständiger trunkierter Operator neu berechnet. Der mikroskopische Filter benutzt alle Energien des 544-dimensionalen Sterns. Damit sind mehrere zuvor nur effektive Bausteine zu kontrollierbaren endlichen Aussa","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T5: Was die Band- und Filterergebnisse tatsächlich schließen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9702,"byte_start":7653,"id":"section:ee962e67774cbc8aef5e","kind":"section","labels":[],"line_end":70,"line_start":60,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":["relation:6b5d1a319b2f5565a35b","relation:8dc252a9772bc4cd88c7","relation:ee077edcfb64f3492f73"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Zunächst die Flavourkontrolle: Für dieselben orthonormalen drei Nullmoden auf linker und rechter Seite liefert ein räumlich konstanter Skalarüberlapp [formula in source] . 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Das ist ein expliziter Test dafür, dass Modenzähl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T6: Parameter brauchen einen gemeinsamen empirischen Test","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10717,"byte_start":9702,"id":"section:5b01dff035ea648f1b6d","kind":"section","labels":[],"line_end":79,"line_start":71,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Für freie massive bosonische Moden mit Lücke [formula in source] hat eine normalgeordnete bilineare Tensorobservable im Vakuum Spektralgewicht erst oberhalb der Zweiteilchenschwelle [formula in source] . Die Gitterproben [formula in source] , [formula in source] , bestätigen die Schwelle eins. Ein transversaler, spurloser Projektor besitzt zwar Rang zwei, verschiebt aber keine Energie zu null. Er erzeugt daher aus di","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T7: Warum ein Tensorbild noch keine Gravitation ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12272,"byte_start":10717,"id":"section:72d2e1c1180fca0216c5","kind":"section","labels":[],"line_end":86,"line_start":80,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Die gemeinsame kontrollierte Ausführung liefert jetzt operative Rohwahrscheinlichkeiten mit bezahlter Präparation, Aufzeichnung und Endprüfung. Sie liefert noch kein physikalisches Quellfunktional, aus dem dieselben Kontrollmöglichkeiten, Zustände, Wirkungen und Observablen folgen. Die fehlende Kante liegt weiter zwischen primitiver Compilerregel und gewähltem Laborvertrag.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T8 und die anderen Arbeitsfronten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13655,"byte_start":12272,"id":"section:7b108addc6d66e5887f5","kind":"section","labels":[],"line_end":99,"line_start":87,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"L10mmL65mmL72mm Tor&Neuer substantieller Beitrag&Fehlender vollständiger Nachweis\\\\ T1&Rang- und Entropievergleich, drei lokal unterschiedliche Vermittlerverträge.&Primitive Auswahl von Zuständen, Alternativen, Phasen und Kopplung.\\\\ T2&Vakuumkoeffizienten, Sektorparität und Halbladungsschranke.&Native Halbladung mit Definitionsmenge, Energie- und Adjungiertenkontrolle.\\\\ T3&Skalierende Wärmetrace-Rechnung und gemein","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die acht Tore bleiben einzeln sichtbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15702,"byte_start":13655,"id":"section:a58b3afd7b66cf7581bc","kind":"section","labels":[],"line_end":110,"line_start":100,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Wer bedient das Labor? Aus einer festgelegten Compilerregel kontrolliertes [formula in source] , Resonanz, [formula in source] , Reset und Kantenisolation ableiten. Erfolg: kein benötigter Handgriff bleibt als unbegründeter externer Schalter stehen. Welche Vermittlerarchitektur wird ausgewählt? Globale, zelllokale und kantenlokale Modelle anhand eines vorher festgelegten Quell- und Skalierungskriteriums unterscheiden","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Sechs nächste Fragen – mit einem klaren Erfolgskriterium","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17799,"byte_start":15702,"id":"section:3399c15f7c1a191d8c2e","kind":"section","labels":[],"line_end":120,"line_start":111,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Die fünf eingereichten Texte N9–N13 sind unverändert archiviert und einzeln durch SHA-256 gekennzeichnet. Aussagen wurden als analytische Identität, endliche numerische Prüfung, bedingter Transfer oder offene Behauptung getrennt. Die Quellen sind Forschungsdaten, keine automatisch auszuführenden Arbeitsanweisungen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Prüfprovenienz und Reproduzierbarkeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":664,"byte_start":0,"id":"section:3e6b641490c9348b66e8","kind":"chapter","labels":["ch:execution15"],"line_end":7,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Wo wir jetzt stehen Wir können mehrere Teile der kleinen mathematischen Maschine konkreter bauen. Die Aufzeichnung braucht weniger Spezialsteuerung; große endliche Spektren lassen sich durch eine tatsächlich vorhandene Symmetrie verkleinern; eine ausdrücklich gewählte Kette besitzt berechenbare kritische Dynamik. Noch nicht bewiesen ist, dass dieselbe ursprüngliche TFPT-Regel gerade diese Steuerungen, Kopplungen, Zus","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Version 1.5: eine einfachere gemeinsame Ausführung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2399,"byte_start":664,"id":"section:02d307d696e24c0d1f2a","kind":"section","labels":[],"line_end":20,"line_start":8,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Die Texte TFPT Universalraum Fortsetzung, 14.09.2026 NEU und TFPT Universalraum Ergebnisse, 14.09.2026 sind mit der v1.4-Grundlage abgeglichen. Ihre unveränderten Originale liegen als N14 und N15 im Quellenpaket. Interne Arbeitsanweisungen werden als Quelleninhalt, nicht als neue Aufträge behandelt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei weitere Eingaben und ihre wirklichen Zusatzinformationen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4171,"byte_start":2399,"id":"section:0737e4e72d2f8b70fb25","kind":"section","labels":[],"line_end":45,"line_start":21,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Die beiden Belegungsalternativen besitzen den hellen Hamiltonblock [formula in source] Ein einzelner Puls erreicht bei [formula in source] höchstens [formula in source] Transferwahrscheinlichkeit. 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Das ist keine neu a","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Feste Verstimmung, positive Zeiten und ein exakter Record","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5414,"byte_start":4171,"id":"section:8a4904f3db83daf395ec","kind":"section","labels":[],"line_end":65,"line_start":46,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Ein positiver Puls der Dauer [formula in source] ist auf dem hellen Raum nicht genau das Inverse, sondern [formula in source] Die Rückfolge [formula in source] hinterlässt also die aktive Sektorphase [formula in source] . Bei abgeschaltetem [formula in source] korrigiert ein positives Warteintervall [formula in source] die Vermittlerphase. Mit [formula in source] lautet die vollständige, von rechts nach links gelesen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Rückfolge und ihre bislang gefährliche Sektorphase","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7196,"byte_start":5414,"id":"section:7018915b84276cc445ea","kind":"section","labels":[],"line_end":80,"line_start":66,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Die Makrooperation benötigt 24 On-Pulse, zwei Off-Intervalle und 23 Q-Aufrufe. 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Ein Q-Zeitfenster wird auf [formula in source] aufgefüllt; die kommutierende Drift verschwin","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Endliche Q-Zeiten und wirkliche Präparationskosten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7289,"byte_start":7196,"id":"section:7fffad6b7d9a81e94ca5","kind":"chapter","labels":["ch:spectrum15"],"line_end":82,"line_start":81,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Eine wirklich vorhandene Vereinfachung des großen Spektrums","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8374,"byte_start":7289,"id":"section:847db7e6074c16c32aa2","kind":"section","labels":[],"line_end":91,"line_start":83,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Auf dem 24024-dimensionalen Spechtraum [formula in source] sei [formula in source] und [formula in source] . Der rationale Projektor [formula in source] besitzt Dimension [formula in source] ; der größere translationsfeste Raum hat Dimension 1764. Die Darstellung [formula in source] erklärt, weshalb dies genau eine Fixlinie je vierdimensionaler Standardkopie isoliert. Auf dem gesamten Isotypieraum ist [formula in sou","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Standardblock ist nicht mehr nur angekündigt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9384,"byte_start":8374,"id":"section:2a989bcbb69f2e5bdd38","kind":"section","labels":[],"line_end":107,"line_start":92,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Der ganzzahlige Gruppenalgebraoperator erhält ein Specht-Schnittgitter in seinem rationalen invarianten Teilraum. Daher ist sein charakteristisches Polynom monisch ganzzahlig. Aus [formula in source] folgt die vorab bekannte Koeffizientenabschätzung [formula in source] Siebzehn Primmoduli liefern einen 452-Bit-CRT-Modulus oberhalb der nötigen 428-Bit-Schranke. Eine achtzehnte Primzahl prüft die Rekonstruktion unabhän","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Rationale Intervalle statt nur Dezimalzahlen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":11340,"byte_start":9384,"id":"section:f2761912173404f296ba","kind":"section","labels":[],"line_end":135,"line_start":108,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Die selbstkonjugierte Youngform besitzt in der orthogonalen Basis die Involution [formula in source] , wobei [formula in source] das Vorzeichen der Zellfolge in Zeilenordnung ist. Die 4-mal-4-Transposition enthält sechs Zelltranspositionen. Damit gelten exakt [formula in source] Alle 1920 Graphautomorphismen sind gerade Trägerpermutationen, also [formula in source] und [formula in source] . Für jeden dieser Automorph","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Tableau-Transposition: 80 wird 40","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12161,"byte_start":11340,"id":"section:cd10aba8ae5fad74afcc","kind":"section","labels":[],"line_end":148,"line_start":136,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Für kantenlokale Vermittler setze [formula in source] und [formula in source] . Dann [formula in source] Die einfache Spiegelung [formula in source] gilt für den korrigierten Hamiltonoperator nicht unverändert. Die G-Blockzerlegung bleibt jedoch richtig. 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Operator-Cauchy liefert [formula in source] Somit verbessert sich die C16-Zellbanksumme auf [formula in source] statt der getrennten Farbabschätzung [formula in source] . 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Auf einem D-regulären Graphen ist deshalb bei [formula in source] der volle Gap genau [formula in source] , wiederum mit gleichförmiger Einanregung als saturierendem Zustand.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der entscheidende Unterschied: innere Kritikalität bei massiven Vermittlern","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":18911,"byte_start":16853,"id":"section:9577b0da3eb137576f19","kind":"section","labels":[],"line_end":245,"line_start":220,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Mit allen 30 ersten Farben und reinem Transfer können sich auf der offenen Kette die geordneten Farben nicht überholen. Bei N Teilchen entstehen [formula in source] isospektrale Farbfolgen. Das erzeugt extensive Restentropie und ist keine Familienableitung.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Farbentartung lässt sich symmetrisch reparieren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18985,"byte_start":18911,"id":"section:30dda9929190a0548a06","kind":"chapter","labels":["ch:clock15"],"line_end":247,"line_start":246,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Rechnen, Zeit und ausgeschiedene Information","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":19968,"byte_start":18985,"id":"section:56afc035f1e82ed4ed06","kind":"section","labels":[],"line_end":257,"line_start":248,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Ein Pointer-Hadamard verwandelt den Record exakt in einen kontrollierten Ququart-Swap: [formula in source] Kodiert man ein Qubit in den Farben 0 und 2, bleibt das zweite Farbbit null und die Operation ist Fredkin. Mit sauberem Hilfsbit [formula in source] sei [formula in source] . Dann ist [formula in source] genau Toffoli, mit zurückgegebenem [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Aufzeichnung und kohärente Logik benutzen dieselbe Matrix","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":21389,"byte_start":19968,"id":"section:64d5bad2cc812343b92e","kind":"section","labels":[],"line_end":268,"line_start":258,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Für ein vorgegebenes Programm [formula in source] setze [formula in source] , [formula in source] und [formula in source] . Der offene History-Hamiltonoperator mit Links [formula in source] und Laplacediagonalen erfüllt exakt [formula in source] Jedes Programm hat also dasselbe Spektrum [formula in source] , wiederholt mit der Datendimension. Feste Zwischenzeit-Auslesungen unterscheiden die Programme, ihre Eigenwerte","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine autonome Uhr ist konstruierbar, aber sie wählt kein Programm","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":22468,"byte_start":21389,"id":"section:d0724b0ddba567f0968a","kind":"section","labels":[],"line_end":279,"line_start":269,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Auf [formula in source] tragen [formula in source] die Ladungen k/2 und l/2. Die bilaterale Verschiebung [formula in source] ist unitär, hat Norm eins und ein explizites Adjungiertes mit umgekehrter Verschiebung. Sie erhält die Gesamtladung, kippt aber die einzelne Systemparität [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Half-Charge: ein einfacher Adapter benennt die fehlende Ressource","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":23604,"byte_start":22468,"id":"section:b3fa0bf2ec3aee86e184","kind":"section","labels":[],"line_end":288,"line_start":280,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Ein universeller unitärer Reset von d orthogonalen Eingaben auf denselben reinen Systemzustand muss d orthogonale Umweltzustände erzeugen. 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Den ganzen Operator samt Zuschauerphasen prüfen, nicht nur Erfolgsamplituden. Gebundene Zwischenzellkoeffizienten: Transfer, Dichte, chemische Verschiebung und Farbaustausch gemeinsam ableiten. Erst eine lokale dynamische Restkontrolle, dann Kritikalität auf der inneren Skala g b","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die sechs nächsten Ziele sind jetzt schärfer","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":29648,"byte_start":28605,"id":"section:039c4674031c8c2cad41","kind":"section","labels":[],"line_end":350,"line_start":346,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Für RH fehlt weiterhin die Identifikation des tatsächlichen signierten Weil-Objekts mit uniformer Positivität und kontrollierten Grenzresten. Das Clock-Spektrum allein kann dies nicht leisten; seine Unabhängigkeit vom eingeschriebenen Programm ist jetzt konkret bewiesen. Der Gatteranschluss liefert für Faktorisierung eine bedingte Quantenrechenressource, aber keine neue klassische Polynomialzeit oder Lösung von P ver","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"RH, Faktorisierung und Hylæan bleiben getrennte Abnahmen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":31204,"byte_start":29648,"id":"section:08e0b2024b357f939989","kind":"section","labels":[],"line_end":358,"line_start":351,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Die eigenen Root-Prüfer umfassen 104 Bedingungen, normal und optimiert identisch, mit sechs abgefangenen Fehlermutationen. Die Kontrollfront umfasst 88 Bedingungen einschließlich vollständiger 44D-/88D-Operatoren und rationaler Prozessstatistik. Die Skalierungsfront umfasst 400 Bedingungen und sechs Fehlermutationen. Das Quartettpaket enthält 273 modulare Bedingungen, die vollständige CRT-Rekonstruktion, rationale Wu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was neu geprüft wurde und was die Prüfzahlen bedeuten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5125,"byte_start":0,"id":"section:b22bc7d2b190ec6acf5a","kind":"frontmatter","labels":[],"line_end":96,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main.tex","status_markers_as_written":[],"summary_excerpt":"TeX Gyre Pagella TeX Gyre Heros Latin Modern Mono arrows.meta,positioning,calc,fit,backgrounds,decorations.pathreplacing chapter navy section navy subsection navy slateTFPT · Universalraum slateErklärung und Rekonstruktion chapter slateForschungsstand 14. September 2026 headsepline=.3pt headsepline slate!35 nosep,leftmargin=1.4em,topsep=5pt toclinesection toclinechapter,section =2em font=small,labelfont=bf,sf,skip=7p","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8216,"byte_start":5125,"id":"section:fbe7c300933d496fb965","kind":"chapter","labels":[],"line_end":112,"line_start":97,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main.tex","status_markers_as_written":[],"summary_excerpt":"tocchapterWas dieses Dokument leisten soll Der Universalraum ist in den vorliegenden Arbeiten die Idee eines gemeinsamen Zusammenhangs von erlaubten Veränderungen, Zuständen und Aufzeichnungen. TFPT soll darin eine besonders strukturierte mathematische Ansicht liefern. Das ist inzwischen mehr als ein Bild: Kleine Prozesse, Zellzustände, Registerexperimente und mehrere Rekonstruktionspfeile sind ausdrücklich berechenb","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was dieses Dokument leisten soll","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9773,"byte_start":8216,"id":"section:0ada8a7b96daae1e4062","kind":"section","labels":[],"line_end":121,"line_start":113,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/main.tex","status_markers_as_written":[],"summary_excerpt":"Diese Fassung führt das vollständige 90-seitige Forschungsbuch v1.1 fort. 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Weitere eigene Ergebnisse: Phasen und robuste Präparation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10604,"byte_start":7925,"id":"section:394a626d7f24069a1e1d","kind":"section","labels":[],"line_end":100,"line_start":84,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/update_body_v14.tex","status_markers_as_written":[],"summary_excerpt":"L10mmL140mm Tor&Neue Rechnung und verbleibende Grenze\\\\ T1&Exakte Rang-Ausnahmen [formula in source] ; Kontext- und Strahlenentropie wählen verschieden. Ohne Auslesevertrag kein eindeutiges Einfachheitsprinzip.\\\\ T2&Vakuum-Ladungskoeffizienten bis Niveau 32 und Halbladungs-Paritätsschranke. Die native Halbladung samt Energie- und Adjungiertenkontrolle bleibt offen.\\\\ T3&Skalierende Wärmetrace-Proben in Dimension eins","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Was auf T1–T8 konkret weitergearbeitet wurde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11603,"byte_start":10604,"id":"section:3f0c12f725bee9607687","kind":"section","labels":[],"line_end":110,"line_start":101,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/update_body_v14.tex","status_markers_as_written":[],"summary_excerpt":"Wer bedient das Labor? Jede verwendete Kontrolle auf konkrete primitive Compileroperationen zurückführen. Welche Bauweise ist wirklich vorgegeben? Zellbank und Kantenmoden anhand der Quelle unterscheiden, nicht anhand des erwünschten Resultats. Ist die Vierfachstruktur beweisbar? Symmetrieprojektoren und zertifizierte Sektoruntergrenzen mit der neuen positiven F4-Form verbinden. Funktioniert es mit Fehlern und vielen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Die nächsten sechs Fragen in einfacher Reihenfolge","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":12325,"byte_start":11603,"id":"section:7e4c1b78d0ed704b564e","kind":"section","labels":[],"line_end":114,"line_start":111,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/update_body_v14.tex","status_markers_as_written":[],"summary_excerpt":"Drei neue unabhängige leichte Prüfer: 1287, 6939 und 6 Bedingungen, insgesamt 8232; normale und optimierte Ausführung bytegleich. Sieben gezielte Fehlvarianten werden erkannt. Hinzu kommt der separate neue 24.024D-Spektrallauf mit acht niedrigen korrigierten Eigenpaaren. Das sind überwiegend einzelne Zustands- und Übergangsprüfungen, nicht 8232 unabhängige Entdeckungen. Die Großrechnung ist numerisch, die analytische","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Prüfumfang dieser Revision","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":880,"byte_start":0,"id":"section:f4119b93d655e9e22017","kind":"chapter","labels":[],"line_end":8,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/update_body_v15.tex","status_markers_as_written":[],"summary_excerpt":"TFPT und Universalraum, Update v1.5 14. September 2026. Ausschließlich Änderungen gegenüber dem vollständigen Hauptbuch v1.4. Das Hauptdokument wird parallel vollständig weitergeführt; dieses kurze Paper ersetzt es nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Weniger Steuerung, mehr Symmetrie, eine kritische innere Skala","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2586,"byte_start":880,"id":"section:3426d6a727982d2f8b01","kind":"section","labels":[],"line_end":19,"line_start":9,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/update_body_v15.tex","status_markers_as_written":[],"summary_excerpt":"Der gleiche Record [formula in source] ist jetzt bei festem [formula in source] konstruiert. Bei [formula in source] führen zwölf positive Hamiltonpulse mit elf aus Q gewonnenen Belegungs-Z-Kicks zum vollen Transfer. Die positive Rückfolge hinterlässt eine exakt berechnete Sektorphase. Zwei Warteintervalle bei [formula in source] schließen sie auf dem ganzen 44D-Raum: [formula in source] Ohne diese Phasenreparatur be","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Aufzeichnung ohne Resonanzschalter und negative Zeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4236,"byte_start":2586,"id":"section:75d6b42f940e2080a43c","kind":"section","labels":[],"line_end":32,"line_start":20,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/update_body_v15.tex","status_markers_as_written":[],"summary_excerpt":"Der Standard-Multiplizitätsblock des führenden C16-Singuletts ist als 80-mal-80-Matrix konstruiert. Der rationale Projektor [formula in source] hat exakt Dimension [formula in source] . Vollständige modulare Intertwiner, ein quadratfreies charakteristisches Polynom und eindeutige CRT-Rekonstruktion unter vorab bewiesener Koeffizientengrenze sichern das Resultat.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Eine tatsächlich übersehene Symmetrie verkleinert das Spektrum","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6282,"byte_start":4236,"id":"section:ccca0f80b13ab61e85dd","kind":"section","labels":[],"line_end":53,"line_start":33,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/update_body_v15.tex","status_markers_as_written":[],"summary_excerpt":"Eine gemeinsame Abschätzung der sechs Farbkanäle verbessert die C16-Stabilitätskonstante für zelllokale Vermittlerbanken von 1920 auf 320; eigene Kantenmoden erlauben 80. Positive Vermittlertransportmatrizen erhalten extensive Untergrenzen. Ihr statischer inverser Wegkernel besitzt einen geometrisch fallenden Rest pro Zelle. Die volle dynamische lokale Reduktion bleibt eine eigene Aufgabe.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Masselose Dynamik braucht nicht masselose Vermittler","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8188,"byte_start":6282,"id":"section:e8fcf627667419ba5fad","kind":"section","labels":[],"line_end":66,"line_start":54,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/update_body_v15.tex","status_markers_as_written":[],"summary_excerpt":"Ein Pointer-Hadamard verwandelt R exakt in einen kontrollierten Ququart-Swap. Auf einer festen Qubitkodierung ist dies Fredkin; zwei Records, vier Pointer-Hadamards, drei zusätzliche CNOT und ein sauberes Hilfsbit liefern einen kohärenten Toffoli. Das ist ein konkreter bedingter Gatteranschluss, kein neuer Faktorisierungs- oder P-vs-NP-Beweis. Die allgemeine Universalität der ergänzten Gatter ist bekannt. https://arx","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Was die Aufzeichnung über Rechnen, Zeit und Information zeigt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":9139,"byte_start":8188,"id":"section:6cb3353d7f1110d683fc","kind":"section","labels":[],"line_end":75,"line_start":67,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/update_body_v15.tex","status_markers_as_written":[],"summary_excerpt":"Für die dokumentierte Regel [formula in source] und das vollständige Starobinsky-Potential gilt in erster Potential-Slow-Roll-Ordnung, ohne große-N-Abschneidung, [formula in source] Die ACT-Tabellenspalte P-ACT-LB2 mit [formula in source] und [formula in source] erreicht zentral nur 0.49299564 der Untergrenze. Das volle Potential repariert den zuvor gefundenen Widerspruch in dieser Ordnung nicht. Amplitudenanpassung ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Ein klarer empirischer Gegentest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10690,"byte_start":9139,"id":"section:d13dfc938bdd5ea8e451","kind":"section","labels":[],"line_end":90,"line_start":76,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-closure-20260914/main-v1.5/update_body_v15.tex","status_markers_as_written":[],"summary_excerpt":"Native Wörter für Wedge, Q, An/aus und Routing des verkleinerten Recordvertrags gewinnen. Die tatsächlichen Zwischenzellkoeffizienten gemeinsam ableiten und ihre dynamische lokale Restkontrolle beweisen. Die übrigen kleinen Spektralblöcke und andere SU(4)-Sektoren global zertifizieren. Das echte Half-Charge-Feld, alle Farbmoden und die chirale 3+1D-Grenze gemeinsam konstruieren. Hintergrund, Moden und gemeinsame empi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Die nächsten entscheidenden Ziele","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":4944,"byte_start":0,"id":"section:024229b64f9d20277306","kind":"frontmatter","labels":[],"line_end":117,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8.tex","status_markers_as_written":[],"summary_excerpt":"arrows.meta,positioning,calc,fit,backgrounds,shapes.geometric,shapes.misc,decorations.pathmorphing,decorations.pathreplacing,patterns,angles,quotes,matrix =3.5em","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"-1.2cm TFPT — Architecture and the [formula in source] Compiler\\\\[2mm] The two axioms [formula in source] , the derivation map, and the Coxeter–cyclotomic [formula in source] construction","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7187,"byte_start":4944,"id":"section:cf8ad1fb378e48fe5236","kind":"part","labels":[],"line_end":146,"line_start":118,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8.tex","status_markers_as_written":["[C]","\\mC","\\mE","\\mO"],"summary_excerpt":"This document develops the architecture layer of TFPT: the two axioms, the derivation map, and the explicit [formula in source] construction. 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Proof of uniqueness. Direct evaluation gives [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] ; so [formula in source] is the only root in [formula in source] . For [formula in source] the forward difference is ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[formula in source] as the Pascal closure","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":109554,"byte_start":108713,"id":"section:93683d7c3fd300bd9861","kind":"subsection","labels":[],"line_end":1796,"line_start":1781,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8"],"relation_ids":["relation:17e19d87ab7da1be889c"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"With [formula in source] , the quadratic hypercharge trace on one family is [formula in source] , and it generates the whole integer chain: The flavor budget, the [formula in source] budget, the [formula in source] count and the second seam defect all hang on the second hypercharge moment [formula in source] . \\ Round-22 sharpening: the moment itself is one symbolic identity, [formula in source] — the Coxeter number ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"One master moment generates [formula in source] , [formula in source] , [formula in source] , [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":110167,"byte_start":109554,"id":"section:33b4fab842cf1417435c","kind":"subsection","labels":[],"line_end":1808,"line_start":1797,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"with [formula in source] and [formula in source] . . 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The whole content is consolidated and verified in the standalone companion note ``The Even Carrier Code and the [formula in source] Coxeter Compiler.'' 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The non-trivial content is the cosmological-constant charge: since [formula in source] . So the ``double overlap'' charge [formula in source] equals the number of carrier-slot pairs [formula in source] on","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The ladder is binomial; [formula in source] singles out [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":265308,"byte_start":264439,"id":"section:af1dfdb3af7eeb583cb9","kind":"subsection","labels":[],"line_end":4164,"line_start":4149,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"The [formula in source] in the action ladder is not merely a rank: it is the square root of the discriminant of the carrier (hypercharge) polynomial. 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Writing [formula in source] , So [formula in source] is the exact leading value (the inverse of the [formula in source] family/gauge compression that sits in the seed [formula in source] , so [formula in source] ), and the deviation is precisely the small topological seed correction [formula in source] , i.e.\\ [formula in source] . Gravity","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Einstein normaliser as a corrected tree value","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":272004,"byte_start":267761,"id":"section:504ad2ae2fb5438f904e","kind":"section","labels":[],"line_end":4282,"line_start":4211,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8"],"relation_ids":["relation:23c8be94258ae9960ccf","relation:6027afbc20c5bcf4a959"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"Machine checks for this section: v60_ lambda_ metrology_ branch.py","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"[formula in source] -anchored metrology closure, and two anchors","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":273462,"byte_start":272004,"id":"section:f21263a5b5ce0586b9f8","kind":"section","labels":[],"line_end":4308,"line_start":4283,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8"],"relation_ids":["relation:073b4b6514b5ad269dec","relation:73780b3d967bf81b4b88","relation:9b71736bbb2e7cb8cd3d"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mC"],"summary_excerpt":"Machine checks for this section: v6_ bootstrap.py v14_ carrier_ uniqueness.py","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The landscape: [formula in source] is overdetermined","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":273910,"byte_start":273462,"id":"section:c65ae1d24385856b2176","kind":"section","labels":["sec:e8"],"line_end":4317,"line_start":4309,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8"],"relation_ids":["relation:8bfbdf6893914cd6f27c","relation:983a43716ff00589d00f","relation:a3f8125359cab42be7f9"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8.tex","status_markers_as_written":[],"summary_excerpt":"In the series [formula in source] is a downstream scale grammar, not a primitive cause: the boundary kernel fixes [formula in source] , the carrier rank, families and admissibility without [formula in source] upstream. Three levels.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The [formula in source] carrier atlas — stated unambiguously","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":275076,"byte_start":273910,"id":"section:6b9dec719137c69d70de","kind":"subsection","labels":[],"line_end":4334,"line_start":4318,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"Coxeter/gauge typing of the lcm–gcd pair. Writing [formula in source] and [formula in source] , the relations become [formula in source] and [formula in source] : the local SM algebra is the gcd of the Coxeter double-period and the [formula in source] rank-occupancy, and the [formula in source] root count is their lcm. Likewise the EW exponent reads [formula in source] (Coxeter principal part plus a rank singlet). \\ ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Level 1 — original [formula in source] data of the series ( )","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":275610,"byte_start":275076,"id":"section:58bbb3baa7f066bb78d7","kind":"subsection","labels":[],"line_end":4343,"line_start":4335,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"with [formula in source] the number of non-empty occupation words of the [formula in source] carrier code.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Level 2 — new exact counting identities ( )","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":280141,"byte_start":275610,"id":"section:4e9f1abfa575088fe498","kind":"subsection","labels":[],"line_end":4404,"line_start":4344,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8"],"relation_ids":["relation:0642534a8e9646a46891","relation:0cef59ea641b538a09f4","relation:21cb1d19eafee5190669","relation:2d8d1d24b307faf548e5","relation:37cc863ea8b81d3ca30f","relation:5f6d83c86c06525b8b50","relation:b9293a044987deb6f5c6","relation:e8b0f4ea721ee64f68cb"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"Identify [formula in source] with the even-weight binary code on five bits. A transition [formula in source] has flip [formula in source] , even and nonempty, so [formula in source] ; per state there are [formula in source] flips, giving and the [formula in source] undirected flips match the [formula in source] [formula in source] root pairs ( , counting). 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The whole integer chain then reads off [formula in source] : The [formula in source] slice is then [formula in source] : one [formula in source] phase slice of the [formula in source] root atlas is exactly the full flavor transport budget. \\ (arithmeti","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Level 2.8 — positive-root moment: [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":283838,"byte_start":282306,"id":"section:73958a4c07e94217d44f","kind":"subsection","labels":[],"line_end":4467,"line_start":4442,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"The three hard carrier atoms — weak rank [formula in source] , color rank / family count [formula in source] , carrier rank [formula in source] — generate the [formula in source] data cyclotomically, without taking [formula in source] as input. 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The one-generation spinor packet is the even exterior algebra, equivalently the even-weight binary code The two carrier roots [formula in source] , [formula in source] generate all hypercharges ( [formula in source] , [formula in source] , [formula in","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Theorem 1 — the even carrier code","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":321249,"byte_start":317452,"id":"section:56705716d23560ea5ccb","kind":"section","labels":[],"line_end":5006,"line_start":4948,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8"],"relation_ids":["relation:4d68534bac991724d39b","relation:69c38ed431ff023852d8"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"tocsectionTheorem 2 On [formula in source] the flip [formula in source] is even, so [formula in source] . The three relations [formula in source] form a symmetric association scheme (the even Hamming scheme on five bits) with The eigenvalues (computed directly) are [formula in source] and [formula in source] , with [formula in source] . The two graphs are named objects: The Standard-Model family is the valency side [","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Theorem 2 — Exterior–Action Duality","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":321962,"byte_start":321249,"id":"section:94752aee14df24cb9255","kind":"section","labels":[],"line_end":5019,"line_start":5007,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"tocsectionTheorem 3 Requiring the even family to equal the action truncation through pair degree, [formula in source] , i.e. the unique positive-integer solution. At [formula in source] the two sides equal [formula in source] , so carrier exhaustion [formula in source] and the Coxeter period [formula in source] coincide only at five slots: [formula in source] and [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Theorem 3 — the Coxeter closure equation selects [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":322965,"byte_start":321962,"id":"section:5a42f7673f3f1cf0707a","kind":"section","labels":[],"line_end":5038,"line_start":5020,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"tocsectionTheorem 4 From the three atoms [formula in source] , with [formula in source] and [formula in source] : The [formula in source] exponents are the primitive residues modulo [formula in source] , and [formula in source] . The local SM algebra and the root atlas are the two arithmetic projections of [formula in source] :","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Theorem 4 — the [formula in source] cyclotomic Coxeter compiler","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":324832,"byte_start":322965,"id":"section:80b04dc909a66aaa2095","kind":"section","labels":[],"line_end":5064,"line_start":5039,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mE","\\mO"],"summary_excerpt":"tocsectionTheorem 5 The directed even-flips of [formula in source] are the complete graph [formula in source] : ( [formula in source] .) So the positive [formula in source] roots are the unordered transitions of one family; the second hypercharge moment, the positive-root count and the sum of the [formula in source] exponents coincide at [formula in source] . The CP pairing [formula in source] of the exponents gives ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Theorem 5 — the root transition atlas and the positive-edge moment","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":329615,"byte_start":324832,"id":"section:0914f65f6af736599813","kind":"section","labels":[],"line_end":5140,"line_start":5065,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8"],"relation_ids":["relation:3e28eb3f294722489846","relation:45b16698684085cff7f0","relation:60dfa12925a2179cb3fb","relation:a9ca0d50ae74e9056c92"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"tocsectionTheorem 6 All discrete budgets and the seam seed are functions of [formula in source] : Two-graph product table. With the carrier-pair graph [formula in source] ( [formula in source] ) and the family-corner graph [formula in source] on [formula in source] ( [formula in source] , [formula in source] ), every large budget is a product of the two graphs: i.e.\\ ( [formula in source] , [formula in source] , [for","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Theorem 6 — downstream readouts from [formula in source]","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":346301,"byte_start":329615,"id":"section:ffca98d84a77b4d4e4ab","kind":"section","labels":[],"line_end":5388,"line_start":5141,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8"],"relation_ids":["relation:00626a41a22c6b6a2e26","relation:01037903ff6a88af16e6","relation:0129f35131e19d265569","relation:10f8fdf3aedcec4c90c3","relation:1322854e0f80bc59ddf3","relation:1a7860788523db8a2822","relation:1bc570ad5e3c7ea9d0d6","relation:1f00d96ac46c3e34ba64","relation:2a6a57fd2a154e1e2e63","relation:2fa00e839592064994d3","relation:33f7e2bd7fe7a9fa81fe","relation:3f30fb41e27b3b91c016","relation:43188e86fd25b6bde36d","relation:44fba55e5015089faa09","relation:518df40d59efb3054433","relation:56f4efec59a1b31d4c0d","relation:5e0f2afa02e9c645681d","relation:64253b2467115a849abe","relation:89514d1f4c0ff663e375","relation:898dedacb4fe19a5fbca","relation:8e478c1692cb547e9636","relation:91054c1d07357fe0b661","relation:990e9a7e6dec7165546c","relation:9cc516295b792d05e09a","relation:9db4e80e765261195bfe","relation:9e02aa5faa5ab2082f2e","relation:9fa300c143f7ac35ab83","relation:9fad3db0053832bcd9cc","relation:af9486736ce6bec1f5b0","relation:b0ca46e543936b03609f","relation:b2191ce18b4243accb17","relation:b72c1c374382a8a08058","relation:c65f97c6a3111cb3ad27","relation:ce86acc764ea28be0b30","relation:cf54388ca17cb26b0acf","relation:e23e31957363ac962d83","relation:e2806a61498ce111135e","relation:e3dcebff6d6a91d7f914","relation:f56ecd98491aaeaa55f0","relation:f8aff4072e0bdce26a40"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"tocsectionTheorem 7 Since [formula in source] , one has the standard chain [formula in source] , with the exact branching (verified dimensions and root/weight counts): The adjoint [formula in source] of [formula in source] is [formula in source] and its spinor [formula in source] is [formula in source] . The TFPT dictionary makes each summand a known object: @llY@ piece & value & TFPT reading \\\\ [formula in source] &","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Theorem 7 — the [formula in source] lift of the [formula in source] atlas","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":350385,"byte_start":346301,"id":"section:6ff4670b89c8b83d4b0f","kind":"section","labels":[],"line_end":5445,"line_start":5389,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8"],"relation_ids":["relation:1122cf278116bb427dc3","relation:567ce45a68c47ec997ec","relation:5fc6ab42437e3d3dd34a","relation:72b14cfca3a13abfc91c","relation:a209e67b78b70313600d","relation:e0caf9648f9ec17fcd45"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"tocsectionTheorem 8 — anchor microcode The parabolic flavor bundle [formula in source] on [formula in source] has splitting type [formula in source] , whose power sums [formula in source] generate the whole compiler budget:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Theorem 8 — the [formula in source] anchor microcode and the [formula in source] -ladder","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":354145,"byte_start":350385,"id":"section:370584071bc7ae53e572","kind":"section","labels":[],"line_end":5495,"line_start":5446,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mC","\\mE","\\mO"],"summary_excerpt":"tocsectionMaster statement Five carrier slots give [formula in source] ,\\ four family corners give [formula in source] ,\\ and [formula in source] gives the [formula in source] atlas. Equivalently: [formula in source] , [formula in source] , [formula in source] ; [formula in source] , [formula in source] , the [formula in source] Coxeter structure and the action ladder read the same five-slot pair-decuple. The Standar","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Master statement and status","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":356885,"byte_start":354145,"id":"section:da684f477b46ca49293a","kind":"section","labels":[],"line_end":5542,"line_start":5496,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"The lift is reproducible by a short script (all entries below verified exactly).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Appendix: machine-checkable [formula in source] construction","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":360513,"byte_start":356885,"id":"section:26a278c5e4594d3a3f3a","kind":"part","labels":["fig:ablation","sec:ablation"],"line_end":5614,"line_start":5543,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8"],"relation_ids":["relation:3f0fca321ba16cf1fb71"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"The single sharpest reviewer test is: was the closure [formula in source] engineered so that [formula in source] comes out? The honest answer is an ablation — vary each input and see which actually move the root. Three one-parameter scans (all others held at their compiler values) separate the load-bearing integers from the fine last-digit selector.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Appendix: ablation of the EM fixed point","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":361775,"byte_start":360513,"id":"section:f0aeeb43e4c7093fbe92","kind":"section","labels":[],"line_end":5634,"line_start":5615,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8"],"relation_ids":["relation:0c09a6e62a98b43718c2","relation:23ed387ee268d4fa3794","relation:4e636a1f2f8735b9dce1","relation:73cc679eee1afe94546d","relation:8cd822ac3542c01fccc6","relation:9d223b424dc8dc1294df","relation:9fc65cae324fd2911142","relation:a17c75c6ac32cc08685b","relation:cb4459e1ca9ca0e52fe3","relation:da1ca71b9e1f6c2f1e42","relation:da845da49b1e08063152","relation:e90858ed841e4a07fa15"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8.tex","status_markers_as_written":["\\mE"],"summary_excerpt":"The load-bearing identities of this document (marked , , ) are re-derived from [formula in source] alone and machine-checked by the suite in the repository folder verification/; the inline tags [verification/ [formula in source] ] point to the exact script. Relevant here: v1_e8_glue.py — the [formula in source] glue ( [formula in source] , [formula in source] , [formula in source] ). v2_carrier_pascal.py — [formula i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Appendix: computational verification","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":60,"byte_start":0,"id":"section:240fbfff4cb56019b14a","kind":"chapter","labels":["ch:idee"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Was mit Universalraum gemeint ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1381,"byte_start":60,"id":"section:41d6246dc3984b9ab859","kind":"section","labels":[],"line_end":9,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Wenn wir gewöhnlich von Raum sprechen, denken wir an eine Bühne: Hier steht ein Tisch, dort fliegt ein Teilchen, und die Uhr läuft im Hintergrund. Die Universalraum-Idee dreht diese Reihenfolge um. Vielleicht sind zuerst Beziehungen und mögliche Veränderungen da. Eine Bühne mit Entfernungen und einer Uhr entsteht erst, wenn viele dieser Beziehungen ein beständiges Muster bilden.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kein zusätzlicher Behälter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3208,"byte_start":1381,"id":"section:87ac1bf66512cf557b74","kind":"section","labels":[],"line_end":33,"line_start":10,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Eine ausreichend konkrete Fassung benötigt mindestens: Zustände: Was ist gegeben, einschließlich relevanter Korrelationen? Operationen: Welche Veränderungen sind erlaubt? Zusammensetzung: Wie dürfen Vorgänge hintereinander und nebeneinander verbunden werden? Aufzeichnungen: Welche Spuren bleiben erhalten und dürfen später erneut benutzt werden? Auslesung: Welche Ergebnisse sind mit welchen Wahrscheinlichkeiten beobac","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die fünf Bestandteile","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4343,"byte_start":3208,"id":"section:5a5744c4805dafb753d4","kind":"section","labels":["eq:op"],"line_end":46,"line_start":34,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Zwei Uhren können jetzt beide zwölf anzeigen und trotzdem verschieden weiterlaufen. Eine ist aufgezogen, die andere steht kurz vor dem Stillstand. Wer nur das Zifferblatt betrachtet, sieht den Unterschied noch nicht. Ein späterer Blick unterscheidet sie.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wann zwei Beschreibungen wirklich dasselbe sagen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5759,"byte_start":4343,"id":"section:1082220a89ad38496bd4","kind":"section","labels":["eq:vorwaerts"],"line_end":60,"line_start":47,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"TFPT liefert eine reichhaltige Grammatik: Träger, Darstellungen, Gitter, markierte Symmetrien, Projektoren und kurze wiederverwendete Zahlenformeln. Die Metapher vom Compiler meint eine Übersetzung zwischen diesen Beschreibungen. Sie sagt nicht, dass bereits ein kosmisches Computerprogramm identifiziert ist.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TFPT als Grammatik und als Übersetzung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5797,"byte_start":5759,"id":"section:23009cd3a3a62e20a174","kind":"chapter","labels":[],"line_end":61,"line_start":61,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Wie die Idee entstanden ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6733,"byte_start":5797,"id":"section:775f0ce5656e705398a5","kind":"section","labels":[],"line_end":66,"line_start":62,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Die Anhänge zeigen keine einzige plötzliche Entdeckung, sondern eine Folge von Verschiebungen der Frage. Zuerst fällt auf, dass kleine geometrische und algebraische Daten in verschiedenen Rechnungen wiederkehren. Der Fünferträger führt zu einem 16-dimensionalen Spinor; die passenden Gitterfaktoren führen zu [formula in source] ; ein komplexer Viererträger zeigt 60 besondere Strahlen. Clocks, Ladungszuordnungen und Fl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vom Wiedererkennen zur gemeinsamen Ursache","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7642,"byte_start":6733,"id":"section:6704f5d643f1dd86cf8d","kind":"section","labels":[],"line_end":71,"line_start":67,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Die älteren, in S09 zusammengefassten Untersuchungen fanden mehrere Räume, die man nicht einfach gleichsetzen darf: eine Kommutantenalgebra, einen Majorana-/Fockraum, einen festen Teilchensektor, eine verdoppelte Familienbeschreibung und eingeschränkte Kanalmodelle. Manche lokalen Ansichten ließen verschiedene gemeinsame Dynamiken zu. Andere Tests konnten unter engeren Voraussetzungen ausgewählte Zustände bestimmen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum Spektren und Einzelbilder nicht genügten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9498,"byte_start":7642,"id":"section:6119c52e64f89eac90ef","kind":"section","labels":[],"line_end":86,"line_start":72,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"L30mmL55mmL65mm Etappe& Erkenntnis& Neue Frage\\\\ Vorarbeiten, in S09 rückblickend beschrieben&Mehrere algebraische Ansichten, Lorentzkegel, verborgene Richtungen, lokale und gemeinsame Kanäle.&Welche Informationen gehen beim Auslesen verloren?\\\\ 13. September: Compiler-Manuskript S09&60 Strahlen, 15 Kontexte, zwei Schatten desselben Prozesses; explizite Vormessung mit Register.&Wer wählt Kreuzkopplung, Kontextgewicht","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die dokumentierte Entwicklung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10684,"byte_start":9498,"id":"section:52198fefe05251ca8062","kind":"section","labels":[],"line_end":94,"line_start":87,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Der eingefügte Gesprächstext spricht von einem Regelwerk mit Logbuch und von Raum und Materie als Mustern seiner Spuren. Das trifft die Forschungsintuition. Die Formulierung „TFPT ist die Grammatik, der Universalraum die Ausführung“ ist als Einstieg hilfreich.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was von der anschaulichen Ursprungserzählung bleibt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":66,"byte_start":0,"id":"section:505018c73f5aab5fe35f","kind":"chapter","labels":["ch:algebra"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die mathematischen Bauteile von TFPT","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1113,"byte_start":66,"id":"section:3bbb9db694838bd28e8d","kind":"section","labels":[],"line_end":12,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Die historische Kurzfassung nennt [formula in source] und einen fünfteiligen Träger. Vollständig gelesen setzt P1 einen orientierten Rand beziehungsweise eine Naht, einen geeigneten positiven Kern und eine Normierung voraus. P2 setzt Art und Struktur des Trägers voraus; die spätere [formula in source] -Lesart wird mit Farb- und schwachen Richtungen verbunden. Orientierung, Positivität, komplexe Struktur und Markierun","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Ausgangsannahmen enthalten mehr als zwei Zahlen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2337,"byte_start":1113,"id":"section:0eb73b56abd4c52160fa","kind":"section","labels":[],"line_end":26,"line_start":13,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Bei fünf komplexen Richtungen kann man antisymmetrische Kombinationen von null, zwei und vier Richtungen bilden. Zusammen erhält man Das ist die gerade Spinorstruktur von [formula in source] . „Antisymmetrisch“ heißt hier: Beim Vertauschen zweier Plätze wechselt ein Vorzeichen. Es ist eine genaue Bauvorschrift, keine bildliche Ähnlichkeit.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vom Fünferträger zum Spinor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4400,"byte_start":2337,"id":"section:00f1246bfb861181bff5","kind":"section","labels":[],"line_end":57,"line_start":27,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Die beiden positiven Wurzelgitter [formula in source] und [formula in source] besitzen Determinante vier und Diskriminantengruppe [formula in source] . Eine Diskriminantengruppe beschreibt hier die möglichen Restklassen, mit denen man das Gitter ohne Verlust der Ganzzahligkeit ergänzen kann. Für passende Generatoren gilt modulo eins Diagonal gekoppelt ist die Summe [formula in source] ganzzahlig. Die vier gemeinsamen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die Verklebung wirklich zu E [formula in source] 8 führt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6023,"byte_start":4400,"id":"section:b2418130b24ed105e6af","kind":"section","labels":["eq:branch"],"line_end":83,"line_start":58,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Die 240 Wurzeln sind besondere Vektoren in einem acht-dimensionalen Raum. Hinzu kommen acht Cartanrichtungen, sodass die Lie-Algebra 248 Dimensionen besitzt. Unter [formula in source] lautet ihre komplexe Zerlegung L47mmrY Sektor& Wurzeln& Generatoren einschließlich Cartan\\\\ [formula in source] &40& [formula in source] \\\\ [formula in source] &12& [formula in source] \\\\ Gemischter Vektorsektor&60& [formula in source] ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wurzeln und Generatoren sind verschiedene Zählungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7221,"byte_start":6023,"id":"section:69972475b78ce5726cfa","kind":"section","labels":[],"line_end":90,"line_start":84,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Ein Strahl ist ein reiner Zustand ohne seine insgesamt irrelevante globale Phase. Ein Kontext ist eine vollständige orthogonale Viererbasis: vier mögliche Ausgänge einer scharfen Messung. Im markierten komplexen Viererträger ergeben sich 60 besondere Strahlen in 15 solchen Kontexten. In der gewählten Kodierung sind dies die reinen Zwei-Qubit-Stabilizerzustände und ihre vollständigen Pauli-Kontexte. S09, Kap. 3 und 9","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das endliche Fenster: 60 Strahlen und 15 Kontexte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8754,"byte_start":7221,"id":"section:9256c7da20a17393ef21","kind":"section","labels":[],"line_end":106,"line_start":91,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"L45mmL31mmL74mm Objekt& Größe& Was die Zahl zählt\\\\ [formula in source] -Wurzeln&240&Besondere Vektoren, keine 240 unabhängigen Raumrichtungen.\\\\ [formula in source] &248&Dimension der Generatoralgebra.\\\\ Ein Viererträger& [formula in source] &Zustände eines Ququarts, hier als zwei Qubits kodiert.\\\\ Vier solche Träger& [formula in source] &Komplexe Hilbertraumdimension der Zelle.\\\\ 15 allgemeine CQ-Blöcke& [formula i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Räume im Größenvergleich","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":71,"byte_start":0,"id":"section:8051e4474a23067ec9bc","kind":"chapter","labels":["ch:prozess"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Ein gemeinsamer Prozess mit zwei Schatten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1558,"byte_start":71,"id":"section:4615f317b2912390595d","kind":"section","labels":["eq:T"],"line_end":19,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Man beginnt mit einem Strahl [formula in source] : Kontext [formula in source] , Ergebnis [formula in source] . Dann wählt man einen nächsten Kontext [formula in source] und misst in dessen Basis. Die Quellkonstruktion benutzt [formula in source] ist eine [formula in source] -Inzidenzmatrix. Sie erlaubt den aktuellen Kontext und sechs andere, mit ihm inzidente Kontexte. Jeder erlaubte Nachfolger erhält in dieser spez","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine einzelne Messrunde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3449,"byte_start":1558,"id":"section:f1e113cb6191e4b25610","kind":"section","labels":["eq:D","eq:shadows"],"line_end":55,"line_start":20,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Die Matrix [formula in source] summiert die vier Ergebnisgewichte jedes Kontexts. Die Matrix [formula in source] liest die 15 nichttrivialen Pauli-Erwartungswerte aus. Mit [formula in source] lauten ihre Einträge Für [formula in source] und [formula in source] ergibt sich exakt Der Systemschatten entwickelt sich somit als depolarisierender Kanal Die Dämpfung [formula in source] entsteht aus der Kontextkombinatorik. B","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kontext und Quantenzustand als zwei Auslesungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4623,"byte_start":3449,"id":"section:19344fe9b3752b2d51ad","kind":"section","labels":["eq:Tfactor"],"line_end":74,"line_start":56,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Die in S01 ausgearbeitete Faktorisierung lautet Hier gelten [formula in source] , [formula in source] und [formula in source] . Die beiden Zeilenräume sind orthogonal. Im selben Kontext haben die Pauli-Vorzeichenvektoren Skalarprodukt drei für denselben Strahl und minus eins für verschiedene Strahlen; bei inzidenten Kontexten bleibt eine gemeinsame Pauli-Richtung. Diese Werte ergeben genau die Einträge von","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die genaue Kompression auf 30 Koordinaten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6433,"byte_start":4623,"id":"section:a6ebae2474862306593c","kind":"section","labels":[],"line_end":96,"line_start":75,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Aus [formula in source] mit Permutationsmatrizen folgt beim gleichgewichteten Mitteln unmittelbar [formula in source] . Zusätzliche Konjugation durch die Symmetriegruppe [formula in source] ändert das nicht: S07 berichtet 5040 Terme über 4500 verschiedene Matchings, gegenüber 24\\,601\\,472 insgesamt möglichen perfekten Matchings des bipartiten Inzidenzbildes. Diese kombinatorische Realisierung ist konkret. Die Gleichg","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum Symmetrie die Gewichte noch nicht auswählt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7204,"byte_start":6433,"id":"section:d4234701f5a0e6e94410","kind":"section","labels":[],"line_end":111,"line_start":97,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Für die Kontextmatrix gilt Ihre Determinante ist negativ. Eine reelle Matrixexponentialfunktion hat jedoch [formula in source] . Deshalb ist [formula in source] auf diesem 15-dimensionalen Raum kein [formula in source] mit reellem [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein Schritt ist nicht dasselbe wie zwei halbe Schritte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7280,"byte_start":7204,"id":"section:e824df40b82386966fdc","kind":"chapter","labels":["ch:memory"],"line_end":113,"line_start":112,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Gedächtnis: Was ein einzelnes Bild verschweigt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9410,"byte_start":7280,"id":"section:560dc1cd2e54859e8ebb","kind":"section","labels":[],"line_end":147,"line_start":114,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Ein klassisch-quantenmechanischer Zustand, kurz CQ-Zustand, besitzt 15 positive [formula in source] -Blöcke [formula in source] . Zusammen haben sie 240 reelle lineare Koordinaten und Gesamtspur eins. Die feste Regel macht jeden Ausgangsblock in seinem Kontext diagonal. Deshalb gilt Es ist also nicht richtig, 240 Koordinaten pauschal als kleinste dauerhaft autonome Hülle dieser festen Ausführung auszugeben.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Allgemeine Kontextblöcke brauchen eine andere Beschreibung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10711,"byte_start":9410,"id":"section:ddd5ab96c713f0f45717","kind":"section","labels":["eq:record"],"line_end":168,"line_start":148,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Für die vier Projektoren eines Kontexts sind [formula in source] Spiegelungen. In Dimension vier gilt Allgemein in Dimension [formula in source] wäre die linke Seite [formula in source] . Der kurze Auslöschungseffekt ist hier also tatsächlich viererspezifisch.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie die Aufzeichnung gebaut wird","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12540,"byte_start":10711,"id":"section:b90fae5c76a48d7a7349","kind":"section","labels":[],"line_end":182,"line_start":169,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Für einen gleichförmigen reinen Eingang in der gewählten Kontextbasis erzeugt eine Vormessung maximale Verschränkung. Ohne Registerblick ist der Systemzustand [formula in source] . Nun gibt es zwei Ausführungen: Derselbe kohärente Speicher wird nochmals gekoppelt: [formula in source] stellt den reinen Eingang wieder her. Ein neuer Speicher wird benutzt: Im reduzierten System wird die Dephasierung wiederholt; [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das Echo des behaltenen Registers","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13348,"byte_start":12540,"id":"section:3b6ec508bf371beedf3f","kind":"section","labels":[],"line_end":192,"line_start":183,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Bei frischen Registern trägt eine Folge von Kontexten den kohärenten Zustand Das Weglassen des Registers summiert Dichteoperatorbeiträge. Eine kohärente Projektion auf eine Registersuperposition summiert Amplituden und beschreibt ein anderes Experiment, einschließlich seiner Erfolgswahrscheinlichkeit.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reihenfolge bleibt wichtig","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15023,"byte_start":13348,"id":"section:a770f0ea28cc2f905c9a","kind":"section","labels":[],"line_end":205,"line_start":193,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Eine nichtverschwindende Beobachtungsfolge eines geschlossenen endlichen Systems mit festem unitärem Schritt ist eine endliche Summe von Phasenfaktoren. Nach Zusammenfassung gleicher Frequenzen besitzt ihr mittleres Betragsquadrat einen positiven Cesàro-Grenzwert. Sie kann daher nicht für alle [formula in source] exakt wie [formula in source] abklingen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Endliches Gedächtnis und scheinbares Vergessen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":72,"byte_start":0,"id":"section:df5ad64ad64fe6325814","kind":"chapter","labels":["ch:zelle"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die Vierträgerzelle: ein gemeinsames Muster","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1404,"byte_start":72,"id":"section:2e99433f2cd11157bd9b","kind":"section","labels":["eq:omega"],"line_end":24,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Vier Träger mit je vier Basiswerten besitzen den total antisymmetrischen Zustand Jedes Basiswort verwendet alle vier Werte genau einmal. Die 24 Permutationen erhalten passende Vorzeichen. Das Ergebnis ist ein reiner gemeinsamer Zustand. Jeder einzelne Träger sieht für sich trotzdem maximal gemischt aus: Die Paarreduktion hat Rang sechs und sechs gleich große Eigenwerte [formula in source] . Die Ordnung steckt in den ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein Zustand, dessen Teile allein nichts verraten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2609,"byte_start":1404,"id":"section:2c46f0ed02162d4a6be3","kind":"section","labels":[],"line_end":38,"line_start":25,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Sei [formula in source] der Projektor auf den symmetrischen Paarraum. Wenn für alle Paare [formula in source] gilt, dann hat jeder Swap Eigenwert minus eins. Da Transpositionen alle Permutationen erzeugen, folgt Für [formula in source] ist dieser Raum eindimensional, für [formula in source] null. Auch gemischte Zustände mit entsprechender Trägerbedingung erfüllen die Aussage. Für [formula in source] existieren aber e","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Hüllensatz und seine genaue Voraussetzung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3902,"byte_start":2609,"id":"section:b4b470f4ca7b9ecd1783","kind":"section","labels":["eq:tet-spec"],"line_end":54,"line_start":39,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Das vollständige Tetramermodell lautet Es besitzt das exakte Spektrum Der Grundzustand ist [formula in source] , die Lücke [formula in source] . Die hochgestellten Zahlen zählen die Zustände pro Energiewert und summieren sich zu 256.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine weiche Energiebedingung erlaubt Bewegung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5057,"byte_start":3902,"id":"section:6e5d74ff53d2a8174c64","kind":"section","labels":[],"line_end":68,"line_start":55,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Der vollständige Graph, ein Stern und ein Pfad besitzen auf vier Trägern denselben antisymmetrischen Grundzustand, aber verschiedene Anregungen. Für gleiche Sterngewichte ist die Lücke [formula in source] statt [formula in source] . S01 nennt für einen Pfad mit Gewichten [formula in source] etwa [formula in source] ; S06 für sechs Gewichte [formula in source] etwa [formula in source] . Die letzten Werte werden hier a","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was ein Zustand über seinen Generator verrät","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5655,"byte_start":5057,"id":"section:367dada71959cebf79e8","kind":"section","labels":[],"line_end":73,"line_start":69,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Der Projektor [formula in source] kommutiert mit allen Swaps. Daher erhält jede rein zellinterne Austauschentwicklung, auch mit zeitabhängigen Gewichten, den Anteil [formula in source] . Kollektive [formula in source] -Drehungen tun dasselbe. Ein Grundzustand kann also bekannt sein, ohne dass der vorhandene Ablauf einen beliebigen Eingang dorthin bringt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum Austausch allein die Zelle nicht herstellt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5734,"byte_start":5655,"id":"section:096c05d4d9199d8a769a","kind":"chapter","labels":["ch:fugen"],"line_end":75,"line_start":74,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Vermittlung und Graph: die Prüfung der fünf Fugen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7886,"byte_start":5734,"id":"section:62bc4be505f1eb0dd25d","kind":"section","labels":[],"line_end":103,"line_start":76,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Der gewünschte positive Austausch lässt sich in einem kleinen Modell genau erklären. Man ergänzt den Paarraum [formula in source] durch einen sechsdimensionalen Vermittler mit Energie [formula in source] . Die partielle Isometrie [formula in source] erfüllt Für bleiben die zehn symmetrischen Zustände bei null; die antisymmetrischen Zustände koppeln paarweise an den Vermittler. Die unteren Energien sind Nach Identifik","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie ein virtueller Zwischenzustand bindet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9877,"byte_start":7886,"id":"section:c60239747b84b69d4f5e","kind":"section","labels":[],"line_end":125,"line_start":104,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"S11 macht die zusätzliche Zuordnung: Ein [formula in source] -Spinorgewicht [formula in source] ist ein Ort; das [formula in source] -Gewicht [formula in source] ist der lokale Viererzustand. Die 64 Gewichte von [formula in source] werden somit als 16 Orte mit je vier inneren Zuständen gelesen. Das ist eine konkrete bedingte Interpretation, keine bloße Umbenennung einer bereits gegebenen räumlichen Geometrie.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Clebsch-Vorschlag: eine genaue neue Graphlesart","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11916,"byte_start":9877,"id":"section:2253eb3b5f895ab9c17f","kind":"section","labels":[],"line_end":134,"line_start":126,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Die Graphkombinatorik folgt aus der angegebenen Ortslesart. Um daraus einen Vielteilchen-Hamiltonoperator zu erhalten, braucht man außerdem eine Fock- oder Tensorproduktstruktur, Besetzungsbedingungen, die Bedeutung der virtuellen Zustände und ihre Energien. Betragsgleiche Chevalley-Strukturkonstanten wählen noch keine physikalischen Kopplungsstärken in normierten Mehrteilchenzuständen aus. Gleiche [formula in source","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Welche Auswahl hier noch hinzukommt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13528,"byte_start":11916,"id":"section:da5a46c8ca006f19824d","kind":"section","labels":[],"line_end":153,"line_start":135,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"L74mmY Clebsch-Cluster bei [formula in source] , nach S11& Berichteter Wert\\\\ Grundenergie& [formula in source] \\\\ Grundzustand&Eindeutiges [formula in source] -Singulett, Form [formula in source] \\\\ Erster angeregter Singulettwert& [formula in source] ; mindestens vier orthogonale Moden, Gap etwa [formula in source] \\\\ Erste adjungierte Anregung& [formula in source] , Gap etwa [formula in source] \\\\ Weitere Multiple","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die berichteten Clusterzahlen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14709,"byte_start":13528,"id":"section:4f5acd9a6f2cc5748f7e","kind":"section","labels":[],"line_end":169,"line_start":154,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"S11 behauptet für den vollständigen Graphen mit [formula in source] einen eindeutigen Grundzustand bei [formula in source] und Gap [formula in source] . Energie und Gap stimmen; die Eindeutigkeit stimmt ab acht Trägern nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neue Korrektur: Singulett heißt nicht eindeutig","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16989,"byte_start":14709,"id":"section:2ffbbff049931424da86","kind":"section","labels":[],"line_end":191,"line_start":170,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Operatoren unterscheiden (v1.3): Das folgende [formula in source] beschreibt eine gleichkontextige Vierer-Aufzeichnung. Das neue binäre Austauschregister [formula in source] ist ein anderer Operator und nachweislich nicht Clifford. Seine zusätzliche Ressourcenanforderung widerspricht der folgenden Darstellbarkeit von [formula in source] nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neue Präzisierung: Aufzeichnung ist nicht durch die 248 verboten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":66,"byte_start":0,"id":"section:abe4384b96949dfd1c3e","kind":"chapter","labels":["ch:two"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Zwei Zellen: aus Verbindung wird Dynamik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":839,"byte_start":66,"id":"section:66c6678f104e95ef2f5d","kind":"section","labels":[],"line_end":7,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Ist eine reduzierte Dichtematrix [formula in source] rein, so muss der gemeinsame Zustand bezüglich [formula in source] und seinem Rest faktorisiert sein. Sein Träger liegt in [formula in source] . Sind alle disjunkten Zellmarginalien unverändert rein, ist der Gesamtzustand ein Produkt über die Zellen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die Zellen beim Verbinden ihre Reinheit verlieren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1875,"byte_start":839,"id":"section:66a07adbbb55f013527b","kind":"section","labels":["eq:Hred"],"line_end":28,"line_start":8,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Zwei vollständige Tetramerzellen mit genau einer Brücke haben Der volle Raum besitzt [formula in source] Dimensionen. Trotzdem bleibt die Entwicklung des Produktzustands in einem zweidimensionalen invarianten Unterraum: Die beiden Vektoren sind orthonormal; [formula in source] und [formula in source] . Es folgt Die Brücke koppelt den Produktgrundzustand an eine gemeinsame adjungierte Anregung. Beide Zellhälften verwe","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein kleiner exakter Raum in einem großen Hilbertraum","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4244,"byte_start":1875,"id":"section:6c03dd92bb9a1a1ff0f7","kind":"section","labels":["eq:alllambda13","eq:gapbound"],"line_end":73,"line_start":29,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Mit lauten die beiden Eigenwerte Die negative Korrektur beschreibt die Absenkung gegenüber dem einfachen Produktwert [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Energie und ein wirklicher Grundzustandsnachweis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5445,"byte_start":4244,"id":"section:ad3208df7043f2109636","kind":"section","labels":[],"line_end":95,"line_start":74,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Der niedrige Eigenzustand lässt sich schreiben als Seine Zellreduktion besitzt das Spektrum Die Entropie in natürlichen Logarithmen ist Bei [formula in source] sind [formula in source] und [formula in source] ; bei [formula in source] gilt [formula in source] . Schon eine endliche einzelne Brücke macht die lokale Zelle gemischt. Energieabsenkung und Verschränkung sind hier keine unabhängig eingesetzten Zusätze.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verschränkung aus derselben Kopplung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6560,"byte_start":5445,"id":"section:f1cf44b5703b7e1fead4","kind":"section","labels":["eq:two-clock"],"line_end":111,"line_start":96,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Starte im Produkt [formula in source] und lasse denselben konstanten gekoppelten Hamiltonoperator wirken. Dann gilt Bei [formula in source] vereinfacht sich dies zu [formula in source] . Der Energieinhalt beider Zellen pulsiert in einem messbaren Muster.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein Uhrsignal ohne zusätzlich gewählten lokalen Tick","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7528,"byte_start":6560,"id":"section:4ae6a758379e532bd502","kind":"section","labels":[],"line_end":120,"line_start":112,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Ein einzelner eindeutiger Singulettgrundraum besitzt keine logische Zustandsvielfalt. Das Produkt solcher Grundräume bleibt eindimensional. Wer alles auf diese Grundräume projiziert, erhält nur eine skalare Energie. Nichttriviale effektive Dynamik muss Anregungen, Randzustände, Multiplizitäten oder zusätzliche Vakuumsektoren behalten.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum viele Zellen noch ein eigener Schritt sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":71,"byte_start":0,"id":"section:919f03f81a25a792cb51","kind":"chapter","labels":["ch:zeit"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Zeit: Takt, Uhrwerk und lesbare Veränderung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1193,"byte_start":71,"id":"section:2454620d644e339ac26b","kind":"section","labels":[],"line_end":15,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Eine zyklische Matrix ist zunächst ein Taktmuster. Eine Dynamik sagt, wann welcher Zustand entsteht. Eine Uhr braucht zusätzlich eine beobachtbare Anzeige und eine Kalibrierung. Diese drei Ebenen müssen zusammenpassen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Drei Bedeutungen des Wortes Clock","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2069,"byte_start":1193,"id":"section:bbda9b8659ff9814f24a","kind":"section","labels":[],"line_end":20,"line_start":16,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Der vollständige gleichgewichtete Tetramer-Hamiltonoperator ist eine zentrale Transpositionssumme. Deshalb kommutiert er mit jedem [formula in source] und jedem [formula in source] . Die Paarenergien ändern sich unter seiner freien Entwicklung nicht. Eine Tabelle, die nacheinander einen lokalen [formula in source] -Tick anwendet, ist somit kein Beweis, dass genau diese Anzeige unter [formula in source] von selbst läu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die Paarenergien unter dem Tetramer stillstehen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":3008,"byte_start":2069,"id":"section:4b88503040319c071da2","kind":"section","labels":[],"line_end":38,"line_start":21,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Ein präparierter nichtstationärer Zustand kann dennoch unter demselben Tetramer laufen. Für einen lokalen spurfreien hermiteschen Pauli [formula in source] mit [formula in source] setze Da [formula in source] , folgt Die lokalen Anzeigen oszillieren gegeneinander; ihre Summe bleibt null. Die Periode ist [formula in source] . Präparation, Ausleserichtung und die Kalibrierung von [formula in source] sind weitere Eingab","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine laufende lokale Anzeige im gesetzten Modell","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4494,"byte_start":3008,"id":"section:2cd5ffed510da1107979","kind":"section","labels":[],"line_end":57,"line_start":39,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Zerlege [formula in source] . Die vier [formula in source] sind orthonormal. Wähle zusätzlich Weil jedes Wort von [formula in source] jedes Energielabel einmal enthält, gilt [formula in source] . Für erhält man [formula in source] . Die Zeiten [formula in source] liefern vier orthogonale Anzeigen. Global ist der Zustand stationär, bedingt auf die Uhranzeige entwickelt sich das System. Das ist eine konkrete Page-Woott","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine relationale Viereruhr ist konstruierbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":5172,"byte_start":4494,"id":"section:9653c027c434993816ba","kind":"section","labels":[],"line_end":62,"line_start":58,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Aus [formula in source] folgt [formula in source] . Die historischen Größen [formula in source] und [formula in source] beschreiben deshalb sechsfach wiederholte Faktoren [formula in source] und [formula in source] . Eine physikalische Rate ist erst [formula in source] für einen festgelegten Schritt [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum ein Logarithmus noch keine Sekunde ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5883,"byte_start":5172,"id":"section:2a5db278522c2c70e6cf","kind":"chapter","labels":["ch:echo"],"line_end":67,"line_start":63,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Verschiedene Präparationsverträge bleiben getrennt Dieses Kapitel bewahrt die ursprüngliche endliche Schaltung mit Erfolg [formula in source] aus dem vorausgesetzten Zweisingulett-Eingang. Der neue Stern-Spektralfilter erreicht [formula in source] aus demselben Eingang, setzt aber kontrollierte kontinuierliche Pulse voraus. Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die ausführbare Präparation und der Mehrzeittest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7250,"byte_start":5883,"id":"section:b4338fb868b3c00b4db1","kind":"section","labels":[],"line_end":89,"line_start":68,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Die Präparationsnotiz S02 geht über den abstrakten Satz „ [formula in source] existiert“ hinaus. Sie beschreibt eine konkrete Schaltung, die aus einem einfachen Eingang den Zustand mit Erfolgsanzeige herstellt, anschließend ein Register schreibt und die Rückkehr ausliest. Laut Quelle wurde die Schaltung exakt simuliert, nicht auf Hardware ausgeführt. Ihr Zugriff auf zusätzliche Hilfssysteme und Nicht-Clifford-Operati","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was S02 tatsächlich geschlossen hat","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8727,"byte_start":7250,"id":"section:bfad84108557374370ff","kind":"section","labels":[],"line_end":104,"line_start":90,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Der benötigte Zustand [formula in source] ist in der Acht-Qubit-Kodierung kein Stabilizerzustand. Schon für einen nichttrivialen lokalen Pauli gilt während reine Qubit-Stabilizerzustände für Pauli-Observablen nur [formula in source] liefern. Ebenso ist der Paarreduktionsrang sechs keine Zweierpotenz. Eine exakte Präparation aus einem Stabilizer-Eingang benötigt deshalb eine zusätzliche Ressource, etwa einen passenden","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die zusätzliche Ressource bleibt sichtbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9859,"byte_start":8727,"id":"section:cd2d5b63e5d87fc44f31","kind":"section","labels":[],"line_end":126,"line_start":105,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Der einfache Eingang lautet Er ist mit dem in S02 angenommenen Clifford-Baukasten präparierbar und besitzt [formula in source] -Anteil [formula in source] . Der Antisymmetrisierer ist Die konkrete Schaltung erzeugt 32 Kontrollzweige, von denen 24 die Permutationen tragen. Acht ungültige Zweige werden markiert. Nach Interferenz und Erfolgsselektion ist der implementierte Operator Somit gilt Der erfolgreiche Zweig ist ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie der Filter den Zustand erzeugt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11835,"byte_start":9859,"id":"section:4a2573e9171f04e5404c","kind":"section","labels":["eq:originalecho"],"line_end":163,"line_start":127,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] schreibe [formula in source] . Dann Ein ignorierter frischer Pointer erzeugt Diese binäre Swap-Aufzeichnung ist ein anderer Kanal als die 15-Kontext-Mischung mit Faktor [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das ursprüngliche Echo: eins gegen siebzehn Zweiunddreißigstel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13337,"byte_start":11835,"id":"section:9237f1d9f3ce11b57f9c","kind":"section","labels":[],"line_end":183,"line_start":164,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Der Endfilter hat den Effekt [formula in source] . Seine beobachtbare Erfolgsrate ist deshalb [formula in source] , nicht [formula in source] selbst. L68mmY Y Statistik& Behalten& Frisch\\\\ [formula in source] -Rückkehr, bedingt auf Präparation& [formula in source] & [formula in source] \\\\ Endfilter erfolgreich, bedingt auf Präparation& [formula in source] & [formula in source] \\\\ Beide Filter erfolgreich, je begonnen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die wirklichen Erfolgswahrscheinlichkeiten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15734,"byte_start":13337,"id":"section:38e149d236a20cf3fb45","kind":"section","labels":["eq:optimal"],"line_end":210,"line_start":184,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Eigene exakte Ergänzung dieser Synthese. Man kann die gleiche Messfrage für einen beliebigen lokalen unitären Tick [formula in source] ausrechnen. Setze Die beiden Swap-Gewichte sind [formula in source] . Daher Der Kontrast dieser Rückkehrstatistik ist maximal, wenn [formula in source] , also [formula in source] . Ein einzelnes CNOT innerhalb des Viererträgers erfüllt [formula in source] . Es permutiert dieselbe Meng","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neue Fortsetzung: der maximal ausgeglichene Echovergleich","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17149,"byte_start":15734,"id":"section:b8f777e4654d123feb92","kind":"section","labels":[],"line_end":218,"line_start":211,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Y r Ressource nach S02& Anzahl\\\\ Systemqubits&8\\ , wiederverwendet&10\\ ätze&2\\ reservierte Qubits&20\\ Erfolgsbits beider Filter&12\\ -Gatter&574\\ CNOT vor Toffoliauflösung&382\\ &26\\ - [formula in source] / Pauli- [formula in source] &276 / 26\\\\T/T^ [formula in source] T-Varianten waren durch lokale Matrixidentität und Ersetzung zertifiziert, nicht zusätzlich als komplette komplexe 20-Qubit-Vektoren simuliert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ressourcen und Beweisgrenze der Originalschaltung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":75,"byte_start":0,"id":"section:af9d77aab9c169252590","kind":"chapter","labels":["ch:seam"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Von der Kette zur E [formula in source] 8-Naht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1943,"byte_start":75,"id":"section:85a42c8b4551103a4c67","kind":"section","labels":[],"line_end":28,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Das Zweizellenmodell benutzt zwei vollständige Vierergraphen mit einer Brücke. Die Vielzellenrechnung in S08 benutzt dagegen Vierersegmente mit nächster Nachbarschaft. Bei [formula in source] wird erst dieses zweite Modell eine uniforme Kette. Derselbe isolierte Singulettzustand garantiert keine identischen Anregungen und keinen identischen Grenzwert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein wichtiger Modellwechsel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3203,"byte_start":1943,"id":"section:d0ca8193388892739149","kind":"section","labels":[],"line_end":44,"line_start":29,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Für den uniformen periodischen Austauschring liefern die Quellen [formula in source] bei acht und [formula in source] bei zwölf Trägern. Der bekannte Vergleich lautet Die Sutherland-Grundenergie pro Träger ist für [formula in source] . S08 nennt die Extrapolation [formula in source] und [formula in source] . Diese endlichen Zahlen passen zur [formula in source] -WZW-Beschreibung des Kettenmodells. Die allgemeine Verb","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die SU(4)-WZW-Theorie hier plausibel ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4699,"byte_start":3203,"id":"section:070dc066291a14e1034d","kind":"section","labels":[],"line_end":70,"line_start":45,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Die zentrale Ladung ist eine Kennzahl einer konformen Feldtheorie. Für die chiralen Niveau-1-Faktoren gilt Das Produkt hat also schon vor einer Kopplung [formula in source] . Ein später gefundener Wert acht allein ist kein Beweis einer [formula in source] -Erweiterung und kein Beweis eines Kondo-Flusses.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Naht braucht mehr als die Zahl acht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6584,"byte_start":4699,"id":"section:8d25f50a3c2086d6d20a","kind":"section","labels":[],"line_end":92,"line_start":71,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"S11 ersetzt die frühere Kondo-Zielbeschreibung sinnvoll durch eine konkrete Erweiterungsaufgabe. Die Kurzschreibweise eines Quotienten durch [formula in source] kann jedoch verschiedene Operationen meinen. Nur auf invariante Zustände des ursprünglichen Produkts zu projizieren ist nicht dasselbe wie eine Simple-Current-Erweiterung mit den nötigen zusätzlichen beziehungsweise entsprechend gekoppelten Sektoren.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum „Z [formula in source] 4-Eichung“ präzisiert werden muss","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7319,"byte_start":6584,"id":"section:cf5d8b59116a174f1c10","kind":"section","labels":[],"line_end":97,"line_start":93,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Eine gewöhnliche kritische SU(4)-Kette hat links- und rechtslaufende Sektoren, mit [formula in source] . Die übliche Kennzahl heißt dabei [formula in source] , nicht sechs. Die chirale Differenz ist null. Eine rein chirale [formula in source] -Naht hat dagegen Differenz acht. Ein zusätzliches ebenfalls nichtchirales [formula in source] -Modell ändert daran nichts.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Chiralitätslücke","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8698,"byte_start":7319,"id":"section:8640f78cf233ec4c920a","kind":"section","labels":[],"line_end":103,"line_start":98,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Die innere Glue- [formula in source] wirkt auf den 248 Strömen mit Phasen [formula in source] auf Sektoren der Größen [formula in source] . Ihre Spur ist null. Die geometrische Vierteldrehung [formula in source] hat auf Stufe eins dagegen Spur [formula in source] . Die Operatoren sind somit nicht identisch. Eine Clock kann eine geometrische Drehung mit innerem Twist kombinieren; die beiden Faktoren bleiben getrennt. ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei Vierteldrehungen und der Index","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":551,"byte_start":0,"id":"section:a1e80b081214c46f9d33","kind":"chapter","labels":["ch:recon"],"line_end":5,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Fortschritt v1.3 Ein gemeinsamer endlicher Träger realisiert nun Aufzeichnung, Näherungspräparation, Reset und Mehrzeitantwort unter einem ausdrücklich angegebenen Ressourcenvertrag. Das beantwortet eine bedingte Existenzfrage. Es wählt weder den Vertrag aus TFPT allein noch ein universelles positives Zustandsfunktional aus. Die nachfolgenden Anforderungen bleiben deshalb nötig; die Konstruktion steht in Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie eine vollständige Rekonstruktion aussehen könnte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1946,"byte_start":551,"id":"section:db544d83df752f64ccfc","kind":"section","labels":[],"line_end":17,"line_start":6,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Eine endliche Liste von Schatten bestimmt im Allgemeinen mehrere Prozesse. Man kann sogar jeden Kandidaten um einen ungekoppelten unsichtbaren Hilfsfaktor ergänzen, auf den alle erlaubten Experimente trivial wirken. Alle Antworten bleiben gleich. Eindeutigkeit ist daher zunächst nur für die minimal beobachtbare Darstellung erreichbar.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vom Wunsch nach Eindeutigkeit zu einer prüfbaren Frage","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2535,"byte_start":1946,"id":"section:23c932932011105e1994","kind":"section","labels":[],"line_end":24,"line_start":18,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Eine Projektion kann wichtige Wahrscheinlichkeiten erhalten und trotzdem die Multiplikation zerstören. S03 gibt einen einfachen Gegenbeleg: Projiziere [formula in source] auf [formula in source] und definiere [formula in source] . Dann Die neue Multiplikation ist nicht assoziativ. Eine nützliche reduzierte Vorhersagebeschreibung darf also nicht ohne zusätzlichen Nachweis als geschlossene physische Operationsalgebra v","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine kleinere Beschreibung ist nicht automatisch eine Algebra","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4676,"byte_start":2535,"id":"section:b0ef1dc0da1dc74ac84d","kind":"section","labels":[],"line_end":52,"line_start":25,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Eine phasentreue Rekonstruktion braucht mehr als eine Tabelle einzelner Wahrscheinlichkeiten. Ein passender Ausgangspunkt ist eine komplexe Algebra [formula in source] mit Einheit, Multiplikation, Adjunktion und einem positiven normierten Zustandsfunktional [formula in source] : Für Operationswörter [formula in source] definiert einen positiven semidefiniten Korrelationskern. Er enthält die relativen komplexen Phasen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was vollständige Phaseninformation zusätzlich bringt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5967,"byte_start":4676,"id":"section:445f6908dabaf392c515","kind":"section","labels":[],"line_end":65,"line_start":53,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Ein Prozesstensor beziehungsweise Quantenkamm ordnet einer Folge von Instrumenten gemeinsame Ergebniswahrscheinlichkeiten zu. Positivität und kausale Normierungsregeln sichern die Konsistenz. Eine tomographisch vollständige Eingriffsfamilie bestimmt einen endlichen Prozesstensor; sie bestimmt nicht automatisch eine eindeutige verborgene Umgebung oder sämtliche unendlichen Horizonte.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Mehrzeitdaten statt einer einzigen Dichtematrix","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7082,"byte_start":5967,"id":"section:cac76c93e3c44bad5f57","kind":"section","labels":[],"line_end":72,"line_start":66,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"S05 schlägt eine nützliche endliche Vorgehensweise vor: Man fixiert zulässige Operationswörter bis Länge [formula in source] , ihre Relationen, Symmetrien und die belegten Auslesungen. Die unbekannten Momente müssen eine positive Momentenmatrix bilden. Dann minimiert und maximiert man eine noch offene Ausgabe [formula in source] über alle kompatiblen Modelle.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein konkreter Auswahltest für offene Größen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9427,"byte_start":7082,"id":"section:dc03f13f573024e8b1a5","kind":"section","labels":[],"line_end":106,"line_start":73,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Die in S03 vorgeschlagene Alternative verwendet als lokalen Viererverknüpfungstensor. An orientierten Verbindungen werden Trägerräume mit ihren dualen Räumen kontrahiert. So verbindet man Amplituden, ohne jede physische Zellreduktion als unverändert reines [formula in source] festzuschreiben.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Zelle als Verknüpfungsamplitude","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10340,"byte_start":9427,"id":"section:6cff8d9cb53f2d88ead4","kind":"section","labels":[],"line_end":111,"line_start":107,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Paarweise kommutierende volle Matrixunteralgebren, die gemeinsam die Gesamtalgebra erzeugen, bestimmen im endlichen Fall eine Tensorproduktstruktur bis auf lokale Basiswechsel und Umbenennungen. Bei nichttrivialem Zentrum können stattdessen Sektoren übrigbleiben. Die Auswahl der privilegierten Unteralgebren aus den Wechselwirkungen ist der eigentliche inverse Schritt. https://arxiv.org/abs/quant-ph/0308043Zanardi, Li","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Teilsysteme aus Beziehungen erkennen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11809,"byte_start":10340,"id":"section:f6ef30f27dea80443f44","kind":"section","labels":[],"line_end":122,"line_start":112,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"S08 untersucht einen neutralen Sektor aus 70 Materiemasken und Schleifenfluss, insgesamt 1190 Zuständen. In einer festgehaltenen lokalen Operatorliste wird über der Generator rekonstruiert. Nach Entfernen trivialer Identitätsrichtungen reproduziert der Grundzustand die Koeffizienten [formula in source] , [formula in source] , [formula in source] und [formula in source] . Ein zusätzlicher angeregter Zustand verbessert","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was das Zustandsgate am Rotor/CAR-Ring prüft","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":85,"byte_start":0,"id":"section:10a9bbb56ad4df026603","kind":"chapter","labels":["ch:physik"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Raumzeit, Materie und Gravitation aus demselben Ursprung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1976,"byte_start":85,"id":"section:ac89cb64abde9dddedc3","kind":"section","labels":[],"line_end":30,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Ein markierter [formula in source] -Block trägt die hermitesche Matrix Ihre Determinante ist exakt Die Eigenwerte sind [formula in source] . Deshalb entspricht [formula in source] dem Zukunftskegel [formula in source] . Die Kongruenz [formula in source] mit [formula in source] erhält die Determinante und den positiven Kegel.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Lorentzkegel: eine echte, aber begrenzte Brücke","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3724,"byte_start":1976,"id":"section:02bed5964036cc999157","kind":"section","labels":[],"line_end":47,"line_start":31,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"S03 formuliert eine nützliche bedingte Brücke. Angenommen, derselbe Prozess liefert einen lokalen kohärenten Zweikomponentensektor mit inverser Zweipunktfunktion Dann folgt Für invertierbares [formula in source] ist dies eine Lorentzform. Jetzt wäre der Kegel aus einem tatsächlichen Propagator gewonnen. Vorausgesetzt sind jedoch ein sinnvoller Impulsraum, ein kontrollierter lokaler Grenzprozess, ein kohärenter Pol un","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der präzise nächste Schritt: den Kegel aus der Ausbreitung gewinnen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4823,"byte_start":3724,"id":"section:716dcf141da26a7eea76","kind":"section","labels":[],"line_end":58,"line_start":48,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Eine mögliche Materieanregung muss stabil oder kontrolliert propagierend sein. Man benötigt ihr Spektrum, ihre Ladungen, chirale Ausbreitung, erlaubte Vertizes und das Verschwinden unerwünschter Spiegelpartner. Eine vorkommende Darstellung allein erfüllt das nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Materie ist mehr als eine Ladungstabelle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5811,"byte_start":4823,"id":"section:5273f46e0e067c67348a","kind":"section","labels":[],"line_end":67,"line_start":59,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Eine Algebra mit Darstellung und geeignetem Diracoperator kann Geometrie kodieren. Beispielsweise macht die Distanzformel sichtbar, warum nicht nur Eigenwerte, sondern die Relation zwischen [formula in source] und den Observablen zählt. Connes' kommutativer Rekonstruktionssatz benötigt starke Spektralaxiome und liefert eine kompakte glatte Riemannsche Mannigfaltigkeit. Er erzeugt keine lorentzsche 3+1D-Welt aus einer","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spektrale Geometrie hilft, ersetzt aber keine fehlenden Daten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":7020,"byte_start":5811,"id":"section:4b55e66e7ac1260a3e3c","kind":"section","labels":[],"line_end":80,"line_start":68,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Die Identität [formula in source] passt zu einer bekannten Normierung. Sie liefert nicht das Feld [formula in source] , einen masselosen quantisierten Spin-2-Pol, zwei physische Helizitäten oder universelle Kopplung.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was für Gravitation noch wirklich fehlen würde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7111,"byte_start":7020,"id":"section:bd34c3fd6f92c56fafe4","kind":"chapter","labels":["ch:zahlen"],"line_end":82,"line_start":81,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die Zahlenprogramme: Nähe, Spannungen und offene Übertragung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8020,"byte_start":7111,"id":"section:4b95841c48a4c11e05dd","kind":"section","labels":[],"line_end":97,"line_start":83,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Die [formula in source] -Zerlegung benutzt Hyperladungen [formula in source] auf den drei Farbplätzen und [formula in source] auf den zwei schwachen Plätzen. 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Ihre Konsequenzen sind von ihrer Auswahl verschieden.&S09; S05/S06\\\\ Die Kontextregel ist symmetrieerzwungen.& [formula in source] ist eine konkrete gleichgewichtete Realisierung; die kovariante Familie [formula in source] bleibt ein Geg","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Korrekturregister und ergänzende Details","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5908,"byte_start":4033,"id":"section:92f259c6dfe5170dc8f1","kind":"section","labels":[],"line_end":37,"line_start":29,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"S09 berichtet für ein früheres Majoranamodell zehn zugängliche und sechs verborgene reelle Richtungen, entsprechend einer [formula in source] -Zerlegung auf Fockebene. Verschränkung allein macht einen verborgenen Zustand nicht am Rand lesbar; eine geeignete Kopplung oder erweiterte Messung ist nötig. Ein dort gebauter Ereigniskanal übertrug Besetzung, besaß aber weiterhin eine nichttriviale Fixalgebra. Übertragung un","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Frühere Nebenstränge, die im Gesamtbild erhalten bleiben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10041,"byte_start":5908,"id":"section:e769ac44e1bb24b41757","kind":"chapter","labels":[],"line_end":74,"line_start":38,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"L34mmL116mm Begriff& Bedeutung in diesem Dokument\\\\ Adjungierte&Die Darstellung einer Lie-Algebra auf ihren eigenen Generatoren durch die Klammer; nicht automatisch der gesamte Raum physischer Zustände.\\\\ Adjunktion [formula in source] &Komplex konjugierte Transposition beziehungsweise die passende Operatoradjunktion. Nicht dasselbe Wort wie adjungierte Darstellung.\\\\ Algebra&Ein Raum von Objekten mit Regeln für Addi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Begriffe in einfachen Worten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10087,"byte_start":10041,"id":"section:cab0ac722c401c01dcf8","kind":"chapter","labels":[],"line_end":75,"line_start":75,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Quellen, Abdeckung und Reproduktion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10437,"byte_start":10087,"id":"section:bf86a5499f8c5072a6cf","kind":"section","labels":[],"line_end":79,"line_start":76,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Die Quellenkürzel S01 bis S11 gelten durchgängig für dieses Buch und sind von den jeweils eigenen Kürzeln der Anhänge zu unterscheiden. Die vollständigen Originalpfade und SHA-256-Werte stehen im beiliegenden Manifest. Hier werden die Dateinamen und inhaltlichen Rollen aufgeführt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die elf Eingabedokumente","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":12676,"byte_start":10437,"id":"section:2508bbb193f110e82a2b","kind":"section","labels":[],"line_end":96,"line_start":80,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Der eigenständige Prüfer importiert keinen Code des ursprünglichen TFPT-Repositoriums. Die Standard-Zwei-Qubit-Kontexte wurden aus den üblichen Pauli-Matrizen rekonstruiert. Das kontrolliert die endlichen im Text angegebenen Beziehungen, ist aber kein erneuter phasentreuer Import des nativen Gauß- [formula in source] -Adapters.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was neu geprüft wurde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13823,"byte_start":12676,"id":"section:480fb1b05e1e3751e175","kind":"section","labels":[],"line_end":108,"line_start":97,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"L16mmL41mmY Quelle& Berichtete Prüfung& Reichweite\\\\ S09&11214 Bedingungen pro Modus, elf Negativvarianten&Ursprungsaudits und Zahlenprüfungen; kein vollständiger Lean-/RH-Neubau.\\\\ S07&325 + 147 Bedingungen, 19 Tests&Inversion und Follow-ups; mehrere spätere Minimalitätskorrekturen erforderlich.\\\\ S06&86 eigene Bedingungen sowie ausgewählte Originalreplays&45-/30-Quotienten, Uhr und Herkunftskontrollen; begrenzte Ke","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie die Quellen ihre eigenen Prüfungen beschreiben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":14798,"byte_start":13823,"id":"section:4427c094b3765b6177dc","kind":"section","labels":[],"line_end":113,"line_start":109,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Das Paket enthält die vollständige LaTeX-Quelle, Kapiteldateien, Vektordiagramme, den eigenständigen Prüfer, die Ergebnisdatei und das Eingabemanifest. Mit einer LaTeX-Installation einschließlich LuaLaTeX, TikZ und den verwendeten Standardpaketen lässt sich das Buch durch zwei Läufe von lualatex main.tex im Quellverzeichnis bauen. Für die endlichen Gegenrechnungen werden Python, NumPy, SymPy, mpmath und Matplotlib be","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproduktionspaket dieser Synthese","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18166,"byte_start":14798,"id":"section:4f73723c9d887413618f","kind":"section","labels":[],"line_end":135,"line_start":114,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Die folgenden Quellen wurden zur fachlichen Einordnung beziehungsweise für den datierten Konstantenvergleich aufgerufen. Sie bestätigen die allgemeinen Werkzeuge, nicht die physikalische Richtigkeit von TFPT. Die spezifischen langen Herleitungen dieses Buches beruhen auf den Anhängen und den ausgeschriebenen Gegenrechnungen. F. A. Pollock et al.: Non-Markovian quantum processes: complete framework and efficient chara","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Externe Primärliteratur und Referenzdaten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18523,"byte_start":18166,"id":"section:7e5930d36377b3b6899c","kind":"section","labels":[],"line_end":137,"line_start":136,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Die Anhänge wurden unverändert gelesen; ihre tatsächlichen Dateiinhalte sind durch SHA-256 dokumentiert. Dieses Buch aktualisiert keinen ursprünglichen Theorievertrag und keinen Abschlussmarker. Es liefert eine neue, zusammenhängende und prüfbare Darstellung mit ausdrücklich abgegrenzten eigenen Fortsetzungen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Abschluss der Dokumentation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":968,"byte_start":0,"id":"section:6e5b0a2159ca56325185","kind":"chapter","labels":["ch:shadow-arithmetic"],"line_end":8,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Was uns ein Schatten verraten kann Wenn wir nur den Schatten eines Rades sehen, erkennen wir vielleicht einen Kreis. Erst wenn wir das Rad drehen, belasten und mit einem zweiten Rad verbinden, erkennen wir seine Achse, seine Zähne und seine Übersetzung. Genau so lesen wir hier Primzahlen, Quanteneffekte und Raumzeit: als verschiedene Antworten, die eine mögliche gemeinsame Struktur gleichzeitig erklären müsste.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Primzahlen, RH und die Musik hinter den Schatten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":2819,"byte_start":968,"id":"section:09eb9fc6220bb5e6686b","kind":"section","labels":["eq:primon-partition"],"line_end":25,"line_start":9,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Jede natürliche Zahl [formula in source] zerfällt eindeutig in Primfaktoren: Die erste Gleichung beschreibt ein Zusammensetzen durch Multiplikation; die zweite übersetzt dieses Zusammensetzen in Addition. Zum Beispiel ist [formula in source] , also [formula in source] . Die Primzahlen sind die unabhängigen Bausteine dieses multiplikativen Systems. Das ist ein Satz über natürliche Zahlen. Es ist noch kein Satz darüber","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"In welchem Sinn Primzahlen Bausteine sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":4018,"byte_start":2819,"id":"section:b3f9953dab3cbf980cb3","kind":"subsection","labels":[],"line_end":36,"line_start":26,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Warum gerade [formula in source] ? Aus [formula in source] allein folgt das noch nicht: Man darf jeder Primzahl zunächst einen beliebigen Wert [formula in source] geben. Eine zusätzliche Ordnungsregel schließt die Lücke. Ist [formula in source] monoton in der natürlichen Zahl [formula in source] , so gilt notwendig Der Beweis ist kurz. Setze [formula in source] . Aus [formula in source] folgen [formula in source] Div","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine bedingte Auswahlregel für die logarithmische Energie","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":7179,"byte_start":4018,"id":"section:d74f5ca730e7c759fe57","kind":"section","labels":["eq:prime-trace"],"line_end":64,"line_start":37,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die häufig verkürzte Aussage Primzahlen tauchen als Quantenenergien auf umfasst verschiedene Sachverhalte. Beim klassischen Zeta–Quantenchaos-Vergleich entsprechen Nullstellenhöhen den Energien eines gesuchten Spektrums. Die Primzahlen spielen auf der anderen Seite die Rolle primitiver periodischer Bahnen; Primzahlpotenzen sind deren Wiederholungen. Eine Bahn wird einmal durchlaufen, zweimal, dreimal. Ihr logarithmis","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was Primzahlen mit Quantenchaos verbindet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":10149,"byte_start":7179,"id":"section:0937cf42f625c8cd7bd4","kind":"section","labels":[],"line_end":81,"line_start":65,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die Unterlagen und der zusätzlich eingesehene Forschungsbestand ergeben keine abgeschlossene RH-Lösung. Sie ergeben jedoch eine ungewöhnlich präzise Landkarte aus positiven Bausteinen und bereits ausgeschlossenen Abkürzungen. Die folgende Verdichtung ordnet die inhaltlichen Familien; sie behauptet keine erneute Prüfung jedes Katalogeintrags.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was unser RH-Zweig tatsächlich beigetragen hat","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11189,"byte_start":10149,"id":"section:db4ce8259c120ac5a95a","kind":"subsection","labels":[],"line_end":96,"line_start":82,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die ersten sechs Werte sind [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] und [formula in source] . Daraus folgt für [formula in source] Hier ist der Primzahlbezug wirklich vorhanden. Die Selbstdualität des Gitters schließt die Poisson-Transformation auf dasselbe Gitter. Poisson-Summation gilt auch für nichtselbstduale Gitter und verbindet dann Gitter und ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der genaue Ertrag der [formula in source] -Schalen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":12659,"byte_start":11189,"id":"section:40fe8261c022327c6fe5","kind":"subsection","labels":[],"line_end":108,"line_start":97,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die entscheidende arithmetische Form enthält eine Differenz: vereinfacht [formula in source] . Zwei positive Matrizen können eine indefinite Differenz besitzen; schon [formula in source] hat die Eigenwerte [formula in source] und [formula in source] . Entsprechend löst ein beliebiger positiver Born- oder Gramkern die signierte Aufgabe noch nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die fehlende Positivität so hartnäckig ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14262,"byte_start":12659,"id":"section:5cd628ffd67a8511bbbb","kind":"subsection","labels":[],"line_end":115,"line_start":109,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Der Jensen/Coxeter-Test r618 findet eine starre [formula in source] -Struktur auf der [formula in source] -Seite, während die verglichenen Jensen-Polynome mit ihrem Index variieren. Die gewählte Identifikation scheitert. Der Selberg-Kontakttest r638 besitzt im untersuchten Fall weiterhin einen negativen kleinsten Eigenwert von ungefähr [formula in source] ; eine Quadratvervollständigung hat die falsche signierte Form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was die negativen Routen konkret lehren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15958,"byte_start":14262,"id":"section:761b4957ca8a4ab8dc48","kind":"section","labels":[],"line_end":126,"line_start":116,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die vorhandene freie fermionische Naht hat bei fester Größe eine endliche Zustandssumme. Das Primonmodell verlangt eine unbegrenzte Primfamilie und andere Besetzungsdaten. Schon für [formula in source] gilt [formula in source] und [formula in source] : Der Pol bei [formula in source] entsteht erst in der unendlichen Familie. Eine endliche Demonstration kann ihn nicht besitzen. Der vorhandene Nahtvergleich findet ents","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Naht braucht mehr als ein paar zusätzliche Takte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16501,"byte_start":15958,"id":"section:103e9b84a65985e6f342","kind":"section","labels":[],"line_end":129,"line_start":127,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Wei und Mitautoren verbinden in zwei gezielt konstruierten Quantensystemen Nullstellen mit dynamischen Phasenübergängen. Berichtet werden ein Fünf-Qubit-NMR-Prinzipversuch und weitergehende numerische Untersuchungen. Die verwendeten Hamiltonoperatoren und Zustandsgewichte sind so gewählt, dass sie Zeta-Daten kodieren. Das macht den Zusammenhang experimentell bearbeitbar; eine Ableitung dieser Wahl aus TFPT oder ein R","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die neue Quantenphasen-Arbeit von 2026","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":18843,"byte_start":16501,"id":"section:82203568b4bfd087d2c7","kind":"subsection","labels":["eq:eta-readout"],"line_end":150,"line_start":130,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Unabhängig vom vollständigen Ressourcenbeweis dieser Arbeit untersuchen wir den folgenden einfachen thermischen Eta-Auslesekanal: Er entsteht durch einen Gibbszustand für [formula in source] und eine diagonal ausgelesene Paritätsphase. Bei festem [formula in source] und [formula in source] konvergiert der Zähler gegen [formula in source] , während [formula in source] Also geht das Rohsignal [formula in source] an jed","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eigene Anschlussrechnung: Ein verschwindendes Signal ist mehrdeutig","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":541,"byte_start":0,"id":"section:6e43b7fc25f2e292068f","kind":"chapter","labels":["ch:shadow-quantum"],"line_end":6,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Nicht nur die Anzahl der Kugeln zählt Zwei Kästen können dieselben möglichen Messergebnisse enthalten und doch verschieden reagieren, wenn wir zuerst an einer anderen Stelle messen oder zwei Teile zusammenführen. Die Quantenphänomene sagen uns deshalb vor allem etwas über die Regeln des Zusammensetzens, über relative Phasen und über erlaubte Eingriffe. Genau diese Daten verliert ein einfacher Schatten leicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was Quantenphänomene über den verborgenen Aufbau sagen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1925,"byte_start":541,"id":"section:1ebeff48a32103ff0f15","kind":"section","labels":[],"line_end":21,"line_start":7,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Für zwei Alternativen mit Amplituden [formula in source] und [formula in source] lautet die Born-Regel [formula in source] Der letzte Term kann verstärken oder auslöschen. Wer ausschließlich die beiden Einzelwahrscheinlichkeiten aufbewahrt, kann ihn nicht rekonstruieren. Das erklärt im Kleinen, warum die behaltenen Register und Echoexperimente der früheren Kapitel mehr verraten als der erste sichtbare Markovschritt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Interferenz verlangt eine Information vor den Wahrscheinlichkeiten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4273,"byte_start":1925,"id":"section:bef195680585ddbfe690","kind":"section","labels":[],"line_end":40,"line_start":22,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Die 15 Zwei-Qubit-Pauli-Kontexte der Synthese enthalten das folgende Mermin–Peres-Quadrat. Hier bedeutet [formula in source] und entsprechend für die anderen Einträge: Jede Zeile und jede Spalte ist gemeinsam messbar. Alle Zeilenprodukte sind positiv, aber das letzte Spaltenprodukt ist negativ. Diese sechs Kontexte gehören zum bereits verwendeten Pauli-System.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der vorhandene Baukasten enthält bereits Kontextualität","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5718,"byte_start":4273,"id":"section:8e99ddedaa23cfb4a30b","kind":"section","labels":[],"line_end":52,"line_start":41,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Für zwei räumlich getrennte Messstellen hat die CHSH-Kombination [formula in source] in einem lokalen Modell mit unabhängiger Wahl der Einstellungen die Grenze [formula in source] . Quantenmechanik erreicht [formula in source] . Mit [formula in source] , [formula in source] und [formula in source] ist der zugehörige Operator [formula in source] ; seine Eigenwerte sind [formula in source] . Beides wurde hier exakt nac","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verschränkung legt die Zusammensetzung fest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6899,"byte_start":5718,"id":"section:8c05f926eff84e5249ce","kind":"section","labels":[],"line_end":68,"line_start":53,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Wähle bei festgehaltenen Labor-Teilsystemen [formula in source] Beide Hamiltonoperatoren haben exakt die Energien [formula in source] . Der Grundzustand von [formula in source] ist ein Produktzustand, der von [formula in source] ein Bell-Zustand. Die Reinheit [formula in source] eines lokalen Teils beträgt entsprechend 1 beziehungsweise [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gleiche Energien können verschiedene Welten beschreiben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8198,"byte_start":6899,"id":"section:71a333f0fdc0b70e9206","kind":"section","labels":[],"line_end":75,"line_start":69,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Die komplexe Vierdimensionalität ist für den bestehenden Pauli-/Spinorbaukasten passend. Eine direkte Ableitung der komplexen Zahlen aus einem einzelnen Quantenphänomen wäre trotzdem zu stark. Renou und Mitautoren untersuchen Quantennetzwerke, in denen die übliche reale und komplexe Theorie unter einer bestimmten Unabhängigkeits- und Kompositionsannahme verschiedene Vorhersagen machen. F10","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was komplexe Zahlen verraten und was offenbleibt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9556,"byte_start":8198,"id":"section:52c829555ca26fb6d001","kind":"section","labels":[],"line_end":81,"line_start":76,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Die bisherigen Registerbeispiele erklären, wie ein global kohärenter Ablauf nach eingeschränktem Zugriff wie ein irreversibler Prozess aussehen kann. Sie liefern noch keine eindeutige Lösung des Messproblems: Insbesondere folgt aus einer diagonalen reduzierten Dichtematrix allein keine Auswahl eines einzelnen Ereignisses. Eine zusätzliche Kollapsdynamik müsste messbare Abweichungen angeben; eine unitäre Beschreibung ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Messung, Zeitpfeil und Statistik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":900,"byte_start":0,"id":"section:20e8f3a2938fc2c29a56","kind":"chapter","labels":["ch:shadow-dimension"],"line_end":8,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"Dimension ist die Antwort auf eine Frage Eine Ameise auf einer dünnen Schnur kann entlang einer Richtung laufen. Auf einem Blatt kann sie außerdem ausweichen. In einem Zimmer kann sie auch über ein Hindernis hinweg. Eine Dimension zählt solche unabhängigen Möglichkeiten. Die Zahl der inneren Zustandskomponenten oder der Knöpfe eines Geräts ist etwas anderes.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Drei Raumrichtungen und eine Zeit: Welche Bedingungen bleiben?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2245,"byte_start":900,"id":"section:25386979000fc3cec141","kind":"section","labels":[],"line_end":23,"line_start":9,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"Ein traceloses hermitesches [formula in source] -Objekt hat genau drei reelle Komponenten: [formula in source] Ergänzt man [formula in source] , ergibt die Determinante [formula in source] Der positive Kegel erfüllt [formula in source] . Das ist die präzise Lorentz-Brücke aus dem Ursprungsteil. Sie zeigt eine passende lokale algebraische Form. Noch fehlen ihre Interpretation als Ereignisse, die Verklebung zu einer Ra","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Drei unterschiedliche Hinweise führen zur Zahl drei","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4446,"byte_start":2245,"id":"section:b826a2aa379f0e9da4ce","kind":"section","labels":[],"line_end":47,"line_start":24,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"Für einen Graph-Laplaceoperator [formula in source] definieren wir die mittlere Rückkehrfunktion und eine skalenabhängige Dimension durch Auf einem großen regelmäßigen dreidimensionalen Gitter entsteht zwischen der Gitter- und der endlichen Systemskala ein Bereich mit [formula in source] , also [formula in source] . Bei einem endlichen zusammenhängenden Graphen geht [formula in source] sowohl für sehr kleine als auch","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine neue Gegenprobe am Clebsch-Vorschlag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5395,"byte_start":4446,"id":"section:a5a77952b740828bd861","kind":"section","labels":[],"line_end":52,"line_start":48,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"In einer gewöhnlichen hyperbolischen Wellengleichung werden lokale Anfangsdaten auf einer räumlichen Fläche vorgegeben und entlang einer ausgezeichneten Zeitrichtung entwickelt. Mehrere Zeitkoordinaten verändern das Anfangswertproblem grundlegend. Unter zusätzlichen nichtlokalen Beschränkungen existieren dennoch wohldefinierte Mehrzeit-Probleme; ein pauschaler Unmöglichkeitssatz wäre falsch. F14","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine Zeitrichtung ist mehr als ein weiterer Zahlenplatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6488,"byte_start":5395,"id":"section:bdd4bd937d2d64ac4e45","kind":"section","labels":[],"line_end":64,"line_start":53,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"Ein elementares mechanisches Beispiel illustriert die Rolle von Constraints. Nimmt man in [formula in source] Raumdimensionen eine Newtonsche Punktkraft mit Gaußgesetz an, lautet das effektive Radialpotential [formula in source] An einer Kreisbahn ergibt sich [formula in source] Unter diesen Voraussetzungen sind solche Kreisbahnen bei [formula in source] stabil, bei [formula in source] instabil und bei [formula in so","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was Stabilität zusätzlich einschränkt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":397,"byte_start":0,"id":"section:6a6f54a45bbdb12ff982","kind":"chapter","labels":["ch:shadow-open"],"line_end":4,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Offene Physik ist kein freier Platz, in den jede neue Idee hineinpasst. Sie ist oft durch viele bekannte Eigenschaften eng begrenzt. Der nützliche Schritt lautet deshalb: Welcher Teil des Phänomens ist beobachtet, welcher Mechanismus fehlt, und welche Antwort müsste unser Modell zusätzlich liefern?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Schwer verstandene Phänomene als zusätzliche Prüfsteine","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1423,"byte_start":397,"id":"section:14796447753e730bca6f","kind":"section","labels":[],"line_end":9,"line_start":5,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Gravitationslinsen und die Verteilung sichtbarer Materie in kollidierenden Haufen liefern eine wichtige Beobachtung: Der aus der Gravitation erschlossene Beitrag muss nicht dem heißen sichtbaren Gas folgen. Die Bullet-Cluster-Analyse ist ein prominentes Beispiel. Sie identifiziert damit noch kein bestimmtes mikroskopisches Teilchen. Zusammen mit anderen kosmologischen Daten ist sie eine starke Anforderung an jede Erk","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dunkle Materie: unsichtbar heißt nicht frei wählbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2590,"byte_start":1423,"id":"section:aaef7ad08e761ec58479","kind":"section","labels":[],"line_end":16,"line_start":10,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Die beschleunigte kosmische Expansion verlangt eine konsistente Erklärung im Gesamtmodell. Für TFPT ist besonders schwierig, eine passende effektive Vakuumwirkung zu erhalten, ohne sie bei jedem neuen Beitrag nachzujustieren. Der Mechanismus müsste seine Größe und Stabilität gegenüber Korrekturen erklären.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dunkle Energie: ein kleiner Rest mit großen Folgen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3656,"byte_start":2590,"id":"section:2883869ce054e725155f","kind":"section","labels":[],"line_end":21,"line_start":17,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Die Schwarzlochfrage verbindet Quanteninformation, Gravitation und die Wahl zugänglicher Teilsysteme besonders eng. In bestimmten berechenbaren Modellen verändern Quanteneffekte die extremale Fläche und damit die Zuordnung rekonstruierbarer Information. Die verallgemeinerte Entropie enthält einen Flächenbeitrag und einen Quantenfeldbeitrag. Das ist erheblicher theoretischer Fortschritt in diesen Modellen, aber noch k","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Schwarze Löcher: Information kann die Aufteilung selbst betreffen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4418,"byte_start":3656,"id":"section:ae60ff44f43ea5c2b434","kind":"section","labels":[],"line_end":26,"line_start":22,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Äquivalenztests wie MICROSCOPE prüfen die Universalität des freien Falls für unterschiedliche Materialien mit hoher Genauigkeit. Eine neue Quelle für Raumzeit muss daher erklären, warum verschiedene innere Zusammensetzungen auf dieselbe effektive Geometrie reagieren. F18","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gravitation muss sehr verschiedene Inhalte gleich behandeln","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6966,"byte_start":4418,"id":"section:54896f2503741a8e7dbd","kind":"section","labels":[],"line_end":43,"line_start":27,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"L32mmL56mmL60mm Thema& Was den Ansatz einschränkt& Was eine Erklärung liefern müsste\\\\ Zeitpfeil&Beständige Aufzeichnungen und irreversible Makroprozesse bei oft reversiblen Grundgleichungen.&Zustandsauswahl, Anfangskorrelationen, Zugriff und Entropiefluss; keine bloße Benennung eines inneren Parameters als Zeit.\\\\ Messproblem&Interferenz und stabile Messergebnisse müssen zusammen beschrieben werden.&Ein vollständige","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Weitere offene Stellen mit unterschiedlicher Beweiskraft","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":947,"byte_start":0,"id":"section:bf2d593480d6c9d6a70b","kind":"chapter","labels":["ch:shadow-synthesis"],"line_end":7,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Die zusammengetragenen Schatten sprechen am stärksten für eine Struktur von Zusammensetzungen und gemeinsamen Antworten. Arithmetik verlangt eindeutig kombinierbare primitive Faktoren. Quantenphänomene verlangen Phasen, Kontexte und eine besondere Zusammensetzung von Teilsystemen. Raumzeit verlangt eine skalenstabile Ordnung von Nachbarschaften, Signalwegen und Anfangsdaten. Keine dieser Forderungen wird durch die Za","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein engeres Bild und ein neues berechenbares Puzzleteil","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2397,"byte_start":947,"id":"section:7941e97c03fab7c3ba55","kind":"section","labels":[],"line_end":20,"line_start":8,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Die bildhafte Aussage Alles ist aus Primzahlen gebaut lässt sich zu einer brauchbareren Hypothese präzisieren: Ein möglicher gemeinsamer Ursprung besitzt elementare, zusammensetzbare Operationen. In einem kommutativen arithmetischen Schatten erscheinen primitive Faktoren. Vor dieser Auslesung bleiben zusätzliche Phasen, Kontexte und Aufzeichnungen erhalten. Räumliche Nachbarschaft und Zeitordnung müssten aus den erla","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine engere Arbeitshypothese","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":4907,"byte_start":2397,"id":"section:9285c3d94e575003043f","kind":"section","labels":["eq:arithmetic-projective"],"line_end":61,"line_start":21,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Die folgenden Formeln sind eine neue Anschlusskonstruktion für dieses Buch. Ihre Zutaten sind Standardoperatoren; sie beanspruchen keine neue allgemeine mathematische Entdeckung. Sie zeigen jedoch exakt, dass ein gemeinsamer arithmetischer Endpunkt unterschiedliche kohärente Geschichten besitzen kann.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein konstruktiver Versuch: gleiche Zahl, verschiedene Phasen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5784,"byte_start":4907,"id":"section:67f1c15a3c2b1f292962","kind":"subsection","labels":[],"line_end":69,"line_start":62,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Ein Kontrollqubit speichert kohärent, welcher der beiden Wege durchlaufen wurde. Setze [formula in source] und [formula in source] . Nach einer Hadamard-Auslesung des Kontrollqubits gelten [formula in source] Ohne die lokalen [formula in source] -Markierungen wäre [formula in source] und damit [formula in source] . Die neue Rechnung kontrolliert dies im Zahlfenster [formula in source] exakt. Die benutzten Wege ab [fo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine vollständig bestimmte Vorhersage im Modell","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7119,"byte_start":5784,"id":"section:276f98ed530d865eac78","kind":"subsection","labels":[],"line_end":76,"line_start":70,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Gelöst ist eine kleine Kompatibilitätsfrage: Unbegrenzte arithmetische Zusammensetzung und ein endlicher lokaler Quantenbaukasten lassen sich in einem expliziten gemeinsamen Modell verbinden. Der rein arithmetische Schatten kann kommutativ sein, während kohärent zugängliche Wegrelationen eine nichttriviale Phase behalten. Das passt genau zum Motiv der vorherigen Echoexperimente.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was damit gelöst ist und was nicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9085,"byte_start":7119,"id":"section:ed6d1cfb4cdb3b9c17ef","kind":"section","labels":[],"line_end":97,"line_start":77,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Man könnte einen arithmetischen Raum, ein Quantensystem und ein geometrisches Modell einfach nebeneinanderstellen: [formula in source] Bei Produktzustand und unabhängig wirkenden Operationen passen dann vielleicht alle Einzelstatistiken. Der gemeinsame Ursprung wäre dadurch nicht erklärt. Nötig sind gemeinsame Relationen und überprüfbare Antworten auf gemischte Eingriffe. Die oben konstruierte Wegphase ist ein kleine","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum getrennte passende Modelle noch keine gemeinsame Quelle sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11082,"byte_start":9085,"id":"section:9f60c19e5234ab0f2da8","kind":"section","labels":[],"line_end":111,"line_start":98,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"L37mmL60mmL51mm Gewonnene Präzisierung& Konkretes Ergebnis& Nächste fehlende Bedingung\\\\ Logarithmische Skala&Multiplikative Additivität plus Monotonie erzwingen [formula in source] .&Native Begründung der Ordnung und Energieskala.\\\\ Unbegrenzte Primfamilie&Endlich viele additive Grundtakte tragen nicht alle [formula in source] .&Eine passende wachsende Familie oder reichere Dynamik.\\\\ Arithmetik und Phase&Zwei Multi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Welche Puzzleteile jetzt enger gefasst sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":82,"byte_start":0,"id":"section:a1da23ce689207c3f070","kind":"chapter","labels":["app:shadow-sources"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Erweiterung: Quellen und genaue Prüfgrenzen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4118,"byte_start":82,"id":"section:7a1e6bf8f15ddab08d5f","kind":"section","labels":[],"line_end":29,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":["relation:7525f9c966deab67db7d"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"Die Erweiterung wurde am 14. September 2026 gegen verfügbare Originalabschnitte im lokalen Repository tfpt-theoryv4 abgeglichen. Der gelesene Git-Stand war 66b91e40e245569f06ab440ead80f446c9be0ee5. Dies identifiziert den Checkout; es behauptet keinen frischen vollständigen Beweis- oder Testlauf. Die tatsächlich verwendeten Dateiinhalte sind zusätzlich mit SHA-256 im Paket erfasst, auch soweit der Arbeitsbaum von Git ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zusätzlicher Einblick in den RH-Forschungsbestand","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6033,"byte_start":4118,"id":"section:dac71bef0a2a07f5c7b3","kind":"section","labels":[],"line_end":38,"line_start":30,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"Der separate Prüfer verify_shadows.py importiert keinen ursprünglichen TFPT- oder RH-Code und keine Nullstellentabellen. Er enthält 126 exakte beziehungsweise symbolische Bedingungen und zwei numerische Kontrollen. Die Nummer der ersten Nullstelle im Eta-Diagramm ist ein ausdrücklich eingesetzter Referenzwert; das Diagramm ist kein eigener Nullstellensuchlauf.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die 128 zusätzlichen Bedingungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10751,"byte_start":6033,"id":"section:2001f0edd2d885ab60a7","kind":"section","labels":[],"line_end":62,"line_start":39,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":["relation:1edda84f43aa33b08084","relation:c77cd89076c0ddd35a6f"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"Die folgenden Quellen wurden zur Erweiterung aufgerufen. Es handelt sich um gezielte Literaturauswahl, nicht um einen vollständigen systematischen Review aller Veröffentlichungen bis September 2026. Eigene Formeln, Gegenbeispiele und Illustrationen sind im Haupttext als solche bezeichnet. Neue Preprints bleiben als Preprints kenntlich. M. V. Berry, J. P. Keating: The Riemann Zeros and Eigenvalue Asymptotics. SIAM Rev","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zusätzliche Primärliteratur","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":11375,"byte_start":10751,"id":"section:9bafa47b240f31812254","kind":"section","labels":[],"line_end":64,"line_start":63,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"Das aktualisierte Quellpaket enthält beide unabhängigen Prüfer, beide Ergebnisdateien, die zusätzlichen drei Vektorplots, die LaTeX-Diagramme, das RH-Quellenmanifest und die ausgewählten Katalogeinträge. Die fünf neuen Hauptkapitel sind in dieselbe LaTeX-Datei eingebunden; ursprüngliche Textteile wurden nur um Versionshinweise und Querverweise ergänzt. Das fertige PDF wird weiterhin mit LuaLaTeX gebaut. Die beiliegen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproduktion der erweiterten Fassung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":76,"byte_start":0,"id":"section:943280cd712db6281a5b","kind":"chapter","labels":["ch:audit13"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die sechs neuen Quellen: geprüfte Korrekturen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":593,"byte_start":76,"id":"section:8443e5ec58d7efb8ed0b","kind":"section","labels":[],"line_end":5,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Die sechs zusätzlichen Unterlagen heißen im neuen Quellenregister N1 bis N6; die ursprünglichen S01 bis S11 bleiben unverändert. Ihr Audit trennt exakte endliche Identitäten, numerische Spektren und zusätzliche Modellannahmen. 100 eigene Bedingungen bestanden: 78 exakte beziehungsweise Integritätsprüfungen und 22 numerische. Die anschließende gemeinsame Ausführung hat einen eigenen 231-Bedingungen-Vertrag. Diese Zähl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was gegenüber v1.1 neu ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":2635,"byte_start":593,"id":"section:5d20f925f7c7187d945b","kind":"section","labels":[],"line_end":28,"line_start":6,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Setze [formula in source] und [formula in source] . Der Wedge-Kanal besitzt Für [formula in source] verschwindet [formula in source] . Beide geordneten Wege enden im gleichen virtuellen Zustand und interferieren. Orthogonale Records für [formula in source] und [formula in source] ersetzen dies durch [formula in source] : Der antisymmetrische Rang-6-Kanal wird zum Rang-12-Kanal. Bei gleichem Energienenner entsteht ein","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die zentrale Reparatur: Wege nicht zu früh unterscheiden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":3264,"byte_start":2635,"id":"section:7e865f5ddb9e959fac56","kind":"section","labels":[],"line_end":35,"line_start":29,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Mit [formula in source] und [formula in source] ist auf [formula in source] unitär und kollektiv [formula in source] -kovariant. Alle [formula in source] liefern für Materieeingänge denselben ersten blockdephasierten Schatten. Dennoch wirkt [formula in source] dort als [formula in source] , während [formula in source] als [formula in source] wirkt: [formula in source] kehrt als [formula in source] oder als [formula i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der erste Schatten wählt die Fortsetzung noch nicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":5090,"byte_start":3264,"id":"section:271716c6303e67b05c0f","kind":"section","labels":[],"line_end":59,"line_start":36,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für genau zwei vollständige [formula in source] -Zellen und eine positive Brücke gelten die Formeln aus Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der allkopplige Zweizellenbeweis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6474,"byte_start":5090,"id":"section:48cd70c4ff928d9c300c","kind":"section","labels":[],"line_end":77,"line_start":60,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Im ausgewiesenen harmonischen Modell eines geteilten Vermittlers lautet der symmetrische aktive Block Sein niedriger Zweig beginnt mit [formula in source] ; der antisymmetrische mit [formula in source] . Deshalb ist auf dem aktiven [formula in source] -Raum Nach Abzug beider Einzelbondkorrekturen [formula in source] bleibt Beide Schreibweisen sind kompatibel. Eine Konstante auf dem aktiven Sektor ist außerhalb davon ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vierte Ordnung und unterschiedliche Subtraktionskonventionen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":7332,"byte_start":6474,"id":"section:bcc2723663ce2abddf27","kind":"section","labels":[],"line_end":90,"line_start":78,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] gilt Mit [formula in source] und [formula in source] folgen Ein kohärentes Achtzweigregister liefert aus dem früheren Zweisingulett-Eingang [formula in source] Erfolg [formula in source] . Alle acht Ausgänge haben Gewichte [formula in source] . Dies ist eine exakte Alternative zur alten 32-Zweigschaltung. Kontrollierte kontinuierliche Sternpulse und Register bleiben zusätzliche Ressourcen. Erz","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein exakter Stern-Spektralfilter unter zusätzlichen Ressourcen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":8009,"byte_start":7332,"id":"section:502e3c4d93731ce3e269","kind":"section","labels":[],"line_end":98,"line_start":91,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"In der Inzidenzfamilie [formula in source] sind die beiden relevanten Entropien Strikte Konkavität liefert verschiedene Maxima: [formula in source] für Kontexte und [formula in source] für Strahlen. Letzterer Prozess hat Rang 60. Erweitert man den Nachfolgerträger, entstehen symmetrieverträgliche Ränge 15 und 16. Weder maximale Entropie noch minimale Rangzahl wählt die Regel ohne erklärte Klasse. Die passive separate","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Einfachheit braucht einen Auslesevertrag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10096,"byte_start":8009,"id":"section:5ddce1c64d360bdb3e26","kind":"section","labels":[],"line_end":113,"line_start":99,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Zwei Singulettläufe finden mindestens vier orthogonale Moden bei [formula in source] über [formula in source] , Residuen unter [formula in source] . Das Dublett ist widerlegt; ein exakter oberer Multiplizitätsbeweis fehlt. -Typen.] 960 gleichgradige Wurzelsummen gehen nach [formula in source] ; gemischt ergeben sich 640 und 192 Summen nach Grad null sowie 64 Cartanfälle. Der vorgeschlagene gemischte Kanal nach [formu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Weitere architektonisch wichtige Korrekturen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":100,"byte_start":0,"id":"section:686c848124abfca08162","kind":"chapter","labels":["ch:execution13"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Eine gemeinsame Ausführung für Record, Präparation und Mehrzeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":798,"byte_start":100,"id":"section:2c4bff8caf5d78ffab75","kind":"section","labels":[],"line_end":7,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Dieselbe korrigierte Vermittlungsoperation erzeugt jetzt Aufzeichnung, kontrollierte Näherungspräparation und Mehrzeitantwort. Die tatsächlichen Quellprojektoren, Paulioperationen und die Dreierclock wurden benutzt. Ein bereits präpariertes [formula in source] oder ein separater Präparations-Hamiltonoperator wird nicht benötigt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine Konstruktion, aber ein ausdrücklich zusätzlicher Ressourcenvertrag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1605,"byte_start":798,"id":"section:a94d389931d6adb93f1f","kind":"section","labels":[],"line_end":27,"line_start":8,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Mit [formula in source] , [formula in source] und [formula in source] gilt Kopiere nur die Vermittlerbelegung, nicht das geordnete Farbwort: Dann ist auf allen 44 Dimensionen Der Vermittler kehrt zurück. Auf Materie und Pointer bleibt [formula in source] , [formula in source] , mit Beide Krausoperatoren gehören zum Instrument; ihre Effekte summieren sich zu [formula in source] . Ein ungemessener Pointer bleibt kohäre","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die vollständige Recordoperation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2895,"byte_start":1605,"id":"section:6384587fee6b1e6bdb7a","kind":"section","labels":[],"line_end":43,"line_start":28,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für vier Materieträger und höchstens einen aktiven Vermittler sei Alle sechs [formula in source] wurden auf dem vollen Materieraum rekonstruiert: [formula in source] , [formula in source] , [formula in source] . Andere Vermittlersektoren bleiben bei einer adressierten Operation unverändert. Die Kanten haben orthogonale Ausgänge; verschränkte Zuschauer sind eingeschlossen. Dies ist ein vollständiges sequenzielles Prot","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein gemeinsamer Träger und ein fester Schritt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3576,"byte_start":2895,"id":"section:513442f85877f1ea03fe","kind":"section","labels":[],"line_end":55,"line_start":44,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Rechenbasis- und uniformer Projektor gehören zu den 60 tatsächlichen Quellprojektoren. Die Swap-Identität verwendet dieselben 16 Quell-Paulis: Für Messausgang [formula in source] und Ziel [formula in source] liefert die Bitverschiebung Damit ist [formula in source] . Vier lokale Resets erzeugen [formula in source] sogar aus verschränktem Eingang. Messung und Feedback bleiben Ressourcen, keine hergeleitete kosmologisc","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Quellseitiger Reset ohne vorpräpariertes Zielreservoir","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5624,"byte_start":3576,"id":"section:38678e5af2ad0bd1712b","kind":"section","labels":[],"line_end":84,"line_start":56,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Akzeptiere in jeder Sternrunde die Recordfolge 111: Alle acht ersten Recordfolgen haben Wahrscheinlichkeit [formula in source] . [formula in source] wird erst zur Zielprüfung definiert. Im 24-dimensionalen Raum der verschiedenen Farbanordnungen gilt exakt Dieser Raum trägt die treue reguläre Darstellung von [formula in source] . Die polynomialen Identitäten der Gruppenalgebra gelten daher auch auf allen 256 Materiedi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wiederholung präpariert den Viererzustand kontrolliert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7259,"byte_start":5624,"id":"section:9c19a58c70d547bdec15","kind":"section","labels":[],"line_end":106,"line_start":85,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Nach erfolgreicher Präparation folgen lokaler Quelltick [formula in source] , zweimal [formula in source] , Rücknahme [formula in source] und dasselbe [formula in source] -Runden-Filter. Ein ideales kostenloses [formula in source] -Messgerät wird nicht eingesetzt. Protokoll R behält denselben kohärenten Pointer; Protokoll F verwendet beim zweiten Schritt einen frischen. Mit [formula in source] lauten die gemeinsamen ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derselbe Filter liest die Mehrzeitantwort aus","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8229,"byte_start":7259,"id":"section:19e63a6768238480db44","kind":"section","labels":[],"line_end":115,"line_start":107,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Das neue Register ist nicht Clifford: Ein vierqubitiger Pauli hat Spur null oder [formula in source] . Noch konkreter erzeugt der Quellinput [formula in source] genau 13 nichtverschwindende Rechenbasisamplituden. Das ist kein reiner Stabilizerzustand, dessen Trägergröße eine Zweierpotenz ist. Nur Cliffordoperationen, Stabilizer-Hilfszustände und Pauli-Messungen reichen auch mit Feedback nicht aus. Andere Kodierungen ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was für eine native Implementierung noch fehlt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9018,"byte_start":8229,"id":"section:18c295a8852966258f47","kind":"section","labels":[],"line_end":122,"line_start":116,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Alle [formula in source] kommutieren mit [formula in source] ; der ungelesene Kanal erhält das Zielgewicht. Seine einzelnen Dephasierungen sind orthogonale Hilbert–Schmidt-Projektionen. Ein Fixpunkt ihres Zyklus kann bei keinem Schritt Norm verlieren und liegt deshalb im Schnitt der Fixräume: in der Kommutante der [formula in source] -Wirkung. Deren Dimension ist Die spurlose Dimension 3875 identifiziert keinen gleic","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ungelesener Austausch ist keine Kühlung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10000,"byte_start":9018,"id":"section:ceb7420c310edbdbbc6d","kind":"section","labels":[],"line_end":126,"line_start":123,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Ein nativer Adapter muss [formula in source] , [formula in source] , Kern und Belegung gemeinsam liefern, beim Half-Charge-Feld zusätzlich mit Domänen- und Energiekontrolle. Er muss den 13-Amplituden-Eingang, beide Recordzweige und die Acht-Runden-Echos reproduzieren, einschließlich Hilfszuständen und Fehlerausgängen. Erst anschließend ist eine skalierende Zellfamilie sinnvoll auf Geometrie, Chiralität und Spin 2 zu ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Abnahmetests und T1–T8-Grenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":87,"byte_start":0,"id":"section:068cb0b2548f414d5140","kind":"chapter","labels":["app:release13"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Versionspaar v1.3: Quellen, Abdeckung und Reproduktion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":812,"byte_start":87,"id":"section:7ee252e73c579b017af6","kind":"section","labels":[],"line_end":7,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"Diese Ausgabe führt das 90-seitige Hauptbuch v1.1 vollständig fort; die kompakte 35-seitige Compiler-Fassung v1.2 ist nicht ihre Basis. Alle ursprünglichen 21 Hauptkapitel und vier Anhänge bleiben zugänglich. Hinzu kommen drei neue Hauptkapitel und dieses Quellenregister.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei Dokumente mit unterschiedlichen Aufgaben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2181,"byte_start":812,"id":"section:66b81bc9da48f9704414","kind":"section","labels":[],"line_end":18,"line_start":8,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"Die alten IDs S01–S11 bleiben unverändert. N1–N6 bezeichnen die sechs bereits archivierten Konsolidierungen: Fable-Konsolidierung, Sol-Rekonstruktion, kurze Universalraum-Konsolidierung, Q-Audit/U-Regel, TFPT-Rekonstruktion und Sechs-Prüfpunkte-Analyse, jeweils vom 14. September 2026. Originaltexte und Hashes stehen im Sechs-Quellen-Auditpaket.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neue Quellen und unveränderte Originale","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":3389,"byte_start":2181,"id":"section:14e7bc55aae4b4730ed6","kind":"section","labels":[],"line_end":30,"line_start":19,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"L37mmL30mmL83mm Paket&Umfang&Prüfgrenze\\\\ Basisbuch v1.1&210 Bedingungen&Historische Basisprüfung; nicht erneut vollständig ausgeführt.\\\\ Schatten v1.1&128 Bedingungen&Historische Erweiterung; alte RH-Aktualitätsgrenze bleibt sichtbar.\\\\ Sechs-Quellen-Audit&100 eigene&78 exakt/Integrität, 22 numerisch; in dieser Ausgabe redaktionell integriert.\\\\ Gemeinsame Ausführung&231 eigene exakte&Für diese Ausgabe erneut ausgef","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Evidenz nicht durch Addition aufwerten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4020,"byte_start":3389,"id":"section:172a568a5caf7da46cd1","kind":"section","labels":[],"line_end":39,"line_start":31,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"Die wissenschaftlichen Pakete liegen unter experiments/theory-contracts/universalraum-six-source-audit-20260914 experiments/theory-contracts/compiler-single-execution-20260914 experiments/theory-contracts/universalraum-paired-release-20260914/new-input-audit Das dritte enthält den neuen endlichen Prüfer, seine Normal-/Optimierungsausgaben und die gesonderte Singulettrechnung. Das Releaseverzeichnis enthält LaTeX, all","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Rechen- und Dokumentpakete","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":4865,"byte_start":4020,"id":"section:c6eede1515919e9c7c63","kind":"section","labels":[],"line_end":43,"line_start":40,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"Der RH-Aktualitätslauf scheiterte an einem fehlenden referenzierten Quellenordner. Der konfigurierte separate Faktorgraph ist nicht verfügbar. Die ausgewählte Originalroute r647 und die verfügbaren Beweise wurden gelesen; keine vollständige globale Aktualität wird behauptet. Es wurde kein RH-Abschlussmarker geändert und keine neue arithmetische Kampagne gestartet.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Aktualität und ausdrücklich fehlende Prüfungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":103,"byte_start":0,"id":"section:8cc09a2737f71633ec5b","kind":"chapter","labels":["ch:newinputs13"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Zwei weitere Eingaben: Mikrodynamik und deterministische Präparation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":929,"byte_start":103,"id":"section:98271a8989c5f037337e","kind":"section","labels":[],"line_end":7,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Die während der Konsolidierung zusätzlich eingereichten Texte N7 und N8 enthalten neue Resultate, nicht nur Zusammenfassungen. N7 berichtet die vollständige vierte Ordnung eines harten CAR-Referenzmodells, einen mikroskopischen Stern und einen Relaxationskanal. N8 konstruiert einen harten Tensorproduktkandidaten mit globaler Bandschranke und eine deterministische ideale Präparation.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Prüfurteil und Modellgrenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2213,"byte_start":929,"id":"section:b5005d379d35ed0169be","kind":"section","labels":[],"line_end":28,"line_start":8,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"N7 verwendet Dieser Operator ist unitär, aber im Gegensatz zu [formula in source] aus Kapitel Das ist kein Widerspruch, sondern eine verschiedene Phase des Rückwegs. Beim Recordaufbau ist der tatsächliche Adjungierte nötig: [formula in source] reproduziert dieselbe Materie-Aufzeichnung wie [formula in source] , unter Einschluss der Pointertensorfaktoren. Blindes Ersetzen beider [formula in source] durch [formula in s","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei richtige unitäre Vertizes, aber nicht derselbe Schritt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4264,"byte_start":2213,"id":"section:9c57f5e07dc050271381","kind":"section","labels":[],"line_end":50,"line_start":29,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] lautet der eingereichte Referenzoperator [formula in source] vertauscht die beiden vollständigen Paare. Die 40 Clebsch-Kanten ergeben 40 Einzelkanten-, 160 überlappende und 60 gleichlabelige disjunkte Beiträge. Jede Labelklasse ist ein Matching; gleiche Labels teilen keinen Endpunkt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der vollständige vierte-Ordnungs-Operator","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5715,"byte_start":4264,"id":"section:473457f2eaaea87ecd6e","kind":"section","labels":[],"line_end":74,"line_start":51,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Der gesamte 24024-dimensionale Singulett-Multiplizitätsraum wurde aus Youngs orthogonaler Darstellung aufgebaut. Ein neuer Lauf mit zwölf niedrigen Eigenvektoren ergab Beim zweiten Niveau wurden vier orthogonale Moden gefunden. Die größte Eigenvektorresiduen-Norm des Laufs liegt unter [formula in source] . Das ist eine hochgenaue endliche Rechnung, kein algebraischer oberer Multiplizitätsbeweis.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die neue Singulettantwort ist unabhängig reproduziert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6794,"byte_start":5715,"id":"section:34601b9d5bfcde505528","kind":"section","labels":[],"line_end":88,"line_start":75,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"N8 definiert 16 harte Ortsfaktoren [formula in source] und sechs Bosonmoden pro Vektorlabel. Bei Gesamtladung [formula in source] ist der Sektor endlich. Für gilt [formula in source] . Denn der antisymmetrische Umwandlungsblock [formula in source] erfüllt [formula in source] und [formula in source] . Die selbstadjungierte Offdiagonalblocknorm ist dieselbe. Daher Der führende Austausch ist dann [formula in source] . D","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine globale Bandschranke, aber kein genauer Niedrigenergiefehler","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8548,"byte_start":6794,"id":"section:68b7fa3f7009ba221762","kind":"section","labels":[],"line_end":105,"line_start":89,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] gilt [formula in source] . Definiere [formula in source] mit [formula in source] . Dann In der Basis [formula in source] ist [formula in source] , [formula in source] , [formula in source] . Die unerwünschte Amplitude ist Sie verschwindet für die angegebene Wurzel exakt. Die ideale Phase ist [formula in source] . Es ist eine konkrete Anwendung bekannter https://arxiv.org/abs/quant-ph/0005055Am","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Deterministische Präparation im idealen erweiterten Gattermodell","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9815,"byte_start":8548,"id":"section:17e8ee61693f7b86625b","kind":"section","labels":[],"line_end":126,"line_start":106,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Gewöhnliche Vermittlerverluste [formula in source] lassen vollständig symmetrische Farbzustände mit Vermittlervakuum dunkel. Auf 16 Trägern hat [formula in source] Dimension [formula in source] . Dieser Raum verhindert einen eindeutigen globalen Attraktor dieser Verlustdynamik.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Relaxation: konstruktiv möglich, aber nicht durch Bosonenverlust allein","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10862,"byte_start":9815,"id":"section:a0ec45bb1b92551d08e6","kind":"section","labels":[],"line_end":143,"line_start":127,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Nach einem Paarabbau am Stern ist sein gemeinsamer Mittelpunkt leer; ein zweiter Paarabbau ist unmöglich. Für den geschlossenen Block aus 256 Materie- und 288 Vermittlerzuständen gilt Die untere effektive Matrix ist deshalb exakt Der volle 544-dimensionale Block wurde unabhängig gebaut und diagonalisiert. Bei [formula in source] , [formula in source] sind die niedrige Lücke [formula in source] und das nackte Materieg","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der isolierte mikroskopische Stern: vollständiger kleiner Block","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11905,"byte_start":10862,"id":"section:219ae4ce3461146919a3","kind":"section","labels":["eq:matched-general"],"line_end":160,"line_start":144,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für beliebige bekannte Zielüberlappung [formula in source] ist die Fehleramplitude nach zwei angepassten Schritten proportional zu Sie verschwindet bei Die Polynomidentität wurde symbolisch geprüft. Für den angekleideten Stern-Grundzustand und nackten Eingang [formula in source] gilt [formula in source] . Daraus folgt die angepasste Phase Verwendet man bei idealem Zugriff auf den angekleideten Zielprojektor dennoch d","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Begonnenes Follow-up: die Präparation an das Mikromodell anpassen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13190,"byte_start":11905,"id":"section:f5c1c76fe003165888ed","kind":"section","labels":[],"line_end":171,"line_start":161,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Bereits der detunierte isolierte Paarblock hat maximale Transferwahrscheinlichkeit Bei [formula in source] , [formula in source] sind das nur [formula in source] . Eine einzelne freie Entwicklung dieses Blocks realisiert daher keinen vollständigen Materie-Vermittler-Tausch [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Begonnenes Follow-up: warum ein einziger fester Puls nicht genügt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14612,"byte_start":13190,"id":"section:983e763a46af21259080","kind":"section","labels":[],"line_end":190,"line_start":172,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Das Einzelpuls-Hindernis legt einen konkreten Ausweg nahe, sofern zusätzliche Kontrollen zugelassen werden. Im isolierten resonanten Paar, also bei auf null gesetzter Verstimmung, sei Dann lautet seine exakte Entwicklung Mit dem relativen Viertelphasenpuls [formula in source] gilt Die volle 22-dimensionale Identität ist symbolisch geprüft. Zwei Belegungsphasen und ein resonanter Transfer genügen somit unter diesem Ko","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein kurzer positiver Kontrollkandidat für die nächste Revision","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16745,"byte_start":14612,"id":"section:de833658af17174b82b1","kind":"section","labels":[],"line_end":203,"line_start":191,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Der singuläre Schur-Satz für [formula in source] benötigt [formula in source] , [formula in source] und [formula in source] . Das Gegenbeispiel [formula in source] , [formula in source] , [formula in source] hat negatives Determinant trotz positivem Schurrest. Kompatible positive Blöcke ergeben eine positive dichte Fortsetzung nur für alle Stufen, die tatsächliche Form und passende Stetigkeit. Die Identität der volls","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Arithmetik: bestätigt ist der Vertrag, nicht die offene Lösung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18707,"byte_start":16745,"id":"section:ce9408501db6e9eaaaab","kind":"section","labels":[],"line_end":219,"line_start":204,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Kann die echte kleine Maschine die nötigen Handgriffe ausführen? Gesucht ist eine kontrollierte Kopplung, die Vermittler hin- und zurückführt und Aufzeichnung erhält. Ein fester freier Puls reicht im geprüften Stern nicht. Abnahme: beide Recordzweige und alle Eingänge, keine versteckten Zielzustände. Können wir den richtigen, angekleideten Zustand auswählen? Die passende Verstärkungsphase ist jetzt berechnet. Es fehl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die wichtigsten nächsten Fragen, einfach ausgedrückt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5154,"byte_start":0,"id":"section:224fa5f39174e8cfccaf","kind":"frontmatter","labels":[],"line_end":96,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/main.tex","status_markers_as_written":[],"summary_excerpt":"TeX Gyre Pagella TeX Gyre Heros Latin Modern Mono arrows.meta,positioning,calc,fit,backgrounds,decorations.pathreplacing chapter navy section navy subsection navy slateTFPT · Universalraum slateErklärung und Rekonstruktion chapter slateForschungsstand 14. 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TFPT soll darin eine besonders strukturierte mathematische Ansicht liefern. 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Der vollständige neue Korrekturterm und seine Wirkung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10855,"byte_start":9509,"id":"section:0229d286fb578b511ed0","kind":"section","labels":[],"line_end":159,"line_start":143,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/update.tex","status_markers_as_written":[],"summary_excerpt":"Für den bekannten Zweisingulett-Eingang [formula in source] mit Zielüberlappung [formula in source] bilden zwei angepasste Verstärkungsschritte den Eingang ideal mit Wahrscheinlichkeit eins auf [formula in source] ab. Die konkrete Phase wurde symbolisch und numerisch bestätigt. Das ist eine Spezialisierung bekannter https://arxiv.org/abs/quant-ph/0005055Amplitudenverstärkung, keine neue allgemeine Methode.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Deterministisch im Idealmodell ist nicht automatisch mikroskopisch","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12441,"byte_start":10855,"id":"section:5a1ff491a7fc059d8c0c","kind":"section","labels":[],"line_end":175,"line_start":160,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/update.tex","status_markers_as_written":[],"summary_excerpt":"Angepasste Phase. Für bekannte Zielüberlappung [formula in source] gilt allgemein Für den angekleideten Stern-Grundzustand und nackten Eingang ist [formula in source] . Die passende Phase beträgt nun [formula in source] statt [formula in source] . Die alte Phase hinterlässt selbst bei idealem Zugang zum neuen Zielprojektor Infidelität [formula in source] . Die neue Phase behebt diesen Fehler im erweiterten Idealvertr","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Erste Follow-ups bereits gerechnet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14060,"byte_start":12441,"id":"section:f8e45e7b2fe875f89157","kind":"section","labels":[],"line_end":191,"line_start":176,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/update.tex","status_markers_as_written":[],"summary_excerpt":"Kann die echte Maschine die benötigten Handgriffe? Nächster Test: eine kontrollierte Pulsfolge oder selektive Operation, die den Vermittler zurücksetzt und beide Recordausgänge korrekt liefert. Kein vorpräpariertes Ziel als versteckter Input. Können wir den richtigen angekleideten Zustand auswählen? Die neue Verstärkungsphase ist berechnet. Es fehlen ihre mikroskopische Umsetzung und eine Endmessung aus denselben Ope","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Die wichtigsten nächsten Fragen in einfacher Sprache","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15150,"byte_start":14060,"id":"section:7e7d3042db970624598e","kind":"section","labels":[],"line_end":198,"line_start":192,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/update.tex","status_markers_as_written":[],"summary_excerpt":"Alle vollständigen T1–T8-Tore bleiben offen: primitive Auswahl, native analytische Naht, gemeinsamer 3+1D-Ursprung, chirales Maß, wechselwirkender Grenzprozess, vollständige Parameter, dynamischer Spin 2 und physikalisches Quellfunktional.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"7. Was ausdrücklich offen bleibt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16147,"byte_start":15150,"id":"section:fa27e32b5f83c323397e","kind":"section","labels":[],"line_end":203,"line_start":199,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/main-v1.3/update.tex","status_markers_as_written":[],"summary_excerpt":"Für diese Ausgabe wurden die gemeinsame Ausführung mit 231 eigenen exakten Bedingungen sowie 1073 getrennten Quell-Präfixprüfungen erneut ausgeführt; Normal/Optimierung sind bytegleich und fünf Negativmutanten werden erkannt. Der neue unabhängige Eingabeprüfer umfasst 891 Bedingungen, darunter 832 vollständige kleine F4-Matrixspalten und sechs C16-Stichproben. Dazu kommt die separate neue 24024-dimensionale Singulett","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"8. Prüfumfang und Begleitdateien","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":60,"byte_start":0,"id":"section:7ab7886d2192d28ab6dd","kind":"chapter","labels":["ch:idee"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Was mit Universalraum gemeint ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1381,"byte_start":60,"id":"section:b674e55a132a2a1056f6","kind":"section","labels":[],"line_end":9,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Wenn wir gewöhnlich von Raum sprechen, denken wir an eine Bühne: Hier steht ein Tisch, dort fliegt ein Teilchen, und die Uhr läuft im Hintergrund. Die Universalraum-Idee dreht diese Reihenfolge um. Vielleicht sind zuerst Beziehungen und mögliche Veränderungen da. Eine Bühne mit Entfernungen und einer Uhr entsteht erst, wenn viele dieser Beziehungen ein beständiges Muster bilden.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kein zusätzlicher Behälter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3208,"byte_start":1381,"id":"section:3f49b7156129fec9632f","kind":"section","labels":[],"line_end":33,"line_start":10,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Eine ausreichend konkrete Fassung benötigt mindestens: Zustände: Was ist gegeben, einschließlich relevanter Korrelationen? Operationen: Welche Veränderungen sind erlaubt? Zusammensetzung: Wie dürfen Vorgänge hintereinander und nebeneinander verbunden werden? Aufzeichnungen: Welche Spuren bleiben erhalten und dürfen später erneut benutzt werden? Auslesung: Welche Ergebnisse sind mit welchen Wahrscheinlichkeiten beobac","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die fünf Bestandteile","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4343,"byte_start":3208,"id":"section:b74bfdb6e542117a9cf1","kind":"section","labels":["eq:op"],"line_end":46,"line_start":34,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Zwei Uhren können jetzt beide zwölf anzeigen und trotzdem verschieden weiterlaufen. Eine ist aufgezogen, die andere steht kurz vor dem Stillstand. Wer nur das Zifferblatt betrachtet, sieht den Unterschied noch nicht. Ein späterer Blick unterscheidet sie.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wann zwei Beschreibungen wirklich dasselbe sagen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5759,"byte_start":4343,"id":"section:9825d9a065de49988a40","kind":"section","labels":["eq:vorwaerts"],"line_end":60,"line_start":47,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"TFPT liefert eine reichhaltige Grammatik: Träger, Darstellungen, Gitter, markierte Symmetrien, Projektoren und kurze wiederverwendete Zahlenformeln. Die Metapher vom Compiler meint eine Übersetzung zwischen diesen Beschreibungen. Sie sagt nicht, dass bereits ein kosmisches Computerprogramm identifiziert ist.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TFPT als Grammatik und als Übersetzung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5797,"byte_start":5759,"id":"section:8928610db2c12843478d","kind":"chapter","labels":[],"line_end":61,"line_start":61,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Wie die Idee entstanden ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6733,"byte_start":5797,"id":"section:984a0d0731e83e0d6481","kind":"section","labels":[],"line_end":66,"line_start":62,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Die Anhänge zeigen keine einzige plötzliche Entdeckung, sondern eine Folge von Verschiebungen der Frage. Zuerst fällt auf, dass kleine geometrische und algebraische Daten in verschiedenen Rechnungen wiederkehren. Der Fünferträger führt zu einem 16-dimensionalen Spinor; die passenden Gitterfaktoren führen zu [formula in source] ; ein komplexer Viererträger zeigt 60 besondere Strahlen. Clocks, Ladungszuordnungen und Fl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vom Wiedererkennen zur gemeinsamen Ursache","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7642,"byte_start":6733,"id":"section:f1d5e05ceca4dd8a9ecc","kind":"section","labels":[],"line_end":71,"line_start":67,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Die älteren, in S09 zusammengefassten Untersuchungen fanden mehrere Räume, die man nicht einfach gleichsetzen darf: eine Kommutantenalgebra, einen Majorana-/Fockraum, einen festen Teilchensektor, eine verdoppelte Familienbeschreibung und eingeschränkte Kanalmodelle. Manche lokalen Ansichten ließen verschiedene gemeinsame Dynamiken zu. Andere Tests konnten unter engeren Voraussetzungen ausgewählte Zustände bestimmen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum Spektren und Einzelbilder nicht genügten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9498,"byte_start":7642,"id":"section:4101d0140d4f5cf154ea","kind":"section","labels":[],"line_end":86,"line_start":72,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"L30mmL55mmL65mm Etappe& Erkenntnis& Neue Frage\\\\ Vorarbeiten, in S09 rückblickend beschrieben&Mehrere algebraische Ansichten, Lorentzkegel, verborgene Richtungen, lokale und gemeinsame Kanäle.&Welche Informationen gehen beim Auslesen verloren?\\\\ 13. September: Compiler-Manuskript S09&60 Strahlen, 15 Kontexte, zwei Schatten desselben Prozesses; explizite Vormessung mit Register.&Wer wählt Kreuzkopplung, Kontextgewicht","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die dokumentierte Entwicklung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10684,"byte_start":9498,"id":"section:8bb84ea2a01053a92cd6","kind":"section","labels":[],"line_end":94,"line_start":87,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Der eingefügte Gesprächstext spricht von einem Regelwerk mit Logbuch und von Raum und Materie als Mustern seiner Spuren. Das trifft die Forschungsintuition. Die Formulierung „TFPT ist die Grammatik, der Universalraum die Ausführung“ ist als Einstieg hilfreich.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was von der anschaulichen Ursprungserzählung bleibt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":66,"byte_start":0,"id":"section:b01191a2668a42d0bb11","kind":"chapter","labels":["ch:algebra"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die mathematischen Bauteile von TFPT","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1113,"byte_start":66,"id":"section:1a2d5258f1b335d55b2b","kind":"section","labels":[],"line_end":12,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Die historische Kurzfassung nennt [formula in source] und einen fünfteiligen Träger. Vollständig gelesen setzt P1 einen orientierten Rand beziehungsweise eine Naht, einen geeigneten positiven Kern und eine Normierung voraus. P2 setzt Art und Struktur des Trägers voraus; die spätere [formula in source] -Lesart wird mit Farb- und schwachen Richtungen verbunden. Orientierung, Positivität, komplexe Struktur und Markierun","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Ausgangsannahmen enthalten mehr als zwei Zahlen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2337,"byte_start":1113,"id":"section:649e7fc3a89ec67e3e50","kind":"section","labels":[],"line_end":26,"line_start":13,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Bei fünf komplexen Richtungen kann man antisymmetrische Kombinationen von null, zwei und vier Richtungen bilden. Zusammen erhält man Das ist die gerade Spinorstruktur von [formula in source] . „Antisymmetrisch“ heißt hier: Beim Vertauschen zweier Plätze wechselt ein Vorzeichen. Es ist eine genaue Bauvorschrift, keine bildliche Ähnlichkeit.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vom Fünferträger zum Spinor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4400,"byte_start":2337,"id":"section:7f1055fc7310c252cfb2","kind":"section","labels":[],"line_end":57,"line_start":27,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Die beiden positiven Wurzelgitter [formula in source] und [formula in source] besitzen Determinante vier und Diskriminantengruppe [formula in source] . Eine Diskriminantengruppe beschreibt hier die möglichen Restklassen, mit denen man das Gitter ohne Verlust der Ganzzahligkeit ergänzen kann. Für passende Generatoren gilt modulo eins Diagonal gekoppelt ist die Summe [formula in source] ganzzahlig. Die vier gemeinsamen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die Verklebung wirklich zu E [formula in source] 8 führt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6023,"byte_start":4400,"id":"section:55fc93b1b1aafa6cc296","kind":"section","labels":["eq:branch"],"line_end":83,"line_start":58,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Die 240 Wurzeln sind besondere Vektoren in einem acht-dimensionalen Raum. Hinzu kommen acht Cartanrichtungen, sodass die Lie-Algebra 248 Dimensionen besitzt. Unter [formula in source] lautet ihre komplexe Zerlegung L47mmrY Sektor& Wurzeln& Generatoren einschließlich Cartan\\\\ [formula in source] &40& [formula in source] \\\\ [formula in source] &12& [formula in source] \\\\ Gemischter Vektorsektor&60& [formula in source] ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wurzeln und Generatoren sind verschiedene Zählungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7221,"byte_start":6023,"id":"section:303878c8acd13ffdff68","kind":"section","labels":[],"line_end":90,"line_start":84,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Ein Strahl ist ein reiner Zustand ohne seine insgesamt irrelevante globale Phase. Ein Kontext ist eine vollständige orthogonale Viererbasis: vier mögliche Ausgänge einer scharfen Messung. Im markierten komplexen Viererträger ergeben sich 60 besondere Strahlen in 15 solchen Kontexten. In der gewählten Kodierung sind dies die reinen Zwei-Qubit-Stabilizerzustände und ihre vollständigen Pauli-Kontexte. S09, Kap. 3 und 9","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das endliche Fenster: 60 Strahlen und 15 Kontexte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8754,"byte_start":7221,"id":"section:8f1ead6cfdbab94c93c2","kind":"section","labels":[],"line_end":106,"line_start":91,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"L45mmL31mmL74mm Objekt& Größe& Was die Zahl zählt\\\\ [formula in source] -Wurzeln&240&Besondere Vektoren, keine 240 unabhängigen Raumrichtungen.\\\\ [formula in source] &248&Dimension der Generatoralgebra.\\\\ Ein Viererträger& [formula in source] &Zustände eines Ququarts, hier als zwei Qubits kodiert.\\\\ Vier solche Träger& [formula in source] &Komplexe Hilbertraumdimension der Zelle.\\\\ 15 allgemeine CQ-Blöcke& [formula i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Räume im Größenvergleich","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":71,"byte_start":0,"id":"section:e65303bf4f274fc0a48c","kind":"chapter","labels":["ch:prozess"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Ein gemeinsamer Prozess mit zwei Schatten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1558,"byte_start":71,"id":"section:0e9d4ba6bbb939c3b6e8","kind":"section","labels":["eq:T"],"line_end":19,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Man beginnt mit einem Strahl [formula in source] : Kontext [formula in source] , Ergebnis [formula in source] . Dann wählt man einen nächsten Kontext [formula in source] und misst in dessen Basis. Die Quellkonstruktion benutzt [formula in source] ist eine [formula in source] -Inzidenzmatrix. Sie erlaubt den aktuellen Kontext und sechs andere, mit ihm inzidente Kontexte. Jeder erlaubte Nachfolger erhält in dieser spez","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine einzelne Messrunde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3449,"byte_start":1558,"id":"section:41de3c2922930307bece","kind":"section","labels":["eq:D","eq:shadows"],"line_end":55,"line_start":20,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Die Matrix [formula in source] summiert die vier Ergebnisgewichte jedes Kontexts. Die Matrix [formula in source] liest die 15 nichttrivialen Pauli-Erwartungswerte aus. Mit [formula in source] lauten ihre Einträge Für [formula in source] und [formula in source] ergibt sich exakt Der Systemschatten entwickelt sich somit als depolarisierender Kanal Die Dämpfung [formula in source] entsteht aus der Kontextkombinatorik. B","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kontext und Quantenzustand als zwei Auslesungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4623,"byte_start":3449,"id":"section:e92dbd8d66abba12c564","kind":"section","labels":["eq:Tfactor"],"line_end":74,"line_start":56,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Die in S01 ausgearbeitete Faktorisierung lautet Hier gelten [formula in source] , [formula in source] und [formula in source] . Die beiden Zeilenräume sind orthogonal. Im selben Kontext haben die Pauli-Vorzeichenvektoren Skalarprodukt drei für denselben Strahl und minus eins für verschiedene Strahlen; bei inzidenten Kontexten bleibt eine gemeinsame Pauli-Richtung. Diese Werte ergeben genau die Einträge von","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die genaue Kompression auf 30 Koordinaten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5895,"byte_start":4623,"id":"section:b9e43133e6f53aff49bf","kind":"section","labels":[],"line_end":93,"line_start":75,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Aus [formula in source] mit Permutationsmatrizen folgt beim gleichgewichteten Mitteln unmittelbar [formula in source] . Zusätzliche Konjugation durch die Symmetriegruppe [formula in source] ändert das nicht: S07 berichtet 5040 Terme über 4500 verschiedene Matchings, gegenüber 24\\,601\\,472 insgesamt möglichen perfekten Matchings des bipartiten Inzidenzbildes. Diese kombinatorische Realisierung ist konkret. Die Gleichg","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum Symmetrie die Gewichte noch nicht auswählt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6666,"byte_start":5895,"id":"section:087d079c1203e4aca5d9","kind":"section","labels":[],"line_end":108,"line_start":94,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Für die Kontextmatrix gilt Ihre Determinante ist negativ. Eine reelle Matrixexponentialfunktion hat jedoch [formula in source] . Deshalb ist [formula in source] auf diesem 15-dimensionalen Raum kein [formula in source] mit reellem [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein Schritt ist nicht dasselbe wie zwei halbe Schritte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6742,"byte_start":6666,"id":"section:f267165f6e35e6032121","kind":"chapter","labels":["ch:memory"],"line_end":110,"line_start":109,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Gedächtnis: Was ein einzelnes Bild verschweigt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8872,"byte_start":6742,"id":"section:d1a02b61970e1e42b24e","kind":"section","labels":[],"line_end":144,"line_start":111,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Ein klassisch-quantenmechanischer Zustand, kurz CQ-Zustand, besitzt 15 positive [formula in source] -Blöcke [formula in source] . Zusammen haben sie 240 reelle lineare Koordinaten und Gesamtspur eins. Die feste Regel macht jeden Ausgangsblock in seinem Kontext diagonal. Deshalb gilt Es ist also nicht richtig, 240 Koordinaten pauschal als kleinste dauerhaft autonome Hülle dieser festen Ausführung auszugeben.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Allgemeine Kontextblöcke brauchen eine andere Beschreibung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10173,"byte_start":8872,"id":"section:e61dd6eb62c77c2400b5","kind":"section","labels":["eq:record"],"line_end":165,"line_start":145,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Für die vier Projektoren eines Kontexts sind [formula in source] Spiegelungen. In Dimension vier gilt Allgemein in Dimension [formula in source] wäre die linke Seite [formula in source] . Der kurze Auslöschungseffekt ist hier also tatsächlich viererspezifisch.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie die Aufzeichnung gebaut wird","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12002,"byte_start":10173,"id":"section:6654401dc8d90c14e6ad","kind":"section","labels":[],"line_end":179,"line_start":166,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Für einen gleichförmigen reinen Eingang in der gewählten Kontextbasis erzeugt eine Vormessung maximale Verschränkung. Ohne Registerblick ist der Systemzustand [formula in source] . Nun gibt es zwei Ausführungen: Derselbe kohärente Speicher wird nochmals gekoppelt: [formula in source] stellt den reinen Eingang wieder her. Ein neuer Speicher wird benutzt: Im reduzierten System wird die Dephasierung wiederholt; [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das Echo des behaltenen Registers","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12810,"byte_start":12002,"id":"section:ab34b5516975fd2b96d5","kind":"section","labels":[],"line_end":189,"line_start":180,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Bei frischen Registern trägt eine Folge von Kontexten den kohärenten Zustand Das Weglassen des Registers summiert Dichteoperatorbeiträge. Eine kohärente Projektion auf eine Registersuperposition summiert Amplituden und beschreibt ein anderes Experiment, einschließlich seiner Erfolgswahrscheinlichkeit.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reihenfolge bleibt wichtig","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14485,"byte_start":12810,"id":"section:47c791f24777cff2885b","kind":"section","labels":[],"line_end":202,"line_start":190,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Eine nichtverschwindende Beobachtungsfolge eines geschlossenen endlichen Systems mit festem unitärem Schritt ist eine endliche Summe von Phasenfaktoren. Nach Zusammenfassung gleicher Frequenzen besitzt ihr mittleres Betragsquadrat einen positiven Cesàro-Grenzwert. Sie kann daher nicht für alle [formula in source] exakt wie [formula in source] abklingen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Endliches Gedächtnis und scheinbares Vergessen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":72,"byte_start":0,"id":"section:81a330dc7dac4f67ca99","kind":"chapter","labels":["ch:zelle"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die Vierträgerzelle: ein gemeinsames Muster","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1404,"byte_start":72,"id":"section:a0b68c12ff57ae1ad04d","kind":"section","labels":["eq:omega"],"line_end":24,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Vier Träger mit je vier Basiswerten besitzen den total antisymmetrischen Zustand Jedes Basiswort verwendet alle vier Werte genau einmal. Die 24 Permutationen erhalten passende Vorzeichen. Das Ergebnis ist ein reiner gemeinsamer Zustand. Jeder einzelne Träger sieht für sich trotzdem maximal gemischt aus: Die Paarreduktion hat Rang sechs und sechs gleich große Eigenwerte [formula in source] . Die Ordnung steckt in den ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein Zustand, dessen Teile allein nichts verraten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2609,"byte_start":1404,"id":"section:7d17238669656dcb0390","kind":"section","labels":[],"line_end":38,"line_start":25,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Sei [formula in source] der Projektor auf den symmetrischen Paarraum. Wenn für alle Paare [formula in source] gilt, dann hat jeder Swap Eigenwert minus eins. Da Transpositionen alle Permutationen erzeugen, folgt Für [formula in source] ist dieser Raum eindimensional, für [formula in source] null. Auch gemischte Zustände mit entsprechender Trägerbedingung erfüllen die Aussage. Für [formula in source] existieren aber e","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Hüllensatz und seine genaue Voraussetzung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3902,"byte_start":2609,"id":"section:9e878cd7fefe209938ac","kind":"section","labels":["eq:tet-spec"],"line_end":54,"line_start":39,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Das vollständige Tetramermodell lautet Es besitzt das exakte Spektrum Der Grundzustand ist [formula in source] , die Lücke [formula in source] . Die hochgestellten Zahlen zählen die Zustände pro Energiewert und summieren sich zu 256.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine weiche Energiebedingung erlaubt Bewegung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5057,"byte_start":3902,"id":"section:894ced3b45fd2e6eb1d3","kind":"section","labels":[],"line_end":68,"line_start":55,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Der vollständige Graph, ein Stern und ein Pfad besitzen auf vier Trägern denselben antisymmetrischen Grundzustand, aber verschiedene Anregungen. Für gleiche Sterngewichte ist die Lücke [formula in source] statt [formula in source] . S01 nennt für einen Pfad mit Gewichten [formula in source] etwa [formula in source] ; S06 für sechs Gewichte [formula in source] etwa [formula in source] . Die letzten Werte werden hier a","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was ein Zustand über seinen Generator verrät","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5655,"byte_start":5057,"id":"section:846135f14f75218e133b","kind":"section","labels":[],"line_end":73,"line_start":69,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Der Projektor [formula in source] kommutiert mit allen Swaps. Daher erhält jede rein zellinterne Austauschentwicklung, auch mit zeitabhängigen Gewichten, den Anteil [formula in source] . Kollektive [formula in source] -Drehungen tun dasselbe. Ein Grundzustand kann also bekannt sein, ohne dass der vorhandene Ablauf einen beliebigen Eingang dorthin bringt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum Austausch allein die Zelle nicht herstellt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5734,"byte_start":5655,"id":"section:b3e2b5d75fa2061eb865","kind":"chapter","labels":["ch:fugen"],"line_end":75,"line_start":74,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Vermittlung und Graph: die Prüfung der fünf Fugen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7444,"byte_start":5734,"id":"section:d8842077c354c0694279","kind":"section","labels":[],"line_end":100,"line_start":76,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Der gewünschte positive Austausch lässt sich in einem kleinen Modell genau erklären. Man ergänzt den Paarraum [formula in source] durch einen sechsdimensionalen Vermittler mit Energie [formula in source] . Die partielle Isometrie [formula in source] erfüllt Für bleiben die zehn symmetrischen Zustände bei null; die antisymmetrischen Zustände koppeln paarweise an den Vermittler. Die unteren Energien sind Nach Identifik","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie ein virtueller Zwischenzustand bindet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9435,"byte_start":7444,"id":"section:5c0e1a883c235dc95861","kind":"section","labels":[],"line_end":122,"line_start":101,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"S11 macht die zusätzliche Zuordnung: Ein [formula in source] -Spinorgewicht [formula in source] ist ein Ort; das [formula in source] -Gewicht [formula in source] ist der lokale Viererzustand. Die 64 Gewichte von [formula in source] werden somit als 16 Orte mit je vier inneren Zuständen gelesen. Das ist eine konkrete bedingte Interpretation, keine bloße Umbenennung einer bereits gegebenen räumlichen Geometrie.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Clebsch-Vorschlag: eine genaue neue Graphlesart","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11474,"byte_start":9435,"id":"section:fb0b4fcd493d88c9fa6d","kind":"section","labels":[],"line_end":131,"line_start":123,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Die Graphkombinatorik folgt aus der angegebenen Ortslesart. Um daraus einen Vielteilchen-Hamiltonoperator zu erhalten, braucht man außerdem eine Fock- oder Tensorproduktstruktur, Besetzungsbedingungen, die Bedeutung der virtuellen Zustände und ihre Energien. Betragsgleiche Chevalley-Strukturkonstanten wählen noch keine physikalischen Kopplungsstärken in normierten Mehrteilchenzuständen aus. Gleiche [formula in source","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Welche Auswahl hier noch hinzukommt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12636,"byte_start":11474,"id":"section:8fdf71502cd567e1fca4","kind":"section","labels":[],"line_end":147,"line_start":132,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"L74mmY Clebsch-Cluster bei [formula in source] , nach S11& Berichteter Wert\\\\ Grundenergie& [formula in source] \\\\ Grundzustand&Eindeutiges [formula in source] -Singulett, Form [formula in source] \\\\ Erster angeregter Singulettwert& [formula in source] , Dublett, Gap etwa [formula in source] \\\\ Erste adjungierte Anregung& [formula in source] , Gap etwa [formula in source] \\\\ Weitere Multiplets& [formula in source] be","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die berichteten Clusterzahlen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13817,"byte_start":12636,"id":"section:70b026942b5f610560dc","kind":"section","labels":[],"line_end":163,"line_start":148,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"S11 behauptet für den vollständigen Graphen mit [formula in source] einen eindeutigen Grundzustand bei [formula in source] und Gap [formula in source] . Energie und Gap stimmen; die Eindeutigkeit stimmt ab acht Trägern nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neue Korrektur: Singulett heißt nicht eindeutig","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15756,"byte_start":13817,"id":"section:6f018fcd6a532e19942a","kind":"section","labels":[],"line_end":183,"line_start":164,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Die Sektortrennung aus S11 ist für die gleichkontextige Kopplung anschaulich: [formula in source] reflektiert den von [formula in source] aufgespannten Vierraum, der in [formula in source] liegt. Auf [formula in source] wirkt es als Identität. Entsprechend lässt dieser spezielle Operator den Paaranteil einer idealen [formula in source] -Zelle unverändert. Bei einer anderen Registerbasis gilt die Aussage nicht automat","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neue Präzisierung: Aufzeichnung ist nicht durch die 248 verboten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":66,"byte_start":0,"id":"section:dd5b4180abd938f2563e","kind":"chapter","labels":["ch:two"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Zwei Zellen: aus Verbindung wird Dynamik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":839,"byte_start":66,"id":"section:94c4eec8515e22ac92ec","kind":"section","labels":[],"line_end":7,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Ist eine reduzierte Dichtematrix [formula in source] rein, so muss der gemeinsame Zustand bezüglich [formula in source] und seinem Rest faktorisiert sein. Sein Träger liegt in [formula in source] . Sind alle disjunkten Zellmarginalien unverändert rein, ist der Gesamtzustand ein Produkt über die Zellen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die Zellen beim Verbinden ihre Reinheit verlieren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1875,"byte_start":839,"id":"section:f080ff62e49feb2bfb1c","kind":"section","labels":["eq:Hred"],"line_end":28,"line_start":8,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Zwei vollständige Tetramerzellen mit genau einer Brücke haben Der volle Raum besitzt [formula in source] Dimensionen. Trotzdem bleibt die Entwicklung des Produktzustands in einem zweidimensionalen invarianten Unterraum: Die beiden Vektoren sind orthonormal; [formula in source] und [formula in source] . Es folgt Die Brücke koppelt den Produktgrundzustand an eine gemeinsame adjungierte Anregung. Beide Zellhälften verwe","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein kleiner exakter Raum in einem großen Hilbertraum","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3778,"byte_start":1875,"id":"section:9977a9a07426fae40e66","kind":"section","labels":["eq:gapbound"],"line_end":67,"line_start":29,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Mit lauten die beiden Eigenwerte Die negative Korrektur beschreibt die Absenkung gegenüber dem einfachen Produktwert [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Energie und ein wirklicher Grundzustandsnachweis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4979,"byte_start":3778,"id":"section:71703acbea71bad3fc62","kind":"section","labels":[],"line_end":89,"line_start":68,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Der niedrige Eigenzustand lässt sich schreiben als Seine Zellreduktion besitzt das Spektrum Die Entropie in natürlichen Logarithmen ist Bei [formula in source] sind [formula in source] und [formula in source] ; bei [formula in source] gilt [formula in source] . Schon eine endliche einzelne Brücke macht die lokale Zelle gemischt. Energieabsenkung und Verschränkung sind hier keine unabhängig eingesetzten Zusätze.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verschränkung aus derselben Kopplung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6094,"byte_start":4979,"id":"section:0c74e9a15e40f27a33f1","kind":"section","labels":["eq:two-clock"],"line_end":105,"line_start":90,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Starte im Produkt [formula in source] und lasse denselben konstanten gekoppelten Hamiltonoperator wirken. Dann gilt Bei [formula in source] vereinfacht sich dies zu [formula in source] . Der Energieinhalt beider Zellen pulsiert in einem messbaren Muster.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein Uhrsignal ohne zusätzlich gewählten lokalen Tick","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7062,"byte_start":6094,"id":"section:de47312b3ac8e90b10f3","kind":"section","labels":[],"line_end":114,"line_start":106,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Ein einzelner eindeutiger Singulettgrundraum besitzt keine logische Zustandsvielfalt. Das Produkt solcher Grundräume bleibt eindimensional. Wer alles auf diese Grundräume projiziert, erhält nur eine skalare Energie. Nichttriviale effektive Dynamik muss Anregungen, Randzustände, Multiplizitäten oder zusätzliche Vakuumsektoren behalten.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum viele Zellen noch ein eigener Schritt sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":71,"byte_start":0,"id":"section:d72d1ec508dae75b950c","kind":"chapter","labels":["ch:zeit"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Zeit: Takt, Uhrwerk und lesbare Veränderung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1193,"byte_start":71,"id":"section:c8957fc6e1107b3c7f9b","kind":"section","labels":[],"line_end":15,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Eine zyklische Matrix ist zunächst ein Taktmuster. Eine Dynamik sagt, wann welcher Zustand entsteht. Eine Uhr braucht zusätzlich eine beobachtbare Anzeige und eine Kalibrierung. Diese drei Ebenen müssen zusammenpassen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Drei Bedeutungen des Wortes Clock","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2069,"byte_start":1193,"id":"section:173c31c1e8a06fb6e43a","kind":"section","labels":[],"line_end":20,"line_start":16,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Der vollständige gleichgewichtete Tetramer-Hamiltonoperator ist eine zentrale Transpositionssumme. Deshalb kommutiert er mit jedem [formula in source] und jedem [formula in source] . Die Paarenergien ändern sich unter seiner freien Entwicklung nicht. Eine Tabelle, die nacheinander einen lokalen [formula in source] -Tick anwendet, ist somit kein Beweis, dass genau diese Anzeige unter [formula in source] von selbst läu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die Paarenergien unter dem Tetramer stillstehen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":3008,"byte_start":2069,"id":"section:1c3604e4c12b843c069b","kind":"section","labels":[],"line_end":38,"line_start":21,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Ein präparierter nichtstationärer Zustand kann dennoch unter demselben Tetramer laufen. Für einen lokalen spurfreien hermiteschen Pauli [formula in source] mit [formula in source] setze Da [formula in source] , folgt Die lokalen Anzeigen oszillieren gegeneinander; ihre Summe bleibt null. Die Periode ist [formula in source] . Präparation, Ausleserichtung und die Kalibrierung von [formula in source] sind weitere Eingab","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine laufende lokale Anzeige im gesetzten Modell","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4494,"byte_start":3008,"id":"section:3c0dda8310b6dbec48dc","kind":"section","labels":[],"line_end":57,"line_start":39,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Zerlege [formula in source] . Die vier [formula in source] sind orthonormal. Wähle zusätzlich Weil jedes Wort von [formula in source] jedes Energielabel einmal enthält, gilt [formula in source] . Für erhält man [formula in source] . Die Zeiten [formula in source] liefern vier orthogonale Anzeigen. Global ist der Zustand stationär, bedingt auf die Uhranzeige entwickelt sich das System. Das ist eine konkrete Page-Woott","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine relationale Viereruhr ist konstruierbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":5172,"byte_start":4494,"id":"section:0cac91ff575e48441883","kind":"section","labels":[],"line_end":62,"line_start":58,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Aus [formula in source] folgt [formula in source] . Die historischen Größen [formula in source] und [formula in source] beschreiben deshalb sechsfach wiederholte Faktoren [formula in source] und [formula in source] . Eine physikalische Rate ist erst [formula in source] für einen festgelegten Schritt [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum ein Logarithmus noch keine Sekunde ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5249,"byte_start":5172,"id":"section:783de4aa6fd8e72203c2","kind":"chapter","labels":["ch:echo"],"line_end":64,"line_start":63,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die ausführbare Präparation und der Mehrzeittest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6616,"byte_start":5249,"id":"section:91de5fe3af310bfb27ab","kind":"section","labels":[],"line_end":86,"line_start":65,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Die Präparationsnotiz S02 geht über den abstrakten Satz „ [formula in source] existiert“ hinaus. Sie beschreibt eine konkrete Schaltung, die aus einem einfachen Eingang den Zustand mit Erfolgsanzeige herstellt, anschließend ein Register schreibt und die Rückkehr ausliest. Laut Quelle wurde die Schaltung exakt simuliert, nicht auf Hardware ausgeführt. Ihr Zugriff auf zusätzliche Hilfssysteme und Nicht-Clifford-Operati","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was S02 tatsächlich geschlossen hat","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8093,"byte_start":6616,"id":"section:fed330d43c9db3f987a7","kind":"section","labels":[],"line_end":101,"line_start":87,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Der benötigte Zustand [formula in source] ist in der Acht-Qubit-Kodierung kein Stabilizerzustand. Schon für einen nichttrivialen lokalen Pauli gilt während reine Qubit-Stabilizerzustände für Pauli-Observablen nur [formula in source] liefern. Ebenso ist der Paarreduktionsrang sechs keine Zweierpotenz. Eine exakte Präparation aus einem Stabilizer-Eingang benötigt deshalb eine zusätzliche Ressource, etwa einen passenden","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die zusätzliche Ressource bleibt sichtbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9225,"byte_start":8093,"id":"section:3dfe7c09d22f1bf766c8","kind":"section","labels":[],"line_end":123,"line_start":102,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Der einfache Eingang lautet Er ist mit dem in S02 angenommenen Clifford-Baukasten präparierbar und besitzt [formula in source] -Anteil [formula in source] . Der Antisymmetrisierer ist Die konkrete Schaltung erzeugt 32 Kontrollzweige, von denen 24 die Permutationen tragen. Acht ungültige Zweige werden markiert. Nach Interferenz und Erfolgsselektion ist der implementierte Operator Somit gilt Der erfolgreiche Zweig ist ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie der Filter den Zustand erzeugt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11201,"byte_start":9225,"id":"section:7096e48075d2e22477d5","kind":"section","labels":["eq:originalecho"],"line_end":160,"line_start":124,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] schreibe [formula in source] . Dann Ein ignorierter frischer Pointer erzeugt Diese binäre Swap-Aufzeichnung ist ein anderer Kanal als die 15-Kontext-Mischung mit Faktor [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das ursprüngliche Echo: eins gegen siebzehn Zweiunddreißigstel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12703,"byte_start":11201,"id":"section:c105f5d2144c359b3f04","kind":"section","labels":[],"line_end":180,"line_start":161,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Der Endfilter hat den Effekt [formula in source] . Seine beobachtbare Erfolgsrate ist deshalb [formula in source] , nicht [formula in source] selbst. L68mmY Y Statistik& Behalten& Frisch\\\\ [formula in source] -Rückkehr, bedingt auf Präparation& [formula in source] & [formula in source] \\\\ Endfilter erfolgreich, bedingt auf Präparation& [formula in source] & [formula in source] \\\\ Beide Filter erfolgreich, je begonnen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die wirklichen Erfolgswahrscheinlichkeiten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15100,"byte_start":12703,"id":"section:1e67db102372afd4add2","kind":"section","labels":["eq:optimal"],"line_end":207,"line_start":181,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Eigene exakte Ergänzung dieser Synthese. Man kann die gleiche Messfrage für einen beliebigen lokalen unitären Tick [formula in source] ausrechnen. Setze Die beiden Swap-Gewichte sind [formula in source] . Daher Der Kontrast dieser Rückkehrstatistik ist maximal, wenn [formula in source] , also [formula in source] . Ein einzelnes CNOT innerhalb des Viererträgers erfüllt [formula in source] . Es permutiert dieselbe Meng","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neue Fortsetzung: der maximal ausgeglichene Echovergleich","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16515,"byte_start":15100,"id":"section:6e714668749a238f0bd7","kind":"section","labels":[],"line_end":215,"line_start":208,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Y r Ressource nach S02& Anzahl\\\\ Systemqubits&8\\ , wiederverwendet&10\\ ätze&2\\ reservierte Qubits&20\\ Erfolgsbits beider Filter&12\\ -Gatter&574\\ CNOT vor Toffoliauflösung&382\\ &26\\ - [formula in source] / Pauli- [formula in source] &276 / 26\\\\T/T^ [formula in source] T-Varianten waren durch lokale Matrixidentität und Ersetzung zertifiziert, nicht zusätzlich als komplette komplexe 20-Qubit-Vektoren simuliert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ressourcen und Beweisgrenze der Originalschaltung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":75,"byte_start":0,"id":"section:2c2e28b54c7904bb604f","kind":"chapter","labels":["ch:seam"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Von der Kette zur E [formula in source] 8-Naht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1943,"byte_start":75,"id":"section:9edca7172a729ba8ed93","kind":"section","labels":[],"line_end":28,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Das Zweizellenmodell benutzt zwei vollständige Vierergraphen mit einer Brücke. Die Vielzellenrechnung in S08 benutzt dagegen Vierersegmente mit nächster Nachbarschaft. Bei [formula in source] wird erst dieses zweite Modell eine uniforme Kette. Derselbe isolierte Singulettzustand garantiert keine identischen Anregungen und keinen identischen Grenzwert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein wichtiger Modellwechsel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3203,"byte_start":1943,"id":"section:3471c426f4dce65973e0","kind":"section","labels":[],"line_end":44,"line_start":29,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Für den uniformen periodischen Austauschring liefern die Quellen [formula in source] bei acht und [formula in source] bei zwölf Trägern. Der bekannte Vergleich lautet Die Sutherland-Grundenergie pro Träger ist für [formula in source] . S08 nennt die Extrapolation [formula in source] und [formula in source] . Diese endlichen Zahlen passen zur [formula in source] -WZW-Beschreibung des Kettenmodells. Die allgemeine Verb","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die SU(4)-WZW-Theorie hier plausibel ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4699,"byte_start":3203,"id":"section:ff41b09a89e52e22fa34","kind":"section","labels":[],"line_end":70,"line_start":45,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Die zentrale Ladung ist eine Kennzahl einer konformen Feldtheorie. Für die chiralen Niveau-1-Faktoren gilt Das Produkt hat also schon vor einer Kopplung [formula in source] . Ein später gefundener Wert acht allein ist kein Beweis einer [formula in source] -Erweiterung und kein Beweis eines Kondo-Flusses.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Naht braucht mehr als die Zahl acht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6584,"byte_start":4699,"id":"section:92ab1ec9f1686b3ac49b","kind":"section","labels":[],"line_end":92,"line_start":71,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"S11 ersetzt die frühere Kondo-Zielbeschreibung sinnvoll durch eine konkrete Erweiterungsaufgabe. Die Kurzschreibweise eines Quotienten durch [formula in source] kann jedoch verschiedene Operationen meinen. Nur auf invariante Zustände des ursprünglichen Produkts zu projizieren ist nicht dasselbe wie eine Simple-Current-Erweiterung mit den nötigen zusätzlichen beziehungsweise entsprechend gekoppelten Sektoren.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum „Z [formula in source] 4-Eichung“ präzisiert werden muss","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7319,"byte_start":6584,"id":"section:c3c4e37c36f78a62060a","kind":"section","labels":[],"line_end":97,"line_start":93,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Eine gewöhnliche kritische SU(4)-Kette hat links- und rechtslaufende Sektoren, mit [formula in source] . Die übliche Kennzahl heißt dabei [formula in source] , nicht sechs. Die chirale Differenz ist null. Eine rein chirale [formula in source] -Naht hat dagegen Differenz acht. Ein zusätzliches ebenfalls nichtchirales [formula in source] -Modell ändert daran nichts.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Chiralitätslücke","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8698,"byte_start":7319,"id":"section:41acf7fde27002fd60f1","kind":"section","labels":[],"line_end":103,"line_start":98,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Die innere Glue- [formula in source] wirkt auf den 248 Strömen mit Phasen [formula in source] auf Sektoren der Größen [formula in source] . Ihre Spur ist null. Die geometrische Vierteldrehung [formula in source] hat auf Stufe eins dagegen Spur [formula in source] . Die Operatoren sind somit nicht identisch. Eine Clock kann eine geometrische Drehung mit innerem Twist kombinieren; die beiden Faktoren bleiben getrennt. ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei Vierteldrehungen und der Index","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":82,"byte_start":0,"id":"section:0ce1fd62e4487ba78b42","kind":"chapter","labels":["ch:recon"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Wie eine vollständige Rekonstruktion aussehen könnte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1477,"byte_start":82,"id":"section:b966205b339a87a7bd6a","kind":"section","labels":[],"line_end":14,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Eine endliche Liste von Schatten bestimmt im Allgemeinen mehrere Prozesse. Man kann sogar jeden Kandidaten um einen ungekoppelten unsichtbaren Hilfsfaktor ergänzen, auf den alle erlaubten Experimente trivial wirken. Alle Antworten bleiben gleich. Eindeutigkeit ist daher zunächst nur für die minimal beobachtbare Darstellung erreichbar.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vom Wunsch nach Eindeutigkeit zu einer prüfbaren Frage","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2066,"byte_start":1477,"id":"section:e3ead478a5ce82c6cc8f","kind":"section","labels":[],"line_end":21,"line_start":15,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Eine Projektion kann wichtige Wahrscheinlichkeiten erhalten und trotzdem die Multiplikation zerstören. S03 gibt einen einfachen Gegenbeleg: Projiziere [formula in source] auf [formula in source] und definiere [formula in source] . Dann Die neue Multiplikation ist nicht assoziativ. Eine nützliche reduzierte Vorhersagebeschreibung darf also nicht ohne zusätzlichen Nachweis als geschlossene physische Operationsalgebra v","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine kleinere Beschreibung ist nicht automatisch eine Algebra","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4207,"byte_start":2066,"id":"section:62ea8fadef4a1ff97648","kind":"section","labels":[],"line_end":49,"line_start":22,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Eine phasentreue Rekonstruktion braucht mehr als eine Tabelle einzelner Wahrscheinlichkeiten. Ein passender Ausgangspunkt ist eine komplexe Algebra [formula in source] mit Einheit, Multiplikation, Adjunktion und einem positiven normierten Zustandsfunktional [formula in source] : Für Operationswörter [formula in source] definiert einen positiven semidefiniten Korrelationskern. Er enthält die relativen komplexen Phasen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was vollständige Phaseninformation zusätzlich bringt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5498,"byte_start":4207,"id":"section:20fbbeca5cc17d0fb6dd","kind":"section","labels":[],"line_end":62,"line_start":50,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Ein Prozesstensor beziehungsweise Quantenkamm ordnet einer Folge von Instrumenten gemeinsame Ergebniswahrscheinlichkeiten zu. Positivität und kausale Normierungsregeln sichern die Konsistenz. Eine tomographisch vollständige Eingriffsfamilie bestimmt einen endlichen Prozesstensor; sie bestimmt nicht automatisch eine eindeutige verborgene Umgebung oder sämtliche unendlichen Horizonte.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Mehrzeitdaten statt einer einzigen Dichtematrix","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6613,"byte_start":5498,"id":"section:e8c36d0518830336f3e1","kind":"section","labels":[],"line_end":69,"line_start":63,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"S05 schlägt eine nützliche endliche Vorgehensweise vor: Man fixiert zulässige Operationswörter bis Länge [formula in source] , ihre Relationen, Symmetrien und die belegten Auslesungen. Die unbekannten Momente müssen eine positive Momentenmatrix bilden. Dann minimiert und maximiert man eine noch offene Ausgabe [formula in source] über alle kompatiblen Modelle.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein konkreter Auswahltest für offene Größen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8958,"byte_start":6613,"id":"section:b750d51e7f7e6febc36f","kind":"section","labels":[],"line_end":103,"line_start":70,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Die in S03 vorgeschlagene Alternative verwendet als lokalen Viererverknüpfungstensor. An orientierten Verbindungen werden Trägerräume mit ihren dualen Räumen kontrahiert. So verbindet man Amplituden, ohne jede physische Zellreduktion als unverändert reines [formula in source] festzuschreiben.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Zelle als Verknüpfungsamplitude","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9871,"byte_start":8958,"id":"section:db019b13eae15f8ec775","kind":"section","labels":[],"line_end":108,"line_start":104,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Paarweise kommutierende volle Matrixunteralgebren, die gemeinsam die Gesamtalgebra erzeugen, bestimmen im endlichen Fall eine Tensorproduktstruktur bis auf lokale Basiswechsel und Umbenennungen. Bei nichttrivialem Zentrum können stattdessen Sektoren übrigbleiben. Die Auswahl der privilegierten Unteralgebren aus den Wechselwirkungen ist der eigentliche inverse Schritt. https://arxiv.org/abs/quant-ph/0308043Zanardi, Li","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Teilsysteme aus Beziehungen erkennen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11340,"byte_start":9871,"id":"section:43a9fb694525dcbd10e6","kind":"section","labels":[],"line_end":119,"line_start":109,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"S08 untersucht einen neutralen Sektor aus 70 Materiemasken und Schleifenfluss, insgesamt 1190 Zuständen. In einer festgehaltenen lokalen Operatorliste wird über der Generator rekonstruiert. Nach Entfernen trivialer Identitätsrichtungen reproduziert der Grundzustand die Koeffizienten [formula in source] , [formula in source] , [formula in source] und [formula in source] . Ein zusätzlicher angeregter Zustand verbessert","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was das Zustandsgate am Rotor/CAR-Ring prüft","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":85,"byte_start":0,"id":"section:7a17747ae3824da3a1b7","kind":"chapter","labels":["ch:physik"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Raumzeit, Materie und Gravitation aus demselben Ursprung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1976,"byte_start":85,"id":"section:7f75285733b686226cc3","kind":"section","labels":[],"line_end":30,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Ein markierter [formula in source] -Block trägt die hermitesche Matrix Ihre Determinante ist exakt Die Eigenwerte sind [formula in source] . Deshalb entspricht [formula in source] dem Zukunftskegel [formula in source] . Die Kongruenz [formula in source] mit [formula in source] erhält die Determinante und den positiven Kegel.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Lorentzkegel: eine echte, aber begrenzte Brücke","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3724,"byte_start":1976,"id":"section:ed52f07439ea4004bcc4","kind":"section","labels":[],"line_end":47,"line_start":31,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"S03 formuliert eine nützliche bedingte Brücke. Angenommen, derselbe Prozess liefert einen lokalen kohärenten Zweikomponentensektor mit inverser Zweipunktfunktion Dann folgt Für invertierbares [formula in source] ist dies eine Lorentzform. Jetzt wäre der Kegel aus einem tatsächlichen Propagator gewonnen. Vorausgesetzt sind jedoch ein sinnvoller Impulsraum, ein kontrollierter lokaler Grenzprozess, ein kohärenter Pol un","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der präzise nächste Schritt: den Kegel aus der Ausbreitung gewinnen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4823,"byte_start":3724,"id":"section:19a99dd1ce9ba07a1c68","kind":"section","labels":[],"line_end":58,"line_start":48,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Eine mögliche Materieanregung muss stabil oder kontrolliert propagierend sein. Man benötigt ihr Spektrum, ihre Ladungen, chirale Ausbreitung, erlaubte Vertizes und das Verschwinden unerwünschter Spiegelpartner. Eine vorkommende Darstellung allein erfüllt das nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Materie ist mehr als eine Ladungstabelle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5811,"byte_start":4823,"id":"section:2fdb32ba1abae907040a","kind":"section","labels":[],"line_end":67,"line_start":59,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Eine Algebra mit Darstellung und geeignetem Diracoperator kann Geometrie kodieren. Beispielsweise macht die Distanzformel sichtbar, warum nicht nur Eigenwerte, sondern die Relation zwischen [formula in source] und den Observablen zählt. Connes' kommutativer Rekonstruktionssatz benötigt starke Spektralaxiome und liefert eine kompakte glatte Riemannsche Mannigfaltigkeit. 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Erfolg ist ein ausführbarer Quellenvertrag; Scheitern ist eine noch frei wählbare Regel, die das Ergebnis verändert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein priorisiertes, entscheidbares Anschlussprogramm","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12925,"byte_start":11778,"id":"section:b143c5f15479323b8a4b","kind":"section","labels":[],"line_end":83,"line_start":77,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/10_ausblick.tex","status_markers_as_written":[],"summary_excerpt":"Der Kandidat, auf den die Dokumente gemeinsam zulaufen Es gibt eine phasentreue Kompositionsregel mit positivem Zustandsfunktional, deren endliche Auslesungen die markierte TFPT-Struktur tragen. Aus ihren gekoppelten Anregungen und Aufzeichnungen entsteht ein kontrollierter gemeinsamer Grenzprozess. Erst dieser Grenzprozess liefert Raumzeit, chirale Materie, Wechselwirkungen und gegebenenfalls Gravitation. Die erste ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die präziseste gemeinsame Hypothese","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4033,"byte_start":0,"id":"section:f6da761ff0ade4f28ed9","kind":"chapter","labels":["app:corrections"],"line_end":28,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"L46mmL77mmL27mm Frühere Formulierung& Konsolidierte Aussage& Herkunft\\\\ Aus zwei Zahlen folgt der ganze Aufbau.&P1/P2 enthalten Orientierung, Positivität, Trägerart und Markierungen. Ihre Konsequenzen sind von ihrer Auswahl verschieden.&S09; S05/S06\\\\ Die Kontextregel ist symmetrieerzwungen.& [formula in source] ist eine konkrete gleichgewichtete Realisierung; die kovariante Familie [formula in source] bleibt ein Geg","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Korrekturregister und ergänzende Details","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5908,"byte_start":4033,"id":"section:6962d6b040922271b3ff","kind":"section","labels":[],"line_end":37,"line_start":29,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"S09 berichtet für ein früheres Majoranamodell zehn zugängliche und sechs verborgene reelle Richtungen, entsprechend einer [formula in source] -Zerlegung auf Fockebene. Verschränkung allein macht einen verborgenen Zustand nicht am Rand lesbar; eine geeignete Kopplung oder erweiterte Messung ist nötig. Ein dort gebauter Ereigniskanal übertrug Besetzung, besaß aber weiterhin eine nichttriviale Fixalgebra. Übertragung un","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Frühere Nebenstränge, die im Gesamtbild erhalten bleiben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10041,"byte_start":5908,"id":"section:a106eb8b337e4ba7c27f","kind":"chapter","labels":[],"line_end":74,"line_start":38,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"L34mmL116mm Begriff& Bedeutung in diesem Dokument\\\\ Adjungierte&Die Darstellung einer Lie-Algebra auf ihren eigenen Generatoren durch die Klammer; nicht automatisch der gesamte Raum physischer Zustände.\\\\ Adjunktion [formula in source] &Komplex konjugierte Transposition beziehungsweise die passende Operatoradjunktion. Nicht dasselbe Wort wie adjungierte Darstellung.\\\\ Algebra&Ein Raum von Objekten mit Regeln für Addi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Begriffe in einfachen Worten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10087,"byte_start":10041,"id":"section:c0ef255740f9a6d33eda","kind":"chapter","labels":[],"line_end":75,"line_start":75,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Quellen, Abdeckung und Reproduktion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10437,"byte_start":10087,"id":"section:dc396e4ac3e45d09a2bc","kind":"section","labels":[],"line_end":79,"line_start":76,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Die Quellenkürzel S01 bis S11 gelten durchgängig für dieses Buch und sind von den jeweils eigenen Kürzeln der Anhänge zu unterscheiden. Die vollständigen Originalpfade und SHA-256-Werte stehen im beiliegenden Manifest. Hier werden die Dateinamen und inhaltlichen Rollen aufgeführt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die elf Eingabedokumente","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":12676,"byte_start":10437,"id":"section:3004d5562bd81280e2c4","kind":"section","labels":[],"line_end":96,"line_start":80,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Der eigenständige Prüfer importiert keinen Code des ursprünglichen TFPT-Repositoriums. Die Standard-Zwei-Qubit-Kontexte wurden aus den üblichen Pauli-Matrizen rekonstruiert. Das kontrolliert die endlichen im Text angegebenen Beziehungen, ist aber kein erneuter phasentreuer Import des nativen Gauß- [formula in source] -Adapters.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was neu geprüft wurde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13823,"byte_start":12676,"id":"section:e0f3aaac71e429fcc69b","kind":"section","labels":[],"line_end":108,"line_start":97,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"L16mmL41mmY Quelle& Berichtete Prüfung& Reichweite\\\\ S09&11214 Bedingungen pro Modus, elf Negativvarianten&Ursprungsaudits und Zahlenprüfungen; kein vollständiger Lean-/RH-Neubau.\\\\ S07&325 + 147 Bedingungen, 19 Tests&Inversion und Follow-ups; mehrere spätere Minimalitätskorrekturen erforderlich.\\\\ S06&86 eigene Bedingungen sowie ausgewählte Originalreplays&45-/30-Quotienten, Uhr und Herkunftskontrollen; begrenzte Ke","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie die Quellen ihre eigenen Prüfungen beschreiben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":14798,"byte_start":13823,"id":"section:d6a19534efe2d25a68fa","kind":"section","labels":[],"line_end":113,"line_start":109,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Das Paket enthält die vollständige LaTeX-Quelle, Kapiteldateien, Vektordiagramme, den eigenständigen Prüfer, die Ergebnisdatei und das Eingabemanifest. Mit einer LaTeX-Installation einschließlich LuaLaTeX, TikZ und den verwendeten Standardpaketen lässt sich das Buch durch zwei Läufe von lualatex main.tex im Quellverzeichnis bauen. Für die endlichen Gegenrechnungen werden Python, NumPy, SymPy, mpmath und Matplotlib be","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproduktionspaket dieser Synthese","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18166,"byte_start":14798,"id":"section:d8cf0986bf9638ebe851","kind":"section","labels":[],"line_end":135,"line_start":114,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Die folgenden Quellen wurden zur fachlichen Einordnung beziehungsweise für den datierten Konstantenvergleich aufgerufen. Sie bestätigen die allgemeinen Werkzeuge, nicht die physikalische Richtigkeit von TFPT. Die spezifischen langen Herleitungen dieses Buches beruhen auf den Anhängen und den ausgeschriebenen Gegenrechnungen. F. A. Pollock et al.: Non-Markovian quantum processes: complete framework and efficient chara","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Externe Primärliteratur und Referenzdaten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18523,"byte_start":18166,"id":"section:140dd5ce5af53d86c7de","kind":"section","labels":[],"line_end":137,"line_start":136,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Die Anhänge wurden unverändert gelesen; ihre tatsächlichen Dateiinhalte sind durch SHA-256 dokumentiert. Dieses Buch aktualisiert keinen ursprünglichen Theorievertrag und keinen Abschlussmarker. Es liefert eine neue, zusammenhängende und prüfbare Darstellung mit ausdrücklich abgegrenzten eigenen Fortsetzungen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Abschluss der Dokumentation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":968,"byte_start":0,"id":"section:50968a8a25060bbb54ca","kind":"chapter","labels":["ch:shadow-arithmetic"],"line_end":8,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Was uns ein Schatten verraten kann Wenn wir nur den Schatten eines Rades sehen, erkennen wir vielleicht einen Kreis. Erst wenn wir das Rad drehen, belasten und mit einem zweiten Rad verbinden, erkennen wir seine Achse, seine Zähne und seine Übersetzung. Genau so lesen wir hier Primzahlen, Quanteneffekte und Raumzeit: als verschiedene Antworten, die eine mögliche gemeinsame Struktur gleichzeitig erklären müsste.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Primzahlen, RH und die Musik hinter den Schatten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":2819,"byte_start":968,"id":"section:6ebd23f6c737fb0bd01d","kind":"section","labels":["eq:primon-partition"],"line_end":25,"line_start":9,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Jede natürliche Zahl [formula in source] zerfällt eindeutig in Primfaktoren: Die erste Gleichung beschreibt ein Zusammensetzen durch Multiplikation; die zweite übersetzt dieses Zusammensetzen in Addition. Zum Beispiel ist [formula in source] , also [formula in source] . Die Primzahlen sind die unabhängigen Bausteine dieses multiplikativen Systems. Das ist ein Satz über natürliche Zahlen. Es ist noch kein Satz darüber","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"In welchem Sinn Primzahlen Bausteine sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":4018,"byte_start":2819,"id":"section:74bb553cd69b234e5ccb","kind":"subsection","labels":[],"line_end":36,"line_start":26,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Warum gerade [formula in source] ? Aus [formula in source] allein folgt das noch nicht: Man darf jeder Primzahl zunächst einen beliebigen Wert [formula in source] geben. Eine zusätzliche Ordnungsregel schließt die Lücke. Ist [formula in source] monoton in der natürlichen Zahl [formula in source] , so gilt notwendig Der Beweis ist kurz. Setze [formula in source] . Aus [formula in source] folgen [formula in source] Div","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine bedingte Auswahlregel für die logarithmische Energie","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":7179,"byte_start":4018,"id":"section:0ddccc22391329361ca3","kind":"section","labels":["eq:prime-trace"],"line_end":64,"line_start":37,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die häufig verkürzte Aussage Primzahlen tauchen als Quantenenergien auf umfasst verschiedene Sachverhalte. Beim klassischen Zeta–Quantenchaos-Vergleich entsprechen Nullstellenhöhen den Energien eines gesuchten Spektrums. Die Primzahlen spielen auf der anderen Seite die Rolle primitiver periodischer Bahnen; Primzahlpotenzen sind deren Wiederholungen. Eine Bahn wird einmal durchlaufen, zweimal, dreimal. Ihr logarithmis","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was Primzahlen mit Quantenchaos verbindet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":10149,"byte_start":7179,"id":"section:5cf0e7678c5c8e4c7f7b","kind":"section","labels":[],"line_end":81,"line_start":65,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die Unterlagen und der zusätzlich eingesehene Forschungsbestand ergeben keine abgeschlossene RH-Lösung. Sie ergeben jedoch eine ungewöhnlich präzise Landkarte aus positiven Bausteinen und bereits ausgeschlossenen Abkürzungen. Die folgende Verdichtung ordnet die inhaltlichen Familien; sie behauptet keine erneute Prüfung jedes Katalogeintrags.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was unser RH-Zweig tatsächlich beigetragen hat","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11189,"byte_start":10149,"id":"section:cea61e7b26dca88ab9e4","kind":"subsection","labels":[],"line_end":96,"line_start":82,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die ersten sechs Werte sind [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] und [formula in source] . Daraus folgt für [formula in source] Hier ist der Primzahlbezug wirklich vorhanden. Die Selbstdualität des Gitters schließt die Poisson-Transformation auf dasselbe Gitter. Poisson-Summation gilt auch für nichtselbstduale Gitter und verbindet dann Gitter und ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der genaue Ertrag der [formula in source] -Schalen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":12659,"byte_start":11189,"id":"section:f135d5fcbd13f9a62182","kind":"subsection","labels":[],"line_end":108,"line_start":97,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die entscheidende arithmetische Form enthält eine Differenz: vereinfacht [formula in source] . Zwei positive Matrizen können eine indefinite Differenz besitzen; schon [formula in source] hat die Eigenwerte [formula in source] und [formula in source] . Entsprechend löst ein beliebiger positiver Born- oder Gramkern die signierte Aufgabe noch nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die fehlende Positivität so hartnäckig ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14262,"byte_start":12659,"id":"section:2905374120a6441d317f","kind":"subsection","labels":[],"line_end":115,"line_start":109,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Der Jensen/Coxeter-Test r618 findet eine starre [formula in source] -Struktur auf der [formula in source] -Seite, während die verglichenen Jensen-Polynome mit ihrem Index variieren. Die gewählte Identifikation scheitert. Der Selberg-Kontakttest r638 besitzt im untersuchten Fall weiterhin einen negativen kleinsten Eigenwert von ungefähr [formula in source] ; eine Quadratvervollständigung hat die falsche signierte Form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was die negativen Routen konkret lehren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15958,"byte_start":14262,"id":"section:18c56d9c9f07fe5c2b63","kind":"section","labels":[],"line_end":126,"line_start":116,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die vorhandene freie fermionische Naht hat bei fester Größe eine endliche Zustandssumme. Das Primonmodell verlangt eine unbegrenzte Primfamilie und andere Besetzungsdaten. Schon für [formula in source] gilt [formula in source] und [formula in source] : Der Pol bei [formula in source] entsteht erst in der unendlichen Familie. Eine endliche Demonstration kann ihn nicht besitzen. Der vorhandene Nahtvergleich findet ents","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Naht braucht mehr als ein paar zusätzliche Takte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16501,"byte_start":15958,"id":"section:a38de49f944db999f39f","kind":"section","labels":[],"line_end":129,"line_start":127,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Wei und Mitautoren verbinden in zwei gezielt konstruierten Quantensystemen Nullstellen mit dynamischen Phasenübergängen. Berichtet werden ein Fünf-Qubit-NMR-Prinzipversuch und weitergehende numerische Untersuchungen. Die verwendeten Hamiltonoperatoren und Zustandsgewichte sind so gewählt, dass sie Zeta-Daten kodieren. Das macht den Zusammenhang experimentell bearbeitbar; eine Ableitung dieser Wahl aus TFPT oder ein R","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die neue Quantenphasen-Arbeit von 2026","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":18843,"byte_start":16501,"id":"section:47166308b98f30b192d4","kind":"subsection","labels":["eq:eta-readout"],"line_end":150,"line_start":130,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Unabhängig vom vollständigen Ressourcenbeweis dieser Arbeit untersuchen wir den folgenden einfachen thermischen Eta-Auslesekanal: Er entsteht durch einen Gibbszustand für [formula in source] und eine diagonal ausgelesene Paritätsphase. Bei festem [formula in source] und [formula in source] konvergiert der Zähler gegen [formula in source] , während [formula in source] Also geht das Rohsignal [formula in source] an jed","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eigene Anschlussrechnung: Ein verschwindendes Signal ist mehrdeutig","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":541,"byte_start":0,"id":"section:e46c385b1925ee3cc617","kind":"chapter","labels":["ch:shadow-quantum"],"line_end":6,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Nicht nur die Anzahl der Kugeln zählt Zwei Kästen können dieselben möglichen Messergebnisse enthalten und doch verschieden reagieren, wenn wir zuerst an einer anderen Stelle messen oder zwei Teile zusammenführen. Die Quantenphänomene sagen uns deshalb vor allem etwas über die Regeln des Zusammensetzens, über relative Phasen und über erlaubte Eingriffe. Genau diese Daten verliert ein einfacher Schatten leicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was Quantenphänomene über den verborgenen Aufbau sagen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1925,"byte_start":541,"id":"section:d95ab565c8eb08940770","kind":"section","labels":[],"line_end":21,"line_start":7,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Für zwei Alternativen mit Amplituden [formula in source] und [formula in source] lautet die Born-Regel [formula in source] Der letzte Term kann verstärken oder auslöschen. Wer ausschließlich die beiden Einzelwahrscheinlichkeiten aufbewahrt, kann ihn nicht rekonstruieren. Das erklärt im Kleinen, warum die behaltenen Register und Echoexperimente der früheren Kapitel mehr verraten als der erste sichtbare Markovschritt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Interferenz verlangt eine Information vor den Wahrscheinlichkeiten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4273,"byte_start":1925,"id":"section:6c92baecb0e6fcd56bb5","kind":"section","labels":[],"line_end":40,"line_start":22,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Die 15 Zwei-Qubit-Pauli-Kontexte der Synthese enthalten das folgende Mermin–Peres-Quadrat. Hier bedeutet [formula in source] und entsprechend für die anderen Einträge: Jede Zeile und jede Spalte ist gemeinsam messbar. Alle Zeilenprodukte sind positiv, aber das letzte Spaltenprodukt ist negativ. Diese sechs Kontexte gehören zum bereits verwendeten Pauli-System.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der vorhandene Baukasten enthält bereits Kontextualität","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5718,"byte_start":4273,"id":"section:80939f85a867f4930719","kind":"section","labels":[],"line_end":52,"line_start":41,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Für zwei räumlich getrennte Messstellen hat die CHSH-Kombination [formula in source] in einem lokalen Modell mit unabhängiger Wahl der Einstellungen die Grenze [formula in source] . Quantenmechanik erreicht [formula in source] . Mit [formula in source] , [formula in source] und [formula in source] ist der zugehörige Operator [formula in source] ; seine Eigenwerte sind [formula in source] . Beides wurde hier exakt nac","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verschränkung legt die Zusammensetzung fest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6899,"byte_start":5718,"id":"section:feaaee9d3eb0c7cb023b","kind":"section","labels":[],"line_end":68,"line_start":53,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Wähle bei festgehaltenen Labor-Teilsystemen [formula in source] Beide Hamiltonoperatoren haben exakt die Energien [formula in source] . Der Grundzustand von [formula in source] ist ein Produktzustand, der von [formula in source] ein Bell-Zustand. Die Reinheit [formula in source] eines lokalen Teils beträgt entsprechend 1 beziehungsweise [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gleiche Energien können verschiedene Welten beschreiben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8198,"byte_start":6899,"id":"section:87c2bc752d179c85412f","kind":"section","labels":[],"line_end":75,"line_start":69,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Die komplexe Vierdimensionalität ist für den bestehenden Pauli-/Spinorbaukasten passend. Eine direkte Ableitung der komplexen Zahlen aus einem einzelnen Quantenphänomen wäre trotzdem zu stark. Renou und Mitautoren untersuchen Quantennetzwerke, in denen die übliche reale und komplexe Theorie unter einer bestimmten Unabhängigkeits- und Kompositionsannahme verschiedene Vorhersagen machen. F10","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was komplexe Zahlen verraten und was offenbleibt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9556,"byte_start":8198,"id":"section:e55a82da55726a9b9b45","kind":"section","labels":[],"line_end":81,"line_start":76,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Die bisherigen Registerbeispiele erklären, wie ein global kohärenter Ablauf nach eingeschränktem Zugriff wie ein irreversibler Prozess aussehen kann. Sie liefern noch keine eindeutige Lösung des Messproblems: Insbesondere folgt aus einer diagonalen reduzierten Dichtematrix allein keine Auswahl eines einzelnen Ereignisses. Eine zusätzliche Kollapsdynamik müsste messbare Abweichungen angeben; eine unitäre Beschreibung ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Messung, Zeitpfeil und Statistik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":900,"byte_start":0,"id":"section:3ec1d3980a525cef8e0f","kind":"chapter","labels":["ch:shadow-dimension"],"line_end":8,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"Dimension ist die Antwort auf eine Frage Eine Ameise auf einer dünnen Schnur kann entlang einer Richtung laufen. Auf einem Blatt kann sie außerdem ausweichen. In einem Zimmer kann sie auch über ein Hindernis hinweg. Eine Dimension zählt solche unabhängigen Möglichkeiten. Die Zahl der inneren Zustandskomponenten oder der Knöpfe eines Geräts ist etwas anderes.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Drei Raumrichtungen und eine Zeit: Welche Bedingungen bleiben?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2245,"byte_start":900,"id":"section:40f148ca46a48b0f3636","kind":"section","labels":[],"line_end":23,"line_start":9,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"Ein traceloses hermitesches [formula in source] -Objekt hat genau drei reelle Komponenten: [formula in source] Ergänzt man [formula in source] , ergibt die Determinante [formula in source] Der positive Kegel erfüllt [formula in source] . Das ist die präzise Lorentz-Brücke aus dem Ursprungsteil. Sie zeigt eine passende lokale algebraische Form. Noch fehlen ihre Interpretation als Ereignisse, die Verklebung zu einer Ra","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Drei unterschiedliche Hinweise führen zur Zahl drei","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4040,"byte_start":2245,"id":"section:2b64e66ef8045fac34cb","kind":"section","labels":[],"line_end":44,"line_start":24,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"Für einen Graph-Laplaceoperator [formula in source] definieren wir die mittlere Rückkehrfunktion und eine skalenabhängige Dimension durch Auf einem großen regelmäßigen dreidimensionalen Gitter entsteht zwischen der Gitter- und der endlichen Systemskala ein Bereich mit [formula in source] , also [formula in source] . Bei einem endlichen zusammenhängenden Graphen geht [formula in source] sowohl für sehr kleine als auch","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine neue Gegenprobe am Clebsch-Vorschlag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4989,"byte_start":4040,"id":"section:031983a3845cc391c762","kind":"section","labels":[],"line_end":49,"line_start":45,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"In einer gewöhnlichen hyperbolischen Wellengleichung werden lokale Anfangsdaten auf einer räumlichen Fläche vorgegeben und entlang einer ausgezeichneten Zeitrichtung entwickelt. Mehrere Zeitkoordinaten verändern das Anfangswertproblem grundlegend. Unter zusätzlichen nichtlokalen Beschränkungen existieren dennoch wohldefinierte Mehrzeit-Probleme; ein pauschaler Unmöglichkeitssatz wäre falsch. F14","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine Zeitrichtung ist mehr als ein weiterer Zahlenplatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6082,"byte_start":4989,"id":"section:010c6c0c21df488b3ecc","kind":"section","labels":[],"line_end":61,"line_start":50,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"Ein elementares mechanisches Beispiel illustriert die Rolle von Constraints. Nimmt man in [formula in source] Raumdimensionen eine Newtonsche Punktkraft mit Gaußgesetz an, lautet das effektive Radialpotential [formula in source] An einer Kreisbahn ergibt sich [formula in source] Unter diesen Voraussetzungen sind solche Kreisbahnen bei [formula in source] stabil, bei [formula in source] instabil und bei [formula in so","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was Stabilität zusätzlich einschränkt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":397,"byte_start":0,"id":"section:81e7b80422159a3d6237","kind":"chapter","labels":["ch:shadow-open"],"line_end":4,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Offene Physik ist kein freier Platz, in den jede neue Idee hineinpasst. Sie ist oft durch viele bekannte Eigenschaften eng begrenzt. Der nützliche Schritt lautet deshalb: Welcher Teil des Phänomens ist beobachtet, welcher Mechanismus fehlt, und welche Antwort müsste unser Modell zusätzlich liefern?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Schwer verstandene Phänomene als zusätzliche Prüfsteine","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1423,"byte_start":397,"id":"section:9760a15c3c83110e1ace","kind":"section","labels":[],"line_end":9,"line_start":5,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Gravitationslinsen und die Verteilung sichtbarer Materie in kollidierenden Haufen liefern eine wichtige Beobachtung: Der aus der Gravitation erschlossene Beitrag muss nicht dem heißen sichtbaren Gas folgen. Die Bullet-Cluster-Analyse ist ein prominentes Beispiel. Sie identifiziert damit noch kein bestimmtes mikroskopisches Teilchen. Zusammen mit anderen kosmologischen Daten ist sie eine starke Anforderung an jede Erk","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dunkle Materie: unsichtbar heißt nicht frei wählbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2590,"byte_start":1423,"id":"section:e332cf5dbd4a63dca8f3","kind":"section","labels":[],"line_end":16,"line_start":10,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Die beschleunigte kosmische Expansion verlangt eine konsistente Erklärung im Gesamtmodell. Für TFPT ist besonders schwierig, eine passende effektive Vakuumwirkung zu erhalten, ohne sie bei jedem neuen Beitrag nachzujustieren. Der Mechanismus müsste seine Größe und Stabilität gegenüber Korrekturen erklären.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dunkle Energie: ein kleiner Rest mit großen Folgen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3656,"byte_start":2590,"id":"section:64008f02eb80b04fb713","kind":"section","labels":[],"line_end":21,"line_start":17,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Die Schwarzlochfrage verbindet Quanteninformation, Gravitation und die Wahl zugänglicher Teilsysteme besonders eng. In bestimmten berechenbaren Modellen verändern Quanteneffekte die extremale Fläche und damit die Zuordnung rekonstruierbarer Information. Die verallgemeinerte Entropie enthält einen Flächenbeitrag und einen Quantenfeldbeitrag. Das ist erheblicher theoretischer Fortschritt in diesen Modellen, aber noch k","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Schwarze Löcher: Information kann die Aufteilung selbst betreffen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4418,"byte_start":3656,"id":"section:2ba806852188a098d0eb","kind":"section","labels":[],"line_end":26,"line_start":22,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Äquivalenztests wie MICROSCOPE prüfen die Universalität des freien Falls für unterschiedliche Materialien mit hoher Genauigkeit. Eine neue Quelle für Raumzeit muss daher erklären, warum verschiedene innere Zusammensetzungen auf dieselbe effektive Geometrie reagieren. F18","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gravitation muss sehr verschiedene Inhalte gleich behandeln","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6966,"byte_start":4418,"id":"section:32928ef332494f994e74","kind":"section","labels":[],"line_end":43,"line_start":27,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"L32mmL56mmL60mm Thema& Was den Ansatz einschränkt& Was eine Erklärung liefern müsste\\\\ Zeitpfeil&Beständige Aufzeichnungen und irreversible Makroprozesse bei oft reversiblen Grundgleichungen.&Zustandsauswahl, Anfangskorrelationen, Zugriff und Entropiefluss; keine bloße Benennung eines inneren Parameters als Zeit.\\\\ Messproblem&Interferenz und stabile Messergebnisse müssen zusammen beschrieben werden.&Ein vollständige","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Weitere offene Stellen mit unterschiedlicher Beweiskraft","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":562,"byte_start":0,"id":"section:6214d3dd82ffb3b0a47d","kind":"chapter","labels":["ch:shadow-synthesis"],"line_end":4,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Die zusammengetragenen Schatten sprechen am stärksten für eine Struktur von Zusammensetzungen und gemeinsamen Antworten. Arithmetik verlangt eindeutig kombinierbare primitive Faktoren. Quantenphänomene verlangen Phasen, Kontexte und eine besondere Zusammensetzung von Teilsystemen. Raumzeit verlangt eine skalenstabile Ordnung von Nachbarschaften, Signalwegen und Anfangsdaten. Keine dieser Forderungen wird durch die Za","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein engeres Bild und ein neues berechenbares Puzzleteil","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2012,"byte_start":562,"id":"section:10dcbf5c5d4510f962a6","kind":"section","labels":[],"line_end":17,"line_start":5,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Die bildhafte Aussage Alles ist aus Primzahlen gebaut lässt sich zu einer brauchbareren Hypothese präzisieren: Ein möglicher gemeinsamer Ursprung besitzt elementare, zusammensetzbare Operationen. In einem kommutativen arithmetischen Schatten erscheinen primitive Faktoren. Vor dieser Auslesung bleiben zusätzliche Phasen, Kontexte und Aufzeichnungen erhalten. Räumliche Nachbarschaft und Zeitordnung müssten aus den erla","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine engere Arbeitshypothese","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":4522,"byte_start":2012,"id":"section:33eaebf9801f6a125b42","kind":"section","labels":["eq:arithmetic-projective"],"line_end":58,"line_start":18,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Die folgenden Formeln sind eine neue Anschlusskonstruktion für dieses Buch. Ihre Zutaten sind Standardoperatoren; sie beanspruchen keine neue allgemeine mathematische Entdeckung. Sie zeigen jedoch exakt, dass ein gemeinsamer arithmetischer Endpunkt unterschiedliche kohärente Geschichten besitzen kann.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein konstruktiver Versuch: gleiche Zahl, verschiedene Phasen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5399,"byte_start":4522,"id":"section:c9a01f4df1faa0cc333f","kind":"subsection","labels":[],"line_end":66,"line_start":59,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Ein Kontrollqubit speichert kohärent, welcher der beiden Wege durchlaufen wurde. Setze [formula in source] und [formula in source] . Nach einer Hadamard-Auslesung des Kontrollqubits gelten [formula in source] Ohne die lokalen [formula in source] -Markierungen wäre [formula in source] und damit [formula in source] . Die neue Rechnung kontrolliert dies im Zahlfenster [formula in source] exakt. Die benutzten Wege ab [fo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine vollständig bestimmte Vorhersage im Modell","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6734,"byte_start":5399,"id":"section:578a04370676bce3bcbe","kind":"subsection","labels":[],"line_end":73,"line_start":67,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Gelöst ist eine kleine Kompatibilitätsfrage: Unbegrenzte arithmetische Zusammensetzung und ein endlicher lokaler Quantenbaukasten lassen sich in einem expliziten gemeinsamen Modell verbinden. Der rein arithmetische Schatten kann kommutativ sein, während kohärent zugängliche Wegrelationen eine nichttriviale Phase behalten. Das passt genau zum Motiv der vorherigen Echoexperimente.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was damit gelöst ist und was nicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8700,"byte_start":6734,"id":"section:deb128b3434891f1c779","kind":"section","labels":[],"line_end":94,"line_start":74,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Man könnte einen arithmetischen Raum, ein Quantensystem und ein geometrisches Modell einfach nebeneinanderstellen: [formula in source] Bei Produktzustand und unabhängig wirkenden Operationen passen dann vielleicht alle Einzelstatistiken. Der gemeinsame Ursprung wäre dadurch nicht erklärt. Nötig sind gemeinsame Relationen und überprüfbare Antworten auf gemischte Eingriffe. Die oben konstruierte Wegphase ist ein kleine","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum getrennte passende Modelle noch keine gemeinsame Quelle sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10697,"byte_start":8700,"id":"section:70ef6e766b74fc1ccaad","kind":"section","labels":[],"line_end":108,"line_start":95,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"L37mmL60mmL51mm Gewonnene Präzisierung& Konkretes Ergebnis& Nächste fehlende Bedingung\\\\ Logarithmische Skala&Multiplikative Additivität plus Monotonie erzwingen [formula in source] .&Native Begründung der Ordnung und Energieskala.\\\\ Unbegrenzte Primfamilie&Endlich viele additive Grundtakte tragen nicht alle [formula in source] .&Eine passende wachsende Familie oder reichere Dynamik.\\\\ Arithmetik und Phase&Zwei Multi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Welche Puzzleteile jetzt enger gefasst sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":82,"byte_start":0,"id":"section:aea4fad0a4366f1857fe","kind":"chapter","labels":["app:shadow-sources"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Erweiterung: Quellen und genaue Prüfgrenzen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4118,"byte_start":82,"id":"section:5627f4ea3d4943cc065d","kind":"section","labels":[],"line_end":29,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":["relation:c8dfb0dc6b9ecad921cf"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"Die Erweiterung wurde am 14. September 2026 gegen verfügbare Originalabschnitte im lokalen Repository tfpt-theoryv4 abgeglichen. Der gelesene Git-Stand war 66b91e40e245569f06ab440ead80f446c9be0ee5. Dies identifiziert den Checkout; es behauptet keinen frischen vollständigen Beweis- oder Testlauf. Die tatsächlich verwendeten Dateiinhalte sind zusätzlich mit SHA-256 im Paket erfasst, auch soweit der Arbeitsbaum von Git ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zusätzlicher Einblick in den RH-Forschungsbestand","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6033,"byte_start":4118,"id":"section:8865be8e7d1edfc6cb89","kind":"section","labels":[],"line_end":38,"line_start":30,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-paired-release-20260914/source-v1.1/TFPT_Universalraum_LaTeX_2026-09-14/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"Der separate Prüfer verify_shadows.py importiert keinen ursprünglichen TFPT- oder RH-Code und keine Nullstellentabellen. 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Im festgelegten Modell ist ein eindeutiger energetisch günstigster Zustand abgesichert. 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Die Zerlegung ist innere Darstellungstheorie, keine neue Teilchenzählung. Sie wurde durch Clifford-Gram und Weyl-Multiplizitäten abgesichert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der bilineare Rest ist vollständig zerlegt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12104,"byte_start":10900,"id":"section:b17bd2fff7814f03175f","kind":"subsection","labels":["korrekturen-und-reichweite"],"line_end":287,"line_start":259,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Update_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Update_2026-09-15_v1.6.7.tex","status_markers_as_written":[],"summary_excerpt":"Der Clock liegt in Spin(10). Nichtskalare Wirkung widerlegt diese Zugehörigkeit nicht; die gegenteilige Eingabe wird korrigiert. Die zusätzlichen SU(4)- und Spin(10)-Stufen haben im N=3-Sektor die Kommutantdimensionen 2247168 und 1648. Verfügbarkeit ist nicht binär. Volle Gruppe plus alle Besetzungen erzeugt bedingt die volle Sektoralgebra. Ohne gewährte Gruppenoperationen bleibt trotz Besetzungsauslese eine nichtska","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Korrekturen und Reichweite","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13327,"byte_start":12104,"id":"section:c535b3009336440bf84c","kind":"subsection","labels":["fundamentale-auswahlfrage-jetzt-als-konkreter-test"],"line_end":315,"line_start":288,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Update_2026-09-15_v1.6.7"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-singlet-observable-20260915/tmp/pdfs/TFPT_Universalraum_Richtige_Kette_Update_2026-09-15_v1.6.7.tex","status_markers_as_written":[],"summary_excerpt":"Bei gleichem W und denselben Symmetrien ergibt sich für dieselbe Referenz","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Fundamentale Auswahlfrage jetzt als konkreter Test","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1656,"byte_start":0,"id":"section:747a88c25e5fca729990","kind":"frontmatter","labels":[],"line_end":42,"line_start":1,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-source-composition-20260915/pdf-header.tex","status_markers_as_written":["[L]"],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5075,"byte_start":0,"id":"section:3487796eca23ba17f9f1","kind":"frontmatter","labels":[],"line_end":130,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Einfach_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Einfach_2026-09-15_v1.6.9.tex","status_markers_as_written":["[L]"],"summary_excerpt":"unicodehyperref hyphensurl dvipsnames,svgnames,x11namesxcolor ngerman, 10pt, a4paper, ]article Scale=MatchLowercase Ligatures=TeX,Scale=1","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5257,"byte_start":5075,"id":"section:748fd5e94dc4dc71993c","kind":"section","labels":["die-verbindung-hinter-den-schatten---einfach-erkluxe4rt"],"line_end":135,"line_start":131,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Einfach_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Einfach_2026-09-15_v1.6.9.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die Verbindung hinter den Schatten - einfach erklärt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5848,"byte_start":5257,"id":"section:bac8505dd6ebdd31873e","kind":"subsection","labels":["der-wichtigste-neue-punkt"],"line_end":147,"line_start":136,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Einfach_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Einfach_2026-09-15_v1.6.9.tex","status_markers_as_written":[],"summary_excerpt":"Wir haben nicht die ganze Weltformel gefunden. Aber wir können jetzt an zwei kleinen, genau gerechneten Beispielen zeigen, wie eine verborgene Verbindung aus ihrer Reaktion sichtbar wird. Das ist ein konkreter Schritt in die Richtung deiner Schatten-Idee.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der wichtigste neue Punkt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6931,"byte_start":5848,"id":"section:377a861badf64acc315f","kind":"subsection","labels":["stell-dir-eine-kleine-kupplung-vor"],"line_end":171,"line_start":148,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Einfach_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Einfach_2026-09-15_v1.6.9.tex","status_markers_as_written":[],"summary_excerpt":"Der ursprüngliche Mechanismus kann zwei Fermionen in ein Boson umwandeln und wieder zurück. Seine innere Struktur ist sehr festgelegt. Die vielen Einträge bedeuten dabei nicht viele unabhängige Maschinen: Das ursprüngliche Modell benutzt bereits 64 gemeinsame Fermionmoden.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Stell dir eine kleine Kupplung vor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9370,"byte_start":6931,"id":"section:55dd94ecaa7d39ee61ab","kind":"subsection","labels":["was-wir-jetzt-wirklich-herausgerechnet-haben"],"line_end":219,"line_start":172,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Einfach_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Einfach_2026-09-15_v1.6.9.tex","status_markers_as_written":[],"summary_excerpt":"Erstens: Die Reaktion verrät die Verbindung. Im Zwei-Kupplungs-Modell stimmen die ersten drei Energiemomente überein. Das vierte verrät die Überlappung eindeutig - innerhalb dieser festgelegten Modellfamilie.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was wir jetzt wirklich herausgerechnet haben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10685,"byte_start":9370,"id":"section:3086c5f24f372aae1a4c","kind":"subsection","labels":["was-hat-sich-gegenuxfcber-v1.6.8-veruxe4ndert"],"line_end":252,"line_start":220,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Einfach_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Einfach_2026-09-15_v1.6.9.tex","status_markers_as_written":[],"summary_excerpt":"@ > p( - 2 ) * 0.5000 > p( - 2 ) * 0.5000@ Vorher & Jetzt \\\\ „Uns fehlt die gemeinsame Verbindung.`` & Zwei kleine vollständige Vergleiche zeigen, was sie verändert und wie man sie zurückliest. \\\\ Zusätzlicher Einzelmoden-Handgriff im Versuch & Derselbe innere Prozess funktioniert mit dem schon dokumentierten Bosonzahl-Kontrolltyp. \\\\ Aufzeichnung musste die Interferenzgrenze beachten & Ein konkreter Zeiger und sein ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was hat sich gegenüber v1.6.8 verändert?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11740,"byte_start":10685,"id":"section:ca3742bc0a34688470d8","kind":"subsection","labels":["wie-kuxf6nnte-das-gesuchte-gesamtbild-aussehen"],"line_end":280,"line_start":253,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Einfach_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Einfach_2026-09-15_v1.6.9.tex","status_markers_as_written":[],"summary_excerpt":"Eine einzige ursprüngliche Regel legt fest, was gemeinsam benutzt wird und was miteinander wechselwirken kann. Aus derselben Regel und demselben Zustand entstehen dann verschiedene Ansichten:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie könnte das gesuchte Gesamtbild aussehen?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13163,"byte_start":11740,"id":"section:d477611097a23f48f9ab","kind":"subsection","labels":["der-kuxfcrzeste-sinnvolle-nuxe4chste-weg"],"line_end":310,"line_start":281,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Einfach_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Einfach_2026-09-15_v1.6.9.tex","status_markers_as_written":[],"summary_excerpt":"1. Zwei ursprüngliche Teile und ihre Verbindung festnageln. Aus den bereits vorhandenen Quellobjekten muss folgen, welche zwei Teile gemeinsam Ressourcen benutzen und wie stark. Nicht die schöne Zahl auswählen, sondern die vollständige Zuordnung herleiten. Unsere neuen Antwortformeln prüfen sofort, ob sie etwas Bestimmtes vorhersagt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der kürzeste sinnvolle nächste Weg","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4622,"byte_start":0,"id":"section:a75ccc50eaaef00313ba","kind":"frontmatter","labels":[],"line_end":119,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Update_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Update_2026-09-15_v1.6.9.tex","status_markers_as_written":["[L]"],"summary_excerpt":"unicodehyperref hyphensurl dvipsnames,svgnames,x11namesxcolor ngerman, 10pt, a4paper, ]article Scale=MatchLowercase Ligatures=TeX,Scale=1","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4883,"byte_start":4622,"id":"section:144b5c94a2fa42100a14","kind":"section","labels":["tfpt-universalraum-update-v1.6.9"],"line_end":130,"line_start":120,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Update_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Update_2026-09-15_v1.6.9.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"TFPT / Universalraum: Update v1.6.9","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5264,"byte_start":4883,"id":"section:d0ebfb949b7a03fa0f46","kind":"subsection","labels":["was-jetzt-neu-ist"],"line_end":138,"line_start":131,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Update_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Update_2026-09-15_v1.6.9.tex","status_markers_as_written":[],"summary_excerpt":"Die zusätzliche Zusammensetzung kann in zwei kleinen Modellfamilien aus ihrer höheren Antwort zurückberechnet werden. Zugleich wurde der native kleine Eingriffsversuch vereinfacht und der relativistische Feldanschluss bis zu einem konkreten Kinetiktest vorangebracht. Eine vollständige TOE folgt daraus nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was jetzt neu ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6618,"byte_start":5264,"id":"section:1fb1538ed9f032d1a453","kind":"subsubsection","labels":["urspruxfcngliche-quelle-und-globale-wiederholung-sind-verschieden"],"line_end":168,"line_start":139,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Update_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Update_2026-09-15_v1.6.9.tex","status_markers_as_written":[],"summary_excerpt":"W verwendet bereits 64 gemeinsame Fermionmoden; jeder erscheint in 15 der 480 Vertices. Eine Wiederholung des ursprünglichen passiven Clocks erzeugt keine sechs unabhängigen hellen Räume: Der Vereinigungsrang bleibt exakt 60 statt 360. Die alte K4-/C16-Architekturauswahl gilt nur für ihren zusätzlichen Vertrag.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Ursprüngliche Quelle und globale Wiederholung sind verschieden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7935,"byte_start":6618,"id":"section:bb760d0748dcc9df2b80","kind":"subsubsection","labels":["gesamtes-zweiladungsspektrum-gleich---huxf6here-dynamik-verschieden"],"line_end":198,"line_start":169,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Update_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Update_2026-09-15_v1.6.9.tex","status_markers_as_written":[],"summary_excerpt":"Eine andere Familie hat eine gemeinsame Bosonbank und normierte symmetrische Kopplung [formula in source] . Die verteilte Wahl [formula in source] und die kollektive Wahl [formula in source] besitzen dieselben gesamten N=2-Spektren. Im N=3-Sektor gibt es bei L=2 und Energie Δ dagegen 0 beziehungsweise 64 Eigenzustände, für Δ 0 und g≠0. Das ist kein Port-Umbenennungseffekt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Gesamtes Zweiladungsspektrum gleich - höhere Dynamik verschieden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":8932,"byte_start":7935,"id":"section:d2029e26be730496f571","kind":"subsubsection","labels":["einfacherer-eingriff-und-richtiger-recorder"],"line_end":217,"line_start":199,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Update_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Update_2026-09-15_v1.6.9.tex","status_markers_as_written":[],"summary_excerpt":"Der neue Bosonzahlimpuls [formula in source] liegt auf dem gemeinsamen Dreizustandsraum in der dokumentierten Algebra aus X und Nb; der frühere Einzelmodenimpuls Z4 liegt außerhalb. Der extra Modenselektor entfällt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Einfacherer Eingriff und richtiger Recorder","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9968,"byte_start":8932,"id":"section:a711cf98813ab9259c52","kind":"subsubsection","labels":["minimaler-lorentzadapter---aber-der-freie-ansatz-ist-null"],"line_end":237,"line_start":218,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Update_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Update_2026-09-15_v1.6.9.tex","status_markers_as_written":[],"summary_excerpt":"Für den gemischthändigen sechsdimensionalen Träger existiert mit einem Impuls P eine eindeutige lineare Auslese C_P in einen Weylspinor, Rang zwei für P≠0. Ein Einsetzer erfüllt [formula in source] . Zeitartig gibt es einen kovarianten Rückweg; lichtartig braucht dieser eine zusätzliche Referenz.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Minimaler Lorentzadapter - aber der freie Ansatz ist null","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11050,"byte_start":9968,"id":"section:dc8e76b4531e83e9d65d","kind":"subsection","labels":["unveruxe4ndert-offen-und-nuxe4chste-entscheidung"],"line_end":259,"line_start":238,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Update_2026-09-15_v1.6.9"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-source-composition-20260915/tmp/pdfs/TFPT_Universalraum_Quellkomposition_Update_2026-09-15_v1.6.9.tex","status_markers_as_written":[],"summary_excerpt":"Alle T1-T8-Gesamtpflichten bleiben offen. 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=3.5em","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"-1.2cm TFPT — [formula in source] Audit, Cascade Bridge and Bootstrap\\\\[2mm] The seven [formula in source] slices as an audit raster, the old cascade as the same even-integer spine, the M\\\"obius self-consistency loop — and the thirty-two-step celestial/twistor route with the measure chain derived","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over 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This note does not introduce new physics. It builds an audit raster: the claim that every load-bearing TFPT number should appear in at least one [formula in source] branching projection. A number that appears in none is suspect; a number appearing in several independent projections becomes structurally strong. All arithmetic identities below are exact ; the physical readings are audit-level \\ ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The [formula in source] secondary-branching atlas","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10677,"byte_start":8998,"id":"section:2dbb611c3086b4a1b61b","kind":"section","labels":[],"line_end":193,"line_start":171,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/sources/input_5_tfpt_3_e8_audit_bootstrap"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-spin-lift-basics-20260915/sources/input_5_tfpt_3_e8_audit_bootstrap.tex","status_markers_as_written":[],"summary_excerpt":"The strongest current form of the theory is a five-layer compiler:","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The compiler core (where this note sits)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":15622,"byte_start":10677,"id":"section:06d63eae80ded6f77f27","kind":"section","labels":[],"line_end":290,"line_start":194,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/sources/input_5_tfpt_3_e8_audit_bootstrap"],"relation_ids":["relation:97c0ccca3469595b23c6","relation:a7ffe267f99a732fbfb9","relation:af9f65cda121631d3f6c"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-spin-lift-basics-20260915/sources/input_5_tfpt_3_e8_audit_bootstrap.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"The parabolic anchor [formula in source] (splitting type of [formula in source] ) is a miniature compiler. 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Bislang haben wir oft nur das Verhalten dieser Paare angeschaut.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das Bild","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6509,"byte_start":5554,"id":"section:f2d497c409fb36e7fca8","kind":"subsection","labels":["was-dadurch-besser-wird"],"line_end":159,"line_start":141,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Einfach_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Einfach_2026-09-15_v1.6.10.tex","status_markers_as_written":[],"summary_excerpt":"Ohne die Verdrehung bleibt im gewählten Viererzyklus ein ganzer Fermionbereich unbeteiligt. Wie ein Zimmer, das an keine Leitung angeschlossen ist. Unterschiedliche Belegungen dieses Zimmers kosten keine zusätzliche Energie. Deshalb kann das ganze Modell so keinen einzigen eindeutig bevorzugten Grundzustand haben.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was dadurch besser wird","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7245,"byte_start":6509,"id":"section:63a1ad054eb1eaaf710b","kind":"subsection","labels":["und-kann-darin-etwas-wirklich-angeregt-werden"],"line_end":173,"line_start":160,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Einfach_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Einfach_2026-09-15_v1.6.10.tex","status_markers_as_written":[],"summary_excerpt":"Ja, ebenfalls innerhalb eines bewiesenen kleinen Bereichs. Entfernt man ein ursprüngliches Fermion mit einer bestimmten Clock-Phase aus genau diesem Grundzustand, landet fast die gesamte Antwort auf einer einzelnen isolierten Energielinie. Je nach Clock-Phase gibt es zwei verschiedene niedrige Linien. Für den passend aufgelösten Modus sind mehr als 99.992 Prozent des Entnahmespektrums kontrolliert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Und kann darin etwas wirklich angeregt werden?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7673,"byte_start":7245,"id":"section:14b61fb216a636573aff","kind":"subsection","labels":["wo-die-grouxdfe-hoffnung-liegt"],"line_end":182,"line_start":174,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Einfach_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Einfach_2026-09-15_v1.6.10.tex","status_markers_as_written":[],"summary_excerpt":"Vielleicht haben wir nicht eine riesige zusätzliche Maschine übersehen, sondern beim Übergang zu den sichtbaren Paargrößen eine kleine, entscheidende Information weggeworfen. In diesem Test wirkt dasselbe Umlaufvorzeichen auf die Kopplung, die Auswahl des Grundzustands und die Anregungen. Es verbindet also mehrere Baustellen tatsächlich.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wo die große Hoffnung liegt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8291,"byte_start":7673,"id":"section:5fad6c20f4e2391a1b13","kind":"subsection","labels":["wo-die-grenze-liegt"],"line_end":195,"line_start":183,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Einfach_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Einfach_2026-09-15_v1.6.10.tex","status_markers_as_written":[],"summary_excerpt":"Wir haben die vier Stationen und ihre gemeinsame Quellenregel für diesen Test festgelegt. Noch nicht gezeigt ist, dass die ursprüngliche TFPT genau diese Regel erzeugt. Auch die bewiesene Kopplung ist viel kleiner als unser bisheriger Prüfwert. Und vier Stationen sind keine abgeleitete dreidimensionale Welt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wo die Grenze liegt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9551,"byte_start":8291,"id":"section:597ff3e9084bbe159d91","kind":"subsection","labels":["was-die-beiden-neuen-texte-zusuxe4tzlich-kluxe4ren"],"line_end":219,"line_start":196,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Einfach_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Einfach_2026-09-15_v1.6.10.tex","status_markers_as_written":[],"summary_excerpt":"Ihr Vorschlag, das Ganze über alle möglichen Handlungsfolgen und ihre Antworten zu beschreiben, ist sinnvoll: Statt getrennte Schatten zu sammeln, beschreibt man den gemeinsam ausführbaren Prozess. Aber ein vollständiges Buch aller Antworten ist noch keine einfache Regel, die dieses Buch erzeugt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was die beiden neuen Texte zusätzlich klären","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10713,"byte_start":9551,"id":"section:0b4b7b5936fda58fa110","kind":"subsection","labels":["was-jetzt-den-unterschied-machen-wuxfcrde"],"line_end":241,"line_start":220,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Einfach_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Einfach_2026-09-15_v1.6.10.tex","status_markers_as_written":[],"summary_excerpt":"Die Fortsetzung hat hier noch eine einfache Regel gefunden. Wenn linke und rechte Nachbarstation verschieden stark beitragen dürfen, funktioniert auch ein unverdrehtes Gegenmodell. Der Clock allein bestimmt das also nicht. Fordert man aber, dass dieselbe Links-rechts-Spiegelung auch den Paarübergang unverändert lässt, müssen beide Seiten gleich stark beitragen. In dieser kleinen Quellenfamilie bleibt dann ohne freie ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was jetzt den Unterschied machen würde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4623,"byte_start":0,"id":"section:815b7c56398bfa4b858b","kind":"frontmatter","labels":[],"line_end":119,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Update_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Update_2026-09-15_v1.6.10.tex","status_markers_as_written":["[L]"],"summary_excerpt":"unicodehyperref hyphensurl dvipsnames,svgnames,x11namesxcolor ngerman, 10pt, a4paper, ]article Scale=MatchLowercase Ligatures=TeX,Scale=1","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4940,"byte_start":4623,"id":"section:c9ec038ee9497d6128e6","kind":"section","labels":["tfpt-universalraum---update-v1.6.10"],"line_end":131,"line_start":120,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Update_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Update_2026-09-15_v1.6.10.tex","status_markers_as_written":[],"summary_excerpt":"September 2026. Bezug: Hauptfassung v1.6.9 und die neu geprüfte Arbeit „Gemeinsame Quelle``, Fortsetzung 1.2.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TFPT / Universalraum - Update v1.6.10","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5595,"byte_start":4940,"id":"section:6f28b5063205b42ff476","kind":"subsection","labels":["die-neue-verbindung"],"line_end":144,"line_start":132,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Update_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Update_2026-09-15_v1.6.10.tex","status_markers_as_written":[],"summary_excerpt":"TFPT enthält bereits einen fermionischen Vierteldrehungsclock mit [formula in source] . Das neue Quellpaper zeigt gleichzeitig, dass Paarantworten ein solches Vorzeichen verlieren können. Diese beiden Befunde wurden nun an derselben festgelegten Viererquelle mit dem unveränderten inneren Tensor W zusammengeführt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die neue Verbindung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7317,"byte_start":5595,"id":"section:50ca9c323361bdf593b4","kind":"subsection","labels":["was-neu-bewiesen-wurde"],"line_end":182,"line_start":145,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Update_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Update_2026-09-15_v1.6.10.tex","status_markers_as_written":[],"summary_excerpt":"Die periodische Variante besitzt 64 völlig ungekoppelte Fermionmoden; die antiperiodische besitzt keine. Ihre gesamten eingeschränkten bosonischen N=2-Antworten sind dennoch gleich. Ein zusätzlicher Fermion-Eingang macht den Unterschied ladungsneutral sichtbar. Für denselben gemischten Einboson-Einfermion-Eingang unterscheiden sich die Bosonrückkehrwahrscheinlichkeiten erstmals durch [formula in source] . Für [formul","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was neu bewiesen wurde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8001,"byte_start":7317,"id":"section:ddfd78f3f4c7420fe84b","kind":"subsection","labels":["was-nicht-verwechselt-werden-darf"],"line_end":196,"line_start":183,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Update_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Update_2026-09-15_v1.6.10.tex","status_markers_as_written":[],"summary_excerpt":"Der bisherige Prüfpunkt [formula in source] liegt außerhalb beider neuen Bereiche. Der neue N=256-Grundzustand ist nicht der alte N=64-Grundzustand einer einzelnen Bank. Der N=3-Vergleich ist ein Diagnoseexperiment und nicht die Grundzustandsantwort. Die C8-Hebung wird nicht mit dem inneren Perioden-sechs-Clock gleichgesetzt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was nicht verwechselt werden darf","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8732,"byte_start":8001,"id":"section:4130aba54f38215c15b7","kind":"subsection","labels":["zwei-methodische-korrekturen"],"line_end":211,"line_start":197,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Update_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Update_2026-09-15_v1.6.10.tex","status_markers_as_written":[],"summary_excerpt":"Die volle assoziative Erzeugung durch quadratische Cliffordwörter ist nicht volle dynamische Steuerbarkeit. Ein einzelner zusätzlicher quartischer Generator würde unter gewährten quadratischen Kontrollen genügen; seine native Realisierung ist nicht bewiesen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei methodische Korrekturen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10515,"byte_start":8732,"id":"section:a06a64f4c701c6817184","kind":"subsection","labels":["die-beiden-zuletzt-eingegangenen-perspektiven"],"line_end":243,"line_start":212,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Update_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Update_2026-09-15_v1.6.10.tex","status_markers_as_written":[],"summary_excerpt":"Der vollständige positive Prozesskern ist ein tragfähiger Rekonstruktionsrahmen, bestimmt aber seine eigenen Daten und Instrumente nicht. Positivität allein genügt ohne passende Multiplikationsrelationen nicht. Gleicher Grundzustand und gleiche statische Beobachtungen bestimmen zudem keine eindeutigen Anregungsenergien.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die beiden zuletzt eingegangenen Perspektiven","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11723,"byte_start":10515,"id":"section:6057ad46ed5a131fc16a","kind":"subsection","labels":["weitergerechnet-auswahl-durch-gemeinsame-spiegelung"],"line_end":266,"line_start":244,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Update_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Update_2026-09-15_v1.6.10.tex","status_markers_as_written":[],"summary_excerpt":"Clock und Grundzustand wählen die Verdrehung allein nicht: Die reelle Quelle [formula in source] hat ebenfalls keinen freien Fermionbereich und bei genügend kleiner Kopplung einen eindeutigen globalen Grundzustand. Sie besitzt allerdings eine andere Paarmatrix als die fixierte gleichstarke Mischung.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Weitergerechnet: Auswahl durch gemeinsame Spiegelung?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12487,"byte_start":11723,"id":"section:37dd70a2a8819994fde7","kind":"subsection","labels":["priorituxe4t"],"line_end":282,"line_start":267,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Update_2026-09-15_v1.6.10"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/TFPT_Universalraum_Spinlift_Update_2026-09-15_v1.6.10.tex","status_markers_as_written":[],"summary_excerpt":"Zuerst die gemeinsame Spiegelungswirkung der TFPT-Seam auf Fermionorte und Paarübergänge prüfen; daran den zustands- und operatorverträglichen Quellenanschluss entscheiden. Danach den Kopplungsbereich erweitern und dieselbe geladene Antwort in einer Größenfolge untersuchen. Das ist eine kleinere, konkrete Forschungsaufgabe als die Suche nach immer weiteren passenden Zahlen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Priorität","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1657,"byte_start":0,"id":"section:9cb65241c970e3ed6a2e","kind":"frontmatter","labels":[],"line_end":42,"line_start":1,"occurrence":1,"owner_documents":[],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-spin-lift-basics-20260915/tmp/pdfs/header.tex","status_markers_as_written":["[L]"],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2415,"byte_start":0,"id":"section:0cf9d4ac86d877bda3c0","kind":"frontmatter","labels":[],"line_end":71,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-two-bank-transfer-20260915/external/exchange/source/articles__2026-08-30__tfpt_thermodynamic_dynamics_en"],"relation_ids":["relation:290c56ba3f191f683664"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-two-bank-transfer-20260915/external/exchange/source/articles__2026-08-30__tfpt_thermodynamic_dynamics_en.tex","status_markers_as_written":[],"summary_excerpt":"colorlinks=true, linkcolor=blue!55!black, citecolor=blue!55!black, urlcolor=blue!55!black","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Thermodynamic Dynamics for the TFPT Finite-Range\\\\ Master-Hamiltonian Class","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2461,"byte_start":2415,"id":"section:3b8afe4964a445ff9fc8","kind":"section","labels":[],"line_end":73,"line_start":72,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-two-bank-transfer-20260915/external/exchange/source/articles__2026-08-30__tfpt_thermodynamic_dynamics_en"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-two-bank-transfer-20260915/external/exchange/source/articles__2026-08-30__tfpt_thermodynamic_dynamics_en.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"The concrete uniformly local class","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5380,"byte_start":2461,"id":"section:c55d5c0e208b3eaef29d","kind":"subsection","labels":["eq:H","eq:ambient","eq:localdim","eq:quasilocal","tab:terms"],"line_end":154,"line_start":74,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-two-bank-transfer-20260915/external/exchange/source/articles__2026-08-30__tfpt_thermodynamic_dynamics_en"],"relation_ids":["relation:bd678e80e52573d218f4"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-two-bank-transfer-20260915/external/exchange/source/articles__2026-08-30__tfpt_thermodynamic_dynamics_en.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] with graph distance [formula in source] and coordination [formula in source] . For a finite [formula in source] , put [formula in source] One cell contains the four representative physical edge modes, a mirror Fock factor, the two positively oriented outgoing finite-group gauge links, and a four-state seam clock. Thus [formula in source] The DET4 numerical analogue has dimension [formula in so","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ambient tensor-product algebra","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6183,"byte_start":5380,"id":"section:531637056ba3e998a467","kind":"subsection","labels":["eq:constants","eq:kappa"],"line_end":182,"line_start":155,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-two-bank-transfer-20260915/external/exchange/source/articles__2026-08-30__tfpt_thermodynamic_dynamics_en"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-two-bank-transfer-20260915/external/exchange/source/articles__2026-08-30__tfpt_thermodynamic_dynamics_en.tex","status_markers_as_written":[],"summary_excerpt":"Define the finite-range interaction moment [formula in source] There are two assigned electric links, four plaquettes, and four bonds incident on a square-lattice cell. Consequently [formula in source] These bounds are independent of [formula in source] . More generally, bounded degree, finite [formula in source] , finite local dimension and finite [formula in source] are the class hypotheses; the displayed numbers a","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Uniform constants","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9188,"byte_start":6183,"id":"section:974106578e6767d57f9b","kind":"section","labels":["eq:LR","eq:LRhyp","eq:TFPTvelocity","eq:iteration","eq:pathweight","eq:poissontail","eq:vLR","thm:LRclassical"],"line_end":267,"line_start":183,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-two-bank-transfer-20260915/external/exchange/source/articles__2026-08-30__tfpt_thermodynamic_dynamics_en"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-two-bank-transfer-20260915/external/exchange/source/articles__2026-08-30__tfpt_thermodynamic_dynamics_en.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be a graph, let every local Hilbert space be finite dimensional with a uniform dimension bound, and let a self-adjoint interaction satisfy [formula in source] For every finite [formula in source] , define [formula in source] . If [formula in source] , [formula in source] , and [formula in source] , then, uniformly in [formula in source] , [formula in source] Thus an admissible Lieb–Robinson ve","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The Lieb–Robinson theorem and explicit TFPT velocity","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12129,"byte_start":9188,"id":"section:95b9cfbad79a7cc11ada","kind":"section","labels":["eq:convergence","eq:duhamel","eq:limit","eq:shell","thm:dynamics"],"line_end":343,"line_start":268,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-two-bank-transfer-20260915/external/exchange/source/articles__2026-08-30__tfpt_thermodynamic_dynamics_en"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-two-bank-transfer-20260915/external/exchange/source/articles__2026-08-30__tfpt_thermodynamic_dynamics_en.tex","status_markers_as_written":[],"summary_excerpt":"For every [formula in source] , the net [formula in source] exists in norm, uniformly for [formula in source] in compact real intervals and independently of the exhausting sequence. It extends uniquely to a strongly continuous one-parameter group of [formula in source] -automorphisms of [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Norm thermodynamic limit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14819,"byte_start":12129,"id":"section:e2e81b99b843b044bd1e","kind":"section","labels":["eq:fixed","eq:gaugecov","eq:projectorcompat","prop:gauss"],"line_end":406,"line_start":344,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-two-bank-transfer-20260915/external/exchange/source/articles__2026-08-30__tfpt_thermodynamic_dynamics_en"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-two-bank-transfer-20260915/external/exchange/source/articles__2026-08-30__tfpt_thermodynamic_dynamics_en.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the group of finitely supported local gauge transformations on the ambient field algebra, and let [formula in source] denote its action. Define [formula in source] The electric and plaquette terms are gauge invariant; the hopping contains its parallel transporter; the determinant projector is a Spin(10) singlet; and the seam charge is neutral as assembled. Thus [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gauss law and the correct consistent family","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17350,"byte_start":14819,"id":"section:93def08f20e0c9beb6ad","kind":"section","labels":["eq:finiteKMS","eq:gibbs","eq:groundineq","eq:smear","thm:states"],"line_end":467,"line_start":407,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-two-bank-transfer-20260915/external/exchange/source/articles__2026-08-30__tfpt_thermodynamic_dynamics_en"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-two-bank-transfer-20260915/external/exchange/source/articles__2026-08-30__tfpt_thermodynamic_dynamics_en.tex","status_markers_as_written":[],"summary_excerpt":"The infinite-volume system [formula in source] , and its invariant subalgebra [formula in source] , have at least one ground state. For every [formula in source] , they have at least one [formula in source] -KMS state.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Existence of equilibrium states","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18876,"byte_start":17350,"id":"section:cd90c6924a0df8bd3f36","kind":"section","labels":["eq:numericconvergence","eq:numericvelocity"],"line_end":512,"line_start":468,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-two-bank-transfer-20260915/external/exchange/source/articles__2026-08-30__tfpt_thermodynamic_dynamics_en"],"relation_ids":["relation:8ff1c73d2ae839eff9a8"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-two-bank-transfer-20260915/external/exchange/source/articles__2026-08-30__tfpt_thermodynamic_dynamics_en.tex","status_markers_as_written":[],"summary_excerpt":"The companion [formula in source] uses the exact nearest-neighbour physical-edge sector of the assembled model while comparing it against the complete class constant earlier IR-universality witness. It reports: [formula in source] For the one-site projector, [formula in source] , and nested open volumes, the specialization of [formula in source] The zeros are numerical precision statements, not analytic finite-speed ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Numeric twin","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":21104,"byte_start":18876,"id":"section:fe2cf43aaf468a3fd438","kind":"section","labels":["thm:combined"],"line_end":562,"line_start":513,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-two-bank-transfer-20260915/external/exchange/source/articles__2026-08-30__tfpt_thermodynamic_dynamics_en"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-two-bank-transfer-20260915/external/exchange/source/articles__2026-08-30__tfpt_thermodynamic_dynamics_en.tex","status_markers_as_written":[],"summary_excerpt":"For the TFPT master-Hamiltonian class finite-dimensional local factors and coefficients of Table the finite-volume dynamics satisfy the uniform Lieb–Robinson bound [formula in source] ; the thermodynamic-limit dynamics exist in norm on all local observables and define a strongly continuous automorphism group; the group restricts consistently to the Gauss-invariant quasilocal algebra, with projector compatibility in t","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Combined theorem and exact boundary","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":23093,"byte_start":21104,"id":"section:c0e96880a60b78a3dc4e","kind":"section","labels":[],"line_end":618,"line_start":563,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-two-bank-transfer-20260915/external/exchange/source/articles__2026-08-30__tfpt_thermodynamic_dynamics_en"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-two-bank-transfer-20260915/external/exchange/source/articles__2026-08-30__tfpt_thermodynamic_dynamics_en.tex","status_markers_as_written":[],"summary_excerpt":"The amended contract makes the continuum limit optional but the thermodynamic limit mandatory. The latter is now proved at the Hamiltonian-class level for the concrete finite-group, finite-local-space TFPT assembly. The proof is insensitive to finite-volume boundary shape and does not infer thermodynamics from a finite scan. Its explicit velocity is conservative, while the numerical witness checks the expected cone, ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conclusion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":60,"byte_start":0,"id":"section:1ac723376fcd16df94bd","kind":"chapter","labels":["ch:idee"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Was mit Universalraum gemeint ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1381,"byte_start":60,"id":"section:68300014fb2475068c62","kind":"section","labels":[],"line_end":9,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Wenn wir gewöhnlich von Raum sprechen, denken wir an eine Bühne: Hier steht ein Tisch, dort fliegt ein Teilchen, und die Uhr läuft im Hintergrund. Die Universalraum-Idee dreht diese Reihenfolge um. Vielleicht sind zuerst Beziehungen und mögliche Veränderungen da. Eine Bühne mit Entfernungen und einer Uhr entsteht erst, wenn viele dieser Beziehungen ein beständiges Muster bilden.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kein zusätzlicher Behälter","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3208,"byte_start":1381,"id":"section:56b7af722c8bbe8ebdaa","kind":"section","labels":[],"line_end":33,"line_start":10,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Eine ausreichend konkrete Fassung benötigt mindestens: Zustände: Was ist gegeben, einschließlich relevanter Korrelationen? Operationen: Welche Veränderungen sind erlaubt? Zusammensetzung: Wie dürfen Vorgänge hintereinander und nebeneinander verbunden werden? Aufzeichnungen: Welche Spuren bleiben erhalten und dürfen später erneut benutzt werden? Auslesung: Welche Ergebnisse sind mit welchen Wahrscheinlichkeiten beobac","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die fünf Bestandteile","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4343,"byte_start":3208,"id":"section:d5cd533c817ab848555a","kind":"section","labels":["eq:op"],"line_end":46,"line_start":34,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Zwei Uhren können jetzt beide zwölf anzeigen und trotzdem verschieden weiterlaufen. Eine ist aufgezogen, die andere steht kurz vor dem Stillstand. Wer nur das Zifferblatt betrachtet, sieht den Unterschied noch nicht. Ein späterer Blick unterscheidet sie.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wann zwei Beschreibungen wirklich dasselbe sagen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5786,"byte_start":4343,"id":"section:45b19e11384dd7b5e54c","kind":"section","labels":["eq:vorwaerts"],"line_end":62,"line_start":47,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"TFPT liefert eine reichhaltige Grammatik: Träger, Darstellungen, Gitter, markierte Symmetrien, Projektoren und kurze wiederverwendete Zahlenformeln. Die Metapher vom Compiler meint eine Übersetzung zwischen diesen Beschreibungen. Sie sagt nicht, dass bereits ein kosmisches Computerprogramm identifiziert ist.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"TFPT als Grammatik und als Übersetzung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5824,"byte_start":5786,"id":"section:fdb2005b26b1814cc82d","kind":"chapter","labels":[],"line_end":63,"line_start":63,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Wie die Idee entstanden ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6760,"byte_start":5824,"id":"section:7fb9c7b945845a89d3cb","kind":"section","labels":[],"line_end":68,"line_start":64,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Die Anhänge zeigen keine einzige plötzliche Entdeckung, sondern eine Folge von Verschiebungen der Frage. Zuerst fällt auf, dass kleine geometrische und algebraische Daten in verschiedenen Rechnungen wiederkehren. Der Fünferträger führt zu einem 16-dimensionalen Spinor; die passenden Gitterfaktoren führen zu [formula in source] ; ein komplexer Viererträger zeigt 60 besondere Strahlen. Clocks, Ladungszuordnungen und Fl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vom Wiedererkennen zur gemeinsamen Ursache","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7669,"byte_start":6760,"id":"section:cb7ed0d105714c1bc904","kind":"section","labels":[],"line_end":73,"line_start":69,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Die älteren, in S09 zusammengefassten Untersuchungen fanden mehrere Räume, die man nicht einfach gleichsetzen darf: eine Kommutantenalgebra, einen Majorana-/Fockraum, einen festen Teilchensektor, eine verdoppelte Familienbeschreibung und eingeschränkte Kanalmodelle. Manche lokalen Ansichten ließen verschiedene gemeinsame Dynamiken zu. Andere Tests konnten unter engeren Voraussetzungen ausgewählte Zustände bestimmen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum Spektren und Einzelbilder nicht genügten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9525,"byte_start":7669,"id":"section:7fcb92d0d09d7a794a33","kind":"section","labels":[],"line_end":88,"line_start":74,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"L30mmL55mmL65mm Etappe& Erkenntnis& Neue Frage\\\\ Vorarbeiten, in S09 rückblickend beschrieben&Mehrere algebraische Ansichten, Lorentzkegel, verborgene Richtungen, lokale und gemeinsame Kanäle.&Welche Informationen gehen beim Auslesen verloren?\\\\ 13. September: Compiler-Manuskript S09&60 Strahlen, 15 Kontexte, zwei Schatten desselben Prozesses; explizite Vormessung mit Register.&Wer wählt Kreuzkopplung, Kontextgewicht","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die dokumentierte Entwicklung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10711,"byte_start":9525,"id":"section:65a1ce1de56942f22629","kind":"section","labels":[],"line_end":96,"line_start":89,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/01_idee.tex","status_markers_as_written":[],"summary_excerpt":"Der eingefügte Gesprächstext spricht von einem Regelwerk mit Logbuch und von Raum und Materie als Mustern seiner Spuren. Das trifft die Forschungsintuition. Die Formulierung „TFPT ist die Grammatik, der Universalraum die Ausführung“ ist als Einstieg hilfreich.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was von der anschaulichen Ursprungserzählung bleibt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":66,"byte_start":0,"id":"section:ab8115dfeb52d25c0b05","kind":"chapter","labels":["ch:algebra"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die mathematischen Bauteile von TFPT","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1113,"byte_start":66,"id":"section:965df915fe3244035611","kind":"section","labels":[],"line_end":12,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Die historische Kurzfassung nennt [formula in source] und einen fünfteiligen Träger. Vollständig gelesen setzt P1 einen orientierten Rand beziehungsweise eine Naht, einen geeigneten positiven Kern und eine Normierung voraus. P2 setzt Art und Struktur des Trägers voraus; die spätere [formula in source] -Lesart wird mit Farb- und schwachen Richtungen verbunden. Orientierung, Positivität, komplexe Struktur und Markierun","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Ausgangsannahmen enthalten mehr als zwei Zahlen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":2337,"byte_start":1113,"id":"section:0e7eb43eac9358040547","kind":"section","labels":[],"line_end":26,"line_start":13,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Bei fünf komplexen Richtungen kann man antisymmetrische Kombinationen von null, zwei und vier Richtungen bilden. Zusammen erhält man Das ist die gerade Spinorstruktur von [formula in source] . „Antisymmetrisch“ heißt hier: Beim Vertauschen zweier Plätze wechselt ein Vorzeichen. Es ist eine genaue Bauvorschrift, keine bildliche Ähnlichkeit.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vom Fünferträger zum Spinor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4400,"byte_start":2337,"id":"section:bd56358ac4b3afeb5b4f","kind":"section","labels":[],"line_end":57,"line_start":27,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Die beiden positiven Wurzelgitter [formula in source] und [formula in source] besitzen Determinante vier und Diskriminantengruppe [formula in source] . Eine Diskriminantengruppe beschreibt hier die möglichen Restklassen, mit denen man das Gitter ohne Verlust der Ganzzahligkeit ergänzen kann. Für passende Generatoren gilt modulo eins Diagonal gekoppelt ist die Summe [formula in source] ganzzahlig. Die vier gemeinsamen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die Verklebung wirklich zu E [formula in source] 8 führt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6051,"byte_start":4400,"id":"section:031ae27da731df5e0775","kind":"section","labels":["eq:branch"],"line_end":85,"line_start":58,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Die 240 Wurzeln sind besondere Vektoren in einem acht-dimensionalen Raum. Hinzu kommen acht Cartanrichtungen, sodass die Lie-Algebra 248 Dimensionen besitzt. Unter [formula in source] lautet ihre komplexe Zerlegung L47mmrY Sektor& Wurzeln& Generatoren einschließlich Cartan\\\\ [formula in source] &40& [formula in source] \\\\ [formula in source] &12& [formula in source] \\\\ Gemischter Vektorsektor&60& [formula in source] ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wurzeln und Generatoren sind verschiedene Zählungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7249,"byte_start":6051,"id":"section:796380daf95ec05ff1ae","kind":"section","labels":[],"line_end":92,"line_start":86,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"Ein Strahl ist ein reiner Zustand ohne seine insgesamt irrelevante globale Phase. Ein Kontext ist eine vollständige orthogonale Viererbasis: vier mögliche Ausgänge einer scharfen Messung. Im markierten komplexen Viererträger ergeben sich 60 besondere Strahlen in 15 solchen Kontexten. In der gewählten Kodierung sind dies die reinen Zwei-Qubit-Stabilizerzustände und ihre vollständigen Pauli-Kontexte. S09, Kap. 3 und 9","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das endliche Fenster: 60 Strahlen und 15 Kontexte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8782,"byte_start":7249,"id":"section:dcc415ad1f88d248f358","kind":"section","labels":[],"line_end":108,"line_start":93,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/02_algebra.tex","status_markers_as_written":[],"summary_excerpt":"L45mmL31mmL74mm Objekt& Größe& Was die Zahl zählt\\\\ [formula in source] -Wurzeln&240&Besondere Vektoren, keine 240 unabhängigen Raumrichtungen.\\\\ [formula in source] &248&Dimension der Generatoralgebra.\\\\ Ein Viererträger& [formula in source] &Zustände eines Ququarts, hier als zwei Qubits kodiert.\\\\ Vier solche Träger& [formula in source] &Komplexe Hilbertraumdimension der Zelle.\\\\ 15 allgemeine CQ-Blöcke& [formula i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Räume im Größenvergleich","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":71,"byte_start":0,"id":"section:11dd24aa21b86cc0953d","kind":"chapter","labels":["ch:prozess"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Ein gemeinsamer Prozess mit zwei Schatten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1558,"byte_start":71,"id":"section:160756f6e39172ceff81","kind":"section","labels":["eq:T"],"line_end":19,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Man beginnt mit einem Strahl [formula in source] : Kontext [formula in source] , Ergebnis [formula in source] . Dann wählt man einen nächsten Kontext [formula in source] und misst in dessen Basis. Die Quellkonstruktion benutzt [formula in source] ist eine [formula in source] -Inzidenzmatrix. Sie erlaubt den aktuellen Kontext und sechs andere, mit ihm inzidente Kontexte. Jeder erlaubte Nachfolger erhält in dieser spez","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine einzelne Messrunde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3449,"byte_start":1558,"id":"section:ff8098498e43a639918f","kind":"section","labels":["eq:D","eq:shadows"],"line_end":55,"line_start":20,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Die Matrix [formula in source] summiert die vier Ergebnisgewichte jedes Kontexts. Die Matrix [formula in source] liest die 15 nichttrivialen Pauli-Erwartungswerte aus. Mit [formula in source] lauten ihre Einträge Für [formula in source] und [formula in source] ergibt sich exakt Der Systemschatten entwickelt sich somit als depolarisierender Kanal Die Dämpfung [formula in source] entsteht aus der Kontextkombinatorik. B","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Kontext und Quantenzustand als zwei Auslesungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4623,"byte_start":3449,"id":"section:42d2743562e0e0c25ccc","kind":"section","labels":["eq:Tfactor"],"line_end":74,"line_start":56,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Die in S01 ausgearbeitete Faktorisierung lautet Hier gelten [formula in source] , [formula in source] und [formula in source] . Die beiden Zeilenräume sind orthogonal. Im selben Kontext haben die Pauli-Vorzeichenvektoren Skalarprodukt drei für denselben Strahl und minus eins für verschiedene Strahlen; bei inzidenten Kontexten bleibt eine gemeinsame Pauli-Richtung. Diese Werte ergeben genau die Einträge von","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die genaue Kompression auf 30 Koordinaten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6465,"byte_start":4623,"id":"section:f98aaf63bec068a59875","kind":"section","labels":[],"line_end":98,"line_start":75,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Aus [formula in source] mit Permutationsmatrizen folgt beim gleichgewichteten Mitteln unmittelbar [formula in source] . Zusätzliche Konjugation durch die Symmetriegruppe [formula in source] ändert das nicht: S07 berichtet 5040 Terme über 4500 verschiedene Matchings, gegenüber 24\\,601\\,472 insgesamt möglichen perfekten Matchings des bipartiten Inzidenzbildes. Diese kombinatorische Realisierung ist konkret. Die Gleichg","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum Symmetrie die Gewichte noch nicht auswählt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7236,"byte_start":6465,"id":"section:4c0e3b526ca432972973","kind":"section","labels":[],"line_end":113,"line_start":99,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Für die Kontextmatrix gilt Ihre Determinante ist negativ. Eine reelle Matrixexponentialfunktion hat jedoch [formula in source] . Deshalb ist [formula in source] auf diesem 15-dimensionalen Raum kein [formula in source] mit reellem [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein Schritt ist nicht dasselbe wie zwei halbe Schritte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7312,"byte_start":7236,"id":"section:f1b350b4f4ff17306de0","kind":"chapter","labels":["ch:memory"],"line_end":115,"line_start":114,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Gedächtnis: Was ein einzelnes Bild verschweigt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9442,"byte_start":7312,"id":"section:7826f65d1a2c58cbc4b7","kind":"section","labels":[],"line_end":149,"line_start":116,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Ein klassisch-quantenmechanischer Zustand, kurz CQ-Zustand, besitzt 15 positive [formula in source] -Blöcke [formula in source] . Zusammen haben sie 240 reelle lineare Koordinaten und Gesamtspur eins. Die feste Regel macht jeden Ausgangsblock in seinem Kontext diagonal. Deshalb gilt Es ist also nicht richtig, 240 Koordinaten pauschal als kleinste dauerhaft autonome Hülle dieser festen Ausführung auszugeben.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Allgemeine Kontextblöcke brauchen eine andere Beschreibung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10743,"byte_start":9442,"id":"section:2cb123856760657c4ede","kind":"section","labels":["eq:record"],"line_end":170,"line_start":150,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Für die vier Projektoren eines Kontexts sind [formula in source] Spiegelungen. In Dimension vier gilt Allgemein in Dimension [formula in source] wäre die linke Seite [formula in source] . Der kurze Auslöschungseffekt ist hier also tatsächlich viererspezifisch.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie die Aufzeichnung gebaut wird","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12572,"byte_start":10743,"id":"section:c7ec14f6c325b400dfc1","kind":"section","labels":[],"line_end":184,"line_start":171,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Für einen gleichförmigen reinen Eingang in der gewählten Kontextbasis erzeugt eine Vormessung maximale Verschränkung. Ohne Registerblick ist der Systemzustand [formula in source] . Nun gibt es zwei Ausführungen: Derselbe kohärente Speicher wird nochmals gekoppelt: [formula in source] stellt den reinen Eingang wieder her. Ein neuer Speicher wird benutzt: Im reduzierten System wird die Dephasierung wiederholt; [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das Echo des behaltenen Registers","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13380,"byte_start":12572,"id":"section:a458cd0a0c48d440679b","kind":"section","labels":[],"line_end":194,"line_start":185,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Bei frischen Registern trägt eine Folge von Kontexten den kohärenten Zustand Das Weglassen des Registers summiert Dichteoperatorbeiträge. Eine kohärente Projektion auf eine Registersuperposition summiert Amplituden und beschreibt ein anderes Experiment, einschließlich seiner Erfolgswahrscheinlichkeit.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reihenfolge bleibt wichtig","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15055,"byte_start":13380,"id":"section:6398629093514ef7e839","kind":"section","labels":[],"line_end":207,"line_start":195,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/03_prozess.tex","status_markers_as_written":[],"summary_excerpt":"Eine nichtverschwindende Beobachtungsfolge eines geschlossenen endlichen Systems mit festem unitärem Schritt ist eine endliche Summe von Phasenfaktoren. Nach Zusammenfassung gleicher Frequenzen besitzt ihr mittleres Betragsquadrat einen positiven Cesàro-Grenzwert. Sie kann daher nicht für alle [formula in source] exakt wie [formula in source] abklingen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Endliches Gedächtnis und scheinbares Vergessen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":72,"byte_start":0,"id":"section:2ed493367af1746e6a15","kind":"chapter","labels":["ch:zelle"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die Vierträgerzelle: ein gemeinsames Muster","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1404,"byte_start":72,"id":"section:2112a15b75cb42207eba","kind":"section","labels":["eq:omega"],"line_end":24,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Vier Träger mit je vier Basiswerten besitzen den total antisymmetrischen Zustand Jedes Basiswort verwendet alle vier Werte genau einmal. Die 24 Permutationen erhalten passende Vorzeichen. Das Ergebnis ist ein reiner gemeinsamer Zustand. Jeder einzelne Träger sieht für sich trotzdem maximal gemischt aus: Die Paarreduktion hat Rang sechs und sechs gleich große Eigenwerte [formula in source] . Die Ordnung steckt in den ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein Zustand, dessen Teile allein nichts verraten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2609,"byte_start":1404,"id":"section:53f042f4f793a04fd88a","kind":"section","labels":[],"line_end":38,"line_start":25,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Sei [formula in source] der Projektor auf den symmetrischen Paarraum. Wenn für alle Paare [formula in source] gilt, dann hat jeder Swap Eigenwert minus eins. Da Transpositionen alle Permutationen erzeugen, folgt Für [formula in source] ist dieser Raum eindimensional, für [formula in source] null. Auch gemischte Zustände mit entsprechender Trägerbedingung erfüllen die Aussage. Für [formula in source] existieren aber e","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Hüllensatz und seine genaue Voraussetzung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3902,"byte_start":2609,"id":"section:d49db396d1064b0b66b6","kind":"section","labels":["eq:tet-spec"],"line_end":54,"line_start":39,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Das vollständige Tetramermodell lautet Es besitzt das exakte Spektrum Der Grundzustand ist [formula in source] , die Lücke [formula in source] . Die hochgestellten Zahlen zählen die Zustände pro Energiewert und summieren sich zu 256.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine weiche Energiebedingung erlaubt Bewegung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5057,"byte_start":3902,"id":"section:ff315a3db540cd23c199","kind":"section","labels":[],"line_end":68,"line_start":55,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Der vollständige Graph, ein Stern und ein Pfad besitzen auf vier Trägern denselben antisymmetrischen Grundzustand, aber verschiedene Anregungen. Für gleiche Sterngewichte ist die Lücke [formula in source] statt [formula in source] . S01 nennt für einen Pfad mit Gewichten [formula in source] etwa [formula in source] ; S06 für sechs Gewichte [formula in source] etwa [formula in source] . Die letzten Werte werden hier a","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was ein Zustand über seinen Generator verrät","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5689,"byte_start":5057,"id":"section:9d377aca6eca6ad1a877","kind":"section","labels":[],"line_end":75,"line_start":69,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Der Projektor [formula in source] kommutiert mit allen Swaps. Daher erhält jede rein zellinterne Austauschentwicklung, auch mit zeitabhängigen Gewichten, den Anteil [formula in source] . Kollektive [formula in source] -Drehungen tun dasselbe. Ein Grundzustand kann also bekannt sein, ohne dass der vorhandene Ablauf einen beliebigen Eingang dorthin bringt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum Austausch allein die Zelle nicht herstellt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6230,"byte_start":5689,"id":"section:0d3ffe2573ee528b84a8","kind":"chapter","labels":["ch:fugen"],"line_end":80,"line_start":76,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Aktualisierung v1.5: ein exakter kleinerer Spektralauftrag Der 80-dimensionale Standard-Multiplizitätsblock ist inzwischen explizit konstruiert und sein einfaches Spektrum exakt zertifiziert. Eine zusätzliche Tableau-Transposition reduziert die führenden Singulettprobleme auf höchstens 131-dimensionale quadrierte Singularwertprobleme. Das beweist noch keine globale Ordnung aller SU(4)-Sektoren. Siehe Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vermittlung und Graph: die Prüfung der fünf Fugen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":8382,"byte_start":6230,"id":"section:1085f0936587c8b168ae","kind":"section","labels":[],"line_end":108,"line_start":81,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Der gewünschte positive Austausch lässt sich in einem kleinen Modell genau erklären. Man ergänzt den Paarraum [formula in source] durch einen sechsdimensionalen Vermittler mit Energie [formula in source] . Die partielle Isometrie [formula in source] erfüllt Für bleiben die zehn symmetrischen Zustände bei null; die antisymmetrischen Zustände koppeln paarweise an den Vermittler. Die unteren Energien sind Nach Identifik","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie ein virtueller Zwischenzustand bindet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10373,"byte_start":8382,"id":"section:a5f147096b897c548944","kind":"section","labels":[],"line_end":130,"line_start":109,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"S11 macht die zusätzliche Zuordnung: Ein [formula in source] -Spinorgewicht [formula in source] ist ein Ort; das [formula in source] -Gewicht [formula in source] ist der lokale Viererzustand. Die 64 Gewichte von [formula in source] werden somit als 16 Orte mit je vier inneren Zuständen gelesen. Das ist eine konkrete bedingte Interpretation, keine bloße Umbenennung einer bereits gegebenen räumlichen Geometrie.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Clebsch-Vorschlag: eine genaue neue Graphlesart","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12412,"byte_start":10373,"id":"section:1ab54f5e1d418098c18f","kind":"section","labels":[],"line_end":139,"line_start":131,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Die Graphkombinatorik folgt aus der angegebenen Ortslesart. Um daraus einen Vielteilchen-Hamiltonoperator zu erhalten, braucht man außerdem eine Fock- oder Tensorproduktstruktur, Besetzungsbedingungen, die Bedeutung der virtuellen Zustände und ihre Energien. Betragsgleiche Chevalley-Strukturkonstanten wählen noch keine physikalischen Kopplungsstärken in normierten Mehrteilchenzuständen aus. Gleiche [formula in source","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Welche Auswahl hier noch hinzukommt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14024,"byte_start":12412,"id":"section:3302301a3838e99c096d","kind":"section","labels":[],"line_end":158,"line_start":140,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"L74mmY Clebsch-Cluster bei [formula in source] , nach S11& Berichteter Wert\\\\ Grundenergie& [formula in source] \\\\ Grundzustand&Eindeutiges [formula in source] -Singulett, Form [formula in source] \\\\ Erster angeregter Singulettwert& [formula in source] ; mindestens vier orthogonale Moden, Gap etwa [formula in source] \\\\ Erste adjungierte Anregung& [formula in source] , Gap etwa [formula in source] \\\\ Weitere Multiple","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die berichteten Clusterzahlen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15205,"byte_start":14024,"id":"section:35d2a7d660e36a19933c","kind":"section","labels":[],"line_end":174,"line_start":159,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"S11 behauptet für den vollständigen Graphen mit [formula in source] einen eindeutigen Grundzustand bei [formula in source] und Gap [formula in source] . Energie und Gap stimmen; die Eindeutigkeit stimmt ab acht Trägern nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neue Korrektur: Singulett heißt nicht eindeutig","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17485,"byte_start":15205,"id":"section:1fe800bdd4895cbe317f","kind":"section","labels":[],"line_end":196,"line_start":175,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/04_zellen.tex","status_markers_as_written":[],"summary_excerpt":"Operatoren unterscheiden (v1.3): Das folgende [formula in source] beschreibt eine gleichkontextige Vierer-Aufzeichnung. Das neue binäre Austauschregister [formula in source] ist ein anderer Operator und nachweislich nicht Clifford. Seine zusätzliche Ressourcenanforderung widerspricht der folgenden Darstellbarkeit von [formula in source] nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neue Präzisierung: Aufzeichnung ist nicht durch die 248 verboten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":504,"byte_start":0,"id":"section:8b57da1e623bb492d3a1","kind":"chapter","labels":["ch:two"],"line_end":5,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Aktualisierung v1.5: der Übergang zu vielen Zellen ist genauer Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei Zellen: aus Verbindung wird Dynamik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1277,"byte_start":504,"id":"section:b8b8c54d2db4ac686444","kind":"section","labels":[],"line_end":10,"line_start":6,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Ist eine reduzierte Dichtematrix [formula in source] rein, so muss der gemeinsame Zustand bezüglich [formula in source] und seinem Rest faktorisiert sein. Sein Träger liegt in [formula in source] . Sind alle disjunkten Zellmarginalien unverändert rein, ist der Gesamtzustand ein Produkt über die Zellen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die Zellen beim Verbinden ihre Reinheit verlieren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2313,"byte_start":1277,"id":"section:c07b1633438c69ba3110","kind":"section","labels":["eq:Hred"],"line_end":31,"line_start":11,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Zwei vollständige Tetramerzellen mit genau einer Brücke haben Der volle Raum besitzt [formula in source] Dimensionen. Trotzdem bleibt die Entwicklung des Produktzustands in einem zweidimensionalen invarianten Unterraum: Die beiden Vektoren sind orthonormal; [formula in source] und [formula in source] . Es folgt Die Brücke koppelt den Produktgrundzustand an eine gemeinsame adjungierte Anregung. Beide Zellhälften verwe","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein kleiner exakter Raum in einem großen Hilbertraum","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4682,"byte_start":2313,"id":"section:765df0a298712b60114d","kind":"section","labels":["eq:alllambda13","eq:gapbound"],"line_end":76,"line_start":32,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Mit lauten die beiden Eigenwerte Die negative Korrektur beschreibt die Absenkung gegenüber dem einfachen Produktwert [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Energie und ein wirklicher Grundzustandsnachweis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5883,"byte_start":4682,"id":"section:8069cafc60ed018d26cf","kind":"section","labels":[],"line_end":98,"line_start":77,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Der niedrige Eigenzustand lässt sich schreiben als Seine Zellreduktion besitzt das Spektrum Die Entropie in natürlichen Logarithmen ist Bei [formula in source] sind [formula in source] und [formula in source] ; bei [formula in source] gilt [formula in source] . Schon eine endliche einzelne Brücke macht die lokale Zelle gemischt. Energieabsenkung und Verschränkung sind hier keine unabhängig eingesetzten Zusätze.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verschränkung aus derselben Kopplung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6998,"byte_start":5883,"id":"section:88ef392cbb45c91a536b","kind":"section","labels":["eq:two-clock"],"line_end":114,"line_start":99,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Starte im Produkt [formula in source] und lasse denselben konstanten gekoppelten Hamiltonoperator wirken. Dann gilt Bei [formula in source] vereinfacht sich dies zu [formula in source] . Der Energieinhalt beider Zellen pulsiert in einem messbaren Muster.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein Uhrsignal ohne zusätzlich gewählten lokalen Tick","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7998,"byte_start":6998,"id":"section:69cca408ac4b087494e1","kind":"section","labels":[],"line_end":125,"line_start":115,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/05_kopplung.tex","status_markers_as_written":[],"summary_excerpt":"Ein einzelner eindeutiger Singulettgrundraum besitzt keine logische Zustandsvielfalt. Das Produkt solcher Grundräume bleibt eindimensional. Wer alles auf diese Grundräume projiziert, erhält nur eine skalare Energie. Nichttriviale effektive Dynamik muss Anregungen, Randzustände, Multiplizitäten oder zusätzliche Vakuumsektoren behalten.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum viele Zellen noch ein eigener Schritt sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":71,"byte_start":0,"id":"section:a07306bcb0d52a262c21","kind":"chapter","labels":["ch:zeit"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Zeit: Takt, Uhrwerk und lesbare Veränderung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1193,"byte_start":71,"id":"section:d2dfcc81b935c074d07d","kind":"section","labels":[],"line_end":15,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Eine zyklische Matrix ist zunächst ein Taktmuster. Eine Dynamik sagt, wann welcher Zustand entsteht. Eine Uhr braucht zusätzlich eine beobachtbare Anzeige und eine Kalibrierung. Diese drei Ebenen müssen zusammenpassen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Drei Bedeutungen des Wortes Clock","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2069,"byte_start":1193,"id":"section:4e45acbb3ebbc050afaf","kind":"section","labels":[],"line_end":20,"line_start":16,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Der vollständige gleichgewichtete Tetramer-Hamiltonoperator ist eine zentrale Transpositionssumme. Deshalb kommutiert er mit jedem [formula in source] und jedem [formula in source] . Die Paarenergien ändern sich unter seiner freien Entwicklung nicht. Eine Tabelle, die nacheinander einen lokalen [formula in source] -Tick anwendet, ist somit kein Beweis, dass genau diese Anzeige unter [formula in source] von selbst läu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die Paarenergien unter dem Tetramer stillstehen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":3008,"byte_start":2069,"id":"section:c3e120046437311947b3","kind":"section","labels":[],"line_end":38,"line_start":21,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Ein präparierter nichtstationärer Zustand kann dennoch unter demselben Tetramer laufen. Für einen lokalen spurfreien hermiteschen Pauli [formula in source] mit [formula in source] setze Da [formula in source] , folgt Die lokalen Anzeigen oszillieren gegeneinander; ihre Summe bleibt null. Die Periode ist [formula in source] . Präparation, Ausleserichtung und die Kalibrierung von [formula in source] sind weitere Eingab","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine laufende lokale Anzeige im gesetzten Modell","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4494,"byte_start":3008,"id":"section:34b9a42f4daf2e4a07c3","kind":"section","labels":[],"line_end":57,"line_start":39,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Zerlege [formula in source] . Die vier [formula in source] sind orthonormal. Wähle zusätzlich Weil jedes Wort von [formula in source] jedes Energielabel einmal enthält, gilt [formula in source] . Für erhält man [formula in source] . Die Zeiten [formula in source] liefern vier orthogonale Anzeigen. Global ist der Zustand stationär, bedingt auf die Uhranzeige entwickelt sich das System. Das ist eine konkrete Page-Woott","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine relationale Viereruhr ist konstruierbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":5172,"byte_start":4494,"id":"section:d9cb81021e9bdd93448f","kind":"section","labels":[],"line_end":62,"line_start":58,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Aus [formula in source] folgt [formula in source] . Die historischen Größen [formula in source] und [formula in source] beschreiben deshalb sechsfach wiederholte Faktoren [formula in source] und [formula in source] . Eine physikalische Rate ist erst [formula in source] für einen festgelegten Schritt [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum ein Logarithmus noch keine Sekunde ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":5883,"byte_start":5172,"id":"section:608449c025bad9fc30ad","kind":"chapter","labels":["ch:echo"],"line_end":67,"line_start":63,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Verschiedene Präparationsverträge bleiben getrennt Dieses Kapitel bewahrt die ursprüngliche endliche Schaltung mit Erfolg [formula in source] aus dem vorausgesetzten Zweisingulett-Eingang. Der neue Stern-Spektralfilter erreicht [formula in source] aus demselben Eingang, setzt aber kontrollierte kontinuierliche Pulse voraus. Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die ausführbare Präparation und der Mehrzeittest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7250,"byte_start":5883,"id":"section:27c4c025206ad3fbb243","kind":"section","labels":[],"line_end":89,"line_start":68,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Die Präparationsnotiz S02 geht über den abstrakten Satz „ [formula in source] existiert“ hinaus. Sie beschreibt eine konkrete Schaltung, die aus einem einfachen Eingang den Zustand mit Erfolgsanzeige herstellt, anschließend ein Register schreibt und die Rückkehr ausliest. Laut Quelle wurde die Schaltung exakt simuliert, nicht auf Hardware ausgeführt. Ihr Zugriff auf zusätzliche Hilfssysteme und Nicht-Clifford-Operati","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was S02 tatsächlich geschlossen hat","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8727,"byte_start":7250,"id":"section:de5eedabec678a46b203","kind":"section","labels":[],"line_end":104,"line_start":90,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Der benötigte Zustand [formula in source] ist in der Acht-Qubit-Kodierung kein Stabilizerzustand. Schon für einen nichttrivialen lokalen Pauli gilt während reine Qubit-Stabilizerzustände für Pauli-Observablen nur [formula in source] liefern. Ebenso ist der Paarreduktionsrang sechs keine Zweierpotenz. Eine exakte Präparation aus einem Stabilizer-Eingang benötigt deshalb eine zusätzliche Ressource, etwa einen passenden","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die zusätzliche Ressource bleibt sichtbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9859,"byte_start":8727,"id":"section:ba7872748216fa4fa3a8","kind":"section","labels":[],"line_end":126,"line_start":105,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Der einfache Eingang lautet Er ist mit dem in S02 angenommenen Clifford-Baukasten präparierbar und besitzt [formula in source] -Anteil [formula in source] . Der Antisymmetrisierer ist Die konkrete Schaltung erzeugt 32 Kontrollzweige, von denen 24 die Permutationen tragen. Acht ungültige Zweige werden markiert. Nach Interferenz und Erfolgsselektion ist der implementierte Operator Somit gilt Der erfolgreiche Zweig ist ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie der Filter den Zustand erzeugt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11835,"byte_start":9859,"id":"section:7529de7f42ae564b940f","kind":"section","labels":["eq:originalecho"],"line_end":163,"line_start":127,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] schreibe [formula in source] . Dann Ein ignorierter frischer Pointer erzeugt Diese binäre Swap-Aufzeichnung ist ein anderer Kanal als die 15-Kontext-Mischung mit Faktor [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das ursprüngliche Echo: eins gegen siebzehn Zweiunddreißigstel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13367,"byte_start":11835,"id":"section:22df9c7e63f401184494","kind":"section","labels":[],"line_end":185,"line_start":164,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Der Endfilter hat den Effekt [formula in source] . Seine beobachtbare Erfolgsrate ist deshalb [formula in source] , nicht [formula in source] selbst. L68mmY Y Statistik& Behalten& Frisch\\\\ [formula in source] -Rückkehr, bedingt auf Präparation& [formula in source] & [formula in source] \\\\ Endfilter erfolgreich, bedingt auf Präparation& [formula in source] & [formula in source] \\\\ Beide Filter erfolgreich, je begonnen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die wirklichen Erfolgswahrscheinlichkeiten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15764,"byte_start":13367,"id":"section:dae95cc3bc24b638e193","kind":"section","labels":["eq:optimal"],"line_end":212,"line_start":186,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Eigene exakte Ergänzung dieser Synthese. Man kann die gleiche Messfrage für einen beliebigen lokalen unitären Tick [formula in source] ausrechnen. Setze Die beiden Swap-Gewichte sind [formula in source] . Daher Der Kontrast dieser Rückkehrstatistik ist maximal, wenn [formula in source] , also [formula in source] . Ein einzelnes CNOT innerhalb des Viererträgers erfüllt [formula in source] . Es permutiert dieselbe Meng","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neue Fortsetzung: der maximal ausgeglichene Echovergleich","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17179,"byte_start":15764,"id":"section:eb321e04e866a4209fbf","kind":"section","labels":[],"line_end":220,"line_start":213,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/06_zeit_echo.tex","status_markers_as_written":[],"summary_excerpt":"Y r Ressource nach S02& Anzahl\\\\ Systemqubits&8\\ , wiederverwendet&10\\ ätze&2\\ reservierte Qubits&20\\ Erfolgsbits beider Filter&12\\ -Gatter&574\\ CNOT vor Toffoliauflösung&382\\ &26\\ - [formula in source] / Pauli- [formula in source] &276 / 26\\\\T/T^ [formula in source] T-Varianten waren durch lokale Matrixidentität und Ersetzung zertifiziert, nicht zusätzlich als komplette komplexe 20-Qubit-Vektoren simuliert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ressourcen und Beweisgrenze der Originalschaltung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":75,"byte_start":0,"id":"section:dd2df0e9eced787c4895","kind":"chapter","labels":["ch:seam"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Von der Kette zur E [formula in source] 8-Naht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1943,"byte_start":75,"id":"section:b5a1f888ed77f46acc78","kind":"section","labels":[],"line_end":28,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Das Zweizellenmodell benutzt zwei vollständige Vierergraphen mit einer Brücke. Die Vielzellenrechnung in S08 benutzt dagegen Vierersegmente mit nächster Nachbarschaft. Bei [formula in source] wird erst dieses zweite Modell eine uniforme Kette. Derselbe isolierte Singulettzustand garantiert keine identischen Anregungen und keinen identischen Grenzwert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein wichtiger Modellwechsel","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3203,"byte_start":1943,"id":"section:505ffacb9945a37ce1fc","kind":"section","labels":[],"line_end":44,"line_start":29,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Für den uniformen periodischen Austauschring liefern die Quellen [formula in source] bei acht und [formula in source] bei zwölf Trägern. Der bekannte Vergleich lautet Die Sutherland-Grundenergie pro Träger ist für [formula in source] . S08 nennt die Extrapolation [formula in source] und [formula in source] . Diese endlichen Zahlen passen zur [formula in source] -WZW-Beschreibung des Kettenmodells. Die allgemeine Verb","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die SU(4)-WZW-Theorie hier plausibel ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4699,"byte_start":3203,"id":"section:336c3e71625e9e754d49","kind":"section","labels":[],"line_end":70,"line_start":45,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Die zentrale Ladung ist eine Kennzahl einer konformen Feldtheorie. Für die chiralen Niveau-1-Faktoren gilt Das Produkt hat also schon vor einer Kopplung [formula in source] . Ein später gefundener Wert acht allein ist kein Beweis einer [formula in source] -Erweiterung und kein Beweis eines Kondo-Flusses.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Naht braucht mehr als die Zahl acht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6584,"byte_start":4699,"id":"section:f67b2b5a5f40d4464384","kind":"section","labels":[],"line_end":92,"line_start":71,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"S11 ersetzt die frühere Kondo-Zielbeschreibung sinnvoll durch eine konkrete Erweiterungsaufgabe. Die Kurzschreibweise eines Quotienten durch [formula in source] kann jedoch verschiedene Operationen meinen. Nur auf invariante Zustände des ursprünglichen Produkts zu projizieren ist nicht dasselbe wie eine Simple-Current-Erweiterung mit den nötigen zusätzlichen beziehungsweise entsprechend gekoppelten Sektoren.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum „Z [formula in source] 4-Eichung“ präzisiert werden muss","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7348,"byte_start":6584,"id":"section:d10d398ee7b09521e73d","kind":"section","labels":[],"line_end":99,"line_start":93,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Eine gewöhnliche kritische SU(4)-Kette hat links- und rechtslaufende Sektoren, mit [formula in source] . Die übliche Kennzahl heißt dabei [formula in source] , nicht sechs. Die chirale Differenz ist null. Eine rein chirale [formula in source] -Naht hat dagegen Differenz acht. Ein zusätzliches ebenfalls nichtchirales [formula in source] -Modell ändert daran nichts.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Chiralitätslücke","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8727,"byte_start":7348,"id":"section:c2b97e76fe5215d296b7","kind":"section","labels":[],"line_end":105,"line_start":100,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/07_seam.tex","status_markers_as_written":[],"summary_excerpt":"Die innere Glue- [formula in source] wirkt auf den 248 Strömen mit Phasen [formula in source] auf Sektoren der Größen [formula in source] . Ihre Spur ist null. Die geometrische Vierteldrehung [formula in source] hat auf Stufe eins dagegen Spur [formula in source] . Die Operatoren sind somit nicht identisch. Eine Clock kann eine geometrische Drehung mit innerem Twist kombinieren; die beiden Faktoren bleiben getrennt. ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei Vierteldrehungen und der Index","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":551,"byte_start":0,"id":"section:1516deeb8b2ef0f40b81","kind":"chapter","labels":["ch:recon"],"line_end":5,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Fortschritt v1.3 Ein gemeinsamer endlicher Träger realisiert nun Aufzeichnung, Näherungspräparation, Reset und Mehrzeitantwort unter einem ausdrücklich angegebenen Ressourcenvertrag. Das beantwortet eine bedingte Existenzfrage. Es wählt weder den Vertrag aus TFPT allein noch ein universelles positives Zustandsfunktional aus. Die nachfolgenden Anforderungen bleiben deshalb nötig; die Konstruktion steht in Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie eine vollständige Rekonstruktion aussehen könnte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1946,"byte_start":551,"id":"section:6e6cffffae9dcd463781","kind":"section","labels":[],"line_end":17,"line_start":6,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Eine endliche Liste von Schatten bestimmt im Allgemeinen mehrere Prozesse. Man kann sogar jeden Kandidaten um einen ungekoppelten unsichtbaren Hilfsfaktor ergänzen, auf den alle erlaubten Experimente trivial wirken. Alle Antworten bleiben gleich. Eindeutigkeit ist daher zunächst nur für die minimal beobachtbare Darstellung erreichbar.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vom Wunsch nach Eindeutigkeit zu einer prüfbaren Frage","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2535,"byte_start":1946,"id":"section:c7c92852bce468fee950","kind":"section","labels":[],"line_end":24,"line_start":18,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Eine Projektion kann wichtige Wahrscheinlichkeiten erhalten und trotzdem die Multiplikation zerstören. S03 gibt einen einfachen Gegenbeleg: Projiziere [formula in source] auf [formula in source] und definiere [formula in source] . Dann Die neue Multiplikation ist nicht assoziativ. Eine nützliche reduzierte Vorhersagebeschreibung darf also nicht ohne zusätzlichen Nachweis als geschlossene physische Operationsalgebra v","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine kleinere Beschreibung ist nicht automatisch eine Algebra","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4676,"byte_start":2535,"id":"section:3844bfbab6365b10ff7d","kind":"section","labels":[],"line_end":52,"line_start":25,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Eine phasentreue Rekonstruktion braucht mehr als eine Tabelle einzelner Wahrscheinlichkeiten. Ein passender Ausgangspunkt ist eine komplexe Algebra [formula in source] mit Einheit, Multiplikation, Adjunktion und einem positiven normierten Zustandsfunktional [formula in source] : Für Operationswörter [formula in source] definiert einen positiven semidefiniten Korrelationskern. Er enthält die relativen komplexen Phasen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was vollständige Phaseninformation zusätzlich bringt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5967,"byte_start":4676,"id":"section:cecd1fffc518395612f8","kind":"section","labels":[],"line_end":65,"line_start":53,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Ein Prozesstensor beziehungsweise Quantenkamm ordnet einer Folge von Instrumenten gemeinsame Ergebniswahrscheinlichkeiten zu. Positivität und kausale Normierungsregeln sichern die Konsistenz. Eine tomographisch vollständige Eingriffsfamilie bestimmt einen endlichen Prozesstensor; sie bestimmt nicht automatisch eine eindeutige verborgene Umgebung oder sämtliche unendlichen Horizonte.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Mehrzeitdaten statt einer einzigen Dichtematrix","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7082,"byte_start":5967,"id":"section:dcc8538b8273033d1bb9","kind":"section","labels":[],"line_end":72,"line_start":66,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"S05 schlägt eine nützliche endliche Vorgehensweise vor: Man fixiert zulässige Operationswörter bis Länge [formula in source] , ihre Relationen, Symmetrien und die belegten Auslesungen. Die unbekannten Momente müssen eine positive Momentenmatrix bilden. Dann minimiert und maximiert man eine noch offene Ausgabe [formula in source] über alle kompatiblen Modelle.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein konkreter Auswahltest für offene Größen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9427,"byte_start":7082,"id":"section:0d70808d36baaa617209","kind":"section","labels":[],"line_end":106,"line_start":73,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Die in S03 vorgeschlagene Alternative verwendet als lokalen Viererverknüpfungstensor. An orientierten Verbindungen werden Trägerräume mit ihren dualen Räumen kontrahiert. So verbindet man Amplituden, ohne jede physische Zellreduktion als unverändert reines [formula in source] festzuschreiben.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Zelle als Verknüpfungsamplitude","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10370,"byte_start":9427,"id":"section:10efc6e126d1ea386739","kind":"section","labels":[],"line_end":113,"line_start":107,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"Paarweise kommutierende volle Matrixunteralgebren, die gemeinsam die Gesamtalgebra erzeugen, bestimmen im endlichen Fall eine Tensorproduktstruktur bis auf lokale Basiswechsel und Umbenennungen. Bei nichttrivialem Zentrum können stattdessen Sektoren übrigbleiben. Die Auswahl der privilegierten Unteralgebren aus den Wechselwirkungen ist der eigentliche inverse Schritt. https://arxiv.org/abs/quant-ph/0308043Zanardi, Li","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Teilsysteme aus Beziehungen erkennen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11839,"byte_start":10370,"id":"section:e685555768557fd96690","kind":"section","labels":[],"line_end":124,"line_start":114,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/08_rekonstruktion.tex","status_markers_as_written":[],"summary_excerpt":"S08 untersucht einen neutralen Sektor aus 70 Materiemasken und Schleifenfluss, insgesamt 1190 Zuständen. In einer festgehaltenen lokalen Operatorliste wird über der Generator rekonstruiert. Nach Entfernen trivialer Identitätsrichtungen reproduziert der Grundzustand die Koeffizienten [formula in source] , [formula in source] , [formula in source] und [formula in source] . Ein zusätzlicher angeregter Zustand verbessert","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was das Zustandsgate am Rotor/CAR-Ring prüft","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":547,"byte_start":0,"id":"section:4b6dea7300454ca9c91c","kind":"chapter","labels":["ch:physik"],"line_end":5,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Raumzeit, Materie und Gravitation aus demselben Ursprung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2438,"byte_start":547,"id":"section:690d85416be58d3b068a","kind":"section","labels":[],"line_end":33,"line_start":6,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Ein markierter [formula in source] -Block trägt die hermitesche Matrix Ihre Determinante ist exakt Die Eigenwerte sind [formula in source] . Deshalb entspricht [formula in source] dem Zukunftskegel [formula in source] . Die Kongruenz [formula in source] mit [formula in source] erhält die Determinante und den positiven Kegel.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Lorentzkegel: eine echte, aber begrenzte Brücke","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4213,"byte_start":2438,"id":"section:64f36ead655457027061","kind":"section","labels":[],"line_end":52,"line_start":34,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"S03 formuliert eine nützliche bedingte Brücke. Angenommen, derselbe Prozess liefert einen lokalen kohärenten Zweikomponentensektor mit inverser Zweipunktfunktion Dann folgt Für invertierbares [formula in source] ist dies eine Lorentzform. Jetzt wäre der Kegel aus einem tatsächlichen Propagator gewonnen. Vorausgesetzt sind jedoch ein sinnvoller Impulsraum, ein kontrollierter lokaler Grenzprozess, ein kohärenter Pol un","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der präzise nächste Schritt: den Kegel aus der Ausbreitung gewinnen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5312,"byte_start":4213,"id":"section:ea0a1a185cb1b02de4c8","kind":"section","labels":[],"line_end":63,"line_start":53,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Eine mögliche Materieanregung muss stabil oder kontrolliert propagierend sein. Man benötigt ihr Spektrum, ihre Ladungen, chirale Ausbreitung, erlaubte Vertizes und das Verschwinden unerwünschter Spiegelpartner. Eine vorkommende Darstellung allein erfüllt das nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Materie ist mehr als eine Ladungstabelle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6300,"byte_start":5312,"id":"section:c21932287174f70f728f","kind":"section","labels":[],"line_end":72,"line_start":64,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Eine Algebra mit Darstellung und geeignetem Diracoperator kann Geometrie kodieren. Beispielsweise macht die Distanzformel sichtbar, warum nicht nur Eigenwerte, sondern die Relation zwischen [formula in source] und den Observablen zählt. Connes' kommutativer Rekonstruktionssatz benötigt starke Spektralaxiome und liefert eine kompakte glatte Riemannsche Mannigfaltigkeit. Er erzeugt keine lorentzsche 3+1D-Welt aus einer","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spektrale Geometrie hilft, ersetzt aber keine fehlenden Daten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":7509,"byte_start":6300,"id":"section:dd67d7e586bc62a55c67","kind":"section","labels":[],"line_end":85,"line_start":73,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Die Identität [formula in source] passt zu einer bekannten Normierung. Sie liefert nicht das Feld [formula in source] , einen masselosen quantisierten Spin-2-Pol, zwei physische Helizitäten oder universelle Kopplung.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was für Gravitation noch wirklich fehlen würde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7600,"byte_start":7509,"id":"section:31c417a02cc08fecd149","kind":"chapter","labels":["ch:zahlen"],"line_end":87,"line_start":86,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die Zahlenprogramme: Nähe, Spannungen und offene Übertragung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8509,"byte_start":7600,"id":"section:2fcf0a1fbf6138e20e4a","kind":"section","labels":[],"line_end":102,"line_start":88,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/09_physik.tex","status_markers_as_written":[],"summary_excerpt":"Die [formula in source] -Zerlegung benutzt Hyperladungen [formula in source] auf den drei Farbplätzen und [formula in source] auf den zwei schwachen Plätzen. 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Aus ihren gekoppelten Anregungen und Aufzeichnungen entsteht ein kontrollierter gemeinsamer Grenzprozess. Erst dieser Grenzprozess liefert Raumzeit, chirale Materie, Wechselwirkungen und gegebenenfalls Gravitation. Die erste ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die präziseste gemeinsame Hypothese","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4033,"byte_start":0,"id":"section:54cd406e1870a104ca2c","kind":"chapter","labels":["app:corrections"],"line_end":28,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"L46mmL77mmL27mm Frühere Formulierung& Konsolidierte Aussage& Herkunft\\\\ Aus zwei Zahlen folgt der ganze Aufbau.&P1/P2 enthalten Orientierung, Positivität, Trägerart und Markierungen. Ihre Konsequenzen sind von ihrer Auswahl verschieden.&S09; S05/S06\\\\ Die Kontextregel ist symmetrieerzwungen.& [formula in source] ist eine konkrete gleichgewichtete Realisierung; die kovariante Familie [formula in source] bleibt ein Geg","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Korrekturregister und ergänzende Details","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5908,"byte_start":4033,"id":"section:953384d78a4527b3cd46","kind":"section","labels":[],"line_end":37,"line_start":29,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"S09 berichtet für ein früheres Majoranamodell zehn zugängliche und sechs verborgene reelle Richtungen, entsprechend einer [formula in source] -Zerlegung auf Fockebene. Verschränkung allein macht einen verborgenen Zustand nicht am Rand lesbar; eine geeignete Kopplung oder erweiterte Messung ist nötig. Ein dort gebauter Ereigniskanal übertrug Besetzung, besaß aber weiterhin eine nichttriviale Fixalgebra. Übertragung un","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Frühere Nebenstränge, die im Gesamtbild erhalten bleiben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10041,"byte_start":5908,"id":"section:3fde3b42361568789419","kind":"chapter","labels":[],"line_end":74,"line_start":38,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"L34mmL116mm Begriff& Bedeutung in diesem Dokument\\\\ Adjungierte&Die Darstellung einer Lie-Algebra auf ihren eigenen Generatoren durch die Klammer; nicht automatisch der gesamte Raum physischer Zustände.\\\\ Adjunktion [formula in source] &Komplex konjugierte Transposition beziehungsweise die passende Operatoradjunktion. Nicht dasselbe Wort wie adjungierte Darstellung.\\\\ Algebra&Ein Raum von Objekten mit Regeln für Addi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Begriffe in einfachen Worten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10087,"byte_start":10041,"id":"section:219518a6c00cf0bab5f8","kind":"chapter","labels":[],"line_end":75,"line_start":75,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Quellen, Abdeckung und Reproduktion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10437,"byte_start":10087,"id":"section:46c94c934456b9a06173","kind":"section","labels":[],"line_end":79,"line_start":76,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Die Quellenkürzel S01 bis S11 gelten durchgängig für dieses Buch und sind von den jeweils eigenen Kürzeln der Anhänge zu unterscheiden. Die vollständigen Originalpfade und SHA-256-Werte stehen im beiliegenden Manifest. Hier werden die Dateinamen und inhaltlichen Rollen aufgeführt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die elf Eingabedokumente","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":12676,"byte_start":10437,"id":"section:81944c5409ee8dedaf85","kind":"section","labels":[],"line_end":96,"line_start":80,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Der eigenständige Prüfer importiert keinen Code des ursprünglichen TFPT-Repositoriums. Die Standard-Zwei-Qubit-Kontexte wurden aus den üblichen Pauli-Matrizen rekonstruiert. Das kontrolliert die endlichen im Text angegebenen Beziehungen, ist aber kein erneuter phasentreuer Import des nativen Gauß- [formula in source] -Adapters.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was neu geprüft wurde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13823,"byte_start":12676,"id":"section:f9b1423d2780004e14fa","kind":"section","labels":[],"line_end":108,"line_start":97,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"L16mmL41mmY Quelle& Berichtete Prüfung& Reichweite\\\\ S09&11214 Bedingungen pro Modus, elf Negativvarianten&Ursprungsaudits und Zahlenprüfungen; kein vollständiger Lean-/RH-Neubau.\\\\ S07&325 + 147 Bedingungen, 19 Tests&Inversion und Follow-ups; mehrere spätere Minimalitätskorrekturen erforderlich.\\\\ S06&86 eigene Bedingungen sowie ausgewählte Originalreplays&45-/30-Quotienten, Uhr und Herkunftskontrollen; begrenzte Ke","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie die Quellen ihre eigenen Prüfungen beschreiben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":14798,"byte_start":13823,"id":"section:e0feb61494348b6a1acf","kind":"section","labels":[],"line_end":113,"line_start":109,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Das Paket enthält die vollständige LaTeX-Quelle, Kapiteldateien, Vektordiagramme, den eigenständigen Prüfer, die Ergebnisdatei und das Eingabemanifest. Mit einer LaTeX-Installation einschließlich LuaLaTeX, TikZ und den verwendeten Standardpaketen lässt sich das Buch durch zwei Läufe von lualatex main.tex im Quellverzeichnis bauen. Für die endlichen Gegenrechnungen werden Python, NumPy, SymPy, mpmath und Matplotlib be","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproduktionspaket dieser Synthese","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18166,"byte_start":14798,"id":"section:0a8869c0873e883c8d6d","kind":"section","labels":[],"line_end":135,"line_start":114,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Die folgenden Quellen wurden zur fachlichen Einordnung beziehungsweise für den datierten Konstantenvergleich aufgerufen. Sie bestätigen die allgemeinen Werkzeuge, nicht die physikalische Richtigkeit von TFPT. Die spezifischen langen Herleitungen dieses Buches beruhen auf den Anhängen und den ausgeschriebenen Gegenrechnungen. F. A. Pollock et al.: Non-Markovian quantum processes: complete framework and efficient chara","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Externe Primärliteratur und Referenzdaten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18523,"byte_start":18166,"id":"section:6cfddf10fb2320d9431d","kind":"section","labels":[],"line_end":137,"line_start":136,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/11_anhang.tex","status_markers_as_written":[],"summary_excerpt":"Die Anhänge wurden unverändert gelesen; ihre tatsächlichen Dateiinhalte sind durch SHA-256 dokumentiert. Dieses Buch aktualisiert keinen ursprünglichen Theorievertrag und keinen Abschlussmarker. Es liefert eine neue, zusammenhängende und prüfbare Darstellung mit ausdrücklich abgegrenzten eigenen Fortsetzungen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Abschluss der Dokumentation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":968,"byte_start":0,"id":"section:be7b1fa3b1a6a606362b","kind":"chapter","labels":["ch:shadow-arithmetic"],"line_end":8,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Was uns ein Schatten verraten kann Wenn wir nur den Schatten eines Rades sehen, erkennen wir vielleicht einen Kreis. Erst wenn wir das Rad drehen, belasten und mit einem zweiten Rad verbinden, erkennen wir seine Achse, seine Zähne und seine Übersetzung. Genau so lesen wir hier Primzahlen, Quanteneffekte und Raumzeit: als verschiedene Antworten, die eine mögliche gemeinsame Struktur gleichzeitig erklären müsste.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Primzahlen, RH und die Musik hinter den Schatten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":2819,"byte_start":968,"id":"section:5868876aa6f1fb2198c4","kind":"section","labels":["eq:primon-partition"],"line_end":25,"line_start":9,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Jede natürliche Zahl [formula in source] zerfällt eindeutig in Primfaktoren: Die erste Gleichung beschreibt ein Zusammensetzen durch Multiplikation; die zweite übersetzt dieses Zusammensetzen in Addition. Zum Beispiel ist [formula in source] , also [formula in source] . Die Primzahlen sind die unabhängigen Bausteine dieses multiplikativen Systems. Das ist ein Satz über natürliche Zahlen. Es ist noch kein Satz darüber","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"In welchem Sinn Primzahlen Bausteine sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":4018,"byte_start":2819,"id":"section:4b5c634773c9ee327127","kind":"subsection","labels":[],"line_end":36,"line_start":26,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Warum gerade [formula in source] ? Aus [formula in source] allein folgt das noch nicht: Man darf jeder Primzahl zunächst einen beliebigen Wert [formula in source] geben. Eine zusätzliche Ordnungsregel schließt die Lücke. Ist [formula in source] monoton in der natürlichen Zahl [formula in source] , so gilt notwendig Der Beweis ist kurz. Setze [formula in source] . Aus [formula in source] folgen [formula in source] Div","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine bedingte Auswahlregel für die logarithmische Energie","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":7179,"byte_start":4018,"id":"section:ac481cc93a7375e601f5","kind":"section","labels":["eq:prime-trace"],"line_end":64,"line_start":37,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die häufig verkürzte Aussage Primzahlen tauchen als Quantenenergien auf umfasst verschiedene Sachverhalte. Beim klassischen Zeta–Quantenchaos-Vergleich entsprechen Nullstellenhöhen den Energien eines gesuchten Spektrums. Die Primzahlen spielen auf der anderen Seite die Rolle primitiver periodischer Bahnen; Primzahlpotenzen sind deren Wiederholungen. Eine Bahn wird einmal durchlaufen, zweimal, dreimal. Ihr logarithmis","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was Primzahlen mit Quantenchaos verbindet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":10149,"byte_start":7179,"id":"section:6b059e720be71c1c1ca0","kind":"section","labels":[],"line_end":81,"line_start":65,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die Unterlagen und der zusätzlich eingesehene Forschungsbestand ergeben keine abgeschlossene RH-Lösung. Sie ergeben jedoch eine ungewöhnlich präzise Landkarte aus positiven Bausteinen und bereits ausgeschlossenen Abkürzungen. Die folgende Verdichtung ordnet die inhaltlichen Familien; sie behauptet keine erneute Prüfung jedes Katalogeintrags.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was unser RH-Zweig tatsächlich beigetragen hat","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11189,"byte_start":10149,"id":"section:d37d314e419001ac9c86","kind":"subsection","labels":[],"line_end":96,"line_start":82,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die ersten sechs Werte sind [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] und [formula in source] . Daraus folgt für [formula in source] Hier ist der Primzahlbezug wirklich vorhanden. Die Selbstdualität des Gitters schließt die Poisson-Transformation auf dasselbe Gitter. Poisson-Summation gilt auch für nichtselbstduale Gitter und verbindet dann Gitter und ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der genaue Ertrag der [formula in source] -Schalen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":12659,"byte_start":11189,"id":"section:68239f15925ac9dbcc02","kind":"subsection","labels":[],"line_end":108,"line_start":97,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die entscheidende arithmetische Form enthält eine Differenz: vereinfacht [formula in source] . Zwei positive Matrizen können eine indefinite Differenz besitzen; schon [formula in source] hat die Eigenwerte [formula in source] und [formula in source] . Entsprechend löst ein beliebiger positiver Born- oder Gramkern die signierte Aufgabe noch nicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die fehlende Positivität so hartnäckig ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14262,"byte_start":12659,"id":"section:935f263a8f293e267233","kind":"subsection","labels":[],"line_end":115,"line_start":109,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Der Jensen/Coxeter-Test r618 findet eine starre [formula in source] -Struktur auf der [formula in source] -Seite, während die verglichenen Jensen-Polynome mit ihrem Index variieren. Die gewählte Identifikation scheitert. Der Selberg-Kontakttest r638 besitzt im untersuchten Fall weiterhin einen negativen kleinsten Eigenwert von ungefähr [formula in source] ; eine Quadratvervollständigung hat die falsche signierte Form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was die negativen Routen konkret lehren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15958,"byte_start":14262,"id":"section:ba4cccf8214bb795184f","kind":"section","labels":[],"line_end":126,"line_start":116,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Die vorhandene freie fermionische Naht hat bei fester Größe eine endliche Zustandssumme. Das Primonmodell verlangt eine unbegrenzte Primfamilie und andere Besetzungsdaten. Schon für [formula in source] gilt [formula in source] und [formula in source] : Der Pol bei [formula in source] entsteht erst in der unendlichen Familie. Eine endliche Demonstration kann ihn nicht besitzen. Der vorhandene Nahtvergleich findet ents","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Naht braucht mehr als ein paar zusätzliche Takte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16501,"byte_start":15958,"id":"section:1b52a48175d6bda1f9ef","kind":"section","labels":[],"line_end":129,"line_start":127,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Wei und Mitautoren verbinden in zwei gezielt konstruierten Quantensystemen Nullstellen mit dynamischen Phasenübergängen. Berichtet werden ein Fünf-Qubit-NMR-Prinzipversuch und weitergehende numerische Untersuchungen. Die verwendeten Hamiltonoperatoren und Zustandsgewichte sind so gewählt, dass sie Zeta-Daten kodieren. Das macht den Zusammenhang experimentell bearbeitbar; eine Ableitung dieser Wahl aus TFPT oder ein R","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die neue Quantenphasen-Arbeit von 2026","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":18843,"byte_start":16501,"id":"section:72f29d8c1095c9462588","kind":"subsection","labels":["eq:eta-readout"],"line_end":150,"line_start":130,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/12_schatten_arithmetik.tex","status_markers_as_written":[],"summary_excerpt":"Unabhängig vom vollständigen Ressourcenbeweis dieser Arbeit untersuchen wir den folgenden einfachen thermischen Eta-Auslesekanal: Er entsteht durch einen Gibbszustand für [formula in source] und eine diagonal ausgelesene Paritätsphase. Bei festem [formula in source] und [formula in source] konvergiert der Zähler gegen [formula in source] , während [formula in source] Also geht das Rohsignal [formula in source] an jed","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eigene Anschlussrechnung: Ein verschwindendes Signal ist mehrdeutig","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":541,"byte_start":0,"id":"section:02345d3f8384cffe6a96","kind":"chapter","labels":["ch:shadow-quantum"],"line_end":6,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Nicht nur die Anzahl der Kugeln zählt Zwei Kästen können dieselben möglichen Messergebnisse enthalten und doch verschieden reagieren, wenn wir zuerst an einer anderen Stelle messen oder zwei Teile zusammenführen. Die Quantenphänomene sagen uns deshalb vor allem etwas über die Regeln des Zusammensetzens, über relative Phasen und über erlaubte Eingriffe. Genau diese Daten verliert ein einfacher Schatten leicht.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was Quantenphänomene über den verborgenen Aufbau sagen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1925,"byte_start":541,"id":"section:71c8271adca0eaf26a77","kind":"section","labels":[],"line_end":21,"line_start":7,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Für zwei Alternativen mit Amplituden [formula in source] und [formula in source] lautet die Born-Regel [formula in source] Der letzte Term kann verstärken oder auslöschen. Wer ausschließlich die beiden Einzelwahrscheinlichkeiten aufbewahrt, kann ihn nicht rekonstruieren. Das erklärt im Kleinen, warum die behaltenen Register und Echoexperimente der früheren Kapitel mehr verraten als der erste sichtbare Markovschritt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Interferenz verlangt eine Information vor den Wahrscheinlichkeiten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4273,"byte_start":1925,"id":"section:d3f1422364dd924851d6","kind":"section","labels":[],"line_end":40,"line_start":22,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Die 15 Zwei-Qubit-Pauli-Kontexte der Synthese enthalten das folgende Mermin–Peres-Quadrat. Hier bedeutet [formula in source] und entsprechend für die anderen Einträge: Jede Zeile und jede Spalte ist gemeinsam messbar. Alle Zeilenprodukte sind positiv, aber das letzte Spaltenprodukt ist negativ. Diese sechs Kontexte gehören zum bereits verwendeten Pauli-System.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der vorhandene Baukasten enthält bereits Kontextualität","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5749,"byte_start":4273,"id":"section:c1a2c45914c77250a38a","kind":"section","labels":[],"line_end":54,"line_start":41,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Für zwei räumlich getrennte Messstellen hat die CHSH-Kombination [formula in source] in einem lokalen Modell mit unabhängiger Wahl der Einstellungen die Grenze [formula in source] . Quantenmechanik erreicht [formula in source] . Mit [formula in source] , [formula in source] und [formula in source] ist der zugehörige Operator [formula in source] ; seine Eigenwerte sind [formula in source] . Beides wurde hier exakt nac","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Verschränkung legt die Zusammensetzung fest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6930,"byte_start":5749,"id":"section:779efc0d19df30be37c1","kind":"section","labels":[],"line_end":70,"line_start":55,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Wähle bei festgehaltenen Labor-Teilsystemen [formula in source] Beide Hamiltonoperatoren haben exakt die Energien [formula in source] . Der Grundzustand von [formula in source] ist ein Produktzustand, der von [formula in source] ein Bell-Zustand. Die Reinheit [formula in source] eines lokalen Teils beträgt entsprechend 1 beziehungsweise [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gleiche Energien können verschiedene Welten beschreiben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8229,"byte_start":6930,"id":"section:fbac93d080510271ae7b","kind":"section","labels":[],"line_end":77,"line_start":71,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Die komplexe Vierdimensionalität ist für den bestehenden Pauli-/Spinorbaukasten passend. Eine direkte Ableitung der komplexen Zahlen aus einem einzelnen Quantenphänomen wäre trotzdem zu stark. Renou und Mitautoren untersuchen Quantennetzwerke, in denen die übliche reale und komplexe Theorie unter einer bestimmten Unabhängigkeits- und Kompositionsannahme verschiedene Vorhersagen machen. F10","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was komplexe Zahlen verraten und was offenbleibt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9587,"byte_start":8229,"id":"section:384396b610cd2426d25f","kind":"section","labels":[],"line_end":83,"line_start":78,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/13_schatten_quanten.tex","status_markers_as_written":[],"summary_excerpt":"Die bisherigen Registerbeispiele erklären, wie ein global kohärenter Ablauf nach eingeschränktem Zugriff wie ein irreversibler Prozess aussehen kann. Sie liefern noch keine eindeutige Lösung des Messproblems: Insbesondere folgt aus einer diagonalen reduzierten Dichtematrix allein keine Auswahl eines einzelnen Ereignisses. Eine zusätzliche Kollapsdynamik müsste messbare Abweichungen angeben; eine unitäre Beschreibung ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Messung, Zeitpfeil und Statistik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":900,"byte_start":0,"id":"section:8630d63e44a2311c51a9","kind":"chapter","labels":["ch:shadow-dimension"],"line_end":8,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"Dimension ist die Antwort auf eine Frage Eine Ameise auf einer dünnen Schnur kann entlang einer Richtung laufen. Auf einem Blatt kann sie außerdem ausweichen. In einem Zimmer kann sie auch über ein Hindernis hinweg. Eine Dimension zählt solche unabhängigen Möglichkeiten. Die Zahl der inneren Zustandskomponenten oder der Knöpfe eines Geräts ist etwas anderes.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Drei Raumrichtungen und eine Zeit: Welche Bedingungen bleiben?","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2245,"byte_start":900,"id":"section:197a2c8ae00eae55da74","kind":"section","labels":[],"line_end":23,"line_start":9,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"Ein traceloses hermitesches [formula in source] -Objekt hat genau drei reelle Komponenten: [formula in source] Ergänzt man [formula in source] , ergibt die Determinante [formula in source] Der positive Kegel erfüllt [formula in source] . Das ist die präzise Lorentz-Brücke aus dem Ursprungsteil. Sie zeigt eine passende lokale algebraische Form. Noch fehlen ihre Interpretation als Ereignisse, die Verklebung zu einer Ra","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Drei unterschiedliche Hinweise führen zur Zahl drei","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4446,"byte_start":2245,"id":"section:0176ba216dd0e4bab3cc","kind":"section","labels":[],"line_end":47,"line_start":24,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"Für einen Graph-Laplaceoperator [formula in source] definieren wir die mittlere Rückkehrfunktion und eine skalenabhängige Dimension durch Auf einem großen regelmäßigen dreidimensionalen Gitter entsteht zwischen der Gitter- und der endlichen Systemskala ein Bereich mit [formula in source] , also [formula in source] . Bei einem endlichen zusammenhängenden Graphen geht [formula in source] sowohl für sehr kleine als auch","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine neue Gegenprobe am Clebsch-Vorschlag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5395,"byte_start":4446,"id":"section:f7adae906c0d5bc63e55","kind":"section","labels":[],"line_end":52,"line_start":48,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"In einer gewöhnlichen hyperbolischen Wellengleichung werden lokale Anfangsdaten auf einer räumlichen Fläche vorgegeben und entlang einer ausgezeichneten Zeitrichtung entwickelt. Mehrere Zeitkoordinaten verändern das Anfangswertproblem grundlegend. Unter zusätzlichen nichtlokalen Beschränkungen existieren dennoch wohldefinierte Mehrzeit-Probleme; ein pauschaler Unmöglichkeitssatz wäre falsch. F14","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine Zeitrichtung ist mehr als ein weiterer Zahlenplatz","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6521,"byte_start":5395,"id":"section:dd97e4626ddae0a4c81a","kind":"section","labels":[],"line_end":66,"line_start":53,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/14_schatten_dimension.tex","status_markers_as_written":[],"summary_excerpt":"Ein elementares mechanisches Beispiel illustriert die Rolle von Constraints. Nimmt man in [formula in source] Raumdimensionen eine Newtonsche Punktkraft mit Gaußgesetz an, lautet das effektive Radialpotential [formula in source] An einer Kreisbahn ergibt sich [formula in source] Unter diesen Voraussetzungen sind solche Kreisbahnen bei [formula in source] stabil, bei [formula in source] instabil und bei [formula in so","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was Stabilität zusätzlich einschränkt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":397,"byte_start":0,"id":"section:bdb86d2dd5fb3bcd0934","kind":"chapter","labels":["ch:shadow-open"],"line_end":4,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Offene Physik ist kein freier Platz, in den jede neue Idee hineinpasst. Sie ist oft durch viele bekannte Eigenschaften eng begrenzt. Der nützliche Schritt lautet deshalb: Welcher Teil des Phänomens ist beobachtet, welcher Mechanismus fehlt, und welche Antwort müsste unser Modell zusätzlich liefern?","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Schwer verstandene Phänomene als zusätzliche Prüfsteine","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1423,"byte_start":397,"id":"section:9caff685777b3c3d383b","kind":"section","labels":[],"line_end":9,"line_start":5,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Gravitationslinsen und die Verteilung sichtbarer Materie in kollidierenden Haufen liefern eine wichtige Beobachtung: Der aus der Gravitation erschlossene Beitrag muss nicht dem heißen sichtbaren Gas folgen. Die Bullet-Cluster-Analyse ist ein prominentes Beispiel. Sie identifiziert damit noch kein bestimmtes mikroskopisches Teilchen. Zusammen mit anderen kosmologischen Daten ist sie eine starke Anforderung an jede Erk","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dunkle Materie: unsichtbar heißt nicht frei wählbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2590,"byte_start":1423,"id":"section:9bd383301a5a4a551411","kind":"section","labels":[],"line_end":16,"line_start":10,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Die beschleunigte kosmische Expansion verlangt eine konsistente Erklärung im Gesamtmodell. Für TFPT ist besonders schwierig, eine passende effektive Vakuumwirkung zu erhalten, ohne sie bei jedem neuen Beitrag nachzujustieren. Der Mechanismus müsste seine Größe und Stabilität gegenüber Korrekturen erklären.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dunkle Energie: ein kleiner Rest mit großen Folgen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3656,"byte_start":2590,"id":"section:25e85720858fbf6d9643","kind":"section","labels":[],"line_end":21,"line_start":17,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Die Schwarzlochfrage verbindet Quanteninformation, Gravitation und die Wahl zugänglicher Teilsysteme besonders eng. In bestimmten berechenbaren Modellen verändern Quanteneffekte die extremale Fläche und damit die Zuordnung rekonstruierbarer Information. Die verallgemeinerte Entropie enthält einen Flächenbeitrag und einen Quantenfeldbeitrag. Das ist erheblicher theoretischer Fortschritt in diesen Modellen, aber noch k","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Schwarze Löcher: Information kann die Aufteilung selbst betreffen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4418,"byte_start":3656,"id":"section:ce780ca6f5b8e674e0a0","kind":"section","labels":[],"line_end":26,"line_start":22,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"Äquivalenztests wie MICROSCOPE prüfen die Universalität des freien Falls für unterschiedliche Materialien mit hoher Genauigkeit. Eine neue Quelle für Raumzeit muss daher erklären, warum verschiedene innere Zusammensetzungen auf dieselbe effektive Geometrie reagieren. F18","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gravitation muss sehr verschiedene Inhalte gleich behandeln","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6966,"byte_start":4418,"id":"section:6d41bd46d33a8712a3b5","kind":"section","labels":[],"line_end":43,"line_start":27,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/15_schatten_offene_phaenomene.tex","status_markers_as_written":[],"summary_excerpt":"L32mmL56mmL60mm Thema& Was den Ansatz einschränkt& Was eine Erklärung liefern müsste\\\\ Zeitpfeil&Beständige Aufzeichnungen und irreversible Makroprozesse bei oft reversiblen Grundgleichungen.&Zustandsauswahl, Anfangskorrelationen, Zugriff und Entropiefluss; keine bloße Benennung eines inneren Parameters als Zeit.\\\\ Messproblem&Interferenz und stabile Messergebnisse müssen zusammen beschrieben werden.&Ein vollständige","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Weitere offene Stellen mit unterschiedlicher Beweiskraft","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":947,"byte_start":0,"id":"section:6270bf272a4c8e401e43","kind":"chapter","labels":["ch:shadow-synthesis"],"line_end":7,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Die zusammengetragenen Schatten sprechen am stärksten für eine Struktur von Zusammensetzungen und gemeinsamen Antworten. Arithmetik verlangt eindeutig kombinierbare primitive Faktoren. Quantenphänomene verlangen Phasen, Kontexte und eine besondere Zusammensetzung von Teilsystemen. Raumzeit verlangt eine skalenstabile Ordnung von Nachbarschaften, Signalwegen und Anfangsdaten. Keine dieser Forderungen wird durch die Za","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein engeres Bild und ein neues berechenbares Puzzleteil","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2397,"byte_start":947,"id":"section:fd626374a8e99ccde304","kind":"section","labels":[],"line_end":20,"line_start":8,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Die bildhafte Aussage Alles ist aus Primzahlen gebaut lässt sich zu einer brauchbareren Hypothese präzisieren: Ein möglicher gemeinsamer Ursprung besitzt elementare, zusammensetzbare Operationen. In einem kommutativen arithmetischen Schatten erscheinen primitive Faktoren. Vor dieser Auslesung bleiben zusätzliche Phasen, Kontexte und Aufzeichnungen erhalten. Räumliche Nachbarschaft und Zeitordnung müssten aus den erla","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine engere Arbeitshypothese","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":4907,"byte_start":2397,"id":"section:981bccdd3d93e7dacfa0","kind":"section","labels":["eq:arithmetic-projective"],"line_end":61,"line_start":21,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Die folgenden Formeln sind eine neue Anschlusskonstruktion für dieses Buch. Ihre Zutaten sind Standardoperatoren; sie beanspruchen keine neue allgemeine mathematische Entdeckung. Sie zeigen jedoch exakt, dass ein gemeinsamer arithmetischer Endpunkt unterschiedliche kohärente Geschichten besitzen kann.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein konstruktiver Versuch: gleiche Zahl, verschiedene Phasen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5784,"byte_start":4907,"id":"section:01c10dcae8c9fdb81afc","kind":"subsection","labels":[],"line_end":69,"line_start":62,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Ein Kontrollqubit speichert kohärent, welcher der beiden Wege durchlaufen wurde. Setze [formula in source] und [formula in source] . Nach einer Hadamard-Auslesung des Kontrollqubits gelten [formula in source] Ohne die lokalen [formula in source] -Markierungen wäre [formula in source] und damit [formula in source] . Die neue Rechnung kontrolliert dies im Zahlfenster [formula in source] exakt. Die benutzten Wege ab [fo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine vollständig bestimmte Vorhersage im Modell","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7119,"byte_start":5784,"id":"section:0bb57280acbd6998f6bd","kind":"subsection","labels":[],"line_end":76,"line_start":70,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Gelöst ist eine kleine Kompatibilitätsfrage: Unbegrenzte arithmetische Zusammensetzung und ein endlicher lokaler Quantenbaukasten lassen sich in einem expliziten gemeinsamen Modell verbinden. Der rein arithmetische Schatten kann kommutativ sein, während kohärent zugängliche Wegrelationen eine nichttriviale Phase behalten. Das passt genau zum Motiv der vorherigen Echoexperimente.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was damit gelöst ist und was nicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9085,"byte_start":7119,"id":"section:13619c0952c87b436292","kind":"section","labels":[],"line_end":97,"line_start":77,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"Man könnte einen arithmetischen Raum, ein Quantensystem und ein geometrisches Modell einfach nebeneinanderstellen: [formula in source] Bei Produktzustand und unabhängig wirkenden Operationen passen dann vielleicht alle Einzelstatistiken. Der gemeinsame Ursprung wäre dadurch nicht erklärt. Nötig sind gemeinsame Relationen und überprüfbare Antworten auf gemischte Eingriffe. Die oben konstruierte Wegphase ist ein kleine","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum getrennte passende Modelle noch keine gemeinsame Quelle sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11082,"byte_start":9085,"id":"section:5ccf2401505e3ebfb626","kind":"section","labels":[],"line_end":111,"line_start":98,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/16_schatten_synthese.tex","status_markers_as_written":[],"summary_excerpt":"L37mmL60mmL51mm Gewonnene Präzisierung& Konkretes Ergebnis& Nächste fehlende Bedingung\\\\ Logarithmische Skala&Multiplikative Additivität plus Monotonie erzwingen [formula in source] .&Native Begründung der Ordnung und Energieskala.\\\\ Unbegrenzte Primfamilie&Endlich viele additive Grundtakte tragen nicht alle [formula in source] .&Eine passende wachsende Familie oder reichere Dynamik.\\\\ Arithmetik und Phase&Zwei Multi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Welche Puzzleteile jetzt enger gefasst sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":82,"byte_start":0,"id":"section:9e6aede2b151b89e62d7","kind":"chapter","labels":["app:shadow-sources"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Erweiterung: Quellen und genaue Prüfgrenzen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4118,"byte_start":82,"id":"section:df883b4e7a2ccf794d52","kind":"section","labels":[],"line_end":29,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":["relation:93a5c22acd6cfa91a428"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"Die Erweiterung wurde am 14. September 2026 gegen verfügbare Originalabschnitte im lokalen Repository tfpt-theoryv4 abgeglichen. Der gelesene Git-Stand war 66b91e40e245569f06ab440ead80f446c9be0ee5. Dies identifiziert den Checkout; es behauptet keinen frischen vollständigen Beweis- oder Testlauf. Die tatsächlich verwendeten Dateiinhalte sind zusätzlich mit SHA-256 im Paket erfasst, auch soweit der Arbeitsbaum von Git ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zusätzlicher Einblick in den RH-Forschungsbestand","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6033,"byte_start":4118,"id":"section:659df24a89a62a734a06","kind":"section","labels":[],"line_end":38,"line_start":30,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"Der separate Prüfer verify_shadows.py importiert keinen ursprünglichen TFPT- oder RH-Code und keine Nullstellentabellen. Er enthält 126 exakte beziehungsweise symbolische Bedingungen und zwei numerische Kontrollen. Die Nummer der ersten Nullstelle im Eta-Diagramm ist ein ausdrücklich eingesetzter Referenzwert; das Diagramm ist kein eigener Nullstellensuchlauf.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die 128 zusätzlichen Bedingungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10751,"byte_start":6033,"id":"section:6848da5a76bc1d3d89ae","kind":"section","labels":[],"line_end":62,"line_start":39,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":["relation:652e2cb6c007181f0d92","relation:fa310ddb98159e13f805"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"Die folgenden Quellen wurden zur Erweiterung aufgerufen. Es handelt sich um gezielte Literaturauswahl, nicht um einen vollständigen systematischen Review aller Veröffentlichungen bis September 2026. Eigene Formeln, Gegenbeispiele und Illustrationen sind im Haupttext als solche bezeichnet. Neue Preprints bleiben als Preprints kenntlich. M. V. Berry, J. P. Keating: The Riemann Zeros and Eigenvalue Asymptotics. SIAM Rev","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zusätzliche Primärliteratur","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":11375,"byte_start":10751,"id":"section:44e862561a8b2194a3be","kind":"section","labels":[],"line_end":64,"line_start":63,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/17_schatten_quellen.tex","status_markers_as_written":[],"summary_excerpt":"Das aktualisierte Quellpaket enthält beide unabhängigen Prüfer, beide Ergebnisdateien, die zusätzlichen drei Vektorplots, die LaTeX-Diagramme, das RH-Quellenmanifest und die ausgewählten Katalogeinträge. Die fünf neuen Hauptkapitel sind in dieselbe LaTeX-Datei eingebunden; ursprüngliche Textteile wurden nur um Versionshinweise und Querverweise ergänzt. Das fertige PDF wird weiterhin mit LuaLaTeX gebaut. Die beiliegen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproduktion der erweiterten Fassung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":76,"byte_start":0,"id":"section:27233be87a9673f74e0f","kind":"chapter","labels":["ch:audit13"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die sechs neuen Quellen: geprüfte Korrekturen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":593,"byte_start":76,"id":"section:6385cd9db19aa22b0551","kind":"section","labels":[],"line_end":5,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Die sechs zusätzlichen Unterlagen heißen im neuen Quellenregister N1 bis N6; die ursprünglichen S01 bis S11 bleiben unverändert. Ihr Audit trennt exakte endliche Identitäten, numerische Spektren und zusätzliche Modellannahmen. 100 eigene Bedingungen bestanden: 78 exakte beziehungsweise Integritätsprüfungen und 22 numerische. Die anschließende gemeinsame Ausführung hat einen eigenen 231-Bedingungen-Vertrag. Diese Zähl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was gegenüber v1.1 neu ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":2635,"byte_start":593,"id":"section:5bc9d0aacdc63094a85b","kind":"section","labels":[],"line_end":28,"line_start":6,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Setze [formula in source] und [formula in source] . Der Wedge-Kanal besitzt Für [formula in source] verschwindet [formula in source] . Beide geordneten Wege enden im gleichen virtuellen Zustand und interferieren. Orthogonale Records für [formula in source] und [formula in source] ersetzen dies durch [formula in source] : Der antisymmetrische Rang-6-Kanal wird zum Rang-12-Kanal. Bei gleichem Energienenner entsteht ein","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die zentrale Reparatur: Wege nicht zu früh unterscheiden","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":3264,"byte_start":2635,"id":"section:c0e41a6fba1d4ce495da","kind":"section","labels":[],"line_end":35,"line_start":29,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Mit [formula in source] und [formula in source] ist auf [formula in source] unitär und kollektiv [formula in source] -kovariant. Alle [formula in source] liefern für Materieeingänge denselben ersten blockdephasierten Schatten. Dennoch wirkt [formula in source] dort als [formula in source] , während [formula in source] als [formula in source] wirkt: [formula in source] kehrt als [formula in source] oder als [formula i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der erste Schatten wählt die Fortsetzung noch nicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":5090,"byte_start":3264,"id":"section:e15e155e279e9c8eec11","kind":"section","labels":[],"line_end":59,"line_start":36,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für genau zwei vollständige [formula in source] -Zellen und eine positive Brücke gelten die Formeln aus Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der allkopplige Zweizellenbeweis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6474,"byte_start":5090,"id":"section:2aa1af74ff59a1ac5ace","kind":"section","labels":[],"line_end":77,"line_start":60,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Im ausgewiesenen harmonischen Modell eines geteilten Vermittlers lautet der symmetrische aktive Block Sein niedriger Zweig beginnt mit [formula in source] ; der antisymmetrische mit [formula in source] . Deshalb ist auf dem aktiven [formula in source] -Raum Nach Abzug beider Einzelbondkorrekturen [formula in source] bleibt Beide Schreibweisen sind kompatibel. Eine Konstante auf dem aktiven Sektor ist außerhalb davon ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vierte Ordnung und unterschiedliche Subtraktionskonventionen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":7332,"byte_start":6474,"id":"section:63f4c64732e210245b88","kind":"section","labels":[],"line_end":90,"line_start":78,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] gilt Mit [formula in source] und [formula in source] folgen Ein kohärentes Achtzweigregister liefert aus dem früheren Zweisingulett-Eingang [formula in source] Erfolg [formula in source] . Alle acht Ausgänge haben Gewichte [formula in source] . Dies ist eine exakte Alternative zur alten 32-Zweigschaltung. Kontrollierte kontinuierliche Sternpulse und Register bleiben zusätzliche Ressourcen. Erz","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein exakter Stern-Spektralfilter unter zusätzlichen Ressourcen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":8009,"byte_start":7332,"id":"section:5e577868641c8c010e69","kind":"section","labels":[],"line_end":98,"line_start":91,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"In der Inzidenzfamilie [formula in source] sind die beiden relevanten Entropien Strikte Konkavität liefert verschiedene Maxima: [formula in source] für Kontexte und [formula in source] für Strahlen. Letzterer Prozess hat Rang 60. Erweitert man den Nachfolgerträger, entstehen symmetrieverträgliche Ränge 15 und 16. Weder maximale Entropie noch minimale Rangzahl wählt die Regel ohne erklärte Klasse. Die passive separate","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Einfachheit braucht einen Auslesevertrag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10096,"byte_start":8009,"id":"section:b6eb85a2f386143c59c2","kind":"section","labels":[],"line_end":113,"line_start":99,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/18_audit_v13.tex","status_markers_as_written":[],"summary_excerpt":"Zwei Singulettläufe finden mindestens vier orthogonale Moden bei [formula in source] über [formula in source] , Residuen unter [formula in source] . Das Dublett ist widerlegt; ein exakter oberer Multiplizitätsbeweis fehlt. -Typen.] 960 gleichgradige Wurzelsummen gehen nach [formula in source] ; gemischt ergeben sich 640 und 192 Summen nach Grad null sowie 64 Cartanfälle. Der vorgeschlagene gemischte Kanal nach [formu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Weitere architektonisch wichtige Korrekturen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":561,"byte_start":0,"id":"section:a119f0430f34dfebca5c","kind":"chapter","labels":["ch:execution13"],"line_end":5,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Aktualisierung v1.5: weniger zusätzliche Steuerung Die hier eingeführte gemeinsame Record-/Präparations-/Mehrzeitausführung lässt sich jetzt bei festem [formula in source] ohne negative Evolutionszeiten anschließen. Endliche Q-Gatezeiten sind unter einem ausdrücklich belegungserhaltenden Gatevertrag mitgerechnet. Wedge-Kopplung, Q, adressiertes An/aus und Reset bleiben zusätzliche Ressourcen; Details in Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine gemeinsame Ausführung für Record, Präparation und Mehrzeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1259,"byte_start":561,"id":"section:b13a3672fe01b6bc0101","kind":"section","labels":[],"line_end":10,"line_start":6,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Dieselbe korrigierte Vermittlungsoperation erzeugt jetzt Aufzeichnung, kontrollierte Näherungspräparation und Mehrzeitantwort. Die tatsächlichen Quellprojektoren, Paulioperationen und die Dreierclock wurden benutzt. Ein bereits präpariertes [formula in source] oder ein separater Präparations-Hamiltonoperator wird nicht benötigt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine Konstruktion, aber ein ausdrücklich zusätzlicher Ressourcenvertrag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2066,"byte_start":1259,"id":"section:b7ca242dbf64e5d55b37","kind":"section","labels":[],"line_end":30,"line_start":11,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Mit [formula in source] , [formula in source] und [formula in source] gilt Kopiere nur die Vermittlerbelegung, nicht das geordnete Farbwort: Dann ist auf allen 44 Dimensionen Der Vermittler kehrt zurück. Auf Materie und Pointer bleibt [formula in source] , [formula in source] , mit Beide Krausoperatoren gehören zum Instrument; ihre Effekte summieren sich zu [formula in source] . Ein ungemessener Pointer bleibt kohäre","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die vollständige Recordoperation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3356,"byte_start":2066,"id":"section:bbf35c1cb0c9581304cc","kind":"section","labels":[],"line_end":46,"line_start":31,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für vier Materieträger und höchstens einen aktiven Vermittler sei Alle sechs [formula in source] wurden auf dem vollen Materieraum rekonstruiert: [formula in source] , [formula in source] , [formula in source] . Andere Vermittlersektoren bleiben bei einer adressierten Operation unverändert. Die Kanten haben orthogonale Ausgänge; verschränkte Zuschauer sind eingeschlossen. Dies ist ein vollständiges sequenzielles Prot","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein gemeinsamer Träger und ein fester Schritt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4037,"byte_start":3356,"id":"section:024883d05b8c169b8dcb","kind":"section","labels":[],"line_end":58,"line_start":47,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Rechenbasis- und uniformer Projektor gehören zu den 60 tatsächlichen Quellprojektoren. Die Swap-Identität verwendet dieselben 16 Quell-Paulis: Für Messausgang [formula in source] und Ziel [formula in source] liefert die Bitverschiebung Damit ist [formula in source] . Vier lokale Resets erzeugen [formula in source] sogar aus verschränktem Eingang. Messung und Feedback bleiben Ressourcen, keine hergeleitete kosmologisc","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Quellseitiger Reset ohne vorpräpariertes Zielreservoir","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6085,"byte_start":4037,"id":"section:205a849e9c661aaa3b0c","kind":"section","labels":[],"line_end":87,"line_start":59,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Akzeptiere in jeder Sternrunde die Recordfolge 111: Alle acht ersten Recordfolgen haben Wahrscheinlichkeit [formula in source] . [formula in source] wird erst zur Zielprüfung definiert. Im 24-dimensionalen Raum der verschiedenen Farbanordnungen gilt exakt Dieser Raum trägt die treue reguläre Darstellung von [formula in source] . Die polynomialen Identitäten der Gruppenalgebra gelten daher auch auf allen 256 Materiedi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wiederholung präpariert den Viererzustand kontrolliert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7720,"byte_start":6085,"id":"section:6b86dbce48e071a54eed","kind":"section","labels":[],"line_end":109,"line_start":88,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Nach erfolgreicher Präparation folgen lokaler Quelltick [formula in source] , zweimal [formula in source] , Rücknahme [formula in source] und dasselbe [formula in source] -Runden-Filter. Ein ideales kostenloses [formula in source] -Messgerät wird nicht eingesetzt. Protokoll R behält denselben kohärenten Pointer; Protokoll F verwendet beim zweiten Schritt einen frischen. Mit [formula in source] lauten die gemeinsamen ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Derselbe Filter liest die Mehrzeitantwort aus","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8690,"byte_start":7720,"id":"section:a086e06951fb6f5936f9","kind":"section","labels":[],"line_end":118,"line_start":110,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Das neue Register ist nicht Clifford: Ein vierqubitiger Pauli hat Spur null oder [formula in source] . Noch konkreter erzeugt der Quellinput [formula in source] genau 13 nichtverschwindende Rechenbasisamplituden. Das ist kein reiner Stabilizerzustand, dessen Trägergröße eine Zweierpotenz ist. Nur Cliffordoperationen, Stabilizer-Hilfszustände und Pauli-Messungen reichen auch mit Feedback nicht aus. Andere Kodierungen ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was für eine native Implementierung noch fehlt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9479,"byte_start":8690,"id":"section:01d17811a6df29ed63d0","kind":"section","labels":[],"line_end":125,"line_start":119,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Alle [formula in source] kommutieren mit [formula in source] ; der ungelesene Kanal erhält das Zielgewicht. Seine einzelnen Dephasierungen sind orthogonale Hilbert–Schmidt-Projektionen. Ein Fixpunkt ihres Zyklus kann bei keinem Schritt Norm verlieren und liegt deshalb im Schnitt der Fixräume: in der Kommutante der [formula in source] -Wirkung. Deren Dimension ist Die spurlose Dimension 3875 identifiziert keinen gleic","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ungelesener Austausch ist keine Kühlung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10559,"byte_start":9479,"id":"section:2a102158cb03538e0db1","kind":"section","labels":[],"line_end":129,"line_start":126,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/19_execution_v13.tex","status_markers_as_written":[],"summary_excerpt":"Ein nativer Adapter muss [formula in source] , [formula in source] , Kern und Belegung gemeinsam liefern, beim Half-Charge-Feld zusätzlich mit Domänen- und Energiekontrolle. Er muss den 13-Amplituden-Eingang, beide Recordzweige und die Acht-Runden-Echos reproduzieren, einschließlich Hilfszuständen und Fehlerausgängen. Erst anschließend ist eine skalierende Zellfamilie sinnvoll auf Geometrie, Chiralität und Spin 2 zu ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Abnahmetests und T1–T8-Grenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":87,"byte_start":0,"id":"section:ed96de30a82e85712ac1","kind":"chapter","labels":["app:release13"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Versionspaar v1.3: Quellen, Abdeckung und Reproduktion","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":812,"byte_start":87,"id":"section:079a9e83111f55be2550","kind":"section","labels":[],"line_end":7,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"Diese Ausgabe führt das 90-seitige Hauptbuch v1.1 vollständig fort; die kompakte 35-seitige Compiler-Fassung v1.2 ist nicht ihre Basis. Alle ursprünglichen 21 Hauptkapitel und vier Anhänge bleiben zugänglich. Hinzu kommen drei neue Hauptkapitel und dieses Quellenregister.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei Dokumente mit unterschiedlichen Aufgaben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2181,"byte_start":812,"id":"section:2674cdfc38ac21ad58d7","kind":"section","labels":[],"line_end":18,"line_start":8,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"Die alten IDs S01–S11 bleiben unverändert. N1–N6 bezeichnen die sechs bereits archivierten Konsolidierungen: Fable-Konsolidierung, Sol-Rekonstruktion, kurze Universalraum-Konsolidierung, Q-Audit/U-Regel, TFPT-Rekonstruktion und Sechs-Prüfpunkte-Analyse, jeweils vom 14. September 2026. Originaltexte und Hashes stehen im Sechs-Quellen-Auditpaket.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neue Quellen und unveränderte Originale","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":3388,"byte_start":2181,"id":"section:ca281b37b0a7908217a5","kind":"section","labels":[],"line_end":30,"line_start":19,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"L37mmL30mmL83mm Paket&Umfang&Prüfgrenze\\\\ Basisbuch v1.1&210 Bedingungen&Historische Basisprüfung; nicht erneut vollständig ausgeführt.\\\\ Schatten v1.1&128 Bedingungen&Historische Erweiterung; alte RH-Aktualitätsgrenze bleibt sichtbar.\\\\ Sechs-Quellen-Audit&100 eigene&78 exakt/Integrität, 22 numerisch; in dieser Ausgabe redaktionell integriert.\\\\ Gemeinsame Ausführung&231 eigene exakte&Für Ausgabe v1.3 erneut ausgefü","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Evidenz nicht durch Addition aufwerten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4019,"byte_start":3388,"id":"section:53b3fb2e34297865007e","kind":"section","labels":[],"line_end":39,"line_start":31,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"Die wissenschaftlichen Pakete liegen unter experiments/theory-contracts/universalraum-six-source-audit-20260914 experiments/theory-contracts/compiler-single-execution-20260914 experiments/theory-contracts/universalraum-paired-release-20260914/new-input-audit Das dritte enthält den neuen endlichen Prüfer, seine Normal-/Optimierungsausgaben und die gesonderte Singulettrechnung. Das Releaseverzeichnis enthält LaTeX, all","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Rechen- und Dokumentpakete","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":4864,"byte_start":4019,"id":"section:1a0475d8c3d66f4c0d06","kind":"section","labels":[],"line_end":43,"line_start":40,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/20_release_v13.tex","status_markers_as_written":[],"summary_excerpt":"Der RH-Aktualitätslauf scheiterte an einem fehlenden referenzierten Quellenordner. Der konfigurierte separate Faktorgraph ist nicht verfügbar. Die ausgewählte Originalroute r647 und die verfügbaren Beweise wurden gelesen; keine vollständige globale Aktualität wird behauptet. Es wurde kein RH-Abschlussmarker geändert und keine neue arithmetische Kampagne gestartet.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Aktualität und ausdrücklich fehlende Prüfungen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":1268,"byte_start":0,"id":"section:0f48945f73c6d39427c3","kind":"chapter","labels":["ch:newinputs13"],"line_end":8,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Aktualisierung v1.5: ein fester Puls ist nicht ein festes Detuning Die unten gezeigte Schranke eines einzigen verstimmten Pulses bleibt richtig. Eine endliche Folge positiver Pulse mit diskreten Q-abgeleiteten Belegungs-Z-Kicks und zwei Off-Intervallen erreicht dagegen vollständigen phasenrichtigen Transfer. Der fehlende Einzelpuls beweist also kein Verbot einer Kompositfolge. Siehe Kapitel Aktualisierung v1.4 Dieses","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei weitere Eingaben: Mikrodynamik und deterministische Präparation","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":2094,"byte_start":1268,"id":"section:45c6f52e23a5ee394892","kind":"section","labels":[],"line_end":13,"line_start":9,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Die während der Konsolidierung zusätzlich eingereichten Texte N7 und N8 enthalten neue Resultate, nicht nur Zusammenfassungen. N7 berichtet die vollständige vierte Ordnung eines harten CAR-Referenzmodells, einen mikroskopischen Stern und einen Relaxationskanal. N8 konstruiert einen harten Tensorproduktkandidaten mit globaler Bandschranke und eine deterministische ideale Präparation.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Prüfurteil und Modellgrenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3378,"byte_start":2094,"id":"section:0d61d81c1268a9a4f082","kind":"section","labels":[],"line_end":34,"line_start":14,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"N7 verwendet Dieser Operator ist unitär, aber im Gegensatz zu [formula in source] aus Kapitel Das ist kein Widerspruch, sondern eine verschiedene Phase des Rückwegs. Beim Recordaufbau ist der tatsächliche Adjungierte nötig: [formula in source] reproduziert dieselbe Materie-Aufzeichnung wie [formula in source] , unter Einschluss der Pointertensorfaktoren. Blindes Ersetzen beider [formula in source] durch [formula in s","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei richtige unitäre Vertizes, aber nicht derselbe Schritt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5429,"byte_start":3378,"id":"section:2c04c314ee8371239dc8","kind":"section","labels":[],"line_end":56,"line_start":35,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] lautet der eingereichte Referenzoperator [formula in source] vertauscht die beiden vollständigen Paare. Die 40 Clebsch-Kanten ergeben 40 Einzelkanten-, 160 überlappende und 60 gleichlabelige disjunkte Beiträge. Jede Labelklasse ist ein Matching; gleiche Labels teilen keinen Endpunkt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der vollständige vierte-Ordnungs-Operator","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6880,"byte_start":5429,"id":"section:eee8fd73a22a4e2140bb","kind":"section","labels":[],"line_end":80,"line_start":57,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Der gesamte 24024-dimensionale Singulett-Multiplizitätsraum wurde aus Youngs orthogonaler Darstellung aufgebaut. Ein neuer Lauf mit zwölf niedrigen Eigenvektoren ergab Beim zweiten Niveau wurden vier orthogonale Moden gefunden. Die größte Eigenvektorresiduen-Norm des Laufs liegt unter [formula in source] . Das ist eine hochgenaue endliche Rechnung, kein algebraischer oberer Multiplizitätsbeweis.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die neue Singulettantwort ist unabhängig reproduziert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":7959,"byte_start":6880,"id":"section:09c9febe9236c6814938","kind":"section","labels":[],"line_end":94,"line_start":81,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"N8 definiert 16 harte Ortsfaktoren [formula in source] und sechs Bosonmoden pro Vektorlabel. Bei Gesamtladung [formula in source] ist der Sektor endlich. Für gilt [formula in source] . Denn der antisymmetrische Umwandlungsblock [formula in source] erfüllt [formula in source] und [formula in source] . Die selbstadjungierte Offdiagonalblocknorm ist dieselbe. Daher Der führende Austausch ist dann [formula in source] . D","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine globale Bandschranke, aber kein genauer Niedrigenergiefehler","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9713,"byte_start":7959,"id":"section:96eb48630489f156f280","kind":"section","labels":[],"line_end":111,"line_start":95,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] gilt [formula in source] . Definiere [formula in source] mit [formula in source] . Dann In der Basis [formula in source] ist [formula in source] , [formula in source] , [formula in source] . Die unerwünschte Amplitude ist Sie verschwindet für die angegebene Wurzel exakt. Die ideale Phase ist [formula in source] . Es ist eine konkrete Anwendung bekannter https://arxiv.org/abs/quant-ph/0005055Am","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Deterministische Präparation im idealen erweiterten Gattermodell","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10980,"byte_start":9713,"id":"section:0575e6986f39621ea44c","kind":"section","labels":[],"line_end":132,"line_start":112,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Gewöhnliche Vermittlerverluste [formula in source] lassen vollständig symmetrische Farbzustände mit Vermittlervakuum dunkel. Auf 16 Trägern hat [formula in source] Dimension [formula in source] . Dieser Raum verhindert einen eindeutigen globalen Attraktor dieser Verlustdynamik.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Relaxation: konstruktiv möglich, aber nicht durch Bosonenverlust allein","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12027,"byte_start":10980,"id":"section:8feea4beaf5803235798","kind":"section","labels":[],"line_end":149,"line_start":133,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Nach einem Paarabbau am Stern ist sein gemeinsamer Mittelpunkt leer; ein zweiter Paarabbau ist unmöglich. Für den geschlossenen Block aus 256 Materie- und 288 Vermittlerzuständen gilt Die untere effektive Matrix ist deshalb exakt Der volle 544-dimensionale Block wurde unabhängig gebaut und diagonalisiert. Bei [formula in source] , [formula in source] sind die niedrige Lücke [formula in source] und das nackte Materieg","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der isolierte mikroskopische Stern: vollständiger kleiner Block","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13070,"byte_start":12027,"id":"section:8f77f8c6fcfc82b45f37","kind":"section","labels":["eq:matched-general"],"line_end":166,"line_start":150,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Für beliebige bekannte Zielüberlappung [formula in source] ist die Fehleramplitude nach zwei angepassten Schritten proportional zu Sie verschwindet bei Die Polynomidentität wurde symbolisch geprüft. Für den angekleideten Stern-Grundzustand und nackten Eingang [formula in source] gilt [formula in source] . Daraus folgt die angepasste Phase Verwendet man bei idealem Zugriff auf den angekleideten Zielprojektor dennoch d","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Begonnenes Follow-up: die Präparation an das Mikromodell anpassen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14355,"byte_start":13070,"id":"section:1ab7c6115e03ba5268e9","kind":"section","labels":[],"line_end":177,"line_start":167,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Bereits der detunierte isolierte Paarblock hat maximale Transferwahrscheinlichkeit Bei [formula in source] , [formula in source] sind das nur [formula in source] . Eine einzelne freie Entwicklung dieses Blocks realisiert daher keinen vollständigen Materie-Vermittler-Tausch [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Begonnenes Follow-up: warum ein einziger fester Puls nicht genügt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15777,"byte_start":14355,"id":"section:2171eb9b53449fc962a9","kind":"section","labels":[],"line_end":196,"line_start":178,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Das Einzelpuls-Hindernis legt einen konkreten Ausweg nahe, sofern zusätzliche Kontrollen zugelassen werden. Im isolierten resonanten Paar, also bei auf null gesetzter Verstimmung, sei Dann lautet seine exakte Entwicklung Mit dem relativen Viertelphasenpuls [formula in source] gilt Die volle 22-dimensionale Identität ist symbolisch geprüft. Zwei Belegungsphasen und ein resonanter Transfer genügen somit unter diesem Ko","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein kurzer positiver Kontrollkandidat für die nächste Revision","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17910,"byte_start":15777,"id":"section:cc48497db6fe6a499272","kind":"section","labels":[],"line_end":209,"line_start":197,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Der singuläre Schur-Satz für [formula in source] benötigt [formula in source] , [formula in source] und [formula in source] . Das Gegenbeispiel [formula in source] , [formula in source] , [formula in source] hat negatives Determinant trotz positivem Schurrest. Kompatible positive Blöcke ergeben eine positive dichte Fortsetzung nur für alle Stufen, die tatsächliche Form und passende Stetigkeit. Die Identität der volls","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Arithmetik: bestätigt ist der Vertrag, nicht die offene Lösung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":19872,"byte_start":17910,"id":"section:c2b11e9e664ccad5f2f7","kind":"section","labels":[],"line_end":225,"line_start":210,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/21_new_inputs_v13.tex","status_markers_as_written":[],"summary_excerpt":"Kann die echte kleine Maschine die nötigen Handgriffe ausführen? Gesucht ist eine kontrollierte Kopplung, die Vermittler hin- und zurückführt und Aufzeichnung erhält. Ein fester freier Puls reicht im geprüften Stern nicht. Abnahme: beide Recordzweige und alle Eingänge, keine versteckten Zielzustände. Können wir den richtigen, angekleideten Zustand auswählen? Die passende Verstärkungsphase ist jetzt berechnet. Es fehl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die wichtigsten nächsten Fragen, einfach ausgedrückt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":96,"byte_start":0,"id":"section:7cd8cbb4d2fd206f26b0","kind":"chapter","labels":["ch:audit14"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/22_audit_v14.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Fünf neue Untersuchungen: Abgleich und stärkere Dynamikkontrolle","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":2247,"byte_start":96,"id":"section:d40794bf028960810354","kind":"section","labels":[],"line_end":18,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/22_audit_v14.tex","status_markers_as_written":[],"summary_excerpt":"Die neuen Originale sind N9 (Fable-Abschlussrunde), N10 (Sol-Runde 2), N11 (Astra-Antwort), N12 (Astra hoch) und N13 (Spark-Gesamtstand). Alle fünf sind unverändert im Quellenpaket archiviert. Ihre internen Arbeitsaufträge sind Forschungsinhalt, keine zusätzlichen Nutzeranweisungen. Der hier ausgeführte Auftrag ist Prüfung, eigene Fortsetzung und anschließende Konsolidierung.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Quellen und drei notwendige Korrekturen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":3400,"byte_start":2247,"id":"section:b6d182d59e23a5987910","kind":"section","labels":[],"line_end":28,"line_start":19,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/22_audit_v14.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] Clebsch-Zellen sind drei Architekturen zu unterscheiden: lrrr Zellen&Eine globale Bank&Eine Bank pro Zelle&Eine Bank pro Kante\\\\ 1&60&60&0\\\\2&280&120&0\\\\3&660&180&0\\\\6&2760&360&0\\\\ Gezählt werden gleichlabelige disjunkte Paarbeiträge vierter Ordnung. Die Formeln sind [formula in source] , [formula in source] und null. Eine endliche Bank pro Zelle bleibt lokal und extensiv, behält aber die inne","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lokalität wählt nicht zwischen zwei lokalen Modellen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":5173,"byte_start":3400,"id":"section:d730ffd0e316d0a9d542","kind":"section","labels":[],"line_end":51,"line_start":29,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/22_audit_v14.tex","status_markers_as_written":[],"summary_excerpt":"Im harten C16-Modell mit [formula in source] sei [formula in source] . Die vollständige Enumeration aller 65536 Ortsmengen bestätigt Gewichte [formula in source] heben im Schurtest die Bosonenwurzeln auf. Die Spaltensumme ist höchstens [formula in source] , die Zeilensumme höchstens [formula in source] . Daher Die daraus gebildete achtstufige Vergleichsmatrix hat Diagonale [formula in source] und Nebendiagonale [form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Bandtrennung bis zum Betriebspunkt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6231,"byte_start":5173,"id":"section:47f7712d36292258028e","kind":"section","labels":[],"line_end":65,"line_start":52,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/22_audit_v14.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] und [formula in source] gilt Dies definiert das endliche allordentliche Problem, ohne seine riesigen Inversen numerisch ausgewertet zu haben. Mit [formula in source] , [formula in source] , [formula in source] , [formula in source] begrenzen zwei Resolventenidentitäten den Rest des energieabhängigen Kerns nach [formula in source] durch Bei [formula in source] reproduziert dies [formula in sour","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der exakte Schurvertrag und seine verbleibende Restlücke","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":7252,"byte_start":6231,"id":"section:232629cfc470428532d6","kind":"section","labels":[],"line_end":78,"line_start":66,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/22_audit_v14.tex","status_markers_as_written":[],"summary_excerpt":"Für [formula in source] , [formula in source] und [formula in source] folgt aus [formula in source] und [formula in source] exakt Jeder Clebsch-Stern besteht aus fünf Transpositionen. In der treuen regulären [formula in source] -Darstellung wurde die ganze ganzzahlige Identität [formula in source] auf 720 Dimensionen geprüft. Mit [formula in source] ist sein Spektrum ganzzahlig nichtnegativ; daher ist jeder Summand p","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine einfache positive Darstellung der lokalen vierten Ordnung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":8609,"byte_start":7252,"id":"section:436739b0f23468528c1c","kind":"section","labels":[],"line_end":94,"line_start":79,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/22_audit_v14.tex","status_markers_as_written":[],"summary_excerpt":"Der eigene vollständige Singulettträger reproduziert beide F4-Varianten: lrr &Zellintern geteilt&Pro Kante lokal\\\\ F4-Grundwert&555,488500364&732,120310942\\\\ F4 auf ersten vier Moden&583,292038666&708,209322519\\\\ Gapkoeffizient [formula in source] &13,901769151& [formula in source] \\\\ Danach wurden die niedrigen Eigenwerte des vollständigen trunkierten Operators [formula in source] neu berechnet: Dimension 24024, ach","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Neue Diagonalisierung statt bloßer Rayleighkorrektur","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":551,"byte_start":0,"id":"section:f1a77702947cfc3b348e","kind":"chapter","labels":["ch:micro14"],"line_end":5,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/23_micro_v14.tex","status_markers_as_written":[],"summary_excerpt":"Aktualisierung v1.5: zwei gültige Präparationsverträge Der unten konstruierte exakt selektive Spektralfilter bleibt gültig unter seinen stärkeren Kontrollannahmen. Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eigene Fortsetzung: ein gemeinsames kontrolliertes Mikrolabor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1453,"byte_start":551,"id":"section:b08bf31f7918684f9823","kind":"section","labels":[],"line_end":10,"line_start":6,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/23_micro_v14.tex","status_markers_as_written":[],"summary_excerpt":"Der geordnete Standard-Gittercocycle [formula in source] wurde unabhängig aus einer einfachen E8-Basis aufgebaut. [formula in source] liefert den Kommutatorfaktor, Bilinearität die Cocycle-Identität. Alle 240 Wurzelkoordinaten sind ganzzahlig. Auf den 40 Clebsch-Kanten bestätigt die exakte F2-Elimination Rang 45 für die Antisymmetriegauge der Ortsfarben und Rang 285 für die zusätzliche kantenlokale Vermittlergauge. F","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vorzeichen aus E8 und die noch fehlende Quellbasis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3255,"byte_start":1453,"id":"section:4fcd073e34179a90a9cc","kind":"section","labels":[],"line_end":29,"line_start":11,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/23_micro_v14.tex","status_markers_as_written":[],"summary_excerpt":"Für ausschließlich kantenlokale Vermittler ohne Hopping sind die lokalen Ladungen erhalten. Aus der vollständig belegten Nullbosonquelle folgt [formula in source] . Besetzte Bosonen bilden deshalb ein Matching: Jede Kante trägt höchstens einen, und zwei besetzte Kanten teilen keinen Endpunkt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein allordentlicher CAR-/Tensoradapter im Matchingsektor","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4116,"byte_start":3255,"id":"section:b245612108968ab3d71c","kind":"section","labels":[],"line_end":41,"line_start":30,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/23_micro_v14.tex","status_markers_as_written":[],"summary_excerpt":"Die Kopplung [formula in source] zwischen 256 Materie- und 288 Vermittlerzuständen wurde neu aufgebaut. Sie erfüllt [formula in source] . Der volle Hamiltonoperator ist Seine 14 verschiedenen Energien sind sieben niedrige Werte sechs obere [formula in source] für [formula in source] und [formula in source] mit Multiplizität 67. Die niedrigen Multiplizitäten sind [formula in source] ; die sechs oberen wiederholen die ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der vollständige Stern, nicht nur sein niedriger Schatten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6346,"byte_start":4116,"id":"section:33c4dbd9d55ba8faa5ea","kind":"section","labels":[],"line_end":62,"line_start":42,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/23_micro_v14.tex","status_markers_as_written":[],"summary_excerpt":"Für jeden anderen Energiewert [formula in source] setze [formula in source] ist der akzeptierte Krausoperator eines Hadamardtests mit kontrollierter Entwicklung. Alle Faktoren erhalten den Zielzustand, und der [formula in source] -te Faktor löscht den Eigenraum zu [formula in source] . Weil sie Funktionen desselben [formula in source] sind, gilt auf dem ganzen Raum Es ist kein gemeinsames kommensurables Wiederkehrint","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein exakter endlicher Filter aus wirklichen Entwicklungszeiten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":7745,"byte_start":6346,"id":"section:7d4ee27b50d562f765fb","kind":"section","labels":[],"line_end":84,"line_start":63,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/23_micro_v14.tex","status_markers_as_written":[],"summary_excerpt":"Eine ideale kohärente Entkleidung ist für erfolgreiche Zustandspräparation nicht nötig. Nach dem Filter wird die Vermittlerbelegung gemessen. Im leeren Zweig bleibt exakt nacktes [formula in source] . Mit gilt auf nackter Materie Dies ist der gesamte akzeptierte Krausoperator und wurde als volle Matrix geprüft. Aus dem elementaren Zweisingulett [formula in source] mit [formula in source] beträgt die Ausbeute [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Noch einfacher: die Hülle messen und die Ausbeute mitführen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9259,"byte_start":7745,"id":"section:728b1ab27185e50853a3","kind":"section","labels":[],"line_end":97,"line_start":85,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/23_micro_v14.tex","status_markers_as_written":[],"summary_excerpt":"Das neue Protokoll beginnt in nacktem [formula in source] , benutzt den mikroskopischen Sternfilter samt Leerbelegungsherald, danach den lokalen Dreierzyklus [formula in source] , zweimal den resonanten Record, den Rücktick und denselben mikroskopischen Filter zur Schlussprüfung. Der Echoanteil wurde im vollständigen 256D-Materieraum gerechnet; wiederholte Farben werden nicht herausprojiziert.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein vollständiger neuer Präparations- und Echovertrag","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10835,"byte_start":9259,"id":"section:bb4444694449ff2fde27","kind":"section","labels":[],"line_end":117,"line_start":98,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/23_micro_v14.tex","status_markers_as_written":[],"summary_excerpt":"Der neue N11-Kanal ist CPTP, mit [formula in source] und [formula in source] . Wegen [formula in source] und [formula in source] folgt Damit ist [formula in source] der einzige stationäre Zustand. 556 Zyklen garantieren [formula in source] Infidelität. Der unabhängige 256D-Lauf kontrolliert die Gewichtsidentität und Kontraktion in jedem der 556 Schritte. Dies ist nicht der ungelesene unitale Recordkanal mit großer Fi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Feedback: Attraktor, Fehlerboden und unabhängige Zellen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1075,"byte_start":0,"id":"section:809a314fe8e6f9788043","kind":"chapter","labels":["ch:fronts14"],"line_end":10,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Aktualisierung v1.5: die aktuelle Frontkarte steht weiter hinten Die folgenden Rechnungen bleiben als v1.4-Befunde erhalten. Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Alle Arbeitsfronten: neue Tests und nächste Beweise","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":2084,"byte_start":1075,"id":"section:df2d867dc25ee357a152","kind":"section","labels":[],"line_end":19,"line_start":11,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Für den bereits konstruierten Strahlengraphen mit betrachten wir die zulässige Lazy-Walk-Familie [formula in source] , [formula in source] . Ein Eigenwert kann nur bei [formula in source] oder [formula in source] verschwinden. Dort sind die Nullitäten 30 beziehungsweise 5; ansonsten ist der Rang 60. Das liefert einen präzisen Rangvergleich innerhalb dieser Familie, aber keine Auswahl über alle denkbaren Compiler.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T1: Auswahl statt nachträglicher Passung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3581,"byte_start":2084,"id":"section:afb66e6fbb394fae3e9d","kind":"section","labels":[],"line_end":32,"line_start":20,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"In einer ausdrücklich zusätzlich gewählten unitären Bosonreferenz liefert das Ladungsfeld [formula in source] auf dem Vakuum die Koeffizienten Der unabhängige Prüfer rekonstruiert diese Identität für [formula in source] bis Niveau 32. Für einen exponentiell abfallenden Modentest [formula in source] ist Dies ist eine konkrete Vakuumkonstruktion und kein Energieabschätzungsbeweis auf allen Zuständen. Das Ladungsfeld li","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T2: Ein konkreter Anfang der analytischen Naht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":4719,"byte_start":3581,"id":"section:4f4015e69b0015ae9c52","kind":"section","labels":[],"line_end":42,"line_start":33,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Für die deklarierte Produktfamilie [formula in source] ist das Spektrum exakt separierbar: Wir berechnen den Wärmetrace ohne eine riesige Matrix anzulegen und bestimmen [formula in source] . Für [formula in source] , [formula in source] ergibt sich näherungsweise [formula in source] . Geprüft wurden [formula in source] und [formula in source] . Die dreidimensionale Probe beschreibt damit 4.194.304 Produktknoten, ohne","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T3: Ein skalierender Raumtest, der seine eigene Grenze zeigt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6590,"byte_start":4719,"id":"section:9e9c96c3b219a890fe42","kind":"section","labels":[],"line_end":54,"line_start":43,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Das einfachste Gitter-Weylsymbol [formula in source] besitzt acht Knoten, je einen an jeder Kombination [formula in source] . Ihre Chiralitäten wechseln; die Summe ist null. Eine anschauliche zweikomponentige Gleichung allein entfernt die zusätzlichen Arten daher nicht. Diskrete Weyl-Walks sind eine mögliche https://arxiv.org/abs/1708.00826Referenzkonstruktion, keine automatische Lösung dieses TFPT-Problems.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T4: Chirale Nullmoden werden gebaut, aber nicht als Familien ausgegeben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7653,"byte_start":6590,"id":"section:3568c8fc1bbcae6af052","kind":"section","labels":[],"line_end":59,"line_start":55,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Die in dieser Revision nachgewiesenen äußeren Bandschranken betreffen die ganze harte Einzelle, nicht nur deren Singulett. Die kantenlokale vierte Ordnung ist positiv und ihre niedrigen Eigenwerte wurden als vollständiger trunkierter Operator neu berechnet. Der mikroskopische Filter benutzt alle Energien des 544-dimensionalen Sterns. Damit sind mehrere zuvor nur effektive Bausteine zu kontrollierbaren endlichen Aussa","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T5: Was die Band- und Filterergebnisse tatsächlich schließen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9702,"byte_start":7653,"id":"section:15346f109af846085b77","kind":"section","labels":[],"line_end":70,"line_start":60,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":["relation:4339ba09e9b5db678f3f","relation:4f08317640c849e9039a","relation:629b53d80f0b95885bda"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Zunächst die Flavourkontrolle: Für dieselben orthonormalen drei Nullmoden auf linker und rechter Seite liefert ein räumlich konstanter Skalarüberlapp [formula in source] . Drei Moden ergeben dann drei gleiche Massen, nicht die beobachtete Hierarchie oder Mischung. Ein zusätzlich gewähltes nichtkonstantes Profil spaltet die Überlappmatrix, führt aber neue Eingaben ein. Das ist ein expliziter Test dafür, dass Modenzähl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T6: Parameter brauchen einen gemeinsamen empirischen Test","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10717,"byte_start":9702,"id":"section:42f54ee06a97e54458a2","kind":"section","labels":[],"line_end":79,"line_start":71,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Für freie massive bosonische Moden mit Lücke [formula in source] hat eine normalgeordnete bilineare Tensorobservable im Vakuum Spektralgewicht erst oberhalb der Zweiteilchenschwelle [formula in source] . Die Gitterproben [formula in source] , [formula in source] , bestätigen die Schwelle eins. Ein transversaler, spurloser Projektor besitzt zwar Rang zwei, verschiebt aber keine Energie zu null. Er erzeugt daher aus di","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T7: Warum ein Tensorbild noch keine Gravitation ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12272,"byte_start":10717,"id":"section:e901986c901ffd404a69","kind":"section","labels":[],"line_end":86,"line_start":80,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Die gemeinsame kontrollierte Ausführung liefert jetzt operative Rohwahrscheinlichkeiten mit bezahlter Präparation, Aufzeichnung und Endprüfung. Sie liefert noch kein physikalisches Quellfunktional, aus dem dieselben Kontrollmöglichkeiten, Zustände, Wirkungen und Observablen folgen. Die fehlende Kante liegt weiter zwischen primitiver Compilerregel und gewähltem Laborvertrag.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T8 und die anderen Arbeitsfronten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13655,"byte_start":12272,"id":"section:54c9e82d4b1c71a5957e","kind":"section","labels":[],"line_end":99,"line_start":87,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"L10mmL65mmL72mm Tor&Neuer substantieller Beitrag&Fehlender vollständiger Nachweis\\\\ T1&Rang- und Entropievergleich, drei lokal unterschiedliche Vermittlerverträge.&Primitive Auswahl von Zuständen, Alternativen, Phasen und Kopplung.\\\\ T2&Vakuumkoeffizienten, Sektorparität und Halbladungsschranke.&Native Halbladung mit Definitionsmenge, Energie- und Adjungiertenkontrolle.\\\\ T3&Skalierende Wärmetrace-Rechnung und gemein","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die acht Tore bleiben einzeln sichtbar","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15702,"byte_start":13655,"id":"section:56e5c6baba7db2916f0f","kind":"section","labels":[],"line_end":110,"line_start":100,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Wer bedient das Labor? Aus einer festgelegten Compilerregel kontrolliertes [formula in source] , Resonanz, [formula in source] , Reset und Kantenisolation ableiten. Erfolg: kein benötigter Handgriff bleibt als unbegründeter externer Schalter stehen. Welche Vermittlerarchitektur wird ausgewählt? Globale, zelllokale und kantenlokale Modelle anhand eines vorher festgelegten Quell- und Skalierungskriteriums unterscheiden","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Sechs nächste Fragen – mit einem klaren Erfolgskriterium","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17799,"byte_start":15702,"id":"section:c89100599a5cea96d680","kind":"section","labels":[],"line_end":120,"line_start":111,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/24_fronts_v14.tex","status_markers_as_written":[],"summary_excerpt":"Die fünf eingereichten Texte N9–N13 sind unverändert archiviert und einzeln durch SHA-256 gekennzeichnet. Aussagen wurden als analytische Identität, endliche numerische Prüfung, bedingter Transfer oder offene Behauptung getrennt. Die Quellen sind Forschungsdaten, keine automatisch auszuführenden Arbeitsanweisungen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Prüfprovenienz und Reproduzierbarkeit","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":664,"byte_start":0,"id":"section:a23b4f5f8f1cdff67f90","kind":"chapter","labels":["ch:execution15"],"line_end":7,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Wo wir jetzt stehen Wir können mehrere Teile der kleinen mathematischen Maschine konkreter bauen. Die Aufzeichnung braucht weniger Spezialsteuerung; große endliche Spektren lassen sich durch eine tatsächlich vorhandene Symmetrie verkleinern; eine ausdrücklich gewählte Kette besitzt berechenbare kritische Dynamik. Noch nicht bewiesen ist, dass dieselbe ursprüngliche TFPT-Regel gerade diese Steuerungen, Kopplungen, Zus","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Version 1.5: eine einfachere gemeinsame Ausführung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2399,"byte_start":664,"id":"section:0514217bbfb6bfd2b2ff","kind":"section","labels":[],"line_end":20,"line_start":8,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Die Texte TFPT Universalraum Fortsetzung, 14.09.2026 NEU und TFPT Universalraum Ergebnisse, 14.09.2026 sind mit der v1.4-Grundlage abgeglichen. Ihre unveränderten Originale liegen als N14 und N15 im Quellenpaket. Interne Arbeitsanweisungen werden als Quelleninhalt, nicht als neue Aufträge behandelt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zwei weitere Eingaben und ihre wirklichen Zusatzinformationen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4171,"byte_start":2399,"id":"section:3275a42ff372533551fd","kind":"section","labels":[],"line_end":45,"line_start":21,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Die beiden Belegungsalternativen besitzen den hellen Hamiltonblock [formula in source] Ein einzelner Puls erreicht bei [formula in source] höchstens [formula in source] Transferwahrscheinlichkeit. Der vorhandene kohärente Belegungszugriff [formula in source] erlaubt aber mit einem separaten Pointer in [formula in source] einen diskreten [formula in source] -Kick. Der Pointer bleibt dabei erhalten. Das ist keine neu a","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Feste Verstimmung, positive Zeiten und ein exakter Record","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5414,"byte_start":4171,"id":"section:58e8dcf107bcda129d44","kind":"section","labels":[],"line_end":65,"line_start":46,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Ein positiver Puls der Dauer [formula in source] ist auf dem hellen Raum nicht genau das Inverse, sondern [formula in source] Die Rückfolge [formula in source] hinterlässt also die aktive Sektorphase [formula in source] . Bei abgeschaltetem [formula in source] korrigiert ein positives Warteintervall [formula in source] die Vermittlerphase. Mit [formula in source] lautet die vollständige, von rechts nach links gelesen","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Rückfolge und ihre bislang gefährliche Sektorphase","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7196,"byte_start":5414,"id":"section:191e29f3a2cdf8ff2b54","kind":"section","labels":[],"line_end":80,"line_start":66,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Die Makrooperation benötigt 24 On-Pulse, zwei Off-Intervalle und 23 Q-Aufrufe. Q-Gates werden nicht als kostenlos ausgegeben. Falls ein zusätzlich deklarierter Generator [formula in source] die Belegung erhält, kann während Q bei [formula in source] geparkt werden. Zum Beispiel realisiert [formula in source] das gewünschte Q. Ein Q-Zeitfenster wird auf [formula in source] aufgefüllt; die kommutierende Drift verschwin","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Endliche Q-Zeiten und wirkliche Präparationskosten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7289,"byte_start":7196,"id":"section:9b70ed6f0a2838f268ad","kind":"chapter","labels":["ch:spectrum15"],"line_end":82,"line_start":81,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Eine wirklich vorhandene Vereinfachung des großen Spektrums","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8374,"byte_start":7289,"id":"section:27a9814c0a03a662d252","kind":"section","labels":[],"line_end":91,"line_start":83,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Auf dem 24024-dimensionalen Spechtraum [formula in source] sei [formula in source] und [formula in source] . Der rationale Projektor [formula in source] besitzt Dimension [formula in source] ; der größere translationsfeste Raum hat Dimension 1764. Die Darstellung [formula in source] erklärt, weshalb dies genau eine Fixlinie je vierdimensionaler Standardkopie isoliert. Auf dem gesamten Isotypieraum ist [formula in sou","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der Standardblock ist nicht mehr nur angekündigt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9384,"byte_start":8374,"id":"section:88e0aa84db8a87a5d248","kind":"section","labels":[],"line_end":107,"line_start":92,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Der ganzzahlige Gruppenalgebraoperator erhält ein Specht-Schnittgitter in seinem rationalen invarianten Teilraum. Daher ist sein charakteristisches Polynom monisch ganzzahlig. Aus [formula in source] folgt die vorab bekannte Koeffizientenabschätzung [formula in source] Siebzehn Primmoduli liefern einen 452-Bit-CRT-Modulus oberhalb der nötigen 428-Bit-Schranke. Eine achtzehnte Primzahl prüft die Rekonstruktion unabhän","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Rationale Intervalle statt nur Dezimalzahlen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":11340,"byte_start":9384,"id":"section:43fa7510b64186bec727","kind":"section","labels":[],"line_end":135,"line_start":108,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Die selbstkonjugierte Youngform besitzt in der orthogonalen Basis die Involution [formula in source] , wobei [formula in source] das Vorzeichen der Zellfolge in Zeilenordnung ist. Die 4-mal-4-Transposition enthält sechs Zelltranspositionen. Damit gelten exakt [formula in source] Alle 1920 Graphautomorphismen sind gerade Trägerpermutationen, also [formula in source] und [formula in source] . Für jeden dieser Automorph","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Tableau-Transposition: 80 wird 40","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12161,"byte_start":11340,"id":"section:9edeabb263801ca530a6","kind":"section","labels":[],"line_end":148,"line_start":136,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Für kantenlokale Vermittler setze [formula in source] und [formula in source] . Dann [formula in source] Die einfache Spiegelung [formula in source] gilt für den korrigierten Hamiltonoperator nicht unverändert. Die G-Blockzerlegung bleibt jedoch richtig. Da [formula in source] ganzzahlige Inhalts-Eigenwerte zwischen 0 und 10 besitzt, folgt [formula in source] Bei [formula in source] bleibt ein garantierter Standardbl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Vierte Ordnung: was erhalten bleibt und was nicht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12242,"byte_start":12161,"id":"section:b1557653481ba4cce1d7","kind":"chapter","labels":["ch:scaling15"],"line_end":150,"line_start":149,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Wie eine niedrige kritische Dynamik möglich wird","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13828,"byte_start":12242,"id":"section:ede34bded5644931575a","kind":"section","labels":[],"line_end":174,"line_start":151,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Für den antisymmetrischen Paarannihilator gilt im harten Materieraum einschließlich Löchern [formula in source] Vier Kanten teilen ein Vermittlerlabel. Operator-Cauchy liefert [formula in source] Somit verbessert sich die C16-Zellbanksumme auf [formula in source] statt der getrennten Farbabschätzung [formula in source] . Eigene Vermittler pro Kante ergeben [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Farbkanäle gemeinsam abschätzen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14656,"byte_start":13828,"id":"section:718039774fdc30d71795","kind":"section","labels":[],"line_end":185,"line_start":175,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Sei [formula in source] eine endliche Zelle mit eindeutigem Grundzustand [formula in source] , Energie [formula in source] und Gap [formula in source] . Auf einem beliebigen endlichen verbundenen Graphen definiere [formula in source] Jeder Swapterm ist positiv. Mit [formula in source] folgt [formula in source] . Der Produktgrundzustand ist eindeutig. Die gleichförmige Einanregung wird von jedem Swap festgehalten und ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein besonders einfaches Verkleben ist als masselose Route ausgeschlossen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16853,"byte_start":14656,"id":"section:b23abbfff15d1a16a854","kind":"section","labels":[],"line_end":219,"line_start":186,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Ein anderer ausdrücklich deklarierter Transfer vertauscht nur [formula in source] mit [formula in source] und verschwindet bei zwei besetzten Zellen: [formula in source] Die Zweizellenblöcke beweisen [formula in source] . Auf einem D-regulären Graphen ist deshalb bei [formula in source] der volle Gap genau [formula in source] , wiederum mit gleichförmiger Einanregung als saturierendem Zustand.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der entscheidende Unterschied: innere Kritikalität bei massiven Vermittlern","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":18911,"byte_start":16853,"id":"section:f4a3f5f63126bf31ba4a","kind":"section","labels":[],"line_end":245,"line_start":220,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Mit allen 30 ersten Farben und reinem Transfer können sich auf der offenen Kette die geordneten Farben nicht überholen. Bei N Teilchen entstehen [formula in source] isospektrale Farbfolgen. Das erzeugt extensive Restentropie und ist keine Familienableitung.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Farbentartung lässt sich symmetrisch reparieren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18985,"byte_start":18911,"id":"section:9dbb0eae727cc7d627c5","kind":"chapter","labels":["ch:clock15"],"line_end":247,"line_start":246,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Rechnen, Zeit und ausgeschiedene Information","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":19968,"byte_start":18985,"id":"section:2164a48369f6c3a9ae4d","kind":"section","labels":[],"line_end":257,"line_start":248,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Ein Pointer-Hadamard verwandelt den Record exakt in einen kontrollierten Ququart-Swap: [formula in source] Kodiert man ein Qubit in den Farben 0 und 2, bleibt das zweite Farbbit null und die Operation ist Fredkin. Mit sauberem Hilfsbit [formula in source] sei [formula in source] . Dann ist [formula in source] genau Toffoli, mit zurückgegebenem [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Aufzeichnung und kohärente Logik benutzen dieselbe Matrix","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":21389,"byte_start":19968,"id":"section:c14f25b3d1f55f826d3e","kind":"section","labels":[],"line_end":268,"line_start":258,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Für ein vorgegebenes Programm [formula in source] setze [formula in source] , [formula in source] und [formula in source] . Der offene History-Hamiltonoperator mit Links [formula in source] und Laplacediagonalen erfüllt exakt [formula in source] Jedes Programm hat also dasselbe Spektrum [formula in source] , wiederholt mit der Datendimension. Feste Zwischenzeit-Auslesungen unterscheiden die Programme, ihre Eigenwerte","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine autonome Uhr ist konstruierbar, aber sie wählt kein Programm","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":22468,"byte_start":21389,"id":"section:0aabd1270e896de4cd4d","kind":"section","labels":[],"line_end":279,"line_start":269,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Auf [formula in source] tragen [formula in source] die Ladungen k/2 und l/2. Die bilaterale Verschiebung [formula in source] ist unitär, hat Norm eins und ein explizites Adjungiertes mit umgekehrter Verschiebung. Sie erhält die Gesamtladung, kippt aber die einzelne Systemparität [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Half-Charge: ein einfacher Adapter benennt die fehlende Ressource","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":23604,"byte_start":22468,"id":"section:812bfb0148c50385e14b","kind":"section","labels":[],"line_end":288,"line_start":280,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Ein universeller unitärer Reset von d orthogonalen Eingaben auf denselben reinen Systemzustand muss d orthogonale Umweltzustände erzeugen. Für m unabhängige Eingaben und finale Infidelität höchstens [formula in source] je Ausgang folgt [formula in source] Man startet die Eingaben maximal gemischt und die Umwelt rein. Unitarität erhält die Entropie [formula in source] ; jeder nahezu reine Ausgang hat Entropie höchsten","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reset ist nur vollständig, wenn die Information irgendwo bleibt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":23689,"byte_start":23604,"id":"section:649061519ddddb4b24fb","kind":"chapter","labels":["ch:frontier15"],"line_end":290,"line_start":289,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die verbleibenden physikalischen Nachweise nach v1.5","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":25540,"byte_start":23689,"id":"section:f381981b6542696bc123","kind":"section","labels":[],"line_end":317,"line_start":291,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Die dokumentierte Massenregel lautet [formula in source] , [formula in source] . Im vollständigen Starobinsky-Potential, mit [formula in source] und [formula in source] , gelten in erster Potential-Slow-Roll-Ordnung [formula in source] Damit erhält man ohne große-N-Abschneidung [formula in source] und die exakte Identität innerhalb dieser Näherung [formula in source] Die betrachtete ACT-Spalte P-ACT-LB2 aus Tabelle 5","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine konkrete empirische Hürde statt freier Nachjustierung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":27129,"byte_start":25540,"id":"section:755f9c59385415ce0682","kind":"section","labels":[],"line_end":335,"line_start":318,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"L13mmL57mmL67mm Tor&Neuer Beitrag&Vollständig fehlender Nachweis\\\\ T1&Fester-Delta-Record, endliche Q-Zeiten, kohärente Logik&Native Wedge-, Q-, Schalt- und Controllerherkunft aus einer primitiven Quelle\\\\ T2&Norm- und energiekontrollierter relativer Half-Charge-Adapter&Renormiertes lokales Feld der tatsächlichen Quelle, E8-/Clock-Zuordnung\\\\ T3&Skalierende Referenzfamilien, exakte Gaps, linearer gefüllter Kettensekt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Alle acht Tore mit genauem Rest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":28605,"byte_start":27129,"id":"section:ffe5c98ef394ea3180e8","kind":"section","labels":[],"line_end":345,"line_start":336,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Native Bedienung: Für jeden Zugriff des kleineren Recordvertrags ein tatsächliches Quellwort oder eine kontrollierte Approximation liefern. Den ganzen Operator samt Zuschauerphasen prüfen, nicht nur Erfolgsamplituden. Gebundene Zwischenzellkoeffizienten: Transfer, Dichte, chemische Verschiebung und Farbaustausch gemeinsam ableiten. Erst eine lokale dynamische Restkontrolle, dann Kritikalität auf der inneren Skala g b","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die sechs nächsten Ziele sind jetzt schärfer","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":29648,"byte_start":28605,"id":"section:51176c1e2c6a0e1d312b","kind":"section","labels":[],"line_end":350,"line_start":346,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Für RH fehlt weiterhin die Identifikation des tatsächlichen signierten Weil-Objekts mit uniformer Positivität und kontrollierten Grenzresten. Das Clock-Spektrum allein kann dies nicht leisten; seine Unabhängigkeit vom eingeschriebenen Programm ist jetzt konkret bewiesen. Der Gatteranschluss liefert für Faktorisierung eine bedingte Quantenrechenressource, aber keine neue klassische Polynomialzeit oder Lösung von P ver","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"RH, Faktorisierung und Hylæan bleiben getrennte Abnahmen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":31204,"byte_start":29648,"id":"section:9ecdb34d612cd3598450","kind":"section","labels":[],"line_end":358,"line_start":351,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/25_revision_v15.tex","status_markers_as_written":[],"summary_excerpt":"Die eigenen Root-Prüfer umfassen 104 Bedingungen, normal und optimiert identisch, mit sechs abgefangenen Fehlermutationen. Die Kontrollfront umfasst 88 Bedingungen einschließlich vollständiger 44D-/88D-Operatoren und rationaler Prozessstatistik. Die Skalierungsfront umfasst 400 Bedingungen und sechs Fehlermutationen. Das Quartettpaket enthält 273 modulare Bedingungen, die vollständige CRT-Rekonstruktion, rationale Wu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was neu geprüft wurde und was die Prüfzahlen bedeuten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":76,"byte_start":0,"id":"section:15b57e7607e72c309a84","kind":"chapter","labels":["ch:v16-labor"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":["relation:894e2b5c0d78c3c950f5","relation:ce5a530fdd47bd3aa8d1"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/26_v16_labor.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"v1.6: Die konsolidierte endliche Ausführung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":706,"byte_start":76,"id":"section:60b18d8885c5860d9ca9","kind":"section","labels":[],"line_end":5,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/26_v16_labor.tex","status_markers_as_written":[],"summary_excerpt":"Die vorläufigen Markdown-Berichte vom 14. September mit Versionsnummer 1.6 waren noch kein aktualisiertes vollständiges PDF. Dieses Kapitel übernimmt ihre wesentlichen Ergebnisse mit ihren jeweiligen Voraussetzungen. Es ersetzt nicht die früheren Beweise, sondern trennt überholte Engpässe, jetzt gelöste endliche Aufgaben und weiterhin fehlende physische Herkunft. Die großen Spektral- und Kosmologieläufe werden hier a","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was neu in dieses Hauptbuch eingeht","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":2936,"byte_start":706,"id":"section:cd1ccf67f76ab8fa53a1","kind":"section","labels":["eq:v16-seed"],"line_end":32,"line_start":6,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":["relation:10d91e88e61447e18ad7","relation:216a441f5d37ca687ce8"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/26_v16_labor.tex","status_markers_as_written":[],"summary_excerpt":"Vier Ququarts werden durch acht Bits kodiert; das erste Bit jedes Ququarts ist niederwertig. Mit dem Swap [formula in source] und [formula in source] sei [formula in source] ist ein Stabilizerzustand. Seine Herstellung aus acht Nullbits benötigt die folgende zeitlich geordnete Schaltung: H auf 0, 1, 2, 5; Z auf 2, 5; CNOT [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein einziger erfolgreicher Record erzeugt die Zelle exakt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5040,"byte_start":2936,"id":"section:ed64c88e81dded625999","kind":"section","labels":[],"line_end":54,"line_start":33,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/26_v16_labor.tex","status_markers_as_written":[],"summary_excerpt":"Die adjungierte Vorbereitung liefert eine aus Operationen zusammengesetzte Schlussprüfung. Man fordert einen neuen Record-Ausgang 1, führt die inverse [formula in source] -Schaltung aus und liest acht Nullbits aus. Der erfolgreiche Krausoperator und sein Effekt sind Der Effekt ist nicht als primitive perfekte Messung eingesetzt. Er wird aus der Schaltung berechnet. Die Messung ist destruktiv und akzeptiert selbst [fo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Schlussprüfung und Mehrzeitvergleich ohne versteckte Ausbeute","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6761,"byte_start":5040,"id":"section:7f6891f1dfbb454c4398","kind":"section","labels":[],"line_end":74,"line_start":55,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":["relation:22fc34bd8eaa053b0838","relation:861cf5bebec52e3df645"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/26_v16_labor.tex","status_markers_as_written":[],"summary_excerpt":"Innerhalb der reinen oder gemischten Acht-Bit-Stabilizerzustände gilt Der dokumentierte Beweis reduziert auf einen Vier-Bit-Stabilizercode mit sechs vorzeichenbehafteten Trägern. Unter allen 307 affinen Unterräumen von [formula in source] sind die maximalen Schnittgrößen für Dimension [formula in source] gleich [formula in source] . Die Schranke [formula in source] gilt in jeder Dimension und wird durch [formula in s","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Optimalität und eine präzise Ressourcengrenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":8064,"byte_start":6761,"id":"section:3b547df8a8d669d5b805","kind":"section","labels":[],"line_end":90,"line_start":75,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/26_v16_labor.tex","status_markers_as_written":[],"summary_excerpt":"Der dokumentierte C16-Nachweis betrifft den gesamten 24024-dimensionalen Singulettsektor des kantenlokalen, abgeschnittenen Operators Unterhalb [formula in source] liegen exakt fünf Eigenwerte: ein nichtentarteter Grundzustand und das folgende Viererband. Die zertifizierten Intervalle lauten mit Lücke größer als [formula in source] . Alle 18 Symmetrietypen wurden im dokumentierten Zertifikat erfasst; die elf übrigen ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Spektren: ein vollständiges Teilproblem, nicht alle Focksektoren","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9600,"byte_start":8064,"id":"section:7e1f9cef9d5de4e210ff","kind":"section","labels":[],"line_end":97,"line_start":91,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/26_v16_labor.tex","status_markers_as_written":[],"summary_excerpt":"In einer ausdrücklich gesetzten Dreiplatz-Wedge-Anordnung mit 112 Zuständen erzeugen die ursprünglichen Vertizes Transport. Für den relevanten Übergang gilt [formula in source] , und die nichtverschwindenden Eigenwerte des angegebenen [formula in source] sind [formula in source] mit Vielfachheit 20 und [formula in source] mit Vielfachheit 4. Die dokumentierte Wahrscheinlichkeit beträgt ungefähr [formula in source] fü","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was bereits wirklich transportiert wurde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11485,"byte_start":9600,"id":"section:4145e7564d61ad844781","kind":"section","labels":[],"line_end":111,"line_start":98,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/26_v16_labor.tex","status_markers_as_written":[],"summary_excerpt":"Die dokumentierte Robustheitsrechnung normiert erst nach Aufsummieren der vollständigen Zweige. Bei [formula in source] und [formula in source] ergibt sie unter den übrigen Idealannahmen Präparationsinfidelität höchstens [formula in source] . Für [formula in source] und [formula in source] bleibt die Vier-Record-Rohtrennung mindestens [formula in source] . Der alte F9-Filter mit dem neuen Eingang [formula in source] ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Fehlerrechnung und gekoppelte Kosmologieprobe","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":104,"byte_start":0,"id":"section:edae03909e3182ed9436","kind":"chapter","labels":["ch:v16-matrix"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":["relation:98c152a664a8f53d5012","relation:ac6f07f0cd1e4fc909ed"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/27_v16_matrix.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"v1.6: Der kleine Matrixkern und das markierte E [formula in source] 8","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1050,"byte_start":104,"id":"section:7dd3c865b32847e10a4f","kind":"section","labels":[],"line_end":7,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":["relation:1ebd7c981624897b042d","relation:56d4e4fbea6d4a050306"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/27_v16_matrix.tex","status_markers_as_written":[],"summary_excerpt":"Die jüngste Eingabe endet mit dem Vorschlag, eine maximale Matrixordnung als möglichen [formula in source] -Träger zu prüfen. Genau diese Rechnung existiert bereits im Repository: compiler-cone-object-audit/ORDER_PROOF.md, Abschnitt 6, und die zugehörige markierte Brücke. Der Prüfer wurde für diese Revision neu ausgeführt, einschließlich der gepinnten Compilerquellen und der Operations- und Clock-Prüfungen. Die frühe","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der übersehene vorhandene Beweis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":2711,"byte_start":1050,"id":"section:0f09d265a168fec90d40","kind":"section","labels":[],"line_end":33,"line_start":8,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/27_v16_matrix.tex","status_markers_as_written":[],"summary_excerpt":"Setze [formula in source] und Die quaternionischen [formula in source] und der zentrale Anker [formula in source] erzeugen einen kleinen gemeinsamen Körper von Operationen. Innerhalb von [formula in source] betrachtet man [formula in source] ist die gaußsche Lipschitz-Ordnung, [formula in source] die hier benannte minimale Erweiterung um die Familieneinheit und [formula in source] ihre im Quellenbeweis bestimmte maxi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Drei Ordnungen im selben kleinen Matrixkörper","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":4698,"byte_start":2711,"id":"section:bdb2bd8a7c116e7faeec","kind":"section","labels":["eq:v16-norm"],"line_end":58,"line_start":34,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":["relation:0ed2b19c7e9f9292996f","relation:4caad19ef28779f5e434"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/27_v16_matrix.tex","status_markers_as_written":[],"summary_excerpt":"Verwendet wird die reelle positive Form Die Spur ist diejenige der komplexen [formula in source] -Darstellung; eine verdoppelte reelle Darstellung darf die Normierung nicht unbemerkt verdoppeln. Aus den vier Matrixeinheiten [formula in source] erhält man die acht ganzzahligen Basisvektoren [formula in source] und [formula in source] . In der Reihenfolge [formula in source] lautet die Gram-Matrix Ihre führenden Hauptm","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum das Längengitter exakt E [formula in source] 8 ist","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6204,"byte_start":4698,"id":"section:29b6f52fcc5f3db32465","kind":"section","labels":[],"line_end":75,"line_start":59,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/27_v16_matrix.tex","status_markers_as_written":[],"summary_excerpt":"Die markierte Quelle verwendet eine Construction-A-Realisierung Für [formula in source] mit [formula in source] definiert der Quellenbeweis Die zugehörige ganzzahlige Basismatrix hat Determinante eins. Sie erhält die Gram-Form, die Wirkung des gaußschen Ankers, die Familienwirkung und alle 240 Wurzeln. Der markierte Repräsentant [formula in source] geht nach [formula in source] . Dies sind wesentlich stärkere Prüfung","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die explizite Brücke zum tatsächlichen Compiler","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":7379,"byte_start":6204,"id":"section:71850c94d0ca15239068","kind":"section","labels":[],"line_end":85,"line_start":76,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/27_v16_matrix.tex","status_markers_as_written":[],"summary_excerpt":"Die hermiteschen Matrizen [formula in source] , [formula in source] , erfüllen [formula in source] . Positivität ergibt einen zukünftigen Lorentzkegel. Das ist eine exakte kinematische Darstellung, aber noch keine Aussage über die Ausbreitung eines Signals.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum Kegel und Clock noch nicht dieselbe Ausführung sind","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":89,"byte_start":0,"id":"section:060f4af037c94c7ade01","kind":"chapter","labels":["ch:v16-operations"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":["relation:8f836bfa3db13c7797a9","relation:f7688ae49f89ac2f0c1c"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/28_v16_operations.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"v1.6: Von inneren Operationen zu wirklicher Bewegung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1054,"byte_start":89,"id":"section:c331bd35a41b015260b6","kind":"section","labels":[],"line_end":11,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/28_v16_operations.tex","status_markers_as_written":[],"summary_excerpt":"Die zweite neue Eingabe unterscheidet selbst einen möglichen Ort [formula in source] , eine [formula in source] -Richtung und ein [formula in source] -Wurzellabel. Diese Trennung ist der richtige Ausgangspunkt. Ein inneres Label kann eine Transformation oder Ladung kennzeichnen, ohne einen räumlichen Platz zu bezeichnen. Eine räumliche Verschiebung braucht dagegen eine Wirkung auf eine Orts- oder Nachbarschaftsalgebr","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Drei Indizes, die nicht vermischt werden dürfen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2668,"byte_start":1054,"id":"section:96571450b6a0f191059a","kind":"section","labels":["eq:v16-walkA"],"line_end":31,"line_start":12,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":["relation:1f0fb7e0a87a439494f6","relation:2bcddc767c560aca81c8"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/28_v16_operations.tex","status_markers_as_written":[],"summary_excerpt":"Verwende die hermiteschen Compiler-Matrizen [formula in source] aus Kapitel Alle acht Matrizen sind von Rang eins; [formula in source] . Der kleinste positive ganzzahlige Faktor, der sie in die maximale Ordnung [formula in source] bringt, ist in allen acht Fällen vier. Dies wurde mit exakt ausmultiplizierten gaußschen Komponenten geprüft. Eine anfängliche symbolische Nichtvereinfachung eines Eintrags ist durch einen ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die positive neue Rechnung: Walk-Amplituden aus dem Matrixkern","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4163,"byte_start":2668,"id":"section:c5d9992d16d41b1cafda","kind":"section","labels":["eq:v16-no-motion"],"line_end":50,"line_start":32,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":["relation:43f027a78f71ca7f1e3c","relation:f339b8e0dc721acc2809"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/28_v16_operations.tex","status_markers_as_written":[],"summary_excerpt":"Eine Bewegung erhält man erst aus auf dem entsprechend skalierten BCC-Gitter. Entfernt man die Ortsoperationen oder wertet nur den inneren Block aus, bleibt Die Identität ist der kleinste scharfe Test gegen eine überstarke Herkunftsbehauptung: Innere Rechenregeln allein verschieben keinen Ort.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der entscheidende verbleibende Pfeil","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5926,"byte_start":4163,"id":"section:ca7fcfb55c11e73128cd","kind":"section","labels":[],"line_end":66,"line_start":51,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/28_v16_operations.tex","status_markers_as_written":[],"summary_excerpt":"In einer orthogonalen Darstellung sind die vier Fundamentalgewichte Es gilt [formula in source] und [formula in source] . Ihre zwölf Differenzen sind die [formula in source] -Wurzeln in einer FCC-Realisierung. Das duale Gewichtsgitter ist BCC. Vier Gewichte sind ein Tetraeder; erst ihre positiven und negativen Richtungen ergeben die acht benannten nächsten Schritte. Wurzelgitter und Gewichtsgitter haben Zellvolumen z","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was die A [formula in source] 3-Geometrie bereits festlegt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7763,"byte_start":5926,"id":"section:2a549e525c5b454eb6cb","kind":"section","labels":[],"line_end":88,"line_start":67,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/28_v16_operations.tex","status_markers_as_written":[],"summary_excerpt":"Für die Knotentabelle wird ausdrücklich die Standardkonvention mit den üblichen Pauli-Matrizen benutzt. Sie ist durch Umbenennung der inneren Achsen mit der Produktbauform verbunden; ein Orientierungswechsel darf Chiralitätsvorzeichen nicht unbemerkt umdefinieren. Die reziproke Gittergruppe ist [formula in source] . Modulo dieser Gruppe bleiben genau vier Knoten: lrrr [formula in source] & [formula in source] & [form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die vier Weyl-Knoten und die nicht gelöste Chiralität","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10148,"byte_start":7763,"id":"section:fea08101b112fe648a25","kind":"section","labels":[],"line_end":105,"line_start":89,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/28_v16_operations.tex","status_markers_as_written":[],"summary_excerpt":"Die bisherige native Bank verwendet 64 Fermionmoden in [formula in source] und 60 Vermittler in [formula in source] . Ihr Paarungstensor [formula in source] besitzt 480 nichtverschwindende ungeordnete Paarungen und Die unabhängige Rekonstruktion aus Außenalgebra-Vorzeichen trifft den gepinnten Tensor exakt. Ersetzt man die relevanten Spinorvorzeichen durch positive Beträge, bleibt die Zeilengrammatrix gleich, aber de","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der native signierte Vertiz und die einfache Feldalternative","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10822,"byte_start":10148,"id":"section:743eb4a2dcdc89bc9730","kind":"section","labels":[],"line_end":107,"line_start":106,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/28_v16_operations.tex","status_markers_as_written":[],"summary_excerpt":"Im selben [formula in source] -Wurzelmodell sind [formula in source] und [formula in source] wechselseitige Zentralisatoren; für eine ausgewählte [formula in source] -Unteralgebra ist der Zentralisator [formula in source] . Die Zerlegung [formula in source] ist richtig, aber sie setzt eine andere Auswahl als eine automatisch erhaltene dreifache [formula in source] -Familie voraus. Die frische Kompatibilitätsrechnung ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum die Familienfrage offen bleibt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":93,"byte_start":0,"id":"section:629256c8e3337e83d6f4","kind":"chapter","labels":["ch:v16-state"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":["relation:40b6f6264048850ca6e6","relation:a351ebb9f80eb6aaae22"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/29_v16_state.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"v1.6: Zustand, Energie und die Grenze der einfachsten Dynamik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1119,"byte_start":93,"id":"section:efa9ad4aa2c7b1bf9f89","kind":"section","labels":["eq:v16-H"],"line_end":15,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":["relation:1c09573cd3e7e86066e2","relation:577015b9f8242c29ed40"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/29_v16_state.tex","status_markers_as_written":[],"summary_excerpt":"Die betrachtete einzelne Bank hat 64 fermionische und 60 bosonische Moden. In einer festen, gepinnten Vorzeichenkonvention definiert [formula in source] die durch Zeile [formula in source] von [formula in source] angegebene Zweifermionenvernichtung. Der Operator lautet mit reellem [formula in source] ; eine gemeinsame Phase kann in diesem Modell absorbiert werden. Er erhält Das Modell ist ein echter Wechselwirkungsop","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Der gemeinsame native Operator als präziser Prüfgegenstand","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2946,"byte_start":1119,"id":"section:710f2871503cd5d96046","kind":"section","labels":["eq:v16-casimir"],"line_end":36,"line_start":16,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":["relation:80ce6ba5fc8bb1044926","relation:adf26ff26b12419de39d"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/29_v16_state.tex","status_markers_as_written":[],"summary_excerpt":"Die für diese Revision unabhängig rekonstruierte Identität lautet Die Normierung ist [formula in source] und [formula in source] . Der neue Prüfer baut beide Generatorfamilien aus Jordan–Wigner-Außenalgebraoperatoren auf und hebt sie auf alle [formula in source] Zweifermionenzustände an. Für die vierfach normierten Casimirs verschwindet die vollständige Matrix exakt. Alle Zwischenkomponenten sind gaußsche ganze Zahle","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine vollständige Operatoridentität statt einzelner Spektralstichproben","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":4913,"byte_start":2946,"id":"section:547e06dee6f25772e80b","kind":"section","labels":["eq:v16-vacuum"],"line_end":67,"line_start":37,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":["relation:93f309a1fa9448aacb30","relation:fbaab4d9c99889ddc3d8"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/29_v16_state.tex","status_markers_as_written":[],"summary_excerpt":"Erweitere Die Wahl von [formula in source] ist hier eine Gegenprobe, kein neuer passend eingestellter TFPT-Parameter. Quadratvervollständigung liefert Bei den konkreten rationalen Werten [formula in source] , [formula in source] folgt Der [formula in source] -Raum besteht nur aus dem leeren Vakuum, dessen Energie null ist. Es ist daher der eindeutige Grundzustand, mit einer bewiesenen Anregungsuntergrenze [formula in","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein exakter Zustandsvergleich auf dem gesamten Fockraum","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6419,"byte_start":4913,"id":"section:021c3e070d015763e2e9","kind":"section","labels":[],"line_end":79,"line_start":68,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":["relation:997d22e6e6808104053a","relation:af43d164219bf1d16c00"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/29_v16_state.tex","status_markers_as_written":[],"summary_excerpt":"Weil [formula in source] , gilt für jeden neutralen Operator [formula in source] mit [formula in source] bei festem präpariertem Eingang Auch ausschließlich neutrale Mehrzeitfolgen unter demselben Eingangsvertrag unterscheiden diese Zeitentwicklungen nicht. Das behauptet nicht, alle physikalischen Experimente seien gleich: Grundzustandspräparation, thermische Gewichte, Ladungswechsel und ein aufgeladenes Referenzsyst","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Welche Beobachtungen die Auswahl überhaupt sehen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":7875,"byte_start":6419,"id":"section:a9f7122bd1ca9ba290f0","kind":"section","labels":[],"line_end":90,"line_start":80,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/29_v16_state.tex","status_markers_as_written":[],"summary_excerpt":"Setzt man mehrere Banken [formula in source] auf einen vorgegebenen Graphen und verbindet nur ihre Vermittler durch [formula in source] , so bleibt an jeder Bank erhalten. Der lokale Vertiz vernichtet oder erzeugt zwei Fermionen; das Hopping verändert überhaupt keine Fermionzahl. Jeder Term kommutiert deshalb mit jeder [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Warum reines Vermittlerhopping keine einzelnen Fermionen trägt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9103,"byte_start":7875,"id":"section:44590c3401a74071197a","kind":"section","labels":[],"line_end":100,"line_start":91,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/29_v16_state.tex","status_markers_as_written":[],"summary_excerpt":"Jede Zeile von [formula in source] enthält acht disjunkte Fermionpaare auf 16 Moden. Der zugehörige normierte helle Zustand [formula in source] hat auf diesen Moden Einteilchenkorrelation [formula in source] und verschwindende anomale Zweipunktfunktion. Für ein enthaltenes Paar [formula in source] ist Die neue Rechnung prüft alle 60 Zeilen. Der Zustand ist damit in diesen physischen Fermionmoden nicht gaußsch. Eine r","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was die Gauß-Vereinfachung leistet und wo sie endet","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":102,"byte_start":0,"id":"section:a70010e51f810a4dfe18","kind":"chapter","labels":["ch:v16-program"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":["relation:20f0210ef97a182d3335","relation:dc3cb1dad2179e013aee"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/30_v16_program.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"v1.6: Das gemeinsame Bild und die nächsten entscheidenden Nachweise","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1689,"byte_start":102,"id":"section:623637bd007f60ba23b8","kind":"section","labels":[],"line_end":11,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/30_v16_program.tex","status_markers_as_written":[],"summary_excerpt":"Die ursprüngliche Intuition ist weiterhin sinnvoll: Ein kleiner gemeinsamer Zusammenhang könnte viele zunächst getrennte Zahlen, Symmetrien und Vorgänge als verschiedene Ansichten erklären. Inzwischen sind einige dieser Ansichten ausdrücklich miteinander verbunden. Die markierte [formula in source] -Struktur besitzt eine kleine Matrixdarstellung; der native signierte Paarvertiz ist rekonstruierbar; ein gemeinsamer en","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wo wir insgesamt stehen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3713,"byte_start":1689,"id":"section:4a20cde77b23c459aba3","kind":"section","labels":[],"line_end":25,"line_start":12,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/30_v16_program.tex","status_markers_as_written":[],"summary_excerpt":"Eine sparsame Arbeitshypothese lautet: Es gibt eine kleine phasentreue Regel für die Zusammensetzung zulässiger Operationen, zusammen mit einem ausgewählten positiven Zustandsfunktional. Die TFPT-Daten sind ihre markierten endlichen Auslesungen. Raum ist die tatsächlich erreichbare Nachbarschaftsstruktur ihrer Anregungen; Zeit ist die geordnete Zusammensetzung ihrer Ausführungen und Aufzeichnungen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die einfachste zusammenhängende Forschungshypothese","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6085,"byte_start":3713,"id":"section:ddea9dde9818ea84c563","kind":"section","labels":[],"line_end":38,"line_start":26,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/30_v16_program.tex","status_markers_as_written":[],"summary_excerpt":"L7mmL48mmL95mm & Frage& Stand und nächster entscheidender Test\\\\ 1&Was ist die kleinste native Quelle?&Die maximale Matrixordnung und ihr markierter Compileranschluss sind bestätigt. Noch ausstehend: erlaubte primitive Operationen samt Normierungen und Zustandsregel. Test: [formula in source] , Record und eine gerichtete Ortsoperation als explizite Ausführung herstellen; zusätzliche Kontrollen offen auflisten.\\\\ 2&Wi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die sechs Fragen mit überprüfbaren Antworten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8920,"byte_start":6085,"id":"section:d7b0a2ba283ad7cf02c6","kind":"section","labels":[],"line_end":53,"line_start":39,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/30_v16_program.tex","status_markers_as_written":[],"summary_excerpt":"L8mmL53mmL89mm Tor& Fortschritt dieser Konsolidierung& Was für den vollständigen Nachweis noch fehlt\\\\ T1&Markierte Matrix-/Gitterbrücke reproduziert; weniger frei hinzugefügte innere Walk-Matrizen; Ressourcenuntergrenze des Records sichtbar.&Auswahl von P1/P2, maximaler Ordnung, Markierungen und Dimension. Native Zulässigkeit von [formula in source] , kohärenter Kontrolle und Normierung. [formula in source] allein e","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T1–T8: tatsächlicher Stand und verbleibende Schließung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8972,"byte_start":8920,"id":"section:599415ac0c42b662b752","kind":"section","labels":[],"line_end":54,"line_start":54,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/30_v16_program.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Die drei priorisierten nächsten Arbeiten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9908,"byte_start":8972,"id":"section:0a38de4b5029322f37e4","kind":"subsection","labels":[],"line_end":59,"line_start":55,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/30_v16_program.tex","status_markers_as_written":[],"summary_excerpt":"Vorab festlegen: tatsächliche Eingangsmoden, Ortsalgebra oder rekonstruierte Teilalgebren, erlaubte Primitive, Hilfsregister und Kosten. Gesucht ist eine kohärente Folge, deren Wirkung zugleich innere [formula in source] -Grade und eine nichttriviale Nachbarschaftsänderung erhält. Die frisch berechneten [formula in source] sind ein Vergleichsziel, nicht der Anfang des Beweises.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Erstens: ein natives gerichtetes Operationswort","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10702,"byte_start":9908,"id":"section:103d70f360dfa81126a1","kind":"subsection","labels":[],"line_end":64,"line_start":60,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/30_v16_program.tex","status_markers_as_written":[],"summary_excerpt":"Für den ersten erfolgreich geschlossenen Operationsvertrag sind alle noch freien skalaren, chemischen und sektorabhängigen Terme zu benennen. Der minimale Test ist die Familie [formula in source] einschließlich erlaubter Präparationen. Auch die Beobachtbarkeit von [formula in source] hängt vom physisch erlaubten Zugriff ab.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Zweitens: die Energie- und Zustandswahl desselben Systems","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11579,"byte_start":10702,"id":"section:a7550aa7194029a54ab0","kind":"subsection","labels":[],"line_end":69,"line_start":65,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/30_v16_program.tex","status_markers_as_written":[],"summary_excerpt":"Die erste nichttriviale Zwei- oder Dreiplatzausführung wird mit unveränderten lokalen Regeln vergrößert. Zunächst prüft man Erhaltung, Stabilität, Ausbreitung und zusätzliche Moden; dann Kontinuum und gemeinsame Geschwindigkeiten. Ein chiraler Index ist über die volle relevante Zone und alle Sektoren zu prüfen, nicht über einen günstig ausgewählten Knoten.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Drittens: erst danach eine skalierende gemeinsame Familie","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12709,"byte_start":11579,"id":"section:b4aa2419f5f5f6759f8d","kind":"section","labels":[],"line_end":74,"line_start":70,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/30_v16_program.tex","status_markers_as_written":[],"summary_excerpt":"Die vorhandene Matrix- [formula in source] -Identifikation wird nicht noch einmal als neue Entdeckung verkauft. Eine zusätzliche passende Zahl ist kein Ersatz für das gerichtete Operationswort. Ein bereits gesetztes BCC-Gitter ist keine neu entstandene Raumzeit. Ein neu gewählter chemischer Parameter ist keine Herleitung des Grundzustands. Eine feste endliche Singulettrechnung ist kein Beweis sämtlicher C16-Sektoren.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was nicht erneut als Durchbruch ausgegeben werden sollte","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":13358,"byte_start":12709,"id":"section:9a8e386511368e13d499","kind":"section","labels":[],"line_end":76,"line_start":75,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/30_v16_program.tex","status_markers_as_written":[],"summary_excerpt":"Die Revision liefert eine echte Vereinfachung an zwei Stellen: eine kürzere vollständige endliche Präparation und eine gemeinsame kleine Matrixsprache für Compiler-Gitter und innere Walk-Amplituden. Sie liefert außerdem eine stärkere unabhängige Zustandsprüfung auf dem ganzen Fockraum des benannten Modells. Der fehlende Schlüssel ist dadurch präziser lokalisiert: native räumliche Zusammensetzung und physische Auswahl","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Fazit: weniger getrennte Bauteile, schärfere offene Verbindung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":84,"byte_start":0,"id":"section:39622264c25f3d722b70","kind":"chapter","labels":["app:v16-evidence"],"line_end":2,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":["relation:158dea9d65ad3575153b","relation:fdd80c2e616f48168871"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/31_v16_evidence.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Evidenz, Eingaben und Versionsabdeckung von v1.6","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1071,"byte_start":84,"id":"section:5762b9b701c20f26ebef","kind":"section","labels":[],"line_end":7,"line_start":3,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/31_v16_evidence.tex","status_markers_as_written":[],"summary_excerpt":"Freigabestand ist der 15. September 2026, Version 1.6. Grundlage ist die vollständige v1.5-Quelldarstellung, nicht die frühere kompakte Compiler-Fassung. Alle 25 bisherigen Kapiteldateien bleiben im neuen Hauptbuch; die Zahl der Dateien ist nicht die Zahl der gesetzten Hauptkapitel, weil mehrere Dateien mehr als ein Kapitel enthalten. Die Freigabeprüfung kontrolliert sämtliche bisherigen Kapitel-, Abschnitts- und Unt","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Version und unveränderte historische Basis","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3467,"byte_start":1071,"id":"section:5603f73f679b20f6b72c","kind":"section","labels":[],"line_end":22,"line_start":8,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":["relation:761f66f6a1afcbf2b8a5","relation:89cf44d50ce51736f8d2"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/31_v16_evidence.tex","status_markers_as_written":[],"summary_excerpt":"L19mmL47mmL84mm ID& Quelle& Verwendung und Bewertung\\\\ V16-U1&Neue Eingabe: „entscheidender Knoten“, 811 Zeilen&Ein-Objekt-Hypothese, [formula in source] , Dimension und Matrixspur. Matrixspur durch vorhandenen vollständigen Beweis bestätigt. Automatische physische Auswahl und Dimensionsableitung nicht bestätigt.\\\\ V16-U2&Neue Eingabe zu [formula in source] , [formula in source] , [formula in source] , 1150 Zeilen&BC","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die Eingaben und ihre konkrete Verwendung","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":4814,"byte_start":3467,"id":"section:35f297f3d128a5398bee","kind":"section","labels":[],"line_end":29,"line_start":23,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/31_v16_evidence.tex","status_markers_as_written":[],"summary_excerpt":"Fünf Programme wurden mit unveränderten Guards normal und unter -OO ausgeführt. Ihre jeweiligen JSON-Ausgaben waren bytegleich. Der vorhandene Kompatibilitätsprüfer besitzt einen eigenen Ausgabe-Schlussteil; im archivierten Replay wird nur dieser inspizierte Schreib-/Druckteil entfernt und der volle Bericht in das neue Versionsverzeichnis geschrieben. Die mathematische Rechnung bleibt unverändert. Der erste direkte L","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was frisch gerechnet und was nicht wiederholt wurde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":5877,"byte_start":4814,"id":"section:2271fcd985a2383a1d55","kind":"section","labels":[],"line_end":43,"line_start":30,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":["relation:1ab7b71044f649e25036","relation:2b2e816c8db3ff8895a7","relation:2e3a95ce326a9ab17186","relation:5f0e4f02dd4fcd19c4e9","relation:8545c86980efc696b027","relation:b617a26b1567b9d96b44","relation:bc8a3cfed05beb7682dd","relation:cf317bac4a196a2614ab","relation:f331fa19b86ee046146e"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/31_v16_evidence.tex","status_markers_as_written":[],"summary_excerpt":"Die neuen Dateien liegen im Repository unter experiments/theory-contracts/universalraum-v16-integrated-20260915/ Die wichtigsten Zuordnungen sind: verify_v16.py, new_checks.json: neue unabhängige Rechnungen; replay.py, read_only_compatibility.py, replay_manifest.json: reproduzierte ältere Prüfer und normal/optimiert-Vergleich; order.json, native.json, weyl.json, compatibility.json: vollständige Ergebnisberichte; sour","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lesbare Dateizuordnung im Quellenpaket","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":7440,"byte_start":5877,"id":"section:2702ec697a4b460c8753","kind":"section","labels":[],"line_end":53,"line_start":44,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/chapters/31_v16_evidence.tex","status_markers_as_written":[],"summary_excerpt":"G. M. D'Ariano, M. Erba, P. Perinotti: Isotropic quantum walks on lattices and the Weyl equation, 2017. https://arxiv.org/abs/1708.00826. Verwendet zur Abgrenzung der bereits vorausgesetzten Dimension und Coin-Struktur. G. Mason, M. P. Tuite: Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces I, 2009. https://arxiv.org/html/0912.0117v1. Verwendet als Standardhintergrund zu Heisenberg-, Gitter- und Ve","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Externe Primärquellen dieser Revision","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":3704,"byte_start":0,"id":"section:41583e86e96a646c4f18","kind":"section","labels":[],"line_end":19,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":["relation:3de0c2111adef777cb3b","relation:f0698f3e630b88433dc2"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/front_v16.tex","status_markers_as_written":[],"summary_excerpt":"tocsectionNeu in v1.6: Ergebnisse, Reichweite und Lesepfad Diese Fassung vom 15. September 2026 führt das vollständige Hauptdokument v1.5 fort. Die 25 bisherigen Kapiteldateien einschließlich aller darin enthaltenen Hauptkapitel und Anhänge sowie sämtliche Abbildungen bleiben erhalten. Dreizehn inhaltliche Einfügungen verbinden die neuen Ergebnisse direkt mit den bisherigen Argumenten. Fünf neue Hauptkapitel und ein ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was Version 1.6 verändert und korrigiert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5151,"byte_start":0,"id":"section:c65b27c634f87034bb56","kind":"frontmatter","labels":[],"line_end":96,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main.tex","status_markers_as_written":[],"summary_excerpt":"TeX Gyre Pagella TeX Gyre Heros Latin Modern Mono arrows.meta,positioning,calc,fit,backgrounds,decorations.pathreplacing chapter navy section navy subsection navy slateTFPT · Universalraum slateErklärung und Rekonstruktion chapter slateForschungsstand 15. September 2026 headsepline=.3pt headsepline slate!35 nosep,leftmargin=1.4em,topsep=5pt toclinesection toclinechapter,section =2em font=small,labelfont=bf,sf,skip=7p","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8242,"byte_start":5151,"id":"section:1c5c4a0f9ddd7946006d","kind":"chapter","labels":[],"line_end":112,"line_start":97,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main.tex","status_markers_as_written":[],"summary_excerpt":"tocchapterWas dieses Dokument leisten soll Der Universalraum ist in den vorliegenden Arbeiten die Idee eines gemeinsamen Zusammenhangs von erlaubten Veränderungen, Zuständen und Aufzeichnungen. TFPT soll darin eine besonders strukturierte mathematische Ansicht liefern. Das ist inzwischen mehr als ein Bild: Kleine Prozesse, Zellzustände, Registerexperimente und mehrere Rekonstruktionspfeile sind ausdrücklich berechenb","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was dieses Dokument leisten soll","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9799,"byte_start":8242,"id":"section:df82eb6aed8287fd9730","kind":"section","labels":[],"line_end":121,"line_start":113,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main.tex","status_markers_as_written":[],"summary_excerpt":"Diese Fassung führt das vollständige 90-seitige Forschungsbuch v1.1 fort. Alle bisherigen 21 Hauptkapitel und vier Anhänge bleiben zugänglich. Die 35-seitige Compiler-Fassung v1.2 war eine andere, kompakte Dokumentlinie und ist nicht die Grundlage dieses Hauptdokuments.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was Version 1.3 verändert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10836,"byte_start":9799,"id":"section:237234c09ded9b5db475","kind":"section","labels":[],"line_end":126,"line_start":122,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main.tex","status_markers_as_written":[],"summary_excerpt":"Fünf weitere Untersuchungen sind geprüft, ihre Widersprüche geklärt und eigene Anschlussrechnungen vor dem PDF-Update ausgeführt. Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was Version 1.4 zusätzlich verändert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12257,"byte_start":10836,"id":"section:abd7f14ea995bf447428","kind":"section","labels":[],"line_end":134,"line_start":127,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main.tex","status_markers_as_written":[],"summary_excerpt":"Diese Version bewahrt das vollständige 126-seitige Hauptbuch v1.4 einschließlich sämtlicher früherer Kapitel und Abbildungen. Zwei weitere Quelltexte sind abgeglichen und eigene Rechnungen in vier parallelen Arbeitssträngen abgeschlossen. Aktualisierungshinweise stehen auch unmittelbar in den betroffenen älteren Kapiteln.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Was Version 1.5 zusätzlich verändert","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13313,"byte_start":12257,"id":"section:686571dcce045a2a6bb3","kind":"section","labels":[],"line_end":148,"line_start":135,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main.tex","status_markers_as_written":[],"summary_excerpt":"L27mmY Markierung& Bedeutung\\\\ Gesetzt&Eine Ausgangsregel, Zustandswahl oder physikalische Zuordnung wird angenommen.\\\\ Exakt&Eine Identität oder ein Beweis gilt unter ausdrücklich genannten Voraussetzungen.\\\\ Numerisch&Ein endliches Rechenresultat stützt eine Aussage mit begrenzter Genauigkeit und Größe.\\\\ Bedingt&Die Folgerung ist korrekt, sobald zusätzliche, noch nicht aus der Quelle gewonnene Daten gelten.\\\\ Hypo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Wie man die Evidenz liest","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":16827,"byte_start":13313,"id":"section:115e9f9b38d73ba2003f","kind":"section","labels":[],"line_end":197,"line_start":149,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/main.tex","status_markers_as_written":[],"summary_excerpt":"Die folgenden Prüfberichte dokumentieren die historische Basisfassung v1.1. Sie behaupten keinen erneuten Lauf ihrer Prüfungen in v1.3 oder v1.4. Evidenz der Version 1.3 steht in Anhang","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Umfang und Versionsgrenze","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":561,"byte_start":0,"id":"section:1c1a8c437943e580a421","kind":"frontmatter","labels":[],"line_end":3,"line_start":1,"occurrence":1,"owner_documents":[],"relation_ids":["relation:3653aa4c9e664ce0a9cd","relation:a09404d7e081d0d647bf"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/revisions/01_idea.tex","status_markers_as_written":[],"summary_excerpt":"Integrierte Präzisierung v1.6: ein Baukasten, mehrere Ausführungen Die Matrixbrücke in Kapitel","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":782,"byte_start":0,"id":"section:e903a2e81b3fe6d21e8d","kind":"frontmatter","labels":[],"line_end":3,"line_start":1,"occurrence":1,"owner_documents":[],"relation_ids":["relation:18118005084803d0bca9","relation:fdea8d0b6ca9a281b827"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/revisions/02_order.tex","status_markers_as_written":[],"summary_excerpt":"Integrierte Ergänzung v1.6: dieselbe Hülle als Matrixordnung Neben der [formula in source] – [formula in source] -Verklebung existiert eine ausdrücklich markierungstreue Darstellung als maximale [formula in source] -Ordnung [formula in source] . Mit [formula in source] ist ihr achtdimensionales ganzzahliges Gitter positiv, gerade und unimodular; es hat genau 240 Vektoren mit [formula in source] . Der vorhandene Compi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":755,"byte_start":0,"id":"section:f9e7f07b7dd1a03b98b4","kind":"frontmatter","labels":[],"line_end":3,"line_start":1,"occurrence":1,"owner_documents":[],"relation_ids":["relation:a833c17128ba3f02561c","relation:c9fbb85aad7713e8d3dd"],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/revisions/03_selection.tex","status_markers_as_written":[],"summary_excerpt":"Integrierte Verschärfung v1.6: Symmetrie wählt auch die Energie nicht Die Unterbestimmtheit betrifft nicht nur Kontextgewichte. 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Die tatsächlichen Zwischenzellkoeffizienten gemeinsam ableiten und ihre dynamische lokale Restkontrolle beweisen. Die übrigen kleinen Spektralblöcke und andere SU(4)-Sektoren global zertifizieren. Das echte Half-Charge-Feld, alle Farbmoden und die chirale 3+1D-Grenze gemeinsam konstruieren. Hintergrund, Moden und gemeinsame empi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Die nächsten entscheidenden Ziele","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":1119,"byte_start":0,"id":"section:8c32cea01cd689d9b5a1","kind":"frontmatter","labels":[],"line_end":19,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/update_body_v16.tex","status_markers_as_written":[],"summary_excerpt":"15mm teal FORSCHUNGSUPDATE · 15. SEPTEMBER 2026 16mm navy 2935 TFPT und Universalraum 8mm navy Version 1.6 12mm Der kleine Matrixkern, die tatsächlichen Operationen und die offene Zustandswahl 16mm Dieses Update enthält nur Änderungen gegenüber dem vollständigen Hauptdokument v1.5. Die ausführliche neue v1.6-Fassung bewahrt sämtliche bisherigen Kapitel und Abbildungen, integriert Korrekturen direkt in die Argumentati","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1982,"byte_start":1119,"id":"section:b7a74aa45de728b9f707","kind":"chapter","labels":[],"line_end":25,"line_start":20,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/update_body_v16.tex","status_markers_as_written":[],"summary_excerpt":"tocchapterDas Ergebnis in einem Bild Der Baukasten ist tatsächlich kleiner geworden. Die markierte [formula in source] -Struktur lässt sich in einer konkreten Ordnung komplexer [formula in source] -Matrizen darstellen. Dieselben inneren Matrizen liefern die Amplituden eines einfachen Weyl-Walks. Ein besonders kurzer Laborablauf erzeugt außerdem den Zellzustand [formula in source] mit einem einzigen erfolgreichen Reco","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Das Ergebnis in einem Bild","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2395,"byte_start":1982,"id":"section:af5e255cd94e2e58f006","kind":"section","labels":[],"line_end":28,"line_start":26,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/update_body_v16.tex","status_markers_as_written":[],"summary_excerpt":"Die Matrix- [formula in source] -Spur war nicht erst neu zu entdecken. Ein vollständiger Beweis samt markierter Compiler-Abbildung lag bereits seit dem 9. September im Repository. Der vorherige Status hatte diesen Abschnitt nicht berücksichtigt. v1.6 korrigiert das, reproduziert den vorhandenen Prüfer und trennt den älteren Beweis von den neuen Anschlussrechnungen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Eine notwendige Korrektur des letzten Status","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":3595,"byte_start":2395,"id":"section:042f40b87371087f206c","kind":"chapter","labels":[],"line_end":44,"line_start":29,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/update_body_v16.tex","status_markers_as_written":[],"summary_excerpt":"Mit [formula in source] und [formula in source] hat die maximale Ordnung unter [formula in source] ein positives gerades unimodulares Gitter vom Rang acht. Die vollständig begrenzte Wurzelsuche findet genau 240 Vektoren mit [formula in source] . Die markierte Isometrie erhält den gaußschen Anker, die Familienwirkung und den tatsächlichen Compiler-Code.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"1. Die Matrixbrücke ist bestätigt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5007,"byte_start":3595,"id":"section:75d5bed5cd6e2597de2b","kind":"chapter","labels":[],"line_end":61,"line_start":45,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/update_body_v16.tex","status_markers_as_written":[],"summary_excerpt":"Die drei hermiteschen Matrizen [formula in source] erfüllen die Pauli-Relationen. Für [formula in source] setze [formula in source] Jede Matrix hat Rang eins und Normquadrat [formula in source] ; vier ist jeweils der kleinste ganzzahlige Faktor, der sie in [formula in source] bringt. Das Produkt [formula in source] ist für alle [formula in source] unitär und hat den linearen Grenzterm [formula in source] . Sämtliche ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"2. Neue Rechnung: Compiler-Matrizen liefern den inneren Walk","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":6702,"byte_start":5007,"id":"section:1ff6e9d7c556b558935f","kind":"chapter","labels":[],"line_end":82,"line_start":62,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/update_body_v16.tex","status_markers_as_written":[],"summary_excerpt":"Für das native Modell mit 64 Fermion- und 60 Vermittlermoden gilt [formula in source] Die Identität [formula in source] wurde unabhängig aus den Generatoren und allen 2016 Zweifermionenzuständen rekonstruiert. Weil beide Seiten normalgeordneten Grad höchstens vier haben und auch die Sektoren null und eins geprüft sind, gilt die Identität im gesamten fermionischen Fockraum.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"3. Neue unabhängige Rechnung: die Zustandswahl bleibt echt","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":7043,"byte_start":6702,"id":"section:99044b3b7d5079904c8d","kind":"chapter","labels":[],"line_end":85,"line_start":83,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/update_body_v16.tex","status_markers_as_written":[],"summary_excerpt":"Die vorläufigen Markdown-Berichte v1.6 vom 14. September enthielten bereits folgende weitergehende Ergebnisse. Sie sind nun im Hauptbuch mit Formeln, Ressourcen und Modellgrenzen enthalten; die großen zugehörigen Läufe wurden in dieser Revision nicht sämtlich wiederholt.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"4. Erstmals in die PDF-Linie integrierte Vorbefunde","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7867,"byte_start":7043,"id":"section:16b7f4ff88ea04f1c1c6","kind":"section","labels":[],"line_end":90,"line_start":86,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/update_body_v16.tex","status_markers_as_written":[],"summary_excerpt":"Ein expliziter Acht-Bit-Stabilizereingang [formula in source] erfüllt [formula in source] . Ein erfolgreicher Record präpariert daher exakt [formula in source] mit Wahrscheinlichkeit [formula in source] . Die aus der rückwärtigen Schaltung aufgebaute Schlussprüfung hat ebenfalls Effizienz [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Ein-Record-Präparation und vollständige Rohstatistik","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8604,"byte_start":7867,"id":"section:9fc4ebc0cc9c3c7f289c","kind":"section","labels":[],"line_end":95,"line_start":91,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/update_body_v16.tex","status_markers_as_written":[],"summary_excerpt":"Im vollständigen 24024-dimensionalen Singulettsektor des benannten abgeschnittenen kantenlokalen Operators sind genau fünf Zustände unter [formula in source] zertifiziert, mit Grundzustandslücke größer als [formula in source] . Das ist kein Zertifikat sämtlicher Nicht-Singuletts oder des vollen mikroskopischen Operators.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"C16-Spektrum und zwei verschiedene Transportzeugen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9153,"byte_start":8604,"id":"section:1bf6936fbfe21011766b","kind":"section","labels":[],"line_end":98,"line_start":96,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/update_body_v16.tex","status_markers_as_written":[],"summary_excerpt":"Die dokumentierte vollständige Modenrechnung der Starobinsky-Branche [formula in source] trifft die verwendeten Zentralwerte für Amplitude und Neigung nicht gleichzeitig. Anpassung an [formula in source] ergibt [formula in source] , [formula in source] ; Anpassung an [formula in source] ergibt [formula in source] und eine etwa 2,05-fach größere Amplitude. Ein Retuning von [formula in source] wirkt gleichzeitig auf di","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Die gemeinsam zu prüfende kosmologische Ausgabe","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10463,"byte_start":9153,"id":"section:90a4c5a46752ef5ee1be","kind":"chapter","labels":[],"line_end":108,"line_start":99,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/update_body_v16.tex","status_markers_as_written":[],"summary_excerpt":"[formula in source] allein erzwingt keine zweidimensionale komplexe Darstellung und keine dreidimensionale physische Raumstruktur. Ein einfacher zweikomponentiger Weyl-Walk besitzt in der vollständig geprüften Zone vier Knoten. Bei Quasienergie null und [formula in source] bleibt je ein Paar entgegengesetzter Chiralität. Falten entfernt keine Spiegelzustände. Die [formula in source] -Verzweigung ist kein automatisch ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"5. Welche starken Schlussfolgerungen nicht halten","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11804,"byte_start":10463,"id":"section:3f331f818cb959d722a8","kind":"chapter","labels":[],"line_end":117,"line_start":109,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/update_body_v16.tex","status_markers_as_written":[],"summary_excerpt":"1. Tatsächlicher nativer Platzwechsel. Ein einziges explizites Operationswort muss innere Markierungen, vollständige Normierung und eine nichttriviale räumliche Änderung erhalten. Keine nachträglich angefügten Shift- oder Hoppingterme als Herkunft ausgeben. Lokale Paritäten und geschlossene Wegoperatoren sind die ersten Negativtests.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"6. Die nächsten drei Abnahmen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13185,"byte_start":11804,"id":"section:156c2fc268043a272253","kind":"section","labels":[],"line_end":125,"line_start":118,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/update"],"relation_ids":[],"semantic_review":false,"source":"experiments/theory-contracts/universalraum-v16-integrated-20260915/main-v1.6/update_body_v16.tex","status_markers_as_written":[],"summary_excerpt":"Fünf Programme wurden normal und unter -OO ausgeführt; ihre JSON-Ausgaben waren jeweils bytegleich. Der neue Prüfer enthält 279 explizite Guards, die wiederholten nativen, Weyl- und Kompatibilitätsprüfer 534, 149 beziehungsweise 7369. Der vorhandene Matrixprüfer kontrolliert zusätzlich seine Quellenpins und die markierte Clockgrenze. Diese Zahlen zählen Bedingungen, nicht unabhängige Entdeckungen.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Prüfung und Quellen","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":3652,"byte_start":0,"id":"section:ba5d01c883e42fcce6e6","kind":"frontmatter","labels":[],"line_end":59,"line_start":1,"occurrence":1,"owner_documents":["document:introduction"],"relation_ids":["relation:10caad899ae3098d2f16","relation:934bc828f43760833a12","relation:ff2aa689f7b8c416707a"],"semantic_review":false,"source":"tex-artefacts/predictions.tex","status_markers_as_written":["\\mC","\\mE"],"summary_excerpt":"@p2.5cmp4.9cmYc@ Observable & TFPT value \\& derivation & Experiment (running / upcoming) & St. \\\\ solar angle [formula in source] & prediction of record [formula in source] ; TBM [formula in source] seam misalignment [formula in source] (cond.) & JUNO: first [formula in source] \\,d run [formula in source] (compatible), precision phase pending & / \\\\ reactor angle [formula in source] & [formula in source] ; seed [form","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"}]},{"byte_end":3424,"byte_start":0,"id":"section:156b954069629fede86f","kind":"frontmatter","labels":[],"line_end":44,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/origin_theory","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8","document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/sources/input_4_origin_theory","document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/sources/input_5_tfpt_3_e8_audit_bootstrap","document:introduction","document:origin_theory","document:tfpt_1_architecture_e8","document:tfpt_2_standard_model","document:tfpt_3_e8_audit_bootstrap","document:tfpt_4_frontier","document:tfpt_5_redteam","document:tfpt_horizon_readouts","document:tfpt_research_contracts","document:tfpt_safeguards","document:universal_room/new-3/TFPT_Universalraum_Spinlift_Pruefpaket_2026-09-15_v1.6.10/sources/input_4_origin_theory","document:universal_room/new-3/TFPT_Universalraum_Spinlift_Pruefpaket_2026-09-15_v1.6.10/sources/input_5_tfpt_3_e8_audit_bootstrap"],"relation_ids":["relation:47ae3430ce8dbf1549d9"],"semantic_review":false,"source":"tex-artefacts/tfpt_docset.tex","status_markers_as_written":[],"summary_excerpt":"Plain language: TFPT (Topological Fixed-Point Theory) is a small discrete compiler. 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Its bridges to continuum/AQFT physics, to gravity and to the lattice/singularity picture build on established mathematics, listed here by topic; the body refers to these by author name.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"External works built upon","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":2584,"byte_start":1116,"id":"section:945c2cb0147875f1d49f","kind":"paragraph","labels":[],"line_end":42,"line_start":20,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/origin_theory","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8","document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/sources/input_4_origin_theory","document:origin_theory","document:tfpt_1_architecture_e8","document:tfpt_2_standard_model","document:tfpt_4_frontier","document:tfpt_horizon_readouts","document:tfpt_research_contracts","document:universal_room/new-3/TFPT_Universalraum_Spinlift_Pruefpaket_2026-09-15_v1.6.10/sources/input_4_origin_theory"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/tfpt_references.tex","status_markers_as_written":[],"summary_excerpt":"M. Takesaki, Tomita's Theory of Modular Hilbert Algebras and its Applications, Lecture Notes in Math.\\ 128, Springer (1970). J. J. Bisognano, E. H. Wichmann, On the duality condition for a Hermitian scalar field / for quantum fields, J. Math.\\ Phys.\\ 16 (1975) 985–1007; 17 (1976) 303–321. K. Osterwalder, R. Schrader, Axioms for Euclidean Green's functions I, II, Comm.\\ Math.\\ Phys.\\ 31 (1973) 83–112; 42 (1975) 281–30","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Modular theory and algebraic quantum field theory.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":4685,"byte_start":2584,"id":"section:419291db9b3bf697f68f","kind":"paragraph","labels":[],"line_end":71,"line_start":43,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/origin_theory","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8","document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/sources/input_4_origin_theory","document:origin_theory","document:tfpt_1_architecture_e8","document:tfpt_2_standard_model","document:tfpt_4_frontier","document:tfpt_horizon_readouts","document:tfpt_research_contracts","document:universal_room/new-3/TFPT_Universalraum_Spinlift_Pruefpaket_2026-09-15_v1.6.10/sources/input_4_origin_theory"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/tfpt_references.tex","status_markers_as_written":[],"summary_excerpt":"I. B. Frenkel, V. G. Kac, Basic representations of affine Lie algebras and dual resonance models, Invent.\\ Math.\\ 62 (1980) 23–66; G. Segal, Unitary representations of some infinite-dimensional groups, Comm.\\ Math.\\ Phys.\\ 80 (1981) 301–342. T. J. Osborne, A. Stottmeister, Conformal field theory from lattice fermions, Comm.\\ Math.\\ Phys.\\ 398 (2023) 219–289, arXiv:2107.13834, doi:10.1007/s00220-022-04521-8. (This is ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conformal nets, vertex operator algebras and lattice constructions.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"}]},{"byte_end":5109,"byte_start":4685,"id":"section:e1dbc2140a6e75ecc576","kind":"paragraph","labels":[],"line_end":79,"line_start":72,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/origin_theory","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8","document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/sources/input_4_origin_theory","document:origin_theory","document:tfpt_1_architecture_e8","document:tfpt_2_standard_model","document:tfpt_4_frontier","document:tfpt_horizon_readouts","document:tfpt_research_contracts","document:universal_room/new-3/TFPT_Universalraum_Spinlift_Pruefpaket_2026-09-15_v1.6.10/sources/input_4_origin_theory"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/tfpt_references.tex","status_markers_as_written":[],"summary_excerpt":"J. H. Conway, N. J. A. Sloane, Sphere Packings, Lattices and Groups, 3rd ed., Grundlehren der math.\\ Wiss.\\ 290, Springer (1999). C. L. Siegel, \\\"Uber die analytische Theorie der quadratischen Formen (the Minkowski–Siegel mass formula), Ann.\\ of Math.\\ 36 (1935) 527–606.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lattices and quadratic forms.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"}]},{"byte_end":5473,"byte_start":5109,"id":"section:ccdf9a18bc4b3c8087f3","kind":"paragraph","labels":[],"line_end":87,"line_start":80,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/origin_theory","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8","document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/sources/input_4_origin_theory","document:origin_theory","document:tfpt_1_architecture_e8","document:tfpt_2_standard_model","document:tfpt_4_frontier","document:tfpt_horizon_readouts","document:tfpt_research_contracts","document:universal_room/new-3/TFPT_Universalraum_Spinlift_Pruefpaket_2026-09-15_v1.6.10/sources/input_4_origin_theory"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/tfpt_references.tex","status_markers_as_written":[],"summary_excerpt":"E. Brieskorn, Beispiele zur Differentialtopologie von Singularit\\\"aten, Invent.\\ Math.\\ 2 (1966) 1–14. J. Milnor, Singular Points of Complex Hypersurfaces, Ann.\\ of Math.\\ Studies 61, Princeton Univ.\\ Press (1968).","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Singularities and geometry.","topic_suggestions":[]},{"byte_end":6213,"byte_start":5473,"id":"section:73013c8dfaf5aa22eb09","kind":"paragraph","labels":[],"line_end":100,"line_start":88,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/origin_theory","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_1_architecture_e8","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-native-exterior-reset-20260915/sources/tfpt_1_architecture_e8","document:experiments/theory-contracts/universalraum-spin-lift-basics-20260915/sources/input_4_origin_theory","document:origin_theory","document:tfpt_1_architecture_e8","document:tfpt_2_standard_model","document:tfpt_4_frontier","document:tfpt_horizon_readouts","document:tfpt_research_contracts","document:universal_room/new-3/TFPT_Universalraum_Spinlift_Pruefpaket_2026-09-15_v1.6.10/sources/input_4_origin_theory"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/tfpt_references.tex","status_markers_as_written":[],"summary_excerpt":"A. H. Chamseddine, A. Connes, The spectral action principle, Comm.\\ Math.\\ Phys.\\ 186 (1997) 731–750. A. Connes, C. Rovelli, Von Neumann algebra automorphisms and time–thermodynamics relation in general covariant quantum theories, Class.\\ Quantum Grav.\\ 11 (1994) 2899–2918. R. M. Wald, Black hole entropy is the Noether charge, Phys.\\ Rev.\\ D 48 (1993) R3427–R3431. H. Casini, M. Huerta, R. C. 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Neutral multipoint limits, without changing the source","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8007,"byte_start":5637,"id":"section:5d5709ce3e52f2ab7b99","kind":"subsection","labels":[],"line_end":158,"line_start":115,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_research_20260909.tex","status_markers_as_written":[],"summary_excerpt":"A different, explicitly declared compact- [formula in source] rotor/CAR test parent keeps [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] and all integer electric fluxes. 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They extend the positive matter/constraint constructions to an interacting scalar/charge model, local charge transport, exact scalar elimination and controlled signed history sums. 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The local positive and constraint-domain branches distinguish the separated completion from the first-vertex-preserving completion, including their different off-shell terms and form domains. The charge branch ret","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"What the intermediate contracts establish.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":3392,"byte_start":2158,"id":"section:e74826b2aac9e22d1901","kind":"paragraph","labels":[],"line_end":65,"line_start":36,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round27_full_reference.tex","status_markers_as_written":[],"summary_excerpt":"Fix [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] , a time step [formula in source] , [formula in source] and [formula in source] . 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Thus [formula in source] ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The common reference.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5828,"byte_start":3392,"id":"section:65b04690e3cfb4c58e6c","kind":"paragraph","labels":["eq:r27-reference"],"line_end":113,"line_start":66,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round27_full_reference.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the sum of moduli before cancellation, resolved into elementary hopping words, initial charge profiles and scalar integrals. Then Every elementary hop changes the complete profile, hence [formula in source] . Scalar spectral Jensen gives [formula in source] . Pinching [formula in source] into its charge blocks [formula in source] contracts the Schatten [formula in source] norm, so [formula ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Full-reference theorem and proof.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":7766,"byte_start":5828,"id":"section:017bee6560ef23a86a7e","kind":"paragraph","labels":[],"line_end":154,"line_start":114,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round27_full_reference.tex","status_markers_as_written":[],"summary_excerpt":"The exact Gram inverse satisfies [formula in source] , so [formula in source] , [formula in source] . On the neutral sector define [formula in source] Let [formula in source] bound all charge coordinates at sampled slice boundaries and [formula in source] bound total elementary hopping order. If [formula in source] , [formula in source] For the first estimate, insert the boundary projection [formula in source] in the","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Three explicit error budgets.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9744,"byte_start":7766,"id":"section:31b26644967c02b83940","kind":"paragraph","labels":[],"line_end":187,"line_start":155,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":["relation:5ce7ad0603c1e48c0a87","relation:b0970865f8478e10f00b"],"semantic_review":false,"source":"tex-artefacts/toe_round27_full_reference.tex","status_markers_as_written":[],"summary_excerpt":"The planner uses integers and fractions, with upward roots, [formula in source] , [formula in source] and [formula in source] for [formula in source] . At [formula in source] , full memory and a [formula in source] omission target, the published Round 26 [formula in source] improve to [formula in source] . Applying the same first-passing-integer search to the old inequalities gives [formula in source] : the gain is n","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproducible certificates and actual remaining cost.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10461,"byte_start":9744,"id":"section:24ba7cc6dbcee43b2c79","kind":"paragraph","labels":[],"line_end":198,"line_start":188,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round27_full_reference.tex","status_markers_as_written":[],"summary_excerpt":"For overlapping original hops [formula in source] and [formula in source] , the word [formula in source] closes with phase [formula in source] because [formula in source] . Its actual hopping matrix-element product is [formula in source] for [formula in source] . Diagonal configuration rephasing telescopes around this loop and cannot remove it. This excludes that particular stoquastic rephasing, not all bases, regrou","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The original sign obstruction and physical frontier remain.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":77,"byte_start":0,"id":"section:996afae3d3024fa672b8","kind":"frontmatter","labels":[],"line_end":1,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round4_proofs.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":475,"byte_start":77,"id":"section:8e9719a571c895639729","kind":"subsection","labels":["sec:toe-round4-proofs"],"line_end":8,"line_start":2,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":["relation:4e942befd3a344ad0d7f"],"semantic_review":false,"source":"tex-artefacts/toe_round4_proofs.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"The following results concern the explicitly stated regulators and algebras. They do not identify a single complete physical [formula in source] D parent. All T1–T8 and TFPT.TOE.COMPLETE.01 remain . The finite regressions are checks of the proofs below, not substitutes for their quantifiers.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Round 4: proved subgates and binding residuals (2026-09-05)","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":1080,"byte_start":475,"id":"section:9e0ba325fdce5ca83fef","kind":"paragraph","labels":[],"line_end":22,"line_start":9,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":["relation:33caaca3593c29764714","relation:5cb3d0d07bff6ae1c74b","relation:88ba6e48e10b53648920","relation:8d771509ef3e784c1059"],"semantic_review":false,"source":"tex-artefacts/toe_round4_proofs.tex","status_markers_as_written":[],"summary_excerpt":"SEAM.MMST.TELB.NORM.01. For the frozen [formula in source] , [formula in source] collar, the original remainder obeys [formula in source] The interval inputs are v1022 (TV and potential), v1025 (C1/C2a), and v1026_ telb_ round4_ closure.py (CF, DG, signed CROSS, validated Fourier core and all-volume aliases). This is not a proof of the historical sharper [formula in source] or Bound-B target [formula in source] . In ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T2: uniform relaxed TEL-B theorem.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":4937,"byte_start":1080,"id":"section:606a1b92b87b8a421027","kind":"paragraph","labels":[],"line_end":113,"line_start":23,"numbered_or_version_tokens_as_written":["R4.1","R4.2"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round4_proofs.tex","status_markers_as_written":[],"summary_excerpt":"Put [formula in source] , [formula in source] , [formula in source] , [formula in source] and let bars denote normalized means over [formula in source] . Define [formula in source] Partial fractions give [formula in source] , [formula in source] , [formula in source] , [formula in source] and [formula in source] , with [formula in source] . The identities used are the standard cotangent and polygamma identities https","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"CF: cell covariance and the periodic corner.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6110,"byte_start":4937,"id":"section:d077bac81f6981c4a521","kind":"paragraph","labels":[],"line_end":142,"line_start":114,"numbered_or_version_tokens_as_written":["R4.3","R4.4"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round4_proofs.tex","status_markers_as_written":[],"summary_excerpt":"The csc-squared finite product identity and trigamma recurrence for the original remainder give, for [formula in source] , [formula in source] where [formula in source] and [formula in source] . Since [formula in source] for [formula in source] , [formula in source] . The [formula in source] -point Peano kernel and [formula in source] imply [formula in source] On each diagonal cell the imaginary mean vanishes, [formu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"DG: original diagonal, not a replacement recurrence.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":7480,"byte_start":6110,"id":"section:5e199a42f4f9fdd9e5fe","kind":"paragraph","labels":[],"line_end":174,"line_start":143,"numbered_or_version_tokens_as_written":["R4.3","R4.5","R4.6"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round4_proofs.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the unitary fractional shift with entries [formula in source] , let [formula in source] restrict to [formula in source] , [formula in source] , [formula in source] , [formula in source] and [formula in source] . Crucially [formula in source] . For the finite unitary overlap [formula in source] and [formula in source] , the source identity is [formula in source] Hence [formula in source] . P","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"CROSS: the sufficient one-sided theorem.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":10508,"byte_start":7480,"id":"section:13c83724c05e526a735d","kind":"paragraph","labels":[],"line_end":242,"line_start":175,"numbered_or_version_tokens_as_written":["R4.6"],"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":["relation:46f7a26f23b5b3b7220c"],"semantic_review":false,"source":"tex-artefacts/toe_round4_proofs.tex","status_markers_as_written":[],"summary_excerpt":"Use the sigma- [formula in source] basis [formula in source] , [formula in source] , [formula in source] . The jump is [formula in source] (zero-based indices), and [formula in source] for [formula in source] . At the 512 midpoint nodes, 256-bit Acb validated eigensystems strictly separate eight occupied and eight unoccupied eigenvalues. The outward matrix DFT [formula in source] obeys the exact midpoint alias formul","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Validated Fourier core and the missing finite-grid aliases.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":13546,"byte_start":10508,"id":"section:7f5d6cd7af591d8d1ecc","kind":"paragraph","labels":[],"line_end":303,"line_start":243,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":["relation:43b22cc44c14df8468c2","relation:b9306371bfad6690f133","relation:c4e1553640ed3da89b85"],"semantic_review":false,"source":"tex-artefacts/toe_round4_proofs.tex","status_markers_as_written":[],"summary_excerpt":"CHIRAL4D.MIRROR.SIGNED.CAR.01. v1027_ signed_ det_ car_ wall.py checks the following algebra and its finite countermodels. The old Hubbard operators [formula in source] satisfy [formula in source] , not CAR, and [formula in source] . For even [formula in source] (in particular [formula in source] ), write [formula in source] and define [formula in source] This is a two-dimensional rotation and identity elsewhere. It ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T3/T4: canonical DET excitations and the signed wall.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":17416,"byte_start":13546,"id":"section:446cca9d3e287a1bdc77","kind":"paragraph","labels":[],"line_end":374,"line_start":304,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":["relation:bd0592fcafe306a3ef12","relation:c7acc93003eefad2303f","relation:d5dcd01e9b18928262f1","relation:e5b2933d9fdf5d89d3fa"],"semantic_review":false,"source":"tex-artefacts/toe_round4_proofs.tex","status_markers_as_written":[],"summary_excerpt":"PARENT.GAUSS.D4.ROUND4.01. v1028_ gauss_ d4_ cap.py uses the full exterior character, not a low-occupation truncation. Let [formula in source] consist of [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] , with charges [formula in source] . For color weights [formula in source] and weak weights [formula in source] , set [formula in source","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T6/T8: full Gauss counts, internal cap and selection rules.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":19967,"byte_start":17416,"id":"section:a30f92068cc57ee2cc03","kind":"paragraph","labels":[],"line_end":422,"line_start":375,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":["relation:b98208f45180c9d4db79","relation:cf19b5ca4fdff35cba42","relation:f81f9ca3d2538ca8cd4e"],"semantic_review":false,"source":"tex-artefacts/toe_round4_proofs.tex","status_markers_as_written":[],"summary_excerpt":"GRAV.SPIN2.LOCAL.CONSTRAINT.01. v1029_ local_ tensor_ constraints.py implements a quadratic target, not a TFPT embedding. For six orthonormal symmetric tensor coordinates, let [formula in source] , [formula in source] , [formula in source] , [formula in source] . Set [formula in source] with constraints [formula in source] , [formula in source] . Direct polynomial algebra gives [formula in source] The four constraint","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"T7: local constraints and zero-mode removal.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":21941,"byte_start":19967,"id":"section:14e92dd5b7273c8c870a","kind":"paragraph","labels":[],"line_end":457,"line_start":423,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":["relation:054441aa041d9785f992","relation:679a928f0ae28b3f97e3","relation:d16401933c5d7113778b"],"semantic_review":false,"source":"tex-artefacts/toe_round4_proofs.tex","status_markers_as_written":[],"summary_excerpt":"SEAM.MMST.ALG2.FRAME.01. v1030_ alg2_ sector_ frame.py does not restore the refuted Vandermonde implication. Suppose, explicitly, [formula in source] and the actual neutral algebra is [formula in source] . Join [formula in source] if [formula in source] . Then [formula in source] precisely when this undirected sector graph is connected: the neutral commutant is [formula in source] , and each nonzero corner forces [fo","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"ALG2: sector generation and conditional uniform section.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":77,"byte_start":0,"id":"section:9f9d087f0d97661dc336","kind":"frontmatter","labels":[],"line_end":1,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_charged_disorder.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2307,"byte_start":77,"id":"section:5389caac9d2d376b994f","kind":"subsubsection","labels":["sec:toe-r7-charged"],"line_end":41,"line_start":2,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":["relation:c099df8d3bc37e0d0ecc","relation:e046895f24a36803e55c"],"semantic_review":false,"source":"tex-artefacts/toe_round7_charged_disorder.tex","status_markers_as_written":[],"summary_excerpt":"The displayed arguments below are the proof-bearing source. The current repository regression is v1033_ charged_ disorder.py; its finite checks audit the implementation and do not replace the universal steps in the proof.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Round 7: a microscopic flux-string disorder operator for the frozen QWZ seam","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":4433,"byte_start":2307,"id":"section:d95e23936444d6608b24","kind":"paragraph","labels":[],"line_end":98,"line_start":42,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":["relation:1ec2cc9cd5b73201e979","relation:7cea85c54a7b5b56f7dd","relation:c8bbcfcca9508cd5ce1e","relation:e96f442fac73c2cd18b1"],"semantic_review":false,"source":"tex-artefacts/toe_round7_charged_disorder.tex","status_markers_as_written":[],"summary_excerpt":"The construction below uses the hopping matrix literally implemented in verification/v988_psi_lambda_reduction.py. With [formula in source] the one-particle QWZ Hamiltonian [formula in source] has mass [formula in source] , open [formula in source] boundary, and on the bond [formula in source] the forward hopping is [formula in source] . Every other longitudinal bond has [formula in source] . The executable v988 camp","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Frozen source and target.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":5456,"byte_start":4433,"id":"section:b8d3048fc1c40ccd7f70","kind":"paragraph","labels":[],"line_end":128,"line_start":99,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_charged_disorder.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] and let [formula in source] be the canonical number-conserving CAR Fock space. Adjoin one four-level link register [formula in source] at the chosen periodic seam. In the basis [formula in source] define [formula in source] If [formula in source] is the forward seam hopping and [formula in source] , set [formula in source] Thus the register is not a decorative sector label: its clock occurs in","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"A common microscopic Hilbert tied to the hopping.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8121,"byte_start":5456,"id":"section:3ac7d5efc86a7f600ae4","kind":"paragraph","labels":[],"line_end":207,"line_start":129,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_charged_disorder.tex","status_markers_as_written":[],"summary_excerpt":"Choose an arc [formula in source] with [formula in source] . Let [formula in source] be the one-particle onsite gauge [formula in source] Define [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The sharp line-ended operator.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10941,"byte_start":8121,"id":"section:c0df02b3e47af264ae61","kind":"paragraph","labels":[],"line_end":266,"line_start":208,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_charged_disorder.tex","status_markers_as_written":[],"summary_excerpt":"For a normalized complex chiral fermion, a twist by [formula in source] has minimal bosonized weight [formula in source] , with [formula in source] . The actual common phase [formula in source] therefore fixes, for the eight complex channels in the source, [formula in source] It has order four but nontrivial spin [formula in source] . The target (1.3) instead has integer spin and weight one. Norm is invariant under a","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Why the constructed operator is not [formula in source] .Psi-lambda","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14467,"byte_start":10941,"id":"section:5345bc5b7683e350181f","kind":"paragraph","labels":[],"line_end":342,"line_start":267,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_charged_disorder.tex","status_markers_as_written":[],"summary_excerpt":"There is a finite-lattice tradeoff that prevents another overclaim. Portability amendment, 2026-09-06. The [formula in source] one-particle operator has an exactly degenerate zero-energy space. Filling the first half of a numerical eigenbasis silently selects a platform-dependent pure vacuum. Let [formula in source] and [formula in source] denote its negative and zero spectral projectors, let [formula in source] , an","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Energy and support diagnostics.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15524,"byte_start":14467,"id":"section:fc90d6ca265ad9a2e57f","kind":"paragraph","labels":[],"line_end":363,"line_start":343,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":["relation:072ea3fabec8058ae043","relation:23b14d5ef55d838c7e3d","relation:ff8e2319e6865a9ccbd8"],"semantic_review":false,"source":"tex-artefacts/toe_round7_charged_disorder.tex","status_markers_as_written":[],"summary_excerpt":"The repository certificate v1033_ charged_ disorder.py audits the frozen sources, proves the finite Weyl/parity/charge identities with rational and symbolic arithmetic, imports the executable v988 QWZ builder and compares it entrywise, verifies the endpoint commutator on the actual [formula in source] hops, and reports finite energy diagnostics.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Executable certificate and claim boundary.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":77,"byte_start":0,"id":"section:819a6820312a3d9bc917","kind":"frontmatter","labels":[],"line_end":1,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_covariant_curvature.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1533,"byte_start":77,"id":"section:6ac3565c8eb496453ec0","kind":"subsubsection","labels":["sec:toe-r7-covariant"],"line_end":26,"line_start":2,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":["relation:253b66298b08432c0353","relation:4d82868cac81db4ce5b7"],"semantic_review":false,"source":"tex-artefacts/toe_round7_covariant_curvature.tex","status_markers_as_written":[],"summary_excerpt":"The displayed arguments below are the proof-bearing source. The current repository regression is v1032_ covariant_ curvature.py; its finite checks audit the implementation and do not replace the universal steps in the proof.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Round 7: a Lorentz-covariant free curvature field on the Round 6 Hilbert space","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":5628,"byte_start":1533,"id":"section:37eed413f0f131fa8225","kind":"paragraph","labels":["eq:toe-r7-covariant-A","eq:toe-r7-covariant-K","eq:toe-r7-covariant-PTT","eq:toe-r7-covariant-positive"],"line_end":124,"line_start":27,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_covariant_curvature.tex","status_markers_as_written":[],"summary_excerpt":"Use [formula in source] and a covariant null momentum [formula in source] All tensor components in this note carry lower indices. For a symmetric metric amplitude [formula in source] , define the linear curvature map It is the Fourier transform of [formula in source] No positive covariant quantum metric potential is assumed. Instead introduce the numerical tensor In a Euclidean orthonormal basis of symmetric [formula","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Conventions and the algebraic bridge.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10590,"byte_start":5628,"id":"section:f414508983a5d5c098ae","kind":"paragraph","labels":["eq:toe-r7-covariant-W","eq:toe-r7-covariant-boost","eq:toe-r7-covariant-norm"],"line_end":230,"line_start":125,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_covariant_curvature.tex","status_markers_as_written":[],"summary_excerpt":"Index the independent pair-symmetric bivector entries by [formula in source] . Define the two-point distribution The Bianchi identities make one of the 21 algebraic components redundant; retaining it with its null relation avoids an arbitrary choice of twenty coordinates.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Positive field, local commutator, and boosts.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12892,"byte_start":10590,"id":"section:6f7843fa91db9ab23965","kind":"paragraph","labels":["eq:toe-r7-covariant-same"],"line_end":273,"line_start":231,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_covariant_curvature.tex","status_markers_as_written":[],"summary_excerpt":"The Round 6 continuum construction has, on the physical TT range, [formula in source] with [formula in source] . In radiation gauge Consequently the spectral electric-electric covariance is [formula in source] , electric-time-derivative covariance is [formula in source] at equal time in the order [formula in source] , and derivative-derivative covariance is [formula in source] . These are precisely one quarter of the","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"It is the same free target, with a larger covariant field family.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14912,"byte_start":12892,"id":"section:7b353eb32ad9cac0c494","kind":"paragraph","labels":[],"line_end":304,"line_start":274,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":["relation:1fd41c7de9dee5128f42","relation:c018071e22fb9ccc53ee"],"semantic_review":false,"source":"tex-artefacts/toe_round7_covariant_curvature.tex","status_markers_as_written":[],"summary_excerpt":"The repository certificate v1032_ covariant_ curvature.py is standalone SymPy code. Its 34 exact checks include the all-momentum polynomial identity, gauge and Bianchi identities, null Ricci contraction, positivity factorizations, a nontrivial rational Lorentz boost, the full null little group, and the exact electric and mixed time-derivative covariance normalization. Four rational fibres supplement, but do not repla","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Validation, provenance, and the remaining obligation.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":77,"byte_start":0,"id":"section:1fd1ac8fa54fea9a2ff3","kind":"frontmatter","labels":[],"line_end":1,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_matter_coupling.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1987,"byte_start":77,"id":"section:ca196b79e1afbcc64810","kind":"subsubsection","labels":["sec:toe-r7-matter"],"line_end":37,"line_start":2,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":["relation:9fa337a55ef10bc4d5bf","relation:a522cbe33564f49a1325"],"semantic_review":false,"source":"tex-artefacts/toe_round7_matter_coupling.tex","status_markers_as_written":[],"summary_excerpt":"The displayed arguments below are the proof-bearing source. The current repository regression is v1035_ matter_ coupling.py; its finite checks audit the implementation and do not replace the universal steps in the proof.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Round 7: first-order matter coupling of the staggered tensor target","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":4507,"byte_start":1987,"id":"section:a244e109391ed59aaaf9","kind":"paragraph","labels":[],"line_end":100,"line_start":38,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_matter_coupling.tex","status_markers_as_written":[],"summary_excerpt":"We state the spatial regulator of the preceding classical and quantum artifacts as the intended real-space interpretation. The checker below instantiates these declared masks algebraically, but does not import a repository implementation. On a periodic cubic lattice of spacing [formula in source] , a component with mask [formula in source] lives at [formula in source] , and [formula in source] Thus [formula in source","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Fixed regulator and conventions.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":9531,"byte_start":4507,"id":"section:500d38321824b366fa03","kind":"paragraph","labels":[],"line_end":211,"line_start":101,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_matter_coupling.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be a symmetric c-number source on the scalar, vector, and tensor staggered cells. Its two Ward equations are [formula in source] At [formula in source] , add the spatial metric coupling and deform both constraints: [formula in source] The lapse and shift multipliers multiply [formula in source] and [formula in source] in the total Hamiltonian. Thus (8) is not merely the isolated [formula in so","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The coupling that actually preserves the constraints.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11806,"byte_start":9531,"id":"section:c10a42ff38ba6dd679d5","kind":"paragraph","labels":[],"line_end":272,"line_start":212,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_matter_coupling.tex","status_markers_as_written":[],"summary_excerpt":"The local curvature variables remain [formula in source] They commute strongly with the gravitational parts of all four constraints: [formula in source] and [formula in source] . The c-number shifts in (8) have zero bracket with them, so [formula in source] remain gauge invariant. They obey [formula in source] and, on [formula in source] , [formula in source] The retarded solution with vanishing past data is therefor","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gauge-invariant retarded curvature response.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"gravity-cosmology"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13092,"byte_start":11806,"id":"section:6d3e61f8853447e7840c","kind":"paragraph","labels":[],"line_end":299,"line_start":273,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_matter_coupling.tex","status_markers_as_written":[],"summary_excerpt":"Let matter have canonical variables [formula in source] and an uncoupled Hamiltonian [formula in source] . If its zeroth-order densities obey (7), then [formula in source] obeys (9) modulo [formula in source] . This is the precise first-order feedback result. It is not exact nonlinear closure. Indeed, even before computing the [formula in source] -correction to the matter stress, [formula in source] plus analogous cu","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Dynamical matter: what is and is not proved.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16358,"byte_start":13092,"id":"section:3fd868ee516e8127a47b","kind":"paragraph","labels":[],"line_end":382,"line_start":300,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_matter_coupling.tex","status_markers_as_written":[],"summary_excerpt":"It suffices to examine a collinear sector; failure there is failure of a purported universal cubic-lattice identity. Set [formula in source] on a periodic one-dimensional row and write [formula in source] The site energy and link flux [formula in source] obey the exact energy equation [formula in source] The continuum-looking averaged-gradient stress [formula in source] does not obey momentum continuity. An exact sam","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Free scalar: a local repair, then a sharp [formula in source] obstruction.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17884,"byte_start":16358,"id":"section:9b27d900a9c3e750aecd","kind":"paragraph","labels":[],"line_end":420,"line_start":383,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_matter_coupling.tex","status_markers_as_written":[],"summary_excerpt":"A second collinear test uses a free chiral fermion whose one-particle Hamiltonian is nearest-neighbour, with dispersion [formula in source] . This is a finite-spacing Ward test, not a claim of a doubler-free [formula in source] dimensional chiral theory. For a bilinear transferring momentum [formula in source] , set [formula in source] The exact divided-difference identity is [formula in source] Consequently the ener","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Free fermion: exact collinear divided-difference vertices.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":19002,"byte_start":17884,"id":"section:b17642999091de491787","kind":"paragraph","labels":[],"line_end":442,"line_start":421,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_matter_coupling.tex","status_markers_as_written":[],"summary_excerpt":"The preceding free tensor construction removed the complete [formula in source] canonical block to eliminate its negative trace direction. At [formula in source] , [formula in source] , so its vacuum local constraints vanish identically. Equation (8) would reduce to [formula in source] A positive-energy matter state normally has [formula in source] , and a state may also have [formula in source] . For [formula in sou","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The homogeneous obstruction.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":20437,"byte_start":19002,"id":"section:54038319b1c08ce7b3d5","kind":"paragraph","labels":[],"line_end":468,"line_start":443,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_matter_coupling.tex","status_markers_as_written":[],"summary_excerpt":"Equation (13) is an exact classical Green-function solution of the conditional staggered Fourier equations and is gauge invariant and Ward compatible there. A smooth compact-time c-number source is expected to define linear forcing of the already-constructed oscillator Fock space, but the CCR import and Kubo commutator needed to prove that quantum statement are not executed here. Thus the generic prescribed-source fi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Quantum meaning and remaining obligation.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":22298,"byte_start":20437,"id":"section:97877f60d519b6bd2cbf","kind":"paragraph","labels":[],"line_end":505,"line_start":469,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":["relation:6f344322a095b4babf5a","relation:975499216ca19b1f17d3"],"semantic_review":false,"source":"tex-artefacts/toe_round7_matter_coupling.tex","status_markers_as_written":[],"summary_excerpt":"The repository certificate v1035_ matter_ coupling.py imports no proof text. It checks the generic prescribed-source polynomial identities with their full complex Fourier signs, a conserved plane-wave witness, the mandatory failure of the old restored- [formula in source] sign, paired Fourier reality, all three declared Bloch transitions, the classical retarded TT step solution, the two collinear Ward complexes and m","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Executable certificate and evidence typing.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":77,"byte_start":0,"id":"section:e872346c37fed22a9e54","kind":"frontmatter","labels":[],"line_end":1,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_parent_mirror.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":2271,"byte_start":77,"id":"section:53d5143975a8c0ba13df","kind":"subsubsection","labels":["sec:toe-r7-mirror"],"line_end":46,"line_start":2,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":["relation:32c8e8754e36b2fc909c","relation:491f9d29e35367c07d61","relation:73635ce6b2c6567b3c97","relation:7992387a023891041502","relation:810277f7aa5ec20a83b2","relation:bd643f4f12db2aa0d168"],"semantic_review":false,"source":"tex-artefacts/toe_round7_parent_mirror.tex","status_markers_as_written":[],"summary_excerpt":"The displayed arguments below are the proof-bearing source. The current repository regression is v1034_ parent_ mirror.py; its finite checks audit the implementation and do not replace the universal steps in the proof.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Round 7: the actual DET parent, its exact factorized gap, and the local-defect obstruction","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":4073,"byte_start":2271,"id":"section:52fe7259f20dc261237c","kind":"paragraph","labels":["eq:toe-r7-mirror-defect","eq:toe-r7-mirror-paritynotnumber"],"line_end":89,"line_start":47,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":["relation:2b0cb671bd276f0e3111","relation:4c3428848b3f75951c61","relation:73aad05b2a3f935a070f","relation:c13d3452b6974aef632a","relation:f21af3eadeb085f54fb8"],"semantic_review":false,"source":"tex-artefacts/toe_round7_parent_mirror.tex","status_markers_as_written":[],"summary_excerpt":"The certificate reads, but does not import, the following landed files at the audited repository tip: lll source & exact object used here & status relevant to this note\\\\ v1002 & [formula in source] on 16 complex modes & onsite projector only\\\\ v1008 & [formula in source] , [formula in source] & momentum-cell scaffold\\\\ v1024 & positive seam/number-square parent & separate construction\\\\ v1027 & [formula in source] ,","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Source contract and nomenclature.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":4766,"byte_start":4073,"id":"section:a9ba40ee6565edd10c45","kind":"paragraph","labels":["eq:toe-r7-mirror-hd"],"line_end":104,"line_start":90,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":["relation:029250d5d0b56f148904"],"semantic_review":false,"source":"tex-artefacts/toe_round7_parent_mirror.tex","status_markers_as_written":[],"summary_excerpt":"The v1008 routine edge_cluster_hamiltonian is The scan uses [formula in source] . This is a separate Fock cell at every sampled momentum, not a real-space hopping Hamiltonian. In particular, a standard symmetric nearest-neighbour term [formula in source] has dispersion magnitude [formula in source] (up to a momentum/phase convention). Matching the v1008 dispersion amplitude would therefore give [formula in source] , ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Exact theorem for the parent that v1008 actually computes.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5307,"byte_start":4766,"id":"section:9aa0dcae086ef4f93183","kind":"paragraph","labels":["eq:toe-r7-mirror-doublet","eq:toe-r7-mirror-intermediate"],"line_end":124,"line_start":105,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_parent_mirror.tex","status_markers_as_written":[],"summary_excerpt":"For [formula in source] , every occupation- [formula in source] state has energy On [formula in source] , after removing [formula in source] , the matrix is with eigenvalues","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lemma 1 (complete one-cell spectrum).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6159,"byte_start":5307,"id":"section:c3d99217a6db444cbd98","kind":"paragraph","labels":["eq:toe-r7-mirror-gx"],"line_end":141,"line_start":125,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_parent_mirror.tex","status_markers_as_written":[],"summary_excerpt":"[formula in source] vanishes on occupation sectors [formula in source] , which gives rank-one matrix specified by polynomial gives","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Proof.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":6667,"byte_start":6159,"id":"section:da73b3f84273cd4e1dd3","kind":"paragraph","labels":["eq:toe-r7-mirror-factgap"],"line_end":154,"line_start":142,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_parent_mirror.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be any finite set of momentum cells, with arbitrary dispersions [formula in source] , and define the graded tensor-product Hamiltonian [formula in source] . Then [formula in source] has a unique product ground state and The same number is the uniform lower edge of canonical one-fermion spectral support.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Theorem 1 (source-fixed all-volume factorized gap).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":7772,"byte_start":6667,"id":"section:a503bfae31300975fb93","kind":"paragraph","labels":[],"line_end":175,"line_start":155,"occurrence":2,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":["relation:fab4418507378a844823"],"semantic_review":false,"source":"tex-artefacts/toe_round7_parent_mirror.tex","status_markers_as_written":[],"summary_excerpt":"For [formula in source] , differentiation of minimum and substitution gives [formula in source] . The other empty/full eigenstate costs at least [formula in source] , and the [formula in source] sector also costs at least [formula in source] , so neither undercuts tensor product and energies add. Any state orthogonal to the product ground excites at least one cell, proving the same bound independently of [formula in ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Proof.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":8349,"byte_start":7772,"id":"section:54d4fd1d894d91dc6fb1","kind":"paragraph","labels":["eq:toe-r7-mirror-realbond"],"line_end":189,"line_start":176,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_parent_mirror.tex","status_markers_as_written":[],"summary_excerpt":"Put two DET cells on a bond and let This is a bare-bond theorem. The numerical choice [formula in source] below is a newly chosen stress analogue, not a real-space coefficient derived from v1008. For even [formula in source] , the full-Fock CAR calculation contains only [formula in source] nonzero output monomials and does not require construction of the [formula in source] matrix.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Why the desired relative-defect bound fails in real space.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":8755,"byte_start":8349,"id":"section:48a9bdcdec853b055be0","kind":"paragraph","labels":["eq:toe-r7-mirror-nonzeroimage","eq:toe-r7-mirror-zeroexp"],"line_end":200,"line_start":190,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_parent_mirror.tex","status_markers_as_written":[],"summary_excerpt":"For every even [formula in source] and [formula in source] ,","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Lemma 2 (minimal kernel incompatibility).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":9575,"byte_start":8755,"id":"section:034f668f6d733dcdbe2c","kind":"paragraph","labels":[],"line_end":215,"line_start":201,"occurrence":3,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_parent_mirror.tex","status_markers_as_written":[],"summary_excerpt":"Only the [formula in source] and [formula in source] components of the product DET vacuum can hop. Each has amplitude [formula in source] . The two hopping orientations and [formula in source] flavours produce [formula in source] mutually orthogonal states, each of modulus [formula in source] , which proves the norm in after the hop, hence both local projectors [formula in source] annihilate the image. [formula in so","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Proof.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":9775,"byte_start":9575,"id":"section:a599c799b5ea47f60a1b","kind":"paragraph","labels":["eq:toe-r7-mirror-nokappa"],"line_end":222,"line_start":216,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_parent_mirror.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Theorem 2 (no finite relative-defect constant).","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11040,"byte_start":9775,"id":"section:d491b7fe2ede80bdf65a","kind":"paragraph","labels":["eq:toe-r7-mirror-ritz"],"line_end":252,"line_start":223,"occurrence":4,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_parent_mirror.tex","status_markers_as_written":[],"summary_excerpt":"If [formula in source] would have zero expectation in [formula in source] by [formula in source] . Since [formula in source] , this would say [formula in source] , contradicting [formula in source]","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Proof.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":13120,"byte_start":11040,"id":"section:b108a2f09b15463e0b72","kind":"paragraph","labels":["eq:toe-r7-mirror-gaugehopping","eq:toe-r7-mirror-gaugeritz"],"line_end":297,"line_start":253,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_parent_mirror.tex","status_markers_as_written":[],"summary_excerpt":"The bare theorem above makes no Gauss-sector claim. For the [formula in source] analogue and [formula in source] , now adjoin an oriented link basis [formula in source] and define This operator is implementable on matter Fock space tensored with the finite link space; it is fermion-even because each summand is a matter bilinear. Take the endpoint Gauss constraints to be [formula in source] and [formula in source] . T","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Gauge-dressed theorem and actual link action.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":15391,"byte_start":13120,"id":"section:9e282712f2da680d7276","kind":"paragraph","labels":["eq:toe-r7-mirror-counterterm","eq:toe-r7-mirror-projectedbound","eq:toe-r7-mirror-rawrepair"],"line_end":345,"line_start":298,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_parent_mirror.tex","status_markers_as_written":[],"summary_excerpt":"The following repair is included to make the result actionable, not to present a new source claim. On a bond let It obeys [formula in source] . For the flavour-diagonal hopping [formula in source] with unit coefficient, [formula in source] exactly. Therefore On a graph of maximum degree [formula in source] , replacing ordinary hopping by its projected version yields For the newly chosen periodic-1D bond analogue [for","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"An exact local repair boundary.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"flavor-masses"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16763,"byte_start":15391,"id":"section:a6223af85b17013c2623","kind":"paragraph","labels":[],"line_end":368,"line_start":346,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":["relation:0ec0e9046187196fa1c4","relation:5459a88176a872b76486","relation:c0b0537117796e3d58ea"],"semantic_review":false,"source":"tex-artefacts/toe_round7_parent_mirror.tex","status_markers_as_written":[],"summary_excerpt":"The repository certificate v1034_ parent_ mirror.py is read-only. Its JSON separates 29 exact algebra checks, six exact source-contract checks, and one floating-grid regression. The printed tag identifies each class. The checker performs an AST source-contract audit, exact [formula in source] onsite algebra, exact symbolic minimization, and a sparse CAR-monomial two-cell calculation. It does not build the [formula in","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reproducibility and claim boundary.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":253,"byte_start":0,"id":"section:f19fc33b9f041a4eae13","kind":"frontmatter","labels":[],"line_end":4,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_proofs.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":2306,"byte_start":253,"id":"section:471620b021170e95a9b8","kind":"subsection","labels":["sec:toe-round7-proofs"],"line_end":45,"line_start":5,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":["relation:027d2e8529e295ca1e7e","relation:2a5aef26e09c36ea35a9","relation:3f10c39da9d3bcba1ae9","relation:5eab26526187abb49377","relation:b7852860d99869647595","relation:c3371a89ab280d00de86","relation:de282f8bc1bb9b3edaaa","relation:e21d856c99fce341dbdd","relation:ed3dbbdf7e7a476b1166"],"semantic_review":false,"source":"tex-artefacts/toe_round7_proofs.tex","status_markers_as_written":["\\mO"],"summary_excerpt":"This supplement records five written proofs and their machine regressions: [formula in source] passing checks. The Round 6 prerequisite contributes [formula in source] checks ( [formula in source] exact and [formula in source] floating regressions) v1031_ quantum_ tensor_ curvature.py. Round 7 contributes [formula in source] checks: [formula in source] exact, [formula in source] source-contract, and [formula in sourc","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Rounds 6 and 7: free quantum curvature, covariant extension, charged disorder, mirror parent, and first-order matter coupling","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":77,"byte_start":0,"id":"section:dd24621601e8c9e7c2f2","kind":"frontmatter","labels":[],"line_end":1,"line_start":1,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_quantum_tensor_curvature.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1410,"byte_start":77,"id":"section:af2f91d682b7a9931b38","kind":"subsubsection","labels":["sec:toe-r6-quantum"],"line_end":31,"line_start":2,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":["relation:8fb6d9662f4017258bb3","relation:ff25cb1be2ef4792aa51"],"semantic_review":false,"source":"tex-artefacts/toe_round7_quantum_tensor_curvature.tex","status_markers_as_written":[],"summary_excerpt":"The displayed arguments below are the proof-bearing source. The current repository regression is v1031_ quantum_ tensor_ curvature.py; its finite checks audit the implementation and do not replace the universal steps in the proof.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Round 6 prerequisite: a free quantum curvature field on the staggered tensor target","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":3930,"byte_start":1410,"id":"section:8f5761ee88a36bf37cdd","kind":"paragraph","labels":[],"line_end":93,"line_start":32,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_quantum_tensor_curvature.tex","status_markers_as_written":[],"summary_excerpt":"Let a periodic cubic lattice have [formula in source] cells and spacing [formula in source] . The six orthonormal symmetric-tensor coordinates are ordered as [formula in source] , with the off-diagonal basis tensors normalized by [formula in source] . Component [formula in source] lives at [formula in source] , where [formula in source] We use the physical-position Fourier phase [formula in source] . The staggered de","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Assumptions and preregistered obligations.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":5615,"byte_start":3930,"id":"section:167e298870a99c8f0c9a","kind":"paragraph","labels":[],"line_end":137,"line_start":94,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_quantum_tensor_curvature.tex","status_markers_as_written":[],"summary_excerpt":"For [formula in source] , let [formula in source] . The orthogonal spin-two projector on symmetric tensors is [formula in source] It has rank two, [formula in source] , and its range is [formula in source] .","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"The exact spin-two commutator projector.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":11114,"byte_start":5615,"id":"section:391db123b8d95a9a2179","kind":"paragraph","labels":[],"line_end":266,"line_start":138,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_quantum_tensor_curvature.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the real finite-volume smearing space of curvature pairs [formula in source] , with the homogeneous fibre absent and with the same reality/Bloch conditions as the fields. Define [formula in source] where [formula in source] and the brackets denote the real lattice inner product. Canonical quantization means [formula in source] The null space of (7) is [formula in source] . We therefore defi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"CCR quotient and finite-volume vacuum.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12329,"byte_start":11114,"id":"section:d722746d450ce510cf7b","kind":"paragraph","labels":[],"line_end":296,"line_start":267,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_quantum_tensor_curvature.tex","status_markers_as_written":[],"summary_excerpt":"Write [formula in source] . Physical-position Fourier coefficients obey [formula in source] and similarly for [formula in source] . Changing [formula in source] by [formula in source] reverses [formula in source] and gives [formula in source] Also [formula in source] . Therefore (7), (10), and (15) descend to the Bloch bundle and respect the real involution. No polarization vectors are chosen, so there is no hidden g","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reality and Bloch gluing.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":14172,"byte_start":12329,"id":"section:041f92aa8b596346dac9","kind":"paragraph","labels":[],"line_end":333,"line_start":297,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_quantum_tensor_curvature.tex","status_markers_as_written":[],"summary_excerpt":"At fixed [formula in source] , extend the covariance symbols by zero at [formula in source] . The estimates [formula in source] show that all symbols are continuous on the compact Brillouin torus. A finite-support smearing has a trigonometric-polynomial Fourier transform. Consequently every entry of (7) and (10) is a Riemann sum of a continuous periodic function. As [formula in source] it converges to the correspondi","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Fixed-spacing thermodynamic state.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"arithmetic-history"}]},{"byte_end":18363,"byte_start":14172,"id":"section:ed05e09fb2cc33ac558b","kind":"paragraph","labels":[],"line_end":433,"line_start":334,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_round7_quantum_tensor_curvature.tex","status_markers_as_written":[],"summary_excerpt":"Take the thermodynamic limit first. For [formula in source] in [formula in source] , let [formula in source] The band-limited interpolation of a lattice kernel is the tempered distribution obtained by integrating its multiplier over [formula in source] . Equivalently, lattice fields with [formula in source] are scaled as [formula in source] distributions, so their smearings are [formula in source] . For Schwartz test","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Continuum distributions and microcausality.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":21229,"byte_start":18363,"id":"section:5f1a3855b96da8117325","kind":"paragraph","labels":[],"line_end":482,"line_start":434,"occurrence":1,"owner_documents":["document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/fortsetzung/source-snapshots/tfpt/tfpt_research_contracts","document:experiments/theory-contracts/universalraum-fable-kernfragen-20260910/context/transformationen/source-snapshots/tfpt/tfpt_research_contracts","document:tfpt_research_contracts"],"relation_ids":["relation:92e0a15a54401ba0adf9","relation:aa08202d0d83e3309f9c"],"semantic_review":false,"source":"tex-artefacts/toe_round7_quantum_tensor_curvature.tex","status_markers_as_written":[],"summary_excerpt":"The repository certificate v1031_ quantum_ tensor_ curvature.py is standalone and imports no proof text. It is a separate implementation check, not an external independent review. Its roles were fixed before execution: exact SymPy polynomial algebra checks (3), (5), (6), and the separate index formula (4); exact rational-momentum fibres, characteristic polynomials, TT action, and the factorization (12); exact Bloch t","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Executable certificate, costs, and remaining limits.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":71,"byte_start":0,"id":"section:210d0b40745aefdcdeaf","kind":"frontmatter","labels":[],"line_end":1,"line_start":1,"occurrence":1,"owner_documents":["document:tfpt_research_contracts","document:tfpt_universalraum_synthesis_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_universalraum_synthesis_20260912.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Front matter / support","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":209,"byte_start":71,"id":"section:6e1860c8f024840a2d59","kind":"section","labels":["sec:universalraum-synthesis-20260912"],"line_end":4,"line_start":2,"occurrence":1,"owner_documents":["document:tfpt_research_contracts","document:tfpt_universalraum_synthesis_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_universalraum_synthesis_20260912.tex","status_markers_as_written":[],"summary_excerpt":"","summary_method":"no sufficiently long opening prose found; support/formula-only content is not paraphrased","title":"Universalraum synthesis: source selection, reconstruction and accessible dynamics","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":1139,"byte_start":209,"id":"section:fc47ee16ddf59584c3f6","kind":"paragraph","labels":[],"line_end":21,"line_start":5,"occurrence":1,"owner_documents":["document:tfpt_research_contracts","document:tfpt_universalraum_synthesis_2026-09-12"],"relation_ids":["relation:803c6d7e434fc4f49fb3"],"semantic_review":false,"source":"tex-artefacts/toe_universalraum_synthesis_20260912.tex","status_markers_as_written":[],"summary_excerpt":"This section consolidates the local primitive-transfer investigation and the latest two available answers from each of four ChatGPT research tasks. It is not an independent rerun of all external certificates, an exhaustive conversation archive, or a derivation of a theory of everything. All T1–T8 and TFPT.TOE.COMPLETE.01 remain open. The local checkout base is 66b91e40e245569f06ab440ead80f446c9be0ee5; additional loca","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Scope and evidence, 12 September 2026.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":3711,"byte_start":1139,"id":"section:ba5e47e21501fa900096","kind":"subsection","labels":[],"line_end":69,"line_start":22,"occurrence":1,"owner_documents":["document:tfpt_research_contracts","document:tfpt_universalraum_synthesis_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_universalraum_synthesis_20260912.tex","status_markers_as_written":[],"summary_excerpt":"The integral compiler commutant, its positive cone, the sixteen-real-mode quadratic candidate, the seventy-state interacting chain, the filled QWZ strip and the compact-U(1) rotor parent are different objects. In particular, the quadratic candidate has eight complex modes and a 256-dimensional full Fock space. The designated [formula in source] is a fixed-four-particle sector of an open four-site, eight-mode model; i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Typed objects and prior local results","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":6946,"byte_start":3711,"id":"section:05986b2011d3791e7ee4","kind":"subsection","labels":[],"line_end":129,"line_start":70,"occurrence":1,"owner_documents":["document:tfpt_research_contracts","document:tfpt_universalraum_synthesis_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_universalraum_synthesis_20260912.tex","status_markers_as_written":[],"summary_excerpt":"The following are attributed task reports; their original finite-field and rank certificates have not all been independently rerun in this consolidation. The archived excerpts retain exact task identifiers and retrieval limitations.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Results reported by the four parallel tasks","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":8815,"byte_start":6946,"id":"section:1843ffffee2452937787","kind":"subsection","labels":[],"line_end":172,"line_start":130,"occurrence":1,"owner_documents":["document:tfpt_research_contracts","document:tfpt_universalraum_synthesis_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_universalraum_synthesis_20260912.tex","status_markers_as_written":[],"summary_excerpt":"For a pure eigenstate and a specified Hermitian family [formula in source] , the covariance form obeys [formula in source] A one-dimensional nonconstant kernel identifies one generator direction, not the origin of the family or state. For a faithful mixed state, [formula in source] instead forces [formula in source] to be scalar. Thermal reconstruction therefore needs its own stationarity-response contract. Adding se","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Reconstruction contracts that must remain distinct","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":10888,"byte_start":8815,"id":"section:aa533949572e21b4b89f","kind":"subsection","labels":[],"line_end":215,"line_start":173,"occurrence":1,"owner_documents":["document:tfpt_research_contracts","document:tfpt_universalraum_synthesis_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_universalraum_synthesis_20260912.tex","status_markers_as_written":[],"summary_excerpt":"For the pinned real matrices, [formula in source] the real ranks are ten and six and [formula in source] . The original boundary cyclic space equals [formula in source] . The induced Fock decomposition is [formula in source] ; with the unchanged split dynamics, finite adaptive boundary protocols depend only on the accessible marginal. Hidden occupation cannot be read out by such protocols, even if other initial corre","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Exact access results in the local quadratic candidate","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"information-code"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":12331,"byte_start":10888,"id":"section:2b3701d613b9b04d510e","kind":"subsection","labels":[],"line_end":252,"line_start":216,"occurrence":1,"owner_documents":["document:tfpt_research_contracts","document:tfpt_universalraum_synthesis_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_universalraum_synthesis_20260912.tex","status_markers_as_written":[],"summary_excerpt":"Let [formula in source] be the Hermitian one-particle lift of the existing edge [formula in source] . It obeys [formula in source] . Define [formula in source] This is a covariant, trace-preserving completely positive map. Averaging the Hamiltonians first instead preserves the [formula in source] split. The two operations must not be confused. For the invariant hidden one-particle state [formula in source] , writing ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"A covariant event channel with an actual boundary response","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":13854,"byte_start":12331,"id":"section:54b8eeee7af8d44f1fd3","kind":"subsection","labels":[],"line_end":286,"line_start":253,"occurrence":1,"owner_documents":["document:tfpt_research_contracts","document:tfpt_universalraum_synthesis_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_universalraum_synthesis_20260912.tex","status_markers_as_written":[],"summary_excerpt":"A possible, explicitly added continuous event model is [formula in source] The event-only semigroup is the Poisson mixture of [formula in source] ; the rate [formula in source] is unselected. With the Hilbert–Schmidt inner product, [formula in source] The Hamiltonian part has zero real quadratic form. Consequently the fixed space of [formula in source] is the common commutant of all [formula in source] and [formula i","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"New continuation: transfer succeeds but state selection fails","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":16299,"byte_start":13854,"id":"section:13353500113bc4f195bc","kind":"subsection","labels":[],"line_end":335,"line_start":287,"occurrence":1,"owner_documents":["document:tfpt_research_contracts","document:tfpt_universalraum_synthesis_2026-09-12"],"relation_ids":["relation:2304a49410e58b0848fe","relation:2e48c8eb2b465adec546","relation:6093e9eff4ad99e51c9d","relation:756f28721dcf043fcf0b","relation:dbf8b7dee08cb14e52dd"],"semantic_review":false,"source":"tex-artefacts/toe_universalraum_synthesis_20260912.tex","status_markers_as_written":[],"summary_excerpt":"The archived 10 September rotor synthesis reports an exact change to residue/carry coordinates retaining the declared parent dynamics, arithmetic covering operations, conditional logarithmic weights, and finite-energy approximations with explicit error costs. Discarding the carry loses electric dynamics. Norm time, electric time and modular time are not interchangeable. A finite factoring example and static E8 counts","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Arithmetic bridges, acceptance gates and provenance","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"e8-geometry"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"history"}]},{"byte_end":16785,"byte_start":16299,"id":"section:7446e557bd8a5894bf08","kind":"subsection","labels":["sec:universalraum-followups-20260912"],"line_end":344,"line_start":336,"occurrence":1,"owner_documents":["document:tfpt_research_contracts","document:tfpt_universalraum_synthesis_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_universalraum_synthesis_20260912.tex","status_markers_as_written":[],"summary_excerpt":"These are proposed investigations, not newly completed results or launched worker tasks. Their common acceptance rule is a forward derivation without importing the desired Hamiltonian, its eigenstates or target couplings. A genuinely independently derived primitive action may itself be the Hamiltonian; it need not be artificially required to be a different object.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Proposed follow-ups and discriminating research directions","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"electromagnetic"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":17254,"byte_start":16785,"id":"section:9555ea49608875a0d622","kind":"paragraph","labels":[],"line_end":352,"line_start":345,"occurrence":1,"owner_documents":["document:tfpt_research_contracts","document:tfpt_universalraum_synthesis_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_universalraum_synthesis_20260912.tex","status_markers_as_written":[],"summary_excerpt":"Obtain and pin the original 17- and 66-family certificates before using their strongest claims as local premises; then audit the non-Slater and cyclotomic irreducibility certificates. Keep the 133-dimensional product extension separate. Success means the same exact ranks, coefficient fields and class definitions, with numerical conditioning reported separately. Unavailable originals mean ``not reproduced'', not ``fal","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"F0: Independent reproduction.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"methods-verification"}]},{"byte_end":17747,"byte_start":17254,"id":"section:b7cd6722b6a2986cc80f","kind":"paragraph","labels":[],"line_end":360,"line_start":353,"occurrence":1,"owner_documents":["document:tfpt_research_contracts","document:tfpt_universalraum_synthesis_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_universalraum_synthesis_20260912.tex","status_markers_as_written":[],"summary_excerpt":"For one original finite sector, map each primitive rule to its operator, phase, support, adjoint and composition. Distinguish physical operations from gauge identifications and elementary generators from composite words. A source-derived filtration or equivalent primitive rule must explain why composition does not automatically introduce independently weighted energy terms. Reject a cutoff chosen only to enforce the ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"F1: Freeze the elementary grammar.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"standard-model"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18300,"byte_start":17747,"id":"section:fb728a422a27b707299d","kind":"paragraph","labels":[],"line_end":369,"line_start":361,"occurrence":1,"owner_documents":["document:tfpt_research_contracts","document:tfpt_universalraum_synthesis_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_universalraum_synthesis_20260912.tex","status_markers_as_written":[],"summary_excerpt":"Construct one source step or collar without the target generator as input. Declare whether the output is a Hamiltonian, a positive Hilbert-space transfer or a reduced quantum channel. Derive weights, step duration and any traced environment from the stated inputs. Test alternative weights with identical symmetry and fixed vector. A freely chosen metric in [formula in source] , pulse angle or event rate remains an add","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"F2: Derive process type and measure.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":18865,"byte_start":18300,"id":"section:0fb52de974ef66f9a8dd","kind":"paragraph","labels":[],"line_end":378,"line_start":370,"occurrence":1,"owner_documents":["document:tfpt_research_contracts","document:tfpt_universalraum_synthesis_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_universalraum_synthesis_20260912.tex","status_markers_as_written":[],"summary_excerpt":"Compute the exact fixed algebra or ground space of the F2 candidate. Use eigenstate covariance, thermal stationarity or full two-particle data only under their respective contracts. Test identical one-body data with different four-point responses, and identical ground rays with different energy ratios. Repetition of the current channel and free flow cannot remove their common fixed algebra. Any operation removing tha","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"F3: State selection and correlation content.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":19405,"byte_start":18865,"id":"section:6727615a78ca0e90e90d","kind":"paragraph","labels":[],"line_end":387,"line_start":379,"occurrence":1,"owner_documents":["document:tfpt_research_contracts","document:tfpt_universalraum_synthesis_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_universalraum_synthesis_20260912.tex","status_markers_as_written":[],"summary_excerpt":"For a source-derived intervention, compare admissible preparations with the same initial accessible marginal at the original boundary. Bound the remainder in the conditional [formula in source] signal on an explicit finite time interval, and include preparation energy, precision and sampling costs. Preserve the no-intervention control. Exact cyclic rank alone is not successful physical control, and arbitrarily small ","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"F4: Operational response and costs.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"foundations"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":19865,"byte_start":19405,"id":"section:cd1723da0d4006f7214f","kind":"paragraph","labels":[],"line_end":395,"line_start":388,"occurrence":1,"owner_documents":["document:tfpt_research_contracts","document:tfpt_universalraum_synthesis_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_universalraum_synthesis_20260912.tex","status_markers_as_written":[],"summary_excerpt":"An explicit map between the successful candidate and H70, the rotor parent or the charged seam must preserve the relevant adjunction, charge/Clock action, states, dynamics and readouts on named domains. Matching spectra, dimensions or group names alone is insufficient. An open chain must not be identified with a winding rotor, nor a free source with an interacting state without the additional operation being derived.","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"F5: Source-to-model maps.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":20901,"byte_start":19865,"id":"section:8b8d6e0ab5f094a9e541","kind":"paragraph","labels":[],"line_end":412,"line_start":396,"occurrence":1,"owner_documents":["document:tfpt_research_contracts","document:tfpt_universalraum_synthesis_2026-09-12"],"relation_ids":[],"semantic_review":false,"source":"tex-artefacts/toe_universalraum_synthesis_20260912.tex","status_markers_as_written":[],"summary_excerpt":"Positive frustrated selection: derive the unavoidable positive minimum and relative defect weights from the source. The failed equal-weight H70 selector is not revived by adjusting its weights to the target. A genuine collar transfer: derive a positive transfer directly from the actual boundary construction and its composition. Reflection positivity must not be inferred merely from a positive Gram matrix. An internal","summary_method":"opening prose excerpt; TeX formatting stripped and formulas explicitly omitted; no semantic paraphrase","title":"Four exploratory hypotheses, not established mechanisms.","topic_suggestions":[{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"boundary-clocks"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"quantum-continuum"},{"match_basis":"curated regex over source path, heading and opening excerpt; not semantic review","relation_type":"lexical_topic_suggestion","topic_id":"universalraum"}]},{"byte_end":21838,"byte_start":20901,"id":"section:5baa612f347f165009b7","kind":"paragraph","labels":[],"line_end":427,"line_start":413,"occurrence":1,"owner_documents":["document:tfpt_research_contracts","document:tfpt_universalraum_synthesis_2026-09-12"],"relation_ids":["relation:01d77e494357dd9c110a"],"semantic_review":false,"source":"tex-artefacts/toe_universalraum_synthesis_20260912.tex","status_markers_as_written":[],"summary_excerpt":"The half-charge, common [formula in source] D parent, chiral, continuum, coupling and gravity obligations remain separate after any finite success. No new RH or factoring mechanism is proposed in this roadmap; future arithmetic work must first consult the existing source-bound proof and counterexample registers. 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